Ticks and Tax: The Joint Effects of Price Discreteness and Taxation on Ex Dividend Day Returns

Transcription

1 Ticks and Tax: The Joint Effects of Price Discreteness and Taxation on Ex Dividend Day Returns C. Bryan Cloyd a, Oliver Zhen Li b, and Connie D. Weaver c, * a College of Business, University of Illinois, Champaign, IL 61820, USA b Mendoza College of Business, University of Notre Dame, Notre Dame, IN 46556, USA c Red McCombs School of Business, The University of Texas, Austin, TX 78712, USA May 1, 2004 Abstract We examine ex-dividend day stock price behavior before and after U.S. stock exchanges converted from discrete to decimal pricing systems in early 2001, as well as the effect of equalizing the federal income tax rates on dividend and long-term capital gain income in May Prior literature reports a robust empirical result that share prices decrease on the exdividend day by less than the amount of the dividend, but there is little agreement about whether this incomplete price adjustment is caused by share price discreteness, differential taxation of dividend income relative to capital gains, or other factors. Two recent studies, Graham, Michaely and Roberts (2003) and Jakob and Ma (2004), report that declining price discreteness (e.g. from 16ths to decimal pricing) had no material effect on the cum- to ex-day price-drop-todividend ratio. Although we report similar findings for the price-drop ratio, we find that ex-day abnormal returns declined significantly as a result of decimalization in 2001, and declined further in response to tax rate equalization in May Thus, our findings support the view that both price discreteness and differential taxation affect ex-dividend day stock price behavior. JEL classification: G12, G35 Keywords: Ex day; Dividend taxation; Price discreteness; Tick size The authors gratefully acknowledge the comments of Larry Brown, Dennis Chambers, Ross Jennings, John Robinson, and workshop participants at the universities of Texas at Austin, Illinois, Georgia State and Notre Dame. * Corresponding author: Tel: ; fax: address: Connie.Weaver@bus.utexas.edu (C.D. Weaver)

2 Ticks and Tax: The Joint Effects of Price Discreteness and Taxation on Ex Dividend Day Returns 1. Introduction The behavior of share prices around ex-dividend dates has been the subject of considerable theoretical and empirical research for nearly 50 years. Prior empirical studies consistently document that, on average, share prices decline on the ex-dividend day by less than the dividend amount, giving rise to positive abnormal returns on the ex-day. However, there is no consensus regarding the explanation for this result. Extant literature provides two primary explanations. First, many studies attribute the ex-day return anomaly to higher shareholder tax rates on dividend income as compared to long-term capital gains (e.g., Elton and Gruber 1970; Michaely and Vila 1995). 1 Related studies argue that, when transactions costs are relatively small, arbitragers will trade around the ex-day to reduce tax-induced abnormal returns to a point where they reflect transactions costs rather than the tax rate differential (e.g., Kalay 1982; Lakonishok and Vermaelen 1986; Michaely et al 1996). Second, positive ex-day returns may be induced by market microstructure, most notably to the pricing of stocks in discrete ticks, which precludes share prices from fully adjusting to dividend payments (e.g., Dubofsky 1992; Bali and Hite 1998). Of particular interest to this study are the microstructure explanation of Bali and Hite (1998) (hereafter, BH), and two recent studies that test implications of BH s model using 1 The effect of differential taxation on share prices has been tested by evaluating (1) the behavior of share prices around the ex-dividend period (e.g., Kalay 1982; Lakonishok and Vermaelen 1983; Eades et al. 1984; Michaely 1991), (2) the relationship between dividend yield and risk-adjusted returns (Brennan 1970; Black and Scholes 1974; Litzenberger and Ramaswamy 1979; Miller and Scholes 1982; Dhaliwal, Li and Trezevant 2002) and (3) share price reactions to changes in tax rates (e.g., Auerbach 1979; Poterba and Summers 1985; Ayers, Cloyd and Robinson 2002). 1

3 decreases in price discreteness from 1/8 ths to 1/16 ths in 1997, and from 1/16 ths to decimals in 2001 (Graham, Michaely and Roberts (2003) and Jakob and Ma (2004), hereafter, GMR and JM, respectively). BH argue that, because stocks trade in discrete ticks but dividend amounts are continuous and, on average, fairly small in amount, the price-drop-to-dividend ratio, or ex-day premium, defined as (P cum P ex )/Div = P/D, will be less than one even in the absence of differential tax rates. BH s basic intuition is compelling a buyer will not pay a full tick to receive a dividend of less than a tick. Accordingly, BH hypothesize that, in pricing stocks on the ex-day, the market systematically rounds down a dividend s value to the nearest tick, so that the change in share price is always less than the dividend amount. Contrary to the tax penalty hypothesis, discrete pricing also explains why share prices change by less than the value of nontaxable distributions (e.g., Eades, Hess and Kim 1984). Both GMR and JM test BH s prediction that, on average, P/D will move closer to unity as the pricing regime becomes less discrete. However, neither study finds evidence to support this prediction and, instead, GMR report that the median values of P/D moved further from unity as the pricing regime moved from 1/8 ths to 1/16 ths to decimals. We utilize two natural experiments to examine the joint effects of price discreteness and differential taxation on ex-day returns. First, following GMR and JM, we utilize NYSE s conversion from 1/16 ths to decimal pricing on January 29, 2001, to study the effect of price discreteness while holding tax rates constant. Second, we utilize a change in the federal income tax rate on dividend income approved by Congress on May 23, 2003, to study the effect of differential taxation while holding constant the pricing regime. Importantly, this tax law change offers the first opportunity to examine tax effects on ex-day share price behavior during a 2

