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CommodityRisk Managementand Finance

CommodityRisk Managementand FinanceTheophilos Priovolos and Ronald C. Duncan,Editors

Published for the World BankOxford University Press

OXFORD NEW YORK TORONTO DELHI

BOMBAY CALCUTTA MADRAS KARACHI

PETALING JAYA SINGAPORE HONG KONG

TOKYO NAIROBI DAR ES SALAAM

CAPE TOWN M.1ELBOURNE AUCKLAND

and associated companies inBERLIN IBADAN

© 1991 The International Bank forReconstruction and Development / The World Bank

1818 H Street, N.W., Washington, D.C. 20433. U.S.A.

All rights reserved. No part of this publicationmay be reproduced, stored in a retrieval system,

or transmitted in any form or by any means,electronic, mechanical, photocopying, recording,

or otherwise, without the priot permissionof Oxford University Press.

Manufactured in the United States of AmericaFirst printing June 1991

The text of this book is printed on paper containingS0 percent virgin pulp, 45 percent recycled preconsumer waste,

and S percent recycled and deinked postconsumer waste.

The findings, interpretations, and conclusions expressed inthis study are the results of research done by the World Bank,

but they are those of the authors and do not necessarilyrepresent the views and policies of the World Bank or

its Board of Executive Directors or the countries they represent.The World Bank does not guarantee the accuracy of the data

included in this publication and accepts no responsibilitywhatsoever for any consequences of their use.

Library of Congress Cataloging-in-Publication Data

Commodity risk management and finance / edited by Theophilos Priovolos andRonald C. Duncan.

p- cm."Published for the World Bank."Includes bibliographical references and index.ISBN 0-19-520867-61. Commodity-backed bonds. 2. Debts. External-Developing

countries. 1. Priovolos, Theophilos. 11. Duncan, Ronald C.,1936-. Ill. International Bank for Reconstruction and Development.HG4651.C694 1991 90-25115332.63'23-dc2O CIP

Foreword

As has been made painfully obvious during the 1980s, the developingcountries face great difficulties in raising external finance and in servicingtheir external debts, due in large part to the sharp fluctuat ons in theprices received for their primary commodity exports. Their terms of tradeare also very susceptible to import price shocks, especially from the mostimportant primary commodity import for most of them-petroleum. Inturn, the terms-of-trade shocks from primary commodity price fluctua-tions are a major problem for the management of firms and, probablymost important, for the macroeconomic management of the developingcountries themselves. It is probably fair to say that the effort that has hadto be devoted to macro management of these economies in the wake ofsuch shocks has detracted seriously from the effort that would haveothervise been given to getting on with the process of development.

As the chapters in this volume showv, there are now commodityprice-related financial instruments that can be used to manage thevolatility in export earnings and import payments and -o shift the risksfrom the developing countries to those more capable of bearing them inworld markets. As a result, revenue and expenditure streams can be mademore stable, debt servicing can be made more reliable, creditworthinesscan be improved, and macroeconomic management can be made lessonerous.

The use of commodity price-related instruments for hedging commod-ity price risks and for raising finance has expanded :apidly in recent yearsin industrial countries. Their use has been minimal in developingcountries, however, in part because they are new, but also because of thelack of understanding by the countries of their risk exposure and lack ofknowledge about private market-based risk management practices. Thislack of knowledge presents an opportunity for the World Bank Group to

v

Vi CONMMODITN- RISK MANAGEMENT AND FINANCE

provide tec.< X .%.' assistance to developing countries. A unit has beenformed in 1, .,national Economics Departmenlt to undertake suchtechnical asska.,:.e to make developing countries, institutions, andenterprises that fare substantial commodity price risk more aware ofcommodity pric;-related instruments; to help them obtain training andexperience in the use of the various risk management instrumentsavailable; and to hielp them to develop appropriate strategies for com-modity risk management. Technical assistance of this nature is presentlybeing undertaken in several countries.

D. C. RaoDirector,

International Economics DepartmentThe World Bank

Con ten ts

Contributors x

Acknowledgments xi

1. Introduction 1Th)eophilos Priovolos and Ronald C. Duncan

Part I. The Pricing of Commodity-Linked Securities

2. Experience with Commodity-Linked Issues 11Theeophilos Priovolos

Introduction I 1Gold-Linked Financing 14Silver-Linked Financing 30Crude-Oil-Linked Financing 31Other Commodity-Linked Issues 37Notes 38

3. The Demand for Commodity Bon;' 39Moctar A. Fall

The One-Consumption Good Case 39The Determinants of the Demand for Commodity Bonds 48The Mulngood Case 51

4. A Review of Methuds for Pricing Commodity-LinkedSecurities 56Tbeophilos Priovolos

Case 1: Uncertain Commodity Price 58Case 2: Default Risk 58Case 3: Interest Rate Risk 58Notes 60

iii

viii CONTENTS

5. Pricing Commodity Bonds Using Binomial OptionPricing 61Ragburatn Rajan

The Model 62Parameter Determination 67Extensionis 70Comparative Analysis of Binomial Model and Schwarrz Model

Results 70Conclusion 78AppendixS -1. The Continuous-Time M,del 79Appendix 5-2. Proof That the Distribution of the Binomial Model

Tends to thc Bivariate Normal Distribution 79Notes 81

Part 1I. Commodity Contingency in the Internal Lendingof Developing Countries

6. Optimal External Debt Managementwith Commodity-Linked Bonds 85Robert J. M)ers and Stanley R. Thomipson

A lklodel of Optimal External Debt Allocation 86Estimation 89The Case of Costa Rica 90Concluding Comments 93Notes 94

7. Integrating Commodity and Exchange Rate RiskManagement: Implications for External DebtManagement 95Stijn Claessens

Issues in joint Commodiry and Exchange Risk Management 97An Analytical Model for Commodity Risk and Exchange Rate

Management 103Empirical Applications in Indonesia and Turkey 106Conclusion 110Notes 111

8. Hedging with Commodity-Linked Bondsunder Price Risk and Capital Constraints 115Richard J. Ball and Robert J. Myers

Hedging with Commodity-Linked Bonds When Producers AreCapital-Constrained 116

Hedging with Commodity-Linked Bonds and ConventionalLoans 121

Conclusion 123

CONTENTS i.

9. Financial Instruments for Consumption Smoothingby Commodity-Dependent Exporters 124Brian Wriobt and David Newvberv

Sovereign Borrowing and Default Prevention 125The Costs of Income Variability 125Consumption Smoothing by Bcrrowing and Lending 126Commodity Bonds issued by 'over,'ign Leniders 127Optimal Dynamic Smoothing Strategies 128Conclusion 131Notes 132

10. Securitizing Development Finance:The Rolc of Partial G'iaranteesand Commodity Contingencv 134Ronald Andersoni, Christopher Gilbert,Und AIUrei.v ozvell

Sovereign Risk 136Securitization 140Securitizing Developing Country Obligations 142The Design of Commodity-Contingent Instrtiments and Associated

Guarantees 145Conclusion 149Notes 151

11. Conclusion 152Theophilos Priovolos and Ronald C. Duncan

Bibliography 157

Inrdex 169

Con tributors

Ronald Anderson, Department des Sciciices Economiques, UniversiteCatholique de Louvain, Belgium

Richard J. Ball, Department of Agricultural and Research Economics,University of California, Berkeley

Stijn Claessens, Debt and International Finance Division, World Bank

Ronald C. Duncan, International Trade Division, World Bank

Moctar A. Fall, Capital Markets Group, Salomon Brothers Inc., NewYork

Cb-;stopher Gilbert, Department of Economics, Queenl Mary andWestfield College, London

Robert ,. Myers, Department of Agricultural Economics, Michiga4nState University, East Lansing

David Newbery, Department of Applied Economics, University ofCambridge

Andrew Powell, Department of Economics, Queen Mary and WestfieldCollege, London

Theophilos Priovolos, Elf Trading S.A., Ger.zva

Raghuram Rajan, Sloane School of Management, MassachusettsInstitute of Technology, Boston

Stanley R. Thompson, Department of Agricultural Economics,Michigan State University, East Lansing

Brian Wright, Department of tgricultural and Research Economics,University of California, Berkeley

Acknowledgmen ts

We owe a substantial debt to the colleague., who have contributed theirpapers to this volume. Special thanks also go to Don Lessard and ToddPetzel who commented on several of the papers in the book and to thethree anonymous reviewers of the Editorial Committee of the WorldBank. We also thank the copyright owners of reproduced articles in theboo.s who gave permission to reprint the articles and the AmericanEconomic Association and American Agricultural Economics Associa-tion for allowing us to present several of these articles at their December1988 Conference in New Yo; E.K We are grateful for the financial supportof the World Bank and, in particular, of its R.search Committee. Weacknowledge with many thanks the encouragement and support ofStanley Fischer, chief economist of the World Bank xvhen this volumewas written, for the risk management work in the International Com-modity Markets Division.

We have also benefited from the comments and suggestions of anumber of others in the World Bank Group, including Jean Baneth,David Bock, Kemal Dervis, Ishac Diwan, Enrique Domenge, RobertGraffam, Ishrat Husain, Ronald Johannes, Peter Jones, Ruben Lamdany,Charles Larkum, Johannes Linn, Carl Ludvik, Herbert Morais, BarbaraOpper, Sanjivi Rajasingham, Lcster Seigel, Andrew Steer, John Taylor,Anthony Toft, John Underw;ood, Frank Vita, Dimitri Vittas, and all ourcolleagnes in the International Commodity Markets Division. In addi-tion, we would like to thank Gerry Pollio of Chemical Bank; GaylenByker and John Grobstein of Paribas; Tony Singleton and Sykes Wilfordof Ch. e Manhattan Bank; Neil-Thalheim of Bankers Trust; Srini Vasanof First Boston; Ian Giddy and Frank Ocwieja of Drexel; Viktor Filatovof Morgan Guaranty; Bob Hormatz, John Goldberg, Mike Schwerin, andTom Demeure of Goldman Sachs and J. Aron; John Rinaldi, Heinz

xi

IntroductionTbeophibos Priovolos and Roniald C. Duincanz

Developing countries are expos i to major financial risks and, inparticular, to commodity price risks. Their exposure to these risks andtheir limited ability to deal with the risks effectively was obvious in the1980s, when sustained declines in commodity prices and sharp increasesin interest rates were followed by increases in indebtedness and debt-servicing difficulties.

One form of financing that has expanded greatly in the financialmarkets of industrial countries in the second half of the 1980s and thatappears to offer considerable potential for risk management in develop-ing countries is commodity-linked financing. This book brings together aseries of papers that examines the various uses of commodity-linkedfinancing by entities in industrial countries and analyzes the merits oftheir use in developing countnres.

The exposure of developing countries to instability in commodityprices is illustrated in table 1-1 by their dependence on commodityexports. This dependence is the highest in Africa, Oceania, and LatinAmerica, while less so in Asia and southern Europe. The share ofcommodity exports accounts for 42 percent of developing countryexports, but only 25 percent of industrial country exports. The exchangerate and interest rate exposure of developing countries is illustrated infigure 1-1, with information on the debt composition of developingcotiuitries. Most public and publicly guaranteed debt is still in U.S.doilars, although increasingly less so since 1982. The shares of U.K.pound, Japanese yen and German deutsche mark (DM) public andpublicly guaranteed debt are increasing. These four currencies accountfor almost all borrowing by developing countries. The noted shift in thepast 10 years toward borrowing at variable interest rates underlines thedependence of developing countries on interest rates in the United States,

I

COMMODITY RISK MANAGEMENT AND FINANCE

Table 1-1 Share of Exports of 33 Primary Cotmmnoditiesfhom Developing Countries by Region, 1982-S4 Average(number of countries)

Share of exports (percent)

Region 0-25 25-30 5S-75 7S-1 00 Total

Latin America 3 10 t1 3 27Africa 6 13 10 14 43Asia 8 5 3 3 19Oceania 0 1 2 1 4Southern Europe S 0 0 0 5Total 22 29 26 21 98

Source: World Bank, 1988a.

United Kingdom, Japan, and Germany. The followving two examplesillustrate the difficulties that many developing countries faced in the1980s in n:anaging tneir commodity exposure.

Coffee, bananas, and beef account for 50 percent of total Costa Ricanexports. This country was hit by a series of severe trade shocks from1978 to 1982. These shocks resulted from falling prices in its majorexport commodities. The initial response appears to have been to treatthe downturn in export earnings as temporary and borrow externally tomaintain domestic consumption and investment levels. With the onset ofthe debt crisis in 1981, however, this strategy was no longer sustainable.The ensuing restrictions on new external borrowing precipitated adisastrous economic slump that began around 1981 and continued to1983. Costa Rica has become a highly indebted country; at present, itsgrowth potential is handicapped by its debt-servicing requirements. Thesecondary market for Costa Rican debt, which trades at a large discount,reflects the market's perception of Costa Rica's ability to service its debt.To ensure that the country does not return to a debt-burdened situationwill require a debt reduction scheme, such as the Brady Plan, accompa-nied by good macroeconomic management and the implementation ofhedging programs.

In Algeria, there was a substantial trade shock in 1986 with the declinein oil prices. Algeria's hydrocarbon exports account for some 90 percentof total exports. In this case too, the country tried to stabilize itsconsumption path by borrowing from abroad. In contrast to the CostaRican situation, the Algerian economy (despite reaching a higher level ofindebtedness than in the past) has been able to absorb the impact of theshock to its terms of trade. Nevertheless, the oil shock has alerted theauthorities to the vulnerability of the economy to the variability of

INTRO DUCT I(ON

hydrocarbon prices and to the need to hedge the doxvnside exposurc of

the economy to reduce the chances of a future deterioration in growth.Although for some developing coUntries (in particular, those that are

highly indebted) the first priority is to reduce their indebtediness, almostall net . to maintain sound macroeconlomic policies-including imple-mentation of effective risk managcment progr"ms. There are, in fact,maniy commodity risk managemenit instruLmileits available to developingcoulitries. They can be categorized into three groups: self-insuranceinstruments, third party insurance instrumeints, and other instrumenits.

The first group includes instruLImenlts such as reserve managementschemes, domestic stabilization scilcimCes, macroeconomnic policies, and

Figure 1-1 Curre'icy Composition of Public and PubliclyGuaranteed Deveilping Country Debt

(billiors of U.S. dollars)

475.3 548.9 593.1 690.7 800.1 905.2

Percent

10 -- - - - --;

90

80

70 .N~~N

50 -!!-~

40 -

30 - - '

20

1982 1983 1984 1985 1986 1987

F1 Other ED French francs E Deutsche marks

El Yen EJ LSTG W U.S. dollars

Source: World Bank (1988).

4 COIMMODITY RISK MANAGEMENT AND FINANCE

diversification programs. The second group includes financial marketinstrLuments such as futures, forwards, options, swaps, and long-termcontracts. among others. The third group includes all other schemes suchas international commodity agreements and compensatory financingschiemes, including th'e STABE,-VS'S33AiN schemes Cof the LLCurp UUU C.11 om_UiUcICommunity (EEC), for example.

One instrument that combines risk inanagement with finance, wvhoseuse has greatly expanded in the late 1980s, is commodity-linked fi-nancing. This financial market instrument (belonging to the second groupof risk management instruments) can help industrial and developingcountri2s alike raise funds, while linking revenues xvith expenses andassets with liabilities. Commodity-linked financing is a hybrid instru-ment: It Is a risk mnanagement instrument as well as a financinginstrument. As commodity-linked financings extend beyond one year,their risk mannaement nronerties are of strategic imnPortance to thecommodity price exposures of the organizations involved. Commodity-linked financing conies in many forms, such as commllnodity bonds,commodity loans, and others.

The chapters in Part I cover the issue of the pricing of commodity-linked securities. Chapter 2 reviews the different forms of commodity-linked financing. A conventional bond makes semiannual coupon pay-ments, determ.ined by a coupon rate, and pays out the principal amountat maturity. The nominal return to the investor is known, but, with theuncertainty of the infiation rate over time, tne reai return is uncertain.With commodity bonds, investors have sought to link their investment toreal assets. Commodity bonds exist in two different forms: those of aforward tVDe. often called convertible or indexed bonds. and those of theoption or warrant type. In commodity bonds of the forward type, thecoupon andlor principa -a...t -r link.d --- z ttdqatt f -I.AJjJUI UILl!vL P) Il.lj)dIFI F4Y III%lLa atLL ILLINL%U t'.i1 a Lat..4 -..jUaIILJLY iJl aX

commodity. A commodity bond of the option type makes normal couponpayments (just as conventional bonds do), but, upon maturity, the holderof these bonds has, in addition to the principal, the .. ption to buy or sella predetermined quantity of the commodity at a predetermined price.Because of rhe inherent value of such an option- the counon navments ofthis bond are lower than they would be in a conventional bond.

U L0 LIC1NE 1libLLU1IICILb VZ ULILN& dL' leasL ,,LUY. LiIIL1aUse of theeisuet sbc a; les;a centuy iThr I h'as b..ena recent awakening of interest in commodity-linked bonds, however,building in late 1986 and 1987. Several dozens of commodity bonds(most linked to gold, silver, and oil) have been issued, at an approximatevalue of US$3 billion-4 billion. Most have been issued in the Euromar-ketc hernicle of i,ncPrtiintv bnout the I.S1. reoildatorv environment Sincethe October 1987 stock market crash, however, the retreat of institu-

INTrRODUCT ION S

tional investors from the Euromarkets has led to a reduction in thevnliime of rnmmondity-!inkied bondscl isiised in thorse mirkets.

The decline of commodity bond issues has been compensated by adraml atic increase in the numuer and volume of commodity loans andprivate commodity bond and note placements. Because commodity loansand private placements are less transparent, the volume of commodity-linked financing is unknown. Commercial banks estimate the volume tobe in excess of US$4 billion per annum.

T)p demand for com,mnA-t, bonds cones frm. Crispecators aInA

hedgers. Chapter 3 discusses a theoretical model of the demand forcommodity bonds. This is an extension of the work done by O'Hara(1984). O'Hara showed that if commodity bonds are priced fairly, theywill be demanded only if there is a minimum necessary consumptionquantity or the bond's payoff negatively correlates with the individual'sportfolio return. The bond is valuable because it provides a form of

insuanc in___ hegig i!_ s f future cons;.mption. In chap--, Fall11113UI,2iiL_% fit IILUr,1li5 L13r3 UL L LIU . i U IZk)LiJ1i. III ~II."FL%~& -J, L UII

shows that the demand function for commodity bonds has two compo-nents, a speculative component and a hedging component, and tnat thedemand for commodity bonds is positive when the investor has a lowverrelative modified risk tolerance than the market (i.e., a higher relativemodified tisk aversion).

In part 1, different approaches to pricing commodity bonds arediscusse.d4 i- chapters 4 aznd 5. A review of tlhe Q, uij (A1982)metho

is presented by Priovolos in chapter 4. The Schwartz model considers theimpact on bond pricing of commodity risk, default risk, and interest raterisk. In chapter 5, Rajan bypasses the mathematical complications of theSchwartz model when default risk is introduced by the use of binomialpricing theory. Neither of these chapters considers sovereign risk.however. The introduction of such risk is particularly important fordeveloping countries, and it is discussed in the last chapter of part 11.

There are five chapters in part II. The issues addressed in this sectionprovide insights on three levels: those that apply to commodity-iinkedfinance whether or not the borrower is a sovereign with the relatedlimitations of contract enforceability, those that apply to a sovereign witha clean financial slate, and those that apply to sov-ereign borrowing in thepresence of an exisdng debt overhang. The chapter by Myers andThompson focuses on the first level computing commodity hedge ratios

for a country facing variance in commodity output, as well as in the priceof its commodity exports. They derive the optimal conditions tor the useof commodity bonds of the for-ward type in a hedge of the external debtrequirements of a hypothetical commodity-dependent country. In chap-tfr 7, Claessens introduces exchange rate risk, in addition to commodityprice risk, in hedging external debt requirements.

6 COMMODITY RISK MN1ANAGEMENT AND FINANCE

The next two chapters by Ball and Myers and WVright and Newberymake important contributions at the first two levels. In chapter 8, Baliand Myers extend the analysis by Thompson and Myers to a sovereignwith a clean financial slate. In chapter 9, Wright and Newbery, withoutreference to the limits of enforceability, quantify the magnitude andwelfare costs of export revenue variance for counltries characterized byconcentrated exports. They also analyze and quantify the relative per-formance of reserve management versus commodity hedging in reducingfluctuations in the foreign income of such countries. Estimates of the costof price variability and the potential benefits from risk reduction as aresult of employing these two mechanisms clearly demonstrate theimportzance of risk management. Wright and Newbery also show, withinthe context of sovereign borrowinig, the way in which alternative types ofcommodity-linked contracts affect the probability of default and, hence,access to external finance in an idealized rational world.

In chapter 10, Anderson, Gilbert, and Powell begini with the problemof sovereign borrowing and the comparative advantage of lenders inbearing particular forms of risk. They find that the required insurancepremiums for guaranteeing sovereign risk are minimized when theinsuring body has a comparative advantage in bearing sovereign risk andwhen the contractual terms of any new financing are contingent onfactors affecting the borrower's present and future earnings. They showthat assets that are contingent on commodity prices may be the mostsuitable form of obligation; for many developing countries. Commoditybonds and loans, long-term commodity options, forwards, and swapshave proliferated in the developed countries in the past few years. Theliquidity of these commodity-risk management instruments, althoughstill not comparable to that of similar foreign exchange or interest rateinstruments, is growing at a very fast pace. Why is it then that developingcountries do not hedge their commodiry exposure wvith these financialinstruments? In part, it is because developing country organizations (withthe exception of some multinational organizations) do not have theknowledge or the institutional basis to hedge their short-term operationaland long-term strategic commodity exposure. Moreover, the hedgingcost for developing countries is substantially higher than that of indus-trial countries. This is due to the perceived sovereign risk of developingcountries.

While chapters 6 and 7 address the issue of how much of one's

exposure to hedge, chapters 8-10 explore the reasons commodity-linkedfinance is important for program and project finance in developingcountries. Here it is shown that the two parts of commodity finance-riskmanagement and finance-can be structured in such a way that theymaximize the welfare (however defined) of an organization. Further-

INTRO DUC-r ON 7

more, in chapter 10, it is show n that within a debt .structuringframework, where negative pledge clauses could be waived, the sovereignrisk assumed by a commercial bank with a properly structured commod-

ity-linked bond or loan is much less than with a conventional bond orloan. In other wvords, the capital of a bank can be better used xvhen itsclients commit to hedge their commodity exposure xvith properly struc-tured commodity loans. In turn, the bank would '.ave to hedge its

commodity price exposure in the financial markets, here it is presumedto do so at a lesser cost than its clients.

The final chapter summarizes the findings in this volumlle and addressesthe costs and benefits of commodity-contingent financinig instruments,from the viewvpoint of both the issuer and the investor. Finally, thepossible role of international development agencies in this area ofdevelopment finance is disCussed.

c ') (m i

n sL,(t ,)1

Z I0 m0

zr .ior* M

Experience w"thCommodity-LinkedIssuesTheophilos Priovolos

In response to the appetite of investors eager to participate in the possibleupswing of long-underperforming commodities and in response to therisk management needs of primary commodity producers-in particular,precious metal producers-commodity-linked securities proliferated inthe late 1980s. Securities linked to the prices of silver, gold, and oil wvereparticularly popular wvith investors. Almost all conmmodity-linked financ-ings were issued by corporations and governments in the developedworld. In developing countries, however, very few offerings occurred.This chapter reviews recent experiences with commodity-linked issues.

Introduction

These kinds of bond issues are by no means a novelty. The first knowncommodity bond, which is the most common form of commodity-linkedfinancing, was issued by the Confederate States of America in 1863 (seeFall, 1986). The Cont'ederates were fighting a costly war against theUnited States of America; their principal asset was cotton and, for thatreason, they decided to issue a bond 'whose payoff would be linked to theprice of cotton. Commodity bonds may also be linked to conimoditiesother than the traditional primary ones. In 1945, for example, the Frenchgovernment's Caisse Nationale d'Energie issued a bond indexed on theprice of electricity to pay for the nationalization of utilities. Investorswere paid a 3 percent coupon and additional income from a fund thatcomprised 10 percent of the gross utilir-- revenues in France.

As stated earlier, commodity bonds ,ay be of two kinds: forward(often called commodity-indexed or conv,ertible bonds) and option (oftencalled commodity warrant bonds). For example, a conventional

12 COMMODITY RISK MANAGEMENTr AND FINANCE

US$1,000 10 percent coupon bond would make annual payments ofUSS5100, while a similar oil bond of a forward type would, for instance,make coupon payments equal to the current monetary valuc of 5 barrelsof Brendt oil. The payoffs to these bonds reveal that they are similar toa conventional bond and a set of forward contracts. Each couponpayment is analogous to a forward contract; howcver, there is one majordifference. In a forward contract, the agreement is that the monetarysettlement will take place at maturity. In a commodity bond, the investorwho holds the long side has already fulfilled his obligation by buying thebond. Forwvard contracts are negotiated betwcen two parties and are notalways easily traded.

In a commodity bond of the option type, one or several call or putoptions are attached to the coupon or princ.pal paymients. In this case,the investor receives the US$1,000 face value and, in addition, has theoption of buying or selling a predetermined quantity of oil at apredetermined price. Because these bonds include an option feature thathas a market value, the coupon rate is generally lower than it wvould havebeen for a conventional bond. Thus, the advantage to the issuer of ti.optionl type is loNver interest payments, with a tradeoff of sharing anappreciation in the price of the commodity by wvriting a call option on thecommodity.

Issuers of commodity bonds are typically governments or corporationsthat have ready access to the underlying commodity and that seek abetter hedge of their liabilities with their assets. The advantage to theinvestor is the ability to take a liquid and divisible position in acommodity, thus benefiting from a price hike (or fall) yet receiving aguaranteed minimum return on the investlilent (through the fixed couponpayments). Commodity bonds of both the option and forward type allowthe holder to take a iong-term commodity position. Thus, it would seemthat commoditv bonds would be popular with investors and issuers whencommodity prices are expected to change significantly in either direction.

The proliferation of commodity bonds linked to precious metals (goldand silver) and to oil in recent years can be attributed to their image asan inflation hedge, their storability, and the natural position of severalcommercial banks in these markets. Uncertainty as to which U.S.agency-the Comnodity Futures Trading Commission (cFrc) or theSecurities and Exchange Commission (SEC)-should regulate these issueshas caused most of the commodity-linked financings to take place in theEuromarkets. Since the October 1987 crash, Euromarket activity hassubsided. At present, most commodity-linked financings are placed in theprivate markets. Australian and Canadian Lflnks have become very activein these markets because of the im-)ortance of commodities to theAustralian and Canadian economie-. Data on pxivate placements are

EXPERIENCE WITH COMMNODITY-LINKED 'SSUES 13

scarce, but recent reports indicate that commodity-linked financingsamount on an average of USS0.3 billion monthly.'

It is noteworthy that commodity-linked financing has taken formsother than those of the forward or option-type bonds. Some of theseforms include those listed below.

Commodity- Indexed Certificates ot Deposit

A banik-issued certificate of deposit (CD) typically pays interest to adepositor based on a percentage of the rise or decline in the price of acommodity or the value of an index during a specified period of time. Thematutity, denomination, and manner in which interest is calculated on antindexed CD can vary substantially, and these differences reflect thedisparate needs of savers In the United States, regulatory problemscaused the abortion of gold CD issues by banks oni the East and WestCoasts in 1987. (See, for example, the Wells Fargo CD offering ofSepteuiber 1987.) In other countries, however, and, in particular, inHong Kong, bear .^nd bull gold CDs are available. (See, for example, theBanque Indosuez issue of February 1988.)

Commodity Variable-Rate Loans

A commodity variable-rate loan is made at an irterest rate that isindexed to or correlates with an accepted benchmark of current marketrates. The borrower's interest payments are adjusted at specified dates toreflect subsequent interest rate fluctuations. Such loans may have mini-mum or maximum rates set at the time of origination. Variable interestpayments may be indexed to the value of a commodity produced by aborrower (see bullion loans below).

Gold Repos

Gold repos refers to an entity wvith excess gold that borrowvs cash froma bank for a specified period. Gold is used as collateral for the loan andis later repurclased by the b. rrower at a margin above a specified interestrate, but less than the cost of carrying gold during the relevant period.Thus, an entity with excess gold is able to meet a short-term fundingrequirement, and the bank makes a fully collateralized short-term loan ata rate higher than the market interest rate.

Bullion Loans

A bank may extend financing to a mining co:;.pany indexed to bullionorices. The producer can use this comparatively low-cost financing tomeet it, working capit.i needs and deliver bullion (or thc cash valuethereof) to satisfy the loan repayment obligation.

14 COMMODI-rY RIsK MANAGEMENT AND FINANCE

Swvaps

Swaps are privately negotiated transactions in which two parties,directly or through an intermediary bank, agree to exchanige a series ofpayments calculated on different bases: fixed-rate interest payments forfloating-rate payments, one type of floatinig-rate paymcut for anothertype of floating-rate payment, dollar-denominated payments for nondol-lar-denominated payments, fixed for floating comnmodity price payments,or payments tied to the price of one index for payments tied to the priceof another. An exchange is arranged between tw%o counterpaf:ics withcomp;ementary needs, and the payments due on the spe^ified dates arenetted. Swap transactions have been structured in innumerable forms andvariations.3

Caps, Floors, and Collars

Caps and floors on commodity prices or other financial instruinents aresimilar to swap transactions, except that the commodity price is fixed ata maximum (cap) or a minimum (floor). The seller of a cap agrees to paythe buyer the price differential bet-ween t!Ac capped and a floating price,with respect to a specified notionml amount, in exchange for the paymentof a fee. The seller of a floor agrees to pay the buyer the price differentialbetween the floor and the floating price, with respect to a specifiednotional amount, in exchange for the payment of a fee. A collar is atransaction in which the purchaser of a cap simultancously sells a floor tothe seller of the cap, thereby deftaying the cost of the cap.

Swaps, caps, floors, and collars are not financing instruments per se.Their hedging properties, however, have made zheir use increasinglyimportant in commodity financing. As previously noted, in 1988, com-modity financing relied more heavily on the types of financial instrumentsdescribed above than on the more traditional Eu':obond types. Thefollowing sections discuss particular experiences w ith gold, silver, oil,and other commodity-specific issues.

Gold-Linked Financing

Gold-linked financing has been ihe most widespread among forms ofcommodity-linked financing. The forward (or indexed) type and theoption (or warrant) type have been the most typical forms of gold-linkedfinancing. One of the best-known cases of gold bonds was that of theGiscard bond. In 1973, the French government appealed to investorswith a gold-indexed bond issue. The "Giscard," as this bond is com-monly referred to-named after the then-French finance minister (and

Table 2-1 Gold Warraid Issues, 1986-88

Implied Strike All-involunir pre- pre-

Issue at ir ue mWin' iniu?? CoverageIssue ;;ead Exercise pnrce 1're,niumt (per- (per- (per- ratio Spotdate managerJ) Host bun I Warrant atid period issue level cent) cent) cent) (percent) US$1OZ

9/12/86 American - 4 n; Wrts eacih US$9.:'0/0.02 oz USSI.50/0.02 oz 15 7 24 - 430Barrick to buy 0.02 oz (US$4iO/oz) (US$75/oz)Resources gold 4 ycars(Merrill . (9/12/86-Lynch 9/25/90)Canada)

9/27!86 Echo Bay Sfr 110 m To each bond US$560 Sfr 542/Nrr 15 30) 42 86 431Mines due 10/29/96 of Sfr 5,000 is 1 5 years approx. (Sfr 90 3/8/oz)Ltd. ci'.s: J.875% Wrt, exercisable (11/30/86- (US$54/oz)(Credit Host bond into 6 oz of/or 9/30/91) (US$90.73/oz)Suisse) and Wrt dollar equivalent (Spot FX =

iSSu'd at 1()( of gold sfr 1.6595/US$)10/11/86 Standard Sfr ISO In To each bond USS565 ZO) Sfr 500/Wrt 28 30 50 48 435

Oil Co. due 11/6/93 of Sfr S,000 is 4 years (SIr 151!5/oz)(Morgan %7I'N: 3.125'Xt attached 1 Wrn, (11/6/87.. (US$90.73/oz)Guaranty) I-lost bond cntitrlitig the 11/6/91) (Spot l:X =

and W!t holder to Sfr 1.67/USS)issued at purchase 3.3 oz100 of gold or

receive thiedifferencebetween spotprice of goJdard exerciseprice

(1Jii,le ccntin*,es on the fullouving page.)

