Ex-day behavior with dividend preference and limitations to short-term arbitrage: the case of...

Journal of Financial Economics 53 (1999) 145}187

Ex-day behavior with dividend preference andlimitations to short-term arbitrage: the case of

Swedish lottery bondsq

Richard C. Green!,*, Kristian Rydqvist"

!Graduate School of Industrial Administration, Carnegie Mellon University, Pittsburgh, PA 15213, USA"Norwegian School of Management, N-1300 Sandvika, Norway

Received 25 March 1998; received in revised form 16 June 1998; accepted 2 April 1999

Abstract

Swedish lottery bonds o!er a unique opportunity to study ex-day e!ects in anenvironment where cash distributions are tax-advantaged relative to capital gains. Thus,in the lottery bond market, we observe a reversal of the preference for capital gains thatresearchers have cited as an explanation for the ex-day behavior of U.S. equities. Further,in this market there are barriers to short-term arbitrage when prices do re#ect the taxpreferences of individual investors. We "nd the bonds are priced around the ex-day tore#ect di!erential tax rates on income and capital gains consistent with the prevailing taxregimes. The bonds consistently experience negative returns over the coupon paymentperiod, and in fact often sell at negative yields prior to the cash distribution, as one would

*Corresponding author. Tel.: 412-268-2302; fax: 412-268-6837.

E-mail address: [email protected] (R.C. Green)qWe have bene"ted from comments about this research by Yakov Amihud, Jonathan Berk,

"yvind B+hren, Peter HoK gfelt, Avner Kalay, Roni Michaely, Richard Priestley, Bjarne S+rensen,Richard Stapleton, and Efrat Tolkowsky, and from seminar participants at the Accounting andFinance Workshop in Tel Aviv, the Duke-UNC joint "nance seminar, the EIASM Workshop onFinancial Risk Management, the First Regional Conference in Sharm-El Sheikh, Humboldt Univer-sity, the Joint Seminar of the Finnish and the Swedish School of Economics, London BusinessSchool, the Norwegian School of Economics, the Norwegian School of Management, the NordicSymposium on Contingent Claims in Finance and Insurance, and the Western Finance Association.In addition we have received information or data from Sture LundeH n of Swedbank, SvanteJohansson of Carnegie Fondkommission, Lennart ForsseH n of Statistics Sweden, and Niklas Alfred-sson of Ekelundgruppen.

0304-405X/99/$ - see front matter ( 1999 Elsevier Science S.A. All rights reserved.PII: S 0 3 0 4 - 4 0 5 X ( 9 9 ) 0 0 0 1 9 - 7

expect given tax-motivated trading between high-tax investors, who buy prior to thedistribution, and low-tax investors, who buy after the distribution. ( 1999 ElsevierScience S.A. All rights reserved.

JEL classixcation: G35; H20

Keywords: Dividends; Taxation

1. Introduction

The ex-day behavior of security prices has been a long-standing object ofinterest, and of controversy, for "nancial economists. As Kalay (1982) states,&. . . the ex-dividend day o!ers a unique opportunity to compare capitalgains (i.e., the price drop) to ordinary income (i.e., the dividend)'. Comparing thevalue investors ascribe to returns in these two forms is important because each istaxed di!erently. How such di!erential taxation in#uences security prices has"nancial consequences for corporations and governments that issue securities,and policy implications for governments that design tax codes and rely on taxrevenues.

We study the behavior of the prices of Swedish lottery bonds. These bonds areobligations of the Swedish Treasury, and have "xed coupon payments from thestandpoint of the issuer. The payments are distributed across the bonds bylottery, however, so that to the holder of any subset of the bonds the couponpayment is random. Like municipal bonds in the U.S., coupon payments on thebonds are tax-exempt, but capital gains and losses are taxed as with othersecurities. Their tax treatment di!ers from other &"xed-income' securities, how-ever, in one notable aspect. Because the coupon payments received by bond-holders are random, interest is not accrued prior to a coupon payment. Instead,the entire price paid prior to the distribution is included in the investor's taxbasis, and the price drop associated with the distribution becomes a capital loss.In short, the bonds are taxed as if they were equities with a tax-exempt&dividend'.

As a result of these features, lottery bonds o!er several unique advantages forthe study of this important problem in tax incidence.

First, the tax treatment of Swedish lottery bonds is the reverse of the treat-ment of U.S. equities. The cash distributions are taxed at a lower rate, zeropercent, than the capital gain or loss. Thus, if the ex-dividend day behavior ofstock prices is driven by the higher taxation of dividends relative to capitalgains, as many researchers following Elton and Gruber (1970) have claimed,then we would expect the behavior to be reversed for the lottery bonds. Theprice should fall by more than the distribution when the bond reaches the

146 R.C. Green, K. Rydqvist / Journal of Financial Economics 53 (1999) 145}187

ex-distribution day, rather than by less than the distribution. This result is, infact, what we "nd.

Second, previous empirical research has focused exclusively on equities,although the theoretical arguments motivating the research would apply to anysecurity for which the price drop over the ex-distribution period is treated asa capital loss. Equities have the disadvantage of having highly volatile returns,which makes it di$cult to precisely estimate the tax e!ects. Bond prices, whichare less noisy, are generally not suitable candidates for study. Since the accruedinterest between coupon dates does not a!ect the investor's basis, passing theex-coupon date does not generate a capital loss. Lottery bonds have much lessvolatile prices than stocks, but interest is not accrued between coupon dates.Thus, they represent a unique opportunity to evaluate the ex-distributionbehavior of a bond that is taxed like a stock. At a minimum, it is of interest toknow whether the ex-day behaviors that have been documented for stockswould also show up in a di!erent type of security.

Third, the interpretation of ex-day returns for equities has been problematicbecause, as Kalay (1982) and Boyd and Jagannathan (1994) have emphasized,the tax status of the marginal investor is ambiguous. The U.S. equity market, forexample, includes dealers and short-term arbitrageurs who are taxed symmetric-ally on dividends and capital gains, and dividend capturers who prefer dividendsto capital gains. The institutional and tax settings in the Swedish lotterybond market preclude the sorts of arbitrage transactions that would allowtraders to exploit and eliminate pricing that re#ected the di!erential taxationfaced by individual investors. Thus, if there is any market where one should beable to see the di!erential taxation re#ected in prices around the ex-day, andwhere relative prices should re#ect the tax rates of individual investors, suchbehavior should be evident here. We "nd that the ex-day returns across taxregimes do re#ect changes in tax rates for the individual investors in the lotterybond market.

There has been considerable debate in the academic literature about whetherobserved prices re#ect marginal tax rates, or transactions costs, or both. Variousresearchers, following Elton and Gruber (1970), have documented that, for U.S.stocks, the stock price falls on average by less than the amount of the dividendon the ex-dividend day. Alternatively stated, the average total return, dividendplus capital gain, on the ex-day is &abnormal' in the sense that, on a pre-tax basis,it is higher than on non-ex-days. Elton and Gruber (1970) argue that thisbehavior re#ects the preferential tax treatment of capital gains, and that di!er-ences in ex-day returns across dividend yield categories re#ect di!erences in thetax status of the clienteles holding those stocks. Investors who hold the stockwith a capital gain, and who are coming to market to sell, may be unwilling tosupply shares on the ex-dividend day, since doing so exposes them to a fullytaxable dividend. If, instead, they sold their shares before the dividend isdistributed, at a price that includes the present value of the imminent cash

R.C. Green, K. Rydqvist / Journal of Financial Economics 53 (1999) 145}187 147

distribution, they would receive a tax-preferred capital gain, rather than thefully taxed dividend. Equilibrium, so the argument goes, requires that sellersbe indi!erent between disposing of their shares cum-dividend or ex-dividend.To induce such investors to supply shares for buyers at both points in time, theprice on the ex-day must compensate sellers for the extra tax liability on thedividend. The relative magnitudes of the expected price drop and the dividendwill then re#ect the marginal tax rates of the clientele holding that particularstock.

This evidence, and the interpretation of it, has proved controversial. Kalay(1982) points out that short-term traders, dealers, and tax-exempt institutionshave incentives to exploit high pre-tax, ex-day expected returns, and that theirtrading will, at a minimum, complicate any inference about the tax rates of themarginal investor. The ex-day return will re#ect the magnitude of transactioncosts faced by short-term traders, as well as relative tax rates. Lakonishok andVermaelen (1986) show that there is abnormally high volume around ex-days forsome stocks, which they interpret as evidence of short-term trading. Karpo! andWalkling (1988) "nd that ex-day returns are correlated with transactions costsfor high-yield stocks after the introduction of negotiated commissions. Boyd andJagannathan (1994) argue that transactions costs faced by di!erent classes oftraders should induce a convex relationship between the dividend yield and theexpected percentage price drop, and argue that the data display this convexity.In summary, it appears likely that the ex-day returns on U.S. equities may wellre#ect preference for capital gains over dividends, but it remains unclear justhow strong that preference is, or for exactly which stocks it is operative.

Our paper joins a number of others by examining these questions in a di!er-ent institutional and tax environment. To the extent that some of the factorsin#uencing ex-day returns are controlled in these studies, one can better inter-pret the empirical results in general. For example, Barclay (1987) "nds that,prior to the introduction of the income tax in the U.S., ex-day price drops wereon average equal to the dividend, and were not correlated with dividend yield.This "nding suggests that the ex-day returns evident in the current regime aretax driven. On the other hand, Eades et al. (1984) "nd abnormal ex-day returnsassociated with stock dividends and splits, which are tax-neutral events. Frankand Jagannathan (1998) document that prices fall by less than the dividend onex-days in Hong Kong, despite the fact that dividends and capital gains are bothuntaxed. Hayashi and Jagannathan (1990) and Kato and Loewenstein (1995)show that stock prices actually rise in Japan, apparently due to spuriousinstitutional factors. These results suggest that ex-day behaviors could be drivenby market ine$ciencies, or institutional and micro-structure factors, rather thanthe tax-based explanations.

The lottery bond market we study also controls for some of the frictions orinstitutional regularities that researchers have o!ered as alternatives to tax-based explanations of ex-day equity returns. Frank and Jagannathan (1998)


explain the ex-day behavior in Hong Kong with a model in which marketmakers have a comparative cost advantage in collecting and reinvesting divi-dends relative to buyers and sellers. Dividends are undervalued relative tocapital gains in their model because they have &nuisance value'. Bali and Hite(1998) point to price discreteness as a possible explanation, and o!er empiricalevidence in support of their argument: If, in bidding for the cum-dividend shares,investors round down to the nearest grid point, then the price drop will appearlow relative to the dividend, and this e!ect will be correlated with the magnitudeof the dividend. The tax regime in the lottery bond market, however, means thatthese frictions, which lead to undervaluation of cash distributions relative tocapital gains, would operate in a direction opposite to that of tax-motivatedtrading. Taxes in the lottery bond market lead investors to prefer cash distribu-tions relative to capital gains, and the price changes we observe are consistentwith these preferences. The frictions identi"ed in the literature may mitigate thee!ects of taxes in the lottery bond market, but they do not substitute for them, incontrast to the case with U.S. equities.