4 decimal pricing era and, consequently, enables us to test the tax hypothesis in a more powerful setting than available in prior studies. Our study differs from GMR and JM in three ways. First, our tests focus on ex-day abnormal returns rather than P/D. Prior research indicates that P/D is a much noisier metric than returns for examining ex-day share price behavior (Eades et al. 1984), particularly for small samples (Boyd and Jagannathan 1994). Second, our post-decimal sample of ex-day observations is considerably larger than that of GMR and JM. Our sample period runs from January 1, 1999, through December 31, 2003, providing nearly three years of post-decimal observations compared to slightly less than one-year of post-decimal observations in each of the prior studies, both of which terminated their samples on December 31, Third, we perform regression analyses to explain cross-sectional variance in ex-day returns as a function of differential taxation, price discreteness, and transaction costs and risks associated with short-term trading. These differences in samples and research design lead us to draw remarkably different inferences about the effect of price discreteness on ex-day stock price behavior. Unlike both GMR and JM, we find that decimalization significantly decreased the relation between dividend yield and ex-day abnormal returns, consistent with microstructure-based arguments that price discreteness is at least partially responsible for positive ex-day abnormal returns. However, consistent with the tax hypothesis, we also find that equalization of the Federal statutory tax rates on dividend income and long-term capital gains in May 2003 further reduced the relation between dividend yield and ex-day abnormal returns. Finally, we find that cross-sectional differences in ex-day abnormal returns are related to differences in transaction costs and risks to short-term traders. In sum, we provide evidence that tick size, differential taxation, and transaction costs all play a role in determining ex-day stock price behavior. 3

5 The remainder of this study is organized as follows. The next section describes prior research and develops our hypotheses. Section two describes our sample. Sections three and four present our research method and results. Concluding remarks are provided in the final section. I. Prior Research and Hypothesis Development A. Differential Taxation A.1. Background In a strict theoretical sense, the expected ex-dividend day stock price drop should equal the dividend per share assuming perfect markets, certainty, and no taxes (Miller and Modigliani 1961). Any other ex day share price change provides arbitrage opportunities if transaction costs are low enough. Early empirical work, however, documents that the ex day price drop is, on average, less than the dividend (Campbell and Beranek 1955; Barker 1959). In explanation of this result, researchers posited that differential taxation of capital gains and dividend income for long-term investors affects the expected price drop and that arbitrage by tax-neutral investors is too costly to eliminate the tax discount. Elton and Gruber (1970) argue that for prices to be in equilibrium around the ex-day, marginal sellers must be indifferent on an after-tax basis between selling the stock on the ex-day, thereby receiving the dividend, or selling the stock on the last cum day. Such indifference requires the following equality: P cum t g (P cum P 0 ) = E(P ex ) t g [E(P ex ) P 0 ] + Div (1 t d ), (1) where P cum is the share price on the last cum day, E(P ex ) is the expected share price on the ex day, P 0 is the shareholder s per share tax basis used in computing capital gain, Div is the dividend per share, t d is the marginal tax rate on ordinary income, and t g is the marginal tax rate 4

6 on capital gains. Rearranging equation (1), Elton and Gruber show that the price-drop-todividend ratio is the marginal trader s tax preference ratio: P D = ( Pcum Pex ) Div = (1 t (1 t d g ) ) = τ (2) The tax preference ratio, τ, simply indicates that the marginal trader is indifferent between receiving a $1 dividend or (1 t d )/(1 t g ) dollars of capital gain. If t d > t g, then dividends bear a tax penalty relative to capital gains. The dividend tax penalty is: ( td t g ) PENALTY = = ( 1 τ ) (3) (1 t ) g Statutorily defined values of t d and t g vary across different types of investors. Long-term individual investors generally incur a dividend tax penalty because t d is often higher than t g. For example, the maximum individual income tax rate on dividend income was 39.6% in 1999 and 2000, 39.1% in 2001, and 38.6% in 2002, while the maximum tax rate on long-term capital gains held steady at 20%. Thus, for individuals subject to the maximum marginal tax rates, the value of τ was approximately 0.76 during these years. However, other types of investors have not historically incurred a dividend tax penalty. In general, corporate investors prefer dividend income to capital gains because they can exclude at least 70 percent of dividends received from other domestic corporations from their taxable income, whereas capital gains are fully taxed. 2 Brokers, dealers, short-term traders, and tax-exempt investors pay the same tax rate on both types of income such that, for these investors, τ is one. The differential tax hypothesis is that P/D is less than one, on average, because the value of the dividend included in P cum reflects the dividend tax penalty imposed on long-term individual investors. 5

