Liquidity and the Post-Earnings-Announcement Drift

Transcription

1 Liquidity and the Post-Earnings-Announcement Drift Tarun Chordia, Amit Goyal, Gil Sadka, Ronnie Sadka, and Lakshmanan Shivakumar First draft: July 31, 2005 This Revision: May 8, 2006 Abstract The post-earnings-announcement drift is a long standing anomaly that is in conflict with semi-strong form market efficiency. This paper documents that the post-earnings-announcement drift occurs mainly in the highly illiquid stocks. A trading strategy that goes long the high earnings surprise stocks and short the low earnings surprise stocks provides a return of 0.24% in the most liquid stocks and 1.79% per month in the most illiquid stocks. The illiquid stocks have high trading costs and market impact costs. Using a multitude of estimates we find that transaction costs account for anywhere from 66% to 100% of the paper profits from the long-short strategy designed to exploit the earnings momentum anomaly. JEL Classifications: G11, G12, C11 Tarun is from the Goizueta Business School, Emory University, Tarun Chordia@bus.emory.edu; Amit is from the Goizueta Business School, Emory University, Amit Goyal@bus.emory.edu; Gil is from Columbia Business School, Columbia University, gs2235@columbia.edu; Ronnie is from the University of Washington Business School, rsadka@u.washington.edu; and Shivakumar is from the London Business School, Lshivakumar@london.edu. We thank Larry Brown, Jon Garfinkel and seminar participants at Emory University, Georgia State University and University of Georgia for helpful comments.

2 1 Introduction In a seminal paper, Fama (1998) once again argues that the null should still be one of market efficiency. However, Fama concedes the existence of two robust and persistent anomalies that still pose a challenge to the efficient markets paradigm. One of these anomalies is the post-earnings-announcement drift or earnings momentum. 1 Earnings momentum refers to the fact that firms reporting unexpectedly high earnings subsequently outperform firms reporting unexpectedly low earnings. Ball and Brown (1968) were the first to note that stock returns continue to drift in the direction of earnings surprises for several months after the earnings are announced. Schwert (2003) shows that a number of market anomalies have typically disappeared, reversed, or attenuated following their discovery. The post-earnings-announcement drift, along with price momentum, is still robust after its initial discovery as several studies have confirmed the robustness of the post-earnings-announcement drift or earnings momentum using more recent data and using data from stock markets other than the U.S., where the phenomenon was first identified. The post-earnings-announcement drift is commonly interpreted as evidence that investors underreact to earnings surprises and, therefore, consistent with market inefficiency and investor irrationality (see Ball and Bartov (1996)). Chordia and Shivakumar (2005) document that a portfolio that is long in stocks with the highest earnings surprises and short in stocks with the lowest earnings surprises provides a return of 90 basis points per month or over 10% annually. Such large profits, from a simple long-short trading strategy, over a period of almost four decades point to a violation of the semi-strong form market efficiency as defined by Fama (1970). In this paper, our goal is to answer the following question. Why have the profits from an earnings momentum strategy been robust over a period of four decades? We also weigh in on the debate between the behavioral and rational asset-pricing models. The recent interest in behavioral models is driven by data that conflicts with the standard frictionless asset-pricing models. We introduce frictions in the form of trading costs to evaluate the profitability of trading strategies that exploit the post-earningsannouncement drift. More specifically, we examine the impact of illiquidity on the trading profits. While liquidity is an elusive concept, most market participants agree that liquidity generally reflects the ability to buy or sell sufficient quantities, quickly, at low trading cost and without impacting the market price too much. Following Ami- 1 The other anomaly is the price momentum, documented by Jegadeesh and Titman (1993). 1

3 hud (2002), we measure monthly illiquidity as the average of the daily price impacts of the order flow, i.e., the daily absolute price change per dollar of daily trading volume. We examine the profitability of the long-short strategy after sorting stocks into decile portfolios based on this illiquidity measure. We find that the post-earnings-announcement drift is prevalent mainly in stocks that are relatively illiquid. The returns from the long-short standardized unexpected earnings (SUE) strategy increases monotonically from 0.24% for the most liquid stocks to 1.79% per month for the most illiquid stocks. Moreover, we demonstrate that the long-short trading strategy that attempts to profit from the post-earnings-announcement drift generates high transaction costs and substantial price impact. Specifically, we use the transaction-cost estimates of Keim and Madhavan (1997), Korajczyk and Sadka (2004), and Chen, Stanzl, and Watanabe (2004) in a dynamic framework to estimate net returns based on a strategy that buys the high-earnings-surprise stocks and sells the low-earnings-surprise stocks. The evidence shows that transaction costs consume anywhere from 66% to 100% of the potential profits. While the presence of statistically significant earnings momentum in individual security returns is undeniable, it is not possible to profit from this predictability. This lack of profitability is consistent with the Jensen s (1978) definition of market efficiency and Rubinstein s (2001) definition of minimally rational markets. 2 The lack of profitability from a long-short strategy that exploits earnings momentum suggests that the violations of the efficient-market hypothesis due to the post-earnings-announcement drift are not so egregious after all. Prior literature has also shown that much of the drift is concentrated around the earnings announcements subsequent to the formation of the long-short SUE portfolios (see Bernard and Thomas (1989)). We show that over a three day period around the next two earnings announcements, the effective bid-ask spread increases, the buy and sell trade sizes increase marginally and the order imbalance increases for both the high and the low SUE stocks. The increase in the effective bid-ask spread suggests that trading costs increase around the subsequent two earnings announcements. The slight increase in trade sizes suggests that it is uninformed or noise traders that are active around the subsequent earnings announcements. The increase in buy trades for the low SUE stocks (which have negative returns) confirms that trading around earnings announcements is mainly non-informational. The presence of negative returns with buy trades suggests 2 The concept of market efficiency with respect to an information set has been defined by Jensen (1978) as the inability to profit from that information. Rubinstein (2001) defines this as minimally rational markets. 2

