Quarterly Patterns in Momentum and Reversal in the U.S. Stock Market: Price Pressure as the Result of Tax-Loss Sales and Window Dressing

Transcription

1 Quarterly Patterns in Momentum and Reversal in the U.S. Stock Market: Price Pressure as the Result of Tax-Loss Sales and Window Dressing Abstract Active investment managers now have strong incentives to realize tax losses and simultaneously window dress taxable portfolios. As a result, stocks with capital losses and gains experience downward and upward price pressure, respectively, near the ends of calendar quarters, and a large share of the positive returns to momentum strategies is earned in these stocks and at these times. This turn-of-the-quarter effect is absent during the early part of a sample from 1927 to 2016, and is particularly evident in big stocks during the later years. Price pressure appears as: abnormal returns in factor model regressions, continuation and reversal in cross-sectional regressions, and visible trends in plots of cumulative abnormal returns. The evidence shows that changes in tax rules and the reporting practices of active managers have changed the patterns of momentum and reversal in U.S. stock returns. Key Words: Momentum, Reversal, Window Dressing, Tax-loss Sale, Capital Loss

2 1. Introduction Listing of those securities with the largest gains and losses in the portfolio can provide a clue to manager style and to account supervision and attention. However, heavy concentration on existing losses has its limitations and can be destructive. As Bob Kirby (Capital Guardian) pointed out so aptly: You don t have to have a very high I.Q. to figure out that if you simply sell the damn things, they won t be in the portfolio anymore and you won t have to flinch under the client s rubber hose every quarter. Claude N. Rosenberg, Jr., Investing with the Best, pg Delegated managers of active investment portfolios in the U.S. have strong incentives to realize tax losses and window dress taxable portfolios simultaneously at the ends of calendar quarters. As illustration, consider that managers may realize capital losses at any time during a tax year while opportunities to window dress portfolios arrive quarterly. Those who manage taxable private wealth in separate accounts are likely to window dress prior to meetings with clients that follow the ends of calendar quarters. 1 As the quotation above suggests, managers avoid unpleasant and difficult discussions with clients and increase the likelihood of productive meetings by removing extreme losers from portfolios. Because losing stocks may also be sold for losses that offset taxable gains, the decisions to window dress and realize tax losses are conflated for managers of taxable portfolios. As a consequence, tax-loss sales are likely to cluster with other portfolio rebalancing by these managers near the ends of calendar quarters. Jegadeesh and Titman (1993) find return predictability in the form of momentum: If a stock is a winner with a high past return, then its return this month is likely to be high, while past losers are likely to continue to lose. My paper demonstrates that tax-loss sales and window dressing create price pressure in U.S. stocks, and that this pressure leads to turn-of-the-quarter effect in momentum. This effect appears as a clustering of the positive returns to Jagadeesh and Titman s (1993) winner-minus-loser (WML) portfolios in the third months of calendar quarters, including March, June, and September as well as December. The effect is sufficiently strong during recent years that some strategies of buying winners and selling losers 1 The value of assets under management in U.S. separate accounts is unknown, but it is not trivial. More than 600 large financial advisers are members of the Investment Advisers Association and collectively manage more than $16 trillion; These advisers each have $100 million or more under management, and are registered with the Securities and Exchange Commission. In addition, the North American Securities Administrators Association counts over 17,000 state-registered advisers with over $250 billion under management; see The IA Switch. Many of these advisers manage money in separate accounts. 2

3 earn positive returns only at the ends of quarters. For example, during the years 2000 to 2016, a WML portfolio of stocks chosen within six style groups earns an average monthly return of -0.33% during the first and second months of quarters, and earns 1.06% per month during month three. 2 Moreover, differencein-difference tests applied to three sub-periods of the data ( , and ) demonstrate that the effect is significant only in the later years of the sample period. Several complimentary hypotheses explain these results. First, revisions of the U.S. tax code and IRS practices during the past century have heightened investors demands to efficiently realize capital gains and losses in order to minimize their tax burdens. Changes include increases in tax rates, eliminations of deductions, broadening the taxpayer base, restrictions on the timing of sales, and changes in the holding periods for short-term gain and loss. Second, active investment managers reduce transaction costs by simultaneously engaging in tax-loss sales and rebalancing portfolios at the ends of calendar quarters. Individual investors sell stocks with losses at the ends of calendar years, but unlike active managers, they do not have institutional incentives to rebalance their portfolios every third month. Third, investors taxdriven trades create price pressure because their calendar-driven incentives are alike and their trades are unwittingly coordinated. Delegated managers concurrently reduce holdings of stocks with capital losses, creating downward pressure on the prices at the ends of calendar quarters while individuals collectively contribute to price pressure in December. Fourth, investors have incentives to realize losses as short-term rather than long-term losses (as these terms are defined by the IRS), and these shared incentives have increased through time, leading to an increase in the turn-of-the-quarter effect. Finally, many active managers hew towards indexes and the stocks in their portfolios cluster within style groups, creating price pressure in the returns of winning and losing stocks selected within style groups. In summary, investors collectively demand immediacy when they realize capital losses or window dress portfolios, and during recent years these demands cluster at the ends of calendar quarters. This paper tests these hypotheses. I estimate average monthly returns and factor-model alphas for WML portfolios for the first, second and third months of calendar quarters, and do so separately for stocks with capital losses and gains. These 2 The returns in January and December are excluded from these results. 3

4 results show predictability in WML portfolio returns that is principally due to returns on stocks with capital losses. For example, during the years 1983 to 2016 a strategy of buying winners and selling losers within the universe of stocks with capital gains earned a monthly Fama-French (FF) alpha of 0.39% while the alpha for the universe with capital losses is five-times larger at 1.94%. Furthermore, the WML portfolio returns for big stocks during this period are significant only in the third months of calendar quarters, while the returns are positive and significant in all months during the years prior to These facts show that momentum profits are due in part to price pressure caused by tax-loss sales, and that this pressure has shifted in recent years to the times when delegated managers are likely to window dress their portfolios. Downward price pressure for stocks with capital losses is significant only for those with high levels of recent past turnover. For example, during the years from 1983 to 2016, the monthly FF alphas of stocks with capital losses and either high or low levels of turnover during the past 12 months are -0.70% or 0.09%, respectively, and the difference between these values is highly significant. Alternatively, for the same period, the alphas for stocks with capital gains are 0.09% and 0.13% for high- and low-turnover stocks, respectively, and the difference between these values is indistinguishable from zero. Because realized short-term capital losses are more valuable than long-term losses, a stock with both capital losses and an elevated rate of recent turnover is likely to be sold by many current holders as they harvest tax losses. This same stock is also likely to be sold by delegated managers as they window dress. For these reasons, we expect downward price pressure to be stronger for stocks with capital losses if they have high turnover. Alternatively, among stocks with gains, there is no reason for price pressure to differ by turnover. The factor-model alphas are consistent with these arguments and the hypotheses noted above. I provide direct evidence of price pressure by estimating Fama-MacBeth models of both weekly and monthly return responses, and interpret the coefficients according to the inventory theories of Grossman and Miller (1987) and Campbell et al. (1993). The negative responses in these theories, namely, reversals are the result of price pressure generated by investors demands for immediacy in trade. Consistent with the evidence of Avramov et al. (2006), the return responses indicate price pressure that is greater in shortterm losers, i.e., in stocks with negative prior return shocks, than in winners. However, we also expect 4

5 differences to arise between stocks with short-term capital losses and gains due to price pressure from taxloss sales. 3 The return responses for weekly returns are consistent with this argument and the inventory theories: stocks with capital losses experience significantly greater reversals than stocks with gains. However, the monthly results are puzzling and unexpected. During the years after 1982, stocks with capital losses exhibit monthly-return reversals if they are short-term winners, but exhibit continuation if they are losers. This means for the stocks with capital losses, winners in one month tend to be losers during the following month, but losers continue to be losers. There is little evidence of continuation in the returns of stocks with capital gains, or in the returns of stocks with losses in the early years of the sample. Visual evidence of continuation in monthly returns appears in plots of cumulative abnormal returns (CARs). Stocks are grouped by capital losses and gains, and independently by market-equity value and status as short-term winner or loser, and CARs are plotted for stocks in the intersections of these groups. The CARs show that the principal driver of a stock s short-term performance (in all months other than January) is its status as one with prior capital gains or losses; whether a stock is a short-term winner or loser is relatively unimportant. Specifically during the months of March, June, September and December: the CARs of stocks with capital losses are negative and decline day after day, suggesting downward price pressure; the CARs of stocks with capital gains are positive and increase regularly, suggesting positive price pressure; and there is little difference between the CARs of short-term winners and losers. Continuation for short-term losers is inconsistent with the predictions of the inventory theories, but it is consistent with tax-loss sales that cluster within periods of several weeks and which are not properly anticipated by liquidity suppliers. Overall, the evidence indicates that delegated managers simultaneously window dress portfolios and realize tax losses at the ends of calendar quarters. It also indicates that investors responses to the U.S. tax code and the common practices of investment managers are root causes of systematic price pressure that creates momentum in the prices of stocks in the U.S. markets. 3 Short-term capital losses/gains as defined by the IRS, on the one hand, and high/low short-term (i.e., weekly and monthly) returns, on the other, are distinguished as follows. If a stock has a negative or positive return excluding dividends during the past 12 months, I say that it has a capital loss or gain, respectively, and is in the gain or loss group, respectively. If a stock has a below- or above average return during the past week or month, I say that it is a short-term loser or winner, respectively. 5