Table 2-1 (continued)

Implied Strike All-involume pre- pre-

Issue at issue miuma miumb CoverageIssue (lead Exercise price Premium (per- (per- (per- ratio Spotdate manager) Host bond Warrant and period issue level cent) cent) cent) (percent) US$Ioz

2/25/87 Credit Sfr 200 m To each bcnd US$565.20 Sfr 500/Wrt 42 15 40.3 50.2 407Suisse due 2/20/97 of Sfr 4,000 are (USS467.98 oz) (Sfr 162/oz)(Credit CPN: 2.875% attached 10 3 years (US$10S.3/oz)Suisse, Host bond Wrts, allowing (3/20/87- (Spot FX =Zurich) and Wrr together the 3/20/90) Sfrl.5385/USS)

issued at purchase of100 I OOg oi finc

gold (I e =31.1035g)

3!3/87 Citibank - 10,000 Wrts US$430/oz Sfr 1,050/Wrt 25 6½/2 23.5 - 403(Citibank exercisable into 2 years (Sfr 105/oz)NA, 10 oz of fine (4/16/87- (US568.2/oz)Zurich) gold or equiv. 4/16/89) (Spot FX =

cash amount Sfrl.5395/USS)3/5/87 Financiere Sfr 100 m To each bond Sfr 2.335/lOOg .ir 540/10 Wrt 40 13 43 41 412

Credit due 3/30/97 of Sfr 5,000 are (US$465.7/oz) (Sfr 167.95/oz)Suisse CPN: 3.25% attached 10 3 years (US$107.7/oz)First Host bond Wrts, allowing (3/30/87- (Spot FX =Boston and Wrt purchase of 3/30/90) Sfrl.56/US$)(Credit issued at lOOg of fin.cSuisse) 100 gold (1 oz =

31.1035g)

3/5/87 Citibank - 10,000 Wrts, US5420/oz Sfr 9SI50[Wrt 24 2 18 - 412(Citibank each exercisable 15 months (Sfr 95/oz)NA, into 10 oz of (4/22/87- (US$60.9/oz)Zurich) fine gold or 10/3/88) (Spot FX =

equivalent cash Sfrl.56/USS)3/6/87 Banque - 15,000 Wrts, US5410/oz Sfr 1.380/Wrt 29 0.Y61 21.7 - 406

Indosuez each entitling 2 years (Sfr 138/oz)(Goldman holder to buy (4/16/87- (Spot FX =Sachs) 10 oz gold 4/16/89) Sfr 1.55/USS)

3/18/87 Morgan - 12,000 Wrts, US$425/oz Sfr 995/Wrt 26.5 4.41 35 - 407Guaranty each to bring 5 41/4 years (Sfr 191/oz)Trust oz of fine gold (4/30/87- (US5124.6/oz)(MG, AG, 7/31/91) (Spot FX =Switzer- Sfr 1.5335/USS)land)

3/25/87 Electricitc Sfr 100m To each notc of Sfr 2.35 0/lOOg Sfr 4.489/15 Wrr 45 15 44.4 28.6 418de France due 4/20/95 Sfr 50,000 are (US!481/oz) (Sfr 186/oz)(Credit CP'N: 3.375%/o attached 15 gold 3 years (US$122.5,'oz)"uisse Host b-snd Wrts issued by (4/30/87- (Spot FX =Zurich) and Wrt Credit Suisse, 4/04/90) Sfrl.5195/USS)

issued at each exercisable100 into 50g of fine

gold4/9/87 Kingdom Sfr 100m To each note of Sfr 2 ,4 5 0/lOOg Sfr 3.666/15 Wrt 39 19 43 30.8 427

of due 4/20,194 Sfr 50,000 are (USS509/oz) (Sfr 152/oz)Belgium CPN: 3.375% attached 15 gold 3 ycars (USSIOI.5/oz)(Credit Host bond Wrts, each (4/30/87- (Spot FX =Suisse and Wrt exercisable into 4/20/90) Sfrl.4972/USS)Zurich) issued at 100 SOg of fine gold

(Table continues on the following page.)


Implied Strike All-involutne pre- pre-

Issue at issue miuma miumb CoverageIssue (lead Exercise price Premium (per- (per- (per- ratio Spotdate manager) Host bond Warrant and period issue level cent) cent) cent) (percent) US$/oz

4/14/87 Citibank - 20,000 Wrts US$440/oz Sfr 610/Wrt 25 - 18.5 - 444NA each to bring 5 21 months (Sfr 122/oz)(Citicorp) oz of fine gold (5/4/87-214/89) (US$82/oz)

(Spot FX =Sfr 1.4878/USS)

4/15/87 Saint- ECu 75m To each bond US$490/oz US$135[Wrt 39.5 10 41 49.5 444Gobain due 5/6/92 of ECU 1,000 is 3 years (Spot FX =(Salomon CPN: 4.50% attached a gold (5/6/87-516190) US$1. 1154/Ecu)Bros.) Host bond Wrt, exercisable

and Wrt into 1 oz of fineissucd at gold100

4/15/87 BNP USSlOOm To each bond USS496/oz US$1SO/oz 45 12 45.5 44.4 444(CSFB) due 5/13/92 of US$1,000 is 3 years

CPN: zero attached 1 Wrt (5/13/87-Host bond to buy I oz of 4/16/90)and Wrt goldissued at 80

4/16/87 Hoffman Sfr 250m To each bond Sfr 2.510/lOOg Sfr 238.5/oz 52 21.7 55 42.2 429La Roche due 9/30/90 of Sfr 5,000 \USS522.2/oz) (US$158.5/oz)(Credit CPN: zero are attached 31/2 years (Spot FX=Suisse) Host bond 10 Wrts, (5/15/87- Sfr 1.495/US$)

and Wrt exercisable into 9/30/90)issued at lOOg of fine80.5 gold

4/16/87 Kingdom Sfr SOm To each note Sfr 2.520/100g Sfr 472/ 34 16.7 38.5 32.4 449of due 4/20/92 of Sfr 50,000 (US$524.3/oz) 3 lOOg = 147/ozBelgium CPN: 3% are attached IS years (US$98.3/oz)(Credit Host bond gold Wrts, each (4/20/87- (Spot FX =Su .j and Wrt exe;cisable into 4/20/90) Sfr 1.495/USS)

issued at 50g100

5/14/87 Aegon Sfr 100m To each bond US$500/oz US$113/oz 37 7.8 32 36.5 46A.(Citicorp) due 6/16/92 of Sfr 50,000 23 months

CPN: 2.S% are attached 5 (6/17/87-Host bond Wrts, each 5/15/89)and Wrt exercisable intoissued at S oz100

5/20/87 Eastman US$ 130m To each bond US$470/oz US$1 18/oz 32 _ 25 47.06 470Kodak & due 6/25/90 of US$5,000 are 23 monthsCo. CPN: 9% attached 5 Wrts, (6/25/87-(uBs) IP: 113.175 each exercisable 5/19/89)

(cum Wrts) into I oz101.375 (exWrts)

5/21/,7 Eksport- US$100m To each bond US$475/oz US$120/oz 32 _ 25 47.5 476finans due 6/22/90 of US$5,000 are 23 months(UBS) CPN: 9% attached 5 Wrts, (6/23/87-

r: 113.18 eachi exercisable 5/22/89)(cum Wrts) into I oz101.18 (exWrts)



Implied Strike All-involume pre- pre-

Issue :t issue mium' miumb CoverageIssue (lead Exercise price Premiuin fper- (per- (per- ratio Spotdate manager) Host bond Warrant and period issue level cent) cent) cent) (percent) US$/oz

5/21/87 General SMr I 2ni To cach bond US$510/oz US$99/oz 38 8.1 29 37.23 472Motors due 6/30/92 of Sfr 50,000 17 monthsCanada CPN: 2.750% arc attached S(Citicorp) Host bond Wrts, each

and Wrt exercisable intoissued at S oz100

5/21/87 uBs Sfr 200m To cach bond Sfr 2.575/lOOg Sfr 495/10 Wrts 34 16 38 44.3 472(UBS) due 6/15/97 of Sfr 5,000 are (Sfr 801/oz) (Sfr 154/oz)

CPN: 31/4% attacihed 10 (US$548/oz) (US$10S/oz)Host bond Wrts, together 3 years (Spot FX =and Wrts exercisable into (6/15/87- 1.4600)issued at lOOg of fine 6/15/90)100 gold

5/29/87 Chris- 'r 50m To each bond Call: strike = Call: USS83.2/oz Call: - Call: Call: 451.25tiania due 7/8/94 of Sfr 5,000 are US$490 Put: US$46.1/oz 34 27 27.1Bank CPN: 21/2% attached 3 call 18 months (until (Spot FX = Put: Put: Put:(Gutz- Host bond and 4 put Wrts 11/30/88) 1.4600 313/4 17 36.1willer) and Wrts on difference Put: strike = Sfr/US$)

issued at London fixing US$420100 and strike per 1 3 years (unitil

oz fine gold 5/31/90)

6/30/87 DNC Sfr 50m To each bond Call: strike = Call: US$83.2Voz Call: - Call: Call: 45: .10(Gutz- due 6/20/94 of Sfr 5,000 are US$440 Put: US$41.7/oz 34 26 27.3willer) CPN: 21/l% attached 3 call 18 months (Spot FX = Put: Put: Put:

Host bond and 4 put Wrts Put: strike = 1.5010 Sfr/US$) 31½/2 19 36.4and Wrts on difference US$410issued at London fixing 3 years100 and strike per

10 oz fine gold7/25/87 Citibank - 10,000 naked US$420/oz Sfr 1.4901Wrt 32 - 13 - 457

NA gold warrants, (until (USS963.89IWrt)(Citicorp) each Wrt allows 10/11/88) (US$96.38/oz)

the holder to (Spot FX =purchase 10 oz 1.5495 Sfr/US$)of fine gold

8/4/87 Rhone Sfr 100m To each bond US$475/oz Sfr 897.7/Wrr 41 - 29 61 475Poulenc due 918195 of Sfr 5,000 is (9/11/87- (Sfr 213.7/oz)(Shearson CPN: 2% attached I Wrt, 5/22V89) ('JS$137.'/oz)Lehman) Host bond exercisable into (Spot FX =

and Wrts 4.2 oz of gold 1.5523 .fr/USS)issued at (public issue)100

8/6/87 Olivetti Sfr IOOm To each bond US$465/oz Sfr 988.3/Wrt 44 - 28.5 67 469(uBs, SBC, due 9/21/96 of Sfr 5,000 is (until (Sfr 214.85/oz)Shearson CPN: 2% attached 1 Wrt, 5/22/89) (US$137.77/oz)Lehman) Host bond exercisable into (Spot FX =

and Wrts 4.6 oz of gold 1.5595 Sfr/US$)issued at (public issue)100



Implied Strike All-involtf,ne pre- pre-Issue at issue ?nium' ?niurmn Coverage

Issue (lead Exercise price Premium (per- (per- (per- ratio Spotdate manager) Host bond Warrant and period issue level cent) cent) cent) (percent) US$/oz8/11/87c SEK Sfr lOOm To cach bond IJS$460/oz Sfr 437.1/Wrt 29.5 - 23.4 42 463

(Warburg due Gf Sfr S,000 is 2 years (Sfr 174.9/oz)Soditic) 10/15/94 attached I Wrt, (US$111.34/oz)

CPN: 23/s8/. exercisable into (Spot FX =Host bond 2.6 oz of gold 1.5705 Sfr/US5)and Wrts (public issue:issued at fees 17/8%)100; 20%amortizationyearly from1990-94

FBDB C$50m To cach bond US$463.1S/oz CS140.79/Wrt 26.5 - 23.2 61 463(Domin- due 11/4/91 of C$5,000 arc 2 years (US$106.98/oz)ion CPN: 101/4% attached S Wrts, (until 9/21/89)Securities) Host bond each one

and Wrts exercisable intoissued at 1 oz of gold113½/2 (public issue)

9/23/87 ATT (UBS) US$100m To each bond US$463/oz IJS$120/oz 35 - 26.2 46 462due of US$5,000 are 2 years10/22/90 attached 5 Wrts, (10/22/87-CPN: 9¼/4% each one 9/21/89)Host bond exercisable intoand Wrts 1 oz of goldissued at (public issue:112-/4 fees 1 l/8%)

- Not available.m = million.a. Defined as strike price/spot price.b. Defined as (exercise price + option premium)/spot price of goldc. The spot price of gold has to increase by this percentage from its current level for

the investor to break even (i.e., recover the option premium).c. This deal was pullcd an(d replaced by a series of zero couponi traniches.Source: Goldman Sachs, London, February 1988.

Table 2-2 Gold Indexed and Convertible Issues

IssuerIssue (lead Amiount Issue Coupons Conversion Conversiondate manager) (denoms) price (percent) Maturity details price Comments

1/16/73 French FFr 6.5 m 100 7 1/16/88 -- - R^demption and coupongovern- (FFr 1,000) are indexed to:ment (I) The price of 1 kg of

gold in Paris on issuedate, i.e., FFr 10.483(2) The average price ofI kg of gold for the 30business days beforeJanuary 1.Coupon (per bond)= (70/10,483) x (2)Redemption (perbond) = (1,000/10,483)x (2)

10/4/86 American US$50 m 100 5¼14 10/31/91 into gold fronm $530/oz Redemption price =Barrick 10/31/91 111V2½Resources(BanqueParibas)

1/24/87 Barrick US$50 m 100 2 2/29/92 Into gold or US$ $406.94/oz --Resources each equivalentguaran- with corn ersionteed by price reducingAmerican by $16 per 1COgBarrick per yearResources cominencing(Banque 2/26/89 (i.e.Paribas) about $S/oz)

Pegasus Sfr 60 m 100 5¾/4 10/10/96 (1) Into shares: (1) Into shares:Gold (Sfr 5,000) until 9/19/96 atCorp. (2) Into cash $9.607/share(Banque equivalent of at FX (SfrGutzwiller) gold during last 1.6S76/US$)

tlhree years of correspondingmaturity to 314 sharcs/

bond(Premiunm= 10.069%)(2) Into gold:to b .y 4.89oz of finegodAbond at5617.25/oz(Premium

= 50'O)

9/19/86 Kingdom US$120 m 1001½ 3 10/20/93 Rccemption linked to

of Two price of gold:Denmark tranchs s: Bull = Par x 1.158(Societe Bull-$6(U m Price of gold atGenerale) Bear-$60 m maturiry/

Price of gold at issue(M426.5/oz)Bear = Par x2.78-1.158 Price ofgold at maturity/Price ofgold at issue ($426.5/oz)



IssuerIssue (icad Amount Issue CopotJ Conversion CoJlversion;date tnanager) (denoins) price (percent) Maturity details price Comments

4/16/87 Interna- US$50,001,107 100 3'/s 5/12/92 (1) Convertible (1) Convertibletional of bonds into gold from into gold atCorona convertible into 5/15/88 to $16.91/gResources gold witlh 5/15/92 (=$526.02/(Banque attached gold (2) 1 Wrt is oz-20%Paribas) call warrants attached to each premium of

bond-a 3-year spot)call on gold .'2) Call on gold

at c 17.62/g(= S54 /.y4/oz-25%premium ofspot)

5/5/87 Hycroft US$12.152 m 105 5 5/28/92 (1) Conversion (1) Conversion(Banque mi,nimum to period: 12V1/87 price = $540/ozGutzwiller) 17.361 m to maturity: (20% over

maximum changeable for premium overl1Og gold spot gold)bullion or(2) For amountequal to currentmarket value ofI OOg goldbullion

- Not available. m=million.Sou-ce: Goldman Sachs, London, February 1988.

EXPERIENCE WITH COIIMMODITY-LINKED ISSUES 29

estimated, however, that since 1986, there have been loans totalilngapproximately 7 million ounces, some 50 percent of which have becenarranged since October 1987. Gold loans arc used primarily to fuxid minedevelopments and expansion. Some loails, howeve., have been used torefinance corporate debt. The unresponsiveness of the equity markets tothe hedging needs of the mining community and -the proliferation ofknow-how in the pricing of these loans have made them increasinglyacceptable to the industry.

The average length of gold loans has also increased in the past fewyears. T-his resulted from the needs of the mining industry. Capit.l1 costsincreased with the exploi;z.tion of deeper or lower quality ores, anid someexogenous factors 'such as the introduction of income taxes for goldmining in Australia) affected the rate of return of the projects. The loanterms have lengthened, but they remain limited by th life of a borrower'sore reserves. The increasing size of loans has led to some dianges inlending and pricing practices. The practice of capping interest rates ongold loans has all but disappeared. Increasing competition and fluctu-ating borrowing costs have reduced lender's margins, making stableinterest rates a matter of history. As the size of loans has increased,lenders have also begun to spread risks by syndicating loans to otherlenders. The move away from single-!;.,der loans 1, moving gold lendingtoward a cost-plus-margin basis (analogous to currency lending).

A variety of references are in use, including agent bank bare rate, leadbank gcoup reference race, ard tender panel and benchmark referencerate. A cu,F.x-reference borrowing rate is determined by Lubtracting afutures market contago from -a relevant London interbank offered rate(LIBOR). The contago may rel.ect a spot-to-forvard or a forward-to-fonvard contango. The LIBOR rate used has a term similar to that of thelongest futures contract used in the contango calculation. The volatilityof gold borrowing rates and average rates have increased recently. Scarcephysical stocks and other factors have often caused rates to reach highlevels. Sourcing of gold for Japan's Hirohito cein and the TaiwaneseCentral Bank gold purchases have depleted exchange stocks, leading totemporary increases in borrowing rates. There is a general agreementamong market participants that interest rate levels have increasedbetwvc - 0.5 percent and 0.75 percent during 1988.

Loan -greements now routinely contain provision for automaticconversion of debt to do%'Ars ii the event of a gold market disruption. Asfar as is known, there have L-en few defaults on gold loans. In November1988, a small Australian producer, Solomon Pacific Resources NL, wasreported to have fallen behind on its gold loan repayments, apparc.ntlydue to higher-than-expected operating costs. In Canada, Pacific Trans-Ocean Resources reportedly ran into problems in meeting its loan

EXPERIENCE WITH CO.Mt.1oDI .Y-LINKED ISSUES 3)

Company decided to issue commodity bonds to try to hedge variations inwvorking capital.

In 1980, the -rmpany raised USS2S mi.ihon with the issue of 81/pe-cent silver-indexed bonds due April 1.5, 1995. The bonds makesem.annual coupon payments, and the largest principal payments areUSS1,000 or the market value of 50 ounces of silver. The boids trade onthe New York Stock Exchange. Under the terms of issue, the bonds canbe redeemed on or a.ter April 15, 1985 if the average silver price for 30consecutive days is greater than USS40 per ounce. The companv has theright ro p.opose redemption of 70 percent of its original issue from 1982and t'nereafter. T-he company is not restric 1 from the creation of seniorindebtedness, but must ma3ntain qualiie. reserves equal to or higherthan 400 pelcent of thf aggregate amount of silver required by alloutstanding si!ver-backed and silver-related securities. The investors cantal-e a position in the silver market %vhJ.e earning a good return from theirinvestment, and the silver producer raises funds at a cost lowser thanotherwise would have been possible.

Sunshii'e IMining Corporation Msued a se:ond silver bond totalingUSS40 million in April 1985 for April 2004 maturity. The coupon was93,'. percent, and the principal is the greatest of callable USS1,000 or 58ounces oc silver. The issue has properties simi!ar to the previous one. (Seetable 2-3.)

Contrary to the case w-ith gold, the volumr of silver loans is notsignificant. The most important reason for the iack of development ofsilver-linked financing is because silver prices have changed little since1980, trading in the range of USS6-8 per ounce during that time. Atthese prices, silver producing companies do not invest in new projects.Operating costs of new venti, es are in the USS4-5 per ounce range.When financing costs and a 20 percent pretax profit margin are added tochese costs, there is little incentive for silver pcoducers to undertake newventures. As with gold, silver-linked financing would increase if silverrices increase substantially from theni present level. In the absence of

such price increases, investment activity wvill only focus on refinancingexistni g ventures and on hedging existing profit margins.

Crude-Oil-Linked Financing

Crud. -oil-iinkcd bonds and other forms of oil-linked financing beganin the !ate 1970s after substantial petroleum price increases, but thei; u sebecame popular oniY in recent years. Indeed, the Reagan administrationconsidered seriously the issuing of bonds l;nl:.d to oil to finance anincrease in the U.S. strategic petroleu- reer^ in early 1981. Amorng the

Table 2-3 Silver-Linked Issues, 1985-88

IssuerI! sue (lead issue Couponc ite manager) Amount price (percent) Maturity Indexation CoinmentApril Sunshine US$40 ni 100 91/4 4/J 5/2004 Each $1,000 bond is The bonds are redeemable1985 Mining redecmed at maturity in whole from 4/1S/90 at

(Drexel at the. greate- of the option of the company,Buinham) $1,000 or the average at the IPA plus accruedLambcrt) market price of 58 oz interest, if the IPA is greater

of silv.-r ("Indexed than or equal to $2,000Princip.il Amount") for a period of 30

consecutive calend-. daysSource: Goldman Sachs, London, February 1988.

EXPERIENCE WITH COM1.MODITY-LINKED ISSUES 33

first known oil bond issues were those by the Mexican government. The"Petrobonds," as the Mexican oil bonds are known, were issued in

bearer form by a trust fund set up by the National Financicre S.A.(NAFINSA). NAFINSA is a development bank owned by the Mexican govern-ment. The Petrobonds are listed on the Mexican Stock Exchange.

The objective in issuing these bonds was to entice back the money thatfled the country following the 45 percent devaluation of the Mexicanpeso in 1976. The first issue took place in April 1977. Almost 2 billionpesos were raised, and the funds were used to finance Mexican oildevelopment. The bonds had a maturity of three years and carried acoupon of 12.66 percent payable quarterly. The coupon was subject to a21 percent Mexican wvithholding tax. After tax, the coupon nettedapproximately 10 percent. At maturity, the bondholder received the pesovalue of a pre-specified number of barrels of Mexican oil net of thenominal value of coupon receipts. The average oil export price for the 25

'days preceding the maturity date was used for the calculation of thepayment. Each bal rel of Mexican oil per bond used in the calculation wasworth 1,000 pesos zr the time of the issue.

With this issue, the government was not only raising new monev at lownominal cost, but also was hedging a part of its oil production. Theinvestors in these bonds were participating in the possible upswing of oilprices. The Mexican government has made five successful issues ofPer:obonds. The importance of oil for the development of the Mexicaneconomy was also recognized by the International Monetary Fund (INIF)

restructuring agreement of the mid-1980s, under which the U.S. govern-ment was committed to increasing the availability of financing to theMexican economy when oil prices dropped below a certain benchmarkand reducing U.S. credit availability when oil prices increased aboveanother.

In 1981, Petro-Lewis Corporation, a Denver-based company in oilexploration and production raised US$20 million with oil-linked notes.The notes carried a 9 perce:? annual coupon rate, and they matured infive years. At maturity, the investors received the principal, its annualcoupon, and an option. The option exercisable at maturity was based onaverage spot prices of several oil types. It was of the call variety and hada cap. By exercising this option, an investor could make at most anadditional US$589 per bond. This kicker makes this type of bondattractive to investors. The borrower raises funds at lower cost thanwould otherwise have been possible, while foregoing some of the upsiderevenur potential from part of its oil assets.

A Ic ng-term call or put commodit', option resemble. a zero commod-ity-linked bond of the option type. In this case, the "cc nventional bond"share in the commodity bond is reduced to zero. Sevcral of these

Table 2-4 Oil-Linked Issues, 198S-88

Issue Issuer Host bonddate (lead manager) (debenture) Warrant Description Comment

9/27/85 Phibro-Salomon Inc. (naked issue) (1) 16,000 call A-exercisable on 5/13/86 at Holder of warrants can(Salomon) Wrts offered in $28/bbl choose between

four series of AA-exercisable on S/13/86 physical and net4,000 per series, at $30/bbl settlement. If neteach Wrt to buy B-exercisable on 11/14/86 ar settlement, the1,000 U.S. barrels $28/bbl following formulaeof wri BB-exercisable on 11/14/86 apply:

at $301bbl (1) Call netsettlement-- 3-day(2) 16,000 put C-exercisable on 5/13/86 at aveme = 3utre

Wrts offered in $23/bbl average call futuresoil-price x 1,000 pricefour series of CC-exercisable on 5/13/86 (2) Put net4,000 per series, at $21/bbl settlement = put 3-dayeach Wrt to sell D-exercisable on 11/14/86 at settle p utures1,000 $23/bbl oil0average price-futures

DD-exercisable on 11/14/86 oil x 1,000 priceat $21/bbl

6/16/86 Standard Oil Co. CPN: 6.30% (s.a.) (1) Indexed Note 1 Redemption = 100 + (wri Bonds issued in(Goldman Sachs) Amt: $300 m CPN: Zero price - 25) x 170" "units," each of which

Denoms: $1,000 Amt: $37.5 m consisted of 8iP: 100% Denoms: $1,000 debentures of $1,000Mat: 6/15/2001 IP: 100% denoms, 1 oil indexed

Mat: 12/15/92 note I (due 1990), and1 oil indexed note 2(due 1990)

(2) Indexed Note 2 Redemption = 100 = (W1lCPN: Zero price - 25) x 200aAmr: $37.5 mDenoms: $1,000ip: 100%Mat: 3/15/92

7/8/87 Kredintbank CPN: 3% (ann) Attached to each Exercise period: 2 years Private placement(Goldman Sachs) Amt: Sfr 50 m Sfr 50,000 note Exercise price: US$21/bblDenoms: Sfr 50,000 are 2 Wrts, each toIp: 100.5% buy 250 U.S.Mat: 8/14/92 barrels of w-n

crude oil(American calls)

7/8/87 Christiania Bank CPN: 25/s% (ann) Attached to each Exercise period: 3 years Public issue that was(Banque Gutzwiller) Amr: Sfr 20 m Sfr 5,000 bond is Exercise price: US$23/bbl pulled (i.e., neverDenoms: Sfr 5,000 1 Wrt to buy 100 actually materialized)iF: 100% U.S. barrels of w-n

crude oil(American calls)

7/12V87 Montedison Finance CPN: 47/A% (ann) Attached to each Exercise period: 3 years Public issue(Morgan Stanley) Amt: Sfr 75 m Sfr 5,000 bonds Exercise price: USS23.55/bblDenoms: Sfr 5,000 are 7 Wrts, each toand 100,000 buy 20 U.S. barrelsIp: 122% of wri crude oilMat: 8/27/92 (American calls)

- Not available.a. Tlhere is a cap on the West Texas Intermediate (wn) crude oil price of $40 per barrel.Source: World Bank data.

36 COMMODITY RISK MANAGEMENT AND FINANCE

long-term (more than a year) commodity options have been written in thelast three to four years. Gold, silver, and oil products were not the on;ycommodities for which long-term options were written. Well-knowncases include nickel, copper, aluminum, and other metals. Unfortunately,because most of these contracts take place outside official exchanges, it isvery difficult to have an accurate estimate of the liquidity of thesemarkets. It is, nevertheless, well known that an increasing number ofcommercial and investment houses are willing to quote a price forcreditworthy organizations. The increased use of these option instru-ments, particularly with oil, has also helped the development of the oilswap markets. These long-term oil options are used for hedging pur-poses. In 1985, for example, Phibro-Salomon Inc., a New-York-basedinvestment and trading house, offered its clients 16,000 West TexasIntermediate (xri) oil puts and as many calls with expiration dates of 8and 14 months. In conjunction with a straight financing arrangement,long-term commodity options can compose the two parts of a commod-ity-linked financing. (As discussed later, however, there are importantbenefits to investors to have the two parts of a commodity-linkedfinancing in one contract rather than in two.)

During the past three years, several oil bond issues took place. (Seetable 2-4.) Almost all were of the forward type. Because of the uncer-tainties of the regulatory environment, only one took place in U.S.financial markets. This was the Sohio Oil Company issue. Sohio, a majorU.S. oil producer, decided to use this method to finance a commonventure with BP and to hedge their oil assets. Sohio issued oil-indexedunits (olus). The offer wvas composed of (1) US$300 million, 6.3 percentoil-indexed debentures (OIDS), due in 2001, priced at 747, and yielding9.59 percent; (2) US$37.5 million detachable oil-indexed notes (OINS) duein 1990; and (3) US$37.5 million detachable OINS due in 1992. Each oiuconsisted of nine OIDS, one 1990 OIN and one 1992 OIN. For the OINS, if thespot price of oil exceeds US$25 per barrel, the note holder gets the excessmultiplied by 170 barrels for each 1990 note and the excess multiplied by200 for each 1992 note-with the excess not to exceed US$15 per barrel.Therefore, the effective yield on each oiu varies from a low of 8.3 percent,if the oi! price is below US$25, to a high of 13.9 percent when oil isUS$40 per barrel. Each US$1,000 oIN is effectively a combination of azero coupon bond priced at US$747 and an attached call option with aninitial value of US$253. The option was coupled to the zero because thecFrc prohibits the existence of naked or securitized options with greaterthan 18 months' maturity, unless the security option is less than 50percent of the value of the bond. The proposed 1989 cFrc ruling onhybrid instruments recommends a lower threshold percentage.

Oil bond issues are expected to increase sharply in the years to come.

EXPERIENCE WITH COMMODITY-LINKED ISSUES 37

The median cost of production of crude oil is still very low in comparisonwith the present prices of crude oil. Oil bonds can help finance theexploration and development of new projects or restructure the financesof existing oil companies.

Other Commodity-Linked Issues

There have also been commodity-linked financings in nickel, copper,zinc, and other commodities. The motivations for these issues weremultiple. The most often quoted reasons, however, were to raise funds atlow nominal cost and to hedge part of production from commodity pricerisks.

Inco, the world's most important nickel producer and an importantproducer of copper, silver, cobalt, and platinum, issued a Can$90 millionbond indexed to nickel or copper prices in 1984. TIhe issue came with a10 percent coupon. The bonds mature in 1991. The bondholders havethe privilege of either requesting the principal at par or to be paid themonetary equivalent of prefixed quantities of nickel or copper. Theexchange right of the investors could have been exercised prior to 1987if the nickel London Metal Exchange (LNIE) cash price exceeded USS2.90per pound or the copper (LNIE cash) price exceeded US$0.80 per pound.Inco had the option to repay in cash or in common shares. In 1984, Incowas experiencing financial difficulties. With this issue, the company wasable to raise funds at a cost substantially below what it would have hadto pay otherwise.

In 1988, Inco considered the issue of a second nickel bond. Its reasonfor doing so this time was to reduce its exposure to nickel pricefluctuations. In 1988, nickel prices had reached unprecedented levels; thecompany was in a strong financial position and did not need to borrowadditional funds. Inco found it more appropriate, however, to hedge itsnickel price risks through long-term contracts with its major customers-thereby locking 25 percent of its production during the next three yearsto prices substantially higher than its average costs.

In 1987, Cominco Ltd., an important Canadian mining company inthe copper and zinc business, raised US$54 million for the financing of itsinvestment program through the sale of preferred shares 2.nd commodity-indexed common share purchase warrants (cis). Each cis orovides theholder with the right to exchange the warrant on or before August 1992for a number of common shares of the corporation to be determinedbased on the average market price of zinc or copper and on the averagemarket price of common shares on the date of the exercise. Each unit was

38 COMMODITY RISK MANAGEIMENT AND FINANCE

offered at US$18, of which US$11.75 was allocated for the preferredshares and US$6.25 for each warrant.

In 1988, Magma, the largest copper producer in the United States,issued an even more innovative structure of notes linked to copper prices.The Us-$200 million issue, due in 1998, linked interest payments tocopper prices. The quarterly interest payments were paying 18 percent atthe time of the issue. The copper-indexed interest rate will range from 21percent per annum at average copper prices of US$2 per pound andabove to 12 percent per annum at average copper prices at US$0.80 perpound and below. The proceeds of the offering wvere used to restructurethe liabilities of the company. The indexing of the interest payments tocopper prices makes this issue one of the best examples of corporatebalance sheet refinancing for risk management purposes. With this issue,Magma .iucceeds in linking expenses with revenues and, in the process,assuring stability in profitability and net worth. The nominal cost offinancing makes this a high yield offering. Institutional and otherinvestors in the high yield market were attracted to this issue.

Several commodity-linked issues have taken place in developing coun-tries. Citibank is reported to have underwritten a small loan linked topalm oil prices in Malaysia. Mletallgesellschaft is reported to havefinanced its copper investments in Papua New Guinea with copper-linkedfinancing. Lack of transparency in privately arranged financings makes itvery difficult to determine an accurate number and amount of commod-ity-linked financings in both developing and developed countries. Con-fidential reports from major banking and commodity trading houses,however, do, indicate extensive use of these methods for financing orrefinancing investment programs in the commodities industries.

Notes

1. One billion equals one thousand million. See proceedings from the Fifth MineralEconomics Symposium, 1989, Toronto, Canada.

2. A version of this CD type-the College Sure cD-provides a return on maturity basedon a multiple of the average cost of a college education to enable depositors to cover thecosts of their children's college education.

3. Swaps are written oii forward and amortizing bases and may include variousoption-like features. The latter are referred to as swap options or "swaptions." Swaps canalso be participating, extendable, or callable and have drawdown provisions.

4. Goldman Sachs has kindly provided us with these tables.S. See Woodward (1989) and Stone (1989).

The Demand forCommodity BondsMoctar A. Fall

One of the most important models in finance theory, the Sharpe-LintnerCapital Asset Pricing Model (cAr.\i), is based on a single-period modelwith very restrictive assumptions (Sharpe, 1964). Although the model hasbeen widely criticized and widely tested by the academic community, it isstill extensively used in the nonacademic world. This chapter derives thedemand funcrions for commodity bonds using a continuous-time inter-temporal model similar to the one derived by Merton (1971, 1973). Themodel applies a dynamic programming technique to the consumption-portfolio problem for a household whose income is generated by capitalgains on investments in tradable assets. The derivations are done innominal terms. The chapter begins with a one-consumption good versionof this model and continues with a multigood extension.

The One-Consumption Good Case

Assumptions

The general assumptions retained for this analysis are similar to theones made in Merton (1973a). Households are assumed to behave asprice takers in a perfectly competiti-ve market, and trading a!ways takesplace at equilibrium prices. Households can buy and sell as much of anasset as they want at market prices and may short-sell any asset with fulluse of the proceeds. It is further assumed that households hold wealth inthe form of risky assets and an instantaneously riskless assct for whichthe borrowing and lending rates are equal. All assets are assumed to beperfectly divisible and have limited liability. Households can tradecontinuously and face no transaction costs or taxes. Finally, asset pricesare assumed to be stationary and log-normally distributed.

39


Most of the assumptions made are the standard assumptions requiredto make a perfect market. 1These have been widely discussed in the financeliterature and are mainly retained for the sake of simplicity, while doingno damage to the analysis. Nevertheless, Fama argues in Cootner (1964)that srock and commodity price changes follow a stable Paretiandistribution with infinite second moments, It is important to note,however, that nothing has been said about the homogeneity of house-holds' expectations, as is required in the derivation of the CAPM andsimilar models.

Asset Returns

In this section, there is a single consumption good, the commoditywhose price is assumed to be generated by an Ito process:

(3-1) p= idt + oridzi

where a, is the expected percentage change in the commodity's price perunit time and al is the instantaneous variance per unit time. Theinstantaneously riskiess rate of interest is assumed to follow the followingdifferential equation:

(3-2) dr = ardt + 0a,dZr

Each individual can hold three assets in the portfolio: a commoditybond, equity, and a default-free bond. The value of the comnmodity bonddepends only on the price of the commodity, the rate of interest, and timeuntil maturity.

(3-3) Q, = Q1(PI, r, T)

The value of the default-free bond, Q3 , depends only on the rate ofinterest and time until maturity.

(3-4) Q3 = Q3(r, T)

The x..niaining asset, in the form of equity, is also assumed to begenerated by an Ito process:

(3-S) dQ2 = R2 dt + a 2dZ2

Ito processes, -- though continuous, are not differentiable, and, thus, atool is needed to manipulate functions that involve Ito processes. Athorough description of Ito processes is given in Ito and McKean (1964),but this discussion will focus only on Ito's lemma.