The ex-distribution behavior of lottery bonds supports tax-based interpreta-tions of ex-day returns. We show that, in an environment where the marginalinvestor is relatively easy to identify, and where the tax-induced preferences ofsuch investors are very di!erent than the dividend case, prices behave just as thetax-based interpretations of ex-day returns would suggest they should. Lotterybonds pay cash distributions that are taxed favorably relative to capital gains,and prices fall by more than the anticipated distribution. On average, we foundprice decreases of 130% of the distribution across all of our sample. Indeed, weshow that the tax-induced preference for the cash distribution can, and in thedata often does, lead the bonds to trade at negative yields. The price of the bondis so high, re#ecting the tax shelter it o!ers, that on a pre-tax basis the internalrate of return is negative. The price drop that occurs over the ex-distributionperiod is larger in periods when marginal tax rates are high, and when the taxcode allows more generous use of the associated capital loss. The tax ratesimplied by the return over the ex-distribution period are less than the maximumstatutory rates, but well within the range of plausibility given the participants inthe market. Tax rates vary from 43% to 55% in the early years of our sample,and from 6% to 24% in the later years. Estimates of average marginal rates fromStatistics Sweden (1995), based on tax returns, are between 52% and 54% in theearly years and a #at 21% in the later years.

The rest of the paper is organized as follows. In Section 2 we describe lotterybonds, our data set, and the tax and trading environment in Sweden, with anemphasis on the factors that are most important for ex-day behavior. Wepresent some results on volume around the distribution period in Section 3.Section 4 studies the curious phenomenon of the negative yields at which thesebonds often trade, and in Section 5, our empirical results are presented andinterpreted. In Section 6, we evaluate the robustness of our results to various


departures from our assumptions regarding transactions costs and expectedreturns. Section 7 brie#y concludes.

2. Institutional and tax background

In this section, we outline the features of the Swedish lottery bond market thatmake it a unique and interesting laboratory in which to study ex-day returns.

2.1. The lottery bond market and data set

Lottery bonds are Swedish government bonds that di!er from regularSwedish Treasury obligations in two major respects. First, coupon payments areexempt from taxes, while capital gains and losses are taxed as they are taxed onother securities. Second, the coupons are distributed by lottery. The totalamount distributed at each coupon payment date is "xed, so that, from thestandpoint of the Swedish government, the liability associated with any givenissue is riskless. The bonds are numbered, however, and payments made toparticular bonds within an issue are based on drawings of these numbers.

The distribution for the cash payments on the bonds is observable, and therisk associated with the lotteries is, by construction, non-systematic. Thus, assetpricing theory would predict that the bonds would be priced, after adjusting fordi!erences in taxation, as perfect substitutes for other Swedish Treasuries. Thisquestion is studied by Green and Rydqvist (1997), who argue that specialfeatures of the lottery make it possible to directly observe the price of non-systematic risk. The bonds are traded in mixed and sequenced form. Mixedbonds are individual bonds, or blocks of bonds with numbers out of order.Sequenced bonds are blocks with numbers in sequence. Since the lottery hasmultiple levels, holding the bonds in sequenced blocks guarantees part of thedistribution. Green and Rydqvist (1997) provide details on this aspect of thelotteries, and show that the sequenced blocks appear to command a premiumbecause of their perceived lower risk. Based on this evidence, it is possible thatclienteles with di!erent tax positions and risk preferences hold the bonds inmixed and sequenced forms. Therefore, we report evidence on the ex-coupon-period returns using prices of both sequenced and mixed blocks.

Over our period of study the Swedish Treasury #oated between one and threeissues of lottery bonds per year. The bonds are, by convention, denoted by theyear and number of issuance. For example, the second issue of 1991 is denoted&91 : 2'. Coupons on the bonds are paid either two or three times per year, andthe bonds in our sample are all issued with between "ve and ten years tomaturity. The bonds have relatively low face values, to accommodate the retailmarket. Lottery bonds are traded on the Stockholm Stock Exchange. On a dailybasis, the Swedish "nancial press reports transactions prices and bid}ask quotes


for the bonds trading in mixed form, and for various sizes of blocks of bondswith sequential order numbers. These prices are reported for blocks of 50 and100 sequentially ordered bonds, and also, for some issues with low face value, forsequenced blocks of 500 and 1,000 bonds. Our data consist of daily end-of-daybid and ask prices for the 46 di!erent lottery bond issues outstanding over theperiod November 1986 to May 1997. In our calculations, we use the bid prices.These prices are the highest bid in the open book of the computerized Stock-holm Stock Exchange. Thus, unlike U.S. bond price data based on phonesurveys, these bid prices represent a commitment to trade.

With most "xed-income securities, when a transaction occurs between cou-pons, the buyer pays the seller accrued interest along with the price of the bond.This extra payment represents that portion of the coupon the seller has earnedby holding the bond through part of the coupon period. The accrued interestdoes not enter the buyer's tax basis. Rather, it reduces the buyer's tax liability byo!setting part of the "rst coupon payment the buyer will receive. Lottery bondsare not treated this way, apparently because the payments to individual bondsare random. Instead, lottery bonds are treated like equities. The higher pricethat must be paid to the seller to compensate her for the interest she has earnedby holding the bond through part of the coupon period is capital gain for theseller, and becomes part the buyer's tax basis. When the coupon is paid, the priceof the bond falls, and if the bond is sold the price drop is treated as a capital loss.Thus, the bonds o!er a unique experiment in the ex-day behavior of a non-equity security.

As equity returns are typically more volatile than bond returns, lottery bondso!er the opportunity to obtain less noisy estimates of the ex-day e!ects. Thisadvantage is somewhat mitigated, however, by two other features of this market.

First, for most of the bonds in our sample, lotteries are held on Monday. Foreach lottery trading is suspended for six business days before the lottery and sixbusiness days after the lottery. Thus, we observe the cum-coupon price and theex-coupon price twelve business days, and twenty calendar days, apart. For thebonds issued from 1996 on, lotteries are held on Wednesday, and the total tradingsuspension has been reduced to six business and eight calendar days. Since manyof the bonds are held in accounts at Swedish banks, the trading suspensions allowtime before the lottery for the bank to register the series and order numbers of anybonds they hold with the treasury authorities, and then to collect the lotterypayments before ownership changes. The period of suspended trading also in-creases the amount of noise in the ex-distribution return, and may bias theestimates of excess returns due to mismeasurement of the expected, or normal,return over the period. However, we "nd negative returns over the ex-distributionperiod, because the price falls by much more than the coupon. Thus, simplyignoring the bias, by assuming the normal expected return is zero, is conservative.

Second, a common problem to all studies of ex-dividend day returns is thatmany ex-days occur on the same calendar day, which leads to correlated error


Table 1Numbers of lotteries and days on which lotteries occurred Swedish lottery bonds bonds issued underdi!erent tax regimes

Numbers in the body of the table indicate the number of lottery days on which the speci"ed numberof lotteries occur, for the subset of the sample associated with a given tax regime. For example, forbonds issued before 1981, our sample includes 19 days, on each of which three lotteries occurred. Forthe post-1990 data, there are 65 days on which exactly one lottery occurred. All bonds issued in1977}1982, and the "rst two issues in 1983 have synchronized lotteries. The bonds issued withina given year pay on the same dates. The bonds issued in 1989, 1991, 1992, and 1995 also havesynchronized lotteries, but there are one or two lotteries held for the "rst bond before #otation of thesecond bond of the year. The bonds issued in 1987, 1988, 1993, and 1994 also have synchronizedlotteries, but the "rst lottery of the second bond of the year is not synchronized with the lotteries ofthe "rst bond, and there are one or two lotteries held for the "rst bond before the #otation of thesecond bond of the year. All bonds issued in 1984, 1985, 1986, 1996, 1997, and the third bond 1983have nonsynchronized lotteries.

Tax regime Number of lotteries per day

1 2 3

Pre-1981 0 0 191981}1990 74 21 1Post-1990 65 107 0Lottery days 139 128 20Total number of lotteries 139 256 60

terms. Overlapping ex-days are particularly problematic for lottery bondsbecause the two or three bonds issued within a given year often have identicalterms, and pay their coupons on the same days. The degree to which this is thecase varies across years. For example, the three bonds issued in 1982 makelottery payments on the same dates, while those issued in 1985 do not. Thus,while we have 455 lotteries in our sample, these occur on only 287 lottery days.Table 1 summarizes the distribution of lotteries and lottery days across the threetax regimes that were operative within our sample period, which are detailedbelow.

We follow other authors (e.g., Eades et al., 1984) by forming portfolios of allbonds with lotteries occurring on the same day, and treating the outcome foreach portfolio as a single data point. Again, this adjustment represents a conser-vative approach, and reduces the number of observations in our tests by a half toa third.

2.2. The tax environment

The interest proceeds from lottery bonds are not subject to income tax inSweden. They are treated like other state lotteries, the payments from which are


subject to a special lottery tax at a #at rate of 20%, but do not contribute toordinary income. Thus, apart from the requisite accounting entries on the partof the Treasury, this tax simply serves to reduce the lottery prizes by 20%.Consistent with prevailing convention in the market, we quote coupon rates netof this special tax. E!ectively, then, the coupon rates as quoted in our data aretax-exempt.

As has been noted already, capital gains and losses are handled in the sameway as with other bonds, except that interest is not accrued. Price appreciationprior to the lottery is treated as a capital gain to a seller, and raises the tax basisof a buyer. Any drop in price associated with the distribution of the lotteryproceeds is a capital loss.

Capital gains on "xed-income securities in Sweden, prior to 1991, were taxedat 100% of the ordinary marginal rate if the asset has been held for less than2 years, 75% if held for 2}3 years, 50% if held less than 3}4 years, 25% if heldless than 4}5 years, and 0% if held for more than 5 years. The top marginalcapital gains rate was 88% in 1979. This rate had dropped to 80% by 1986,when our sample period begins. The top capital gains rate continued to dropyear by year until it reached 65% in 1990. Since the 1990 tax reform in Sweden,all realized capital gains, both short and long term, are taxed at a #at rate of30%, as is other investment income, such as dividends and interest.

Prior to 1981, losses on lottery bonds could be fully utilized to o!set any otherincome. In 1980, this feature was changed. On bonds already issued, capitallosses could o!set only gains on equities and lottery bonds, but since the 1980ssaw dramatic increases in Swedish equity prices, the losses from these bondscould generally be fully utilized. For bonds issued after 1980, only gains fromlottery bonds could be o!set with lottery bond losses. The 1990 tax reform inSweden liberalized the use of lottery bond losses, and also #attened the taxschedule. After 1990, 70% of capital losses on lottery bonds can be used to o!setany investment income, and non-investment income up to a limit of 100thousand Swedish Kronor (SEK).1 Beyond this limit, 49% of lottery bond lossesare deductible against additional income. For example, suppose an investor hascapital gains on equity of 1 million, and salary income of 200,000. Seventypercent of capital losses on lottery bonds up to 1.1 million can be utilized, andwill generate tax savings at a rate of 21% of the losses, calculated as the 30% taxrate times the 70% loss utilization rate. If the capital losses on lottery bonds are1.2 million, the last 100,000 will only yield tax savings at a rate of 14.7%, 30%times 49%. Presumably, most investors who are engaged in ex-day trading inlottery bonds have other investment income. If this is the case, the limit of100,000 is not binding. Findings of lower implicit tax rates in the more recent

1The Kronor traded at an average of roughly 6 SEK to 1 USD over our sample period.


Table 2Tax rates applying to capital losses in Sweden, November 1986 to May 1997

The middle column contains the maximum statutory tax rates for each period. The right columnreports, for 1986}1990, the average marginal realized tax rates estimated from tax forms in StatisticsSweden (1995). From 1991}1997, investment income, including realized capital gains, is taxed at30%, but only 70% of losses on lottery bonds can be used to o!set this income, leading to the rate of21%, as shown.

