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CPA REVIEW PROGRAMMECPA REVIEW PROGRAMMEFINAL STAGE: MODULE FFINAL STAGE: MODULE F

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P17: INTERNATIONAL FINANCEP17: INTERNATIONAL FINANCEDERIVATIVE INSTRUMENTS: OPTIONSDERIVATIVE INSTRUMENTS: OPTIONS

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1. INTRODUCTION

Options are unique financial instruments that confer upon the holder the

right to do something without the obligation to do so. More

specifically, an option is a financial contract in which the buyer of

the option has the right to buy or sell an asset, at a pre-specified

price, on or up to a specified date if he chooses to do so; however,

there is no obligation for him to do so. In other words, the option

buyer can simply let his right lapse by not exercising his option. The

seller of the option has an obligation to take the other side of the

transaction if the buyer wishes to exercise his option. Obviously, the

option buyer has to pay the option seller a fee for receiving such a

privilege.

Options are available on a large variety of underlying assets including

common stock, currencies, debt instruments, and commodities. Also

traded are options on stock indices and futures contracts (the

underlying asset is a futures contract and futures-style options. While

over-the-counter option trading has had a long and chequered history,

option trading on organized options exchanges is relatively recent.

Options have proved to be a very versatile and flexible tool for risk

management in a variety of situations arising in corporate finance,

stock portfolio risk management, interest risk management and hedging of

commodity price risk. By themselves and in combination with other

financial instruments, options permit creation of tailor-made risk

management strategies.

Options also provide a way by which individual investors with moderate

amounts of capital can speculate on the movements of stock prices,

exchange rates, commodity prices and so forth. The limited loss

features of optios is particularly advantageous in this context.

2. CURRENCY OPTIONS

2.1 Currency Options Defined

A currency option may be defined as a contract which gives its holder

the right (not the obligation) to buy or sell, on or by a specified

date, a specified amount of a particular currency at an exchange rate

determined at the time of the signing of the contract. In December

1982, the Philadelphia Stock Exchange began trading options on the

pound. Currently, options are offered on the pound as well as the

Australian dollar, the Canadian dollar, the German mark, the French

franc, the Japanese yen, and the ECU. Currency options are also traded

on the Chicago Board Options Exchange and the London International

Financial Futures Exchange (LIFFE).

2.2 Categories of Currency Options

There are two categories of options, viz, American style options and

European style options. If an option can be exercised on any date during

its lifetime it is called an American style option but if it can be

exercised only on its expiration date, it is called a European style

option. American options offer buyers more flexibility in that they can

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be exercised on any date up to and including the maturity date of the

option. Also, the term European style has nothing to do with European

terms for quotations; rather, it has to do with when the option buyer

can exercise the option, that is, buy or sell the currency at the strike

price. European options can be exercised only on the maturity date of

the option. They cannot be exercised before that date.

Basic Option Concepts

Option Writer and Holder. An option is a contract, and there are

two sides or counter parties to each contract. The writer (or

seller) of the option sells to the holder (or buyer) the right to

buy or sell the amount of the currency specified in the contract.

In return for this privilege, the holder of the contract pays the

writer no matter what happens, that is, irrespective of whether

the holder decides to exercise or not. It is essential not to

confuse the buying and selling of the option with the buying and

selling of the underlying currency. The writer of the option

sells the right to buy or sell the currency, and hence is the

seller of the option who receives, in return, the premium. The

writer has an obligation to comply with the holder’s decision

should the latter decide to exercise the right of buying and

selling the currency. The holder of the option, on the other

hand, buys the right to buy or sell the currency, and hence is the

buyer of the option who pays the premium. If the holder chooses

not to exercise this right, then the premium will be lost (by the

holder)

Call and Put Options. An option gives the holder the right to buy

or sell a currency. A call option gives the holder the right to

buy a currency. In this case, the writer must comply by selling

the currency to the holder if the latter decides to exercise. A

put option, on the other hand, gives the holder the right to sell

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a currency. The writer must comply by buying the currency from

the holder if the latter decides to exercise.

Naked and Covered Option. An option is described as ‘naked’ if

there is no corresponding spot position in the underlying

currency. For example, if the writer of an Australian dollar call

option does not have a spot position in the Australian dollar, the

option in naked. This is because, if the holder of this option

decides to exercise, the writer cannot comply unless he or she

buys the required amount on the spot market. With a covered

option, the writer can comply without resorting to the spot market

as the writer can sell Australian dollar holdings. The writer of

a naked option is required to deposit a margin.