6 Section 2 presents a brief summary of the literature on momentum and reversal, it describes the predictions of the inventory models for return reversals, and it lists several significant revisions to the U.S. tax code regarding capital gains and losses during the past century. Section 3 describes the data. Section 4 analyzes the intra-quarter patterns of WML portfolio returns, and it tests for shifts in momentum profits towards the ends of quarters across time. Section 5 compares the returns of WML portfolios of stocks with capital gains versus stocks with losses, and of stocks with high and low levels of turnover. Section 6 studies short-term reversals and continuation of stock returns, and the CARS of stocks with capital gains and losses. Section 7 concludes and addresses questions about the paper s results: Given that momentum is a worldwide phenomenon, are the results relevant outside the U.S.? Do they suggest that end-of-quarter trading is the only explanation of momentum? Has the turn-of-the-quarter effect been evident in the recent past? 2. Momentum, Reversal and the Demands for Immediacy Explanations of momentum in stock returns are abundant. Jegadeesh and Titman (1993) argue that the market is slow to incorporate stock-specific information in prices, but find no evidence of slow incorporation of information about systematic factors. Chan et al. (1996) demonstrate that security analysts forecasts react slowly to past news, and suggest that investors respond slowly to public firmspecific information. Investors in the model of Barberis et al. (1998) react slowly to information as a consequence of their conservatism, and price momentum is a result. Momentum trading is profitable in the models of Daniel et al. (1998) and Ma (2013) because investors exhibit a self-attribution bias, and they react repeatedly to old news. Hong, et al. (2000) find that momentum is greater in stocks with low than high analyst coverage, and they attribute this to a slow diffusion of information among investors, a result that is predicted by the theory of Hong and Stein (1999). Momentum appears in the prospect theory of Grinblatt and Han (2005) because investors evaluate stocks separately, according to their individual gains and losses, and assign fundamental values below and above market prices to stocks with prior gains and losses, respectively. A disposition effect in Frazinni s (2006) theory leads many investors to react slowly to bad or good news for stocks with capital losses or gains, respectively, and creates predictability in the stocks returns. Lou (2012) concludes that stock price momentum is partly driven by capital that flows 6

7 from retail investors to mutual funds to individuals stocks. The central evidence in this paper does not contradict these theories of momentum, but it also does not support them. These theories do not explain why profits in momentum strategies now cluster in the months of March, June and September; or why the degree of clustering at the ends of calendar quarters has increased through time. Rozeff and Kinney (1976) document a January (or turn-of-the-year) effect, showing that stocks offer abnormally high returns in that month. Following their work, Jones et al. (1991) find no January effect in U.S. stocks prior to the War Revenue Act of 1917, which substantially raised personal income taxes. Poterba and Weisbenner (2001) demonstrate that the January effect weakens when the interval of time required under U.S. tax law for claiming long-term capital gains is reduced from one year to six months. Sias and Starks (1997) show that the effect is stronger in stocks held primarily by individuals than in those held by institutions. Considered broadly, these researchers conclude that the effect is due in part to rebounds in January prices that follow downward price pressure from tax-loss sales by individual investors in December. On the other hand, Ng and Wang (2004) show that among small stocks, the magnitude of the effect is stronger at times when institutions are likely to window dress portfolios, while Tinic et al. (1987) find a January effect in Canada prior to the introduction of income taxes. In contrast to these authors, this paper documents price pressure at the ends of calendar quarters. In a manner similar to Grinblatt and Moskowitz s (2004), who find that tax-loss sales are contributors to stock predictability in December, I conclude that delegated managers acts to window dress portfolios and simultaneously harvest tax losses create significant predictability in the months of March, June and September. Stock returns exhibit seasonality. Heston and Sadka (2008, 2010) demonstrate that historical samecalendar-month returns of individuals stocks are stronger predictors of current returns than other-month returns. Keloharju et al. (2016) find this effect also in the returns of portfolios of stocks grouped on firm characteristics such as size, value and price-earnings ratios, but do not find seasonality in momentum portfolio returns. This research extends the work of Sias (2007), who documents a rise in the turn-of-thequarter effect over time, and attributes the rise to an increase in the influence of institutional investors trading in the stock market. The evidence in this paper suggests instead that the rise of price pressure at the 7

8 ends of calendar quarters is a consequence of revisions in the US tax code and an increase in incentives for delegated managers to trade in a tax-efficient manner. Unlike prior work, this paper presents formal tests for changes in the seasonal patterns of returns across time. It also shows that profits to momentum strategies are now principally earned within the group of stocks with have experienced high levels of turnover and capital losses during the past year Inventory Models and Reversals in Stock Returns Following the work of Jegadeesh (1990) and Lehmann (1990), Avramov et al. (2006) document price pressure as reversals in weekly stock returns that are largest for illiquid stocks and short-term losers. Black (1986) describes long-term reversals as the result of noise trades driving stock prices away from value, followed by reversion to value as information traders enter the market. In contrast, Grossman and Miller (1988) and Campbell et al. (1993) say that short-term reversals provide compensation to liquidity suppliers who trade with investors demanding immediacy. Random events in their inventory models lead investors to be first net sellers and then buyers, or to be buyers and then sellers. Market makers supply immediacy by their continuous presence, buying when others are selling, selling when others are buying, and bearing risk by holding an inventory of shares, either long or short. As a consequence, price changes exhibit negative autocorrelation. In Grossman and Miller s model, the correlation of changes at dates t and t+1 is where, 0 (1), and Cor increases as: (i) the number of market makers decreases, (ii) risk aversion increases, (iii) the volatility of demands for immediacy increases, or (iv) price volatility increases. Expected returns in inventory models rise after abnormal demands by investors to sell shares, and fall after abnormal demands to buy. These changes provide compensation for the temporary risks borne by liquidity suppliers. If window-dressing-cum-tax-loss-sales are demands for immediacy, the effect of increasing gives the following simple hypothesis regarding price pressure in stocks: as the likelihood of these sales 8

9 increases, the likelihood of short-term return reversal rises. For example, stocks with capital losses and that are short-term losers in one period are likely to be winners in the following period. This paper presents evidence regarding this hypothesis using cross-sectional regressions and CARs The Federal Tax Code Regarding Capital Gains and Losses The U.S. federal tax code has changed through time, making tax avoidance more difficult, and changes to the code directed at capital gains have increased investors incentives to efficiently realize gains and losses. 4 The income tax was first collected on net realized capital gains and other income earned in Tax forms were originally filed by March 1 and taxes were paid in the year after the receipt of income. During World War II and the Korean War, Congress passed a number of bills aimed at increasing both the numbers of taxpayers and tax rates. The Current Tax Payment Act of 1943, for example, required employers to withhold taxes on earned income and required quarterly payments of taxes on capital gains; this act increased the likelihood of full payment of taxpayers obligations. The wash sale rule was introduced in 1923, and it requires a 30-day interval between the sale and repurchase of a security when capital losses are realized. Seventy-four years passed after the wash sale rule, however, before shorting against the box was prohibited by the Taxpayer Relief Act in 1997; this strategy was used to postpone realization of net capital gains from one year to the next. 6 Congress passed the Tax Equity and Fiscal Responsibility Act (TEFRA) in 1982, and it introduced substantial penalties for noncompliance with the code, and required securities brokers to report their clients holdings to the IRS. TEFRA was later judged by the Congressional Budget Office to have substantially increased the receipts of taxes paid on capital gains. 7,8 4 See Tempalski (1998) for brief descriptions of 39 major tax bills passed by Congress between 1940 and 1997, and for estimates of their effects on tax revenues. 5 The Lincoln Administration introduced an income tax during the Civil War, but it was later declared unconstitutional. See Blakey and Blakey (2006). 6 See Dyl (1979). 7 See the Staff Report of the Congressional Budget Office (1986), page IV.46. One passage reads: capital gains enforcement provisions were significantly tightened in TEFRA, enacted in Under one provision of TEFRA, securities brokers were for the first time required to report transactions of customer to the Internal Revenue Service and also to furnish information returns to customers. It is believed that there was significant noncompliance prior to 1982; a preliminary 1981 IRS estimate that capital gains reporting was below 60 percent was cited by the Joint Tax Committee as one reason for the new enforcement provisions in TEFRA If improved compliance is responsible for the apparent upward shift in capital gains realizations in 1983, then this higher rate of realizations should continue 8 Tempalski (1998) estimates that the Revenue Act of 1942 led to the biggest increase in tax receipts during the 1940 to 1967 period, and that TEFRA led to the biggest increase during the 1968 to 1998 period. 9