THE DENMAND FOR COMMIOUITY BONDS 41

LEMMA Let F + F(X1 , . . ., X,,, t) be a function at least twicedifferentiable where the Xi's are generated by Ito processes, then itsdifferential is given by:

H "~OF I oa2F(3-6) dF= E -X dX, + Fdt + E dX-

,= X d ' at 2 .= I ,= dX, dX,dX,where the product dX,dX, is defined by the rule(3-7) dz,dzj = p,xdt i, 1,...and

(3-8) dz,dt = C i - 1, ..and pi, is the correlation coefficient betv-wcn the (Gauss-Weiner processesdz, and dz,.

Now, equipped with Ito's lemma, the percentage change in thecommodity bond's price can be determined, as well as t!-at of thedefault-free bond.

(3-9) dQ = Q dPQ + IQ' 2Q dP;dPOPI O aT 2ap

2 dr2Q dr + dP-d dPdr2 Or2 - aP 1dr

However, T is defined as time until maturity, so that dT --dt.Furthermore, as an application of the multiplicatioi, rule v yen in Ito's

lemma, the following products are obtained:

(3-10) dP2 = P2[a Idt + sldz1]2 = P2s2dt

(3-11) dr2 = [a,dt + crdzz] = ardt(3-12) dP,dr = P1[o-1dt + sldzi][ardt + 0rdZ,] = PIS1 07 prP dt

With these new expressions, equation 3-9 becomes:

OQl PI ar', a arOQ 1 P2SI 21 + 1 ar2 aQ(Qi [ C)l O: dP Q O r 2 Qi ap2 2 Qi ar2

PIS10ar 02QI 1 QI+ Plr0d r d t

+ SiP QdP dz. + Q dZr,

Similar derivations for the default-frce bond, yield:

(3-14) dQ3 = dr dr + - dT + 2- -2 dr2ar 1T 2 ar2

42 COMMODITY RISK MANAGEMENT AN.) FINANCE

and

dQ3 [ar dQ3 1 tf 02Q3 1 aQ31 (Jr d(3-15) -- dt+--dz

Q3 [Q3 ar 2 Q3 ar2 Q-3 'T I Q3 arFurthermore, it is assumcd that interest rates are nonstochastic so thator. = 0. The commodity bond's price elasticity is defined as

Pi dQlel = Q dP .

As a result of these new specifications, asset returns are now fullyexpressed by:

dQIC r a Ql 1 P I 2Q I 1 d +Q(3-16) Q = ale, + Q d + 2 dt + eSdzQi Q, r 2 Q' P Q, aT

(3-17) dQl -- Rdt + oJldz1Qi

dQ 2(3-18S) -u- = R 2dt + ..rdz2

(3-19) Q3 [a-Q3 Qr aQ-- dt= R 3dt= Rfdt

Budget Equation

To derive the individual's budget equation, the framework followed isone in which all the wealth is held in the assets, income is generated bycapital gains, and the individual must reduce asset holdings to consume.A discrete model with time periods of length h is first developed beforethe continuous model is derived by taking h to 0.

Let W(t) and Qi(t) be wealth and asset prices at the beginning of periodt. Ni(t) represents the number of shares of asset i held at date t. Thus,

3

(3-20) W(t)= 2 N5(t)Qi(t)i = I

To consume between dates t and t + h, the individual must reduceasset holdings at date t. All of that consurrmption is in the form of thecommodity, according to this model, and C,; is the rate of consumptionper unit time.

Consumption is thus given by:

3(3-21) 2'[Ni(t) -N,(t + h)]Q,(t) = PI(t).C(t).h

THE iDEMAND FOP. COmMODITY BONDS 43

Thus,3 3

(3-22) W(t + h) - W(t)= N,(t + h)Q,(t + b) - X N,(t)Q,(t)*;1 i= I

= N,{t + h)[Q2(t + h) - Q,(t)] - PI(t'.C(t).h,=,

and

(3-23) W(t + h) - W(t) 3 r Qi(t + b) -(323) N#h = E N,(t + h ]

-P(t).C(.t)

As h? goes to 0, the continu.'us version of this equation is as follows:

3

(3-24) dW(t) = N,(t)dQ,tt) - P1 (t).C(t).dt

Now introduced is co,, the proportion of the portfolio held in asset i.

(3-25) N{t) W(t)W(t)

Equation 3-24 becomes:

(3-26) dW= ,W -i- P.C.dt

2

Using equation 3-18 and o3 =1- cwi, the budget equationbecomes:

2 2

(3-27) dW = wi,W(Ri - Rf)dt + (WRf - P1C)dt + v w IWo,dz1t= l i= I

Maximization Problem

Each individual is f.ced with the problem of choosing a portfolio and

consumption parern that will maximize the expected value of a time-

additive von Ne .mann-Morgenstern utility function and bequest func-

tion.The problem is formulated as:

(3-28) Max Eo U1jjC(t), t]dt + B[W(T), T]

subject to equation 3-27 and W(O) = WO.The utility function U is assumed to be strictly concave in C, and . 4e

Original page # 44 is missing.

THE DFIAND FOR COMMrIODITY BONDS 45

T1she terms of the covariance mairices defined by aoi = p,,or,o, and thecondition o3 = 0, however, imply that a3i = 0 for ail i.

For a similar reason, V,j = piiS*Uj implies Vb3 = 0. The first-orderconditions thus become:

(3-381 Uc = PlJw

(3-39) 0 = (RI - Rf)Jw + WJ,wX( u13' 1) + PiJ

2

(3-40) 0 = (R2 - R/)Jw + WJ-Ww 0 O214i + P1!1wV!2.= I

(3-41) A R'WJw

(3-42) I = ,c

Demand Functions

The analysis just described the portfolio choice problem faced by anindividual and enables the opcinal asset portfilio to be derived.

Equation 3-38 states that, at the optimum, the mirginal utility ofconsu mption must equat; the' marginal utility of *vealth. In matrix form,equations 3-39 and 3-40 can be rewritten:

34) l tIl2 W,W i =1XV RI - R _ PIJIw I V1lCl 2 022 tc 2W Jww { - - Rf JWW I V121

The %arious terms of the variance-covy.riance matrix are defined by:

(3-44) a,j = po-a,ap denotes the correlation coefficient between the commodity and theequity asset, so that

(3-45) 12 = Ppor

(3-46) C1ll = tI

(3-47) (r22 = 02

Furthermore, it is assumed that p2 # 1, so that the variance-covariancematrit - .s nonsingular. The demand functions -an now be derived for thevanious assets by matri;c inveis;on in equation 3-43.

(3-48) IO 1W I- -JW 22 - pCaIC2 RI -Rf|tw)2W I Jw l2(1 _-p2) -Po122 oj I R 2 - Rf

2

PJIXw -2 PCr1a2 | ll

Jwwcq2 2(1 - p2) -parC, 2 - OJWWO-Y.72 -PO-ltT2 SI ol~~~Cr


and

(3-49) wOW = W --_ wW- Cw2 WAfter simplifications, these equations are written:

-Jw [(RI - Rf) (R2 - Rf)l PlJiw s1(3-50) CIW = _~ p' _P _lO2 Jw

-Jw !-(R, - Rd) (RI - Rf)(3-SI) ,,W V -- 2 I=l J2

(3-52) W., W - COIXW - 2W

To express the last term of equation 3-SO as a function of the othervariables, Fischer (1975) points out that the consumption decision by theindividual is guided by commodity price changes rela.ive to wealth, sothat consumption is a functicn of real wealth.

(3-53) C = C(W/P,, t)By differentiating this equation to W and to PI, one obtains:

(354) dC= C d(W/P1) C 1

(355) ac d(WIP,) _ w(3-55) dP=Cl-d = Cl p2

and thus the followir relationship holds:

(3-56) aC -PI aCd_W _W dP,

Furthermore, when equation 3-38 is differ: fiated relative to W and toPI, it yields:

(3-57) Uccac =Jw + PIJIW

(3-58)Uc PIPJ-U J ac_ -PIUcc dW=Pljww =Ucc W dP -W (Jw + PiJlw)ac w ap, w (wP1w

As a result,

(3-59) = w WJwvw Jww

The individual's absolute risk tolerance T is defined as T- -UI/U<c.Note that T > 0 because more is better (Uc > 0), and the utility functionis assurred to be concave in C or the first units of consumption are worthmore to the individual than the subsequent units.

rHE DEMAND FOR COMMODITY BONDS 47

Thus, MT=-JwIJw;.V is defined as the individual's "mo.iified" risktolerance.

(3-60) JW W U a T a TJww 8cc ac ac c

CC8W a W

High values of this variable are obtained for high values of T and/or lowvalues of the marginal propensity to consume. Cw can be expected to bea decreasing function of W. There could conceivably exist individuals forwhom Clv = 0. These individuals have so much wvealth that any increasein that wealth would not induce them to consume more. At the otherextrcme, very poor individuals would consume all of their additionalgains, and, for them, Cw = 1, for at least W lower than a certainsubsistence level.

With these simplifications, the demand equations for each individual kcan be written:

wkWk k (RI Rd~ (R 2 - Rfl WK k(3-61) MTI ( , (R2 - K -,) (l MT)

(1 kp )R2 (1 - R ''I -

(3-62) w4Wk = MTk[ (R2 R) ( p Rl-R,)[(I _ P2) (I - P')0'102J

(3-63) w~kWk = Wk _- kWk - wOkWk(3-63) W3W = t. ,1* W 2 T,

A look at the demand equations reveals that the demand for the equityasset is only comprised of a speculative component and is equal to thedemand for a risky asset by a single period mean-variance maximizinginvestor. The demand for the: commodity bond, liowever, is also com-prised of a similar speculative component and a hedging component. Aand B denote the bracket terms in equation 3-61 and 3-62, and theseequations become:

(3-64) w)Wk = MTk. A + (Wk - MTk)el

(J-65) w10 Wk = MTk.B

We define MTM " ' MTk as the market's modified risk tolerance.k

By aggre.gating equations 3-64 and 3-65, one obtains:

(3-66) @AS. M = MTM. A + (M - MT"')e

(3-67) w2M. M = MTM. B

Substituting the values of A and B obtained from these equations backiito equat:ons 3-64 and 3-65, one is able to derive anothier expression forthe demand functions:

48 COMMODITY RISK .1MANAGEIMENT AND FINANCE

kWk CI MT' wvk r MTkIWk1;3-68) w 1W = wA. M + W[1_ M7 IW ]MTM el P MT"'IM

(3-69) coWk 2 MTk-

The Determinants of the Demand for Commodity Bonds

Now consider the case in which the equity asset is the market portfoliobefore the introduction of commodity bond:.. Modern portfolio theoryindicates that investors would hold the marktr portfolio, levered up ordown according to their aversion to risk. 1-wo approaches can be takenhere. One can analyze the change in the individual's portfolio mix afterthe introduction of a positive amount of commodity bonds or one cananalyze and determine who would want to issue or hold such bonds, ifthey did not exist.

The latter approach will be taken here in justifying the introduction ofsuch bonds. In this case, W= 0, and equation 3-68 becomes:

(3-70) ,.Wk = W [1 _ MTk/W kI el[ MTAI/M

Thus, if MTk/Wk < MTm/M, then A Wk > 0. This is the result that isintuitively expected: When individual k has a lower relative modified risktolerance than the market or a higher relative modified risk aversion, theindividual would have a positive demand for commodity bonds.

A comparison of equations 3-70 and 3-64, however, reveals that, evenin this case, the demand for commodity bonds is not limited to thehedging component. Samuelson (1985) points out that sellers of suchbonds will be those least averse to price risk as they are bribed to take onsome of the irreducib.. variability by an appropriate market-clearingpremium. For such individuals, their attitude toward commodity bondswill be guided by their speculative demand. Samuelson also notes that ifthe supply of commodity bonds were to come only froin individualswzi!ling to take a little more risk for a premium, the market forcommodity bonds would not be viable. This market must also be drivenby a commercial function with the involvement of major players, bigcorporations, or governments, which are seeking to hedge the variationsin their production costs or revenues.

Now tal:e a closer look at the determinants of the demand forcommodity bonds. Fronm equation 3-61, it can be seen that the determi-nants depend on the required rates of return for three assets: thecorrelation between the commodity and the market, their respectivevolatilities, and the individual's modified risk tolerance.

THE DEMAND FOR COMMODITY BONDS 49

From this point on, Dk will denote individual k's demand for asset i:

(3-71) Di = cowWk

In taking the partial derivative of equation 3-61 with respect to R 1, oneobtains:

(3-72) - > °

This is a general property of most demand functions as they aredecreasing with respect to price. Equation 3-72 indicates that if R1increases or the price of the commodity bond goes down, the demand forit will go up.

Before taking the partial of equation 3-61 with respect to R2, note thatwhenever p > 0, the market serves as a hedge against inflation in thesense that the value of this asset goes up at the same time that investorsneed it the most: when commodity prices go up.

(3-73) =I_~pT(R 2 (1 - p2 )alr. 2

aD'Therefore, if P > 0, is implied. In other words, whenever R2 de-

creases or Q 2 goes up, the demand for commodity bonds will also go up.Thus, when p > 0, commodity bonds and the market act as substitutes.

(3-74) aR 1- ooaRf (1- p2)a - (Pal - 2)

The commodity bond's market beta is introduced and defined as:

(3-7S) 1 cov (R, E2) pal1var (i2) 02

and notice that when /31 > 1, it irnplies poa - o2 > 0.Equation 3-74 indicates that when default-free bond prices go down so

that Rf goes up, there will be a greater demand for commodity bondswhen their market beta is greater than 1. Remembering that o = elsl,the commodity bonds' market beta is el times the commodity's marketbeta.

aD'i MTk [ (R 2 - Rf) (RI -R)R(3-76) = p - -2 -

dsrl (1p2)0. a 02 al

By using a continuous-time framework, Breeden (1979) derived anintertemporal pricing relationship that must hold at each instant in time:

J) U t-OMMODITY KISK MANAGEMENT AND tINANCE

(3-77) R 1 - Rf= (R 2 - R)132,

where p3j, is the consumption-beta for asset i, defined by:

(3-78) ~~~~coy (ij, din Q(3-78) 13k= var (d In C)

With the use of these relationships, equation 3-76 becomes:

dD_ MTk. (R 2 - Rf) [L,1 Ž1(3-79) a- 1 (1 - p2 ) _[o _I a32cJ

This still assumes p > 0. A similar analysis can be made for p < 0. Ingeneral, 1 2, > 0 as individuals increase their rate of consumption whenthe market is going up. The sign of 3,l is ambiguous, however. Ifcommodity prices and consumption are correlated negatively, which iswhat would happen if higher commodity prices induced individuals toreduce their rate of consumption, equation 3-79 indicates a greaterdemand for commodity bonds when commodity prices become morevolatile. Such would be the case as long as

(3-80) I1c < PJP2cC71/202

Furthermore,

(D_ pMT'(R2 - Rd)(3-81) O2 (1 -Aao- (1 -p2)0-10-2

When p is positive, it has been shown that the market and commoditybonds act zs substitutes. As the market becomes more volatile, it is a lessaccurate hedge against price changes. This increases the demand forcommodity bonds.

-D- MT (rR I..~ -1d(2-R(3-82) M1T _ [ - (1 + p2) (R- Rf)

ap cr1(1 - 2 ) 2 [P O7

In using Breeden's intertemporal pricing relationship, equation 3-82becomes:

3 aD MT'(R2 - R) [2p Pc6 _ (1 -

(3-83) P c(1-p) ['1t2 2Jdp orl(l _r 2.2 L 1 . 2, Oa2

With the above-stated assumptions of p > 0 and Plc < P f 32c o-1/2o2,one notes that aDi/Op>O. An intuitive explanation lies in the fact thatwhen the commodity's correlation with the market decieO.ses, the marketbecomes a less desirable hedging tool. Furthermore, it can easily beshown that when p decreases, the variance of the total portfolio decreases

TIIE DEMAND FOR CO.MMb1ODITY BONDS Si

due to the inclusioni of commodity bonds. As a result, the latter becomemore attractive.

The previous analysis derived in the case of a single-good economy isalso valid when relative commodity prices are fixed and individualsconsume the same consumption bundle. In that case, the commoditybond described would be a cpi-bond. These assumptions are veryrestrictive, however, because commodity prices are known to fluctuatesomewhat independently, and individuals have differing tastes. The nextsection thus extends the analysis to the case of a multigood economy withstochastic consumption opportunities.

The Multigood Case

The model presented in this section is a multigood extension of theprevious analysis. There have been verv few attempts to extend Merton'sintertemporal asset pricing model and incorporate the case of manyconsumption goods. Long (1974) took such an approach, but only in thecase of a discrete-time economy. A satisfactory extension was made byBreeden (1979, 1984) in the derivation of a consumption asset pricingmodel and in the examination of the allocational roles of futures marketsin a multigood and multiperiod economy and by Cox, Ingersoll, and Ross(1985).

The Model

All the assumptions made in the single-good case are repeated in thissection for a description of the economy. One can now examine the casein which there are m consumption goods, among which I are commoditygoods with I s mi. The price dynamics for these goods are assumcd to begenerated by Ito processes.

(3-84) dpi -=adt + s,dx j1,...,m

where a, and s, are constant.There are n assets with returns that are also assumed to be generated

by Ito processes. The first I assets are commodity bonds with I s m ' n.

(3-8S) dQQ'= R,dt + oa,dz, i = 1, . . . , nQi

The default-free bond's return is given by

(3-86) dQ, l = Rn + Idt = Rfdt+ i

52 CONIMODITY RISK MANAGEMENT AND FINANCE

Along the same lines as the single-good case, each commodity bond isa function of its own commodity price, the interest rate, and the timeuntil maturity.

(3-87) Q,=Q(P, r, T) I = 1, . . .,I

As an application of Ito's lemma, it is easy to see that dx, = dz, forj=1, . . , I and that each commodity bond is perfectly correlated with itsown commodity price.

CI denotes the rate of consumption of good j by individual k by C*,and

i= I

is defined as the individual's rate of nominal expenditure. An analysissimilar to that of the previous section shows that individual k's budgetconstraint is given by

n n

(3-88) dWk >,R - Rf)Wkdt + (WkRf - ek)dt + > aWYo,dzii=1 i= 1

or in matrix form

(3-89) dWk = wk(R - Rf)Wkdt + (WkRf - ek)dt + WIkWoadza

where ck is the portfolio weights vector for individual k, Ra the assetsreturn vector, o-J, the P. x n diagonal matrix of assets standard deviation,and dza the Gauss-Weiner processes vector.

At each instant, individual k is assumed to maximize a time additivevon Neumann-Morgenstern utility function given by,

(3-90) E[f T ku (Ck, Y)dy + pk[Wk (T), T7J]

where Ck denotes the rate of consumption vector for individual k: Ck(Ct),. Let Uk(ek, P', t) = Max uk(Ck, t) describe individual k's indirectutility function for consumption expenditures and P' the transpose of theconsumption-good price vector. The dynamic programming methodol-ogy described in the previous section, yields the following first-orderconditicns:

(3-9 1) UI(ek, P', t) = Jkw(Wk, S', t)

(3-92) ekwk = a(3-9) kw -jkVJ(Ra Rd- V;1-- V w

Jw. iw kwW

where S' is the transpose of the state variables vector (that is, variablesthat describe the investment, income, and consumption opportunities


sets), V,a is the n x n variance-covariance matrix of asset returns, and Vasthe n x m covariance matrix of asset returns with the state variables.

The Demand Functions

From this point onward, the ce,nmodiry prices are chosen to be thestate variables. By differentiating equation 3-91 with respect to W, oneobtains:

(3-93) U' (ek, P', t) * e' = J' w(Wk, S', t)

Equations 3-91 and 3-93 combined, yield:

(394) -A-Tik W 7

Jww V¢e.eU

The last term in equation 3-92 denoted

Mt- -JAWAtw

was shown by Merton (1973a) to represent individual k's hedgingdemands against adverse changes in the consumption-investment oppor-tunity set. Equation 3-92 thus becomes:

(3-95) &JkWk = MTVaL(Ra - Rf) + VaL'VsMHs

by aggregating across all individuals, one obtains:

(3-96) wMWM = MTMVa'(Ra - Rf) + VL2VasH;"

where

(3-97) H1?= HSi.k

Equations 3-9S and 3-96 together present a new expression for the assetdemand functions:

(3-98) wtskWk = MT'. M HM + itk- MTk(3-98) MTM 'lV.V(HS MTM

With an argument similar to that of the previous section, the netdemand for any commodity bond acreos -he market should be ze.o,thereby yielding at( = 0 for i = 1, . .. , /. Furthermore, Breeden (1979)has shown that VL'VVa 5 has, for column!, the portfolio of assets mosthighly correlated with the state variables; here, those state variables arethe .ommodity prices. Hence, column j gives the portfolio that has themaximum coirelation with state vari:"I' Pi. As an application of Ito'slemma, it is evident that this price is periectly correlated with commoditybond Qj. Thus XjV,, = (s), where F is an I x I diagonal matrix that can


be normalized to unity by proper scaling of state variables. With thesenew results, equation 3-98 can be rewritten:

(3-99) &w*Wk = Hk -- MTH i 1, ... .,

and

(3-100) ZWIk Wm MT'i(M = I + 1, . . . , nMTkM M

These equations are similar to equations 3-69 and 3-70 derived in thesingle-consumption-good case. To obtain the exact link between the twosets of equations, Hi must be expressed in terms of known parameters.To that effect, the additional assumption that individuals have time-additive isoelastic utility functions is introduced. Under this condition,Dieffenbach (1976) has shown that individual k's vector of percentagecompensating variations in wealth for changes in the state variables is nota function of k's wealth lcvel. or:

J4

(3-101) Wk = -A

where Ak does not depernd on Wk, but does, in general, depend on the P,s.By differentiating with respect to Wk, one obtains:

{. ,02) jk Wkj& j]k[jl + Wkjk W] = °('02) Jrwkf~ I t W~w]

Replacing Jk with its expression from equation 3-101, the conditionbecomes:

(3-103) Ji = -At[Jl + WkJlWW]

or

(3-104) Hk =-= A(Wk -MTk)JAw

By aggregating across individuals, one obtains:

(3-105) HIM= A M M-Am MTM

where AM = M 'kA*WkandAA, = 1 M A kMTk. The-efore, theM k MTM k

demand for commodity bonds is given by

(3-106) &);jk = A4Wk - AMTk _ MT . M AM + MTkAMI I I ~~MTM £i,T

By rearranging these terms, a more useful expression for the demand forcommodity bonds can be derived.


(-_107) wzWk = AsW [I- MT/WM + A4Tk (M -l)(A -1 A)L MT'I/M (T

+ MTk(Am -AM)]

The demand for commodity bonds is thus comprised of three terms,the first of which is similar to the expression obtained in equation 3-70.The reason for this is that if all individuals consumed the same bundle inthe same quantities, A!' would be equal across individuals, and Ak = A,implies both AM = Ai and A'- = A, so the last two terms of equation 3-107cancel out. Futhermore, when all individuals consun;e the same bundle,it can be considered as one consumption good, and the same results arefound as in the previous section. This first term examm:ed has a positivecontribution to the demand for commodity bonds whenever individual khas a lower relative risk tolerance than the market or a higher relativerisk aversion. T he second term reveais that when the market is relativelymore risk averse than unity, individua! k would have an additionaldemand for commodity bond i when the individual is more affected thanthe average individual by changes in that commodity's price. This wouldtend to be the case for commodities for which individual k has a veryinelastic demand. The sign ^Žf the last term is the same for all individualsand does not play a major r--!c in the analysis of the demand forcommodity bonds.

4A Review of Methodsfor PricingCommodity-LinkedSecuritiesTk:eophilos Prio volos

The model for pricing commodity-linked securities uses the optionpricing framework as pioneered by Black and Scholes (1973), extendedby Merton (1973b) and Cox and Ross (1976), a-d furti er refined bySchwartz (1982). The model for pricing commo:., -convertible bondsuses the option pricing framework of commodity-linked bondsl or themodel of pricing convertible bonds as presented among others byBrennan and Schwartz (1980). As commodity-convertible bonds areequivalent to appropria'.-ly specified commodity bonds without war-rants, the discussion here focuses only on the latter type of bonds. Thekey assumption of the rrodel is that the underlying commodities, thecommodity-linked bonds, and the equities of the firm issuing the bondsare continuo.isly tzaded in frictionless markets.

The Schw; rtz model considers commodity price risk, default risk, andinterest rate risk and takes the form of a second-order partial differentialequation in four variables that governs the value of the commodity-linked boiid at any point in time. Let P be the value of the referencecomn..odity bundle, V the value of the firm issuing the bonds, and r theinstantaneously riskiess rate of interest and assume that they followcontinuous paths described by the following stochastic differential equa-tions:

(4_1) dP ap dt + op dzp

(4-2) dV= Da-(V' t) dt + o-,dz,

(4-3) dr ar(r) dt + ar,(r) dZr

S6

METHODS FOR PRICING COMMODITY-LINKED SECURITIES S7

where D is the rate of total payouts of all the security holders of the firm(dividends, interest, etc.); crp, a,. are constants; and dzp, dzv, and dz, areGauss-Weiner processes with

(4-4) dzp * dzv = p dt, dzp * dzr = Pp * dt, dz * dz,r = p,, dt

The total value of the commodity-linked bond can be expressed as

(4-5) B = B(P, V, r, T)

where T is the time until mO -urity. If a portfolio is formed by investing

X, in the underlying commodity, PX2 in the firm, VX3 in a risk'.ss discount bond, GX4 in the commodity-linked bond,2 B

then the instantaneous total retu;n on this portfoiio dY will be

(4-6) dYXdP dV+ Ddt dG dB + Cdt(4-) dY=X,p+X 2 V4 B

G is assumed to depend only sn r and T, that is, G(r, T); c is the COUSronpayment of the commodity bond. By applying Ito's lemrma, one obtains:

(4-7) dG dt + aG dZr

If we apply Itc's lemma in 4-S and introduce the result in 4-6 with 4-1,4-2, and 4-7 and choose XI, X2, X3, X4 so that the portfolio returnbecomes riskless, the following partial differential equation governing thevalue of the commodity-linked bond at every point in time is derived:

(428) 1 2P2P B + 1 a2V2BLv, + I r2Brr + OrpvPVBpv + 0p,PBp,

+ o-,VB", + rPBp + (rV - D)BV, + (a, - A cr,)B, - BT - rB + C = 0

The value of the bonds will be independent of the exptcted return on thecommodity and on the firm; it will only depend on the current values ofthe reference commodity bundles and the firm (P, V). The promisedpayment on the bonds at maturity is equivalent to the face value of thebond (F), plus an option to Luy the reference commodity bundle at aspecifizd exercise price (E). The promised payment can be made only ifthe value of the firm at maturity is greater than that amount.

It is assumed that in case of default, the bondholder takes over the firm.The boundary condition at maturity can be expressed as

(4-9) r ^' V, r, 0) = min [V, F + max (0, P - E)]

Because the solu:.jn of 4-8 and 4-9 is very difficult, the following threesimplified versions of the model can be obtained.

METHODS FOR PRICING COMNMOI)DITY-LINKED SECURITIES 59

appropri; tely replaced in 4- 3, then the derived new 4-S function r,may besolved suliject to the boundary .onditioll

(4-15) S.P, r, 0) = F + -max (0, P - E)

If the commodity-linked bond is o; the Jiscourit type, its vIJue can beexp-,ssed as

(4-1 6) B(P, Q, r) = F Q + W(P, Q, T)

where the value of optio; X'(P, Q, T) can be obtained from Merton(1973b).

Several numerical examples by Schwart-7 (1982) using -ases I to 3sihow interesting properties of comrnodit' bonds. In case 1, the higher thestandard deviation of the comInG. ty price (op), the higher the value ofthe oprion (W) and the lower the icquired coupon ratc (C/F). When thevalue of the reierence bundle (Plf) becomes zero, the bond becomerriskless, and U/F equates to r. When PIF = 1, that is, the value of therefe-ence bt"ndle equals the face value of the bond, the equilibrium_ol:pon rate is negativ:.

'n case 2, h boi!ndai)e :,r iition indicates that default at maturitydepends not only or. che value of the firm, but aico on the value of thecommodity bundle. X higher stanaXird deviation on the return on thecommodity (a.) has two opposing effects on bond values: First, it is wellknown that the value of an option increases with the stand ard deviationof its underlving security; second, the probability of default a'so increaseswith ar, and this tends to iower bond values. The first effect dominaresthe second for low comnmodity bundle prices, for high firm values, and forshorter maturity dates. Default risk thus has a significant impact on bondvalues, and most of this r.- cories not Lrom the ficm being unable to naythe face value of the cc r.modity bonds, as in the case for regularcorporate bonds, but from the firm being unable to pay the value of theopticn for high commodity prices even under substantial increases in thevalue of the firrr :A higher correlation be;ween the return on thecomr. 'dity and the return on the firm increases bond values. As the riskof dfault decreases, the value of the bond approaches the solution for theno-default, constant-i -ercsc-zate case.

The analysis involving case 3 sho;-.s that when pricing commoditybonds, it is quite safe to use the constant i.-:rest rate model as long as therelevant interest rate used is the one to the matunri of the bond.

It is noteworthy that seime of the assumptions used to derive theSchwartz mode; :re questionable. The model assumes, for example, thatthe iuiderlying comr-idity is pe:fecdly tradable. The model neglects taxescorrpletely. Also, like most of the option pricing literature, the modelassumes c^nstan. variances. More complex capital structures and bond

60 COMIMODITY RISK MANAGEMENT AND FINANCE

characteristics-such as call features, sinking funds, and convertibilityinto the reference commodity bundle before maturity if convertiblecommodity bonds ate considerd-could be introduced at the cost ofhavkng to use complicated numerical procedures to solve th. appropriatepartia! differential operations.4

Tlhe next section describes pricing commodity bonds with the use ofbinomial option pricing. This method has a number of advantages overthe Schwartz ai,proach.

Notes

1. A commodity-convertible bond can be shown to be e.uivalent to an appropriat-lyspecified commodity bond with "American"-type warrants.

2. The commodi-y-linked bond is a conventional bond with commodity (call) warrantsattached to coupon or principal payments.

3. The Black-Scholes fcrmula is

W(P, T) = PN(x) - E:-TN(x - aoVT where

log (PlEr7)! IT

X o-VT 2- 4. Fall (1986) extends the Schwartz model by including the convenience yield of holding

and scoring the commodity. He argues that his version is more reliable. Brer.nan (1986) has,nowever, shown that conv-.nience yields ar very difficult to estimat. This could be thereason for the differences in the pricing ot commodity bonds berweern Schwartz and Fall.

Pricing CommodityBonds Using BinomialOption PricingRaghuram Rajatn

Interest in commodity-linked securities has increased considerably re-cently. For the developing countries, these securities offer the possibilityof hedging against commodity price risk, thereby enhancing their cred-itworthiness. Such instruments also link debt repayments to abilitv to pay(Priovolos, 1987a).

Conventional bonds pay a stated interest rate (coupon) and a fixedprincipal redeemable at maturity. A commodity bond makes repaymentssubject to the fluctuations in the price of the underlying commodity.Thus, both the coupon and the principal repayment may be a function ofthe commodity price. A variety of commodity-bond-type instruments canbe devised, resulting in different kinds of risk sharing and return. Two ofthe more popular variants are the Commodity Convertible Bond (ccB)

and the Commodity Linked Bond (CLB). With the CCB, the holder canchoose on redemption day either the nominal face value or a prespecifiedamount of the commodity bundle. The CLB consists of a conventionalbond with an attached option or warrant to buy a certain amount of thecommoditv at a predetermined exercise price. In some markets (not in theUnited States), the option can b! detached and sold separately. In returnfor the convertibility/option feature, the issuer receives a lower interest rate.

Issues of commodity bonds can assist liability management by tailoringpayments to ability to pay. In a ccB/cLB, the coupon provides a "floor"yield. When the price of the commodity increases, however, the yield tomaturity for the bond increases and vice versa when the commodity pricefalls (limited by the floor level).

Formulas for pricing commodity-linked bonds have been developed bySchwartz (1982) and Carr (1987). Both use the standard continuou s-timeoption pricing method to arrive at a differential equation. The extended

61

62 CO.MMODITY RISK NIANAGEMENT AND FINANCE

form of the differential equation (incorporating convenience yields) isshown in appendix 5-1. Schwartz states that the solution to the generalproblem is difficult even by numerical methods and proceeds to makesimplifying assumptions about the nature of the bond to obtain asolution. Even thc simplified form of the bond has a mathematicallycomplex, closed-form solution. The need for a simpler, more intuitive,and flexible formulation has been felt.

This chapter presents a method for pricing commodity-linked bonds inthe presence of default risk and commodity price risk. The advantage ofthis method is that extensions are very simple. Fulther, the method ismore intuitive than the continuous-time method, although it is equivalentin the limit. Most important, it is flexible and comprehensive. Finally, itcan be used to model any bond instrument based on two or morestochastic processes.

Evnine (1983) first extended the Cox, Ross, and Rubinstein optionpricing model to incorporate an option on two or more stocks. Themodel developed here is basically a simplification and reformulation ofEvnine's model and an application of the model to commodity bonds.

In "The Model," a simple version of the bond is priced to make theprocess transparent. In "Parameter Determination," the parameters ofthe model are derived from real world values. In "Extensions," the modelis extended to incorporate the various features that these bonds caninclude. In "Comparative Analysis of Binomial Model and SchwartzModel Results," some values obtained by the model are compared withthose obtained by Schwartz. Further, some of the additional features areadded and priced, and observations about some interesting phenomenaare made. While appendix S-1 describes the differential equation that hasto be solved and Schwartz's solution to the simplified form, appendix 5-2shows the logic behind the values of the chosen parameters.

The Model

Assumptions

(1) The commodity-linked bond consists of a zero coupon paying facevalue F at maturity, plus an option to buy a predefined quantity of thecommodity with value at maturity date equal to P* at an exercise priceof E., The option is European,2 with the maturity date the same as theredemption date.

(S-1) B* = F + max [O, F'-]

where B* is what the bond ought to pay at maturity.(2) At maturity, however, the firm's value V* (consisting of the total

PRICING COMMODITY BONDS USING BINOMIAL OPTION l)RICING 63

value of its assets to its creditors) may be greater than or less than B'. If

the firm is unable to pay, the bondholders get the residual value of thefirm.3

Thei-iore, the value of the bond is equal to:

(5-2) min [V*, F + max (0, P° - E)]

(3) There are no payouts from the firm to the shareholders orbondholders before the maturity date of the bond.

(4) The commodity bundle price and the firm value follow multiplica-tive binomial processes4 over discrete periods.