The Exercise Exchange Rate. Also called the strike exchange rate

(or price, in general), it is the exchange rate at which the

holder of the option buys (in the case of a call) or sells (in the

case of a put) should the holder choose to exercise. Let E be the

exercise exchange rate and S the actual spot exchange rate

prevailing when the decision whether or not to exercise is

considered. Assume also that these exchange rates are expressed

as the number of units of currency x per one unit of currency

y(x/y) where y is the currency to be bought or sold by the holder

of the option. Ignoring the premium for the time being, the

following rules hold:

The holder will exercise a call option if S>E. Profit is made by buying

currency y at E and selling it at S. Gross profit per unit of

currency y is S-E. if S<E, there is no point in exercising a call

option, since it is cheaper to buy currency y on the spot market.

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The holder will exercise a put option if S<E. Profit is made by buying

currency y in the spot market at S and selling it at the exercise

exchange rate, E. Gross profit per unit of currency y is E-S. if S>E,

there is no point in exercising the put option, since this will produce

a loss.

The difference between the actual and the exercise exchange rates (or

vice versa) is called ‘gross’ profit, as opposed to ‘net’ profit,

because the premium that is paid by holder to acquire the option is

not considered. Let us now reconsider the rules by introducing the

premium, . In the case of a call option, net profit per unit

currency y is S-(E+).

In the case of a put option, net profit per unit of currency is E-

(S+). Notice that while the profit obtained by the holder is

unlimited, there is an upper limit on the loss, which is the premium.

The worst that could happen is that the holder chooses not to

exercise, in which case the holder loses the premium only. On the

other hand, the maximum the writer of an option can gain is the

premium, while his or her loss is unlimited.

Long and Short Positions.

The holder or buyer of the option is described as holding a long

position, while the writer or the seller of the option holds a short

position on the same option. A long position gives a right, while a

short position creates a commitment. The following are various

possibilities:

1. A long call position gives the right to buy a currency;

2. A long put position gives the right to sell a currency.

3. A short call position implies a commitment to sell a

currency to the holder of the option if the latter decides to

exercise.

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4. A short put position implies a commitment to buy a

currency from the holder of the option if the latter decides

to exercise.

Expiry Date, American Options and European Option.

An option gives the holder the right to buy or sell a currency on or

before a certain date, known as the expiry (or expiration) date after

which the contract terminates, that is, the date after which the

holder’s right to buy or sell the currency will no longer be valid.

An American option can be exercised on or before the expiry date,

while a European option can be exercised only on the expiry date.

Because an American option gives a greater privilege than a

corresponding European option, the premium paid on the former must be

higher.

In the Money and Out of the Money. An option is in the money if

it can be exercised at (gross) profit. If S>E, then a call option

is in the money while a put option is out of the money.

Conversely, if S<E, then a put option is in the money while a call

option is out of the money. If S=E, then the option is at the

money. If an option is in the money this does not necessarily

mean that it can be exercised at net profit. This will only

happen if it is in the money by an amount that is greater than the

premium.

Intrinsic Value and Time Value. The intrinsic value of an option

is the extent to which the option is in the money. At any point

in time during the life of an option, the greater the difference

between the actual exchange rate prevailing then and the exercise

exchange rate (or vice versa), the greater is the intrinsic value

of a call (put) option. For a call option the intrinsic value is

given by.

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where Vi,t is the intrinsic value at time t, and St is the spot

exchange rate prevailing then. If St,<E, then Vi,t=0. For a put

option

Vi,t=E-Si and hence, if St>E, then Vi,t=O.

Over-the-Counter and Exchange Traded Option. An over the counter

(OTC) traded option is an option created by a writer to meet the

specific requirements of a buyer, given that such an option is not

generally traded on the floor of an exchange. An Example is an

option to buy AUD 242 000 by 12 May at an exercise exchange rate

of 0.7650 USD/AUD). This kind of option is obviously non-

standardised. On the other hand, an exchange traded option is

one of a class of standard options that have predetermined

specifications with respect to size, exercise price and expiry

date.