4 that price changes (at least for the low SUE stocks) around earnings announcements occur due to the incorporation of information contained in the announcement and not due to order flow from traders who exploit the drift. This paper is related to a recent strand of the literature that re-examines market anomalies in the context of transaction costs. For instance, Korajczyk and Sadka (2004) examine the impact of transaction costs on price-momentum strategies. Avramov, Chordia, and Goyal (2006) show that the short-run reversal strategies at the weekly and monthly frequencies are not profitable once transaction costs are taken into account. Hanna and Ready (2006) find that the Haugen and Baker (1996) trading strategies do not provide attractive returns after accounting for transaction costs. Hou and Moskowitz (2005) show that the post-earnings-announcement-drift is prevalent in stocks which have the most friction as measured by the delay with which their prices adjust to information. Our contribution is to provide a detailed examination of transactions costs that could inhibit prices from adjusting completely and quickly to earnings information. The remainder of the paper proceeds as follows. Section 2 presents the data. Section 3 presents the results. A detailed discussion of transactions costs is presented in Section 4. Section 5 examines liquidity around earnings announcement dates and Section 6 concludes. 2 Data Our sample consists of all NYSE-AMEX firms with data available on the monthly CRSP and quarterly COMPUSTAT files for the period January 1972 through December We focus only on common stocks, and eliminate ADRs, REITs, American Trust Components, units, and closed-end funds from the sample. In order to avoid the extremely illiquid securities, stocks with prices less than five dollars at the start of each month are eliminated from the sample. 3 The average number of stocks in the sample is 1,841. Our tests use standardized unexpected earnings (SUE) to capture the post-earningsannouncement drift (PEAD). Following Chan, Jegadeesh and Lakonishok (1996), in each month, SUE for a firm is computed as the most recently announced quarterly earnings less the earnings four quarters ago. 4 This earnings change is standardized by its standard 3 In the context of long-term contrarian investment strategies, Ball, Kothari, and Shanken (1995) show that microstructure issues can create severe biases amongst low-priced stocks. We obtain qualitatively similar results when stocks with prices less than one dollar are eliminated from the sample - both the gross profits and the transaction costs are higher for low-priced stocks. 4 We also compute SUE after allowing for a drift in earnings and SUE from analyst revisions. The 3

5 deviation estimated over the prior eight quarters. Specifically, SUE is calculated as: SUE it = E iq E iq 4 σ iq, (1) where E iq is the most recent earnings, for quarter q, announced either in month t or in the prior three months, and σ iq is the standard deviation of (E iq E iq 4 ) over the prior eight quarters. The Amihud (2002) illiquidity measure is the average daily price impact of order flow and is computed as the absolute price change per dollar of daily trading volume: ILLIQ it = 1 D it D it t=1 R itd DV OL itd 10 6, (2) where R itd is the daily return, DV OL itd is the dollar trading volume of stock i on day d in month t, and D it is the number of days in month t for which data is available for stock i. We compute the Amihud illiquidity measure at the monthly frequency. We require at least ten days with trades for each stock each month. Since turnover has often been used as a measure of liquidity, 5 one may expect the illiquidity measure to be related to turnover. However, the cross-sectional correlation between turnover and illiquidity is only The information in the Amihud illiquidity measure is not subsumed by that in turnover. 6 Table 1 presents summary statistics for SUE-sorted decile portfolios. In each month, sample firms are sorted into deciles based on the most recent SUE. The breakpoints for sorting on SUE are determined by the distribution of SUE computed in months t 4 to t 1. The SUE-sorted portfolios are held for the subsequent six months. We follow Jegadeesh and Titman (1993) in forming decile portfolios in order to avoid test statistics based on overlapping returns. With a six month holding period, each monthly measure is an equal-weighted average of the past six month ranking portfolios. In each month, and within each portfolio, we average the SUE s of firms constituting the portfolio to obtain the portfolio s SUE. By design, the average SUE increases monotonically from -3.7 for the lowest SUE-decile portfolio to 3.2 for the highest SUE-decile portfolio. The higher SUE portfolios (six through ten) are more liquid than the lower SUE portfolios results from these alternative calculation are virtually unchanged and not reported in the paper. 5 See, e.g., Brennan, Chordia, and Subrahmanyam (1998) and Chordia, Subrahmanyam, and Anshuman (2001). 6 Hasbrouck (2003) compares effective and price-impact measures estimated from daily data to those from high-frequency data and finds that the Amihud (2002) measure is the most highly correlated with trade-based measures. 4