(5) The interest rate is constant and positive.(6) The firm's debt consists only of Lommodity bonds; that is, there is

no senior debt.(7) No taxes or transaction costs exist, and short sales are allowed.

i:urther, assets are perfectly divisible.(8) There is no convenience yield from the commodity. Assumptions

(1), (3), (5), (6), and (8) can be relaxed.Let the price of the commodry bundle and the value of the firm follow

the continuous-time diffusion processes describci below:

(5-3) dP pdt + o dzp

(5-41 dsX = V ,, dt + or. dz,1

(5-5) dzp dz, = or. dt

Where crp is the volatility of the commodity price, oa, is the volatility ofthe firm value, and op, is the covariance between the two. Also ,tlp and ,,

are the drifts of the corresponding price movements.In this model, the continuous-time diffusion processes will be approx-

imated with binomial jumps.If the commodity price and firm value moved independently, it would

be easy to mode] the two as a two-step sequence of independent jumps.To introduce the covariance term, however, a third step is needed inwhich the price of the commodity bundle and the firm value movetogether (i.e., because there are two underlying stochastic processes and

the processes are not independent, a three-step process will be assumed),Assume three assets: the commodity bundle with price P, the firm with

value V, and a risk-free bond of face value B. Let ; be 1 + the riskiess rateof return per period. (Each jump is considered to occur in a period.)

SEP 1. Price of commodity bundle P moves up by uW with probabilityq1 or down by d, with probability (1 - ql). The value of the firm Vaccrues at the riskless rate ;. This is because there is no uncertainty about

64 COMMIODITY RISK MANACEMENT AND FINANCE

Vigure 5-1 The Binomial TPee

At the end of each three-step unit, the values of the twvo statevariables Pand Vare as follows.

A if C

q3 ul u3 Pr, u2 u3 V

q2 Ui Pr, u2 Vr (I ) ul d3 Pr d2 d3 VF

____-- Pd 2 V q3 uI u3 Pr d2 u3 VF

q1 ~u1 ) Vr (.q)u 1 d3Pi d2 d3 Vr1~v ~ IZZZj d1 uPr

d1P~u2Vi (1-q3 ) ud d~(I dle Vrq3 U3.Pi 2 2 d3 Vr

(I d 1 23Vr (1 U2 d3 l

(1-q2) dPr,d2 Vr ddu3lP 2 3V

( -q3) d)d 3 P d2 d3 VF

Trhe bond values at the end of the third step are as shown below.

A B C D

Culu2u3

C 41 u 2 l-q3 Culu2d3

Cu1 d2 u3C q2 Culd2 1

ql Cu1 1 q3 Culd2 d 3

3zZ2EIZI Cdlu 2 u 3

q2 CdIu2 1-q 3 Cd1 u2 d 3

I q2 Cdd2 q3Cd 2 3

1q 3 Cd 1 d2 d 3

Step 1 Step 2 Step 3

PRICING CONMMODITY BONDS USING BINO.MIAL OPTION PRICING 65

the value of the firm in this step; hence, it is a riskiess asset. Therefore, itshould accrue at the riskless rate.

STEP 2. Value of firm moves up by U, with probability q2 or down byd2 with probability (1 - q2). The commodity bundle accrucs at theriskless rate ;.

STEP 3. P and V together n,OvC Llp by 143 with probability q3 or downby d3 with probability (1 - q3).

Now folding the tree backward, one can find the expected value of thebond at node A. (See figure 5-1.) This would require knowledge of theprobabilities of the upward and downward movement at eaC: step.

Surprisingly, by creating equivalent portfolios and applying the con-dition that if two assets have the same value in all possible states of theNvorld, in the next period they should have the same value as in thecurrent period, one finds the value at node A of the bond without everhaving to know the probability of upward or dowvnward movement.

At node C, a portfolio is created that contains A * u1il of the commoditybundle and A u12 ; of the firm and B risk-free bonds paying ; per period.(B indicates both the risk-free bond and the quantity thereof; A is somenumter.)

Choose A and B such that this portfolio, if formed at C, has the samevalue as the commodity bond at D. That is, choose A and B such thatA[u1Pi + u2V;Ju3 + iB = C,, 4. , where C,lu ,, is the valuc of the bondafter three steps, when the price of the commodity bundle has moved upoy uju 3 r and the value of the firm by U21u3 ;. Also,

(5-6) 51 uIPr + u2V ]d3 + iB = C", ,d,

We get

(S-7) A = _ _ _ _ _ _ _ _ _

(U3 - d3)(u 1, P; + U2 V)UI3Cu,u,d, d3u- u

(5-8) B (3= -d 3 i -(U3 -d3);

If there are to be no riskless arbit' age opportunities when the bond inthe next period has the same valt .. in all states as the portfolio, the valueof the bond in the present period must equal the value of the portfolio inthe present period.

(5-9) Cu= C 5u,42 (u41P; + 42VA)A + B

3 -d3) +( d3) C /+


Setting P, = (r - d3/u3 - d3) and 1 - P3 = (U3 - ;3 - d3 ), one canwrite

(5-10) C.u,1 = [P3C. 1,., 1 + (1 - P3)CuXu 1 d/

Similarly all the bond values at nodes below C in figure 5-1 can befound in terms of values at the terminal nodes D. At node B, a portfoliocontaining Al of firm value V and B1 risk-free bonds can be created.

Using the same procedure as above, one finds

(S-11) Cu' = [(X2 - d,)C,ul2 + (U2 - dCu1djl/r

= [P2C.J, + (1-P2)C.,dll

where

(5-12) P2 - d2 )

Finally, using a portfolio of A2 of commodity and B2 of bonds, one canshow

(5-13) C = [PIC., + (1 - PI)Cd1 ]/;

where

(5-14) P1 = r dir - di

Joined, one gets the recurrence relation for the bond value at period iin terms of the bond values at period i + 3.

(5-15) C = [PIP2 P3 C.IU2UJ + PIP2 (1 - P3 )Cuud,

+ PI( - P2 )P 3 C.,d,., + P1 (1 - P2 )(1 - P3 )C,,d2d

+ (1 - Pl)P2P 3 Cd,u.xJ + (1 - P)P 2(1 - P3)Cd,.,d,

+ (1 - P1)(1 - P2)P 3Cd,d 1 ,, + (1 - P1)(1 -PJ

* (1 -P3)Cd,d,]/;3

where

(5-16) CU,1 2U, = min [u2u3 ;V,F + max (u 1 u3PP - E,O)]

The formula for the bond price after 3n periods is derived below.

PRICING COMMODITY BONDS USING BINOMIAL OPTION PRICING 67

(S-17) C = -3n{ 2 2 2 (.1 n! Pli( - Po)'n i*.=0 j'=o k=o 0i(n W)

___ ,________ _____________ _ __ ) )*!(n-)~ ~~ _ n! 3 !(n - k)

mm Pi( 2) (! k)! PI'(1 )fmin [uutd V, F + max (0 uiu3d7id3ykiP - E)]}

Parameter Determination

Having derived the recurrence relation for the value of .ne bond afterthe three-step process-and thus the bond price after n in such three-stepsequences-one must discover how the parameters can be derived fromthe obs ;ved variables.

After 3n periods, assuming that there are i steps for process P aloneand j steps for process V alone and k steps jointly:

(5-18) P =u * din -. 3d3in

(5-19) log = i log- + n log d + k log + n log d 3 t-n logr

(5-20) E[lo ()] P E[i] g ()+ E[k] log (23) + d1d3 i

(-20) E[log (p)] [ log (d) + n3log (dl) + log d jd3 ijn

(5-22) var [log (p)] = var i[log d 2 + var k[logo d]

+ 2 cov [i, k] log [ru] log [3]

= nql(1 - ql)olog d + nq3 (0 - q3)

* [log ]2

(As covariance, (i, k) = 0 because the two steps are independent.)Similarly, the mean and the variance for the return on V at the end of


the third step can be found by substituting u2 and d2 for ul and d1 andq2 for q, in the above equations.

Finally, to find the covariance term,

(S-23) Covariance {log ( p ), log (2V )} = E{log (ip*) log (l V)-Elg(p ) jElo ( ]

After substituting and then taking expectations (and sparing sometedious algebra), one gets:

(S-24) = [k2 - (nq3)2]4log [Ž]]2

= ivariance [k] log [U3]]2

= nq3(1 - q4) log (d)12

For the covariance of the binomial process to equal the covariance ofthe continuous-time process, in the limit is designated as n o o

(5-5 cy[lg (p), (lV)] = nq 3(1 - q3 )[log(3)] crP ,t

Further, for the means to be equal:

(5-26) [q3 log U) + log d3n =i 3 t

where O-p is Lhe covariance and A3 is the mean contributed by the thirdprocess, t is the time left for maturity of the bond, and 3n is the totainumber of steps. (Because there is ns real equivalent of p.3, it is set asequal to A,, - r/3.) Setting the values of the other parameters at (reasonsfor specific values for parameters can be clearly seen in appendix 5-2)

(5-27) q3 = +

O'Pv 2

and

(S-28) U3 = e + / -v d3 = e - / nvn nthe covariance is provided by the third step

(5-29) o-pn = [-pv - 3(t)

PPICING COMMODITY BONDS USING BINOMIAL OPTION PRICING 69

that in the limit tends to the required value

(5-30) opn opvt as n - X

For the other two binomial processes, include

[ udi)]2 23)

= 2 t

Or ini the limit as n -. o

(5-32) n[q!(l - qlj(log (Ud))2] = [p -pt

Similarly,

(5-33) n[q2(1 - q2)[1og (d2) ] [cv opL]t

For the means of the distributions to be equal it requires that

(5-34) lim [q log (u) + q3 1og + log did3 j n =ipt

and similarly for A.,t.The discount rate per period r should satisfy 3n = e" where r is the

annualized risk-free rate and t the time to maturity in years. By setting

(5-35) -j d = e

(S-3 6) q(j+ (p - (±3 + r/3) 1 (t)(5-36) 41 = 2[1 + ( -2 _ O,) /(~n)

(5-37) u2 = e -(2 - 0rw)v d2 = e -

and

(5-38) q2 =[1+ - + /3(t)

the required values hold in the limit.Note that ;L3 is arbitrary, and q, and q2 play no part in the valuation

of the bond except to reassure that the processes are identical. So far, allthat is assured is that the means and the variances of the binomial processcan be made to tend to the required values. In appendix 5-2, it isdemonstrated that the p,-r ceF .ends in the limit to the same probabilitydistribution as the bivariate normal.

70 C(MMODI . IY RiSK .\IANAGE.MEN AND FINANCE

iy) Payouts by firn. If I is the fraction of firm ValUC paid out aSdividcnd every ycar, it can bc incorporatecd by dinnishing the firm valuICevery nlt iteranionls by 8V. Pan kruptcV Would not occur as the '1 aluc of thefirim could never go to zero as a rcsuilt of a fractional pay out.

(2) Coupon paymnients on ondl. If . the yearly fixed coupon paymenton thc bond, it could be dpictued by diminishing the vallIC of the firmevery nit periods by C (and chcckinig for default). T-he nt coupon (afterdefault) could be added to the bond valu2 at that node, and the standardprocess could be follou%ed to evaluate the bond Value.

(3) Stochastic interest rate. Iihis could bc incorporated by having afourthi step (plus more for covariancc terms).

(4) Senior clebt. Senior debt could be Incorporated by changinig theterminal conditions: That is, if S be the amount of senior debt, the bondvalue at maturity

(5-39) = IMII [ V - S, F - max [0, P - E]]

(5) ConzIeniLncc yield. Convenienice yield on the cornmoditv optioncan be treated in the samie way as dividends on a stock option 'Fall,1 9S6). If C, is the convenicnce yiced per period, it diminlishies the value ofthe conmmodity price by (I - C1) ^verv period.

(6) Terminal conditions. Different terminal conditions could be incor-porated by mcrely changing the functioni that describes the bond value onteriminal date. Nothinig clse will have to change. Hencc, an lnc\eJCommodity Option Note, which has a sliding stream of pavrnc::L.> onmaturity date with the underlying amount itself being a funcr:o:i of theprice, ca basily h priced. Pricing a cap is a trivial extern,

Comparative Analysis of Binomioal Model a.nd Sctlhwartz,Model Results

The miodel describcd earlier was prograrmmed using Turbo Basic on anInternational Business Machines (IB,M) A-F Personal compLter (rc). First,the case assumed by Schwartz was ulsed as a check. The extensionspossible with this nodc' were then incorpora-ted and priced. Checks weremade by taking extreme cases in which the expected resLult is known.

The basic case assumed by Schwartz is that of a company having issueda zero coupon with face value F = 100, maturing in five years. Atmaturity date, the bondholder has the right to buy a certain commoditybundle with initial value P and price volatility cr,. and is correlated withthe commodity price movement v ith correlation coefficient p.


Table 5-1 Commodity-Linked Bond Values for Different CommodityBundle Prices, Firm Values, and Correlations Usinig the BinomlialPricing A_'w!el/E = F = 100, r = 0.12, T = 5.0, a =,0.4, a-, = 0.3, number of iterations N = 10)

Commoditv Pricing p Defaultpnrce model 0.0 0.3S 0.70 free

Firm value, V - 200P = 100 Binom;al 86.22 93.59 103.19

Schwartz 85.45 93.34 102.54Difference (%) 0.90 0.27 0.63

P = 80 Binomial 77.48 83.46 89.46Schwartz 77.34 83.20 89.26Diffet.nce (%) 0.18 0.31 0.22

P = SO Binomial 65.38 67.83 69.76Schwartz 65.01 67.67 69.62Difference (%) 0.57 0.24 0.20

Fi,!n -t!_, V = 400P = 100 Binomial 99.89 105.00 109.16

Schwartz 99.00 104.66 108.70Difference (%) 0.90 0.32 0.42

P = 80 Binomial 86.88 90.53 92.30Schwartz 86.57 90.02 92.35Difference (%) 0.36 0.57 -O.OS

P = 50 Binomia! 69.30 70.22 70.59Schwartz 68.89 70.14 70.58Difference (%) 0.60 0.11 0.01

Firm value, V = 1,000P = 100 Binomial 107.95 109.08 109.58 109.41

Schwartz 107.15 108.92 109.40 109.41Difference (%) 0.75 0.15 0.16 0.00

P = 80 Binomial 91.59 92.50 92.42 92.42Schwartz 91.45 92.41 92.60 92.60Difference (%) 0.15 0.10 -0.20 -0.19

P = 50 Binomial 70.64 70.58 70.61 70.61Schwartz 70.39 70.61 70.64 70.64Hifference (%! 0.36 -0.04 -0.04 -0.04

Table 5-1 shows the rrice of the bond tor various values of thecovariance between the commodity price and the valuc of the firm, aswell as various values of the firm and the commodity bundle. The averagedifference in the prices obtained from the two models is about 0.3 percentwith the maximum being 0.9 percent and the minimum being 0. This isafter 10 iterations of the binomial model. In the limit, the binomial modeltends toward the Schwartz model. The advantage is not just simplicity:The binomial method enables the incorporation of senior debt, payouts

PRICING COMMODITY BONDS USING BINOMIIAL OPTION PRIC.NG 73

'able 5-3 Fffect of a Cornmncdity Pr.ce C.-o on the Commodity BondValue

Firm: valf- C.ise A Case B(V) (with c ap = 105) (no cap) Case C

200 66.97 93.5' 26.62400 68.32 105.00 36.68

1,000 68.40 109.08 40.38

Note: Nack-Scholes va'ec of cap = 39.74.

however, the valuP is not dimirished by the fLll valuLe of the option. Thisis because the issuer would r.at pay for the high com-nodity price statuswhen barikriptc- is declared. Thercfore. an increase in the risk of defaulton the bona would decrease the value of ? -ap. In the limit, a cap wouldilave no value if the bond alway;s defaulted a.ad paid nozhing, although itwoulA equal the value of tLe optiov 'f there was no default risk.

Now, in moving beyvonie th-, Schwi rtz model, additions are maae thatare permitted bv th: biromial model. T1he startin6 point will be the basicbond, and features wili be addcd so that each fearjre's effect on the priceo' ii: botl can be seen. Ilhe followirng assumptions -,re made:

Face value = F = 100 Time *o maturity = 4 yearsFxerci: price = 100 Inizial commodity pricc = 100Coupon =- 103 a 0.4o,, = 0.3 p 0.7Risk-fr- rte - 0.12

No a-fault risk is assum. d initia"Iy.Table 5-4 shows that i coupon adds value to the bond, ane convc-

nience yitld diminishes t!E valuc of the bond. A can, in the ALsence ofdefault risk, reduces the value or the bond by the vaiie of an option with

TaDic 5-4 li-pact nf Additional F?atures on Bond Vaiuc

idond value Incremen:al value

Original bond 110.62

Additic. ! fat: resCoup- i at 10 pe.rcent 14C.'2 29.90Conv-'.jcr,ce yiela at ' pemcent 124.94 -15.58Cap at lS0 iO3.34 -21.60Default ris-z ( - 200) 100.70 -2.64Scnio: debt (=50) 93.46 -7.24Payout ratio (1.0) of firm 80.5 -13.01

74 COMMODITY RISK MANAGENMENT AND FINANCE

exercise price equal to the cap. (The value of the cap is estimated at 21.28in the Black forn!'ia as compared with 2i.60 here.) Increased payout andsenior debt have no effect if default risk is not considcr. d. In the presenceof default risk, however, senior debt diminishes the value of the bond, asdo pavouts to equi:y or other bonds. Tlh cap, however, will be worthless.

Some Comparative Statics

The various parameters will be now varied for the bond above, and theva'ues of the zero-bond (principal and option repayment) and couponswill be established.

The effects of varying are as follows:(1) Firm value. Coupons are paid whenever they are due. Therefore,

the defauilt on the coupon is only likely when the firm value is comparableto the size of coupon ',ayments. This car be seen in figure 5-2 wheredefault on the coupon starts only when .! initial firm value is below SO.Above SO, however, the coupon is no: defaulted on and maintains aconstant value. Similarly, default on the principal and o; .ivn repaymentbecomes negligible at a firm value higher thar 600.

Figure 5-2 Bond Valuesfor Different Firm Values

Zero bond and coupon value1:0

100 _

90 _ TotalW

80 / Bond

60 _ /

50

4 / ,'Coupon30 - -…

20 _ ,'

10

0

0 0.2 0.4 0.6 0.8 1Initial firm value (thousands)


Figure 5-3 Bond ValuesforDiff>rent Coupon Rates

Zero bond and coupon valueltO)

90 Total (zero + coup:Jn)

80

70

606 . .Zerobond

50

40

30 - Coupon

10 _ , , ,, , , , , . , I

0.04 0.06 0.08 0.1 0.12 0.14 0.16

Coupon rate

(2) Coupon rates. Higher coupon rates increase the present value of thecoupon, but simultaneously decrease th: value of the zero bond. (Seefigure 5-3.) This is because a higher coupon diminishes the value of thefirm more and leaves a lower amount to repay the principal/option. Thenet effect is that a higher coupon does not increase the value of the bondas much in the presence of defau!t risk as it would a default-free bond.

(3) Convenience yields. The effect of convenience yields is important asthese are fairly volatile for some commodities, such as oil. From figure5-4, it can be seen that a sharp charge in convenience yields, for example.from 20 to -20 percent, changes the total bond value by about 10percent.

(4) Senior debt. Here, senior debt refers ro debt maturing at the sametime as the bond, but being senior to the bond. The larger the senior debt,the greater the chance of default on the principal/option, as seen in figure5-5. Dividend or other payouts earlier than the bond maturity have asimilar effect. (See igure 5-6).

(5) Caps. Caps are effective as long as they are at price levels that havehig.h probabilities of being attained; at higher levels, they are of negligiblevalue. (See figure 5-7.)

76 COMMODITY RISK MANAGEMF.NT AND FINANCE

Figure 5-4 Bond ValuesforDifferent Convenience Yields

Zero bond and coupon value85

84

83 -

82 T Total (zero + coupon)

81-

80-

79-

78

77 l l_l-0.2 -0.1 0 0.1 0.2

Convenience yield

Figure 5-51 BG .-, Valuesfor Different Senior Debt Amounts


100 _

90

eIo Total (zero + coupon)

70-

60 ''- Bond\

50

40

30 ______________''_,_-Coupon

20

10

0 20 40 60 80 100 120 140Amount of senior debt

PRICING COMMODITY BONDS USING BINCMIAL OPTION PRICING 77

Figure 5-6 Bond Values for Different Payout Ratios


900 ~ = oupon)90

80

60 Bond -.

50

40

30 - - - - - - - - - - - - - - - - - -

20_ Coupon

10

-0.1 -0.06 -0.02 0.02 0.06 0.1 0.14 0.18

Payout ratio

Figure 5-7 Bond Values for Dfferent Caps

Zero bond and coupon value100 f -

90 _

80

70 -Bond

60 - ---- - - - -- .--- - - - - -- - - - -

50 _

40

Coupon20

10

0 , , * . ,

0.1 0.3 0.5 0.7 0.9

Cap value (thousands)

78 COMMODITY RrsiS MANAGEMENT AND FINANCE

Figure 5-8 Bond 1l}uesforDifferent Correlations

Zero bond and coupon value81 0

808

806 - Total (zero ± coupon)

O.-I.

80.2

80.0

79.8

79) 6

79.4

79.2

79.0 i0.3 0.4 0.5 0.6 t7

Correlation

(6) Correlation. Cor:elation between the firm value and the commod-

ity bundle price decreases the default risk and, hence, the value of the

bond. (See figure 5-8.)

Conclusion

The binomial model is an effective way ot pricing a commodity bond

in the presence of commodity price risk and default risk. Extensions to

incorporate other sources of risk can be made easiiy. The limiting factor

in all this is computationa! powcr, but it becomes significant only in the

presence of features like fixed coupon payments or fixed payouts.

Vlie application of this intuitive method to commodity-linked bonds is

just one of the many applications possible. For example, secondary

mnarket developing country debt could be priced by suitably redefining V

(the value of the firm) and P (the price of the commodity).

PRICINNG COMMIODITY BONDS USING BINOP,IAI. Ol'TION PRICING 79

Appendix 5-1. The ContinLuouis-Time Model

Using the traditional continLous-time option pricing method, it can beshown that if the price of the commnodity bundle P and the value of theirm V follow stochastic processes:

(5-40) dp 1Pdt + ao dZp

(5-41) d dt + V,Zv

and

(5-42) dZpdZ. = rp,Ldtthe differential equation to be solved is

(5-43) cjI'-Bpp + !o.2V2B,., + op.l)VBP,

+ PBp(r - 8} + B,{rV- D] - Bz - rB + C- 0where B is the value of the bood, Z is the time to expiration, 8 is theconvenience yield, D is the total payout by firm per year, and C is theyearly coupon attached to the bond.The boundary conditions are:

(5-44) B(P, V, 0) = min [V, F + max (0, P -- E)]

where F is the face value of the bond.If payout D is assumed to be a fixed fraction d of the firm value V and

the coupon C is a fixed fraction c of the face value of the bond, defaultmust be checked every time the coupon is paid; that is, V Ž C.

The solution to this equation (if at all possible) would be verycurnbersome, even by most numerical methods.

Appendix 5-2. Proof That the Distribution of the BinomialModel Tends to the Bivariate Normal Disvribution

To show that the binomial model tends in the limit to the bivariatenorri;al distribution, the characteristic function of -he former is shown totend toward the lat.er.

Consider the three-step process in figure 5-1. There are eight terminalnodes at D that are numbered from top to hottom 1 to 8. Al ;he top-moctnode, the commodity price is PuIu3r. Therefore, the log of the return onthe commodity over the three steps at node 1 is

(5-45) log RI = log ul + log U3 + log1


Similarly, the log return on the firm is

(5-46) log R2 = log u2 + log U3 + log

To determine the characteristic function of joint returns (log RI, logR 2), denoted as 0(0,, 0-)

(5-47) P(01, 0-) = E [exp (i0i log RI, iO2 log R2)]

The expectation over the three-step process is the sum of eight terms,each arising from a particular outcome of (log R1, log R,)

(5 48) 'k(t01 ,u2)= D

where

(5-49) DI = qlq2 q3 exp [iOi(log ul + log U3 + log ;)

+ i02(0og U2 + log U3 + log ;)]

_qIq2[11 + A 3 b2 0 X3 Pe; [iUi(r3 /h + aa/h + log rt/3n)

+ i02(0-3Vh + ObIh + log rt/3n)]

where h = tln.03 = V/cppv,ria = /(ap - OV),cb = oAw,2)- ap)

(5 50) DI = qIq2 11 t A3ih2 exn {/h[i 1 (cr3 + a,)

+ i0 2 (o 3 + Ab)] + h[iO1 r/3 + i82 r/3]}

Expanding the exponential as a power series, multiplying out, andrearranging, one gets:

(5-51)

= qq21 + + iO.(C-3 + a) + iO2(0 3 + ab)DI=2 1 L Vb ba

+ h[-iO,(a3 + 'a) + ai8 2 (a 3 + ab)

+ iO1r/3 + iB2r/3- 2 (0- 3 + aa)2

-+ + )2 ( + C)2+-0 102(CT3 + Ua.)(0r3 + 0_b) - -f(0'3 + 0-b) + o(b)}


where o(h) indicates power of h higher than 1, which will be negligible inthe limit.

Summing over all the eight nodes (i.e., finding the correspondingexpression to DI above one for D2 :D8 and then adding them alltogether), a tedious but necessary process, and then simplifying, one gets:

(5-52) 0(01,92) = I + V/h[io 1co,(2q, - 1) + i02Ob( 2 .'12 - 1)] +

+ h[iSlll3 + iO2/u3 + ilr/3 + i0 2r/3 + 021 (cy2 + _42)

0-2 (oj + crI) + 01 02(0r2)

+ (2q, - 1)(2q2 - 1)0affb] + o(h)

Setting

2 [ ( p (+ r13)) q2 = 1- rl3

and substituting back for 7a, o,s, o'3 one gets:

(5-53) k(01, 02) = 1 + h{[iGlp. + i02A 2]

_ 1 [020uf2 + 0_ia2 + 20102apJ} + o(h)

After n such sequences, it is known that

(5-54) fn(09,02) = 0-[4(v,02)]"

occurs from the independenc- of successive processes. Therefore, allow-ing n -+ x such that h = tin -. 0, one gets

(5-55)

liM 0(01,02) = 1 + t{i0i,iL + i07p. -2 (02a2 + 02jo + 20iG2 upV)}

But the characteiist;c function for the joint lognormal diffusion processwith parameters up, A., op, a0 is

(5-56)

11(001,02) = 1 + (i6 11 It + i62j 2 t)0 (-122t + 2oa-vt + 20102apvt)

that is the limit of the binomial.

Notes

1. All starred (') terms are values on the date of maturity.2. The European option differs from an Amcrican one in that it can be exercised only

.upon eYpiration, rather than at any time.3. This is not the case 'or a sovereign isje. In a developing country, when a corporate

bondholder defaults, government authorities often assume foreign obligations.4. See COA, Ross, and Rubenstein (1979).

PART II

CommodityCon tingencyin the InternatioonalLending ofDeveloping Countries

6

Optimal External DebtManagement withCommodity-LinkedBondsRober yJ. Myers and Stanley R. Thompson

MIuch of the spectacular growth in cxtcrnal borrowing by developingcountries t...t occurred during .he 1970s was in the forr.i of generalobligation loans denominated in U.S. dollars at floating interest rates. Itis now well understood that this strategy involved substantial risks inrespect to exchange rates, interest rates, and commodity prices. Theserisks became all too clear follom ing the developing country debt crisisthat began in 1982. The deterioration in the developing countries' termsof trade quickly eroded their ability to service their burgeoning debts. Inturn, this led to restricted access to new external credit and a period offorced adjustment in consumption and investment. A disturbing numberof heavily indebted countries have not yet emerged from the resultingdifficulties.

This chapter examines the way in which commodity-linked bondscouid be used by developing countries to hedge the risks associated withtheir external debt position. Commodity-linked bonds are bonds thathave principal, and possibly coupon payments, linked to future realiza-tions of a specified set of commodity prices. By issuing bonds linked tothe prices of commodities that they export, developing countries wouldbe hedging against the risk of a deterioration in export earnings becauseof a fall in these prices. If developing country debt had been issued in theform of commodity-linked bonds, debt service obligations would havefallen along with commodity prices, thus easing the burden of adjustingto the external shock. Of course, other commodity-linked financialinstruments, such as futures and options contracts, could be Lsed forsimilar hedging purposes. Futures and options, however, do not exist formany commodities and typically have only short maturities. Thus, for

8S

86 COMMNIODITY RISK MANAGEMENT AND FINANCE

many developing countries, commodity-linked bonds show considerablepotential as a financial risk management instrument.

The characteristics of alternative international financial instruments,including commodity-linked bonds, have been discussed extensivelyelsewhere. (See Lessard, 1977a; Lessard and Williamson, 1985; andO'Hara, 1984.) The specific purpose hicre is to provide an operationalrule for choosing an optimal external debt portfolio consisting ofcommodity-linked bonds and conventional debt. To begin, a simpledynamic model is used to derive optimal rules for issuing commodity-linked bonds and conventional debt in a small, open economy. Next,estimation methods that allow these rules to be operationalized arepresented. The approach is then illustrated with an application to CostaRica, where the optimal external debt portfolio wvould contain a signif-icant proportion of commodity-linked bonds.

A Model of Ootimal External Debt Allocation

Consider a small, open economy in which all external debt is issued bythe government. The government has a utility function, u(mr.), definedover real imports of goods and services per capita in period t. This utilityfunction is meant to capture the contribution that imports make todomestic consumption and growth. It satisfies the von Neumann-Morgenstern axioms, as well as the conditions u'(m,) > 0 and u"(mt,) <0. Commodity exports by the country are assumed to follow anexogenous stochastic process that is not influenced by t'ie government'sexternal debt decisions. Real exports per capita in period t are denoted xr

Without external finance, the value of imports must equal the value ofexpo-ts so thar the current account is in balance each period. It isassumed, however, that the government has access to two sources ofextern. ! finance. First, it can take out conventional loans at the constantreal interest rate r. Real rotal debt per capita held in the form ofconventional loans at the end of period t is denoted d,. Second, thegovernment can issue bonds linked to each of n commodities. Whenissued, th-ese bonds have real prices w, = (wlt, w2t, . . . , w,,) and the realprices of the u.iderlyi- g commodities are denoted P, = (pit, P2t, - . ,Pnt)

Future commoc'ity pi ices are stochastic when the government issues thebonds. The bonds mature in one period and require a financial paymen.at maturity that is equal to the price of the underlying commodity.l TcGsimplify the analysis, no coupon payments on the bonds are assumed.T.e per capita quantity of bonds issued by the government at time t isdenoted b. - (bit, b 2 ,... , bni)'.

MANAGEMIENT WITH CO.MMODITY-LINKED BONDS 87

With these assumptions, the constraint facing the government when itchooses an external debt portfolio is

(6-1) mt + rdt - I + p1b, -xt + (dt - dt I) + wvtb,.

The government is also restricted in that it cannot borrow indefinitely tofinance ever-increasing current account deficits. This constraint is im-posed by requiring

(6-2) lim dT = rim bT= --

The go%ernnient's problem is now to choose issues of conventiona' debtand commodity-linked bonds that maximize thc discounted time-additiveexpected utility function

(6-3) E,3 v BtIr

subject to the sequence ot constraints in equation 6-1 and the transver-saliry conditions in equa'!:;i! 6-2.

The solution to the governiment's problem must satisfy 6-1 and 6-2,plus thc Euler equations

(6-4) u'(m;) -j3(1 + r)E,u'(mr, l) = 0

and

(6-5) u'(m,)uw, - I3E[4u'(int + I)Pt + = 0.

Finding a closed form solution is generally impocsible without placingstrong restrictions on the form of the uti!ity function and on theprobability distribution of prices and exports. Here, however, in accor-dance with the literature on the permanent income theory of consump-tion, it is assumed that the optimal import path can be defined2 as

(6-6) mt = a [ (I + r) - 'E,(x, 4 )- , I -(1 + r)d,

Notice that this is just a version of the permanent income theory ofconsumption--imports are set equal to some proportion, a, of "perma-nent" exports (a discounted sum of expected fu:-ure export revenues,minus current external debt).

Equation 6-6 is not yet a decision rule because the terms E,(x,.i) mustbe eliminated by expressing them as a function of variables known by thegovernment at time t. Suppose that x, is the first element of a vector,

Yt = (x^, Plts P2,, ... , pnt, se)', that also contains the commodity pricesand any other state variables useful for predicting future exports. Thevector y, is assumed to follow the autoregre~ sive process

(6-7) A(L)y,= et

MANA.UE.ENTr wuvrii COMMOD!TY-LINKED BONDS 89

are important, however, and the optimal portfolio must be; eiglitedaccordingly.

Estimation

Estimation of thc optima. conmodirv-linked bond portfolio revolvesaround the vector autoregressive process A(L)y, w which was definedin the previous section. Remenibering that , contains all of the com-modity prices that are linked to bonds (as well as x, and other statevariables helpful in p:edictirg futrure export revenucs), thenl the condi-tional covariance matrices Qp,. and f2) in 6-13 are clearly just compo-nentr of fQ, the covariance matrix of T. Thus, estimation of the vectoraut-regressive process for y, will provide an estimate of Q that, in turn,can be usei directly to operationalize 6-13.

Estimation of the vector autoregressive process for Y, is also useful foranother reason. To compute opt;rnal bond issues from 6-13, one needs toknow the parameter vector y. From 6-8, recall that y representscoefficients on y, in the optimal prediction of a discounted sum of futurerealizations of export revenues, given current and past values of v,. Froma formula derived by Hansen and Sargent, this optimal predictor is

(6-14) 2 (1 + r) - 'E,(x, + 1) = A[I4/(1 - r)] - l'v + B(L)y, - 2

wvhere X is a row vector with a one in the first column and zeroselsewvhere, and B(l' satisfies

(6-15) B(L) = OA[1/(1 + r)]7 (1 + rYkAk]Li+ 1

Thus, y is simply the first row of A[ 1/(1 + r) -f'. Evidently, estimation ofthe autoregressive pararneters in A1(L) provides a direct estimate of y(conditional on knowledge of the real interest rate r). Actual estimationof the parameters in A(L.) and fl can be accomplished via vectorautoregression.4

The final piece of the estimation puzzle lies in obtaining an estimate ofthe real interest rate, r. Once r has been found, and A(L) and fl have beenestimated, then cornputing the optimal commodity-linked bond issues isstraightforward using 6-13. In many cases, prior information will beavailable on real interest rates. In the following application to CostaRica, optimal external debt portfolios for a number of different realinterest rates are presented, and the results indicate that they are notsensitive tor ;.s value.