2.3 Pricing Currency Options.

Pricing currency options means determining the value of the premium, per

unit of the underlying currency, that must be paid by the buyer to the

writer of the option. The total cost of acquiring the option is,

therefore, equal to the product of the premium and the number of units

of the underlying currency in the option. If the underlying exchange

rate is x/y, then the premium is also expressed as units of x (normally

a fraction of one unit of x) per one unit of y. if the contract has Q

units of y, the total cost of the option is Q. Option dealers quote a

bid premium and an offer premium for each contract: the bid is what the

dealer is prepared to pay to buy the option, and the offer is what the

dealer must be paid to sell. The dealer must state whether the

underlying option is a call or a put, and whether is an American or a

European option, as well as the exercise price and the date of expiry.

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2.3.1 Factors Determining Option Prices

The following factors determine the premium or the price of a currency

option:

The Exercise Exchange Rate: The higher the exercise exchange

rate, the lower the premium on a call and the higher the premium on a

put. This is straightforward. A call option that gives the holder

the right to buy a currency at a lower exercise exchange rate should

be more valuable than when the right can be exercised at a higher

exchange rate. The lower the exercise exchange rate, the more likely

it is that it will be below the market exchange rate, in which case

the holder can exercise the option at a profit. The reverse argument

applies to the case of a put option

Time to Expiry: The longer the time to expiry, the greater is the

premium. This is because the probability that an out-of-the-money

option becomes in the money increases with the time to expiry. On or

very close to the date of expiry, an out-of-the-money option will be

worth nothing because there is a zero probability that it will be in

the money. Thus, it has a zero intrinsic value and a zero time

value, and hence the premium should be zero.

Intrinsic Value: The higher the intrinsic value – that is, the

more the option is in the money – the higher the premium. This is

because the greater the intrinsic value, the higher is the

probability that the option will be exercised at a profit.

Exchange Rate Volatility: An option is like an insurance policy,

and so it costs more where there is a greater underlying risk, which

in currency options arises from exchange rate volatility. If the

options are spot transactions, the relevant volatility is that of the

spot rate. If the options are on futures contracts, the relevant

volatility is that of the futures exchange rate. Since the

volatility of the spot rate determines the volatility of the futures

rate, it is the volatility of the spot rate that matters. Exchange

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rate volatility is normally measured by the standard deviation of the

exchange rate as calculated from historical data.

Type of Option: For a given exercise exchange rate, volatility

and time to expiry, the premium on an American option should be

higher than the premium on a European option.

Interest Rate on the Currency of Purchase: If the underlying

exchange rate is x/y, then y is the currency to be bought and sold in

accordance with the contract, while x is the currency of purchase,

that is, the currency in which the premium is valued and paid. The

higher the interest rate on the currency of purchase, the lower is

the present value of the exercise price. A higher interest rate,

therefore, has the same effect as a lower exercise price. Thus, a

higher interest rate is associated with a higher value of calls and a

lower value of puts.

The Forward Spread and the Interest Rate Differential: If

currency y is expected to appreciate, then a call option on y should

become more valuable while a put option becomes less valuable. For

reasons which will become clear in Chapters 10 and 11, the

possibility of currency y appreciating increases as the forward

spread and the interest differential increase

2.3.2 The pricing Formula

The Black-Scholes (1973) model was developed to explain the

determination of the premium on stock options. Garman and Kohlhagen

(1983) adapted the Black-Scholes formula to come up with a currency

option pricing formula. The price of a European call option, ’, is

given by

’= √T)

such that;

d= log(S/E)+T(i-i * + 2 /2)

√T

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where S is the actual spot rate prevailing at the time of trading, E is

the exercise exchange rate (both expressed as the price of one unit of

the option’s underlying currency in terms of the currency of purchase),

i is the interest rate on the currency of purchase, i* is the interest

rate on the underlying currency, is the standard deviation of the

exchange rate, T is the option’s maturity expressed as a fraction of a

year (365 days) and N(.) is the standard normal cumulative distribution

function. All the parameters of equation are readily available, except

, which can be estimated either from historical data or from a similar

option having the same maturity but a different exercise exchange rate.

’= √T)

which can be simplified to: ’=[FN(d)-EN(d-√T)eiT

where: d= log(F/E)+T 2 /2

√T

The relevance of the forward rate is that the spot rate, S, and the

interest rates, i and i* (which are related to the forward rate via

covered interest parity) appear in the formula. The price of a

corresponding put option, p, may be calculated from the put-call parity

relationship;

p=’+

Alternatively, the price of the put option can be obtained directly from

the following equation.

p=e-iTE[1-N(d-√T)]- [1-N(d)]

which can also be written in terms of the forward rate as

p={F[N(d)-1]-E[N(d--√T)-1]}eit

2.3.3 Measures of Sensitivity

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Obviously, the price of an option depends on several parameters. There

are various measures of the sensitivity of option prices with respect to

these parameters.