6 (one through five). The Amihud illiquidity measure is 0.64 for the lowest SUE portfolio and 0.43 for the highest SUE portfolio. This shows that positive earnings surprise firms are, on average, more liquid than the negative earnings surprise firms, possibly reflecting more information asymmetry and/or uncertainty among bad-news firms (see Hayn (1995)). However, our results regarding the liquidity level of SUE portfolios do not provide an explanation for the existence of the anomaly. To the extent that liquidity level carries a premium, one would expect low-liquidity firms to have higher expected returns than high-liquidity firms. However, our results indicate the opposite phenomenon the high-sue firms are more liquid than low-sue firms, yet high-sue firms outperform low-sue firms. The average monthly returns (computed from a six month holding period) vary almost monotonically from 0.88% per month for the lowest SUE portfolio to 1.62% for the highest SUE portfolio. The difference in the monthly returns between the two extreme decile portfolios is about 0.73% per month. 7 Thus, the post-earnings-announcement-drift strategy of going long the high-sue stocks and short the low-sue stocks results in a return of about 4.4% over the following six months. The monthly alpha is a statistically significant 0.74% from the market model and 0.87% from the Fama and French (1993) model. When the Fama-French factors are augmented by a price momentum-based factor, UMD, the alpha is 0.65% per month. Given that the SUE portfolios differ in their level of liquidity, it is natural to ask whether the loading on a liquidity risk factor explains the above long-short portfolio returns. Thus, we also augment the Fama-French factor by UMD and the Pástor and Stambaugh (2003) liquidity factor (PS). We use a value-weighted factor that is long stocks with high sensitivity to the PS non-traded liquidity factor and short stocks with low sensitivity to the non-traded liquidity factor. 8 The risk-adjusted long-short portfolio alpha is 0.48% when using the Fama-French factors along with UMD and this traded liquidity factor PS. Moreover, the beta on PS of the long-short SUE portfolio in insignificant. This suggests that while high SUE firms are more liquid in levels than low SUE firms, they are not more sensitive to the liquidity risk. 9 We also check that the 7 When SUE is computed after allowing for a drift in earnings, the difference in the monthly returns between the two extreme decile portfolios is 0.70%. We also compute the earnings surprise using the analyst based measure as in Chan, Jegadeesh and Lakonishok (1996). The results are essentially the same. Over the sample period , the monthly returns using a six month holding period are 0.60% based on the analyst forecast revisions and 0.62% based on SUE. 8 We thank Ľuboš Pástor for the traded liquidity factor. 9 Sadka (2006) shows that a liquidity factor based on the Kyle (1985) model may explain as much as half of the abnormal returns to PEAD. Since the Sadka factor is non-traded, we do not use it for this paper. However, we note that the loadings of the long-short SUE portfolio on Sadka s factor are also 5

7 factor loadings in each of the above models are insignificant suggesting that the longshort portfolio does not load on the standard risk factors. The only exception is positive and significant loading on the momentum factor. This suggests that earnings and price momentum are related and is consistent with the results in Chordia and Shivakumar (2005). We conclude that the standard asset-pricing models do not capture the profits from an earnings-momentum strategy. 3 Results Table 2 presents the average monthly returns of portfolios that are sorted independently on SUE and illiquidity. The returns are, once again, computed over a six-month period after the formation of the SUE-illiquidity portfolios. The returns are equally weighted within each portfolio. Thus, there are total of one hundred portfolios with the sort on SUE and illiquidity. Since the portfolios in Table 2 are formed by sorting stocks independently on SUE and illiquidity, it is natural to ask whether the various portfolios are well-populated. We check to ensure that all the portfolios are indeed populated and the results are not being driven by outliers, even in the highly illiquid stock portfolios. The returns of these portfolios generally increase with SUE. For instance, for the illiquidity portfolio 10, the returns increase from 0.25% for the lowest SUE portfolio to 2.04% for the highest SUE portfolio. Returns increase (decrease) with illiquidity for the high (low) SUE stocks. For the SUE portfolio 1, returns decrease from 0.99% for the most liquid stocks to 0.25% per month for the most illiquid. On the other hand, returns increase from 1.23% for the most liquid portfolio to 2.04% for the most illiquid portfolio, for the SUE portfolio 10. This is consistent with the underreaction, to bad news in the SUE portfolio 1 and to good news in SUE portfolio 10, being concentrated in the illiquid stocks. Given that the return of the SUE portfolio 1 decreases with illiquidity and that of SUE portfolio 10 increases with illiquidity, the difference in returns between the high- SUE portfolio and the low-sue portfolio increases monotonically with illiquidity. For the most liquid stocks this difference is only 0.24%, but for the most illiquid stocks this difference is more than seven times higher at 1.79% per month. This shows that the profits from a strategy that exploits the PEAD, by buying the high-sue stocks and selling the low-sue stocks, are higher for the more illiquid stocks. In fact, for the four insignificant. 6