7 A.2. Tax Hypotheses Expression (2) can be rewritten as follows to express the effect of differential taxation on ex-day pricing in terms of a return on P cum : ( P P + Div) Div = (1 τ ) (4) P P ex cum RETURN = cum cum From this expression it can be seen that whenever (1 τ) is positive (because t d > t g ), the ex-day return is increasing in dividend yield (Div / P cum ). Thus, our first tax hypothesis is: HYPOTHESIS 1: Ex-day abnormal returns are increasing in dividend yield when t d > t g. On May 23, 2003, Congress voted to lower the maximum statutory dividend and longterm capital gain tax rates for individuals to 15%, thereby mitigating the tax penalty on dividend income to long-term individual investors. 3 Nevertheless, these investors may still face a relative tax penalty on dividend income because dividend taxation is immediate, whereas the capital gains tax is deferred until the stock is sold. 4 Thus, despite the post-may 2003 equality between these statutory rates, the present value of t g is still less than t d for long-term investors. Our second tax hypothesis is that the positive relation between dividend yield and ex-day returns, 2 Corporation must meet several tests to qualify for this dividends received deduction. For example, a corporate investor must hold the dividend-paying stock for at least 45 days during the 90-day period centered on the ex-day. 3 The Jobs and Growth Tax Relief Reconciliation Act of 2003 was approved by both the House and Senate on May 23, Although the Act cleared the House by a comfortable margin ( ), approval by the Senate required the tie-breaking vote of Vice President Cheney (51-50). Ultimate approval by President Bush was assured. The 15% maximum rate on dividend income was made retroactive to January 1, 2003, while the rate reduction on long-term capital gains applied to sales occurring after May 5, However, because the legislation passed by such a narrow margin, investors were unlikely to fully impound these new rates into their pricing decisions until after they were approved by Congress on May 23, Individual investors could avoid capital gains taxation entirely by holding their shares until death. The investor s heir would receive a stepped-up basis in the shares equal to their fair market value at the date of death, and could sell the shares immediately thereafter without incurring a capital gains tax. This is consistent with the tax-timing option put forth by Constaninides (1984) and summarized by Allen and Michaely (2002). 6

8 created by the dividend tax penalty, will be smaller for ex-day observations after May 23, 2003, than before. HYPOTHESIS 2: The positive relation between dividend yield and ex-day abnormal returns is smaller after equalization of the Federal statutory tax rates on dividend and long-term capital gain income for individuals (May 23, 2003) than before. A.3. Tax Clienteles, Tax Rate Arbitrage and Transaction Costs The preceding section provides a tax explanation for the positive relation between dividend yield and ex-day abnormal returns, but also recognizes that tax rates vary across different types of investors. Heterogeneous tax rates across investors may mitigate the predicted positive relation between dividend yield and ex-day abnormal returns in three ways. First, investors may sort themselves into distinct tax-induced clienteles based on dividend yield. For example, individual investors who face a large dividend tax penalty may limit their investments to non-dividend paying stocks. On the other end of the spectrum, corporate investors may be the dominant investors in high-dividend yield stocks. In the extreme, a fully taxminimizing allocation of stocks across tax-induced clienteles could eliminate any overall relation between dividend yield and observed ex-day returns. Prior research suggest that while taxinduced clienteles exist, they are not so pervasive as to eliminate this relation (Lakonishok and Vermaelen 1986; Michaely and Vila 1996). Michaely (1991) finds an increasing and convex relation between dividend yield and P/D, which he attributes to potential clientele effects for stocks with high dividend yields, implying an increasing and concave relation between dividend yield and abnormal ex day returns. 5 Similarly, Naranjo et al. (2000) find a negative relation between ex day abnormal returns and dividend yield in their sample of very high-dividend-yield 5 We use the term concave (convex) relation to mean a negative (positive) second derivative. 7

9 stocks, for which they expect a corporate investor clientele. 6 In sum, the existence of tax clienteles with different τ values suggests that the overall relation between dividend yield and ex day abnormal returns is positive but concave at very high levels of dividend yield. Second, tax-neutral short-term traders may exploit tax-rate arbitrage opportunities if the dividend tax penalty reflected in cum-day share prices exceeds the short-term trader s round-trip transaction costs. Such dividend capture strategies would tend to bid up prices in the cum period to the point that any discount remaining in the cum price would be equal to the short-term trader s round trip costs rather than the dividend tax penalty incurred by long-term individual investors (Kalay 1982, 1984). In the limit, abnormal returns on the ex day would reflect these transaction costs, less the effects of any selling pressure as short-term traders close their positions. 7 Karpoff and Walkling (1988) provide evidence that ex day abnormal returns are positively related to transaction costs, and that short-term trading is most evident in high-yield stocks. Also consistent with short-term trading, prior research documents positive abnormal trading volume around the ex day (Lakonishok and Vermaelen 1986; Michaely and Vila 1995, 1996). Third, heterogeneous tax rates create incentives for long-term investors who decide to trade for non-tax reasons to strategically time these trades around the ex day such that the dividend is received by the investor who values it the most on an after-tax basis. Both types of tax-induced trading around the ex day would diminish the expected tax-induced relation between dividend yield and ex-day abnormal returns. 6 Recall that corporations have τ values greater than one reflecting their tax preference for dividend income. 7 Short-term dividend capture is most likely conducted by tax-neutral traders. Corporations are unlikely to engage in short-term dividend capture trading because they must hold the stock for a minimum of 45 days to claim the Footnote continued on the next page. 8