1. Delta (δ) : Delta measures the change in the premium

corresponding to a small change in the spot exchange rate, S. It

also reflects the probability that the option will expire in the

money. Thus, delta, ranges in value between zero for far out-of-

the-money option to 1.0 for deep in-the-money options. A delta

of 0.5 means that a one-point change in the spot exchange rate

will cause a 0.5-point change in the value of the option. Long

calls and short puts have positive deltas, because a rise in the

spot exchange rate leads to an increase in the value of the

option. Short calls and long puts have negative deltas. The

value of delta is affected by volatility and the time to expiry.

- Delta is given by : (δ)=ΔΔS

In general, the higher the delta, the greater the probability of

the option expiring in the money

2. Gama (γ) : This parameter measures the rate of change of delta

with respect to the spot exchange rate. Thus, a low gamma

reflects a stable delta. A positive gamma indicates that

profits increase when the exchange rate moves in a favourable

direction, and that the loss-making rate declines as more

losses are incurred if the exchange rate moves in an

unfavourable direction. Long options have positive gammas,

while short options have negative gammas.

- Gamma can be calculated as. γ=ΔδΔS

3. Theta (θ) : Theta measures the anticipated change in the

premium resulting from a change in the time to expiry. As the

time to expiry declines, so does the time value of the option.

Theta quantifies the change in the value of the option as the

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time to expiry declines. A theta of –1 means that each day

will cause a decrease in the option’s value of –1/365. Long

option positions have negative thetas, because as time passes

the holders lose some value of their investment in terms of the

premium. Short option positions have positive thetas for the

opposite reason.

- Theta is given by: θ= ΔΔt

Where t is time measured in days. The relationship between the

premium and the time to expiry is nonlinear, implying time-

varying θ. This means that option prices decline at an

increasing rate as the expiry date approaches. In general, the

option loses the bulk of its values in the final thirty days

prior to expiry.

4. Vega (ν) : This parameter is a measure of the rate of change

of the premium with respect to volatility. Long options have

positive Vegas, while short options have negative Vegas.

- Vega is calculated as ν = ΔΔ

The problem that arises here (and also in trying to implement the

option pricing formula) is that volatility is unobserved. Thus,

volatility is viewed as (i) historical, which is evaluated from

historical data, (ii) forward-looking, when historical volatility

is altered to reflect expectations about the future; and (iii)

implied, which is derivered from the pricing formula.

5. Rho (р): Rho meares the rate of change of the premium with

respect to the interest rate. Remember that the interest rate

is used as a discount factor, and so rho tends to be higher for

options with longer time to expiry. It is also possible to

distinguish between р and р*, depending on whether the

sensitivity is measured with respect to i or i*, ‘The effect of

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the two interest rates may also be viewed through the effect on

the forward rate. A change in either or both interest rates

leads to a change in the forward rate, and hence in the forward

premium as implied by equations (7.6 and 7.7) р and р* can be

calculated as

- р= Δ <0 Δi

- р*= Δ >0 Δi*

2.4 Uses of Currency Options

Currency options provide the corporate treasurer another tool for

hedging foreign exchange risks arising out of the firm’s operations.

Unlike forward contracts, options allow the hedger to gain from

favourable exchange rate movements, while being protected against

unfavourable movements. However, forward contracts are costless while

options involve up-front premium costs.

Investors may speculate in the currency options market based on their

expectations of the future movements in a particular currency. For

example, if the speculators expect that the Japanese yen will

appreciate, they will purchase Japanese yen call option. When the spot

rate of Japanese yen appraciate, they can exercise their option by

purchasing yen at the strike price and then selling the yen at the

prevailing spot rate.

For every buyer of a currency call option, there must be a seller.

A seller of a call option is obligated to sell aspecified currency at a

specified price (the strike price) up to a specified expiration date.

Sometimes, when the speculators expect the currency to depreciate in the

future, they may want to sell a currency call option. And the only way

a currency call option will be exercised will be when the spot rate is

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higher than the strike price. In this way, when the option is

purchased, the seller of the currency call option will receive the

premium. He can keep the entire amount if the option is not exercised.