8 portfolios with highest liquidity, the PEAD strategy profits are less than 50 basis points per month. Only the three most illiquid portfolios have PEAD strategy profits greater than 1% per month. The alphas from various factor models for the long-short SUE portfolios are generally significant only for the more illiquid stocks. For example, alpha for the most illiquid long-short SUE portfolio is 1.74% from the market model, 1.86% from the Fama-French model, and 1.74% from the Fama-French models augmented by UMD. Since conditioning on illiquidity has a large impact on the gross returns to the SUE portfolios, we once again calculate an alpha from the Fama-French model augmented by UMD and PS liquidity factor and find that it is still significant at 1.69% for the most illiquid portfolio. Table 3 presents descriptive statistics for the various two-way-sorted portfolios in Table 2. Specifically, Panel A of Table 3 presents the equally weighted average illiquidity, turnover, dollar trading volume, and the decile size rank for each of the portfolios. These characteristics are calculated over the six-month holding period after the portfolio formation date. The results clearly show that while the firm characteristics do not change much with SUE, there is considerable variation with illiquidity. Holding SUE constant, firm size, turnover and dollar trading volume decrease with illiquidity. For instance, in the SUE Portfolio 10, average dollar trading volume (turnover) decreases from $8.5 million per month (0.77%) for the most liquid stocks to $0.007 million per month (0.23%) for the most illiquid stocks. The average decile size rank (calculated using NYSE breakpoints) also decreases monotonically from 9.6 to 1.5. Panel B of Table 3 presents the bid-ask spread and the quoted depths of the various portfolios over the period 1988 through These measures are obtained from transactions data and are available for NYSE stocks only. 10 The proportional effective and the proportional quoted spread increase and depth decreases with the Amihud illiquidity measure. For example, the proportional effective (quoted) spread increases from 0.21% (0.32%) for the most liquid stocks to 1.80% (2.77%) for the most illiquid stocks while the quoted depth decreases from 701 to 182 shares for SUE portfolio 10. To summarize, even after adjusting for the standard risk factors, the long-short portfolio returns are well in excess of 1% per month. However, these excess returns are obtained only in the highly illiquid stocks (Table 2). The fact that the PEAD strategy profits are confined to the most illiquid stocks suggests that these profits may not be easily realizable because it is precisely the illiquid stocks that have high transaction costs, high market-impact costs measured by bid-ask spreads, low trading volume, and 10 See Chordia, Roll and Subrahmanyam (2001) for details on this data. 7

9 low quoted depths (Table 3). 3.1 Does size proxy for illiquidity? Prior research has shown that the post-earnings-announcement drift is more prevalent in small firms. It is also the small firms that are typically the most illiquid. We, therefore, ascertain the marginal importance of liquidity by forming portfolios conditionally sorted on size and illiquidity. Since size and liquidity are correlated, it is important to sort conditionally rather than independently to ensure that all portfolios are well-populated. Table 4 presents the results on average monthly returns to these portfolios which are held for a six-month period. In Panel A, we first sort the sample firms into four size quartiles and then sort firms in each of the four size quartiles into quartiles based on illiquidity. Finally, we sort firms in each size and illiquidity group into quartiles based on SUE. Thus we have a total of 64 portfolios. Consider the smallest size quartile. As in Table 2, the returns of the smallest SUE portfolio decrease with illiquidity from 0.75% to 0.43% per month while those of the highest SUE portfolio increase with illiquidity from 1.85% to 2.01% per month. Also, the returns of the highest SUE stocks less the lowest SUE stocks increase with illiquidity from 1.11% to 1.58% per month. The earnings momentum effect is much smaller in the largest size quartile as compared to the smallest size quartile stocks. In the largest size quartile, returns increase with illiquidity for both the high and the low SUE portfolios. Also, the difference in returns of the high- and low-sue portfolios decreases with illiquidity. In Panel B of Table 4 we first sort stocks by illiquidity and then by firm size. Within each size portfolio we further sort on SUE. Across the high- and low-liquidity portfolios, except for the low-sue stocks that are illiquid, returns generally decrease with size. Also, the returns of the highest SUE stocks less the lowest SUE stocks decrease with firm size. More importantly, for our purposes, regardless of firm size, the returns are generally higher for the more illiquid stocks. Moreover, the returns of the highest SUE stocks less the lowest SUE stocks are also higher when illiquidity is higher. The highest return to a portfolio that is long the highest SUE stocks and short the lowest SUE stocks is obtained for the small illiquid stocks suggesting that both size and illiquidity are important determinants of the post-earnings-announcement drift. All these results suggest that illiquidity is an important determinant of earnings momentum. 8