10 B. Price Discreteness If share prices are constrained to trade in discrete ticks while dividend amounts are continuous, then the ex-dividend day price drop cannot, in most cases, equal the dividend amount. How far the expected price drop [E( P) P cum E(P ex )] deviates from the dividend amount is a function of the tick size, the dividend amount, the buyer s and seller s tax rates, and whether shares trade at the bid price or, on average, somewhere in between the bid and ask prices. BH argue that discreteness causes E( P) to be strictly less than the dividend amount but within one tick of the dividend (page 127), leading to their conclusion that discreteness causes P/D ratios to be less than one but increasing toward one over the broad range as dividends approach $1 (page 134). Consequently, BH argue that differential taxation is not necessary to explain why observed values of P/D are, on average, less than one. Furthermore, because dividends and dividend yields are positively correlated, BH argue that tax clienteles are not necessary to explain why average P/D ratios tend towards one for high-dividend yielding stocks. Both of BH s conclusions regarding the unimportance of differential taxation and tax clienteles depend critically on their assumption that cum-day trades always occur at the bid price. BH argue that the market always will round down the value of a dividend to the tick just below the dividend because no buyer will pay a price greater than the dividend (page 132). In effect, BH assume that competition among arbitrageurs will force marginal prices to the highest level possible subject to the tick size (i.e. the tick just below the dividend amount), and that arbitrageurs are content to buy up all shares available at the tick below the dividend (pg. 136) dividends received deduction. Rather, corporate investors are more likely attracted to high-yield utility stocks Footnote continued on the next page. 9

11 because their transaction costs are very low. At this price level, the per share marginal cost of short-term trading could not exceed one tick, and in many cases would be less than one tick. We question BH s key assumption for two reasons. First, the assumed level of arbitrage costs in BH s model seems implausibly low. If short-term traders expect to incur the spread when buying and again when selling (Elton et al. 1984), a lower bound on their expected roundtrip trading cost is two ticks even without considering other direct costs of trading. Using data from NYSE s Trades and Quotes (TAQ) database, GMR report that the median effective spread for NYSE trades in the 1/16 ths era was $ on both the cum-day and ex-day, producing a median expected round-trip cost of $ By comparison, the median dividend in our sample is $0.12. Thus, short-term trading would appear to be a losing proposition for the majority of dividends unless arbitrageurs are able to trade within the spread via transactions that are not reported in TAQ. This analysis ignores other risks (e.g. overnight price fluctuation) that further reduce expected arbitrage profits. Second, even if short-term traders would offer a bid price equal to the tick below the dividend, this bid would be unacceptable to sellers in many cases. We argue that no seller will accept a cum-day price for the dividend that is less than the after-tax value the seller could realize by holding the stock until the ex-day. Consider a 12 cent dividend (our sample median) where prices are constrained to 1/16ths, the seller is long-term individual investor for whom τ = 0.76, and the buyer is a short-term trader with negligible transaction costs (per BH s assumptions). 8 Like BH, we initially assume that both parties hold common beliefs about E(P ex ), (Naranjo et al. 2000) or preferred stocks (Erickson and Maydew 1998). 8 Investors for whom τ < 1.0 have a tax incentive to sell their shares before the ex-day (or defer buying new shares until the ex-day). In contrast, investors for whom τ 1.0 have a tax incentive to buy shares before the ex-day (or defer selling shares until the ex-day). Thus, with differential taxation it is reasonable to assume that the cum-day seller is likely to be long-term individual investor while the cum-day buyer is likely to be at least tax-neutral. 10

12 which is an exact tick multiple, so that any difference between their ask and bid prices is driven by differential pricing of the dividend. The buyer is unwilling to pay more than one tick ($0.0625) for the dividend, yet the seller is unwilling to accept less than two ticks ($0.125) for the dividend because its after-tax value of $ ($0.12 x 0.76) exceeds one tick. Under these assumptions we would have to predict that the stock will not trade cum-dividend. Yet this prediction does not square with the empirical observation of abnormally high trading volume on the last cum-dividend trading day. Reconciling this simple example to empirical observation requires that we relax the assumption that both parties hold common beliefs about E(P ex ). The difference between these expectations could be quite small, but sufficient to cause some stocks paying 12 cent dividends to realize price drops of one tick while others realize price drops of two ticks. That is, some trades will occur at the bid price while others will occur at the ask price. In the cross-section of stocks, we would expect trades at the bid or ask to occur with equal probability such that the average price drop is $ and the average value of P/D is In contrast, BH s model predicts P/D of 0.52 for a $0.12 dividend ($ / $0.12). Our relaxed and more realistic assumption about E(P ex ) is consistent with JM s empirical observation that ex-day price drops equal to the tick below or the tick above the dividend amount occur with approximately equal frequency (JM, page 9). Moreover, this example illustrates that discrete pricing alone cannot explain why P/D ratios are less than one. Without differential taxation, both parties would value the dividend at its full amount ($0.12) and there would be no systematic explanation for why sellers would, on average, be willing to accept less than two ticks for the dividend. Our arguments and JM s empirical evidence are both inconsistent with BH s assumption that the market will always round down the price of a dividend to the tick just below the 11