YU (COMMODITY KISK IMANAGEMENT AND PINANCE

The Case of Costa Rica

Costa Rica is a small country that depet;ds on a handful of agriculturalcommodities for the bulk of its export earnings. In recent years, coffee,beef, and bananas have accounted for more than half of total exportrevenues. Figure 6-1 shows gross national product (GNP), consumption,and investment for Co, A Rica betveen 1966 and 1986, all in real percapita terms. The pronounced slump that began around 1981 andcontinued into 1983 is indicative of the problems that many developingcountries have experienced since the onset of the debt crisis. Figure 6-2shows Costa Rica's terms of trade index and their total foreign debt inU.S. dollars. The data suggest that the economic slump of 1981-83 waspreceded by a sharp negative terms of trade shock and a dramaticincrease in debt servicing requirements. By linking debt service require-ments to conmnodity price realizations, commodity-linked bonds mighthelp facilitate adjustment and avoid future slumps of this severity.

Figure 6-1 Real per Capita Gross National ProductConsumption and Investment for Costa Rica, 1966-86

1980 Colones per capita

20,000

18,000 GNP

16,000 -

14,000 -/-

12,000 _ / ~ Consumption

10,000

8,000

6,000 - Investmnent

4,000 -

2,000-

1966 1968 1970 1972 1974 1976 1978 1980 1982 1984 1986

Source: World Bank data.

MANAGENIENT WITH COMMODITY-LINKED BONDS 91

Figure 6-2 Terms of Rhade and Per Capita Total ExternalDebtfor Costa Rica, 1966-86

Tenns of trade (1980 = 100)

150 2,000

140 -

Terms of trade / 1,500

130 / Exteral debt

120 1 1,eOo

110 /

1~~~~~ ~-500

100

1IQ6i 1968 1970 1972 1974 1976 1978 1980 1982 1984 1986

Source: World Bank data.

To illustrate the estimation of optimal external debt portfolios, a CostaRican portfolio of conventional loans and bonds linked to three majorexport commodities-coffee, beef, and bananas-was examined. Realprices of these commodities are denoted Pa, Pb,, and Pat respectively. Thefirst task was to estimate the vector autoregressive process for realexports and the three real commodity prices. To simplify, the possibilityof including other variables in the model was not considered. Nominalprices and nominal export revenues, all in U.S. dollars, were each deflatedby an index of import prices for Costa Rica. The commodity prices wereobtained from World Bank (1985), and all other data are from WorldBank (1988). The data are annual, and the sample runs from 1966through 1985.

In view of Lhe small number of available observations, an equation-by-equation approach to model specification was used. Preliminaryinvestigations revealed no strong evidence of nonstationarity or hetero-

92 COMMODITY RiSK MANAGEMENT AND FINANCE

Table 6-1 Estimation Results

x, = 219.55 + 0.63 x, I - 0.11 xt - 2; K2=0.36(3.78) (4.14) (0.78)

pc = 2.82 + 0.42 pc - 0.10 p_ ; R2 =0.23(3.92) (2.63) (0.65)

pb = 0.61 + 0.84 pb_ - 0.05 pb 2; 20.57

(1.13) (3.87) (0.22)

pf = 0.05 + 0.48 p, -+ 0.65 pa -2 0.04 pb 1; R2 =0.58

(1.12) (3.11) (3.75) (4.14)

[ 2,238.4 39.2 9.9 0.9 1n- 39.2 0.99 0.15 0.02

9.9 0.15 0.44 - 0.019_ 0.9 0.02 - 0.081 0.001 J

Note: Values in parcnthcess are t-values.

scedastic errors, so the models were estimated in the levels of eachvariable, assuming a constant conditional covariance matrix. Initially, anoverfitted equation was specified with lags of all four variables included.

len F-tests were used to test zero restrictions on sets of coefficients.Estimation results for the final model specification are shown in table 6-1,where the system was estimated using seemingly unrelated regression.Table 6-1 also contains the resulting estimated conditional covariancematrix.

The optimal external dt'Nt portfolio was computed for 1985, the lastyear of the sample. The n:atrices QY,, and flpp come directly from table6-1, and the parameter vector y is computed from the estimates in thetable (as shown above). Each optimal commodity-linked bond issue was

Table 6-2 Optimal Portfolios in 1985 as a Proportion of TotalExternal Debt

Generalobligation

r loans Coffee Beef Bananas

0.00 .655 0.144 0.035 .0.1660.05 .652 0.145 0.036 0.1670.10 .649 0.147 0.036 0.168

MANAGENIENT WITH COMMODITY-LINKED BONDS 93

multiplied by an estimate of its price. This estimat. as obtained by usingthe vector autoregression to forecast commodity prices into 1986 (giveninformation available in 1985) and then discounted back using the rei!interest rate. The final revenue figure was then expressed as a proportionof the actual level of total external debt in Costa Rica in 1985.

The estimated optimal external debt portfolio is presented in table 6-2under three different real interest rate assumptions. Clearly, the portfo-lios are not very sensitive to the real interest rate used. The results suggestthat more than 30 percent of total debt should be issued in the form ofcommodity-linked bonds, with the bulk of these issues being splitbetween coffee and bananas. The optimal portfolio of external debt forCosta Rica in 1985, therefore, appears to contain a significant proportionof commodity-linked bonds.

Concluding Comments

This chapter provideK a simple dynamic model that can be used toestimate optimal portfolios of external debt. It focuses on the potentialrole of commodity-linked bonds in hedging against the possibility of adeterioration in a country's terms of trade. The approach wvas applied toCosta Rica, where it was found that a significant proportion of externaldebt should be issued in the form of commodity-linked bonds.

The framework could be extended in a variety of directionis. Inparticular, although optimal portfolios of external debt have beencomputed, the extent of reductions in the variance of real imports has notyet been determined. This information is critical in determining thehedging effectiveness of commodity-linked bonds. Future research mightalso examine expanded portfolios, perhaps looking at other commodity-linked instiuments, such as futures, options, and bonds linked to indicesof commodity prices.

There are a number of practical difficulties associated with commodity-linked bonds that deserve add:tional attenzion. In this paper, it has simplybeen assumed that markets for these instruments exist, and that suchmarkets have no risk premia. It seems likely that commodity-linkedbonds would be priced at a discount, however, especially if issued bydeveloping countries subject to sign, icant default risk. In fact, the size ofrisk premia may be an important reason why there is currently such littleuse made of commodity-linked bonds. Nevertheless, the analysis pre-sented above suggests a potential hedging role for commodity-linkedbonds, provided that diversified markets for these contracts can emergeand grow.

94 COMMODITY RiSK MANAGFIMENT AND FINANCE

Notes

1. For simplicity, attention is restricted to bonds with a one-period maturity. Anextension to longer-term maturities, however, would be relatively straightforward.

2. Assumptions sufficient to guarantee this equation is an exact solution are: (I) theexpected real return to holding bonds is equal to the real interest rate E,[W,. 1 - P, ,+,(1+ r) = 0 for i = 0, 1, . . . ; and cither (2) utility is qua .atic or (3) utility features constantabsolute risk aversion and m, is normally distributed with a variance that depends only oni or (4) utility features constant relative risk aversion and log mi, is normally distributed witha variance that depcnds only on i. See Evans (1988) and the refcrences therein for moredetails on the latter three conditions. A complete derivation of equation 6-6 under theseconditions is available from the authors on request.

3. This implies that there are no risk preniia in commodity-linked bond prices. Ifinvestors are risk adverse and cannot diversify all of the risks of investing in the bonds, thenthe bonds may be priced at a discount to conventional debt. (Schwartz, 1982)

4. No discussion of vector autoregression estimation techniques is included here. Thoseinterested should consult Engle and Bollerslev (1986), Engle and Granger (1977), Sims(1980), and others.

7Integrating Commmodityand Exchange RateRisk Manlagement:Implications for ExternalDebt ManagementStijn Claessens

Other things being equal, a strengthening of the dollar will worsen theterms of trade of net commodity exporters and hence reduce theirwelfare. For net commodity importers, the reverse pattern will hold.I

... for some countries, the fall in the dollar increased the burden ofdebt relative to their economies.2

Who is right, ex ante and ex post, about the effect of a cross-currencymovement on the welfare of developing countries? Even though bothquotations are, of course, deliberately placed out of context, they doillustrate some of the unresolved issues regarding the effect of cross-currency movements on the welfare of developing countries. The aim ofthis chapter is to at least clarify, and potentially resolve, some of theseoutstanding issues. Furthermore, the chapter attempts to present concep-tual and practical guidelines that will help with external debt manage-ment generally.

During the past decade, many developing countries have been affectedby the large volatility in cross-currency exchange rates and commodityprices as a result of the impact of these changes on the relative burden of

95


their external deF- service. Cross-culrrency exchange :.- lhanges haveaffected the struct re, as well as the level, of many de . i ; countries'external debt. This is, for instance, demonstrated by .; <ct that theshare of dollar-denominated debt has varied substantially in the 1980sdue to large swings in the dollar vis-a-vis other lending currencies anddue to the fact that a substantial part of developing countries' debt isdenominated in non-U.S. dollar currencies.3 The external debt of manydeveloping countries as measured in U.S. dollars has thus fluctuatedconsiderably during the 1980s as a result of movements in the dollar.4Commodity price movements in the 1980s have also had a dramaticimpact on many developing countries' exports earnings. This is demon-strated, for instance, by the changes in the World Bank index foragricultural raw material prices, which fell from an index value of 100 in1980 to 78 in 1985 and bounced back up to 120 in 1988.5

The interactions between cross-currency exchange rate fluctuationsand commodity price changes-and the combined effects of the two-have affected the structure and the level of many developing countries'external debt relative to their debt-servicing capacity. For an example inwhich these two effects interacted in an adverse way, one can look to thecase of Indonesia. The debt service-to-exports ratio for Indonesia rosefrom 8.2 percent in 1981 to 27.8 percent in 1987-an increase of whichmore than 65 percent can be explained by the depreciation of the U.S.dollar since 1985 and the fall in oil and other commodity prices since1986. As a further example, rough calculations indicate that if commod-ity prices and exchange rates had remained at their end-of-1982 values,and assuming no reduction or increase in financial flows, the debtservice-to-exports ratio for all developing countries would have beenapproximately 17 percent in 1987 in contrast to the actual level of 24percent.

Entities in developed countries are able to hedge against exchange ratechanges by purchasing currency futures or other short-term hedginginstruments on organized or over-the-counter markets. They can alsohedge against commodity price movements by buying commodity hedg-ing instruments. Most developing countries, however, do not havesufficient access to these markets because of institutional and creditconstraints, as well as for other reasons.

An alternative hedging instrument that can be used to reduce theimpact of the combined effect of cross-currency exchange and commod-ity price uncertainty, and that is more likely available to a larger groupof developing countries, is the currency composition of external debt.Developing countries (or agents within these countries) can minimizetheir vulnerability to the combined effects of currency and commodityprice risks by optimizing the currency composition of their external debt

IMPLICATIONS FOR EXTERNAL DEBT MANAGEMIEN-r 97

with respect to established relationships between (lenders') exchangerates and the cash flows with which they service their debt (i.e., exportearnings). Even though an optimal currency composition of external debtmight be difficult to attain for some developing countries-because theymight be constrained in choosing and altering the currency compositionof their new and existing borrowings (such as in the case of bilateralloans from foreign governments) and because they might not be able touse long-term financial market hedging teclhniques, such as currencyswa ps, -o alter the currency composition of their existing debt-knowingwhat the optimal currency composition of external debt would be andwhat (marginal) changes are required to achieve such a composition Nvillstill lead to substantial benefits in terms of reducing the vulnerability oftheir economies to exchange rate and commodity price uncertainty.

Ex post, one could determine an optimal portfolio in terms of currencycomposition; however, this does not necessarily help in developing policyrules on the way in which developing countries can minimize theirvullerability to exchange risks and commodity price risks ex ante. The exanti problem has not been given much attention in the analyticalliterarure, and only a few empirical applications of optimal currencycomrlposition of external debt exist. The purpose of this chapter is, therefore,first to review all the existing, mostly policy-oriented literature and sugges-tions as to the way in which external debt should be allocated acrossdifferent currencies. Second, this chapter will discuss the weaknesses of theseguicdelines. Then, a theoretical model of optimal currency composition ispresented, wvhich is an abbreviated version of the model given in Claessens(1988). Some empirical results for Indonesia and Turkey, derived on thebasis of this theoretical model, are then summarized. These were reported inearlier work (Kroner and Claessens, 1988).

Issues in Joint Commodity and Exchange Risk Management

Diversification

Before discussing some of the issues regarding the hedging potential ofthe currency composition of (long-term) external liabilities, one shouldnote that there are other options open to a country to reduce its exposureto external factors. First, the country can engage in real diversificaEionthrough the sourcing, producing, and expor,ing of a mix of products thatis close to opcimal, given the relationships between exchange rates,goods' prices, and other external factors. Of course, the composition ofexports and, to a lesser extent, of imports cannot be changed easily in theshort run, but one can expect significant contributions from closer-to-optimal real activity diversification in thd long run. Second, a range of


instruments is available to private firms in developed financial markets tomanage short-term exposures, and some of these instruments could beused to manage a country's external exposures. Transfer of certain risksto market participants more able to absorb them, or able to transfer theserisks to others, can substantially benefit a developing country by reducingrisks at reasonable costs.6

Real activity diversification and use of short-term hedging instruments,howvever, might leave little room for hedging because the country is likelyto be constrained in the short term (and the long term) on the real sideand may not have access to (short-term) financial hedging instruments.The country might, thzrefore, want to use the currency composition ofnew external capital flows as a hedging instrument against unanticipatedexchange rate and commodity price movements. In addition, the countrymight want to influence the currency comr sition of its existing long-term external liabilities in light of the country's exposure to externalfactors. The currency composition of the external liabilities of thecountry can, however, only be a useful tool in managing the exposure tocommodity price movements to the extent that the movements inexchange rates and goods prices are correlated.

Hedging versus Speculative Activity

The integration of exchange risk and commodity risk managementthrough external liability management requires decisions based oncomplex tradeoffs. In general, the external liability management decisioncan, much like the standard finance portfolio theory, be split up into ahedging and a speculative decision.7 The hedging decision in this contextshould be based upon the appropriate measure of exposure of theeconomy to the effects of exchange rate uncertainty in relation to thebehavior of relevant commodity prices and other external variables andshould assume no views on future (relative) movements of exchangerates, commodity prices, and other external variables-beyond thoseviews that the world financial markets imply through arbitrage condi-tions. The speculative decision involves answering the question of howthe country should position the currency composition of its externalliabilities in the light of its anticipations-which can be different from themarket at large-regarding future developments in exchange rates,commodity prices, and other relevant external variables. The final aUlocationof the liability portfolio between the hedging and the speculative set shouldbe made taking into consideration the country's risk-costs tradeoff, that is,its degree of risk aversion. This chapter, however, focuses mainly on thehedging aspect of external liability management.

The hedging component of the currency composition decision cannot

IMPLICATIONS FOR EXTERNAL DEBT MIANAGEMENT 99

be based or exchange rate movements alone, but will have to bedetermined in relation to the uncertainty of the real burden of serving thedebt obligations-that is, relative to the ability of the country to generateforeign exchange. Therefore, one must take into account interactionsbetween exchange rates and the factors that determine the ability of thecountry to generate net foreign exchange cash flows, such as commodityexports earnings, to service the external debt.

Relations between Exchange Rates and Commodity Prices

Changes in cross-currency exchange rates have a direct effect on goods'prices, as has been observed in the traditional inverse relationshipbetween the dollar exchange rate and the price of (primary) commodi-ties-at least up to the most recent deDreciation of the dollar.8 Inaddition, as cross-currency exchange rate changes affect the relativecompetitiveness of countries with which a developing country competesin a particular export market, developing countries' market shares andprofit margins can be affected by movements in cross-currency exchangerates. Similar effects of exchange rate changes exist on the import sidebecause cross-currency exchange rate changes can be expected to influ-ence import prices. It has generally been postulated that the impact ofexchange rates on intermediate goods (generally a large component ofdeveloping countries' imports) is not as strong as it is in the case ofprimary cornmodities.9 As a result, exchanges rate changes can have asubstantial impact on many developing countries because a large share oftheir export earnings is derived from primary and other commodities,which are exchange-rate sensitive, and because their imports (prices) canalso be exchange-rate sensitive.

Hedging-Policy Guidelines

Now, some concepts and principles will be discussed that have beenprc-sosed for the hedging decision in external liability currency man~:rc-ment, as well as the strengths and weaknesses of the proposed rules.10The most often proposed strategies in respect of the composition ofexternal liabilities relate to the following: the pattern of the country'strade and other noninterest current account flows; the currency denom-ination of its noninterest current account export re znues or flows; andthe composition of the basket of currencies with respect to the manage-ment of the domestic currency.

The pattern of trade rule implies that a country should b-Hrrow incurrencies according to the distribution of its net trade (and otlher flows)among lender countries in the expectation that when the currency of anexport market appreciates, increasing its debt service, then the borrow-


er's terms of trade are likely to improve. This will (partially) offset thehigher costs of servicing debt in that currency (and the opposite would betrue for the imports o. ;'e country). The rule assumes that an apprecia-tion of the currency of an importing country is accompanied by anincrear icn the exporting country's ability to pay as its exports to thatmarket and terms of trade improve. It is not clear, a priori, that theappreciation of a currer'cy of an export market has to mean animprovement in the country's terms of trade and an increase in debtservicing capacity. In fact, the value of U.S. imports from debtorcountries dropped greatly during the time the dollar rose. Anotherexample that demonstrates how misleading this rule is would be thesituation in which two different count.ies were exporting the same goodto the same country. The cross-exchange rate between the two exportingcountries could be equally, or more, important for the relative compet-itivenesi and market shares and mrrket volumes of the two countries inthe importing country (and, thus, fo: the debt servicing capacity of thecountries) than the value of currency oS the importing country vis-a-viseach of the individual countries."I

The rule to base the currency composition ot external debt on thecurrencies of invoice or denomination of exports (or of net noninterestcurrent account flows) could equally be criticized. There is ampleevidence that the relationship between the nominal denomination and thereal value of exports can, at times, be perverse. As noted before, the realprice of commodities has historically been inversely related to the realvalue of the dollar, even though most commodities are nominallydenominated and traded in terms of dollars. The inverse relationshipimplies that -he dollar would not necessarily be the optimal currency inwhich to boirow because its value could have a perverse relationshipwith the coun ry's ability to generate foreign exchange through exportsof (primary) commodities-even though exports could be priced orinvoiced in dollars. Because the depreciation of the dollar implies anappreciation of other currencies, a positive relationship might existbetwe,n the value of othe. currencies and commodity prices: When thedollar appreciates, commodity prices decline. Other currencies depreciatetoo, however, which might instead make nondollar currencies goodexternal liabilities for primary commodity exporters. In sum, a currencycomposition based on a country's trade denomination pattern does notnecessarily reduce real risks, and might even increase them.

The composition of the foreign currency basket with respect to whichthe country manages, its domestic currency could itself serve as anindicator for the optimal composition of the country's external liabilities,provided the composition of ti.e basket is determined optimally. Anoptimal determination of the weights in the currency basket should tak:

IMPLICATIONS FOR EXTERNAI. DEBT NMANAGEMENT 101

into account the interaction between exchange rates and the prices of thegoods the country exports and imports. It should also consider thecountry's relative competitiveness in export markets, the demand andsupply elasticities for traded goods, the sensitivity of capital flows, andother factors that are equally important in determining the optimalcurrency composition of external debt '2 It turns out that if the currencybasket is indeed determined optimally in light of these tradeoffs, then itsweights will be very similar to the optimal weights of currencies in thecomposition of external liabilities. In other words, even though the ruleis !argely correct, it only defers the problem to the determination of theoptimal currency basket weights.

Real Risks

In general, the nominal dimension cannot be the only anid necessarilycorrect determinant for the currency choice of external debt. If one usesthe nominal denomination of trade flows, the U.S. dollar would be thepredon- nant currency for most developing countries.13 When it isrealized that prices in world commodity and manufaztures markersdepend on the interaction between demanders and suppiiers in differentcurrency zones, however, it is clear that the rcminal currency denomi-nation of a good or the nominal direction of tr. does not have to reflectthe "real" currency denomination of the price of a commodity or manufac-ture. In world markets for commodities and manufactures, suppliers be-come more (or less) competitive depending not only on the changes in theirown currency, but also on the changes in other suppliers' home currencies.Similarly, demanders will consider goods more (or less) attractive dependingon the movements of the exchange rates of multiple suppliers. As a result,the changes in the price of a particular good or commodity as a result ofexchange rates changes will, inter alia, depend on the type of marketstructure (perfectly competitive, oligopolistic, etc.). Demand and supplyelasticities and, thus, the market structure play a crucial role in distr.butingthe effects of exchange rates in terms of (nominal and real) price andquantity changes over the different market participants. 14

The policy-oriented rules on the hedging decision discussed so far canthus be criticized as not being explicitly related to a specific goal orobjective and not being based on an explicit definition and measurerrentof real risk. It might also be the case that these rules increase, rather '.handecrease, the f'uctuations in the cost of borrowings over time. A rrioreintegrated approach would base the hedging decision as to the currencycomposition choice of external liabilities on t. > uncertainty of the realeffective costs in a particular currency-where th. costs are related to theability of and the opportunity costs to the country in generating foreign

Original page # 102 ismissing.

INMPLICATIONS FOR EXTERNAL DEBT MANAGEMENT 103

An Analytical Model for Commodity Risk and Exchange RateManagemenit

Consider a world that consists of a small, open economy (the homecountry) and N developed countries.)7 Let each of the N developedcountries, in whose currencies external debt can be denominated, have anexchange rate e(i), i = 1, . . . , N, which follows the diffusion process:18

(7-1) de() = v,(,)dt + oe(,)dZe,), i = 1,..., Ne(i)

Here e(s) is written in terms of the home country's currency per unit ofthe foreign currtncy (e.g., pesos per U.S. dollar), and dZ,(,, is a Wienerprocess. So E(dZ) = 0 and VAR(dZ) = dt. Thus, this differentialequation says that the expected value of the depreciation of the ithexchange rate during the time period dt is v(,) and its standard deviationis 'Te(,. It is assumed that the exchange rate depreciations are approxi-mately normal for small intervals dt and that the exchange ratesthemselves are lognormal.19

Surpose also that the means and standard deviations Ve(,) and ¢e(,) area)'owed to depend on bor,i time and a vector of state variables (whichwill be defined later). co,

(7-2) Ve(j S = , t) and o.,p, = e,(S, t)

where S is a (S x 1) vector of state variables that are assumed to followIt6 processes. Thus, there are N foreign currencies in which the homecountry can denominate its liabilities and invest its wealth, which areassumed to follow the process

(7-3) = de,)(S, t)dt + oe,,(S, t)dZd,,

Suppose that each country in the "world" hzE one no,ninal riskless(instantaneous) bond. Let B*( j) be the price in the jth currency of theforeign country j's riskless bond and B be the price in the home currencyof the home country's riskless bond. The dynamics for B*(j) are- given by

(7-4) =dB*(i) R*(j)dt, j = 1, .. . , N(74) ~~B*(j)

where R*(j) is the instantaneous nomninal rate of return on the jth bondin cLrrency j, which is assumed to be constant. Also, let R be theinstantaneous nominal return on the safe domestic bond. All interestrates are assumed to be constant.

DJefine the excess return of the jth foreign bond for a domestic investor,dP(B-(J))1H(B*(i)), as the return on one unit of domestic currency

104 COMMODITY KI' ..: .',UANAGENIENT AND FINANCE

invested in the foreign bond, financed by borrowing at the interest rate Rin the domestic country, that is,

(7-5) dH(B*(j)) = R*(j)dt + (() - Rdt, j=1, ... ,N

-(R*(1j) + Ve(j) - R)dt + Oe(j)dZe(;)

Notice that the foreign bonds are risk-free in their own country, butexchange rate risks make them risky for investors from the "homecountry" and that their excess returns are perfectly correlated with thechanges in the corresponding exchange rate.20

Next, suppose there are K commodities consumed in the homecountry, whose domestic currency prices follow the differential equation

(7-6) dP(i) = vp(I)dt + op(,)dZp(a,) i = 1, . .. , KP(i) =lpjd

Again, vp(,) and up(,) are allowed to be functions of both time and a vectorof state variables. So the commodity price changes have a mean of vp(,,(S,t) and a standard deviation of qp(,j(S, t) over short time intervals dt.21

The first K elements in the (S x 1) vector of state variables are assumedto be the changes in the logarithms of the commodity prices; the next Nelements are assumed to be the changes in the logarithms of the exchangerates, and the remaining (S - K - N) elements are assumed to be otherunspecified exogenous variables.

r ially, it as assumed that the domestic investor maximizes a time-ac:aitive von Neumann-Mcrgenstern lifetime expected utility functionthat depends only on the consumption of the K commodities and time,that is, Et{f7 U[cj(z), . . . , ck(z)]e-' dz} where 6 is the intertemporal rateof time preference and c; is the consumnption rate of good i. Thisassumption completes the model, and allows one to solve for the optimalliability portfolio.22

Let b be the optimal amounts of foreign liabilities; let V be the (N x1) vector of excess returns; let Vaa be the (N x N) covariance matrix ofexcess returns to the foreign bonds; and let V, be the (N x S) matrix ofcovariances between the excess returns and changes in the state variables,which include the K commodity prices. Notice that, because the excessreturns on foreign liabilities are perfectly correlated with changes in theexchange rate, Vaa is the same as the covariance matrix of exchange ratedepreciations, and Va, is the same as the matrix of covariances betweenthe exchange rate depreciations and changes in the states variables-where the first K state variables are the commrodity prices.23 It can beshown (see Svensson, 1987; Stulz, 1981; or Breeden, 1979) that theoptimal F ,s of foreign bonds b = 1/C,,[-Uc/Uc,V-'v - VJ VasCS,

IMPLICATIONS FOR EXTERNAL DEBT MANAGEMENT 105

where C = C(W, S, t) is the consumption expenditure function of theinvestor, W is wealth, and subscripts refer to partial derivatives. Noticethat this is a linear combination of (s + 1) column vectors, each of which(when appropriately scaled) can be interpreted a; a mucual fund portfo-lio. The first portfolio is a mean-variance ehicient portfolio (i.e., aspeculative portfolio), given by V-'v, and the remaining s portfolios arehedging portfolios, given by the s columns of

(7-7) aa as

The weights in the linear ce-nbination depend on the parameters of theutility function (such as degree of risk aversion and the consumptionshares of the different goods), although the portfolios themselves do not.The weight on the speculative portfolio is - lCw(U,'Uc/) where UJU,, isthe inverse of the coefficient of absolute risk aversion, and the we;ghts onthe hedging portfolios are -Cs/Q,. For a country with a high degree of(relative) r.sk aversion, the hcdging mutual funds will clearly be relativelymore important in the overall optimal holding of foreign bonds than thespeculative mutual fund. Assuming that most developing countries arerelatively risk averse, and using the assumption that the expected costs ofborrowings in different currencies, after adjusting for exchange ratechanges, are all equal (i.e., v = 0), the focus of the rest of this chapter willbe on hedging portfoiios.24

The hedging portfolios are the portfolios that provide the maximumcorrelation with the state variables S; hence, they can be used to hedgeagainst unanticipated changes in the state variables. This is because, aftera shock to a state variable, the hedging portfolio leaves the investor'swealth and welfare "as near as possible" to what it was originally, where"nearness" depends on the degree of correlation of that portfolio withthe state variable.

The state variables that are of most concern here, and against which acommodity exporting developing country would want to hedge most, arethe K commodity prices that determine its welfare level. The model saysthat the optimal way to hedge the K commodity prices (and, thus, theconsumer's welfare) against changes in the exchange rates is to borrowaccording to the first K elements of the matrix V-1 V because then achange in each currency leaves the investor's net welfare the least affectedand would insulate the country from relative prices shocks, which areassumed to be the only external shocks affecting the country.2 5 Thehedging portfolio has to be determined in light of the interaction betweenexchange rates and relative (commodity) prices movements.

In the empirical application of this model, the K commodities p..have been collapsed to one price-the difference between the logaritihriiof the export price and the logarithm of the import price, that is, the

106 CONMMODITY RISK MANAGEMENT AND FINANCE

country's terms of trade.26 The terms of trade indicate the opportunitycosts of foreign good consumption in terms of foreign goods earnings.The hedging portfolio of foreign liabilities will then insulate the countryas well as possible against increases in the prices of import goods relativeto the prices of export goods.27

Empirical Applications in Indonesia and Turkey

The Econometric Model

On the basis of the theoretical model, a portrolio of foreign assets isdesired that has maximum correlation with the changes in the terms oftrade.28 This optimal hedging portfolio can be found by solving equation7-7, where V,,, is now the vector of covariances between the changes inthe termr,s of trade and the changes in the exchange rates. Notice thatVa'VaV is a simple ordinary least squares (o0s) regression (withoutintercept' -,f the changes in the state variable on changes in the exchangerates. Sui one could calculate the optimal portfolio shares by running asimple oLs regression of the terms of trade changes on the exchange ratechanges and use the parameter estimates for the slopes as the shares. Thisprocedure implicitly assumes that the variances and covariances of theexchange rate changes are constant through time, however, an assump-tion that has been proven false many times in the literature. It wouldseem appropriate, then, to use an estimation procedure that allows thecovariance matrix to change with time.

Autoregressive Conditional Heteroskedasticity (ARCH) is an economet-ric technique developed by Engle (1982) to do just that. In the univariateversion that he presents, the conditional variance of a time series isallowed to depend on lagged squared residuals in an autoregressivemanner. This means that during periods in which there are large unexpectedshocks to the variable, its estimated variance will increase, and, duringperiods of relative stability, its estimated variance will decrease.

Kraft and Engle (1982), Bollerslev (1986), and others have generalizedthe ARCH model in much the same way that an Autoregressive model isgeneralized to an Autoregressive Moving Average (ARMA) model. Thismodel, called Generalized ARCH or GARCH, is the same as an ARMA modelin squared residuals. Just as the ARMA model allows the mean to changewith time, the Acti- (and GARCH) model allows the variance to changewith time. The generalization of the univariate ARCH models to multi-variate ARsCH models involves allowing the whole covariance matrix tochange with time, instead of allowing just the variance to change withtime. The model used in the application reported here was developed byBollerslev (1987). Although somewhat restrictive (because it imposes the

IMPLICATIONS FOR EXTERNAL DEBT MANAGENMENT 107

restriction that the correlation matrix is constant through time, while thecovariance matrix changes), it is relatively simple to estimate.

The Optimal Portfolios

The GARCH process was estimated for weekly exchange rates for the fivemajor lending currencies: Japanese yen (-Y), deutsche mark (DM), Swissfranc (SwF), pound sterling (£), French franc (Ff) and U.S. dollar (US$)for nine different subperiods; each consecutive subperiod covered anadditional quarter of observations.29 Each of the nine subperiods coveredthe period from the first available data point until the start of the quarterfor which the optimal portfolio was to be calculated. As a result, a seriesof (conditional) forecasts of the variance-covariance matrix of exchangerate depreciations for the next three months resulted, that is, (Va,). Theinverse (V-') was calculated and multiplied by the vector of forecastedcovariances between exchange rate depreciations and changes in thezerms of trade, (V 1 V,,5).30

The r. Its for the optimal portfolio shares for Indonesia are shown intable 7-1, where the portfolios are scaled to sum to one and where anegative portfolio share implies that a country should invest its foreigncurrency assets in the currency to hedge terrns of trade risk. As can beobserved, the relative shares of the currencies change quite a bit fromquarter to quarter, and, as it turns out, the unscaled portfolios alsochange. Note, however, that the effective currency distribution of theportfolio does not change much through time once one accounts for thehigh correlation between the period-to-period changes of the Europeancurrencies over this period. The sums of the shares of the Europeancurrencies (DM, SwF, £, and Ff) are for each quarter (from the firstquarter of 1986 through the first quarter of 1988): 10.9, 13.8, 7.4, 18,34.4, 19.7, 25.8, 11.1, and 6.1 percent. The combined European share is

Table 7-1 Optimal Portfolios for Indonesia

Period AC DM SwF £ Ff US$

1986.1 -0.005 0.307 -0.055 0.007 -0.154 0.9001986.2 -0.022 0.320 -0.028 0.028 -0.182 0.8841986.3 -0.001 0.164 -0.012 0.021 -0.100 0.928

1986.4 -0.027 0.384 0.019 0.027 -0.252 0.8491987.1 -0.009 0.801 0.026 0.150 -0.632 0.6651987.2 0.006 0.462 0.015 0.075 -0.354 0.7971987.3 -0.033 0.703 -0.017 0.030 -0.479 0.7771987.4 0.044 0.323 0.001 0.029 -0.243 0.847

1988.1 0.031 0.191 -0.005 0.014 -0.139 0.907


Table 7-2 Optimal Portfolios for Turkey

Period y DM SwF £ Ff USS

1986.1 0.911 -0.311 -0.893 0.255 1.131 -0.0931986.2 0.335 -0.677 -0.589 0.531 1.265 0.1351986.3 0.799 -0.479 -0.833 0.718 1.019 -0.2251986.4 0.548 -0.365 -0.974 0.932 0.867 -0.007

1987.1 0.390 -0.363 -1.022 0.857 1.086 0.0521987.2 0.362 -0.159 -0.863 0.618 1.190 -0.1471987.3 0.237 -0.123 -1.234 0.483 1.783 -0.146

1988.1 0.115 -0.086 -1.842 0.498 2.511 -0.197

thus significantly more stable than the individual shares, a reflection ofthe high correlation among the European currencies.3' The sum of theunscaled portfolio weights ranges between about 7 and 48, whichsuggests different absolute levels of borrowing.

Similar analysis can be conducted to find the currency portfolios thathedge against changes in export prices, export values, import prices, orimport values.

Comparing these portfolios of terms of trade hedges with Indonesia'sactual portfolio composition during this period suggests that a movetoward the optimal portfolios could have resulted in a large reduction inthe variance of Indonesia's net position, as the optimal portfolios differedsubstantially from their actual portfolios.32 It turns out that rollingforward optimal portfolios (calculating each portfolio using data to thatpoint in time) for each quarter between early 1986 and early 1988 waseffective in reducing the variance of the debt service relative to thecountry's terms of trade, when compared with rolling forward a portfoliothat had the actual currency composition of Indonesia's debt at the endof 1985. Presumably, the movement in Indonesia's borrowing portfolioaway from 4X to I JS$ resulted in increased stability of the country's debtservice burden relative to the purchasing power of exports.