10 3.1.1 Cross-sectional Tests In these tests, we confirm that illiquidity has an important impact on the post-earningsannouncement drift. We rely on cross-sectional asset-pricing tests with individual stocks rather than portfolios. Our asset-pricing tests extend the approach of Brennan, Chordia, and Subrahmanyam (1998), henceforth BCS. BCS test factor models by regressing riskadjusted returns on firm-level attributes such as size, book-to-market, and turnover. Under the null of exact pricing, such attributes should be statistically insignificant in the cross-section. This approach avoids the data-snooping biases, that are inherent in portfolio-based approaches (see Lo and MacKinlay (1990)), and the use of individual stocks as test assets is robust to the sensitivity of asset-pricing tests to the portfolio grouping procedure. We run the following cross-sectional Fama and MacBeth (1973) regressions of riskadjusted returns on firm characteristics: R jt R ft K ˆβ jk F kt = c 0t + k=1 M c mt Z mjt 2 + e jt, (3) where ˆβ jk is the beta estimated by a first-pass time-series regression of the firm s stock return on the Fama and French (1993) factors over the entire sample period with nonmissing returns data, 11 Z mjt is the value of characteristic m for security j at time t, and M is the total number of characteristics. We report the time-series averages of these coefficients, ĉ t. The standard errors of these estimators are obtained from the time series of monthly estimates and are corrected for errors-in-variables following Shanken (1992). The firm characteristics included are (i) Sz: Size, measured as the natural logarithm of the market value of equity, (ii) BtoM: Ratio of book value of equity to market value of equity calculated following the procedure in Fama and French (1992), (iii) DVol: Natural logarithm of the dollar volume of trading, (iv) Ret12: Cumulative return over the last twelve months, (v) SUE: Standardized unexpected earnings, measured as in Table 1, and (vi) Illiq: Amihud s illiquidity measure, computed based on the ratio of absolute returns to dollar volume. All the characteristics are lagged by two months relative to m=1 the month in which the dependent variable is measured. The results are presented in Table 5. The first regression essentially repeats earlier results in BCS and Avramov and Chordia (2005). Firm characteristics matter small 11 While this entails the use of future data in calculating the factor loadings, Fama and French (1992) have shown that this forward looking does not impact any of the results. 9

11 stocks, high book-to-market stocks, stocks with low dollar trading volume and stocks with high past twelve month returns all have higher risk-adjusted returns. The second regression shows that the coefficient on SUE is positive and highly significant suggesting that stocks with high earnings surprises have higher average returns. With SUE as one of the dependent variables the coefficient on the past twelve-month returns declines and becomes statistically insignificant at the 5% level (see Chordia and Shivakumar (2005)). Our innovation for the cross-sectional tests is the use of interaction terms. The third regression introduces an interaction term of firm size and SUE. The coefficient on the interaction term is significantly negative suggesting that small firms exhibit more earnings momentum than large firms. 12 The interaction term indicates that the impact of SUE and firm size on returns is ( Sz)SUE. Taking the partial derivative with respect to SUE, suggests that for firms larger than $4.5 billion (exp(0.185/0.022)) the impact of SUE on risk-adjusted returns is negative. For the very large firms, riskadjusted returns decrease with SUE. In the fourth regression we introduce an interaction term of SUE and the Amihud illiquidity measure. The coefficient on this interaction term is significantly positive suggesting that the impact of SUE on risk-adjusted returns is higher in more illiquid stocks. The fifth regression uses both interaction terms as dependent variables. The coefficient estimates on both interaction terms become statistically insignificant, possibly because firm size and illiquidity are (negatively) correlated. To assess the independent impact of illiquidity, we regress firm size on illiquidity and use the residual from this regression (denoted SzResid) along with illiquidity as an interaction term. The last regression in Table 5 shows that the coefficient on SzResid is insignificantly different from zero but the impact of illiquidity is still important. Overall, the post-earnings-announcement drift is prevalent mainly in illiquid firms. Firm size also has an impact on the drift but its effect could obtain because it proxies for illiquidity. 4 Transaction Costs The previous section shows that the potential profits on long-short SUE portfolio can be substantial. However, since most of these profits obtain amongst the illiquid stocks, 12 We also use an interaction term of stock price and SUE (see Bhushan (1994)). This coefficient is negative but statistically insignificant. 10