13 dividend amount. The effect of this assumption on BH s predictions is greater for larger dividend amounts, and is solely responsible for the conclusion that discrete pricing can explain why observed P/D ratios tends to get closer to one for high-dividend yielding stocks. To see this, consider the E( P) for a $0.95 dividend. BH predict the price will drop by $ producing a P/D ratio of 0.987, which is very close to one. However, because the after-tax value of a $0.95 dividend for a long-term individual investor is only $0.722, the seller s minimum asking price is $0.75. In a broad cross-section of stocks, we would expect trades at tick intervals between $0.75 and $ to occur with equal probability, such that the average price drop is $ and the average value of P/D is Tax clienteles or tax-induced arbitrage around the ex-day may push P/D ratios higher, but discrete pricing by itself would not. Although we question BH s assumption that E( P) will always equal to the tick just below the dividend amount, we do not disagree that price discreteness affects P/D ratios and ex-day abnormal returns. Because BH argue that discrete pricing is the only reason why P/D ratios are less than one, their model predicts that decimalization will substantially eliminate positive ex-day abnormal returns. 10 An alternative view is that differential taxation of dividend and capital gain income, and heterogeneous tax rates across traders, causes buyers and sellers to value the dividend component of P cum differently. The magnitude of this difference, as a percentage of share price, is increasing in dividend yield. The traded value of this tax-induced price wedge is a function of price discreteness (and transaction costs if the buyer is a short-term trader). Greater discreteness will, on average, cause the price wedge to be larger, whereas lesser 9 If the cost of short-term trading exceed the difference between the dividend amount and the next lowest tick, the maximum bid price would be a lower tick interval (e.g. $0.875), driving the average price drop P/D still lower. 10 BH s model does not predict that decimalization will entirely eliminate positive ex-day returns because dividend amounts often include fractional cents. 12

14 discreteness enables the price wedge to be smaller. Returning to our earlier example of a $0.12 dividend, a seller for whom τ = 0.76 will have a minimum asking price of $0.10 under decimal pricing. Depending on the amount and relevance of transaction costs, a tax-neutral buyer might bid as much as $0.12. Any price in this range would lead to a higher P/D ratio and smaller exday abnormal return than predicted when prices are constrained to 1/16ths. Thus, both perspectives lead to the following hypothesis: HYPOTHESIS 3: The positive relation between yield and ex-day abnormal returns is smaller after decimalization than before. Both GMR and JM test BH s prediction that P/D ratios will be closer to one after decimalization than under discrete 1/16ths pricing. The sample period used in both studies ended on December 31, 2001, permitting a relatively small sample of post-decimalization observations, and both studies based their primary tests on P/D ratios rather than ex-day abnormal returns. Neither study found any evidence that reduced discreteness lead to higher P/D ratios. Two additional microstructure-based explanations for positive ex-day returns have been suggested in the literature. Dubofsky (1992) argues that under certain conditions positive ex day returns can be explained by NYSE rule 118 governing the ex-day adjustment of open limit orders to buy stock. This rule requires specialists to reduce open limit orders to buy stock by the dividend amount on the ex-dividend day. If the resulting stock price is not a tick increment, then the limit-buy order price is reduced to the next lower tick increment. Open limit orders to sell stock are not reduced. The asymmetric adjustment of open limit orders to buy versus sell further increases the price difference between these orders. If the ex-day bid-ask spread is constrained by these open limit orders, then the bid-ask spread will be wider than normal on the ex-day and the mid-quote will be lower on the ex-day than on the last cum-day. If, on average, shares trade at the mid-quote each day, then ex-day abnormal returns would be positive (negative) for stocks 13

15 with dividend amounts greater (less) than half a tick. The potential effect of rule 118 on ex-day returns is unaffected by decimalization except for reducing the breakpoint defined by half a tick ($ before versus $0.005 after decimalization). On average, Dubofsky s model would predict higher ex-day returns post-decimalization simply because the breakpoint is much lower than before. However, Dubofsky points out that the effect of rule 118 is likely to be evident only for low-yielding, thinly traded stocks, and is less likely to be observed when returns are measured using closing prices. The effect of NYSE rule 118, if any, would be opposite that predicted by hypothesis 3. Frank and Jagannathan (1998) (hereafter, FJ) show that if the nuisance cost incurred by normal traders to collect dividends is high enough, positive ex-day returns will result even without differential taxation. Market makers, for whom collection costs are lower, will buy shares cum-dividend at the bid price and sell share ex-dividend at the ask. The resulting shift in pricing from bid to ask causes positive ex-day returns. The critical element of FJ s model is that the bid-ask spread is smaller than the investor s cost of collecting the dividend, which causes sellers (buyers) to favor trading before (after) the ex date even though they are relatively more likely to incur the cost of the spread. FJ support their model using data from the Hong Kong Stock Exchange from 1980 to 1993, a period during which that exchange required cumbersome physical settlement procedures for stock transactions. Because Hong Kong does not tax dividends or capital gains, differential taxation could not explain FJ s results. 11 Kadapakkam (2000) shows that after Hong Kong introduced electronic settlement procedures, ex-day abnormal returns were no longer significantly different than zero. Consequently, FJ s model is 14