Year Highest marginal rate Average marginal rate

1986 0.80 0.5211987 0.77 0.5321988 0.75 0.5431989 0.73 0.5431990 0.65 0.5211991}1997 0.21 0.210

sample periods, however, could be consistent with the e!ective marginal tax ratebeing lower than 21%. Thus, in the period 1991}1996, lottery bond lossesgenerally generate tax savings at a rate 21%. The maximum tax rates that wouldapply to lottery bond losses are detailed year to year in Table 2.

Corporate tax rates could in#uence ex-coupon returns. Prior to 1991, how-ever, corporate tax rates, at 52%, were low relative to individual rates. In morerecent years, the maximum corporate rate was 30%, from 1991}1993, and 28%from 1994}1997.

By purchasing lottery bonds immediately prior to the suspension of tradingfor the lottery period, and then selling afterwards at the ex-distribution price, aninvestor taxed in Sweden could earn a tax-free coupon, and generate an expectedcapital loss. While the coupon distribution is random, the risks associated withthe transaction can be dramatically reduced by holding portfolios of the bondswithin an issue. Since the bonds are issued with low face values of 200, 1,000,5,000 or 10,000 SEK, this diversi"cation is easy to achieve for wealthy, high-taxinvestors. Ownership data for lottery bonds issued in 1996}1997 indicate thatholdings are widely dispersed and include many small individual investors.Certainly many holders of the bonds would "nd diversi"cation within an issuedi$cult to achieve because of wealth constraints. On the other hand, the traderswho are actively involved in tax-motivated trading around the ex-day, and whoare therefore important to price formation in that period, are likely to be fromwealthy, high-tax clienteles. Since the lotteries are drawn across millions ofbonds within a given issue, the payments to each bond are almost independentand identically distributed, so the diversi"cation is very e!ective. The higherprizes in the lotteries are drawn without replacement. Thus, payo!s are notperfectly independent across bonds. The small levels of negative correlation thispayout structure induces actually increase the bene"ts of diversi"cation.


As a result, tax-motivated trading in the lottery bonds has been extremelypopular. Indeed, in the early years of our sample, when tax rates were very high,an active forward market in the bonds developed to reduce the risks associatedwith holding the bonds over the lottery period. The Swedish Treasury hasmoved to control this quasi-arbitrage by limiting the extent to which lotterybond losses can o!set other income.

Our sample covers three tax regimes. On bonds issued prior to 1981, lossescould be fully utilized. The last such bond in our sample matured in 1990. In theperiod 1986}1990, the top marginal rate fell from 80% to 65%, and the taxschedule was quite progressive. Thus, we might expect to see ex-coupon periodreturns on these bonds re#ecting high tax rates. On bonds issued after 1980, buttrading before 1991, losses were only valuable to investors with capital gains onlottery bonds. Thus, we would expect to see much lower implicit tax rates in theex-coupon period returns for these bonds, and perhaps we should observereturns consistent with tax-neutral investors. On bonds trading after 1991,lottery bond losses generate a tax shield of 21% for most investors.

2.3. Restrictions on tax neutral traders

A major problem with interpreting ex-day returns for U.S. equities, as empha-sized by Kalay (1982), is ambiguity regarding the identity of the marginal traderin the market. If the price falls by less than the dividend, so that, as Elton andGruber (1970) conjecture, long-term holders of the stock are indi!erent betweenselling cum- or ex-dividend, then there are incentives for short-term investors,dealers, or tax-exempt institutions to buy at the cum-dividend price, capture thedividend, and then sell the security. An interesting feature of the lottery bondmarket is that there are no investors in an obvious position to exploit pricingthat re#ects the desirability of coupons to taxable investors.

First, for a given tax rate, the positions of a long-term holder of the bond anda short-term tax arbitrageur are symmetric. Following Elton and Gruber (1970),suppose we ignore uncertainty and discounting over the ex-coupon period. Aninvestor holding the bond with basis PH, with tax rate q, can sell at thecum-coupon price, P#, and receive

P#!q(P#!PH). (1)

Alternatively, he can wait, receive the coupon of C, and sell at the ex-couponprice, yielding

P%#C!q(P%!PH). (2)

Equating the two gives:

P#"P%#C

1!q, (3)


which is the analogue of the condition that Elton and Gruber (1970) derive tocharacterize the indi!erence of the long-term investor, except that here the cashdistribution is tax-preferred. In our case, a short-term investor, with the sametax rate, who buys at the cum-coupon price, captures the coupon, and then sellsat the ex-price would be indi!erent to doing so if:

!P##P%#C!q(P%!P#)"0, (4)

which also yields Eq. (3).Only a low-tax or untaxed short-term investor would have motives to trade if

Eq. (3) prevailed, but such an investor would wish to reverse the transactiondescribed above. She would wish to short-sell the bond, at a price that re#ectsthe full value of the tax loss to a high-tax investor, and then pay the coupon andcover the short position at the ex-period price. While there is a developedrepurchase market for regular Swedish Treasuries, there has never been a shortsale of lottery bonds. There seem to be at least two reasons for the absence ofshort sales. First, the tax-exempt status of the coupon payment cannot be passedthrough the short sale. The interest payment made by the short seller to theowner of the bond, in lieu of the coupon, is taxable. If the tax rates of the twoinvestors were the same, then a taxable payment could be negotiated that wouldleave them each willing to trade, but this payment would be unique to everytransaction, and in any case would make the trade unattractive to a low-taxshort seller borrowing from a high-tax bondholder. Second, the short positionwould have to be collateralized against the possibility that one of the bondsinvolved won the largest payment in the lottery. The top lottery prizes on thebonds are one million SEK. Indeed, it could be the case that passing the lotterythrough to the owner of the bond would be construed as violating the Swedishstate's legal monopoly on lotteries.

Finally, foreign access to the lottery bond market is limited. Because the bondsmake tax-exempt interest payments, and tax rates in Sweden have at times beenquite formidable, they trade at very low yields. The low yields make lottery bondsunattractive to anyone who would be taxed on the interest payments, and limitsthe set of relevant possible marginal investors under consideration.

For these reasons, trading against pricing that re#ects di!erential taxation ofcash distributions and capital gains is di$cult, even for tax-exempt investors.Thus, we fully expect prices to conform to Eq. (3) in this market. A "nding thatprices did not behave in this manner would cast doubt on tax-based interpreta-tions of ex-day returns in other markets, where the assumptions behind theproposed relationship are on shakier ground.

2.4. Transactions costs and price discreteness

The presence of transaction costs will bias our estimates of implicit tax ratesdownwards. The implicit tax rate is the rate of an investor who would be


Table 3Average bid}ask spread for Swedish lottery bonds across tax regimes

Bid}ask spread for Swedish lottery bonds are expressed as a percentage of the midpoint price.Sequenced bonds are sold in blocks of 100 bonds, and entitled to a guaranteed distribution. Mixedbonds have the same expected distribution, but none of the distribution is guaranteed. In addition tothe spread, there is also commission of 0.30% per transaction, and during 1989}1992, a transactiontax of 0.15%. Data are daily price quotes from the Stockholm Stock Exchange, 11/1986}5/1997.

Tax regime Mixed bonds Sequenced bonds

Pre-1981 0.48 0.421981}1990 0.86 0.51Post-1990 0.94 0.93

indi!erent to trading or not trading for a given expected ex-period price drop.As transactions costs reduce the net after-tax receipts from a series of tax-motivated transactions, tax rates would have to be higher than those weestimate when ignoring transactions costs to encourage tax-motivated transac-tions. At the end of Section 5, we provide some diagnostics to evaluate thequantitative importance of transactions costs for our empirical "ndings.

Table 3 reports the bid}ask spread as a percent of the midpoint price. Inaddition to the spread, there is a commission of 0.30% and a special transactionstax in 1989}1992 of 0.15%. Thus, the round trip trading cost amounts tobetween 1% and 2% of the value of the trade. This cost is generally much lowerthan the coupon yield per lottery, so that, at reasonably high tax rates, taxarbitrage would be pro"table if the price fell only by the amount of the cashpayout. It is also evident from the table that the spreads are lowest in the periodswhen tax rates were highest, and in the periods when loss utilization provisionswere most liberal.

The lottery bond market we study naturally controls for nontax explanationsrecently proposed in the literature on ex-day equity returns. These explanationsrely on frictions that, while possibly present in this market, work in directionsthat are opposite to the tax e!ects.

Frank and Jagannathan (1998) study ex-day price changes on the Hong Kongstock exchange. In Hong Kong, neither capital gains nor dividends are taxed,yet they show the price drops on average by less than the dividend. They o!era theoretical explanation based on the &nuisance value' of the dividend. Marketmakers, who are assumed to bear lower transactions costs in collecting andreinvesting dividends, intermediate between sellers, who prefer to trade cum-dividend to avoid these costs, and buyers, who prefer to trade ex-dividend. Therents earned by the market makers due to their cost advantage are re#ected ina price drop of less than the full dividend. Their empirical tests support thisexplanation.


These arguments suggest that price drops of less than the full dividend in theUS markets may not be tax driven, because the tax e!ects and the nuisancevalue both operate in the same direction. Both considerations reduce the valueof dividends relative to capital gains. In the Swedish lottery bond market,however, the tax e!ects and the nuisance value would move prices in oppositedirections. The cash distribution is tax preferred. If it is also a nuisance of thesort described by Frank and Jagannathan (1998), this nuisance value wouldmitigate any tax e!ects present. The possibility of nuisance value for thedistribution renders our "ndings of price drops well in excess of the cashdistributed stronger, not weaker, evidence of tax e!ects.

Similar arguments would apply to the concerns raised in Bali and Hite (1998),who argue that even in a tax-neutral environment, price discreteness could leadto ex-day price drops that are less than the dividend amount. The cum-dividendprice re#ects both the present value of the imminent distribution and of ex-dividend price. If investors &round down' in determining what cum-dividendprice they will pay, the expected price drop will be less than the dividenddistribution. Since, with U.S. equities, the tick size is generally a large fraction ofthe dividend, this e!ect can be quite signi"cant. For their sample, Bali and Hite(1998) report a median dividend of 20 cents, to be compared to a tick size of 12.5cents. Since the tick size does not vary with the dividend, the ex-day return willalso be correlated with the magnitude of the dividend, leading to the appearanceof tax-induced dividend clienteles.

Once again, these e!ects suggest an undervaluation of dividends that could beconfused, in the US equity markets, with a tax penalty for dividends. In thelottery bond market, however, the relative tax treatment of the cash distributionand capital gains are reversed. While it may lead us to underestimate the taxe!ects and the implicit tax rates, this consequence of discreteness cannot explainour "ndings unless, for some reason, in this particular market investors roundup. Moreover, the tick size is inconsequential in the lottery bond marketrelative, to the size of the distributions. Table 4 reports minimum tick size, whichdepends on the face value of the bond, along with statistics describing thecoupons for the bonds at each di!erent face value in our sample. As the tableshows, the tick size is a very small fraction of the coupon in virtually all cases,and is much smaller than the excess price drops we report.

3. Abnormal volume

A "rst step in evaluating a tax-based hypothesis for ex-distribution returns isto consider whether volume around the ex-distribution period is unusually high.Abnormal levels of trading around the ex-distribution event do not necessarilyimply that there will be tax e!ects in relative prices. However, the absence ofevidence of unusual amounts of trading around distribution periods would


Table 4Distribution of coupons and tick size for di!erent face values of Swedish lottery bonds

Data cover lottery bonds trading from November 1986 to May 1997, and were supplied by theStockholm Stock Exchange and the Swedish Treasury. Face values, coupons and tick size arereported as Kronor per bond. The right-hand column reports the total number of days on whichlotteries for bonds with a particular face value were held.