10 I test for differences in momentum in stock returns across time, between three sub-periods of the data: 1927 to 1952, 1953 to 1982 and 1983 to Because the historical acts of Congress are spread across time, the sub-periods are not distinct regimes. Nevertheless, if the acts altered investors behavior, we expect systematic differences in patterns of price pressure in the stock markets between the sub-periods, and with 26, 30 and 34 years, respectively, each of the sub-periods is roughly one third of the sample. The first period ends in 1952 because stocks were traded six days per week prior to June of this year, and five days thereafter, and a break at this date is convenient for the calculations of CARs. 9 The third period begins in 1983 for two reasons: tax receipts on capital gains increased significantly following TEFRA in 1982, and the sample periods used in the original research on the January effect end prior to this year. I use the subperiods to document and test for changes in the patterns of price pressure in stock prices across time. 3. Data and Empirical Measures I use data in the daily and monthly stock files of the Center for Research on Security Prices (CRSP) at the University of Chicago. With restrictions and exceptions noted below, portfolios are constructed using all NYSE, Amex and NASDAQ common stocks with CRSP share codes 10 or 11. Risk-free rates and stockreturn risk factors are from Professor French s website at Dartmouth College. Compustat data is used to calculate book values of stocks and to sort stocks into style portfolios. Monthly portfolio returns are alternatively value- and equal-weighted averages of stock returns including dividends. 10 Each month t from January 1927 to December 2016 is a measurement period, and each preceding twelve-month interval is a ranking period. In month t, intermediate-term momentum is calculated by compounding monthly returns over the ranking-period, skipping the month t-1. Jegadeesh and Titman (1993), Lee and Swaminathan (2000), Novy-Marx (2012) and others define momentum using various time intervals, while I use a ranking period that is equal to or longer than the period defining shortterm gains in the U.S. tax code. For each stock, market capital is calculated as the product of a monthly closing price and shares outstanding at the beginning of each measurement month and at the beginning of 9 CARs are calculated across days of Standard Months, which are described in Appendix B, and these have 25 days from January 1927 to May 1952 when stock trading was 6 days per week, and they have 21 days thereafter. 10 The return for the month in which a stock is delisted includes the CRSP delisting return. 10

11 each ranking period. These calculations have different uses. Value-weighted portfolio returns in month t are averages of returns weighted by market capital at the end of month t-1. Market capital at the end of month t-13 denotes size, and it is used to sort stocks into groups in a manner that is described below. The three sub-periods noted above are used to document changes in the timing of momentum in returns within calendar quarters. Because 1982 is the year that trading volume for NASDAQ stocks first appears in CRSP, and because these stocks enter my sample in January 1983, I avoid confounding influences by excluding the NASDAQ stocks from the tests for time effects that are reported in Table 2 of the following section, while all other analyses include these stocks. For each measurement month, stocks monthly returns without dividends are compounded over the ranking period, excluding the return on the final day of the period. 11 A stock has a capital loss or gain in this analysis if its cumulative return is negative or non-negative, respectively. Although investors holding periods for stocks are heterogeneous, it is natural to define capital gains and losses using returns over oneyear intervals. Investors sell losing stocks to offset the capital gains on which taxes are paid. Short-term losses are more valuable than long-term losses, because short-term gains generally suffer higher tax rates than long-term gains, and long-term losses must first be netted against long-term gains before they are used to offset short-term gains. Thus, investors have incentives to sell stocks to realize losses within the shortterm holding period defined under IRS rules. This holding period is one year or less in the data. 12 Stocks are ranked on size in each month t to form groups Big, Mid and Small, holding stocks above the 70 th percentile, between the 70 th and 30 th percentiles, and below the 30 th percentile, respectively, of the rankings of the NYSE stocks. Similarly, for the years 1983 to 2016, stocks are ranked independently on the book-to-market ratios BE/ME observable in month t-13 to form three valuation groups, Growth, Blend 11 This method avoids the creation of a spurious correlation between the ranking-period capital gain/loss and the measurementperiod return that would appear if the bid-ask spread at the end of month t-1 entered both calculations. 12 Poterba and Weisbenner (2001) give the holding periods that distinguish long- from short-term gains and losses during and July 1984 through 1987 as 6 months, during 1977 as 9 months, and during January 1978 to June 1984 and for the years 1988 to 1996 as one year. Examination of historical IRS instructions online at shows that the period for also was one year, while it was 18 months for Multiple categories of gains and losses are defined during the years 1934 to 1938, with a declining schedule of tax rates applied to different minimal holding periods out to 10 years. There is no distinction between long- and short-term gains prior to

12 and Value, using the 30 th and 70 th percentiles of the rankings of NYSE stocks. 13 Finally, nine style portfolios hold stocks in the intersections of the size and valuation groups. The size, value and style groups represent the stock universes of active managers who tilt their portfolio holding toward indexes. This behavior narrows a manger s opportunities for window dressing and tax sales. For example, a portfolio benchmarked to the Standard & Poor s 500 Index holds mainly Big stocks at the beginning of a ranking period, and principally holds the stocks in the index. Capital losses or gains, and measures of momentum for stocks in the Big group during the ranking period are directly relevant to the manger s decisions regarding purchases and sales during the measurement period, while those for stocks in the Mid and Small groups are not. Thus, in a market with price pressure, Big stocks returns during the ranking period should be strong predictors of those stocks returns during the measurement period, when compared to the ranking-period returns of other stocks. This means that the turn-of-thequarter effect in the returns of a WML portfolio is likely to be stronger when the winners and losers in the portfolio are chosen from a size group instead of from the collection of all stocks. Similar arguments can be made for WML portfolios constructed from style groups when managers hew towards indexes representing, for example, Big-Value stocks or Small-Growth stocks. The universe of stocks for month t includes those with non-missing values of each of the following: the month t return; closing prices and shares outstanding for months t-1 and t-13; and positive daily volumes for at least 120 days of the ranking period. Table A.1 of the Internet Appendix reports summary statistics for each of the sub-periods, and describes both the universe of stocks and the returns of value-weighted portfolios of stocks formed within the size groups and within gain and loss groups. There are 1080 months of data in the sample, with 312, 360 and 408 months in the first, second and third sub-periods, respectively. Returns were volatile during the first sub-period, with sample standard deviations nearly twice those of other periods. Because this period also has fewer sample months, we expect large standard errors for coefficient estimates for this period. During the third sub-period, stocks in the Big group are 81 percent of 13 Here, BE is the sum of common equity, deferred taxes and investment tax credits reported by Compustat for the fiscal year ending during the interval from month t-29 to month t-18, and ME is the market equity value in month t-18. Stocks with zero or negative values of BE are excluded from the valuation groups. 12

13 the total market capital at the beginning of the measurement period (month t-1), while the Mid and Small stocks account for about 14 and 5 percent, respectively. During the first sub-period, Big stocks account for 88 percent of the total. Similarly for the third sub-period, stocks in the Loss and Gain groups represent 34 and 66 percent of market capital at the beginning of the ranking period (month t-13), and represent 27 and 73 percent, respectively, 12 months later, at the beginning of the measurement month (t-1). 4. Differences in Intermediate-term Momentum Between Months in Calendar Quarters Do the returns of momentum portfolios differ between the months of calendar quarters, and are there differences in the quarterly patterns between the sub-periods? Simply put, is there a significant turn-of-thequarter effect in stock market momentum during the later years of the sample? These questions are addressed by estimating factor-model regressions for stocks grouped by size and momentum. The differences between the sub-periods of the intra-quarter patterns of the estimates are documented, and the hypothesis that the patterns are homogeneous between the sub-periods is tested Risk Adjusted Returns by Months in Quarters Table 1 reports the coefficients of market model regressions using NYSE, Amex and NASDAQ stocks. To obtain these results, stocks are ranked on momentum within each size category, Big, Mid and Small, and ten value-weighted portfolios are constructed from stocks in the deciles of the rankings. Losers and winners are in portfolios 1 and 10, respectively. Using ordinary least squares, portfolios monthly excess returns are regressed on excess market returns. The same is done with the returns of WML portfolios that are long winners and short losers, where the dependent variable r Wt r losers. The intercepts of these regressions are average risk-adjusted returns. where Two sets of regressions are reported. For portfolio i, the regressions are it ft i i mt ft it Lt is the difference in returns of winners and r r Alpha RMF r r e, (2) Alphait is constant in one case and it varies between months of quarters in a second case: Alpha Jan 1 One 1 Two 1 Three 1 Dec 1. (3) i i Jt i 1t i 2t i 3t i Dt 13