16 unlikely to apply in our setting because the NYSE used electronic settlement procedures throughout our sample period, and a U.S. investor s cost of collecting dividends is often trivial and certainly lower than historic bid-ask spreads (NYSE 2001). II. Sample and Descriptive Statistics A. Sample Derivation Our initial sample includes all NYSE common stocks with ex-dividend days for cash dividends between January 1, 1999, and December 31, 2003, recorded in the CRSP daily stock files. This initial sample contains 30,785 ex-dividend day observations with monthly (code 1222), quarterly (1232), semi-annual (1242), or annual (1252) taxable cash distribution codes. We require that each sample stock have daily return and volume data from day -45 to day 45 around the ex-day, and closing price and market capitalization on the last cum-dividend day. Imposing these data requirements leaves 25,268 observations. Following prior literature (e.g., GMR), we simultaneously trim the upper and lower ½ percentiles of P/D, as well as a driftadjusted P/D ratio and variables in later regressions, so that outliers do not drive our results. Our final trimmed sample consists of 23,736 ex-dividend day observations. The NYSE exchange converted from quoting stocks in 1/16 th s to decimals on January 29, However, in pilot tests of conversion procedures, certain NYSE stocks converted to decimals somewhat earlier. To ensure proper classification between pricing regimes, we obtain the exact conversion date for each stock from reports filed with the SEC. In general, the 1/16 th regime extends from January 1, 1999 through January 28, 2001 (11,163 observations); the pretax decimal regime runs from January 29, 2001 through May 23, 2003 (10,608 observations); 11 On the other hand, one could view the nuisance cost of collecting dividends under these procedures as a differentially higher implicit tax on dividends that could not be arbitraged away because all traders were subject to Footnote continued on the next page. 15

17 and the post-tax decimal regime runs from May 24, 2003 through December 31, 2003 (1,965 observations). Approximately 94 percent of dividends in our sample are 50 or less. This distribution of dividend amounts is consistent across regimes and with previous research. For example, BH report that 92 percent of taxable cash dividends in their sample are 50 or less. B. Descriptive Statistics for Measures of Price Change Table I reports descriptive statistics for two measures of the ex-dividend day price-dropto-dividend ratio ( P/D and P/D*, as defined below) and abnormal returns by regime. The first measure of the ex-dividend day premium, P/D, is the unadjusted difference between the closing prices on the last cum-dividend day and the first ex-dividend day, divided by the dividend amount [i.e., (P cum P ex )/Div]. Our sample period provides the opportunity to examine 1) the change from 1/16 ths to decimal pricing while holding tax rates constant (January 1, 1999 May 23, 2003) and 2) the equalization of dividend and capital gains tax rates while holding price discreteness constant (January 29, 2001 December 31, 2003). The discrete pricing hypothesis predicts that P/D will increase after decimalization. Comparing panels A and B of Table I, we see that median P/D decreased from the 1/16 to pre-tax decimal periods ( vs , Z = 0.52), while the mean P/D increased ( vs , t = -1.09). However, neither difference is statistically significant. These descriptive results for changes in P/D across pricing regimes are comparable to those reported by GMR (pg. 2621). Furthermore, contrary to the tax hypothesis that P/D will move closer to one after May 23, 2003, comparison of panels B and C shows that both the the same settlement procedures. 16

18 median ( vs , Z = 3.63) and mean ( vs , t = 3.28) values of P/D moved further from one between the pre-tax and post-tax decimal regimes. [INSERT TABLE I ABOUT HERE] Our second measure of the ex-dividend day premium, P/D*, recognizes that the closing price on the ex-day is affected by the stock s normal daily return and attempts to adjust for this price drift. If the drift in daily returns is positive (negative), then P/D will be biased downward (upward), and the extent of this bias is increasing in share price. Following prior research (Kalay 1982; Michaely 1991; and Naranjo et al. 2000), we address this problem by adjusting the ex day closing price for the normal return [i.e., P ex * = P ex /(1 + DRIFT)], which we define as the valueweighted average return for all dividend paying stocks on the ex day, excluding any stocks that also went ex-dividend that day. Contrary to the discrete pricing hypothesis, both the mean and median values of P/D* moved further from one between the 1/16 (panel A) and pre-tax decimal regimes (panel B), though neither shift is statistically significant. Also, contrary to the tax hypothesis, neither the mean or median value of P/D* moved significantly closer to one between the pre-tax (panel B) and post-tax decimal regimes (panel C). Although premium measures are intuitively appealing because of their theoretical relation to the tax preference ratio, τ, we hesitate to base any conclusions on P/D or P/D* because both are subject to measurement problems that make them ill-suited for empirical tests. First, because both measures are divided by a dividend amount that can be quite small, the effect of any price change that is unrelated to the dividend (error variance in the numerator) on the ratio is negatively related to the dividend amount. Scaling by Div creates high variance in the ratio and heteroskedastic error terms (Eades et al. 1984). The high variance of these ratios is evident in the distributional statistics reported in table I. Second, because P/D does not control for normal 17

19 returns included in P ex and the dollar amount of these returns is related to share price, error in this measure is also heteroskedastic with respect to share price. In sum, P/D and P/D* are extremely noisy measures. As GMR document, the standard deviation and kurtosis statistics indicate that P/D and P/D* are extremely volatile and not normally distributed. 12 These problems with the premium measures exist even after trimming the upper and lower tails from the distribution. Our third measure of ex-day price change, EXRET, avoids both of the problems described above. The ex day raw return is (P ex P cum + Div)/P cum such that, if the price drop equals Div, then the raw return is zero. We calculate the daily abnormal return, EXRET, for each stock as the ex day raw return minus the expected return for the stock, E(R it R ft ), calculated from the market-model as follows: E(R it R ft ) = α i + β i (R Mt R ft ) + ε i (5) The expected return is based on market-model parameters estimated over the 80-days between days -45 to -6 and days +6 to +45. We use the CRSP value-weighted return as a proxy for the market return. From Table I, the pattern of differences in mean EXRET across the three regimes is consistent with both the discrete pricing ( vs , t = 2.33) and tax hypotheses ( vs , t = 0.22), although only the earlier difference is statistically significant. Likewise, median EXRET decreased between the pre-tax and post-tax decimal regimes ( vs , Z = 0.89), although this difference is not statistically significant. Univariate tests of differences between means (or medians) do not control for other factors affecting EXRET. More powerful 12 Our kurtosis measure is standardized by the normal distribution; thus, a reported kurtosis value of zero approximates a normal distribution (Greene 1993). 18