12 we suspect that transaction costs may render any trading strategy unprofitable. This suspicion is amplified when examining the effective spreads in Table 3. The proportional bid-ask spread of the highly illiquid stocks with the lowest (highest) SUE is 1.88% (1.80%). Thus, the total round-trip cost of the long-short position is 3.68%. The potential profit is 1.79% per month or 10.7% over six months. Thus, the bid-ask spreads account for about 33% of the potential profits of the post-earnings-announcement drift. However, this estimate does not take into account market impact costs, commissions or short sale costs. Therefore, the proportional spread of 3.68% may be an understatement and a more precise estimation of the trading costs is warranted. We now explicitly examine institutional transaction costs by conducting the analysis in a dynamic framework to replicate the real-time trading experience of an investor trying to exploit this anomaly. We use the institutional transaction cost estimates of Keim and Madhavan (1997) (henceforth KM), Korajczyk and Sadka (2004) (henceforth KS), and Chen, Stanzl, and Watanabe (2004) (henceforth CSW). Appendix A gives a short description of the features of these studies relevant to our analysis. 4.1 KM Estimates of Transaction Costs First, we present some back-of-the-envelope calculations. KM provide estimates of market impact as well as commission costs for buy and sell trades for NYSE-AMEX stocks (as well as NASDAQ stocks) traded by 21 large institutions during 1991 to Their transaction-cost data is categorized by trade size as well as firm size. We focus on the smallest trade sizes to minimize trading costs. We also use the various size classifications from Table 3. We focus on the most illiquid stocks because the potential profits are the highest for these portfolios. As reported in Table 2, the strategy of going long the high-sue stocks and short the low-sue stocks results in monthly returns of 1.79%. The stocks in this portfolio belong to the smallest size quintile. According to KM, the cost of a small buy trade for NYSE-AMEX stocks in the smallest size quintile is 0.39%, and the cost of a small sell trade is 0.75% for a total cost of 1.14%. The round-trip trading cost of 2.28% has to be compared to the paper profits of 10.7% over a six month period. The caveat with the above calculations is that the data in KM pertain to institutional trades during but the earnings momentum profits are calculated over the period While, the above costs includes commissions as well as market-impact costs, KM show that there is large variation in trading costs across institutions, invest- 11

13 ment styles, and trade difficulty. Trading costs are likely to be higher during the early part of the sample. Using revenues from broker and dealer firms to estimate trading costs, Stoll (1995) finds that costs have declined by over 40% over the period We, therefore, conduct a dynamic analysis of trading costs by using the methodology in Cooper, Gutierrez, and Marcum (2005). This methodology applies the trading-cost estimates from Stoll (1995) to the sample specific estimates of KM. To be conservative, we (i) estimate costs for value traders since they have the lowest trading costs, (ii) set the trade size to zero, and (iii) place a cap of 2.5% on the trading costs for each stock. The results are presented in Panel A of Table 6. Consider the portfolio which has the most illiquid stocks and the lowest SUE. From Table 2, the gross average monthly return of this portfolio is 0.25%. After adjusting for the Keim and Madhavan cost estimates of 0.63%, the net monthly return is -0.38%. Similarly, the most illiquid, high-sue portfolio has a gross average monthly return of 2.04% and with cost estimates of 0.59%, the net return is 1.45%. The raw returns for the high-sue minus the low-sue portfolio decline from 1.79% in Table 2 to 0.56% after adjusting for transaction costs of 1.22% (0.63%+0.59%). Transaction costs amount to about 67% of the potential profits. The potential profits, in Table 2, from the long-short SUE portfolios range from 0.24% to 1.79%. After accounting for transaction costs, the profits range from 0.21% to 0.56% per month. Thus, while the paper profits seem large, a large fraction of these profits are not realizable. Recall that we have been quite conservative in estimating these costs. The costs may actually be even further understated because (i) KM use data for trades that were actually consummated. If some trades were abandoned due to high transaction costs then the KM estimates of trading costs would be biased downwards, (ii) The transaction-cost estimates in KM do not include short-selling costs, and (iii) Since transaction costs have been estimated for a zero-trade size, the above analysis has abstracted from marketimpact costs. For any meaningful trade size there will be substantial market-impact costs. 4.2 KS Estimates of Market-Impact Costs KS use intraday transactions data to estimate market-impact costs. These costs are calculated each month for each stock over the period January 1993 through May Using cross-sectional relationships between these market-impact costs and firm characteristics, the costs are then estimated for the entire sample period. The estimated 12