14 The dummy variables indicate the first, second and third months of calendar quarters, with January and December separate from other months. For example, 11 t 1 when month t is either April, July or October and is 0 otherwise, and the month-in-quarter coefficient One is the average risk-adjusted return for the first months in calendar quarters sans January. Abnormally large or small values of these coefficients are evidence of positive or negative price pressure during the corresponding months. Panels A, B and C of Table 1 report results separately for the sub-periods, while the subpanels report results for the Big, Mid, and Small groups. In each sub-panel the constant intercept is reported as Alpha in the first line, and as the month-in-quarter coefficients of equations (2) and (3) in following lines. The market factor loading is RMF, and t-statistics are reported in parentheses. The month-in-quarter coefficients are marked as significant at the 1%, 5% or 10% levels by three, two or one asterisks, respectively. 14 With exceptions noted below, significance is judged in this paper using two-sided tests of the hypothesis that a coefficient is equal to zero. Table 1 demonstrates a turn-of-the-quarter effect during the years 1983 to 2016, but provides little evidence of this effect during the prior years. As illustration, consider the WML portfolio of Big stocks during the last two sub-periods as shown in Panels B.3 and C.3. The values of One, Two, Three and Dec in Panel B.3 are large, positive, and all but Dec are significantly different zero at a 1% level. Furthermore, they are relatively homogeneous. In other words, ignoring January (for the moment), there is little evidence of seasonality in the WML portfolio s returns. In contrast, the values of Three and Dec in Panel C.3 are 2.54% and 3.79%, respectively, and are much larger than One and Two, which are 0.10% and 0.51%, respectively. Also in Panel C.3, Three and Dec are significant at the 1% level, while One and Two are insignificantly different from zero. A comparison of the Panels B.2 and C.2 shows similar patterns across the sub-periods for WML portfolios of Mid stocks, and to a lesser extent Panels B.1 and C.1 show these patterns for Small stocks. This is evidence that the positive returns to holding winners long and losers short shifted toward to the ends of calendar quarters and to the months of March, June, September and December between the second and third sub-periods. 14 The factor loading is not reported in Table 1 for the first case. Throughout this paper the significance of coefficients of risk factors are not marked, and standard errors and t statistics of all coefficients of the factor models are calculated using the heteroskedasticity-consistent covariance matrix of White (1980). 14

15 Similarly, Panel A of Table 1 shows little evidence of a turn-of-the-quarter effect in the returns of the WML portfolios during the first sub-period. The coefficient Three A is positive and significant for Mid stocks, but it is negative for Small stocks and it is insignificantly different from zero for Big stocks. The coefficients One and Two are positive for all size groups, and several are significant or larger than Three. Thus, the WML portfolio returns were not exceptional during the months of March, June and September during the years 1927 to Table 1 provides considerable evidence that losers are regularly sold in December months creating downward price pressure. For each sub-period and each size group, Dec is large and negative for portfolios 1 and 2, and it is significantly different from zero at the 1% or 5% level for portfolio 1. Moreover, this endof-the-year effect is particularly noticeable during the early years. In Panel A, the values of Dec are negative and significant (to varying degrees) for all of the portfolios 1 through 5 within each size group, with values ranges ranging from -0.57% to -6.86%. By comparison, the values of One, Two and Three are uniformly smaller in magnitude for each size group, and very few of these estimates are significant. One conclusion is that profits from WML portfolios were principally earned in December during the years 1927 to There is evidence of a strong small-firm-in-january effect. Small stocks earned positive abnormal returns during January of each sub-period, including both loser and winner portfolios, and this is shown by large and positive values of Jan for all portfolios 1 through 10. The abnormal returns tend to be larger during the first and second sub-periods than the third, but the values of Jan for the years 1983 to 2016 are economically large; they range from 0.55% for portfolio 10 to 5.41% for portfolio 1. Table 1 shows that the overall average risk-adjusted returns of momentum strategies for Big and Mid stocks have changed only a little with time. The values of Alpha of the WML portfolios in Table 1 are of the same order of magnitude in the Panels A, B and C for these stocks. For Big stocks Alpha =1.04%, 1.32% and 1.00% for the first, second and third periods, respectively, and for Mid stocks Alpha =1.82, 1.71 and 1.33 percent. This indicates that the hedge portfolios produced similar levels of profits across the subperiods. However, the source of the profits has changed. During the years after 1982, a lion s share of abnormal returns came from shorting losers; this result is consistent with the conclusion of Hong et al. 15

16 (2000), who use data from 1980 to The Alphas in Panel C for winners (portfolio 10) in all size groups are about 0.25%, while those for losers (portfolio 1) are much larger in magnitude: -1.82%, -1.07% and % for Small, Mid and Big stocks, respectively. In comparison, during the years prior to 1982, winners and losers contributed roughly equally to the WML portfolio returns. In each of Panels A and B, the winner and loser Alphas are of roughly the same magnitudes, and for Small stocks the portfolio 10 values are larger than the portfolio 1 values. In summary, the evidence demonstrates a turn-of-the-quarter effect during the later years of the sample period. The positive returns to momentum strategies shifted away from the first and second months of calendar quarters and towards the months of March, June and September during the years 1983 to In addition, the share of WML profits from selling losers has grown through time. The WML portfolios returns in the months of January and December have changed only modestly. The average risk-adjusted December returns were positive, large, and both economically and statistically significant throughout the sample. Finally, January is unlike other months with losers beating winners, leading to large negative returns to WML portfolios, and this is particularly true of portfolios of Small stocks Tests of the Timing of WML Portfolio Returns Differences-in-differences are used to test for a significant turn-of-the-quarter effect. That is, the difference between the early and late sub-periods in the difference of the average returns of WML portfolios between early and late in calendar quarters is calculated as a test statistic. First, the years 1927 to 1952 are excluded, and tests are reported for the second and third periods, and then the years 1953 to 1982 are excluded, and tests are reported for the first and third periods. In each case, only NYSE and Amex stocks are used. Average returns and risk-adjusted returns in the market and Fama-French (1992,1993) three-factor models are estimated for the WML portfolios returns, and dummy variables indicate the sub-periods and the early and late months of calendar quarters. The three-factor regression is r r Jan 1 Jan21 1 One 1 Two 1 Three 1 Dec 1 Dec21 1 Wt Lt Jt Jt P2, t 1t 2t 3t Dt Dt P2, t mt ft P2, t SMB, t + Dif RMF r r SMB r Value r 3t 1t 2t P2, t mt ft SMB, t HML, t RMF2 r r SMB2 r 1 1P2, t Value rhml, t 1P2, t et 2. (4) 16

17 Here, r Wt r Lt is the WML portfolio return, and rsmb, t and rhml, t are the Fama-French size and value factors. The dummy variable 1P2, tindicates the third sub-period; 1 P2, t1 during the years 1983 to 2016 and it is 0 otherwise. Thus, RMF, SMB and Value are the factor loadings during the years from 1953 to 1982 in the first case, and during the years from 1927 to 1952 in the second case. We have1jt 1 P2, t=1 only when month t is January during 1983 to 2016, so the values of Jan2 and Dec2 estimate the incremental riskadjusted returns expected in January and December, respectively, during the third sub-period. Similarly, RMF2, SMB2 and Value2 estimate the incremental market, size and value factor loadings for these years. We have =1 or -1 in (i) month three or (ii) months one and two, respectively, 3t 1t 2t P2, t for the years 1983 to 2016, and it is zero otherwise. In particular, this variable is zero for all months during 1927 to The coefficient Dif measures the difference in the turn-of-the-quarter effect between two sub-periods. The values of One, Two and Three are month-in-quarter estimates of expected risk-adjusted returns during the early period, while One-Dif, Two-Dif and Three+Dif are estimates for the corresponding months during the third sub-period. If Dif 0 the difference between the average returns in month three, on the one hand, and in months one and two, on the other, is no greater during the third sub-period than the earlier period. Alternatively, Dif >0 indicates that the positive returns to momentum strategies have shifted toward month three during the years after Hence, the null hypothesis The turn-of-the-quarter effect is no greater during the third sub-period than an earlier sub-period of the sample is rejected when Dif is significantly greater than zero. For this reason, one-tailed tests are reported for Dif. Panel A of Table 2 reports the results in the first case, using the second and third sub-periods, with the three models reported in the sub-panels. In Panel A.1 the risk-factor loadings of equation (4) are set to zero, and in Panel A.2 the loadings on the size and value factors are set to zero. The four columns of each panel report results separately for WML portfolios of all stocks and each of the three size groups. In a regression using all stocks, a WML portfolio is long and short the 10% of stocks at the top and bottom of rankings on momentum, respectively, and in the regression of stocks in a size group, a WML portfolio is long and short one-third of stocks in the upper and lower tails of the rankings in the group, respectively. 17