Also, when it appears that an option will be exercised there will still

be sellers of options. But such options will sell for high premiums

because of the increased risk of the option being exercised at some

point.

2.5 Options Market Structure: Exchange Traded and OTC Options

Options are purchased and traded either on an organised exchange or in

the over-the-counter (OTC) market. Exchange traded options or listed

options are standardised contracts with predetermined exercise prices,

standard maturities (one, three, six, nine, and 12month), and fixed

maturities (March, June, September, and December).

OTC options are contracts whose specifications are generally negotiated

as to the amount, exercise price and rights, underlying instrument, and

expiration. OTC currency options are traded by commercial and investment

banks in virtually all-financial centers.

The OTC options market consists of two sectors:

(1) A retail market composed of nonblank customers who purchase

from banks what amounts to customised insurance against adverse

exchange rate movements and

(2) A wholesale market among commercial banks, investment banks,

and specialized trading firms; this market may include interbank

OTC trading or trading on the organised exchanges.

The interbank market in currency options is analogous to the interbank

markets in spot and forward exchange. Banks use the wholesale market to

hedge or ''reinsure'' the risks undertaken in trading with customers and

to take speculative positions in options.

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Exchange-traded and OTC options comparedExchange-traded OTC

Contract terms, includingamounts

Standardized Fixed to suitcircumstances; terms arenot standard

Expiration Standardized Determined byrequirements of customer

Transaction method Stock exchange typemedium

Bank-to-client or bank –to-bank.

Secondary market Continuous secondarymarket

No formal secondarymarket

Commissions Negotiable Negotiable, but usuallybuilt into the premium

Participants Exchange members andclients

Banks, corporations andfinancial institutions

Exchange Listed.

The other market for FX options is the exchange-listed market of the

various stock and futures exchange around the world. The principal

centres are Philadelphia, where the stock exchange lists options on spot

FX and Chicago, where theMerchantile Exchange lists options on its FX

futures contracts. In both cases, quotations are in the form of

currency (rather than volatility).

Access to the market is through brokers who impose commissions for each

contract traded. The market operates on the floor of the exchange where

brokers gather to reflect their clients’ orders with market makers or

specialists providing the prices. The markets have specified opening

and closing times for each currency contract. Also, the exchanges have

widened the availability by extending trading hours.

2.6 Advantages of Currency Options

Advantages

Options are used by buyers just like an insurance policy against

movements in rates. Thus, they are alternatives to using the

futures market or to the forward exchange market.

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The main advantages of using options are:

The option buyer, at the outset, judges the worst-case

scenario. Once premium is paid, no further cash is payable

and when the main objective is to limit downside risk, this

is a powerful advantage.

Since there is no obrigation to exercise an option, options

are ideal for hedging contingent cashflows which may or may

not materialise, such as tenders.

Options provide a flexible hedge offering a range of prices

where the option can be exercised, whereas forward or future

markets only deal at the forward prices which exist at the

time the deal is made.

Options provide major possibilities in the rang eof toools

available to treasures and traders. They can be used on

their own to hedge or they can be combined with the forward

and futures markets to achieve more complex hedges.

Futures require daily margins to cover credit risk while

forwards require bank credit line. An option buyer can

dispense with either depending on the specific market in

which he operates.

3 INTEREST RATE OPTIONS

3.1 Definitions and Types

A less conservative hedging device for interest rate exposure is

interest rate options. A call option on interest rate gives the holder

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the right to borrow funds for a specified duration at a specified

interest rate, without an obligation to do so. A put option on interest

rate gives the holder the right to invest funds for a specified duration

at a specified return without an obligation to do so. In both cases,

the buyer of the option must pay the seller an up-front premium stated

as a fraction of the face value of the contract.

3.2 Interest Rate Cap and Interest Rate Floor

An interest rate cap consists of a series of call options on interest rate or

a portfolio of calls. A cap protects the borrower from increase in

interest rates at each reset date in a medium-to-long-term floating rate

liability. Similarly, an interest rate floor is a series or portfolio

of put options on interest rate which protects a lender against fall in

interest rate on rate rest dates of a floating rate asset.

3.3 Interest rate Collar

An interest rate collar is a combination of a cap and a floor.