Facevalue

Minimumtick size

Meancoupon

Mediancoupon

Minimumcoupon

Maximumcoupon

Lotterydays

200 0.10 5.94 5.98 4.00 7.50 1301000 1.00 20.04 19.25 10.00 32.00 1335000 5.00 164.06 161.25 161.25 172.50 4

10000 5.00 384.25 400.00 185.00 400.00 20

throw tax-based explanations of pricing behavior into doubt. Tax-based ex-planations of ex-period returns appeal to the incentives of taxable agents totrade immediately before and after the distribution.

The evidence of abnormal levels of trading around ex-distribution periods isvery strong in the case of Swedish lottery bonds. Fig. 1 shows average dailyvolume during periods surrounding the lotteries for each of the three taxenvironments that prevailed during our sample. Tax-motivated trading appearsmost dramatic for the bonds issued before 1980, for which losses could be fullyutilized.

Table 5 provides statistics regarding trading volume. For US equities,Michaely and Vila (1996) show that abnormal trading volume during an elevenday window around the ex-day is 196.3% for high yield stocks, and about 52%for medium and low yield stocks. Michaely and Murgia (1995) report thatcorresponding numbers for Italian common shares are 566%, and for Italiansavings shares, which are tax neutral, are 96%. The abnormal volumes in theSwedish lottery bond market are an order of magnitude larger, as can be seen inTable 5. In this table, we report cumulative abnormal volume calculated ina manner similar to that used in Michaely and Vila (1996) (see Eqs. (1)}(6) in thatpaper). We "rst compute average daily turnover using data from the non-lotteryperiod, beginning "ve trading days after the last lottery and ending "ve tradingdays before the current lottery period. For each of the "ve trading days prior toand following the current lottery, we compute the daily turnover in excess of thisaverage, as a fraction of the average. We then accumulate these percentageexcess turnover ratios over the "ve trading days before and after the distribu-tion. This procedure was repeated using a window of ten trading days before andafter the lottery.

The amount of abnormal trading around the lottery period is high under allthree tax regimes, but clearly is highest for the pre-1980 bonds. For these bonds,


Fig. 1. Trading volume around lottery. Daily average trading volume in millions of kronor from 50trading days before to 50 days after the lottery. Day 0 represents the ex-distribution period. Data arefrom the Stockholm Stock Exchanges, and cover the period November 1986 through May 1997.


Table 5Cumulative abnormal trading volume by tax regime and form of trading for Swedish lottery bonds,

Daily volume for lottery bonds trading in mixed and sequenced form were supplied by theStockholm Stock Exchange 11/1986}5/1997. Numbers in the body of the table are cumulativeabnormal volumes computed using two windows, "ve trading days before and after the distributionperiod, and ten trading days before and after the distribution period. For each trading day within"ve days before and after the distribution period, abnormal volume was calculated as that day'svolume divided the average daily volume over the period beginning six trading days after theprevious distribution and ending six days before the current distribution. These measures ofabnormal volume for each day were then accumulated over the "ve days before and after thedistribution to provide the cumulative abnormal volumes in the center columns of the table. Thesame procedure was repeated using ten days before and after the distribution, to compute the lastcolumn. The bonds sold in sequenced blocks receive a guaranteed portion of the distribution, whilebonds trading in mixed form do not. In each panel, the "rst row refers to bonds issued before 1980,the second to bonds issued from 1980 on, but trading before 1991. The third row refers to bondstrading from 1991 on.

Tax regime Abnormal volume over days around lottery

Ten days Twenty days

Panel A: All bonds

Pre-1981 2,758.9 4,939.81981}1990 1,153.1 1,562.8Post-1990 758.8 1,096.8

Panel B: Mixed bonds

Pre-1981 3,079.1 4,876.41981}1990 1,856.4 2,466.4Post-1990 668.3 1,011.7

Panel C: Sequenced blocks

Pre-1981 2,171.9 4,581.61981}1990 1,498.0 1,828.8Post-1990 816.7 1,194.2

full use of the tax losses from trading over the ex-period was permitted, and thetime period in our sample which includes these bonds is one when tax rates werequite high.

4. Negative yields to maturity

The role of di!erential taxation in the pricing of lottery bonds is perhaps mostevident in the negative yields at which these bonds trade immediately prior to


Fig. 2. Yield to maturity for a Swedish lottery bond issued in 1980 and maturing in 1990.Suspensions of trading around lotteries generate the gaps in the time-series. Yields are calculatedfrom daily price quotes from the Stockholm Stock Exchange.

the cash distributions close to maturity. Negative yields are also particularlystrong evidence of barriers to arbitrage by traders who are untaxed, or who aretaxed symmetrically on interest income and capital gains from the bonds. Recallthat the risks associated with the lotteries are purely idiosyncratic, and can bedramatically reduced through diversi"cation across the bonds within an issue.Thus, negative yields would be close to &free money' to any diversi"ed tax-neutral investor able to sell the bonds short.

Absent such tax-neutral arbitrageurs, however, negative yields to maturitycan prevail. Because the price drop associated with the bond passing throughthe ex-coupon can be utilized to o!set taxable income, the discounted value ofthese tax shelters can raise the bond price to the point that it exceeds the sum ofthe pre-tax payments. Fig. 2 plots the daily yield to maturity for the "rst bondissue of 1980 (issue 80 : 1) based on closing bid prices for 100-bond sequences,treating the coupon payouts as certain. The gaps in the plotted yields corres-pond to the periods around the lotteries when trading is suspended. Thebehavior for this bond is characteristic of those issued before 1981. For thesebonds, investors could fully o!set gains from other investments with capitallosses around the distribution. The yields around the coupon dates depicted in


the "gure suggest that the prices rise by more than the time value of the comingdistribution, or the &accrued interest', as the lotteries approach. This leads tonegative yields in some cases. After the distribution, the price drops by morethan the distribution, and the yields return to positive levels. This behavior alsoappears to become more pronounced as the bond approaches maturity. As istypical of lottery bonds, the "nal lottery occurs several months before the bondsmature, and thus the "nal set of yields are all positive.

In Fig. 3, we show the yields, averaged across bonds, around each of the "nallottery periods. Clearly, the evidence of negative yields before the distribution,and large jumps in yield around the distribution, becomes more pronounced asthe bonds approach maturity. The negative yields are most striking for the "nallottery period. The yields are very volatile in the last days of the bonds' lives, asis evident in Panel 4 of Fig. 3. The yields are very sensitive to small pricevariations, due to frictions such as tick size, when the bonds are extremely closeto maturity. For example, the derivative of the continuously compounded yieldon a pure discount, with respect to the price, is !(1/¹!t)(1/P), where ¹!t isthe time remaining to maturity. This quantity explodes as ¹!t goes to zero.

That such behavior is a natural response to the tax treatment of the bonds canbe easily illustrated for the certainty case. We o!er a simple example here, toillustrate how taxes can give rise to negative yields. A number of features of themodel, such as constant interest rate, a #at term structure, and 100% turnover inthe bonds, are counterfactual, and this example falls short of a comprehensivemodel of how the bonds are priced. Consider a bond maturing at date ¹ at thetime of the "nal distribution, date ¹!1. For simplicity, we will ignore the timedi!erential between the last trade cum-distribution and the "rst trade ex-distribution. We denote the coupon as C, and assume a "nal payment of facevalue 100 occurs in one period at date ¹. Assume that there are two types ofpotential holders of the bond, high-tax investors with tax rate q

H, and low tax

investors with rate qL. Nothing in this example precludes the case where these

rates are equal, or where the lower rate is zero. Both types of investors valuefuture after-tax payments by discounting them at an after-tax interest rate, r.Assume that at each point in time, investors compete in Bertrand fashion to buythe bond. In this example, then, demand is in"nitely elastic at the privatevaluation of the highest value holder. Under these assumptions, Lemma 1 in theAppendix derives expressions for the price immediately before and after the "naldistribution. The ex-coupon price is

P%T~1

"

100(1!qL)

1#r!qL

, (5)

and the cum-coupon price is

P#T~1

"

C

1!qH

#

100(1!qL)

1#r!qL

. (6)


Fig. 3. Yield to maturity around four "nal lottieries. Daily average yield from 50 trading days beforeto 50 days after the "nal lottery before maturity. Day 0 repreents the ex-distribution period. Yieldsare calculated using daily price quotes from the Stockholm Stock Exchange from 1986}1997.

The yield to maturity on the bond before the distribution, yT~1

, must satisfy,P#T~1

"C#100/(1#yT~1

), and will be negative if P#T~1

!C'100. Substitu-ting from Eq. (6), and simplifying, a negative yield will require

100r

1#r!qL

(CqH

1!qH

. (7)


Fig. 4. Numerical example of yields for Swedish lottery bonds. Yields are calculated for a bondissued with twenty periods to maturity, assuming three annual lotteries, a coupon rate C"6/3 per100 kronor of face value, a constant after-tax interest rate r"6/3%, a marginal tax rate fora high-tax investor of q

H"60%, and a marginal tax rate for a low-tax investor of q

L"30%.

This inequality can be satis"ed at very reasonable parameter values. With hightax rates, and when coupons exceed the discount rate, r, for the time remainingto maturity, yields are likely to be negative. Many of the bonds in our samplehave three lotteries per year. Assume, therefore, that C"6/3, r"0.06/3,qL"0.3, q

H"0.6, and that the last lottery is held four months before maturity.

The annualized yield at the ex-coupon price for this case is 8.57%, and at thecum-coupon price the yield is !0.67%.

The results of generalizing this example to multiple periods can be seen inFig. 4, which plots the yields against time to maturity. We assume certainty anda constant after-tax discount rate of 0.06/3 across maturities, dates, and inves-tors. At each date we determine the cum-coupon and the ex-coupon price bysetting them equal to the valuation of the highest value investor. We determinethe valuation for each investor by calculating the present value of after-taxreceipts for each possible realization strategy, and maximizing over these strat-egies. The payo!s to each realization policy, assuming the bond is purchasedat date t, depend on subsequent prices, but not on prices prior to date t.


Thus, starting as above at ¹!1, we can recursively determine prices and yieldsat each date through the bond's life. In this valuation, the computations aresimpli"ed considerably by two lemmas, stated and proved in the Appendix, thatrule out certain realization strategies as dominated. These establish that thehigh-tax investor, who is the high-value buyer of the bond cum-coupon, will "ndit optimal to immediately sell at the next ex-coupon price. Thus, at any date, thecum- and ex-coupon prices are related as follows:

P#t"

C

1!qH

#P%t, (8)

where qH

is the tax rate of the highest tax investor. Accordingly, once wedetermine the valuation of the highest value purchaser at the ex-coupon pricefor each date, we calculate the cum-coupon price using Eq. (8).

Numerical experiments with other parameter values, which are not reportedin detail suggest several things about the presence of negative yields for thebonds. First, the yields at the ex-distribution prices are always higher than at thecum-distribution prices, but there are some cases where, as in the data, bothyields are negative. For example, with two periods to maturity, C"9/3,r"0.03/3, q

H"0.6, and q

L"0.3, the cum-coupon yield is !8.63%, and the

ex-coupon yield is !2.33%. As the one-period analysis suggests, negative yieldsare more prevalent when tax rates are more heterogeneous and when interestrates are low relative to the coupon rates on the bonds.