18 The coefficients Two and Three are positive, statistically significant and economically large in each column of the table. The same is true for One, with the exception of that for Big stocks. In each column, the three coefficients tend to be similar in magnitude, implying that the abnormal risk-adjusted returns from simple momentum strategies were distributed about equally across the months of the calendar quarters, aside from January and December months, during 1953 to The coefficient Dif is positive and economically large in each column, with values ranging from 0.48% to 1.17%. It is smallest for Small stocks using the three-factor model, and it is largest for all stocks using average returns. Consider Big stocks in Panel A.3 as an example for interpretation. Here, One=0.45%, Two=0.72%, Three=0.74% and Dif=0.66%. Taken together, these values provide estimates for the years 1983 to 2016 of average riskadjusted returns of the WML portfolios of -0.21% and 0.12% and 1.40% in months one, two and three, respectively. All values of Dif are significantly different from zero at the 1% levels for Big and Mid stocks, and all but one of the values are significant at the 5% level using all stocks and Small stocks. Additional statistical power is gained by estimating the models for the size groups simultaneously and testing the null hypothesis that Dif=0 for all groups. 15 For the average-return model and the two- and three-factor models, two-sided Wald tests are 23.27, and 18.84, respectively, and are significantly different from zero at the 1% level, respectively. These results together with those for the individual models imply that we should reject the null hypothesis for the stocks in each of the size groups. Panel B reports the results for the second case using the years from 1927 to 1952, and while Dif is positive and economically meaningful in each column, the evidence rejecting the null hypothesis is modest in comparison to Panel A. The values of Dif for Big stocks are significant at the 1% or 5% level, depending on the model, suggesting rejection of the null hypothesis, while those for Small and Mid stocks tend to be smaller than those in Panel A and only the values for Mid are (marginally) significant for the one- and three-factor models. Similarly, the two-sided Wald tests of the equality Dif=0 for all size portfolios are 15 Seemingly-unrelated regression are used to correct for the cross-sectional correlations of errors across the 3 size groups, and the White (1980) correction for heteroscedasticity is used. The covariance matrix of the estimators is Ω, where is the 3 matrix of independent variables, with n and k the numbers of observations and variables, respectively, and Ω is a 3 3 block-diagonal matrix, with n blocks that have non-zero elements, where i and j index the equations. To conserve space, the estimated coefficients are not reported. 18

19 13.40 and 9.12, and these are significant at the 1% and 5% levels using the three- and one-factor models, respectively, while the test statistic is 3.78 and is insignificant using the average-return model. Overall, the evidence suggests rejection of the null hypothesis for Big and Mid stocks. It shows that momentum profits for these stocks cluster at the ends of calendar quarters during the years 1983 to 2016, and they do so in a manner that is different from both the first and second sub-periods of the sample. The evidence for Small stocks supports rejection for the comparison of the second and third sub-periods but not for the first and third periods Winners and Losers within Style Groups A significant turn-of-the-quarter effect also appears in the WML portfolios of stocks within style groups, e.g., large-growth and small-value stocks. To demonstrate this result, stocks are sorted each month into winners and losers within nine style groups, which are the intersections of the three size and the three valuation groups described in Section 3. These are the stocks with ranking-period returns above and below a within-group median return, respectively. A WML return in this case is the difference between the returns of equal-weight portfolios of winners and losers. I estimate regressions without risk actors, r r Jan 1 One 1 Two 1 Three 1 Dec 1 e, (5) Wt Lt i Jt i 1t i 2t i 3t i 3t it and each coefficient is an estimate of expected returns for one of the months in calendar quarters. Table 3 presents the results. Each of the nine columns describes a long-short strategy that active managers could have chosen at the beginning of the ranking period for a style-based portfolio, and the coefficient values measure the differential influence of price pressure for winners versus losers within style groups. On the one hand, weak evidence of the turn-of-the-quarter effect is expected here because winners and losers in this analysis are not chosen from the extreme tails of a ranking of all stocks on momentum; they are instead one-half of stocks within a style group. On the other hand, strong evidence of the effect is 16 An alternative structure combines the first and second sub-periods, and tests the null hypothesis for the two periods, 1927 to 1982 and 1983 to These tests using the one- and three-factor model alphas reject the hypothesis at either the 1% or 5% level for all size groups, Small, Mid and Big stocks, and for All stocks. The tests using average returns reject the hypothesis at the 5% and 1% levels for Mid and Big stocks. The estimates of Dif in these tests range from 0.61% to 0.91% 19

20 expected because managers hew towards indexes and the within-style sorting on momentum captures the incentives for tax-loss sales and window dressing of these managers. In fact, Table 3 provides substantial evidence of a turn-of-the quarter effect. The values of One and Two in Table 3 for Mid and Big stocks are of mixed signs and all are insignificantly different from zero, while for Small stocks all of these coefficients are positive and only one appears significant. Thus, there is no evidence of profits earned by momentum strategies in style portfolios during the first and second months of calendar quarters, except for the very smallest of stocks. All values of Jan are negative, representing losses to WML portfolios, and all of those in the Small group are significant at the 1% level. Most importantly, the coefficients Three and Dec are large and positive. There is a strong turn-of-thequarter effect for each style group; each value of Three is significant at the 1% level, except that for Big- Value stocks, which is significant at the 5% level. This shows winners beating losers during March, June and September; the average hedge returns are economically large, ranging from 73 to 138 basis points across the groups, and the returns in these months are much larger than those for other months. There also is a strong end-of-the-year effect in the Small and Growth groups. Among Small stocks, winners beat losers in December by an average return more than 1.5% in each of the valuation categories Growth, Blend and Value, and across the size groups, the average WML returns are largest and significantly different from zero in the Growth group. In summary, style portfolios holding winners long and losers short earned large positive average returns at the ends of calendar quarters during the years 1983 to Capital Gains and Losses, Turnover and the Turn-of-the-Quarter Effect Two sets of questions are now addressed. First, do the intra-quarter patterns of returns of momentum portfolios differ between those with capital gains and losses, and if so, do the differences appear to be a consequence of end-of-quarter tax-loss sales or window dressing? Second, given that stocks with high rates of turnover are more likely to be sold to realize short-term capital losses, is there evidence of significant differences in unexpected sales of stocks with losses between those with low and high rates of turnover? 17 Risk-adjusted returns for one- and three-factor models are also estimated for the style portfolios. The values of Three are positive, larger than those in Table 3 and significantly different from zero at the 1% level in each model for all nine portfolios. 20

21 5.1. Momentum in Stocks with One year Capital Gains or Losses Stocks are placed each month into loss or gain groups according to whether past 12-month returns (without dividends) are negative or non-negative, respectively, and the stocks within each group are ranked on momentum. Ten value-weighted portfolios are formed using the stocks within the quintiles of the rankings for the two groups. Portfolios 1 and 5 hold losers and winners, respectively, which are the 20% of stocks in either a loss or gain group with the lowest or highest momentum, respectively, and a WML portfolio is long the winners and short the losers within a group. Table A.1 in the Internet Appendix shows that stocks with capital losses earned much smaller average returns than stocks with gains in each sub-period. During the years 1983 to 2016, for example, the average excess returns of loss and gain portfolios were 0.27% and 0.70% per month, respectively. These results are not a surprise. Stocks with capital losses or gains tend to be in the lower or upper tiers of rankings on momentum, respectively, and because of prior evidence that winners beat losers, we expect stocks with prior capital gains to beat those with losses. where Two sets of Fama-French factor-model regressions of the portfolios returns are estimated,,, r r Alpha RMF r r SMB r Value r e, (6) it ft it i mt ft i SMB t i HML t it Alphait is constant in one case and it follows equation (3) in a second case. Table 4 reports the results. 18 The first two sub-periods are grouped together to conserve space, and Panels A and B report results for 1927 to 1982 and 1983 to 2016, respectively. In the left and right sub-panels are the results for the loss and gain groups, respectively. The constant Alpha is in the first line of each panel, and the monthin-quarter coefficients of equation (3) and the risk-factor loadings are in the following lines. A striking feature of the table is the differences between risk-adjusted returns of the WML portfolios reported in the sub-panels B.1 and B.2, respectively; these differences measure the relative contributions of the loss and gain groups to momentum profits. For 1983 to 2016, One, Two, Three and Dec for the WML portfolio in Panel B.1 are positive, economically large and significantly different from 18 The numbers of stocks in loss and gain groups and in the momentum portfolios of the groups vary, and in some months are near (but not equal to) zero. Table 4 reports the results of the regression (6) using all sample months. Regressions were run after eliminating months with fewer than 10 stocks in a group, but these produced qualitatively the same results as those in Table 4. 21

22 zero, while Jan is negative but insignificant at conventional levels. Similarly, the value of Alpha of 1.94% is large and significant. The values of these coefficients for stocks with gains in Panel B.2 are much smaller than the corresponding values in Panel B.1, and this is particularly true at the ends of calendar quarters. For example, Alpha differs by 1.55% (=1.94%-0.39%), while Three and Dec differ by 2.18% (=3.00%-0.82%) and 4.36% (=4.56%-0.20%), respectively, between the Panels B.1 and B.2. An important conclusion is that economically large profits may have been earned after 1982 by holding winners and selling losers within the loss group, while the potential for profits in the stocks with capital gains was considerably less. Of course traditional momentum strategies short the losers and buy the winners among all stocks, and not among loss and gain groups. The point is, however, that the profits of the strategies are due in large part to the cross-sectional dispersion of the returns of stocks with losses, which are stocks in the lowest tiers of a ranking on momentum. A second conclusion is that a large proportion of profits came near the ends of calendar quarters, consistent with the conclusion drawn earlier. The differences between stocks with losses and those with gains during the years 1927 to 1982 in Panel A stand in contrast to the corresponding differences in Panel B. Although the monthly intercepts in Panel A for the WML portfolios are mostly economically large and statistically significant, they are not uniformly larger for stocks with losses than for those with gains. Three is smaller in Panel A.1 than in Panel A.2, and each of the coefficients One and Two in Panel A.2 is significant, unlike the corresponding values in Panel B.2. Furthermore, Alpha differs by 0.39% (=1.44%-1.05%) between Panels A.1 and A.2, compared to the difference 1.55% in Panel B noted above. In other words, the proportion of momentum profits due to the dispersion of returns among stocks with losses increased through time. The values of Three in Panel B.2 of Table 4 are average factor-risk-adjusted returns during the months March, June and September for stocks that experienced capital gains during the prior year, calculated for the years 1983 to Positive and negative values are consistent with persistent end-ofquarter price pressure due to buying and selling, respectively. The values of Three in Panel B.2 are positive, tend to increase left to right, and those in columns 3, 4 and 5 are economically large and significantly different from zero at the 5% level. By comparison, the values of One and Two are small and insignificant. 22