The case for Turkey was analyzed similarly. Applying the strategydescribed above, table 7-2 presents the optimal portfolios for eachquarter. Here, one notices the large changes in the optimal portfolioshares through time, unlike Indonesia where they were relatively stable.

The sum of the unscaled portfolio weights ranged between about 0.9and 2, suggesting, similar to the results for Indonesia, different absolutelevels of borrowing. The sums of the shares of European currencies forthe nine quarters were as follows: 18.2, 53, 42.6, 45.9, 55.8, 78.5, 90.9,77.7, and 108 percent. The sums suggest a somewhat more stable weight

IMPLICATIONS FOR EXTERNAL DEBT MANAGEMENT 109

Table 7-3 Optimal Portfolios, Shares Positive, for Turkey

Period X DM SwF £ USS Surn

1986.2 0.075 0.000 0.000 0.337 0.349 0.239 0.5541986.3 0.338 0.000 0.000 0.462 0.200 0.000 0.5761986.4 0.117 0.000 0.000 0.677 0.067 0.138 0.705

1987.1 0.000 0.000 0.000 0.582 0.233 0.180 0.7461987.2 0.020 0.000 0.000 0.436 0.544 0.000 0.7591987.3 0.000 0.000 0.000 0.228 0.769 0.003 0.6271987.4 0.037 0.000 0.000 0.251 0.712 0.000 0.663

1988.1 0.000 0.000 0.000 0.124 0.876 0.000 0.375

for the European currencies as a whole compared with the individualEuropean currency weights.

There is a relatively large difference between Turkey's actual debtportfolio (as of late 1988) and the calculated optimal debt portfolios,which suggests that there was room for considerable hedging by modi-fying the external debt portfolio. Application of a similar methodology,as was used for Indonesia, resulted in no significant variance reduction,however, most likely because of the large volatility in portfolio sharesfrom period to period.

Restricting the portfolio shares to be positive, that is, not ahiowing anyinvesting in foreign currencies, resulted for the nine quarters in theportfolios for Turkey shown in table 7-3. Restricting the weights of thecurrencies to be positive led to less skewed and somewhat more stableportfolios. In addition, the sum of the unscaled portfolio amounts (theright-hand column of the table) was more stable.

Overall, the results for Turkey need to be interpreted with extremecaution because the weights turn out to be very unstable over time. TFhiscan most likely be explained by the fact that Turkey's economy hasundergone significant structural changes in its export and import patternsduring this period.33 As the structure of the underlying model is changingover time, it prevents the calculation of portfolios that can serve aseffective hedges. Imposing more restrictions, while solving for theportfolio weights, and/or using different econometric techniques wouldtherefore be unlikely to lead to more stable results.

The results for both countries point up some general pitfalls in theempirics. One rests in the data for the terms of trade, which traditionallyhave been of poor quality for many developing countries. The majorpitfall of the empirical applications, however, is most likely that therelationships between the terms of trade and exchange rates changes arenot stable or sufficiently robust over time that the optimal portfolio for

110 CONMMODITY RISK MANAGEMENT AND FINANCE

the next period can be determined with accuracy. Correlations betweenterms of trade and foreign exchange rates for both countries wererelatively low. As for topics for further empirical research, several cometo mind. One is to perform these types of analyses with a larger set ofcurrencies. Another research topi, vould be to experiment with the useof an instrumental variable to forecast the developing country's currencychanges and obtain the deviations from the expected exchange ratechanges. This econometric technique might be necessary because many ofthe developing countries' exchange rates are not "market" rates andoften do not follow the assumed random walk (in first differences). Otherresearch extensions would be to account for the movements of thelender's interest rates in calculating the effective costs of foreign borrow-ings and to expand the set of possible liability instruments by including,for example, commodity-linked bonds.

Conclusion

This chapter has examined the issues involved in integrating commod-ity and exchange risk management. It has pointed to weaknesses in thecurrently accepted guidelines regarding derivation of the optimal cur-rency composition of a country's external liability and has presented amodel that can be used to calculate the optimal debt portfolio for acountry that wishes to hedge against exchange rate and commodity pricefluctuations. The chapter has also summarized estimates of the optimalcurrency composition of Indonesia's and Turkey's external debt, derivedon the basis of this model. The optimal portfolio calculated for Indonesiafor a recent period was an effective hedge, reducing the variance of thecosts of borrowing relative to Indonesia's terms of trade. The applica-tions of the theoretical model show that even though developing coun-tries might have only limited access to organized currency futures andcommodity hedging markets, they can manage their external exposureeffectively if they can at least structure their external debt in light of therelationships between exchange rates and commodity prices.

It seems fair to conclude that there can be significant benefits fromintegrating currency risk management with commodity risk manage-ment, particularly as dollar/nondollar currency movements are likely tohave offsetting effects on the relative level of the country's debt burden inthe form of primary commodity price movements. Because many devel-oping countries depend heavily on exports earnings from primarycommodities to service their external debt obligations, a certain amountof nondollar external debt obligations could be a good external liabilitypolicy. The optimal amount of nondollar obligations and the division

IMPLICATIONS FOR EXTERNAL DEBT NMANAGEMENT 111

aniong the specific nondollar currencies will depend on the relationshipsbetween the commodity prices and exchange rates in question. Becausethese relationships might not be very strong and may be unstable overtimne, care has to be taken in implementing the portfolio comnpositionsr(:sulting from the empirical work. The policy guidelines discussed earliermight still be of use in verifying the properties of the portfolio compo-s Ltions.

Notes

1. Dornbusch (1985), p. 335.2. The World Bank, Anniual Report, 1987, p. 49.3. The share of dollar-denominated external liabilities of all developing countries

reporting to the World Bank Debt Reporting System (DRS) hovered around 63 percent in theearly 1980s and then steadily declined from 66 percent to around 50 percent in 1987. Thedecline since 1985 has been in part due to the depreciation of the U.S. dollar and in part dueto the relative retreat of U.S.-dollar-based lenders from sovereign lending.

4. For example, the. U.S.-dollar-rre sured level of external debt of all DRS-reportingdeveloping countries was USS102.7 tillion.

5. In general, movements in import as well as export prices have affected the developingcountries. *Vebb and Zia (1988) have performed some counterfactual scenarios in whicilthey demonstrate that, assuming that the change in resource flows as a result ofterms-of-trade changes was met by increased or decreased external debt buildup (using theactual volumes of exports and imports in the 1980s), for a number of developing countries,their external debt in 1986 would have been substantially less (as much as 25 percent oftheir gross domestic product) if the terms of trade for these countries had remained at theiraverage level of the 1969-78 period.

6. For exampkc, weli -diversified financial institutions can transform an external liabilitydenominated in one currency into a liability of another currency through a forwardtransaction at a cost that can be substantially below tb: opporrunity costs for a liabilityholder such as a developing country.

7. The conditions necessary to separate the hedging and speculative decision are welldocumented. See, for example, Breeden (1979).

8. The recent increase in commodity prices seems to confirm the inverse relationshipbetween the dollar exchange rate and commodity prices. The slump in commodiry prices inthe first years after the recent dollar depreciation can be, in part, explained by developingcountries' needs to raise foreign exchange through the export of commodities whosedemand was inelastic. Gilbert (1988) concluded that the long-run elasticiy of commodityprice indices with respect to change in the value of the dollar-corrected for, among others,developing country debt servicing-wa-, approximately unity. This would imply thatcommnodity prices rise and fall inversely to dollar appreciation or depreciation and couldhave important implications for external liability management of a (primary) commodityexporting nation. He alsco concluded that there are suggestions that the interaction betweendollar appreciation and the dollar-denominated debts has been responsible to a significantextent for the low primary commodity prices in the years during and immediately after thedollar appreciation. Dornbusch (1985) found an elasticity of the real commodity price onthe real U.S. dollar exchange rate of approximately -0.82. Using lagged values for the realexchange rate, the elasticity became - 1.5.

112 COMMIODITY RISK MANAGEMENT AND FINANCE

9. See Giovannini (1985) and Dornbusch (1987) for their ideas and empirical work inthis regard.

10. Lessard and Williamson (1985) is a good example of this literature.i1. Of course, whether or not purchasing power parity (PpP) holds plays an important

factor in this matter. .f Prp held perfectly, currency tluctuations would presumably not affectreal export earnings and costs of imprcts. For strong and conclusive rejections of nPp, seeFrankel (1981) and Cumby and Obstfeld (1984).

12. For further information on the optimal currency basket literature, see Branson andKatseli (1982) and Lipschitz and Sund&rnrajan (1982). Williamson (1982) surveyed manyof the issues on currency baskets.

13. Pagee (1981) reported that, in the late 1970s, approximately 55 percent of worldexports were denominated in U.S. dollars.

14. For further analysis of this issue, see, for example, Dornbusch (1987), Giovannini(1985), Flood (1986), and Varangis and Duncan (1990). Dornbusch (1987) has a simplemodel in which the real dollar exchange rate enters in the commodity pricing function.

15. See Ahamed (1988) for a very useful discussion on optimal currency management,which is similar to the discussion here. Ahamed mentions real income as a potentialunderlying variable t-. niedge. A rule of thumb on currency management for countries withoil exports, for .xample, which has been popular during some periods, was that thesecountries should borrow British pounds or Norwegian kroner because these currencieswere more likely to be correlated with the price (and export earnings) of oil.

16. 1 v-ante deviations from uncovered risk parity will be due, apart from transactioncosts, to risk premia. As these risk premia will be largely determined in the developedcapital markets that, compared with developing countries, have an advantage in carryingrisk-because of factors like the wider portfolio choice in developed countries-it seemsvalid to argue that these risk premia will be relatively small :ompared with the risk-reducing benefits for the developing country involved. As long as the developing countriesare more riskc adverse than what the developed countries' capital markets im.ply, transfer-ring risks from the developing to the developed countries can be a Pareto improvement.

17. This section is a brief summary of a restricted version of the model presented inClaessens (1988), which is also reported in Kroner and Claessens (1989). See the first paperfor the general model and some further references. See Wells (1989) for similar work.

18. It is assumed that forward and futures markets for foreign exchange and commodityprices are insufficien0v available to allow the country to hedge these risks.

19. See Merton (1971) and Fischer (1975) for descriptions of the properties of Wienerprocesses ancI stochastic differential equations. The general equilibrium implications ofthese and other assumptions are not discussed here.

20. If one had assumed that foreign interest rates were not constant, the domesticcurrency return on a foreign bond would not necessarily have been perfectly correlated withthe exchange rate, as foreign interest movements could have offset or increased cxchangerate movements. Short-term foreign currency deposits would still have a relative exposure(i.e., elasticity) of one with respect to exchange rates, but the exposure on the rcturns (orcosts) of long-term fixed and/or floating instruments could have been different from one.Adler and Simon (1986), however, have shown that during the period from 1973 to 1980,the exposure on rcturns on foreign long-term bonds was essentiallv one with respect to theirown currency and that exposure with respect to other currencies was essentially zero. Thiswould imply that longer-term foreign, liabilities would present equal hedging potentialagainst their own exchange rate changes as the short-term instruments used here. Theverdict on the post-1986 period is still out and could very well be different because theinteraction between interest rate changes and exchange rate changes has, if ai.ything,become more complex.

INIPLICATIONIS FOR EXTERNAL DEBT MIANAGEIMENT 113

21. One m ist not assume that the law of one price holds necessarily for all goods (northat ppp holdsi; that is, P(i) $ P' (i, j)e(j) necessarily for all i and i, where P(i, j) is the priceof the traded ,ood i in terms of foreign currency j. Neither is it assumed that changes in theterms of trad, are perfectly correlated with the (weighted average of the) changes in theexchange rates.

22. The representative consumer technique is used hel? to mimic the sitiation in whichthe government acts perfectly in the interest of the indivildual citizen of the country and hasinstruments at its disposal to allocate (nondisrortionary) transfers to private citizens.Alternatively, the government can decide to hedge only the exposure of its own welfare orrevenue and expenditures streams. Depending on, among other things, whether privatecitizens have access to foreign financial he ,,ing instruments, the two approaches can leadto different outcomes.

23. If the interest rates on the foLeign liabilities would not have been constant, then theexcess return variance-covariance matrix could not have been replaced with the exchangerate covariance matrix nor the covariance of excess returns with prices with the covariancematrix of exchange rates with prices.

24. High risk aversion in developing countries and low risk premia (v n arecompatible, provided the risk premium is largely determined in the lending counn..- andthe level of risk is relatively low in lending countries.

25. The borrowing shares would apply to the country's net foreign liabilities, that is, thegross debt minus foreign exchange reserves and foreign exchange assets. The K pricesshould be interpreted as the prices nf goods that are importeci, relative to their opportunitycos n terms of domestic consumprton foregone (as export, have to be generated to payfor :mports). In other words, the K comr-qdiry prices are the relative terms of trade of theinldi;'!ddal K goods, zhat is, irdivieual import prices relative to the general level of exportprices. Because the model does not deal with nontradable goods, it is not necessary to reflectin the relative price of goods the relative price of nontradables as well.

26. The use of one pnce variab!e-terms of trade-instead of K can be justified if theutility function to be maximized exhibits constant consumption shares. The covariances ofthe terms of trade with the exchange rates can then be written as a function of thecovariances of the individual prices with the exchange rates. The empirical application laterdoes not consider the use of foreign liabilities to hedge against domestic state variables oragainst nontradable assets. The only state variable is the terms of trade.

27. Empirical research on capital mobility has found that the extent of portfoliodiversification, at least among developed countries, is too low to be explained by standardmodels of financially linked economies. Or, said differently, international as',et markets arenot used extensively to facilitate the :ransfer of external risks. This has led a number ofresearchers (e.g., Cole and Obstfeld, 1988) to conjecture that real markets, such asinternational commodity trade, can make international asset trade redundant, as fluctua-tions in international terms of trade may play an important role in automatically poolingnational economic risks. As strong restrictions on preferences and technologies are rc, icedto make international asset markets completely redundant (e.g., commodity marketdemands have to be unit elastic with respect to price), the analyses would indicate thatinternational asset trade (e.g., external trade) can lead to welfare-increasing risk poolingarnong natinns-as a supplement and in addition to commodity trade.

28. This section summarizes work reported in more detail in Kroner and Claessens(1988).

29. The period covered was April 1, 1977 to March 31, 1988. The analysis itself wasbased on the logarithms of the exchange rates and the logarithms of the terms of trade,multiplied by 100. This is in harmony with the literature on exchange rates and gives theadditional benefit of being able to interpret differenced logs as percentage change5 Recall

1.14 COMMODITY RISK MANAGEMENT AND FINANCE

that the theoretical framework requires all the data to be differenced, so that one will dealwith percentage changes. The five currencies chosen cover a currency share of approxi-mately 80 percent of all developing countries' external debt.

30. The forecasts of the covariances betwcen the exchange rate depreciations and thechanges in the terms of trade turned out to be the unconditional covariances estimated overthe respective period because the hypothesis that the covariances were not changing overtime cou!d not be rejected.

31. The (simple) corr^lation coefficients among the Ff, SwF, and DM varied between 0.85and 0.91 during 1981-88. The correlation between the £ and other European comriencieswas somewhat weaker ant' varied around 0.63.

'2. The actual portfolio composition of Indonesia's externa' debt for these periods is notreported here; however, it was roughly one-third yen, one-third dollars, and one-thirdEuropean currencies.

33. For example, the share of Turkey's total exports :o the Middle East has variedbetween 20 ,nd 45 percent between 1980 and 1987. Similarly, exports to and imports fromOrganisation for Ecor<mic Co-operation and Developmen. (OECD) coun.ries haveundergone significant cha.iges, not only in (relative) levels, but, more important, also interms of composition, as Turkey has begun to produce a different and higher valued rangeof products.

Hedging withCommoditv-Linked Bondsunder Price Risk andCapital Constrain tsRichard J. Ball and Rtobert J. Myers

This chapter investigates whether commodity-linked bonds can offercapital-constrained producers an effective means of raising capital andhedging against output price risk. Two issues are examined. First, theoptimal levels of commod ty production and bond issue are determnnedfor a risk-averse producer who has no initial wealth, no access to futuresmarkets, and no conventional source of investment funds. Second, theassumption of no initial wealth and no futures markets is maintained, 'utproducers are provided with the opportunity to obtaii conventionalloans, as well as issue comrnodity-linked bonds. In tiiis case, interestcenters not only on the output and bond issue decisions, but also onconditions under which issuing bonds or taking out conventional loanswill be the dominant strategy for raising capital.

These issues are studied graphically in mean-standard deviation space.In a recent paper, Meyer (1987) has shown that expected utilitymaximization is equivalent to ranking altcrnatives based on their meanand standard deviation, provided a location and scale (Ls) condition issatisfied. The Ls condition is shown to hold in the case of the capital-constrained commodity producer studied here. Thus, the graphicalmean-standard deviation analysis is fu!ly consistent with an expectedutility model. The advantages of graphical analysis are that proofs aresinplified, and results are rnore intuitive. Meyer and Robison (1988)recently used the Ls condition in a graphical analysis of futures markethedging under output price randomness.

FHEDGING wiT-rH CONIMNODITY-LI;KED BONDS 117

mn:an (scale). This means that the producer's decision sa i.ies IMever's LS

condition, which can be stated formally as follows.

DEFINiTION. A decision problem satisfies the Ls condition if every twocumulative distribution functions, F,(r.) and F(-,(), describing elcmiienitsin the choice set satisfy Fl(ir) = F,(a + 67,) for all r, and for somtle a andsome ,B > 0.

IMever has shown that when :he Is condition is satisfied, maxirnizationof expected utility is equivalent to maximizing a preference function V(ua,oc) of the mean and standard deviation of profits. From the many propertiesof V(gA, uj that are discussed it. Meyer's paper, twvo are particularlyinmportant for this analysis. First, the slope of a risk-averse producer'sindifference curves in mean-standard deviation space is always positive:

(8-4) S(,u, a) = - V'(A' a)/V/A,l, cr) > 0.

Second, V(y, cr) is concave, so that indifference curves in mean-standarddeviation space are convex to the origin.

Beforc investigating the shape of the pioducc--r's opportuhIkty set, thefo!lowing impcrtanlt assumption is made.

ASSUNMTION 1. Bond issuers Must F..1y bor-'holders a risk preiiiium tohold the boi ds, plw > (1 + r).

T-his assur iprion says that the expected gross return on holding bondsis greater th in the gross rate of return on a riskless asset. Becauseconimodiy-iin.ked bonds are risky fnancial instruments, and the certaininterest ra;e r s available to investors, this assumption simply states thatthere is the asual risklreturn tradeoff among assets.

Nowv co%,ider the opportuinity set of a capital-constrained producer inmean-standard deviation space. The mean and standard deviation ofprofits are

(8-5) / = (1 + r)[it'b - c(q)] + p(q- b); and

(8-6) cr = iq -blop

where: p = expected output price and op = standard aeviation of the outputprice. The shape 4 the producer's opportunity set in mean-standarddeviation space is llustrated graphically in figure 8-1. The opportunity setcan be derived in three steps using 8-S, 8-6, and assumption 1.

First, suppose that the quantity produced is fixed at some level, and bis set equal to this production level. b - q. Substituting the equality into8-5 and 8-6 gives ,u = (1 + r) [wq - c(q)] and ur = 0. TMis defines a pointon the ;I axis that is in the opportunity set. (See 'igure 8-1.)

Sccond, suppose that the quantity produced remains fixej at q and bis decreased below the point at which b = q. Then differentiating 8-S and8-6 gives


Figure 8-1 Optimal Bond Issues under Cpital Constraints

Panel (a) p

gb=~~c(qlw

b=q q

Panel (b) A

IO

b=q

Panel (c) P

=C(/)w/

b=q

. . . . . . . . . . . . .

HEDGINCG WITH COMNIMODITY-LINKED BONDS 119

(8-7) dp = [(1 + r)w - F] db; and

(8-8) dr= -rrp db.

Dividing these cquations gives the slope of the opportunity set as bdecreases:

(8-9) d/do- = [p - (I + r)w]/o-p.

This part of the opportunity set is indicated by the positively sloped raymoving out from the . axis in figure 8-1. Assumption I ensures that theslope is positive as b decreases. Ncvertheless, b cannot fall too far belowq because of the capital constraint. That is, the opportunity set becomestruncated at the point at which the revenue raised by issuing bonds is justequal to the cost of producing the fixed output q. Any further reductionsin b beyond this point are unfeasible because there would not be enoughrevenue available to purchase the inputs required to produce q. Thistruncation point is also illustrated in figure 8-1.

Third, suppose that tiw nLuantity produced remains fixed at q and b isincreased above the poi,:i . - vhich b = q. Then 8-8 becomes do- = c-pdpand the slope of the opp,.. nulity set is now

(8-10) d,41d./r = -i - (1 + r)v]/o-p.

This part of the opportunity set is indicated by the negatively sloped raymoving out from the 1i axis in figure 8-1. Assumption 1 ensures that theslope of the opportunity set is negative as b increases. In this case,however, there is no truncation point because mote and more revenue isbeing raised from bond issues.

The opportunity set shown in figure 8-1 is for changes in bond issues,while the quantity produced is kept constant. Notice, however, thatchanges in q simply move this opportunity set up and down the ,u axis.Furthermore, because the producer prefers higher profit means to lowerones, and the slope of the opportunitv set does not depend on the quantityproduced, then the optimal q maximizes the intercept of the opportunity seton the ,u axis. The optimal quantity produced therefore satisfies

(8-11) c'(q) - w= 0.

Thus, the optimal production level depends only on marginal costs andthe bond price. This separation property is a familiar result from theliterature on futures market hedging, where it has been found that theoptimal quantity produced depends only on marginal costs and thefutures price (Danthine, 1978; Holthausen, 1979; Meyer and Robison,1988). Equation 8-l1 shows that a similar result holds in the case of acapital-constrained producer issuing commodity-linked bonds, exceptthat the bond price, not the futures price, is the action certaintyequivalent price for the producer's output decisionl.

120 COMMODITY RiSK MANAGENMENT AND FINANCE

Having determined the optimal quantity produced, the next step is tocharacterize the optimal bond isoae graphically in mean-standard devia-tion space. Three possible cases are illustrated in figure 8-1. In each case,the negatively sloped portion of the opportunity set is irrelevant becauseindifference curves are convex and positively sloped.

In panel (a) of figure 8-1, the optimum is defined by a -angencybetween the producer's indifference curve and the opportunity set. In thissituation, the producer issues less bonds than the quantity being pro-duced, b < q. The revenue raised by issuing bonds, however, is greaterthan the cost of production, so the excess is invested at the knowninterest rate r. The payout the producer expects to make on the extrabonds is greater than the sure return from investing the excess revenue.Nevertheless, the extra bonds provide an output price hedge for theproducer, and this is why they are issued.

Panel (b) of figure 8-1 represents an optimum in which the slope of theproducer's indifference curve is greater than the slope of the opportunityset. This is a corner solution in which the optimal bori issue equals thequantity produced, b = q, and the variance of profit is reduced to zero.It will occur when producers are very risk averse and want to eliminateall risk. Once again, the optimal hedge requires bond issues that raiserevenue in excess of the amount required to finance production costs, andthe excess is invested at the interest rate r.

Finally, panel (c) of figure 8-1 illustrates a constrained optimum inwhich the slope of the producer's indifference curve is less than the slopeof the opportunity set. In this case, the producer is not very risk averseand would like to issue less bonds for hedging purposes (remember thatthe producer must pay the bondholder a risk premium to invest in thebond). Bonds sufficient to cover production costs, however, must alwaysbe issued, and so the optimum occurs at the truncation point on theupward-sloping portion of the opportunity set.

These results illustrate the effect of producer risk preferences on theoptimal risk/return tradeoff from issuing commodity-linked bonds. Therisk premium on the bonds causes mean profit to fall whenever theproducer issues more bonds. The p;incipal payment on the bond,however, is positively correlated with the commodity output price. Thus,the bonds provide a hedge against output price risk. If the producer isvery risk averse, then there will be a compiete hedge, b = q. If theproducer is not very risk averse, then the bond issue will cover onlyproduction costs. If producer risk preferences lie between these twoextremes, the revenue raised by bond issues will be greater than thatrequired to finance production costs, but not great enough to provide acomplete hedge and eliminate all risk.

HEDGING WITII COMMODITY-LD.-KF.) BONDS 121

Hedging with Commodity-Linkecd Bo3nds and ConventionalLoans

Suppose that the producer of the previous section now has access toconventional loans at a known intcrest rat., r. Everythinig else remains asbefore, including the existence of a m;larket tor commodity-linked boncds.Th, availability of convenltional loans does not change the profit function°-1 because the producer has exactly the same revenues and costs asbefore. What docs change is the capital conlstrainit, 8-2. Because anyamount can be borrowed or lent at the interest rate r, the producer is nolonger constrained to issuc enoughi bonds to cover production costs-themoney can always be borrowed instead.

The effects that conventional loans hlave on optimal productiorn andbond issue decisions are easy to derive graphically. To begin, consider theshape of the producer's opportunity set when conventional loans areavailable. Given somtle fixed level of OUtplut, q, the opportunity set forchanges in b is almost identical to the previous case (witlhout conven-tional loans). The only difference is that the positively sloped ray is nolonger truncated at the point at which revenue from bond sales equalsproduction costs. Because production costs can now be financed byconventional loans as well as bonds, bond issues can feasibly be reducedall the way to zero. The nonnegativity constraint, 8-3, however, contin-ues to hold so that truncation now occurs at b = 0. This opportunity setis illbstrated in figure 8-2.

Optimal output and bond issue decisions are characterized by consid-eration of preference maximization, subject to remaining in this oppor-tunity set. Three different situations are illustrated in figure 8-2. In panel(a), the optimum is defined by a tangency between the producer'sindifference curve and the opportunity set. This rnay occur whererevenues raised from bond issues are greater than, less than, or equal toproduction costs. At this solution, bond sales are strictly positive and theoptimal output level satisfies, 8-11. The producer is risk averse enough tohedge by issu;,,g bonds, but not risk averse enough to eliminate all riskby setting b = q. Panel (b) of figure 8-2 illustrates the corner solutionwhen the producer is very risk averse and issues sufficient bonds to reducethe profit variance .o zero.

Panel (c) shows the interesting case in which conventional loansdominant commodity-linked bonds, b = 0. This oc -urs when the slope ofthe indifference curve is smaller than the slope of the opportunity set atthe optimum:

(8-12) S(Ai, o-) < [p - (I + r)w]v/op.


1-igure 8-2 Optimal Bond Issues with Conventional Loans

Panel (a)

b=o

b=q < <

Panel (b)

b=O

b=q q

b>q

Ll~~~~~~~~~~~~~~CPanel (c) i

Z.Io

b=q ~ ~ ~ ~ ~ =b=q C b<q

b>q

a5

HiEDGING wi ryH COMMNioMvrY-LINKED i7ONDS 123

Equation 8-12 has an intuitive econoilic incerpretation. The slope of thindifference curve represenrts the "cost" of producing unhedged outputand bearing the full risk of outpult priLe uncertainty. The slope of theopportunity set represents the "cost" of the risk premium that producersmust pay to bondholders to facilitate a transfer of risk. If this "cost" ofproducing unhedged output is less thaln the "cost" of paying the riskpremiumii, all production Losts are financed with conventional loanis, andno bonds are issued. rFlc less risk averse are producers, the inore likelythat conventional loanls will dominlate coltimodity-liniked bolnds.

The final task is to deterimiine the optimal output level whenl b = 0. Ifno bonds are issued, then output is completely unlledged. TuLs, at anoptimum, q Imlust satisfy

(8-13) S(A, (r) = [p-(1 + r)c'(q)/luj,.

The slope of the producer's indiffercnce curve in mean-standard devia-tion space equals the slope of an opportunity set defined by variations inq with bond issues fixed at b = 0.

Conclusion

This chapter examined the behavior of capital-constrained commodityproducers managing output price risk with commodiq -linked bonds. Thestudy w as motivated by the problems of heavily indebted developingcountries that have exhausted conventional sources of credit, but still facecommodity price risks. Futures markets are not available because manycommodities produced by developing countries do not have futures mar-kets, and those that do exist are typicallv located in major internationalfinancial centers, where developing countries may face substantial basis risk.

Results of the investigation indicate that commodity-linked bondscould have an important role to play in hedging commodity price risks.If producers are highly risk averse, and the risk premium in the bondprice is "not too high," then the optimal bond issue will equal thequantity produced, and the producer will be fully hedged. As producersget less risk averse and the risk premium on the bonds gets bigger, theoptimal bond issue declines. If the risk premium is high enough andproducers are "not too risk averse," then no bonds will be issuedprovided conventional loans are available. If conventional loans are notavailable, only enough bonds to cover production costs will be issued.

These results were derived using a graphical mean-standard deviationapproach that is fully consistent with expected utility maximization. Thegraphical approach is more intuitive and leads to simple proofs for thevarious results.

Financial Instruments forConsumption Smoothingby Commodity-DependentExportersBrian Wright a?zd Iavid Newbery

Loans and other investn:-nt contracts are widely perceived as legallyenforceable in lende~r ountries but not in debtor countries. In thatcontext, this paper shows how novel financing arrangements usingcommodiry bonds with put options for the seller can be used to stabilizerisks associated with export prices.

Given the substant;a! inst,.bility in all primary commodity markets,one would expect countries that depend on a single primary export formost of their foreign earnings to experience especially sharp fluctuationsin export earnings and their underlying wealth., To the extent that thesefluctuations affect consumption, they are costly, and one would expectsuch countries to seek ways of managing these fluctuations, therebyreducing their costs.

In many countries, the nature of the resource endowmrent and itscomparative advantage rule out production diversification as a signific;ntnear-term strategy, and it is not included here. In addition, diversificationis ruled out via exchange of equity investments with foreigners. In thischapter, the cost of export risk is co-nsidered and commodity bonds areshown, in fact, to be capable of achieving efficient smoothing of i.i.d.export price disturbances in some cases and eventually complete smooth-ing in others-if that is what countries really want or need.

What are commodity bonds? Commodity bonds are bonds whoseprincipal repayment (and perhaps dividend payments) may be made inunits of physical commodity (or the terminal value of some appropriate

124

COM.MODITY-DEPENDENT EXPORTERS 125

futures contract). Typically, the bond f -yer has the option to receive thenominal face value or the commodity bundle. In the finance literature,stucdies of the pricing cr commnodity bonds (Schwartz, 1982; Carr, 1987;and Priovolos, 1 987a) do not d-inguish bonds issued by foreigngovernments from priate corporate bond issLuCs. The literature onforeign borrowing, however, recognizes that the distinction is crucial.

Sovereign Borroxving and Default Prevention

T'he main distinction betwveen corporate and sov,'reign borrowilng,described in masterly fashion by Keynes (1924) and incorporated in theseminal work of Eaton and Gersovitz (1981), is that collateral isgenerally unavailabie to creditors of a sovereigin borrower because theassets of the latter are located within its borders. Onlv in exceptionalcases c.an they be attached by lenders in the event of default.

The absence of a final distribution of assets to creditors, as seen indomestic bankruptcy, also changes the nature of default. It arises in thecontext of a sequence of strategic moves by creditors and the sovereigndebtor who retains (and, in fact, cannot credibly foreswvear) the power tomake subsequent decisions that affect the interests of creditors.

Here, the focus is on income-smoothing financial transactions betweeninvestors in developed countries and in developing countries, Nvhich areheavily dependeint on a single commodity subject to substantial revenuefluctuations. The default penialty is enforcement of debt seniority clausesin the courts of all potential borrower-lealder nations, so that a defaulte.'sforeign investments or servicing of newv debt would be subject to seizure.Default means permanent eliminaticin of foreign borrowing or lendingopportunities.

The Costs of Income Variability

,onsider a country that has economically unresponsive production(zero supply elasticity) and seeks to maximize the discounted expectedutility of its representative consumer

(9-1) V, = E (1 + 8) -'U (cd*=0

where E is the expectation operator, 8 is the discount rate, c, isconsus-nption in period t, and u is felicity, it' > 0, u" < 0. There is nostorage. Output and price are each subject to one discrete i.i.d. randomdisturbance per period.


To dramatize the issues, assume that exports from a single commodityaccount for 33 percent of GNP on average and suppose that the coefficientof variation (cv) of output and price of the commodity are both 30percent and that the correlation betwveen output and price can be ignored.Suppose also that all other income is nonstochastic and that the countryoptimally shares risks intemnally. There is, however, no saving orborrowing or othe- intertemporal income smoothing. Using the standardformulas2 for the c, 'st of risk, if the coefficient of relative risk aversion isR (defined for one-period variations in consumpticn) and .f the cv ofconsumption is s, then the cost of risk, p, is defined implicitly by u(c -p) = Eu(c,) (where a bar over a variable indicates its expected value), andthe relative cost, pIc, is approximately (exactly if utility is quadratic inincome per period) Rs2 /2. If consumption must be equal to income eachyear, then s -- 0.33e where e is the cv of export revenlue. If output andprice are independently normally distributed, then e2 = 0.19 (and thiswill hold approximately, even if output and price are not normal). In thiscase, if R has the not-unreasonable value of 2, the cost of risk isapproximately 2 percent of average income, the amount representativeconsumers would be wiliing to forego each year in return for a stabilizedconsumption stream of c.

Consumption Smoothing by Borrowing and Lending

Can a country optimally smooth consumption by borrowing andlending from overseas sources? If the utility function is quadratic, then 8can be interpreted as the rate at which future consumption is discountedby the representative consumer; if this is equal to the rate of interestabroad, r, then the country has no motive for saving or bor;:owing otherthan to smooth cons- mption. This assumption is made here to focus onthe consumption smuothirig aspect of international borrowing. It isassumed that the exports are subject to random i.i.d. price disturbances.Then the optimally "smooched" consumption of a borrower committedto borrowing and lending only for smoothing and to meeting its interestpayment obligations is c, = E,(c,. 1) = - rL,.3 Under this scheme,sccumulated debt, L, follows a discrete random walk with incrementequal to the difference between income y, and its mean, y. For permanentsmoothing, there must be no limit on L. In finite time, however, L willpass the value at which repudiation becomes more attractive thancontinued interest payments, even if all borrowing and lending opportu-nities are then cut off.4 Thus, competitive lenders will not make unlimitedloans. Any feasible loans would offer, at best, only incomplete and/orimpermanent smoothing.