In the data, as shown in Fig. 2, and in our numerical experiments, displayed inFig. 4, the yields jump when the bond passes through the ex-distribution period.The intuition for this resonse is simple. Investors can only shield taxes on theex-day, so that the present value of remaining tax shields is discontinuous intime. When the bond reaches the ex-distribution period, there is one less taxshelter opportunity remaining. Investors can earn interest, on the other hand,through the price appreciation of the bond any day, so that the time value factorevolves continuously. Alternative, nontax-related explanations for the low ornegative yields we observe would not, presumably, lead to such discontinuities.For instance, in the example under consideration, if all tax rates were zero, yieldswould be constant and equal to r, while prices would drop discontinuously ateach coupon date by the amount of the coupon.

Negative yields after the "nal coupon would also be inconsistent with atax-related explanation, and there are a few such observations. A few of thebonds issued in 1977 and 1982 were retired through exchanges on morefavorable terms than par value. They have been excluded from all our yield plotsand calculations. For bonds issued in 1985}1987, the Treasury paid handlingfees at maturity to dealers who collected and redeemed the bonds. Once the dataare purged of these two special cases, yields are all positive after the "nalcoupon.


The tax regime prevailing after the 1991 tax reform in Sweden does notsupport the above arguments for negative yields. Only 70% of capital losses cano!set other income or realized gains, which are taxed at 30%. Thus, thepurchasers of the bonds at the ex coupon price face a higher rate (30%) than thatfaced by investors buying cum-coupon and selling ex-coupon (21%). Neverthe-less, there were some occasions when yields became negative between April 1996and May 1997. This occurrence is due to some peculiar and dramatic liquiditye!ects at this time. On April 29, 1996, the Swedish treasury redeemed the 86 : 2bond, which was worth 11.6 billion SEK, while aggregate daily volume of alllottery bonds at the time was about 10 million SEK. The outstanding stock oflottery bonds fell 17% from 64.8 to 53.2 billion SEK. Holders of this unusuallylarge issue were so anxious to reinvest the proceeds in other lottery bonds thatthey forced prices into a range that implied negative yields. The same period alsosaw large purchases of lottery bonds by Bingo-Lotto, a non-pro"t foundationthat conducts prize drawings on a Swedish television station and pays its prizesin lottery bonds.

5. Ex-coupon returns

In Table 6, we provide some basic descriptive statistics for variables asso-ciated with the ex-period returns. We report these statistics for bonds in bothsequenced and mixed form. We also report separate statistics calculated treatingeach lottery as a separate observation and forming portfolios across all bondswith lotteries on the same day.

In comparison to similar statistics for U.S. equities (see, e.g., Boyd andJagannathan, 1994, Table 1, Panel A), the average price drop is much larger, asa percentage of the payment or of the cum-distribution price. The standarddeviation of the price drop as a percentage of the dividend is several orders ofmagnitude lower, as one would expect of a bond. This lower volatility prevailsdespite the longer period between observation of the cum-distribution and theex-distribution prices, two weeks versus one day. The standard deviations of theprice drop as a fraction of the cum-distribution price, and of the distribution asa fraction of the price, are very similar to what have been reported for U.S.equities.

5.1. Test methods

There are a number of methods researchers have employed to documentthe behavior of ex-day returns. Generalizing Eq. (8), while ignoring therequired return over the ex-period and any risk premium associated with the


Table 6Descriptive statistics for ex-period returns of Swedish lottery bonds, 1986}1997

In each panel the "rst row reports statistics for the price drop, over the ex-distribution period,divided by the expected coupon. The second row gives the price drop as a fraction of thecum-distribution price per bond. The "nal row reports on the coupon as a fraction of thecum-distribution price. Panels A and C give statistics computed treating each lottery as a separateobservation, even when those lotteries were held on the same days. Panels B and D report statisticsfor portfolios of the bonds having lotteries on the same days. Panels A and B give statistics for bondstrading in mixed form, which are not entitled to a partial guarantee, while Panels C and D reportsresults for bonds trading as sequenced blocks, which are entitled to a guaranteed portion of thedistribution.

Variable Mean Standarddeviation

Minimum Maximum

Panel A: Mixed bonds, separate observations (N"455)

Price drop over coupon 1.185 1.087 !5.555 5.882Price drop over pre-distribution price 0.029 0.025 !0.100 0.142Coupon over pre-distribution price 0.025 0.006 0.010 0.042

Panel B: Mixed bonds, portfolios (N"287)


Panel C: Sequenced Bonds, separate observations (N"435)


Panel D: Sequenced Bonds, portfolios (N"267)


lottery risk, gives

E(P#!P%)"1

1!qE(C). (9)

Boyd and Jagannathan (1994) estimate the simple regression:

P#!P%

P#"a#b

C

P##e (10)


and then ask whether the intercept is equal to zero and whether the slopecoe$cient, b is equal to 1/(1!q). A slope coe$cient of one suggests that taxpreference for one form of return over another does not a!ect pricing. Thismodel can also be estimated with the intercept constrained to be zero. By savingon parameters, this approach will produce smaller standard errors, when, as isour case, there is relatively little cross-section dispersion in the coupon yield.

Setting the intercept to zero and dividing both sides of Eq. (10) by C/P# yieldsthe empirical model tested by Elton and Gruber (1970):

P#!P%

C"b#

eC/P#

. (11)

As many authors have pointed out (e.g., Barclay, 1987), the Elton and Gruberequation is heteroskedastic. The variance of the error term decreases with thecoupon yield.

An alternative approach is provided by Eades et al. (1984), who focus onabnormal returns during the distribution period, above the expected dailyreturn, which is assumed to be constant. In the US equity data employed byEades et al. (1984), the time interval over which returns are measured is onetrading day, whether or not a dividend is paid over that interval. For our data,the return is calculated over one trading day when no distribution is paid, andover multiple days when there is a lottery payo! included in the return. Theirapproach is readily adapted to our setting. A more elaborate estimation methodcould incorporate information about current interest rates in estimating theexpected return. Our approach here is more directly analogous to that of Eadeset al. (1984), however, and the results appear robust across the estimationmethods we employ.

Let E(r) denote the average expected daily return, across both securities andtime, as in Eades et al. (1984). In any non-ex-period, the return earned by themarginal investor will conform to the following model:

Pt`1

!Pk

Pt

(1!q)"kE(r)#k+i/1

et`i

, (12)

where k denotes the number of calendar days associated with one trading day(e.g., 1 for weekdays, 3 for weekends). In the ex-period, if that period correspondsto k calendar days, the return will conform to:

Pt`k

!Pt

Pt

(1!q)#C

Pt

"kE(r)#k+i/1

et`i

. (13)

Algebraic manipulation of these two equations yields the following regressions.For the non-ex-period returns, where k"1:

Pt`1

!Pt

Pt

"

E(r)

1!q#

et`1

1!q. (14)


For the ex-period returns:

Pt`k

#C!Pt

Pt

"

E(r)

1!qk!

q1!q

C

Pt

#

1

1!qk+i/1

et`i

. (15)

We can estimate these equations with a pooled time-series and cross sectionalregression of the returns on two variables:

Rj"c

0xj0#c

1xj1#e

j, (16)

where Rj

is a return over either a day or an ex-period, xj0"k, and where

xj1"C

Pt, if j is an ex-period observation, and x

j1"0 otherwise. This regression

will give us c0"E(r)

1~q and c1" ~q

1~q. Since we use portfolios of bonds payingcoupons on the same dates, correlation between the errors due to this source willbe limited, but this regression clearly involves heteroskedastic errors. We reportresults using both unweighted, ordinary (OLS) least squares and weighted(WLS) least squares. The weights in the WLS regressions are simply 1

Jxj0.

5.2. Test results

Table 7 reports results of the tests involving ex-period returns alone, poolingdata from the three tax regimes in our sample. In Panels A and B of Table 7, the"rst row displays the sample mean of the price drop as a fraction of the expectedcoupon, as in Elton and Gruber (1970). The regression reported in Table 7 is themodel from Boyd and Jagannathan (1994), as shown in Eq. (10), with andwithout an intercept. Table 8 reports results of estimating the Eades et al. (1984)regression, Eq. (16), using the pooled sample data. (Hereafter, we refer to this asthe EHK model.) We report results using prices of bonds in mixed and se-quenced form. Bonds with lotteries occurring on the same day are combinedinto portfolios to reduce the impact of correlated errors from contemporaneouslotteries.

We have also conducted these tests using prices from 50-bond sequencedblocks. These tests yield results that are qualitatively similar to those reported,with estimated tax rates that lie between those associated with the mixed and100-sequence prices, consistent with the "nding in Green and Rydqvist (1997)that the 50-bond blocks are generally priced between the mixed and 100-bondblocks. We have also run these regressions treating each ex-period for each bondissue as a separate observation. Doing so approximately doubles the number ofobservations, but produces point estimates and standard errors close to thosereported in Table 7. For example, the slope coe$cient for the 100-bond se-quence in the larger sample regression is 1.641, versus 1.432, with a standarderror of 0.202, versus 0.215.

In each of the models we estimate, Eqs. (10), (11), and (16), the regressioncoe$cients are non-linear functions of the tax rates. We can invert this function


Table 7Regression results for ex-coupon returns

Data are from the Stockholm Stock Exchange, and cover the period 11/1986}5/1997. Observationsare pooled across tax regimes, and bonds having lotteries on the same day are combined intoportfolios to form a single observation. Sequenced bonds have a guarantee of part of the distribu-tion. Mixed bonds do not. There are 287 observations in the mixed bonds regression, and 267observations for sequenced bonds. The mean price drop is computed as the average change in priceover the ex-distribution period divided by the coupon, as in Elton and Gruber (1970). The regressionmodel, as in Boyd and Jagannathan (1994), projects the percentage price drop over the ex-distribution period on a constant and the coupon yield. The model with no intercept forces theregression equation through zero. The tax rate, q, is the rate of the marginal investor implied by theestimates of the model. Standard errors for coe$cients are in parentheses. The F-statistic tests thehypothesis that the intercept is zero and the slope is one, with the P-value in parentheses.Asymptotic standard errors for tax rates are computed using the delta method.

Variable Intercept Slopecoe$cient

F-statistic R2 q

Panel A: Mixed bonds

Mean price drop } 1.135 } } 0.119(0.060) (0.046)

Regression model 0.002 1.067 3.4 0.096 0.063(0.005) (0.194) (0.036) (0.171)

Regression model, no intercept } 1.128 } } 0.113(0.051) (0.040)

Panel B: Sequenced bonds

Mean price drop } 1.300 } } 0.230(0.065) (0.038)

Regression model !0.003 1.432 8.4 0.143 0.301(0.005) (0.215) (0.000) } (0.105)

Regression model, no intercept } 1.321 } } 0.243(0.057) (0.032)

to solve for point estimates of the implicit tax rates in terms of the pointestimates of the coe$cients. Using this transformation, we can also computeasymptotic standard errors for the tax rates using the delta method (see, e.g.,Greene, 1997, p. 278). Under the Boyd and Jagannathan (1994) model,for example, b"1/(1!q), so the point estimate of q is q("g(bK )"1!1/bK .The asymptotic variance of the tax rate is estimated withvar(q( )"[g@(bK )]2var(bK )"var(bK )/bK 4. Note that the non-linear nature of the


Table 8Estimates of abnormal returns

Data are from the Stockholm Stock Exchange, and cover the period 11/1986}5/1997. Observationsare pooled across tax regimes, and bonds having lotteries on the same day are combined intoportfolios to form a single observation. Sequenced bonds have a guarantee of part of the distribu-tion. Mixed bonds do not. There are 23,745 observations in the mixed bonds regression, and 21,356observations for sequenced bonds. The regression model projects the return over a trading period onthe number of days in the period, which is one for normal trading days and larger over ex-distribution periods, and the coupon yield during the trading period, which is zero on normaltrading days and positive during the ex-distribution period. The coe$cient on the number of days isc0, and the coe$cient on the coupon yield is c

1. The tax rate is the rate of the marginal investor

implied by the estimates of the model. The weighted least squares regression weights observationswith the inverse of the square root of the number of trading days. Asymptotic standard errors for thetax rates are computed using the delta method. The F-statistics, which measure the joint signi"canceof the coe$cients, are all signi"cant at traditional levels.