23 This suggests that delegated managers bought relative winners as they sold stocks with capital losses, and supports the hypothesis that portfolio window dressing and tax-loss sales occur simultaneously at the ends of calendar quarters Turnover and the Realization of Capital Losses If a stock has experienced both a capital loss and a high rate of turnover during the past 12 months, it is more likely than others to suffer downward price pressure in the near future. This is for two reasons. First, high turnover indicates that a large number of current shareholders have recently purchased the stock and have a short-term tax basis above the current share price. Because short-term capital losses are more valuable than long-term losses, there is an incentive to sell now instead of allowing the short-term period to expire. Near the end of a calendar year individuals are likely to sell to realize losses, instead of postponing the benefits for 12 months. Alternatively, delegated managers who recognize the needs of their clients but who also window dress are likely to sell near the ends of calendar quarters. Second, among stocks with capital losses, high turnover during the recent past indicates a greater likelihood that delegated managers will soon collectively sell a stock as they window dress their portfolios. A manager who reports a stock with a short-term loss to a client must work to explain why the recent purchase of the stock was not an error in judgment. The same cannot be said for a stock with a long-term loss, say over a period of a few years, but which now has a short-term gain. A low or high rate of turnover for a stock during the past year suggests that few or many managers, respectively, now hold it with a shortterm loss in their portfolios and are likely to sell it as they window dress. For these two reasons, we expect downward price pressure at the ends of both calendar quarters and calendars years to be stronger for stocks with capital losses when they also have high rates of past turnover. This turnover hypothesis is tested using the models of the prior sections, regressing the monthly returns of portfolios of stocks grouped by levels of turnover as well as by gains and losses. Here, turnover is the ratio of daily share volume to shares outstanding, and stocks are ranked in each month t on the average turnover across days during the months t-12 to t-1, using a triple sort. Because turnover in the NASDAQ market includes inter-dealer trades and is higher than in the NYSE and AMEX markets, NASDAQ stocks 23

24 in the gain and loss groups are ranked on turnover separately from the others. All stocks in the loss and gain groups are placed into one of two portfolios, High or Low. These portfolios hold one half of the stocks within a gain/loss group with an average turnover rate that is above or below the median level in an exchange group, respectively. Also, hedge portfolios (HML) hold long the stocks in High and short the stocks in Low, and they represent bets that high-turnover stocks offer larger returns than low-turnover stocks. To again conserve space, Panels A and B of Table 5 report results for two periods, 1927 to 1982 and 1983 to As in Table 4 the regression intercepts as constants are reported in the first line of each panel, and the month-in-quarter values follow. The results in Table 5 support the turnover hypothesis. The hypothesis predicts downward price pressure in stocks with capital losses to be stronger for those with higher rates of turnover. With this in mind, consider the first row of the table for stocks with capital losses. In the Panels A.1 and B.1: the Alpha values for the Low and High portfolios are either negative and significant, or insignificant; the values for the hedge portfolios HML are and -0.79, respectively; and these estimates of expected risk-adjusted returns for the HML portfolios are significant at the 1% level. These results indicate that investors demand immediacy when they sell stocks to realize capital losses, and the likelihood of unexpected selling of a stock increases with its prior rate of turnover. In contrast, in the Panels A.2 and B.2 for stocks with gains: the Alpha values for the Low and High portfolios are positive but are approximately equal to each other, and the values for the HML portfolios are insignificantly different from zero. These results indicate that there is no difference in unexpected buying pressure among stocks with gains between those with low and high rates of turnover. The turnover hypothesis also predicts that unexpected demands to sell increase near the ends of calendar quarters, and this is particularly true for high-turnover stocks. The month-in-quarter coefficients for the years after 1982 support this prediction. In Panel B.1, for the portfolio High: each of the coefficients One, Two, Three and December is negative; the values are greater at the ends of calendar quarters, with values -0.50, -0.46, and -2.17, respectively; and Three and December are significant at the 1% level. In the same panel, for the portfolio Low, the coefficients One and Two are positive, while Three and 24

25 December are negative, and only December is significantly different from zero (at the 10% level). Thus, unexpected selling pressure among stocks with high turnover grows larger as the end of a calendar quarter approaches, while pressure among stocks with low turnover is not apparent. This is evidence that delegated managers tend to sell the stocks that have had high rates of turnover during the past 12 months, and is consistent with both selling to realize short-term losses and selling to window dress their portfolios. 19 Also in Panel B.2 of Table 5 the monthly coefficients One through Dec for the HML portfolio are not significantly different from zero, indicating that price pressure for stocks with low and high rates of turnover within the gain group are statistically indistinguishable. As in Table 4, evidence of upward price pressure appears near the ends of quarters. For example, the coefficients Three for the Low and High portfolios are positive and significantly different from zero, and the same is true of Dec for the Low portfolio. However, these coefficients do not differ significantly between Low and High, and they suggest delegated managers do not favor stocks with high rates of turnover to purchase when they window dress. 6. Tax-Loss Sales and Price Pressure Does short-run price pressure differ between stocks with capital gains and losses? Does that pressure increase towards the ends of calendar quarters? While the prior analysis suggests affirmative answers to these questions, I address them further using cross-sectional regressions and plots of CARs of portfolios of stocks grouped by gains and losses. The regressions describe short-term returns of individual stocks, and CARs describe the daily performance of stocks with capital gains and losses within months and quarters. 6.1 Cross Sectional Regressions and Return Responses Cross-sectional Fama-MacBeth (1973) regressions of monthly and weekly returns are run, similar to those of Jagadeesh (1990), Avramov et al. (2006) and Heston and Sadka (2008): * * rit it it ri, t1rt 1 eit. (7) 19 The robustness of these conclusions is checked by running regressions using average excess returns instead of factor-model intercepts. Again the stocks with capital losses and with high rates of turnover experience large negative returns near the ends of calendar quarters, while those with low turnover do not. 25

26 In the first case, r it is the percent return of stock i in month t, and r r * * it, 1 t1 is difference between the return in month t-1 calculated from daily returns, but excluding the final day of the month, and the cross-sectional average return. The coefficients it and it are estimated each month by OLS regression, and they may vary across stocks in a manner described below. The return responses it give information in one month s returns regarding the next month s returns. 20 There is reversal ifit 0, and continuation if it 0. If 0, for example, the regression predicts that stocks with below-average returns in one month have it above-average returns in the following month. For infrequently traded stocks, reversals are observed if bid or ask prices enter the returns for two temporally adjacent months. Alternatively, reversals may represent price pressure, which is a temporary change in either prices or the midpoints of spreads due to abnormal volumes of orders to buy or sell, representing demands for immediacy as in the inventory models. Because we look for evidence of price pressure, rit, 1and r are calculated without using a common month-end * it, 1 closing price. Stocks are short-term winners or losers in month t if for the prior month r r 0 or <0, * * it, 1 t1 respectively. Weekly returns are calculated by compounding daily returns from Thursday of one week to the following Tuesday, and r * it, 1 rit, 1 in this case. By skipping Wednesdays, a common price does not enter the returns in adjacent weeks. Two models are estimated for both weekly and monthly returns. Coefficients in Model 1 are constant across stocks and it t and it t. Coefficients in Model 2 differ according to a stock s status as one with either capital loss or gain and with status as a short-term winner or loser: 1 1 L L N L L N (8) it Lt it LNt it it Gt it GNt it it L L N 1L 1 L N, (9) it Lt it LNt it it Gt it GNt it it 20 Heston and Sadka (2008) say it, is a return response. Stocks with minimum prices during month t-1 below $1 are excluded. 26