14 market-impact costs are then used to compute the cost of establishing positions in the different illiquidity-sue portfolios each month. We present results for five million dollars of a long position and five million dollars of a short position each month. In 1972, five million dollars were equivalent to about $23 million in 2004 dollars. The reason we choose to present results for five million dollars is because ten (one) million created market impact costs that were too large (small). Panel B of Table 6 shows that upon adjusting for market-impact costs the strategy of going long the high-sue stocks and short the low-sue stocks results in net returns that are significantly lower than the gross returns. For the highest illiquidity portfolio, the net returns from a long-short strategy are 0.58% per month. For the second highest illiquidity portfolio, the corresponding returns, while positive, are only 0.37%. Thus, long and short position as small as five million dollars has enough market-impact costs to eliminate the potential profits from a strategy that exploits the post-earningsannouncement drift. Even KS costs may understate the true transaction costs because they do not account for commissions or short-sale costs. In Table 2 of their paper, KM show that commissions for institutional investors can be as high as 60% of the trading costs. Adding these commissions would eliminate profits on all of the long-short SUE portfolios in Table CSW Estimates of Market-Impact Costs CSW also use transactions data to estimate market-impact costs. However, they allow for a non-linear price-impact function. In their model, trading volume non-linearly impacts price changes as measured by the mid-point of the bid-ask quote. They provide parameter estimates of the model by size decile. We use these estimates to measure the market-impact costs for a five million dollar long and short position each month. The results in Panel C of Table 6 suggest that market-impact costs have a substantial impact on the net returns of the long-short SUE strategy. The average net returns are, once again, either negligible or negative. For the most illiquid stocks, the net return is 0.20% per month. The highest net return is an economically insignificant 0.17% per month. Once again, the market-impact-cost measures of CSW may actually understate the total trading costs because they do not account for commissions and for short-selling costs. 13

15 4.4 Subsample Analysis Trading costs have declined over time. Chordia, Roll, and Subrahmanyam (2001) document a steady decrease in bid-ask spreads over time. In this subsection, we, therefore, explore the profitability of long-short SUE portfolios over time. We split our sample into two periods: and Table 7 presents the results for the longshort portfolios. Costs have indeed declined substantially over the two subperiods. For instance, during , the KM trading costs for a long-short position range from 0.05% per month for the liquid stocks to 1.75% per month for the most illiquid stocks. During , the KM trading costs are lower and they range from 0.01% for the liquid stocks to 0.74% per month for the most illiquid stocks. A similar pattern exists for the KS and CSW estimates of the market-impact costs. For the most illiquid stocks, the KS (CSW) estimates of costs declined from 3.47% (2.68%) during to 1.72% (1.36%) during While the costs have declined over time, the potential profitability of the postearnings-announcement drift has also declined over time. During , the gross returns ranged from 0.30% for the liquid stocks to 1.84% for the most illiquid stocks. During , the corresponding returns ranged from 0.18% to 1.74% per month. The risk-adjusted returns have also declined over time. For the most illiquid stocks, the alpha from the Fama-French model has declined from 2.05% per month during to 1.74% per month during After controlling for transaction costs the net profitability is actually higher during the latter half of the sample period. For the most illiquid stocks, the net returns, after adjusting for KM transaction costs, are 0.09% per month during and 1.01% per month during The net return after adjusting for KS estimates of trading costs are 1.62% per month during the first half of the sample and 0.02% per month during the second half of the sample. Finally, the net return after adjusting for CSW estimates of trading costs is 0.84% per month during the first half of the sample and 0.38% per month during the second half of the sample. The overall conclusion is that while the potential returns from the long-short strategy have declined over time, trading costs have declined even more. Thus, the potential profits from the long-short strategy are higher during the second half of the sample. Even so, after adjusting for transaction costs including market-impact costs, the potential profits are not realizable. Figure 1 presents five-year moving averages of the gross returns from the long-short 14

16 strategy for the most illiquid stocks as well as the transaction costs obtained using the analysis of (i) KM, (ii) KS for a five million dollar long and short position, and (iii) CSW also for a five million dollar long and short position. The potential profits as measured by gross returns are quite variable. These profits were high in the early 1990s and also in the period The KS transaction costs are estimated using transactions data over the period and have been estimated out of sample, from and , by using a cross-sectional relation between the costs and firm characteristics. Since firm characteristics are quite variable, the KS estimates of transaction costs are also quite variable. The KM and CSW estimates of costs are not as variable because we only have these estimates for different size groups over a short time interval. By design, all the cost estimates decrease over time in line with the pattern observed by Stoll (1995). The transaction-cost estimates obtained on the basis of CSW are consistently lower than those obtained using KS, even though both methods capture market-impact costs. The reason for this is that we have cost estimates for each individual stock from KS but only the estimates for size deciles from CSW. Within the smallest size decile, the average cost estimate of CSW is likely to understate the actual trading costs. The KS estimates of transaction costs are likely to be more accurate because these estimates are available at the individual stock level. Focusing on the KS estimates of transaction costs we see that the potential profits, from a long-short position in high-sue stocks and low-sue stocks respectively, are lower than the cost estimates for almost the entire period. The only exceptions are the periods and During the period , the potential profits are higher than the costs but only marginally so. The potential profits are as much as a hundred basis points higher than the costs for the period However, at the end of 2004, the difference between the potential profits and transaction costs is only 20 basis points. The high realizable profits in are likely to disappear if commission costs and short-sale costs are accounted for and as the size of the long and short position increases above five million. 4.5 Summary of Transaction Costs This paper analyzes trading costs from a number of different perspectives, including proportional effective bid-ask spreads, dynamic institutional trading costs, and the marketimpact costs. Consider the most illiquid stocks. The proportional effective bid-ask- 15