Sample c0

c1

Tax rate R-squared F-statistic

Panel A: Ordinary least squares

Mixed bonds 0.00018 !0.262 0.208 0.003 51.47(0.00003) (0.026) (0.016)

Sequenced bonds 0.00021 !0.489 0.328 0.019 222.73(0.00003) (0.026) (0.012)

Panel B: Weighted least squares

Mixed bonds 0.00021 !0.288 0.224 0.001 31.13(0.00003) (0.040) (0.024)

Sequenced bonds 0.00024 !0.511 0.338 0.005 85.62(0.00003) (0.039) (0.017)

transformation can change the relative magnitudes of the point estimates andtheir standard errors, since a function of the estimated coe$cient can be eithermore or less sensitive to sampling error than the coe$cient itself, depending onthe derivative of the function.

For all of the models we estimate, the null hypothesis of interest is that the taxrate re#ected in the ex-day returns is zero. This would correspond to a slopecoe$cient of one in the Elton and Gruber (1970) and Boyd and Jagannathan(1994) models. For the EHK model, it would correspond to a slope coe$cient onthe coupon yield, c

1, of zero.

The tables show that, on average, the price falls by considerably more than theexpected coupon, so that the estimated implicit tax rates are positive. The slope


coe$cients in Table 7 all exceed unity. The slope coe$cients in the EHK modelare negative, indicating an abnormally negative return over the ex-period. Theevidence that taxes a!ect pricing over the ex-distribution period is, therefore,robust across methods of estimating the ex-day expected return.

There are some discrepancies, however, between the di!erent estimationprocedures. One method, the Boyd and Jagannathan (1994) regression usingmixed bonds with a freely estimated intercept, produces a tax rate that, whilepositive, is insigni"cant, economically and statistically (see Table 7). The esti-mates for the 100-bond sequences, however, are similar in magnitude to thoseproduced by other methods, but still appear to be somewhat impreciselyestimated. The intervals of two standard errors for the coe$cients in the Boydand Jagannathan (1994) regression include zero for the intercept and unity forthe slope. The F-test of these joint restrictions on the parameters, however,rejects them. Since the intercept is economically close to zero, we estimate theregression forcing the intercept to be zero. This change leads to much tighterstandard errors for the slope coe$cient, with minimal reduction in the R2. TheR2 drops from 0.0957 to 0.0953 for mixed and 0.1431 to 0.1423 for sequencedbonds. The standard errors in the EHK model are orders of magnitude smallerthan the absolute values of the coe$cients. While the F-tests for the EHKregressions demonstrate that the model has explanatory power, the R2 statisticsfor this model are very low. This low level of explanatory power is attributableto the fact that, in contrast to the other models, we use all the daily returns, ofwhich only a small fraction are ex-distribution period returns. The variables inour regression are constants on all days except the ex-distribution days, so it isnot surprising that the regressions only explain a small fraction of the totalvariation.

The EHK model also assumes that the after-tax daily discount rate isa time-series constant, which cannot be true. Returns vary with interest ratesand possibly across bonds, and all of this variation is left to the residual. Thisfeature will also lead to cross-sectional dependence in the errors. As a result, theestimated standard errors will be smaller than the true standard errors. A simplerobustness check is to let the intercept vary with the interest rate, such that

Rj"c

0(y

t) x

j0)#c

1xj1#e

j, (17)

where ytis the daily before-tax yield of a six month Swedish Treasury bill. The

tax rates and standard errors we obtained from this regression, however, werevirtually indistinguishable from those in Table 8, so we do not report them indetail.

Each of the estimation methods we report has some advantages over theothers. The estimates of the sample mean, after Elton and Gruber (1970), are thesimplest and most parsimonious. The Boyd and Jagannathan (1994) regressionstest more fully the implications of the Elton and Gruber (1970) arguments. TheEHK regressions use data from non-ex-distribution returns to better estimate


the daily expected return, and thus provide a better assessment of whether thereturns over the ex-distribution period are abnormally high on a pre-tax basis.While the methods produce estimates that di!er in precision and slightly inmagnitude, they share common qualitative implications. Prices fall by substan-tially more than the coupon, on average, and the tax rates implicit in theex-distribution returns are within a range that is plausible, given average taxrates over the sample period.

Our results demonstrate that the ex-day return is much lower, and the implicittax rate considerably higher, for the 100-bond sequences than for the mixedbonds. There are two likely explanations for this result, which need not bemutually exclusive.

The di!erence may re#ect di!erent tax clienteles for the bonds in mixed versussequenced form. High-tax investors, engaged in tax-motivated trading aroundthe ex-distribution period, would "nd the sequenced bonds attractive becausethey are traded in large blocks. They also have lower administrative andhandling costs, since winning numbers can be veri"ed by checking an intervalrather than a hundred individual numbers. The mixed bond prices includetrades for small numbers of bonds being purchased by individuals who havelower tax rates, but hold the bonds because they have low face value, or becausethey value a highly skewed distribution and have no interest in diversifying.

Alternatively, the lower implicit tax rate may re#ect a higher expected returnthat is required by holders of the mixed bonds as a premium for the perceivedextra risk they bear. The sequences provide the holder with a guarantee for partof the distribution. Green and Rydqvist (1997) show that the sequences areconsistently priced at a premium over the mixed bonds, despite the non-systematic nature of the extra lottery risk, and despite the opportunities to avoidit through diversi"cation across lottery bonds themselves. Given that theyappear to earn higher expected returns by holding the mixed bonds, it isreasonable to expect much or most of the extra average return to be earned overthe lottery period, as that is when the uncertainty about the lottery is resolved.

The latter explanation receives some support from the evidence presented inTable 9. Along with price data for blocks that qualify for the partial guaranteeand mixed bonds that do not, we also have, for some of the bonds, price data forlarger sequenced blocks that also qualify for the partial guarantee. For example,for the issues between 1982 and 1987, the bonds trade as mixed, in 100-bondblocks that carry the partial guarantee, and in 1000-bond blocks that also carrythe partial guarantee. The table provides pairwise tests for di!erences in pricechanges over the lottery period on these various blocks. In each case, the meandi!erence in the price drop over the ex-distribution period is signi"cant whenone compares the mixed bonds to the smallest-sized block that quali"es for thepartial guarantee. In contrast, the di!erence between the price drops for blocksof di!erent sizes, each of which gets the partial guarantee, is economically andstatistically insigni"cant.


Table 9E!ects of guarantee versus block size

Matched price drops, as a fraction of the coupon, between mixed bonds and bonds with a partialguarantee, and between two di!erent sequences with the same partial guarantee. All issues in thesample trade in mixed form. For the bonds issued in 1982}1985, the second issue of 1986, and thetwo issues in 1987, the same partial guarantee goes to sequences of both 100 and 1000. For issues in1993}1994, sequences of 50 and 100 bonds receive the same partial guarantee. For bonds issued in1995, sequences of 10 and 20 bonds receive the same partial guarantee. The sample of large blocks iscomposed of the larger of the sequenced blocks within each pair. The mean di!erences and theirstandard error provide a paired test of the hypothesis that the price change is the same for bondstrading in the di!erently sized blocks. The estimates are based on portfolios of bonds having lotterieson the same day. The number of observations is 139.

Statistic (a) (b) (c)Mixed bonds,no guarantee

Small block,guarantee

Large block,guarantee

Mean 1.001 1.214 1.362Standard error 0.085 0.076 0.123

Di!erence (b)!(a) (c)!(b)Mean 0.213 0.148Standard error 0.058 0.104

5.3. Controlling for tax regime

Since tax rates vary across the tax regimes, it is natural to conjecture that theex-distribution returns would re#ect these changes. To evaluate this issue, wereport regressions using interactive dummy variables for the tax regimes. Forexample, we estimate the following dummy variable version of the Boyd andJagannathan (1994) regression:

P#!P%

P#"a#b

1A¹0-$)C

P#B#b2A¹.*$

)C

P#B#b3A

C

P#B#e, (18)

where ¹0-$

is a dummy variable for bonds issued pre-1980, and ¹.*$

is a dummyvariable for bonds issued post-1980 with the lotteries occurring before 1991.Corresponding versions of the no-constant model and of the Elton and Gruber(1970) tests can be estimated as well. Since we are interested in the tax rates,we sum b

1#b

3to solve for an estimate of the tax parameter for the old

bonds, and b2#b

3to obtain the tax parameter of the new bonds before 1991.

Results for these regressions using the ex-distribution period price changes, arereported in Table 10.


Table 10Joint estimation of e!ects of tax regimes

Data are from the Stockholm Stock Exchange, and cover the period 11/1986}5/1997. Bonds havinglotteries on the same day are combined into portfolios to form a single observation. Sequencedbonds have a guarantee of part of the distribution. Mixed bonds do not. There are 287 observationsin the mixed bonds regression, and 267 observations for sequenced bonds. In each model, thecoe$cients result from regressing the dependent variable against the independent variable interactedwith a dummy variable for the tax regime. The coe$cient b

1applies to observations on bonds issued

before 1981, b2

applies to observations on bonds issued from 1981 on and trading before 1991, andb3

to bonds trading from 1991 to 1997. The mean price drop is computed as the average change inprice over the ex-distribution period divided by the coupon, as in Elton and Gruber (1970). Theregression model, as in Boyd and Jagannathan (1994), projects the percentage price drop over theex-distribution period on a constant and the coupon yield. The model with no intercept forces theregression equation through zero. The tax rates, q

0-$, q

.*$, and q

/%8, are the rates of the marginal

investor implied by the estimated coe$cients for each tax regime. Standard errors for estimatedparameters are in parentheses. Asymptotic standard errors for tax rates are computed using the deltamethod.

Sample Intercept b1

b2

b3

q0-$

q.*$

q/%8

R2

Panel A: Mean price drop

Mixed } 0.650 0.250 1.008 0.397 0.205 0.008 0.032(0.241) (0.127) (0.076) (0.083) (0.064) (0.075)

Sequenced } 0.967 0.343 1.117 0.520 0.315 0.105 0.065(0.249) (0.136) (0.081) (0.054) (0.051) (0.065)

Panel B: Regression model

Mixed 0.010 0.763 0.400 0.524 0.223 !0.083 !0.909 0.162(0.005) (0.191) (0.111) (0.230) (0.155) (0.223) (0.838)

Sequenced 0.012 1.130 0.572 0.477 0.378 0.047 !1.009 0.250(0.006) (0.202) (0.131) (0.277) (0.107) (0.193) (1.215)

Panel C: Regression model, no intercept

Mixed } 0.703 0.317 0.935 0.390 0.201 !0.069 0.151(0.189) (0.103) (0.070) (0.065) (0.048) (0.081)

Sequenced } 1.019 0.428 1.036 0.513 0.317 0.034 0.237(0.197) (0.112) (0.079) (0.043) (0.037) (0.074)


A similar dummy variable version of the EHK model, which estimatesabnormal returns over the ex-distribution period, Eq. (16), is given by

Rj"c

01(¹

0-$) x

j0)#c

02(¹

.*$)x

j0)#c

03(x

j0)

#c11

(¹0-$

)xj1

)#c12

(¹.*$

)xj1

)#c13

(xj1

)#ej, (19)

where, again, xj0

is the number of days over which the return is calculated, andxj1

is the coupon yield during the ex-period, and zero otherwise. Since interestrates were not stable across the di!erent subperiods, we interact the tax-regimedummies with both the number of days variable and the coupon yield variable.Estimates that do not apply the tax-regime dummies to x

j0lead to very similar

tax rates and standard errors for the tax rates, suggesting the results are robustto this choice. The tax rates implicit in the parameter estimates of this model,Eq. (19), are reported in Table 11, along with the R2-statistics for the corres-ponding regressions.