27 where N it =1 if r * * it, 1 rt 1 0, and N it =0 otherwise, and L it or 1 Lit indicates that stock i has a capital loss or gain, respectively. 21 In this model and are return responses for stocks with losses and gains, Lt Gt respectively, while and are the additional responses when these stocks are also short-term losers. LNt GNt The models allow asymmetric responses to demands for immediacy, which is unlike the theories of Grossman and Miller (1988) and Campbell et al. (1993). Prices in the theories respond symmetrically to unexpected investor demands to buy and sell, and this is a consequence of parametric restrictions that provide analytic solutions. In a world of asymmetric responses to tax rules, however, we expect asymmetry in price pressure. For example, Sias and Starks (1997) say that tax-loss sales by individuals create downward pressure on prices in December that is relieved in January. For this reason, we expect Lt Gt and LNt 0 when months t and t-1 are January and December, respectively. In this case, Lt Gt indicates higher average returns for stock with capital losses because these stocks prices bounce back early in January after tax-loss sales in December, and LNt 0 indicates that stocks January returns increase as with the degree of downward price pressure in December. Table 6 reports averages of the estimates of the regression coefficients for weekly returns in Panels A and C, and for monthly returns in Panels B and D. The sub-panels report results separately for the sub-periods 1927 to 1952, 1953 to 1982 and 1983 to The t-statistics are calculated using Newey-West (1987) standard errors for the time series of estimates. 22 Model 1 shows strong reversals during the early years, and modest evidence of reversals during the late years of the sample. The weekly responses in Panel A for stocks with capital gains are more than twice as large for the first and second sub-periods than the third, with values =-0.063, and for the three sub-periods. Similarly for monthly returns, declines across time and the estimate in Panel B.3 21 The estimated coefficients of Model 2 are noisy in any month t in which the number of stocks in any of the groups defined by the dummy variables L and N is small. I require it M it L N for each t, where M is a minimum number of stocks, and i it it similarly for the products 1Lit N, L it 1 N it it, 1L 1N it it. Results are reported using M=20, and in this case 35 months are eliminated from the sample for the period 1927 to No months are eliminated from the period 1983 to * The rt 1 in the regression (7) is the mean of all stocks for Table 6, and is the mean of stocks within the size groups (Small/Mid and Big) for Table 7. 27

28 (-0.005) is indistinguishable from zero. These results indicate that stock market liquidity has risen over time, making monthly returns unpredictable (in this linear model) for the period 1983 to Panel C shows asymmetry in weekly return responses, with larger reversals for short-term losers than for winners. The values of LN and GN in Model 2 are negative, and five of the six values are significant at either the 1% or 5% level. As in Avramov et al. (2006), the evidence shows an aggregate demand for immediacy that is greater when investors sell than when they buy. One reason for asymmetry is that investors may trade with less patience if there is either an approaching end of a period defining a short-term loss, or a desire to claim a loss before the end of a tax year. There is an incentive to sell soon in each case. A second explanation of asymmetry is concurrency in trade. If many investors sell stocks and realize capital losses at approximately the same time, there is greater immediacy in aggregate demands to sell than to buy, and this is true even if investors individually trade with equal patience as they sell and buy. Asymmetry is evident also in monthly return responses, but it is different from that in weekly returns. Unlike Panel C, there is no evidence in Panel D of Table 6 that reversals are stronger for shortterm losers than winners. Instead, reversals in monthly returns are weaker for short-term losers; the values of LN and GN in Panels D.2 and D.3 are positive, and those of LN are large and significant at the 1% level. Most surprising is the evidence for the years after 1982 and for stocks with capital losses that shortterm losers experience continuation. In Panel D.3, L is negative and is significant at the 1% L LN level, demonstrating reversals for winners, but , demonstrating continuation for shortterm losers. In comparison, and for stocks with capital gains in the same panel are small and G GN indistinguishable from zero. Because evidence of continuation is counter-intuitive, the results in Panel D.3 are decomposed by reporting in Table 7 the averages of the coefficients of Model 2 for individual months of calendar quarters during the period 1983 to 2016, and for Small/Mid stocks in Panel A separately from Big stocks in Panel B. Surprisingly, the results give additional evidence of continuation in stocks with capital losses. In all columns of the table L 0, indicating reversal for stocks that are targets for tax loss sales after the months 28

29 in which their returns are above average. However in 10 of the 12 columns, 0 so that shortterm losers experience continuation. For Small/Mid stocks, in Panel A is significantly different from zero at either the 1% or 5% level in all months but January, and for Big stocks there is evidence of continuation late in calendar quarters with LN and Big stocks, LN is significant at the 1% level using all months. 29 LN significant in months Two and Three. For both Small/Mid The evidence of continuation in monthly returns for the years 1983 to 2016 in Tables 6 and 7 is odd for several reasons. It is inconsistent with results for the earlier sub-periods in Panels D.1 and D2 of Table 6, and it is unlike the results of Avramov et al. (2006), who find no evidence of continuation in either weekly or monthly returns. Most importantly, the inventory theories do not explain continuation; reversals appear symmetrically for both short-term winners and losers in these models. The fact that the return responses are significant for stocks with capital losses but not for those with capital gains suggests stocks that are likely targets for tax-loss sales suffer negative price pressure. Particularly late in calendar quarters, Table 7 Panel B says that if a stock has a capital loss and earns an above average return in the second month of the quarter, it will do poorly in the third month. If instead it does very poorly in the second month, earning a return that is below average, it is also likely to earn a below-average return in the following month. 6.2 Visual Evidence of Reversal and Continuation Cumulative Abnormal Returns Visual evidence of reversal and continuation in stock returns appears in plots of cumulative abnormal returns (CARs) of 18 active portfolios. Each active portfolio holds the stocks in one of the size groups Big, Mid or Small that: (i) have either capital gains or losses, or (ii) have either gains or losses, and are either short-term winners or losers. The CARs demonstrate that short-term performance is driven principally by status as a stock with capital gain or loss, and not by status as a winner or loser. A CAR is the cumulative daily performance of a buy-and-hold portfolio in excess of a benchmark, which is a portfolio of all stocks in a size group. The active portfolios and benchmarks are rebalanced monthly to equal weights. Because a CAR starts each month at zero and it accumulates daily abnormal returns, we expect it to meander as a random walk in the absence of price pressure that creates series of positive or negative abnormal returns. Alternatively, CARs will decline when investors orders to sell L LN

30 cluster in time, and they will rise during periods when orders to buy regularly cluster. For this reason, we look for differences in the CARs of the active portfolios between months and between sub-periods. CARs for active portfolios are plotted in Figures 1-4. Each row of a figure corresponds to a size group, and the columns of panels correspond to standard months (SMs) that have uniform numbers of days per month. 23 Writing M as a map of calendar month m to a standard month, January if m January, One if m April, July or October, M m Two if m February, May, August or November, Three if m March, June, or September, December if m December. As a consequence, a SM corresponds to a month-in-quarter coefficient in the earlier analysis. For example, the CARs for One represent the average performance of a portfolio during the calendar months April, July and October. Similarly, the CARs for Two and Three each represent several calendar months, while those for January and December represent their respective calendar months. The details of the SMs and the CARs are in Internet Appendix B. Simply put, a CAR measures the historical average performance of a hypothetical active manager, relative to the performance of stocks in the size group that is his/her universe. Figures 1, 2 and 3 show CARs for the gain and loss portfolios that indicate systematic differences in price pressure for these portfolios between the three sub-periods. The figures demonstrate the consequences of increased needs of investors to efficiently realize gains and losses and increased end-ofquarter trading by delegated managers, creating seasonality in stock returns. Consider first the CARs for the standard months One, Two and Three. Widening gaps appear in each figure between the CARs for stocks with losses and gains, but the magnitudes of the gaps differ systematically between the sub-periods. The gaps in Figure 1 are modest. Although the CARs of the loss and gain portfolios at the ends of months are mostly below and above zero, respectively, the CARs show only modest drift from the zero level. This demonstrates very modest trading to realize capital losses during the years 1927 to The CARs for the gain and loss portfolios in Figure 2 are positive and negative, respectively, the gaps between them 23 Standard months have 25 trading days during the period from January 1927 to May 1952, and have 21 days after this date, while calendar months have various numbers of trading days. 30

31 increase day by day, and the end-of-month gaps are much larger than in Figure 1. This is evidence of regular and persistent demands to sell stocks with capital losses, leading to negative abnormal returns for those stocks during the years 1953 to It suggests that investors incentives to efficiently realize capital losses increased as a result of changes in the tax code during the first two sub-periods. In Figure 3 the gaps at the end of month Three are larger than the gaps for months One and Two, and this is particularly true for Mid and Big stocks. This evidence is consistent with Table 2 and other tables in this paper that demonstrate a strong turn-of-the quarter effect in risk-adjusted monthly stock returns that is mostly apparent in Mid and Big stocks during the third sub-period. Late in calendar quarters during the years 1983 to 2016, the stocks with capital losses and gains experienced negative and positive price pressure, respectively. Speaking broadly, the differences between the CARs for months One, Two and Three in the figures show that changes in the tax code and in managers window dressing activities are manifest in stock market prices. The CARs for January and December document a strong turn-of-the-year effect in each of the subperiods. The gaps between the CARs in January first grow rapidly and then flatten or shrink, indicating that most of the January activity is in the first few days. These results are consistent with Keim s (1983) finding of positive abnormal returns for small stocks early in January, and Reinganum (1983) showing that January returns are particularly large for stocks with losses. Unlike the prior research, however, Figures 1, 2 and 3 demonstrate an important effect during December: the gaps in CARs regularly widen throughout December, except for a small reversal during the final few days of the year. This shows that stocks with losses or gains experience negative or positive price pressure, respectively, during December. Furthermore, the January effect for the gain and loss portfolios is apparent in Big and Mid stocks as well as in Small stocks during the years after these studies. 24 Overall, the figures demonstrate price pressure during December that creates negative abnormal returns for stocks with capital losses, and an opposite result during January. 24 The January effect documented by Keim (1983) and Reinganum (1983) is principally in small stocks. The sample periods of these studies are within the second sub-period of my data. 31