20 multiple regression analysis is required. Also, relative to either price drop ratio, the skewness and kurtosis coefficients reported in Table I indicate that EXRET is more normally distributed. [INSERT FIGURE 1 ABOUT HERE] Figure 1 graphically illustrates the cumulative daily abnormal returns (CAR s) over the 11 days surrounding the ex day (day 0) for the three sub-samples created by forming separate portfolios for the 1/16, pre-tax decimal and post-tax decimal periods. We make two observations concerning Figure 1. First, the overall pattern of CAR s during the 11-day window is similar across the sub-samples. Consistent with prior research, CAR s are positive in the cum-dividend period, reaching a peak on the ex day and drop off thereafter (Lakonishok and Vermaelen 1986). This pattern suggests that dividend-capture strategies by short-term traders may create selling pressure and negative returns after the ex day. Any selling pressure that occurs on the ex-day itself would tend to mask the positive abnormal returns predicted by the tax hypothesis. Second, among the three groups, stocks during the post-tax decimal period experience the smallest positive CAR s on day -1 and the ex-day. This is consistent with the idea that both discrete pricing and the equalization of the dividend and long-term capital gain tax rates decreased ex dividend day abnormal returns. In the next section we describe our test of the hypotheses based on ex day abnormal returns. III. Tests of Abnormal Returns We estimate the following regression model to test our hypotheses while controlling for other factors identified by prior studies as affecting ex day abnormal returns: 2 EXRET i = γ 0 + γ 1 D i + γ 2 T i + γ 3 YIELD i + γ 4 YIELD i D i + γ 5 YIELD i T i + γ 6 YIELD i + γ 7 1/P CUMi + γ 8 LSIZE i + γ 9 σ εi /σ Mi + e i (6) where, 19

21 EXRET i D i = the ex day return for stock i minus the stock s expected return calculated from the market-model as computed in equation (5), = an indicator variable equal to one if the ex-dividend day occurs after the stocks decimalization conversion date, and zero if it occurs during the discrete pricing period, T i = an indicator variable equal to one if the ex dividend day occurs after May 23, 2003 (the date Congress approved the tax rate change), and zero if it occurs on or before May 23, YIELD i = the dividend per share for stock i divided by stock i s closing price on the last cum dividend day, 1/P CUM i = the inverse of the stock i s closing price on the last cum-dividend day (a proxy for transaction costs), LSIZE i σ εi /σ Mi = the natural log of the market capitalization of stock i as of the last cum-dividend day (a proxy for liquidity), and = the standard deviation of the residuals from a market-model regression of stock i s daily return on the CRSP value-weighted market return computed over the 80- day period from day 45 to day 6 and day 6 to day 45 relative to the ex-dividend day, normalized by the market risk (a proxy for idiosyncratic risk). Our first tax hypothesis (H1) is that, when the dividend tax rate exceeds the long-term capital gains tax rate, ex day abnormal returns are increasing in YIELD because, holding share price constant, the dividend tax penalty increases in the dividend amount. H1 would be supported by a positive coefficient on YIELD. Our second tax hypothesis (H2) predicts that the relation between ex day abnormal returns and YIELD will decline after the equalization of statutory tax rates on dividends and long-term capital gains because the relative tax penalty is diminished. H2 would be supported by a negative coefficient on YIELD T. The discrete pricing hypothesis (H3) predicts that the positive relation between ex day abnormal returns and yield will decline post-decimalization, and would be supported by a negative coefficient on YIELD D. We have no expectations regarding the coefficients on D or T, but we include these variables for control purposes. The coefficients on D and T may reflect differences in market 20

22 conditions relative to the 1/16 pricing era that have not been completely removed by our measure of abnormal returns. Prior research finds evidence of tax-induced clienteles based on dividend yield, which suggests that the overall relation between dividend yield and ex day abnormal returns is increasing but concave at very high levels of dividend yield (Michaely 1991; Naranjo et al. 2000). Thus, to the extent tax-induced clienteles exist, high-dividend-yield stocks may experience smaller (or even negative) abnormal returns on the ex day. We include YIELD 2 in equation (6) to capture this potential non-linearity, and expect a negative coefficient on this variable. The extent to which short-term traders can profit by trading around the ex day is limited by transaction costs. Following prior research (e.g., Karpoff and Walkling 1988; Naranjo et al. 2000), equation (6) includes the inverse of the closing stock price on the last cum-dividend day (1/P CUM ) as a proxy for transaction costs. A positive relation between ex day abnormal returns and transaction costs is typically interpreted as evidence of short-term trading activity around the ex day. Consistent with prior research, we predict a positive relation between excess returns and 1/P CUM (Lakonishok and Vermaelen 1986; Karpoff and Walkling 1988, 1990; Michaely et al. 1996; Naranjo et al. 2000). To control for potential liquidity effects, we include LSIZE, measured as the natural log of the stock s market capitalization on the last cum dividend day (Naranjo et al. 2000). Because shares of large-capitalization stocks are more liquid, such stocks are better candidates for shortterm trading than small-capitalization stocks. Accordingly, we expect ex day abnormal returns to be negatively related to LSIZE. Finally, we include σ εi /σ M as a proxy for idiosyncratic risk 21