COI...-IODITY-DEPENDEN1 EXPORTERS 127

The nature of the evolution of general obliga.son loan contracts forsovereign borrowers is a currently active research area.5 At this stage, itseems clear that full consumption smoothing by sovere; ,n borrowersusing conventional borrowing and lending is unfeasible if the contract isnot renegotiated. If it is, then the quest for a better instrument makessense.

Commodity Bonds Issued by Sovereign Lenders

To simplify the discussion, assume that the commodity bond underdiscussion is a zero-coupon bond wi. payment upon maturity consistingonly of a completely specified commodity bundle. The issuer is Lc-uinedto be competitive and the market risk-neutral with respect to this bond.(See O'Hara [1984] for an analysis of the demand side of the market forcommodity bonds under other assumptions.) As above, assume initiallythat all contracts are always honored.

Under these assumptions, if the country issues commodity bonds(which in this model need only be one-period bonds) and if these can beissued (and indefinitely reissued) at the present value of the expected price

-L lazxt period, then their risk-reducing properties in the steady state areexactly the same as those of an optimal forward or futures hedge at thesame price. Newbery and Stiglitz (1981)6 show that, in the case ofstationary, uncorrelated output and price disturbances, the ratio ofincome variance withi and without optimal forward hedgir,-' is rouighly1/(1 + k2 ), where k is the ratio o. the cvs of price and output. In thenumerical example above, k equals 1. If there is no other means ofconsumption smoothing by lending and borrowing, then conmmoditybonds will halve the steady stave costs of the risk-to 1 percent of GNP inthe example above. If the cv of income were the same, but only price werestochastic, then commodity bonds eliminate risk, worth 2 percent of GNP.

Assume, henceforth, that no other borrowing is possible and that allinco.ne variation is due to price. Then, with credible commitment,complete smoothing is achieved by selling commodity bonds for thewhole (deterministic) output. The count-y then has constant income andconsumption and delivers all output of random value to the lender.

In low-price states, the smoothing raises income, so there is noincentive at all to default. But in high-price states, delivery to the lenderreduces current income, yt, by (Yt - y). This, plus the expected presentvalue of autarkic future consumption, may, in some high-price states,exceed the maximum. expected present value of the consumption path,given default does not occur now. Then, those states will rationallydefault; a no-default commitment is not credible.

128 ( ,. tIMODITY RISK MANAGEMIENT AND FINANCE

The credibility of a no-default commitment by a commodity bondissuer depends on the parameters of the model. Consider the simple casewith a two-point probability de- ity for the multiplicative incomedisturbance that is i.i.d., u = tv, with probabilities of outcomes +v and-v equal to one-half. Assume mean income is unity and utility isquadratic over the consumnption range, I - v to 1 + tv. Then the anlualcost of risk in the stochastic steady state (and the value of access tocommodity bonds) is in dhis case, with all uncertainty, due to price: p* =Rv 2/2 and the present value is p*/5 = Rv2 /28. Now consider thestochastic steady state, in which a fraction (1 - a) of output, 0 < a < 1,is delivered each period in payment for commodity bonds issued oneperiod earlier, and all consumption is financed from current sales ofcommodity bonds and the uncovered fraction (a) of output. If the incomedraw is high at v, then default is the expected-utility-maximizing decisio:iif-and only if-the curren- -ooi? gain, v - av, exceeds the presentvalue of the risk cost incurred. The change in per period risk cost isRv 2(1 - a 2)/2. Default occurs if the one-shot gain exceeds the presentvalue of the increased risk cost, that is, if 8 > Rv (1 + a)/2, so fullcoverage is feasible if and only if 8 c Rtv/2; some fractional coverage isfeasible if and only if 5 < Rv.

As the cv, v, the relative risk aversion, R, or the uncovered fraction aincreases, the minimum 8 consistent with default rises. Default on fullcoverage is not a problem in this case if income is risky enough and/orrisk aversion is high enough.

Optimal D)ynamic Smoothing StraL'gies

Default Constraint Nonbinding

As noted earlier, the commodity bonds may be default-free in thestochastic steady state with an i.i.d. price disturbance in wliich consump-tion equals the mean value of output, discounted one period. If so, onedescription of the optimal infinite horizon smoothing plan for implemen-tation in period 0, given current income, yo (assumed tor this expositionto be entirely from export of one commodity at price p) and the discountrate equal to the interest rate is as follows: Invest 63yo, where ,3 - 1/(1 +r), overseas for a certain periodic rate of return of r, take out acommodity bond to cover all output, with current sale price ,B y, andconsume r,ByO + #y; in each period 0, 1, 2.... Full efficient consumptionsmoothing is immediLtely achieved forever. (A short forward contractplus a loan on the anticipated proceeds could replicate the abovecontract.)

The opportunities for overseas investment at the (certain) market

COMCMODIlY-DEPENDENT EXPORTERS 129

interest rate and for sale of commr.dity bonds at unbiased prices are allthe financial facilities needed for rhis plan. Furthericore, note that if theinitial income, yo, is invested where it can be collateralized for thecommodity bond loan (for example, in the lending country), the defaultconstraint is relaxed relative to the comparative static analvsis above,which assumed all income %vas from sales of commodity bonds and noneof the current income in cht period in wvhich commodity bonds wereintroduced was saved. So, even if full commodity bond coverage seemedinfeasible in that analysis, the above strategy may work.

Default Constraint Binding

On the other '-and, wvhat if the default constraint binds? The immedi-ate transition to full c. nsumption snmoothing is precluded. Or.c asks whatthe optimal consumption smoothing contract is in suck cases, followingthe analysis of Worrall (1987) and Kletzer (1988), and then sees theextent to which it can be replicated by existing financial instruments.Suppose the export price in any period t can take one of S valuescorresponding to S states of the world, p,(s) = p(s) = p(l) < p(2) < ...p(S), and associated with these values, the income of the country, valuedat the spot price, is y(s) = p(s) 4, s = 1, 2, . . . , S. The optimal contingentborrowing contract is a level of borrowing, b, and a schedule forrepayment in tne next period, M,5 -- A(, - in,, p,+,(s) + 1(s)jcontingent on the price realization p,; I(s) that maximnizes the borrower'sutility subject -' the desire not to default. If the present value function isV, then V is the solution to the problem

(9-2) V(yt - in,) = Max 4()', - in, + b,) + E[V(y(s) - M,s)]/(1 + r)

where y, and mi, are the levels of income at current price p, and debtrepaymen- in the ctirrent , -riod t, and consumption c, = y, + , -tn,This is to be maximized by cH-osing [b,, M,J subject to the constrainttha. the borrower does not wish to default in any state s and, thus,foregoes any future lending or borrowing oppor-unities:

(9-3) V(y - M,.,) - u(y(s)) + E[u(y)3lr, s = 1, 2, . . . , S

and subject to the zero profit constraint that, for risk-neutral lenders, is

(9-4) - b, + /3E[M,4] = 0.

From the envelope condition, u'(y, - m. + b,) = V vy, - in,), V(.) isstrictly concave, implying the e):istence or a unique optimum. Thefirst-order conditions from this constrained maximization problem are

(9-5) u'Vc,) = (1 + uW)V'(y(s) - Al,,), s = 1, 2, . . . , S

where 4, is proportional to the multiplier on the default constraint instate s, which will be zero if the constraint does not bind.

COMMODITY-DEPENCENT EXPORTERS 13.1

consumprior. is cl = yl + b+ - ml - c0. Consumption never falls;assumring the maxirnum price p(S) has positive prLbability, in finite timc(period zv), i: occurs, and c,+, < p(S) -q is constant for = 0, 1, Z, 3....(A longer maturity ofers no additional advantages in this model.) In eachperiod, an instrument that can a-hieve this is a zero-coupon, one-periodcommodity bond payable in dollars or in a specified commoditv bundleat the seller's option. This instrument contrasts with the typical com-moditv-cow"ercible or commodity-ii1 .ked bond that contains a call optionfor the purchaser, rathcr than a put for the seller.

When .hc default constrainc hirnds, this scheme is not fuily efficient ingeneral (though it is for the mto-point disturbance distribution in theexar ipe above). It would be weakly dominzted by the scheme presentedabove in which pavments *vere fully state-contin,,ent for each of the highbtates.8 (Here the repaymenr m, made by the borrower when the put is!.ot exer.ised does not vary with the s -ite.) Under either scheme theconsuirmptior path exhibits the same distinctive qualitative features ofupward ratchcting and eventua! complete smooth.ng of consumption,given i.d. disturbances. The difference in welfare effects of the twosch--mes 'n man! cases will rot be large, and the much greater simplicityof our commodity bonds over flli state contingency gives them a strongernpirica! advantage.

Before closing this section, rote that the thcory used here assumes thatsovereign defaults are penalized by withdrawal of all lending andborrowing opporzunidies. The historical record, however, (Lindert andNMorton, 1987; Eichenlgreen, 198.7) does not clearly show the expecteddifferentiation in availabiliry of loans and their terms bet-ween countriesthat have defaulted several :imes and those that have never done so. Onthe other hand, despite 1he apparent'y lenient treatment of sove, igndefaulters, the overall e' post rate of return has substantially exceededthe return on lending wyithin the creditor countries themselves. (SeeLiridert ar4d Morton, 1987.) )3orrn.wers o;ten appear to make netrepayrr1ents in circumstances in whic-l i. is difficult to demonstrate thattheir efforts are in tneir own self inteiost, even where the latter isrecognized as ex.cnding well beyond stabilization. 9 Resolution of thesepuzLles ,s currently an active area of theorn ical and empirical investiga-tion.

Conclusion

ConsurnDtio1-smoothing cculd, in principle, be quite valuable to manycountries in the absence of any other risk-reducing strategies. Commod-it) bonds can achieve consumption smoothing in the face of random

132 COMIMODITY RiSK MANAGEMENT AND FINANCE

- poet prices for commodity-dependent developing countries that dom-inates smoothing using other international arrangements, such as inter-national buffer funds or attempts to create longer-term futures markets.'0

Dependinig on ;i.,ir;ai conditions, the smoothing may be immediatelycomplete (and constrained Pareto optimal) and use a straight commoditybond, or it m.ght involve a nondecreasing consujmption path, whichbecomes constant if and wvnen the highest income level is attained. In thelatter case, the bond could be constructed as a conventional loan withartached put for the seller; equivalently, it could be constructed as a bondwith a nominal face value at maturity and an attached commodity value,delivery of either to be at the seller's option. rhis type of commodlitvbond contrasts with the observed forms, which generally offer the buyera similar choice. The consumption-smoothing achieved reduces downsideexposure of the seller, while leavinig the seller a sufficiently large share ofhigh realizations so that there is no temnptation to default.

Although thils has only been shown in the case of pure price uncertaintywith i.i.d. disturbances (and, hence, no interperiod storage), availabilityof a constant risk -free ate of return and market risk neutrality of leniders,the results sugg:st furt&.er investigation of the smoothing possibilities ofthese instruments in more general circumstances. Whether such smooth-ing is what commodity exporters want or need is another question.ContinLued access to the benefit of income-smoothing, however, is oftenidentified as a major inducement for honoring loan contra, inallymotivated by other objectives such as economic developm aton,Gersovit.t, ancl Stiglitz, 1986), although the observed procyclical natureof much borrowving raises questions about the smoothing objective(Gersovitz, I Q85). (See also, Fishlow, 1987.) Integration of this analysiswith the extensive literature on swaps, renegotiations, and -. Iatedmatters is an obvious extension of this approach.

Notes

1. This chapter is a substantial revision of an invited paper for the 1988 WinterAmerican Sc cial Sciences Association Meeting for the session, "Financial Risk ManagementNeeds of Developing Countries," which was published under the same title in the AmericanJournal of Agricultural Economics, vol. 71, no. 2 (Mlay 1988). We thank, with the usualcaveat, Doug Christian for research assistance; Jim Vercammen, Ken Kletzer, and T;mWorral for pointing ( .i errors in a previous draft; and seminar participants at theUnivL'simy of California-Berkeley and Larry Karp, Ken Kletzer, Peter Linderr, and BarryEichengreen for helpful discussions.

2. If consumption c is a random variable with a coefficient of variarion s, u(E(c) - p)= Eu(c). Expand both sides in a Taylor series: u(E(c)) - pu'(E(c)) u(E(c)) +0.Ss2E(c)u'(E(c)) or PIE(c) - 0.Ss 2R.

3. Newbery and Stiglitz (1981), pp 201-02.

COMMODITY-DEPENDENT EXPORTERS 133

4. If only borrowing opportun'ries are losr, but the country may invest the payments itsaves overseas at the same interest rate, it can actuially achieve exactly the same con-sumption stream for periods beyond t + k, as if it did not default (or never borrowed at all).See Bulow and Rogoff (1988). The partial smoothing is similar to that ichieved bycommodity sterage. See Wright and Williams (1982).

5. Sec Eaton, Gersovitz, and Stiglirz f 1986) for a recent survey. Sce also Kletzer (1988)and Bulow and Rogoff (1987). Alternative instruments are reviewed in Lessard andWilliamson (1985).

6. Newbery and Stiglirz 1981), p. 186.7. Worrall (1987), pp. 5-6, Results 1-3.S. This difference was pojinted out by our colleague, Ken Kletzer; the issue was also

mooted in a private communication by Tim Worrall.9. There is a significant body of literature following the pioneering work of Feder and

Just (1977) on estimation (as distinct from explanationi) of debt-service behavior.10. See Finger and de Rosa (1980) for a cautionary analysis of the Compensatory Finance

Facility of the IMF. Finger and de Rosa found that, on average, it did not even stabilize theannual export incomes of participants.

10Securitizing DevelopmentFinance: The Role ofPartial Guarantees andCommodity ContingencyRonald Anderson, Christopher Gilbert, andAndrew Powell

Throughout tile 1980s, the scale of indebtedness of many developingcountries has, in conjunction with high interest rates and adverse termsof trade, meant that very little new private finance has been .ivailable tothem. The lack of finance for investment has been a major impediment toeconomic growth in these countries. At the same r e, the poor servicerecord on much of this debt has created major balan:e sheet problems forcredizor banks.

The largest component of developing country debc in private hands isin the form of general obligation bank loans. It is widely acknowledgedthat these problems would be lessened if this general obligation debtcould be, in whole or in part, securitized-that is, if it coiild be traded inmore or less standard form on liquid secondary markets, in the same wayas are developed country bonds. Securitization would provide marketvaluations of existing debt and would allow debtor countries to raise newfinance on terms that reflect their repayment potential; it would alsopermit creditor banks to adjust their balance sheets at relatively low cost.A number of proposals aimed at securitization have been proposedduring the p3st few years, but, to date, none has attained any markeddegree of success.

134

PARTIAL GUARANTEES AND COMMODITY CONTINGENCY 135

The major difficulty standing in the way of securitization is that debtsof developing country govermnents and their immediate agcncies bearsovereign risk. In circumstances in which private-sector debtors fail tohonor contractual obligations, it is possible for the creditors to takeenforcement action through the courts. This possibility is not open tocreditors when the counterpart is a sovereign government. In such cases,debt service is, in an important sense, voluntary. Sovereign risk istherefore a major source of the illiquidiry of current developing countrydebt. A prospective purchaser of an existing obligation must makedetailed enquiries into the debtor country's economic and politicalsituation, its likely need for new finance (which will provide an incentiveto service current obligations on schedule), and its other outstandingobligations. Obligations of different countries will trade on differentterms even in situations in which the contractual conditions are identical.Different potential purchasers will put different valuations on the samedebt depending on their differing abilities to obtain service.

The sovereign risk problem has been seen as intractable; however,progress is possible through a two-pronged attack. First, it is necessary toseparate the default (sovereign) risk component of .he risk associatedwith the debt. Then it is possible to associate this default risk wvith athird-party guarantee priced at an actuarially fair rate. This guaranteeddebt could then either trade in the same way as obligations issued bydeveloped country governments or could provide the collateral againstwhich new securities would be issued. The insurance premia associatedwvith these obligations may be so high as to make the provision ofinsurance appear unfeasible. The second component of the plan is to findmeans of reducing the likelihood of default risk and, therefore, the size ofthe default insurance premia as well.

To analyze the likelihood of default, a formal model of the default-rescheduling process is required. Using an extensive form game, anexpression for the rescheduled payments is derived; if rescheduling takesplace and the conditions under which default will be threatened arechanlged, then rescheduling negotiations will follow. It is this lattercondition that is crucial to the argument. It combines "willingness topay" with "ability to pay." Throughout the 1980s, general obligationdebt has carried the implication that developing countries' ability to payhas been negatively associated with their contractual obligations, and thishas resulted in high default probabilities. Adjustment of contractual debtrepayment terms to give a positive association between ability to pay andcontractual obligations will result in significantly lower default proba-bilities and, therefore, in lower default insurance premia.

An obvious mechanism for obtaining the required positive associationis to introduce commodity price contingency into contractual debt


obligations. This proposal replaces standard interest payments with amixture of interest payments and payments linked to primary commodityprices. Powell and Gilbert (1988) argued that this form of debt would beadvantageous to developing countries that have high levels of commodityprice dependence. Hcre, the argument may be generalized because it ispossible to see any country as a portfolio of productive assets, many ofwhich will be associated with the price of an internationally traded good.Consequently, countries can issue a portfolio of debt with the associatedrepayment characteristics, and each of these components of the overallportfolio can provide the basis for a secure obligation.

The chapter is organized as follows. First, a model of sovereign debt isdeveloped. Then, the general terms necessary for securitizing debt will bediscussed, including a brief reference to the experience in securitizingmortgage debt. Next, the model developed initially is applied to the mainproblems faced in securitizing developing country obligations. Severaldifferent instrument designs are compared in an effort to determine thosemost suitable for securitization. Finally, the institutional framewvork inwhich these securities could be issued is examined.

Sovereign Risk

In standard financial applications, a default occurs when one of theparties to a contract fails to honor the terms of the contract. When theborrowing party is a country, the conditions that imply default are ratherelastic; a default occurs whenever the lender declares that the borroWerhas violated the terms of the ooligation. This approach emphasizes thatthe declaration of default is an option available to the lender that thelender may not wish to exercise.

In a private financial contract, declaration of default will trigger legalactions that will give the lender all or part of the sums owed. Theseactions are not available if the borrower is a sovereign nation or itsimmediate agent. In the case of sovereign debt, the declaration of defaultmay penalize the borrowing country by denying it subsequent access tointernational credit markets. Recourse to this action may be relativelyinfrequent for the reason that declaration of default removes the threat ofsanctions and, therefore, reduces the prospect of recovering the sumsowed.

A simple framework for understanding sovereign risk is an adaptationof a model used by Eaton, Gersovitz, and Stiglitz (1986). The defaultdecision is based on a comparison of the cost of honoring the contractterms with the penalties resulting from default. The borrowing countrywill choose to not honor the contract if its payments exceed the penalty.

PARTIAL GUARANTEES AND CONMMODITY CONTINGENCY 137

Figure 10-1 7he Default Decision

Borrower de h /

R(-R, R)

Lender Declares ReschedulesdeauX t

(-PA4 P-L) (-Q, Q)

This, in turn, will lead to a rescheduling decision on the part of thelender. This can be illustrated as the simple extensive form game in figure10-1. Here, the amounts in parentheses are the flow payoffs to theborrower and the lender respectively.

The borrowing cotuntry is scheduled to make a payment of R to thelender, but alternatively may threaten default. In that case, the lendermay declare default, resulting in the borrowing country making somecash payment, P, as a penalty. In addition, the borrowing country willlose future access to capital markets. Thus, if A is the value of this access,the net payoff to the defaulting country is -P - A. The lender will receivean amr v- t P - L where L is the deadweight loss associated withdeclan.g default.

On the other hand, if the lender faced with nonperformance does notdeclare default, the lender will enter into a negotiation to determine apayment, Q, of the rescheduled loan. The lender will choose negotiationiif Q > P - L. What will determine Q? Because by agreeing to reschedule,the dc3dweight loss L and the loss of access A are avoided, it appears thatthere is an incentive to bargain. The rescheduling negotiation can berepresented by the Nash bargaining game depicted in figure 10-2. Anysuccessful bargain must leave each side as well-off as in formal default.The outcome most favorable to the borrowing country is at ,B whereQ = P - L. The best outcome for the lender is at a where Q = P + A.Thus, in figure 10-2, the bargaining set is confined to the segment of the


Figure 10-2 The Rescbeduling Subgame

Lender'spayoff

\

L ~~~~~~~~~~L

Borrower's -PA 0payoff

downward sloping 45 degree line to the northeast of the threat point(-P - A, P - L). Any point in this set would be a conceivable solutionand can be represented by

(10-1) Q=P+wA-(1-w)L

for 0 < w < 1. For exaniple, setting w = 0.5 gives point y and constitutesthe Nash bargaining solution to this game.

This model implies that payment will be made according to schedule ifR < Q. Using equation 10-1, one sees that this arises if A > [R - P +(1 - w)L]/w. That is, if for the borrowing country the value of futureaccess to capital markets is sufficiently high, it will pay on schedule.Otherwise, it will threaten default. Taken strictly, the model implies thatdefault will never occur because rescheduling will always offer a Paretianimprovement; in practice, default threats by sovereign debtors typicallydo result in rescheduling.

This model may seem to overstate the case for Walter Wriston's viewthat "countries don't go bust." In fact, when lenders deal iepeatedly withsovereign borrowers, there can be a role for formal declarations ofdefault in that these may enhance the creditor's reputation as a tough

PARTIAL GUARANTEES AND CONIMODITY CONTINGENCY 139

negotiator. This bargaining power would tend to translate into anexpectation of favorable future bargains for the creditor (a high iv) and,thus, a high value of Q. The result would be to reduce the frequency ofnonperformance. A full discussion of these reputational issues can beinvestigated in a repeated game extension of the model (Grossman andvan Huyck, 1985).

The approach to sovereign risk adopted here stresses the voluntarynature of both deb service payments and default declaration. This doesnot imply, how-ever, that contractual terms are irrelevant because, asnoted here, the service obligation determines the set of circumstances inwhich default will be threatened and rescheduling will take place. Thus,although this approach is closer to the "villing to pay" model, "abilityto pay" does play an important rcle. In particular, if the default penaltyP and the value A of access to credit are treated as state dependent, therescheduled payment is,

(10-2) Q(s) = P(s) + wA(s) - (I - w)L.

In favorable states for the borrower, resulting perhaps from strongdemand or high prices for its exports, the borrower is likely to perceivea high value A(s) of future access and will be aware that the lender canextract a higher default penalty P(s). Consequently, if scheduled pay-ments, R, are not state dependent, the borrower is likely to pay onschedule. In adverse states, the opposite holds, and the country is likelyto violate the schedule. Notice that the way in which "ability to pay"feeds into the borrower's and lender's decision process is very different tothe often mechanistic relationships used in the "solvency" literature.

This general formulation is compatible with a variety of specificationsof penalties that have appeared in the literature. Cooper and Sachs(1985) and Sachs and Cohen (1982) assume that the penalty to default isproportional to income, Gersovitz (1983) introduces a penalty that isdependent on the importance to the debtor of the opportunity to trade,and Eaton and Gersovitz (1981) employ a penalty dependent on thecountry being excluded frorn the market for physical capital. Each is aspecial case of this formulation.

Even a powerful creditor will not be able to assure performance ifother '.-tors create a strong incentive to threaten default. That is, in theterminology of the model here, even if the creditor can bargain hard(achieve a high w), the '5orrower may still threaten default because thepayment terms (R) are severe, the default recovery (P) is low, or the valueof future access (A) is low. Clearly, the nature of these variables is crucialto the predictions of this model.

The value of future access to credit markets (A) will reflect thedeveloping country's perception of the likely future demand for its


products. This, in turn, will depend on the country's resources andcapabilities, the level and mix of world prod:!ct demand, and the patternof international trade barriers. There is little that can be said about thesewithin the scope of this chapter. It is clear, however, that anything thatis conducive to the prospects for fuzure development will tend to raise Aand, as a result, to reduce the problem of sovereign risk.

The creditor's loss of declaring defau!t (L) includes the direct costs ofexacting a penalty from the borrower. More important than this,however, could be the indirect effects of a declared default. Banks mayrnaintain nonperforming loans on their books at full value. Were they todeclare a default on the loans, they would be forced to take a chargeagainst the capital of the firm. This in turn could mean that they wouldnot meet capital adequacy requirements, thus forcing them to shrink theirentire balance sheet. Creditors in this situation may place a very highvalue on the loss of declaring default. The model used here suggests thatthis tends to enhance the probability of threatened default. However, ifa creditor has made an effort to remove this constraint through theprovision of loan loss reserves, L need not be so large. Our model showsthat this tends to improve the renegotiated terms for the creditor with theeffect of decreasin, the likelihood of default.

The value or the payment (P) that can be extracted upon default willdepend upon the legal means available to the creditor for enforcing thecontract. In the most extreme form of sovereign risk, the creditor has nolegal recourse (P = 0). Somewhat counter-intuitively, this apparentadvantage for the debtor will mean that nonperformance will be v;.wedas relatively more likely, so that amounts that can be borrowed at giventerms will be limited. A sovereign borrower can overcome this problemby precommitting to relatively severe penalties in case of default. Themost obvious way that this can be done is by placing some significantasset as collateral in an entity that falls under some legal regime otherthan that controlled by the borrower. It may be that a pa ticular contractform may have a legal status that is relatively advantageous from thisviewpoint. This point, as well as the possibility that payments schedules(R) can be written to minimize nonperformance, is addressed later in thischapter.

Securitization

A security is generally taken to be a financip! obligation whose termsare standardized so that the holders of a parcicular type of security willbe treated equally. Standardization is important in determining whether

PARTIA; GUARANTEES AND CO1MMODITY CONTINCr-r ^ 141

an instrument is traded successfully in a secondary market. When asecondary market is active, a holding in the security may be quite liquidin the sense that it could be sold quickly without a great effect on its price.Secondary trading is also promoted when a security's credit risk is readilyassessed. If an issuer's credit standing is not well established, its securitiesmay be very liquid if they have been guaranteed by a separate, credit-worthy institution.

Typically, an elaborate and costly process is involved in the issuing ofsecurities, including registration with regulators, legal drafting, andmarketing. What are the merits of securitization that justify these costs?The principal advantage of issuing securities derives from the liquiditythat can result. By making it possible to trade in and out of positions ina security, the range of investors wvho may be willing to hold . isexpanded. Consequently, the supply of funds is increased, and the pricepaid for the funds is reduced.

A further implication of active secondary trading is that the value ofthe security is established in the marketplace. By contrast, an existingbank loan that is held on the books of the originating banks is nottypically valued in a market. Consequently, because of changing marketconditions or the conditions of the borrower, variations in the value ofthat obligation are not typically reported, except in extreme cases such asnonperformance. In the terminology of principal-agent theory, thelending institution is h. principal, and the borrower is the agent. Theobservability of actions taken by the borrower will be enhanced becausemarket prices aggregate information available to a wide group of agents.As a result, actions that tend to decrease the value of the securities will bediscouraged. In this way, market valuation of securities provides anelement of discipline for managers.

Although these arguments are most often applied to private profit-making enterprises, they are equally valid in the context of sovereignborrowing. One of the major problems with the current structure ofdeveloping country debt is that it is bome most heavily by the sharehold-ers of the commercial banks in developed countries. Providing access toother sources of finance would be a major advantage for many develop-ing countries, and market valuation of these debts would providereassurance to bank shareholders. Furthermore, the pri.e of existingsecurities will indicate the terms that developing countries will likely faceon new issues, and this provides an incentive to maximize the value ofthese securities.

The fact that a very large proportion of developing country borrowinghas taken the form of general obligation bank loans despite the advantages of securitization is testimony to the obstacle to securitizationresulting from sovereign risk. It will not be possible to completely

142 COMMirODITY RIsK MANAGEMENT AN[) FINANCE

eliminate these difficulties, but it may be possible to minimize theirimpact. This can be done, first, by iso!ating the sovereign risk from theother components of risk and, second, by adopting contract specifica-tions that reduce the former component at the expense of the latter.

Secuiritizing Developing Co-try Obligations

In considering expanding the scope of securities in developmentfinance, interest has tended to focus on debt/equity swaps. The use ofequity finance may have considerable potential in some developmentprojects. Its use in the presence of sovereign risk, however, is likely to berestricted. The reason is that equity is a claim on a residual profit stream.The performance of the stock will depend upon the actions of themanagers of the assets. VNYhen monitoring and control are difficult, thereis Ar. agency probl mv. which means that the return to shareholder equity.an suffer. Such pioblems have the potential of becoming extreme in thepresence of sovereign -:sk. Consequently, one would expect considerableinvestor reluctance to acquire the residual income claims against sover-eign borrowers.

Banking relationships are widely recognized as means of overcomingproblems of asymmetric information. This may explain the widespreadreliance on general obligation bank loans for development finance inrecent years. The performance of these loans in the 1980s has made itclear that even if such relations are advantageous from the point of viewof information, the problem of sovereign risk can mean that bank loaxismay be de facto residual income claims. Recognition of this has meantthat banks have been resistant to extending further general obligationcountry loans.

Recent experience has shown that a number of activities that werepreviously thought of as the exclusi- 9. province of bank lending can besuccessfully given access to securities markets through appropriateinstrument design. A prime example of this has been the development ofthe secondary mortgage market in the United States. The U.S. mortgagemarket is complex; however, most of the new securities used in thisindustry, referred to as mortgage-; acked securi:ies (NlBss), fall alongrairly standard lines., In most cases, [he underlying assets in the securityare individual mortgages that are, to some extent, standardized withrespect to terms (e.g., maturity date, coupon rate, and so on). Typically,these underlying mortgages imply a certain risk that the property willdefault, in which case the mortgage holder receives the liquidation valueof mortgaged property. Furthermore, property owners typically have the

PARTIAL GUARANTEES AND COMMODITfY CONTINGENCY 143

option to prepay so that the mortgage holders are uncertain with respectto the duration of these obligations.

The process of crealing an MBs can be viewed as the splitting of therisks containtd in a se t of mortgages. First, in most cases, an NIBS isendowed with a guarantee against default granted in return for aninsurare^e premium. by some third part. The MIBS itself is a title to aproport'inate share of the total revenues from the underlying mortgagesincluding interest, scheduied payments of principal, prepayments ofprincipal, and default insurance claims.2 In effe~:t, the insuring bodyassumes and prices the default risk. The prepayment (i.e., duration) riskis red,iced through the efiect of the law of large numbers applied to a poolof mortgages. The remraining prepayment risk and the interest rate riskare left to be priced in che market for \tBss.

The rapid developmen t of the U.S. sNBS market suggests tha- if it ispossible to isolate and goarantee performance risk, the rer..ainingcomponents of risk may be assumed and priced by the market.3Analogously, an important srep towsard facilitating the sec,iritization ofdeveloping country obligationls would be to find a means of channelingthe sovereign risk component of these obligations into the hands of thosewho have a comparative advantage in bearing this risk.4 The vehicle foraccomplishing this would be for the appropriate body to insure theperformance of the developirg country loans in return for an insurancepremium. In the case of ronperformance by the borrower, the insurerwould pay the lender the s,.heduled paymniei and, in return, wouldassume the nonperforming loans as a portion of its portfolio. The insurerwould then negotiate rescheduling with the nonperforming borroweragainst the threat of declarinl, the borrower in default.

An important question is which agency or agencies should provideperformance guarantees. Expe rience in the NIBS market indicates that theguarantees may originate from either the private or the public sector.1hus, the Government Nationlal Mortgage Association (Ginnie Mae) is a*ub1ic-sector body, the Federal National M'ortgage Association (FannieVae) is a quoted corporation with agency status, and the Federal r'omeLoan Mortgage Corporation (Freddie Mac) is a private corporation alsovith agency status (Thyge.-son, 1985).

Ar agency will have a comparative advantage in tHis function if it can)ffer this insurance at a lower premium than other aL .ncies. From figureL0-1 and equation 10-2, one notes that, allowing for general contingentayoffs, R(s), the insurarce premium will be

10-3) f (R(s) - Q(s))f(s) ds

PARrIAI GUARANTEES A OM.MODITY CONTINGENCY 145

The Design of Cormrnodit,-Contingent Instrumentsand Associated Guarantees

!n principle, this franuwork implies a simple criterioii for determiningthose securities most appropriate for issue by developing countries.Securities with different payoff profiles, R(s), will generallv implv dif-feren- 'ike!ihoods of default and, consequently, different insurancepremia. One erion for security* design is te minimize the insurancepreimium, ubject to the constraint that the default-risk-free value of thesecuritics equals or exceeds the finance required.7 Gi-ren the functions,P(s) and A,s), this is a straightforward problem.

In practice, the func.ions P'(s) and A(s) are not necessarily well knownso that the issue o' optimal contract design u- Id r qrlire considerableinvestigation. Here some of the considerations that appear importalnt ilight of recent experiences are noted. First, consider the general specifi-cation of a contingeent instrument, R(s). Note that in the 1980s, manycemnmodity-dependent Jeve!oping countries found chat repayments due,R(s), were higlh in those r.,es precisely when incomes were low. Thisnegative associatiot. cf Qks) and R(:) makes threatened default andrescheduling a very likely outcome in states adverse for the borioN,.r. Incontrast, wri 'ng contract terms so that R(s) is positively correlated withQ(s) V.'ould , the probability of default risk.

Earlie,, it :uggested th?.t Q(s) is likely to be posirively correlatedwith current and anticipated future export earnings X(s). This suggestsmaking the repaynments schedule state dependent through X(s) asR(X(s)). T-here are, howeve: twvo strong arguments against this proposa .Firsr, contingency on export revenuesu will introduce mora! hazardcon.siderations through output and stock decisions. Second, this form ofcontingency would work against standardization-a contract issuedagainst Zaire's export revenues wvould have different characteristics froma contrae: against Peru's export revenues, even though both countries aremajor copper exporters. P.-ovided that m-rkets are competitive, bothdifficui:ies can be circum-.xented by introducrng contingency throughinternationally cquoted prices and exchange rates. 8 If the relevant price isC(s) and if the devek ping country's oblige-ons are contingent on theprice, R(C(s))-, the country's scheduled net revenues in state s fot oneunit9 of exports are,

(10-4') Y(s) = C(s) - R(C(ss)).

If the default penalty, P, and the value of future access, A, are functionsof the price of the country's product, the condition to induce theborrower to respect the contract terms can be wA'ritttn as

(i0-S) R(C(s)) < P(C(ss)) + E 4(C(ss)) - (I - w)L.