32 Figure 4 plots CARs for the portfolios of stocks with either gains or losses, and that are either winners or losers during the years 1983 to These CARs are marked gain/winner, loss/loser, etc, and they demonstrate continuation that is consistent with the return responses in the Fama-MacBeth regressions. The CARs of the loss/winner and loss/loser portfolios tend to overlap during these months, and are nearly identical at the ends of months Three and December. Similarly, the CARS of the gain/winner and gain/loser portfolios for these months are close in value. These results demonstrate that near the ends of calendar quarters, the stocks with capital losses and gains experience downward and upward price pressure, respectively, and the price pressure exists independently of whether the stocks had a negative or positive return shock during the prior month. Therefore, among stocks with capital losses we expect losers to continue to lose, and among stocks with gains, short-term winners continue to win. January is an exceptional month. Unlike other times and particularly unlike other first months of quarters, a stock s abnormal performance in January is critically dependent on its performance in the prior month. The loss/loser portfolio in each size group has a positive CAR at the end of January, while the loss/winner portfolios have negative or near-zero CARs. Similarly, the gain/winner portfolios show negative CARs, while the gain/loser portfolios show either near-zero CARs (for Small and Mid stocks) or negative CARs of similar magnitude to those of the gain/winners (for Big stocks). This is evidence of price pressure in December that is relieved at the end of the tax year, leading to reversal of WML portfolio returns in January. However, there is little evidence that price pressure in month Three is followed by short-term reversal in month One. The end-of-month-one CARs for the gain/loser and gain/winner are positive or near zero, while those for the loss/loser and loss/winner are negative or near zero. The comparison of the CARS during January to those during month One suggests that the responses of liquidity suppliers to price pressure caused by individuals tax loss sales at the end of the year, on the one hand, are different from their responses to price pressure created by delegated managers trading during March, June and September, on the other. One conjecture is that tax loss sales by individuals in one year are temporarily exhausted at the end of December and do not continue into January, whereas tax-loss sales by managers at the ends of calendar quarters tend to continue into the following quarter. It is also possible 32

33 that liquidity suppliers are not cognizant of the clustering of tax loss sales at the ends of quarters that are documented in this paper. This issue deserves further study. 7. Concluding Remarks This paper provides evidence that the U.S. tax code and the reporting practices of investment managers lead to systematic patterns in price pressure across the months of calendar quarters, and that investors demands for immediacy in trade are one root cause of momentum and reversal in U.S. stock prices. Price pressure creates a turn-of-the-quarter effect during the years after passage of the Tax Equity and Fiscal Responsibility Act in 1982, where this act substantially increased the payments of taxes on capital gains to the IRS. Specifically, average returns of winner-minus-loser (WML) portfolios are economically large and positive in the third month of a calendar quarter, and they are small in other months. A lion s share of the profits of momentum strategies is due to the dispersion of expected return across stocks with capital losses compared to the dispersion across stocks with gains, and these profits are much larger in the stocks with high versus low turnover. Whereas price pressure might create reversal of WML returns across monthly intervals, with relative losers becoming winners and winners becoming losers, the evidence suggests this occurs only in January. There is no evidence of these reversals in other first months of the year. Although momentum has been documented in many markets and countries, I focus on the U.S. stock market. Institutional characteristics differ between markets and between countries, and seasonal patterns of returns, if they exist in other markets, are likely driven by characteristics different from those described in this paper. In particular, if capital gains are defined differently than in the U.S., if tax payments on gains are not enforced or if active managers do not report their results each calendar quarter, we may not see a turn-of-the quarter effect in security returns outside the U.S. 25 Tables 4 and 5 show that end-of-quarter tax sales and window dressing give an incomplete explanation of momentum. Panel B of Table 4 shows negative price pressure early in calendar quarters during 1983 to 2016 for stocks with capital losses: the coefficients One and Two of WML portfolio in Panel 25 Because capital markets of many countries are integrated, U.S. tax policies and the activities of U.S. investors may cause price pressure in other countries markets, and vice versa. 33

34 B.1 are positive, economically large and significantly different from zero, while they are insignificant for stocks with gains. Similarly in Panel B of Table 5, One and Two are large and negative for the stocks with high levels of turnover, which are the stocks most likely to be sold to realize short-term capital losses, and are positive for stocks with low levels of turnover. However, this evidence of momentum in stock prices during the first and second months of calendar quarters is largely attributable to Small and Mid stocks. Table A.2 of the Internet Appendix demonstrates this point by reporting the results of Table 4, but using only Big stocks. One and Two for the WML portfolio for the period 1983 to 2016 in Panel A of Table A.2 are positive, but are considerably smaller, less than 1/2 the size of the corresponding values in Table 4, and they are insignificant. It is unclear why the evidence of momentum in Small and Mid stocks early in calendar quarters appears in Table 4. Perhaps it is explained by the theories discussed in Section 2, or it might instead be due to tax-loss sales by individuals during the first and second months of calendar quarters. Cooley and Roenfeldt (1975) and Lee and Swaminathan (2000) show that average returns are higher for low- than high-turnover stocks. 26 Miller (1977) argues that this is a consequence of short-sale constraints. In his theory: short sales are costly; the beliefs of many pessimistic investors are not registered in stock prices; prices are biased and optimistic averages of investor opinions; and the bias rises with the heterogeneity of investors opinions. Miller also argues that turnover and heterogeneity of opinion are positively related in the cross-section of stocks. As a result, stocks with high turnover earn low returns. The evidence here suggests an alternative explanation of a turnover effect in returns, namely that negative price pressure caused by tax-loss sales is more evident in stocks with high turnover. The results in Table 5 support this idea. For the years 1983 to 2016, the values of Alpha of the HML portfolios in Panels B.1 and B.2 are -0.79% and 0.04%, respectively, and only the first value is significantly different from zero. This indicates that among stocks with high turnover, low returns are principally earned by those with capital losses. In addition, Miller s theory does not predict a turn-of-the-quarter effect, but Table 5 shows clearly 26 This result is confirmed in my data. High and Low portfolios are constructed by ranking stocks on average daily turnover (during the ranking period) within 10 size groups, and they hold one half of stocks with turnover above or below the median of a size group, respectively. HML returns are the difference of returns of High and Low, and they are regressed on the Fama-French risk factors. The average risk-adjusted monthly returns are -0.21% and -0.26% for the years 1927 to 1982 and 1983 to 2016, respectively, and each is significantly different from zero at the 1% level. 34

35 that the negative abnormal returns are much larger near the ends of calendar quarters during the years 1983 to Thus, tax-loss sales and window dressing may explain a turnover effect in average stock returns. Recent research shows that the abnormal returns of WML portfolios and returns to other anomalies have attenuated in recent years, relative to the periods in which they were first documented. Chordia et al. (2013) attribute the declines to increases in market liquidity and arbitrage activity, while McLean and Pontiff (2016) show that the publication of financial research contributes to the decline. For this reason, the average returns of the style-based WML portfolios are calculated using the years 2000 to These results are reported in Table A.3 of the Internet Appendix, and are similar to those in Table 3, which used the years 1983 to In this table, average returns are reported for months one and two of calendar quarters as a single group and are reported as the coefficient OneTwo. Also, coefficients of a summary regression using the average of the WML returns of the six style groups is reported in the column All. The estimates of Three in Table A.3 are positive, many are larger than the corresponding values in Table 3, and many values are significant at the 1% or 5% level despite the short sample period. In comparison, the estimates of OneTwo are mixed in sign, and all values are statistically indistinguishable from zero. For example, the average of WML returns across the six style portfolios gives values of Three and OneTwo of 1.06% and -0.33%, respectively. These results indicate that the turn-of-the-quarter effect in the style portfolios is as strong during the recent years than in the past. We conclude that there has been periodic price pressure in stock market returns during recent years, and tax-loss sales and window dressing still go hand-in-hand near the ends of calendar quarters. 35

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39 Figure 1. Cumulative Abnormal Returns of Active Portfolios, January 1927 to May 1952 Stocks with Capital Gains or Losses by Standard Months and by Market Equity Value (size) 39

40 Figure 2. Cumulative Abnormal Returns of Active Portfolios, June 1952 to December 1982 Stocks with Capital Gains or Losses by Standard Months and by Market Equity Value (size) 40

41 Figure 3. Cumulative Abnormal Returns of Active Portfolios, January 1983 to December 2016 Stocks with Capital Gains or Losses by Standard Months and by Market Equity Value (size) 41

42 Figure 4. Cumulative Abnormal Returns of Active Portfolios, January 1983 to December 2016 Stocks with Capital Gains or Losses, and that are Short-term Winners or Losers 42