3.4 The Put-Call Option Parity

Interest rates parity relates the forward (and futures) rates

differential to the interest differential. Another parity conditions

relate options prices to the interest differential and, by extension, to

the forward differential. We are now going to derive the relation

between put and call option prices, the forward rate, and domestic and

foreign interest rates. To do this, we must first define the following

parameters:

C = call option premium on a one-period contract

P = put option premium on a one-period contract

E = exercise price on the put and call options (dollars per unit of

foreign currency)

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eo = Current spot rate (dollars per unit of foreign

currency)

e1 = End-of-period sot rate (dollars per unit of foreign

currency)

f1 = One-period forward rate (dollars per unit of foreign

currency)

rh = US. Interest rate for one period

rf = Foreign interest rate for one period

The parity relations are presented by the following equations:

C = e0/[1 + rf] – E/[1 + rh] + P

According to interest rate parity,

e0/[1 + rf] = f1/[1 + rh]

Substituting the Second Equation into Equation One yields a new

equation:

C = [f1 – E]/[1 + rh] + P

or C - P = [f1 – E]/[1 + rh]

These parity relations say that a long call is equivalent to a long put

plus a forward (or futures) contract. The term f1 - E is discounted

because the put and call premia are paid upfront whereas the forward

rate and exercise price apply to the expiration date.

3.5 Interest Rate Exposure

3.5.1 Nature and Measurement

Fluctuations in interest rate affect a firm’s cash flows by affecting

interest income on financial assets and interest expenses on

liabilities. To put it in another way, the market values of a firm’s

portfolio of financial assets and liabilities fluctuate with interest

rates. For a non-financial firm, fluctuations in interest rates causes

corresponding fluctuations in operating earnings and rates of return on

projects.

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Effective assessment and management of interest rate exposure requires

first of all a clear statement of the firm’s risk objectives. The

financial manager must then translate these into operational guidelines

for monitoring key parameters which will reveal the firm’s total

exposure. Leach (1988) has suggested a classification into primary and

secondary objectives as follows:

Primary Objective:

i. Net interest income, i.e. interest income on assets minus

interest expense on liabilities. Monitoring of this account

will of this account will reveal the sensitivity of the firm’s

profitability to changes in interest rates.

ii. Net equity exposure, i.e. sensitivity of the firm’s net worth

to interest rates

The first of these is more suitable for a non-financial corporation with

relatively few financial assets as the latter measure requires

estimating the changes in values of non-financial assets as interest

rates change. The second measure is more suitable for a financial

institution with predominantly financial assets and liabilities.

Secondary Objective.

i. Credit exposure which is really a measure of default risk.

Most firms would wish to limit their exposure to any one

individual or firm.

ii. Basis risk arises when interest rate exposure on one

instrument, e.g. commercial paper is offset with another

instrument, e.g. Eurodollar futures or when floating rate

assets tied to one index, e.g. prime rate are funded by

floating rate liabilities tied to another index, e.g.

Eurodollar CDs.

iii. Liquidity risk pertains to timing mismatches between cash

inflows and outflows, e.g. when a longer duration assets is

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funded by a shorter duration liability which will have to be

refunded at maturity, possibly at a higher cost.

The measure of exposure selected must incorporate these objectives.

The most often used device to assess interest rate exposure is Gap

Analysis. It focuses mainly on the liquidity risk. The entire planning

horizon is divided into sub periods. For each subperiod, the difference

between the assets and liabilities which mature or are repriced during

that interval is designated as the ‘gap’. If the gap is positive there

will be a net cash surplus while if it is negative there will be a

deficit.

A more sophisticated approach uses the concept of duration discussed in

detail in Appendices. Duration of an interest bearing security measures

the sensitivity of its market value to changes in yield. Another

interpretation brings out the tradeoff between reinvestment market

value. Consider a coupon bond. An increase in interest rate reduces

the market price of the bond but allows the coupons to be reinvested at

a higher rate of return.

Duration can be interpreted as the period over which these two effects

balance each other. Since durations obey additivity, the duration of a

portfolio is simply the weighted sum of the durations of components of

the portfolio. A firm with a portfolio of financial assets and

liabilities can minimize interest rate exposure by equating as nearly as

possible the duration of its assets and liabilities.

3.5.1.1 Forward Rate Agreement (FRA)

A Forward Rate Agreement (FRA) is an agreement between two parties in which

one of them (the seller of the FRA), contracts to lend to the other (the

buyer), a specified amount of funds, in a specific currency, for a

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specified period starting at a specified future date, an interest rate

fixed at the time of agreement.

© ABDUL 2007

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