Table 10 reports the results for the tests that use ex-period returns alone. Onceagain, the Boyd and Jagannathan (1994) model with a free intercept leads tohigh standard errors for the several slope coe$cients with some negative, butinsigni"cant, estimates of the implicit tax rates. The tax rates using the othermethods are all positive and of reasonable magnitude in the earlier periods. Thestandard errors are small relative to the magnitude. Tests of the hypothesis thatthe intercept is zero, while the slope coe$cients sum to one, which would beconsistent with a tax-neutral price drop, lead to F-statistics with small P-valuesfor all tax regimes.

Table 10 shows implicit tax rates falling across the three tax regimes. Ofparticular interest are the relatively low estimated implicit tax rates for bonds inthe post-1990 environment, in which losses shielded income at rates of either21% or 14.7%. Tests reported in the next subsection suggest this result may bedue to our failure to account for the bias induced by assuming a zero after-taxdiscount rate over the ex-period. Estimates of the implicit tax rates based on theEades et al. (1984) methodology, however, fall within range of prevailing mar-ginal tax rates in all subperiods, as can be seen in Table 11. These estimated taxrates are all over two standard errors from zero, except for the OLS estimatepost-1990 for the mixed bonds. The tax rates decrease across the three taxregimes, as one would expect.

Table 12 decomposes the estimated average bond returns into ex-period andnon-ex-period components. The decomposition is based on the estimated coe$-cients from the EHK regression in Eq. (19). For each tax regime, the "rst rowdisplays the estimated intercept muliplied by the number of days in the year.This calculation yields the average annualized daily non-ex-period return. Thesecond row gives the slope coe$cient, multiplied by the average coupon yieldand the number of coupon periods during a year. This "gure represents theaverage extra return earned during the ex-coupon periods through a year.


Table 11Estimated tax rates from abnormal return regressions, by tax regime

Data are from the Stockholm Stock Exchange, and cover the period 11/1986}5/1997. Bonds havinglotteries on the same day are combined into portfolios to form a single observation. Sequencedbonds have a guarantee of part of the distribution. Mixed bonds do not. There are 23,745observations in the mixed bonds regression, and 21,356 observations for sequenced bonds.Estimated tax rates are functions of the estimated coe$cients in a regression model that projectsthe return over a trading period on the number of days in the period, which is one for normaltrading days and larger over ex-distribution periods, and the coupon yield during the tradingperiod, which is zero on normal trading days and positive during the ex-distribution period.Each of these variables is interacted with a dummy variable for the tax regime. The R2-statisticsare also reported for each of these regressions. The weighted least squares regression weightsobservations with the inverse of the square root of the number of trading days. The separate taxrates are for bonds issued before 1980 (old), issued after 1980 but trading before 1991 (mid), andtrading after 1990 (new). Asymptotic standard errors for the tax rates are computed using the deltamethod.

Sample Tax rates

R2 q0-$

q.*$

q/%8

Panel A: Ordinary least squares

Mixed bonds 0.009 0.426 0.252 0.062(0.029) (0.022) (0.034)

Sequenced bonds 0.033 0.532 0.356 0.163(0.018) (0.016) (0.028)

Panel B: Weighted least squares

Mixed bonds 0.004 0.439 0.253 0.125(0.043) (0.033) (0.045)

Sequenced bonds 0.009 0.542 0.359 0.227(0.026) (0.023) (0.035)

Adding the two rows together, we have the average holding period return duringthe year. The last row reports the average yields. The table shows that, for theoldest bonds, the tax bene"ts from trading the bonds are so large that ona pre-tax basis they have slightly negative average holding period returns. Thefact that the coupons on the lottery bonds are large in comparison to dividendson U.S. equities means the abnormal returns we report are also much larger inabsolute value. For example, Barclay (1987) reports quarterly abnormal returnsof about 0.15%, or 0.6% when annualized, while the older lottery bondsin our sample earn abnormal ex-distribution returns of !6.5%, on average,in a year.


Table 12Decomposition of annual returns on lottery bonds by tax regime

Return calculations are based on the regression of returns on the number of days over which thereturn is earned and the coupon yield. Each of these variables is interacted with a dummy variablefor the tax regime. The "rst row of the table is, for each tax regime, the coe$cient on the number ofdays multiplied by the number of days in a year, or the annualized average daily return fornon-ex-distribution period. The second row is the coe$cient on the coupon yield multiplied by thenumber of coupon periods in a year, or the average extra return earned during the ex-distributionperiods in a year. The average before-tax return is then the sum of the "rst two rows. Data are fromthe Stockholm Stock Exchange, from 1986 to 1997. On bonds issued before 1981, investors couldfully utilize capital losses on lottery bonds to o!set other income. For bonds issued from 1981 on,but trading before 1991, losses could only be used to o!set gains on lottery bonds. In the post-1990period, losses on lottery bonds generate tax savings at a rate of 21%.

Portion of return Pre-1981 1981}1990 Post-1990

Non-exdays 0.059 0.050 0.102Exdays !0.065 !0.037 !0.018Before-tax return !0.006 0.013 0.084

6. Robustness checks

In the original arguments of Elton and Gruber (1970), transactions costs playno role. Investors are assumed to be coming to market as either buyers or sellers,and the only decisions they make involve the timing of their trades. Consistentwith the abnormal volume we observe, in our setting tax e!ects in prices can bedriven by short-term trading aimed at capturing both the coupon and thecapital loss. High-tax investors will bid the cum-coupon price up to more thanthe present value of the coupon and the ex-coupon price because of the value, tothem, of the capital loss. The price at which they are willing to buy, cum-coupon,will re#ect transactions costs they face and the opportunity costs of the fundsthey commit to the position. Thus, these frictions will a!ect our estimates of thetax rates implicit in the ex-distribution return. In this section we evaluate therobustness of our estimates to some simple adjustments for these factors.

6.1. Holding period returns

Across the three sets of results we have reported, the Elton and Gruber (1970)and Boyd and Jagannathan (1994) methods are estimated assuming the discountrate is zero over the ex-coupon period, while the EHK model does not make thisassumption. As we noted in Section 2.1, this assumption is conservative, as it willbias the estimates of the implicit tax rates downward. It may not be surprising,then, that the EHK method produces consistently higher point estimates.


In particular, the estimates for the post-1990 regime are close to the statutoryrates for the EHK model (see Table 11) while they are not signi"cantly di!erentfrom zero when obtained from the mean price drop, as in Elton and Gruber(1970), or from the coe$cients in a regression on the coupon yield, as in Boydand Jagannathan (1994) (see Table 10).

To check whether this assumption is in fact the source of the low pointestimates obtained using the Elton and Gruber (1970) and Boyd and Jagan-nathan (1994) methods, we reestimated these models discounting the ex-dayprice in the Boyd and Jagannathan (1994) model, Eq. (10), and in the Elton andGruber (1970) model, Eq. (11), to account for the time value of money. Thiscorrection is in the spirit of Kalay (1982). To compare the models on a commonbasis, we use as the discount rate the daily average return from the non-ex-coupon periods given by the intercepts in the EHK model in Table 8, which are0.00018 for mixed bonds and 0.00021 for sequenced bonds. The results arereported in Table 13. Using the EHK intercept produces estimates of the taxrates that are very close to those from the EHK model. Thus, we "nd that thevarious methods we have employed to estimate the ex-period abnormal returnall produce similar results after consistent adjustment for expected holding-period returns. This "nding is also reassuring, as it shows the EHK results holdup under methodologies where the cross-sectional dependence of the residualsdue to changing interest rates is less of an important consideration.

6.2. Bid}ask bounce

The estimates reported in earlier sections all use bid prices to computereturns. Since we have data on both bid and ask prices available, we nowinvestigate how the estimates change if we assume that the round-trip traderwould always buy cum-coupon at the higher ask price, and always sell ex-coupon at the lower bid price. For comparison, all other combinations are alsochecked: bid-to-bid, which is the basis for our earlier results, ask-to-ask, andbid-to-ask. This comparison allows us to evaluate the possibility that thetime-series variation in the estimated tax rates is driven by changes in thebid}ask spreads, and that the di!erence between mixed and sequenced bonds isexplained by the di!erence in bid}ask spread for the two forms.

Estimated tax rates are reported in Table 14 using the EHK approach andweighted least squares. The tax rates for the old bonds are very stable, simplyre#ecting that the bid}ask spreads were small for those bonds. In fact, thebid}ask spreads are probably unrealistically wide for the oldest bonds, sincemany transactions were carried out with forward contracts with smaller spreads.On the other hand, the tax rates for the new bonds are sensitive to how thereturn is computed. The estimated tax rates move from highly positive rates tonegative numbers, although the standard errors associated with the negativenumbers are large. Of course, short-term, round-trip tax-motivated trading


Table 13Ex-distribution period return estimates with positive expected returns

The ex-distribution period regression models from Table 10 are adjusted for positive expectedholding period returns by discounting the ex-distribution price by the estimated intercept from theEHK model, reported in Panel A of Table 8. Data are from the Stockholm Stock Exchange, andcover the period 11/1986}5/1997. Bonds having lotteries on the same day are combined intoportfolios to form a single observation. Sequenced bonds have a guarantee of part of the distribu-tion. Mixed bonds do not. There are 287 observations in the mixed bonds regression, and 267observations for sequenced bonds. In each model, the coe$cients result from regressing thedependent variable against the independent variable interacted with a dummy variable for the taxregime. Standard errors are in parentheses. The three tax regimes are observations on bonds issuedbefore 1980 (old), bonds issued after 1980 but trading before 1991 (mid), and bonds trading from1991 on (new). Tax rates for each regime, q

i, functions of the estimated parameters, and their

standard errors are computed using the delta method.

Sample Intercept b1

b2

b3

q0-$

q.*$

q/%8

R2

Panel A: Mean price drop

Mixed } 0.603 0.197 1.155 0.431 0.260 0.134 0.026(0.240) (0.127) (0.076) (0.074) (0.056) (0.057)

Sequenced } 0.874 0.263 1.287 0.537 0.354 0.223 0.050(0.249) (0.136) (0.081) (0.050) (0.046) (0.049)

Panel B: Regression model

Mixed 0.013 0.751 0.377 0.531 0.220 !0.101 !0.883 0.156(0.005) (0.190) (0.111) (0.229) (0.155) (0.230) (0.812)

Sequenced 0.015 1.080 0.533 0.495 0.365 0.268 !1.022 0.236(0.006) (0.202) (0.130) (0.276) (0.111) (0.200) (1.127)

Panel C: Regression model, no intercept

Mixed } 0.674 0.270 1.065 0.425 0.251 0.061 0.139(0.189) (0.103) (0.071) (0.058) (0.042) (0.062)

Sequenced } 0.942 0.354 1.188 0.550 0.352 0.158 0.216(0.197) (0.112) (0.079) (0.040) (0.033) (0.056)

involves buying cum-coupon at the ask price and selling ex-coupon at the bid.This activity increases the cum-coupon price relative to the ex-coupon price, andpushes the implicit tax rate up. In any case, regardless of how the return iscalculated, the variation across tax regimes remains the same, and the di!erencebetween mixed and sequenced bonds is the same. Thus, the spread does notappear to be the source of these behaviors.