When the obligation is straighc debt, the nayment is a constant in allstates, R(s) = R0. If for low values of the commodity price the penaltyand v-.lue of access are low, then there will be a critical commodity piiceCG below which the country will have an incentive to threaten default.That is,

(10-6) Ro > ?(C(s)) + tvA(C(s)) - (1 - w)L for C < C*.

This situation is broadly what has been demonstrated by the ex--rt-nceof many developing countries in thle 1M'3Os and providcs . L .icmctivation for seeking to introduce some form of :Or.on. V.. cntin-gency in the payments of the de-'eloping countries.

A basic way of i.5trvducing commodity contingency when a projectfaces co.nmodity price uncertainty is to protect against low commodityprices by hedging in forward or futures markets if they are available.

e-v v speciically, by financing through a combination of straight debtand forward sales at a forward price F, the payment terms become,

(10-7) R(C(s)) = Ro + C(s) - F.

This will assure a constant income Y(s) -- F - Ro under the contracts,although this does not necessarily assure an incentive to fulfill thecontract terms. For, under 10-7, the inequality 10-S may or may not bemaintained in all states depending upon the precise way that P(C(s)) andA(C(s)) va7r with C. If P(C) = C and the hedgeab' value exceeds thefixed pay.rent, F> Ro, however, then 10-5 necessarily u 'l hold. In tact,one of the possible advantages of a commodity forwatd contract at amarket falling outside of the borrower's legal jurisdiction may beprecisely that, in case of default, the borrower's commodity deliveries in,he marlket may be attached through legal means.

Several considerations suggest that straight debt combined with for-% -rd sales may not be the best means of assuring that the problem of

'ign risk is reduced to the point that insu'rance would be feasible.l )roblem that arises with this combination is that generally creates

two credit risks, not one. To illustrate how this Liuld have adverseeffects, suppose that the ca,mmodity price is low. The borrower willsimultaneously have an incentive to perform on the forward sale and yetto threaten default on the debt contract if the depressed commodity pricereduces the -alue of access and if the penalty on the debt contract is lowor nonexistent. One way around this is to make the forward contractitself part of the collateral for the debt contract. The alternative would beto combine the payment features of the debt plus forward sale into asingle instrument-that, in effect, would become a commodity-contin-gent bond.

Even if combining the characteristics of straight debt and a forward

PARTIAL GUARANTEES AND COMMODITY CONTINGENCY 147

sale into a commodity bond can reduce the problems of rr iltiple creditrisks, it does not necessarily assure that relation 10-S will hold in allstates. In particular, because, under 10-7, the payment rises with thecomr- *dity price, favorabie states might create an incentive to default ifP and A do not rise to keep pace with the commodity price. It may wellbe that if a commodity producer can retain the profits of a commodityprice boom, the value of future access to credit may not rise and mayactually fail as C rises beyond a certain range. A package to circumventthis problem is a combination of straight debt, the sale of a commodityforward at F, and the purchase of a commodity call with a strike priceK > F, which can be wri ten as,

(10-8) R(s) = Ro + C(s) - F - max(0,C(s) - K)

Thus, the m.ximum payment would be Ro + (K -F).So far, this discussion has ignored a number of constraints that rnay

impinge on instrument design. For instance, the schedule outlined inequation 10-8 may imply zero or negative payments in some states ifcommodity prices fal1 below a critical level (i.e., if C(s) < F - Ro). Thisfeature may be unacceptable to investors. A solution to this would be todesign an instrument that possessed both a minimum and a maximumpayoff. For example, straight debt combined with a call purchase andwritten call at a lower strike price results in

(10-9) R(s) = Ro + max(0,C(s) - K,) - max(O,C(s) - K2),

where K2 > KI. This double-call feature guarantees a minimum paymentR(s) = Ro, it has a range of commodity prices in which payments increaseas the commodity price rises, and it has a maximum payment of R(s) =Ro + K2 - K. If penalties from nonpayment fall when commodity pricesfall bclow K1, this type of instrument will necessarily increase theinsurance premium. This fcarure might be viewed as necessary to ensurethat a sufficient volume of funds is forthcoming from investors.

In this discussion, the institutionai structure that would be mosteffective in the process of securitization has not been specified. In fact,many arrangements might be effective. An interesting possibility is toconsider the guarantee as a put option on the value of the loan. Thus, theholder of the guarantee pays a premium and obtains a put optioncovering a portion of the loan at a specified e cercise price. The holder ofthe put compares the value of that portion of the loan covered with theexercise price of the option and exercises the put if the value of the loan,for whatever reason, falls below the exercise price. On exercising the put,the holder receives the exercise price, and the put writer assumes tha-portion of the loan covered. Note that, if t}-. writer of the put has acomparative advantage in bearing aovereign risk, then there should be a


Figure 10-3 A Financing Structure

Com t cInvestorso

Commodity contingentsecurities

Commodity contingenloans

Developing countryfinancial institution

premium for the put that would be acceptable to the purchaser, but thatwould make put writing on average profitable.

The flexibility of this arrangement is very great indeed. In particular,the maturity of the put option and the times within its life that it may beexercised (referred to as "exercise windows") can both be altered.Furthermore, the exercise price of the option can be fixed at particularlevels and could, in principle, be made contingent on the commodityprice. This flexibility can be used to design a guarantee that providesmaximum insurance against sovereign risk elements at minimum cost.

Figure 10-3 illustrates the concept of the put option guarantee for agiven set of relations between various institutions. The developed countryfinancial institution could be a commercial bank with exist .g loans to aparticular developing country or might be a new type of lender entirely.The characteristic of this structure is that the lender offers commodity-contingent loans and issues commodity-backed securities to a wide classof investors. Attached to the commodizy-contingent loans are put optionsheld by the developed country financial institution covering some portionof the loan to the developing country. These options will ensure a highercredit rating for securities backed by such -loans. The put optionguarantee separates out significant elements of the sovereign risk fromother types of risks-akin to the separation of different types of risks inthe U.S. mortgage backed securities market discussed earlier.

These instrument designs and potential lending strcictures are onlyintended to be illustrative of the implications of this discussion ofsovereign risk. Considerable further research is required. Given more

PARTIAL. GUARANTEES AND) CO.MMODI rY CONTINGENCY 149

precise information on the nature of default penalties and the value ofaccess and investor preferences, it should be possible to design appropri-ate payment schedules and structure guarantees to suit.

Conclusion

It has been argued here that insured, contingent-payoff securities couldreplace much of the general-obligationi governmental borroNving as asource of developing country finance. Furthermore, for reasons ofstandardization and moral hazard, income (export revenue) contingenlcyis a less promising avenue than contingency on a publicly observable,nonmanipulatable variable such as competitive commcdity prices orexchange rates. A possible objection to this is that contingency oncommodity prices and foreign exchanlge may be of limited relevance tomany larger and more diversified developing countries, particularly thosewith substantial exports of manufactures. These problems are notinsurmcuntable. A country may be viewed as a portfolio of productiveassets, each having a value more or less linked to the price of its good(s)in world trade. Thus, the finance for a country would give rise to acorresponding array of commodity-contingent liabilities, plus someamount of noncontingent obligations for activities for which contingencyis unfeasible.

In effect, securing general developing country obligations can beviewed as creating a "strip" of commodity-contingent claims, each ofwhich is isolated from country-specific sovereign risk. As in the case ofmany MBSS, by unbundling the risks this way, they can be sold to agentswith comparative advantages in bearing these risks at advantageousprices so that their value is greater than when bundled.

The strip concept reinforces the argument for standardization. Thus,given the appropriate third party insurance against default, countriessuch as Zaire and Peru would both have an interest in issuing standard,copper-contingent bonds (backed by thehi copper export revenues) withthe same payoff profiles, R(s). These securities will appear identical toprospective purchasers, in the same way that the purchaser of a futurescontract does not need to know the identity of the seller. Nevertheless, itshould be recognized that the insuring body will view these as differentrisks because the values of future access, A(s), and the penalties, P(s), maybe different. In this event, the inr,urance premia required would differ.

Another possible objection to this proposal is that the developingcountry sovereign risk is not insurable bccause it will be highly correlatedacross countries. The one important reason for this degree of correlationis that developing countries are extremely dependent upon a relatively


small group of commodities for their export earnings. As a result, ageneral depression of commodities has an adverse impact on manycountries. Because of this, there is yet further reason for commodity-contingent securities. Once commodity price exposure is split, developingcountry sovereign risk will be a residual that is more likely to beindependent and thus more readily insurable.

It is not only, and perhaps not mainly, governments who will be theissuers of these new insured, contingent securities. In fact, many arrange-ments appear possible. In many cases, countries may find it effective todecentralize the finance decision and allow specialized enterprises toobtain their own finance and issue liabilities whose contingency matchesthe enterprise's earnings profile. Alternatively, the borrower might be aprivate corporation whose ability to borrow is compromised by aperceived threat of nationalization or expropriation. Again, it could be aprivate commercial bank that would post as collateral a portfolio of(existing or new) developing country loans.

What would be the market for the new securities? Once the sovereignrisk insurance is arranged, the success of the issues is largely a functionof the abilities of the financiers in designing the payoff profiles and inmarketing. These skills have been well developed elsewhere, and there isevery reason to think they are applicable here. In particular, commodity-contingent bonds may well behave much like equities of private com-modity producers. Consequently, combined with commodity futures andforwards, there may be ample scope for hedging and arbitrage with theconsequence that the liquidity of the insured, contingent claims may bequite high.

Finally, it is impossible to state here which institutions are best capableof offering the required sovereign risk insurance. This analysis shows thatit is a matter of who can offer a given insurance at the smallest premium.This, in turn, will depend on which institution can extract the greatestpenalties, have the biggest impact on future access to finance, and bargainhardest. There is a presumption that this would be a large, verycreditworthy institution that has been a long-term participant in inter-national lending. It needs to be emphasized that the insurance describedhere would be self-financing along actuarial grounds. Consequently, theinsuring body could be a private, profit-seeking organization. Mostimportant, no matter whether the insuring body would be priva,: orgovernmental, the guarantee would not require access to governmentaltax revenues.

PARTIAL GUARANTEES AND COMMIODITY CONTINGENCY 151

Notes

1. In 1983, the outstanding valuc of ,oBS obligations was $278 billion (Seiders, 1985), afigure comparable to the approximately S249 billion of outstanding nonguaranteeddeveloping country debt (short and long term) in private hands at that time. See the WorldBank (1988), pp. 87-88.

2. This describes a "pass-through," such as a Ginnie Nae. Othcr forms of mhIBss strip outthe interest and various tranches oi principal repayment.

3. In the context of lending to de% eloping country governments and their agencies, theserisks would be associated with var.-bilhry in export earnings, exchange rates, and interestrates.

4. The concep. of comparative advantage in bearing divcrse typcs of risks is discussed inLessard (1986).

S. Later, the 'ontiactual payments R will also become state dependent.6. In the United ..>ates, the cffect of guarantecing institutions requiring that mBss confornm

to certain standard forms was to create a high degree of standardization, which aided thegrowth of active secondary trading.

7. This critcrion is appropriate for a risk-neutral borrower. Risk aversion or intertem-poral consumption smoothing may also bc a consideration affecting the supply of securities.Most of the literature on commodity contingency takes this to be the sole objective forcontingency. This analysis shows that the facilitation cr sccuritization is another, possiblymore significant, consideration in structuring payoffs. In effect, this deals wiiti the demandfor securities.

8. If markets are noncompetitive, price-contingent cont-acts may alter the incentivesborrowers face in their production decisions. In this case, the price-contingent contractsmay be manipulatable. See Anderson and Sundaresan (1984) and Newbery (1984). Moregenerally, price contingency may affect borrower's invcstment allocation decisions. SeeBesley and Powell (1988).

9. Here, the figure has been normalized to ;llow for a quantity of unity. This is a harmlesssimplification given that quantiry uncertiinty is being subtracted in this discussion.

ConclusionTheophilos Priovolos and Ronald C. Duncan

The collection of papers brought together in this volume was written toadvance knowledge about the demand, pricing, and use of commodity-linked finance.' Fall extended the work of O'Hara on the demand forcommodity bonds and showed that the demand function for commoditybonds has two components-a speculative component and a hedgingcomponent-and that the demand for commodity bonds is positive whenthe investor has a lower relative modified risk tolerance than the market,that is, a higher relative modified risk aversion. Rajan simplified the workof Schwartz on the pricing of commodity bonds by introducing the use ofbinomial pricing theory. Thompson and Myers extended the typicalone-period, mean-variance framework for the computation of the opti-mal commodity hedge ratio by the use of vector autoregression; thus,they were able to capture variations in both export patterns anddepartures from random walks in commodity prices. Claessens extendedthe typical optimal hedge methodology to include exchange rate risk, inadditioIn to commodity price risk. Ball and Myers further extended thisoptimal hedge methodology to a sovereign borrower without anyexisting debt.

The Wright and Newbery paper quantifies the costs of export revenuevariability and the potential for risk reduction through reserve manage-ment and commodity hedging and demonstrates the importance of riskmanagement for consumption smoothing. Employing a model of defaultbased on the tradeoff between the borrower's expected future consump-tion smoothing benefits from external finanr, and the cost of meeting itsobligation, Wright and Newbery show that, with commodity bonds, theprobability of default is reduced. Such contracts reveal the "permanent"level of income that the country could count on from its commodityexports.

I52

CONCLUSION 153

Anderson, Gilbert, and Powell show that borrowers and lenders do notalways have a comparative advantage in hedging all types of risks. Theyshow that the probability of default risk reduces w'hen the contract termsof an obligation are written so that the repayments schedule dependls onincome. Moral hazard and cost standardization concerns constitute twostrong arguments against using "income" such as export earnings.Provided markets are competitive, both difficultics can be circumve:itedby introducing contingency through internationally quoted price andexchange rates. They show that, for low values of commodity prices, thedefault penalty and the value of future access to finance are low (if theyare a function of commodity prices) and that, beyond a critical commod-ity price level, developing countries will have an incentive to default.

A standard recommendation has been that when a project facescommodity price uncertainty, it should be protected against the risk oflow commodity prices by hedging in fornvard markets or other similarmarkets (such as futures, options, swaps, etc.) if they are available. Morespecifically, by financing through a combination of straight debt andforward sales, this will assure a constant income for the borrower. Thisstrategy does not necessarily assure the incentives to fulfill the contractterms, however. Anderson, Gilbert, and Powell find the likely conditionsunder which incentives will exist to ensure that the terms of the contractare fulfilled. Several considerations suggest that straight debt comrbinedwith forward sales may still not be the best means of assuring that theproblem oi sovereign risk is substantially reduced.

One problem that arises with this combination is that it generallycreates two credit risks, not one. Anderson, Gilbert, and Powell point outthat one way around this difficulty is to make the forward contract itselfpart of the collateral for the debt contract; another way is to combine thepayment features of the debt and the forward sale into a single instru-ment. This would become a commodity-contingent bond. If the defaultpenal.-y or the vaiue- of access does not keep pace with the commodityprice, the commodity bond will not necessarily assure that the contractwill not be circumvented. It may well be that if a commodity producercan retain the profits of a commodity pricc boom, the value of futureaccess to credit may not increase and may actually fall as prices risebeyond a certain range. A package to circumvent this problem is acommodity bond that combines a straight debt, the sale of a commodityforward, and the purchase of a commodity call at a strike price higherthan that for which it was sold forward.

Clearly, such an instrumcnt could be marketed best by the institutionproviding insurance at the smallest p:emium for any residual sovereignrisk. This, in turn, will depend on who can extract the greatest penalties,have the biggest impact on future access to nnance, and bargain hardest.


There is a presumption that this would be a large, very creditworthyinstitution, which has been a long-term participant in internationallending. It needs to be emphasized that the insurance the three authorsdescribe could be self-financing along actuarial grounds. Consequently,the body could be a profit-seeking organization. There is also the pointthat the residual guarantee will be significantly less than that required ifsecuritization of straight debt is contemplated. In other words, theinstitution's capital would be able to finance a greater amount of loans (ifthey were structured in the commodity-linked form) with the sameamount of risk it would have otherwise been willing to assume.

Commodity-linked financings have impo'tant advantages in the exter-nal financing of developing counzries relative to the traditional alterna-tives of foreign currency denominated, general obligation borrowing, ordirect foreign investment. They allow developing countries that areovere-posed to particular risks, relative to those in the world economy,to shitt these risks to world capital markets on an ex ante basis. Bycontrast, general obligation financing also shifts risk, but only on an expost basis through nonperformance with its attendant deadweight pen-alties. In contrast with direct investment and other forms of finance thatalso shift risk on an ex an:te basis, commodity finance is linked toobservable, exogenous outcomes and does not require the same degree ofcost.y monitoring or intrusion of foreign forces into domestic decisionmaking. Commodity price-linked finance is preferable to other forms ofindexed finance because moral hazard and standardization consider-ations work against such other forn.-.

To sum up, commodity-linked financings have expanded rapidly in thelate 1980s, but they have been mainly confined to entities in industrialcountries. Creditworthiness questions handicap the developing countriesin their access to this type of financing. Unless their credit standing canbe enhanced, maybe through a third-party guarantee, many developingcountries will find it difficult to have independent access to internationalfinancial markets for such finance, and they may have to depend onbilateral and multilateral aid and development agencies for their externalfunding needs. It is clear that the insurance premium required for suchthird-party guarantees is minimized when the insuring body has acomparative advantage in bearing sovereign risk and when the contrac-tual terms are contingent on factors affecting the borrower's present andfuture earnings. Commodity-price-contingent instruments are shown tobe the most suitable obligation for the developing country needs.

To achieve better risk management in the commodity-dependentdeveloping countries, the implications for the practices of internationaldevelopment agencies on the basis of the findings of the papers includedhere are:

CONCLUSION 155

* To support, with technical assistance, enhancement of institutionaland human resources capacity in developing countries in the area offinance, in particular, in commcdiay price risk management

* To support better risk managemnent practices in project and programlending in developing countries through technical support and/orappropriately tailored lending

o To support commercial cofinancing with the use of partial guaran-tees and to make their own loans commodity price-contingent

* To support, in the context of restructuring of commodity-dependentdeveloping countries' debt, the exchange of existing debt for appro-priately tailored commodity price-contingent debt

* To institute methods to hedge appropriately the derivative commod-ity exposure in the financial markets by commodity price-linkedfinancings.

Note

1. We would like to thank Todd Petzel and Donald R. Lessard for their enlighteneddiscussion of several of the contributions in this book wlien they were presented during the1988 American Agricultural Economics Association meetings in New York. This chapterincorporates as best as possible their major comments. For riore details, see Petzel (1989)and Lessard (1989).

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(Page numbers in italics indicate material in tables.)Africa, dependence on commodity exports Caisse Nationale d'Energie, bond issued

in, 1 by, 11Algeria, trade shock in, 2 Call option, 12, IS, 33-34, 147Aluminun-linked financing, 36 Canada, 12, 29-30, 37Andersor., Ronald, 6, 153 Capital: hedging with commodity-linkedAsia, dependence on commodity exports bonds and, 116-20, 123; hedging with

in, 1 conventional loans andAsset returns (demand function analysis), commodity-linked bonds and, 121-23

40-42 Capital Asset Pricing Model (CAPM), 39,Australia, 12, 29 40Autoregressive conditional Ca ; (commodity price), defined, 14; in

hereroskedasticiry (ARCH), 106, 107 pricing model, 72-74, 7SAutoregressive moving average (ARMA), Carr, Peter, 61, 125

106 Central Bank (Taiwan), gold puirchase by,29

Ball, Richard J., 6, 152 Certificates of deposit (CD), commodityBananas, 2, 91, 93 indexed, 13Beef, 2, 91 Citibank, loan underwriting by, 38Belgium, use of gold bonds in, 16 Claessens, Stiin, 5, 97, 152Binomial pricing model: assumptions Coffee, 2, 91, 93

about, 62-67; bivariate normal Cohen, Daniel, 139distribution in, 79-81; caps in, 72-74, Collars (commodity price), defined, 1475; compar-d with Schwartz model, Cominco Ltd., 37-3870-78; commmodity bundle price in Commodity bundle price in pricing model,63, 72; continuous time model in, 79; 63, 72convenience yield in 63, 70, 75; coupon Commodity Convertible Bond (CCB),rate in 62, 70, 75: debt in, 63, 70, 72, defined, 6175; extensions in, 70; firm value in, Commodity Futures Trading Commission62-63, 65, 70-72, 74; interest rate in, (CFTC), 1263, 70; parameter determination in, Commodity indexed certificates of deposit,67-69; payouws in, 63, 70 13

Black, Fischer, 56 Commodity-linked bonds:Bollerslev, T. B., 106 capital-constrained producers and,Bond International Gold (mine), gold 11G-20, 123; conventional loans and,

loans and, 16 121-23; estimation of optimal portfolio

Bonds (see particular kind of bond) of, 89; external debt allocation modelBreeden, D. T., 50, 51, 54, 104 and, 86-89, 93; external debt allocationBrennan, M. J., 56 model empirical application (CostaBudget equation (in demand function Rica) and, 90-93; historical

analysis), 42-43 background on, 4-5, 11; issued byBullion loans, 13 sovereign lenders, 125, 127-28; issuers

169

170 INDEX

of, 12; kinds of, 11-12, 13-14, 61, Cox, J. C., 51, 56, 62124-25. See also Demand; ;'ricing Crude-oil-linked financing, 31-37

commodity-linked securities Currency: commodity exporters and

Commodity-linked financing: importers and, 95; debt composition

aluminum-linked, 36; copper-linked, 36, and, 1-2; gold-linked financing and, 16,

37-38; developing countries and, 11, 30145-49; gold-linked, 13, 14-30; Currency composition: altering, 97;

nickel-linked, 36, 37; oil-linked, 31-37; commodity risk and exchange rate

proliferation of, 11, 12-13; as risk management model and, 103-06;

management program, 4; silver-linked, commodity risk and exchange rate

12, 30-31, 32; uncertain commodity management model application and,

price and, 58, 59. See also particular 106-10; cross-currency movement and,

kinds of bonds; Pricing of 95-97; external liability and, 98, 100,

commodity-linked bonds 101; hedging and, 99-101; real risks in,

Commodity price risk, 1, 155 101-02; speculative decisions and,Commodity prices: caps, floors, and 98-99, 102

collars on, 14; hedging instruments and Currency swaps, 97uncertain, 96; pricing ofcommodity-linked securities and, 58, Danthine, J. P., 11959, 62; relations between exchange rate Debt: Algerian, 2-3; commodity bondand, 99; risk and external debt pricing and, 61, 63, 79; commoditymanagemnent and, 97, 101-02; bond pricing model and senior, 70, 72,securirization and, 149, 150; volatility 75; composition of developing country,in, 95-96 1-2; crisis in Costa Rica, 2, 90-93;

Commodity risk and exchange rate currency choice and external, 101, 102;management model, 103-06; empirical currency composition and, 100, 101;

application of (in Indonesia and general obligation bank loans as, 146;Turkey), 106-10 hedging instruments anid external,

Commodity variable-rate loans, 13 97-9g, 99; model for allocating optimalConsumption smoothing external, 86-89, 93; portfolio

(commodity-dependent exporters), 152; estimation, 89; sovereign debt risk and,

by borrowing and lending, 126-27; 135, 136-40, 141, 142, 143, 144,commodity bonds issued by sovereign 147-48, 149lenders and, 127-28; default and, Debt service, 1, 85, 116, 123; in Costa

127-28; default constraint binding and, Rica, 2, 90; cross currency exchange129-31; default constraint nonbinding rate risk and, 96; exports and, 96-97;and, 128-29; default prevention and, hedging policy and, 100-01; in

125; export risk and, 124; income Indonesia, 108, 110; securitization and,variability costs and, 125-26. 127, 128, 135; sovereign debt risk and, 139; in129; interest rates and, 129; risk and, Turkey, 109, 110128; sovereign borrowing and, 125 Default, 57, 152, 153; choice of

Continunus time model, 39, 79 commodity-contingent instrument and,Convenience yield (commodity bond 146, 149; consumption smoothing

pricing), 63, 70, 75 (commodity dependent exporters) and,Cooper, R. N., 139 127-31; loan insurance and, 144;Coomner, P. H., 40 mortgage market and, 143; risk and

Copper-linked financing, 36, 37-38 pricing of co,nmodity-linked securities,

Costa Rica, trade shock in, 2; optimal 58-60, 62, 73; sovereign borrowingexternal debt allocation analysis and, and prevention of, 125; sovereign debt

90-93 risk and, 135, 136-40Coupon rate in pricing model, 62, 70, 75 Deficit (current account), 87

INDEX 171

Demand: continuous-time intertemporal Fall, M. A., 11, 152model for, 39; determinants of, 48-SI; Federal Home Loan Mortgagefunctions, 45-48, 53-55, 152. See also Corporation (Freddie Mae), 143Multigood case; One-consumption good Federal National Mortgage Associationcase model (Fannie Mae), 143

Developing countries: commodiry-linked Financing. See Aluminum-linkedfinancing and, 11, 145-49, 154; financing; Commodity-linked financing;commodity pricc risk and, 1; debt Copper-linked financing; Gold-linkedcomposition in, 1-2; exchange rate financing; Nickel-linked financing;hedging in, 96; secu inzation and, 135, Oil-linked financing; Silver-linked142-44, 149-50 financing

Deviation analysis (hedging with Firm value in pricing model, 62-63, 65,commodi:y-linked bonds), ilS, 117, 7R72, 74120 Fishlow, Albert, 132

Dieffenbachl, B. C., .54 Floors (commodity price), 14, 61Dive-sification, 97-98, 124 France, 11, 14-15

Eaton,'tonathan, 12.5, 132, 136, 139 Generalized Autoregressive ConditionalEaton lonthan 12S 132 136 139Heteroskedasticity (GARCH), 106, 107

Echo Bay Mines, Ltd., gold-linked security et eresticity G ,an, '51 Germany, interest rates in 2,

and, 15-16 Gersovitz, Mark, 125, 132, 136, 139Eichengreen, Barry, 131 Gilbert, Christopher, 6, 136, 153Electricity, bond indexed to price of, 11 Giscard bonds, 14-IS

Engle, R. F., 106 Gold-linked financing, 13; convertibleEuromarket, S, 12 issues in, 26-23; examples of, 14-15;Evnine, Jeremy, 62 length of loans in, 29; price of goldExchange rate: commodity prices and, 99; and, 30; size of loans in, 16, 29;

commodity risk and exchange rate warrant issues in 16, 17-25management model and, 103-06; Gold repos 13commodity risk and exchange rate Goverment National Mortgagemanagement model, empirical Associati-'n (Ginnie Mae), 143application, 106-10; cross-currency, Gross.-n.. 1-, 13995-96, 99, 102

Exports, 85, 152; Algeria's commodity Hansen, L. P., 89exposure and, 2-3; choice of Hedging: commodity-linked bonds and,commodity-contingent instrument and, 116-23; debt service and, 100-01;145, 149, 150; consumption smoothing demand analysis and, 47, 49;and, 124-32; Costa Rica and, 2 , 91; diversification and, 97-98; exports and,debt-service-to-export ratio fluctuations 99, 100, 102; external debt allocationand, 96-97; dependence on commodity, and, 93; in forward markets, 153;1; diversification and, 97; exchange rate imports and, 100; policy guidelines for,and, 99; external debt allocation model 99-101; portfolio (commodity risk andand, 86, 87, 89; fluctuations in earnings exchange rate management model),from, 124; nedging policy and, 99, 100, 103-06; portfolio example (empirical102; sovereign debt risk and, 139 application of model), 106-10; risks of

External debt allocation model: external debt position and, 85;application of in Costa Rica, 90-93; speculative activity versus, 98-99;estimation methods for operationalizing uncertain commodity prices and, 96rules and, 89; rules for issuing Holthausen, Duncan, 119commodity-linked bonds and, 86-89, Hong Kong, gold CDs :n, 1393 Hirohito gold coin, 29

172 INDEX

Imports: diversification and, 97; exchange Location and scale (LS) condition, 115,rate and, 99; external debt allocation 117model and, 86, 87, 88; hedging policy Long, J. B., S5and, 100

Inco, commodity-indexed bonds and, 37 McKean, H. P., 40Income variability (consumption Magna, commodity-indexed bonds and,

smoothing), 125-26, 127, 128, 129 38Indonesia, 96, 108-10 Mlalaysia, palni oil prices in, 38Ingersoll, J. E., S1 Maximization problem in deManumInsurance: loan, 143-44, 149; risk function analysis, 43-45

management programs and, 3-4; Merton, R. C., 39, Sl, 53, 56, 59sovereign risk and, 150 Metallgesellschaft, commodity-indexed

Interest rates: consumption smoothing bonds and, 38analysis and, 129; copper-linked Mexican oil bonds (petrobonds), 33financing and, 38; in Costa Rica, 93; Meyer, Jack, 1 15, 117, 1 '9Giscard bonds and, 15; gold loans and, Mortgage market, 142-43, 14929, hedging with conventional loans Morton, P. J., 131a:id, 121; morgage market and, 143; Multigood case model (in demandoption type bonds and, 12; pricing of function analysis): demand functions in,commodity-linked securi6es and, 56, 53-55; the model, 51-5358-60, 61, 63, 70; replacing standard, Myers, Robert J., 5, 6, 152136; risk, 58-60; shift in, 1-2; Nationalization, 11, 150speculative rates and, 102; swaps and, Newbery, David, 6, 127, 15214; variable rate loans and, 13 Newmont (mine), gold loans and, 16

Ito, Kiyoshi, 40, 41 Nickel-linked financing, 36, 37

Japan, interest rates in, 2; sourcing of O'Hara, Maureen, 5, 86, 127, 152gold in, 29 Oil-linked financing: bond issues i.;,

34-35, 37; development of, 31, 33, 36Keynes, J. M, 125 Oil shock, effect of, 2

Kraft, D. F, 106 One-consumption good case modelKroner, Kenneth, 97(demand functions analysis): assetreturns in, 40-42; assumptions for,Latin America, dependence on commodity 39-40; budget equation, 42-43;

exports in, 1 demand ofuntionsin, 48-SI;Lessard, D. R., 86 dtriavo h eadi,4-1Lessard, D. R., 86 ~~maximization problem in, 43-45Liability management, commodity bonds Opportu n s rtb(edging wit 4

and, 61 ~~~~~~Opportunity set (hedging withand, 61 commodity-linked bonds), 117, 119,Lindert, P. H., 131 120Loans, 116; bullion, 13; commodity Outut price risk, 115, 120, 121, 123

variable-rate, 13; consunmptionsmoothing analysis and sovereign Papua New Guinea, copper investmentslenders and, 125, 127-28; in, 38crude-oil-linked financing and, 31-37; Payouts in pricing model, 63, 70debt and gencial obligation bank, 134; Peru, 145, 149gold-linked financing and, 14-30; Petro-Lewis Corporation, and oil-linkedhedging with conventional, 121-23; notes, 33insurance, 143-44, 149; securitization Phibro-Salomon Inc., and oil options, 36and, 141; silver-linked financing and, Placer Dome (mine), gold loans and, 1630-31, 32 Powell, Andrew, 6, 136, 153

INDEX 173

Prices. See Commodits prices; OutpUt and, 135, 142-44, 149-50; generalprice risk terms for, 140-42

Pricing commodiry-linked bonds: default Self-insurance instruments, 3, 4risk and, 57, 58-60, 62, 73; interest Separation property, 119rate risks and, 56, S8-60, 61, 63, 70; Sharp,, W./ F., 39%harpe-Lintner Capital Asset N'odel for, Sharpe-Lintner Capital Asset Pricing_9. See also Binomial pricing mL iCl; Model (CAPM), 39Schwartz pricing model Silver-linked financing, 12, 30-31, 32

Privolos, Theophilos, 5, 61, 125 Sohio Oil Company, oil bond issue by, 36Put option, 12, 16, 33-34, 147, 148 Solomon Pacific Resources NL, gold loan

repayrnents by, 29Rajan, Raghuram, 5, 152 Sovereign debt risk, 135, 136-40, 141,Refinement Intemational Company, 142, 143, 144, 147-48, 149. See also

gold-indexed bonds and, IS DebtRisk: commodity-linked securities pricing Sovereign lenders, 125, 127-28. See also

and default, 57, 58, S9, 62, 73; Loan,commodity-linked securities pricing and Speculation: demand analysi, and, 47;interest rate, 56, 58-60, 61, 63, 70; external liability decisions and, 102;commodity price, 1, 62; demand hedging vs., 98-99function analysis of assets and, 39, 55; Stiglitz, J. E., 127, 132, 136export, 124; external debt allocation Strip (commodiry-contingent claims)model and, 93; external debt position ^ - nept, 149and, 85; managemen1t cf commodity Stliz, R. M., 104and exchange, 97-102; management Sunshine Mining Company, silver-linkedprograms, 3-4; mortgage .narket and, financirg by, 30-31143, 149; output price, 115, 120, 121, Svensson, L. E. O., 104123; securitization and credit, 141; Swaps, 14; curren,y, 97sovereign debt, 13S, 136-40, 141, 142,B

143 14 14'48 i9; sverein' ' Taiwanese Central Bank, gold purchases143, 144, 147-48, 149; sovereign b,2lenders and, 128, 150 by, 29

Robison, L. J., 115, 119 Third party insurance instruments, 4, 154Ross, S. A.,1, 56, 162 Thompson, Stanley R., 5, 152Rubinstein, M., 62 Thygerson, K. J., 143

Trade shocks, 2, 90Sachs,J. D., 139Samuelson, P. A., 48 Uncertain commodity price version ofSargent, T. S., 99 Schwartz model, SSScholes, M. t., 56 United Kingdom, interest rates in, 2Schware, E. S., 5, 56, 59, 60, 61-62, 70 United States, 1, 4, 12, 13, 30-31, 33, 36,

71, 73, 125, 152 38, 143Schwartz pricing model, 56-60; compared Value of firm (commodity bond pricing),

with binomial pricing model, 70-78; 62, 63, 65, 72, 74default risk version of, 58-60; interest van Huyck, J. B., 139rate risk version of, 58-60; uncertaincommodity price version of, 58 Warrants, 15-16, 17-2S, 'O, 37-38

Secondary rortgage market, 142-43, 149 Williamson, John, 86Secondary trading of securities, 141 Worrall, Tim, 129Securities and Exchange Corr .*_-^n Wright, Brian, 6, 152

(SEC), 12 Wriston, Walter, 138Securitization. 147; debt obligations and,

134; developing country obligations Zaire, 145, 149

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