23 because short-term trading opportunities are limited by risk. 13 Following Michaely and Vila (1996), we measure σ εi /σ M as the standard deviation of the residuals from a market-model regression of daily returns for the dividend-paying stock on daily market returns, divided by the standard deviation of daily market returns. Because the ability of short-term traders to capture arbitrage profits decreases in risk, we expect σ εi /σ M to be positively associated with ex day abnormal returns. Table II reports descriptive statistics for the regression independent variables by regime. YIELD is computed as the per-share dividend amount divided by the share s closing price on the last cum-dividend day. The mean and median values of YIELD decline significantly (p <.05) over the three regimes (e.g., the mean value of YIELD is in the 1/16 regime, in the pre-tax decimal regime, and in the post-tax decimal regime). It appears that this decline is attributable to an increase in cum-day closing prices between periods rather than a decline in dividend amounts. The increase in cum-day stock prices over the sample period is evident by the significant decrease in median values of 1/P cum over the three regimes (0.0505, , for the 1/16, pre-tax decimal, and post-tax decimal regimes, respectively). 14 LSIZE and σ εi /σ M also show significant differences in medians between the three regimes, suggesting the importance of including these control variables in the regression. [INSERT TABLE II ABOUT HERE] Table III, column (1), reports the regression results from our analysis of ex day abnormal returns in the full sample for which we simultaneously estimate the effects of differential 13 We do not include a proxy for systematic risk in equation (6) because the dependent variable is a market-model adjusted abnormal return. 14 Mean and median per-share dividend amounts (untabulated) are not statistically different for the three regimes. 22

24 taxation and discrete pricing. 15 In column (2), we restrict the sample to decimal-era observations, and in column (3) we restrict the sample to pre-may 24, 2003 observations. The coefficients on YIELD T in column (2) and YIELD D in column (3) are consistent with those reported in column (1), indicating that a three-way interaction term is not necessary in the column (1) regression. The following discussion of regression results refers to column (1) unless otherwise noted. Consistent with our first tax hypothesis (H1) that ex day abnormal returns are increasing in dividend yield due to the dividend tax penalty, the coefficient on YIELD is positive and significant (0.5533, t = 8.55). This result corroborates the findings of prior tests of the tax hypothesis based on samples from the earlier 1/8ths pricing regime (e.g. Michaely and Vila 1995 and Naranjo et al. 2000). The second tax hypothesis (H2) predicts that the relation between YIELD and abnormal returns will decline after the equalization of statutory tax rates on dividend and capital gain income. Consistent with this hypothesis, the coefficient on YIELD T is negative and significant ( , t = -2.96). These results provide strong evidence that differential taxation is partially responsible for positive ex day abnormal returns. Importantly, no part of the effects that we attribute to differential taxation can be attributed to discrete pricing because we find the same effects in column (2) using a sample that is entirely based on decimal pricing. [INSERT TABLE III ABOUT HERE] The discrete pricing hypothesis (H3) predicts that ex day abnormal returns will decline after decimalization because price adjustments are no longer constrained to relatively broad tick increments. Consistent with H3, the coefficient on YIELD D is significantly negative ( , t 15 In supplemental tests, we identify outliers and influential observations using Belsley, Kuh, and Welsch (1980) techniques. Our results are robust to removing these observations; and the R 2 value increases to

25 = -5.53). Note that the estimated coefficients on YIELD and YIELD D in column (3), based on a sample for which tax effects are held constant, are nearly identical to those reported in column (1). These results support the argument that price discreteness contributes to positive ex day abnormal returns, consistent with arguments by BH. However, contrary to BH s model, it is clear that price discreteness by itself does not explain why ex-day abnormal returns are positive. The magnitude of the coefficient on YIELD D is less than half that of the coefficient on YIELD. The sum of these coefficients ( = ) is approximately equal to the coefficient on YIELD in column (2), which is based entirely on data from the post-decimalization era. The estimated coefficient on YIELD 2 is significantly negative ( , t = -7.25). This relation between abnormal returns and yield, which persists after decimalization (column 2), is consistent with the traditional tax-induced dividend clientele argument [i.e., high (low) dividendyield stocks are held by low (high) tax rate investors] (e.g. Elton and Gruber 1970; Naranjo et al. 2000). Alternatively, the relatively lower abnormal returns predicted for high-yield stocks, due to the negative coefficient on YIELD 2, may indicate that short-term traders are more successful in arbitraging away the dividend tax penalty for high-yield stocks. Estimated coefficients for the control variables provide mixed evidence of short-term trading activity around the ex day. The significantly positive coefficient on σ εi /σ M (0.0006, t = 2.68) is consistent with short-term trading. Abnormal returns are increasing in idiosyncratic risk that short-term traders are likely to avoid. However, contrary to expectations, the coefficient on LSIZE is significantly positive (0.0002, t s 1.82) in columns (1) and (3), and the coefficient on 1/P cum is significantly negative ( , t = 2.04) in column (2). The coefficient on D is significantly positive (0.0013, t = 3.22), indicating the ex-day abnormal returns are, on average, higher after decimalization than before. Although this effect is 24