Table 14Sensitivity of estimated tax rates to bid}ask bounce

Data are portfolios of bonds having lotteries on the same days. There are 23,745 observations in themixed bond regression, and 21,356 observations for sequence bonds. Sequenced bonds are entitledto a partial guarantee of the lottery distribution, while mixed bonds are not. The table displaysestimated tax rates for bonds issued before 1980 (old), issued after 1980 but trading before 1991(mid), and trading after 1990 (new). The tax rates are computed from coe$cients in weighted leastsquares regressions of returns against the number of days in the trading period and the coupon yield,both interacted with dummy variables for the tax regime. Standard errors, in parentheses, for the taxrates are computed using the delta method. Each row in the table reports tax rates estimated usingreturns calculated by buying at one price and selling at another. For example, the estimates in therow ask}bid were computed using returns calculated assuming the bond was purchased at the askprice, and sold at the bid.

Purchase and sales price Tax rates

q0-$

q.*$

q/%8

Panel A: Mixed bonds

Ask}bid 0.507 0.376 0.372(0.034) (0.024) (0.023)

Bid}bid 0.439 0.253 0.125(0.043) (0.033) (0.045)

Ask}ask 0.462 0.115 0.006(0.040) (0.047) (0.058)

Bid}ask 0.380 !0.161 !0.821(0.053) (0.081) (0.194)

Panel B: Sequenced bonds

Ask}bid 0.583 0.434 0.480(0.022) (0.018) (0.016)

Bid}bid 0.542 0.359 0.226(0.026) (0.023) (0.035)

Ask}ask 0.558 0.342 0.201(0.025) (0.025) (0.039)

Bid}ask 0.511 0.236 !0.652(0.030) (0.034) (0.163)


Table 15Sensitivity of estimated tax rates to commission and transaction tax

Data are portfolios of bonds having lotteries on the same days. There are 23,745 observations in themixed bond regression, and 21,356 observations for sequence bonds. Sequenced bonds are entitledto a partial guarantee of the lottery distribution, while mixed bonds are not. The table displaysestimated tax rates for bonds issued before 1980 (old), issued after 1980 but trading before 1991(mid), and trading after 1990 (new). The tax rates are computed from coe$cients in weighted leastsquares regressions of returns against the number of days in the trading period and the coupon yield,both interacted with dummy variables for the tax regime. Standard errors, in parentheses, for the taxrates are computed using the delta method. Returns used in the estimation for the ex-distributionperiods incorporate round-trip commissions and transaction taxes.

Sample Tax rates

q0-$

q.*$

q/%8

Mixed bonds 0.507 0.366 0.307(0.034) (0.025) (0.029)

Sequenced bonds 0.592 0.447 0.377(0.022) (0.018) (0.024)

6.3. Commission and transaction tax

In this section, we ask how the estimates react to inclusion of commissionsand transaction taxes. For all non-ex-distribution returns, we ignore the trans-actions costs. For the ex-distribution periods, however, we compute the returnsassuming the costs of a round trip transaction, while ignoring the bid}askspread. The return over the lottery period is computed assuming the bond ispurchased at PK #"P##0.0030]F, where F is the face value, and the bond issold at PK %"P%!0.0030F. An additional deduction from the return of0.0015]P##0.0015]P% is made during 1989}92 to account for the transac-tions tax during this period.

Estimated tax rates are reported in Table 15 using the EHK approach andweighted least squares. As would be expected, the transaction costs shift all taxrates up, but the pattern across tax regimes, and between mixed and sequencedbonds, is the same.

7. Conclusion

Using a sample of Swedish lottery bonds, we have provided evidence in thispaper that investors respond to tax incentives in their trading behavior, and that


prices re#ect this response. The taxation of the bonds encourages trading ina direction opposite to that associated with dividend distributions for equities.In the case of the lottery bonds, the cash distribution is tax-preferred to thecapital gain, while for most equities, the dividend is taxed at higher rates thancapital gains. This reversal in the tax preferences for one type of return overanother is associated in the data with a reversal in the behavior of ex-dayreturns. While the prices of equities fall by less than the dividend, prices oflottery bonds fall, on average, by substantially more than the coupon over theex-distribution period. Further, the magnitude of this e!ect di!ers across timeperiods and categories of bonds in the lottery bond market in a manner thatre#ects the prevailing tax regime.

Along with illustrating the e!ects of taxation on relative prices in thisparticular market, these results may shed light on ex-day return behavior moregenerally. Appeals to tax-based motives for trade would suggest that the relativevaluations of cash distributions and capital gains should be reversed in thelottery bond market, and this behavior is, in fact, what we observe. Thisobservation is not conclusive evidence that the ex-dividend behaviors in theequity markets are entirely tax induced, rather than attributable to micro-structural or other market frictions. There are a wider array of relevant clientelesin the equity markets. It is reassuring, however, that observed behavior in thismore limited market corresponds so closely to what tax-based argumentspredict.

Appendix A

Lemma A.1. The price of the bond immediately following the xnal distribution is:

P%T~1

"

100(1!qL)

1#r!qL

, (A.1)

and the price of the bond immediately prior to the xnal distribution is:

P#T~1

"C#P%T~1

#qH(P#

T~1!P%

T~1)"

C

1!qH

#

100(1!qL)

1#r!qL

. (A.2)

Proof. Denote the valuation of the investor with tax rate qi, i3MH, ¸N as

<%T~1

(qi).

Purchasing the bond at the ex-coupon price, P%T~1

, gives the buyer:

<%T~1

(qi)"

100

1#r!

qi(100!P%

T~1)

1#r. (A.3)


As long as P%T~1

(100, this valuation will be higher for the low tax rate investor,so

P%T~1

"

100

1#r!

qL(100!P%

T~1)

1#r, (A.4)

which when rearranged gives Eq. (A.1). As conjectured, this quantity is less than100.

An investor buying the bond cum-coupon receives

C#P%T~1

#qi(P#

T~1!P%

T~1), (A.5)

if he sells immediately at the ex-distribution price.Buying and holding for one period gives a present value of

C#

100

1#r!

qi(100!P#

T~1)

1#r"C#

100

1#r!

qi(100!P%

T~1)

1#r#

qi(P#

T~1!P%

T~1)

1#r

)C#P%T~1

#qi(P#

T~1!P%

T~1). (A.6)

The inequality follows from Eq. (A.4), the fact that qi*q

L, and the time value of

the tax shield qi(P#

T~1!P%

T~1). Comparing Eq. (A.6) to Eq. (A.5) shows it is

better for the high-tax investor to buy and sell immediately at the ex-distributionprice. It follows that the cum-coupon price is given by Eq. (A.2).

Lemma A.2. Let qL

be the tax rate the lowest tax investor pays on capital gains. Forany taxable investor, with q

i*q

L, who purchases the bond at a cum-coupon price,

the optimal realization strategy is to immediately sell at the next ex-coupon price.

Proof. Consider an investor with tax rate q. Suppose this investor buys at thecum-distribution price at date t, and optimally plans to sell at some future datet#k at price PH, other than P%

t. Denote the discount factor d,1/(1#r). Let

P<H be the present value of the dividend stream received up to the sale at t#k.Then the present value of the future payments from this conjectured realizationstrategy is:

P<H#[PH!q(PH!P#t)]dk"P<H#[PH!q(PH!P%

t)]dk!q(P%

t!P#

t)dk

)P%t!q(P%

t!P#

t)dk

)P%t!q(P%

t!P#

t). (A.7)

The "rst inequality follows from the fact that, by de"nition, P%tis the maximum,

over all possible subsequent realization strategies and over all investors, of theafter-tax payo!s given a tax basis of P%

t. Since P<H#[PH!q(PH!P%

t)]dk is the

present value of a particular realization strategy, it must be less than P%t. The

"nal expression on the right-hand side is the present value of the proceeds fromimmediately realizing the losses at the ex-distribution price.


Lemma A.3. Any taxable investor who purchases the bond at an ex-coupon price willweakly prefer to sell the bond at a future cum-coupon price rather than at anex-coupon price.

Proof. Consider an investor with tax rate s holding the bond with tax basis PH.We will show that the present value of after-tax payments, which we denote as<k

#, from selling at any future date t#k at the cum-distribution price weakly

dominates the value of selling at the same date at the ex-distribution price, <k%.

Selling k periods ahead at the ex-distribution price gives a present value ofafter-tax payments equal to:

<k%"

k+s/1

Cds#dk(P%t`k

!q(P%t`k

!PH)). (A.8)

Selling at the cum-distribution price k periods ahead yields a payo!with presentvalue:

<k#"

k~1+s/1

Cds#dk(P#t`k

!q(P#t`k

!PH)). (A.9)

Substituting for the cum-distribution price in Eq. (A.9), using Eq. (8), gives

<k#"

k~1+s/1

Cds#dkAP%t`k

#

C

1!qH

!q(P%t`k

#

C

1!qH

!PH)B"

k~1+s/1

Cds#dkC1!q1!q

H

#dk(P%t`k

!q(P%t`k

!PH)). (A.10)

Comparing Eq. (A.10) to Eq. (A.8), it is evident that the high-tax investor isindi!erent between the two realization strategies, while any investor witha lower tax rate prefers to sell at the cum-distribution price.

References

Bali, R., Hite, G.L., 1998. Ex dividend day stock price behavior: discreteness or tax-inducedclienteles? Journal of Financial Economics 47, 161}188.

Barclay, M.J., 1987. Dividends, taxes and common stock prices: the ex-dividend day behavior ofcommon stock prices before the income tax. Journal of Financial Economics 19, 31}44.

Boyd, J., Jagannathan, R., 1994. Ex-dividend price behavior of common stocks: "tting some pieces ofthe puzzle. Review of Financial Studies 7, 711}741.

Eades, K.M., Hess, P.J., Kim, H., 1984. On interpreting security returns during the ex-dividendperiod. Journal of Financial Economics 13, 3}35.

Elton, E., Gruber, M., 1970. Marginal stockholder tax rates and the clientele e!ect. Review ofEconomics and Statistics 52, 68}74.

Frank, M., Jagannathan, R., 1998. Why do stock prices drop by less than the value of the dividend?Evidence from a country without taxes. Journal of Financial Economics 47, 161}188.


Green, R.C., Rydqvist, K., 1997. The valuation of non-systematic risks and the pricing of Swedishlottery bonds. Review of Financial Studies 10, 447}480.

Greene, W.H., 1997. Econometric Analysis. Prentice-Hall, Upper Saddle River, NJ.Hayashi, F., Jagannathan, R., 1990. Ex-day behavior of Japanese stock prices: new insights from new

methodology. Journal of Japanese and International Economics 4, 401}427.Kalay, A., 1982. The ex-dividend day behavior of stock prices: a re-examination of the clientele e!ect.

Journal of Finance 37, 1059}1070.Karpo!, J.M., Walkling, R.A., 1988. Short-term trading around ex-dividend days. Journal of

Financial Economics 21, 291}298.Kato, K., Loewenstein, U., 1995. The ex-dividend-day behavior of stock prices: the case of Japan.

Review of Financial Studies 8, 817}848.Lakonishok, J., Vermaelen, T., 1986. Tax-induced trading around ex-dividend days. Journal of

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ex-dividend day: evidence from the Milan Stock Exchange. Review of Financial Studies 8,369}400.

Michaely, R., Vila, J., 1996. Trading volume with private valuation: evidence from the ex-dividendday. Review of Financial Studies 9, 471}509.

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