17 spread cost for the long-short portfolio calculated over the sample period 1988 through 2002 is 3.68%. The dynamic cost analysis of institutional trading costs using KM data suggests that transaction costs including commissions (but excluding market-impact costs) are 1.21%. The market-impact costs (not including commission costs) using the KS methodology amount to 2.37% for a long and short position of five million dollars. Finally, the market-impact costs using the CSW estimates (not including commission costs) amounts to 1.99%. The market impact costs are instrumental in eliminating the potential profits from a long-short strategy that exploits the post-earnings-announcement drift. The overall conclusion is that most of the paper profits disappear upon accounting for trading costs. The transaction costs account for 66% to 100% of the potential profits from the earnings-momentum strategy. The main reason is that the largest potential profits are obtained for the highly illiquid stocks that have high trading costs. Bernard and Thomas (1989) also examine transaction costs as an explanation for earnings momentum. Using rough cost estimates from Stoll and Whaley (1983) with a 78% turnover in portfolio content each quarter, they find that the transactions costs including bid-ask spreads and commissions are approximately equal to the 60 day abnormal returns. In this paper, we conduct a more comprehensive analysis that examines three different cost estimates that include market impact costs computed at the individual stock level using transactions data. Bernard and Thomas (1989) perform yet another test to assess the impact of transactions costs. The idea is that prices would adjust to the transactions cost threshold and no further. The hypothesis to be tested is that, if the drift is caused by costs that impede trading, the post-earnings-announcement-drift should remain less than these costs regardless of the SUE differences between extreme portfolios. If the transactions cost threshold is x% then prices would adjust until it reaches this threshold. Thus, regardless of how finely the portfolios are sampled (quartiles, quintiles, deciles and so on) the earnings momentum profits would not exceed x%. This is precisely what Bernard and Thomas find. They find an upper bound to the drift regardless of the SUE differences between the portfolios. This result is consistent with a transactions cost based story. However, Bernard and Thomas (1989) raise some interesting questions for transactions based explanation. A large fraction of the earnings momentum return obtains around the next two earnings announcement. Why is so much of the drift concentrated around the next quarter s earnings announcement? Also, why do market makers not move the price to the correct level after the subsequent earnings announcements? These are the questions that we turn to next. 16

18 5 Earnings Announcements Prior literature has shown that a large fraction of the post-earnings-announcement drift occurs at the subsequent earnings announcements. For instance, Chan, Jegadeesh, and Lakonishok (1996) document that of the 6.8% return to the long-short portfolio over the six-month formation period, 3.2% is obtained around the earnings-announcement dates over the same six-month formation period. In other words, 47% of the drift is realized around the subsequent earnings-announcement dates. The returns around earnings announcement date t are measured over a three-day period from t 2 to t + 1. Since trading volume is usually higher around earnings announcement days than other days, it might be the case that liquidity is higher and transaction costs are lower. With lower transaction costs it is possible that the long-short portfolio strategy becomes profitable around earnings announcement days. In this section, we examine liquidity around the subsequent earnings-announcement dates after the formation of the SUE portfolios. More specifically, we examine the average bid-ask spreads and quoted depths for the highest and lowest SUE deciles of NYSE stocks around earnings announcement dates from t 2 to t + 1, over the period Our benchmark daily liquidity measures for non earnings announcement days are computed relative over t 10 to t 6 and t + 6 to t Table 8 reports the difference between the daily average liquidity measures around earnings announcements (t 2 to t + 1) and the daily average over periods outside the earnings-announcement period (t 10 to t 6 and t + 6 to t + 10). The results are grouped by illiquidity and are the average of low and high SUE for each illiquidity rank. Trading volume increases around earnings announcements for all stocks regardless of the level of illiquidity. For the most liquid stocks, the daily trading volume increases by an average of 368,738 shares but for the most illiquid stocks the increase is only 2,305 shares. The result for the quoted depth is mixed. It increases for some of the illiquidity deciles and decreases for others. The overall daily change in depth is a decrease of about 180 shares. For the most illiquid stocks, depth increases by a negligible 19 shares. The proportional quoted spread increases for all stocks except for the most illiquid stocks where it decreases by 0.034%. The proportional effective spread, which arguably is a more reliable measure of actual trading costs, increases across all stocks. For the most illiquid stocks, the proportional effective spread increases by 0.024% over the three day period t 2 to t + 1. This is consistent with Lee, Mucklow and Ready (2003) who also find that spreads increase around earnings announcements. 17

19 In sum, the transaction costs are unlikely to be lower around earnings announcements. Moreover, while only 47% of the earnings momentum returns obtain around the subsequent earnings announcement days the transactions costs are not lower. In fact, since we are examining the subsequent two earnings announcements, the transactions costs will have to be incurred twice. In other words, net of transactions costs, trading around earnings announcements will be unprofitable because while the costs have not decreased the post-earnings-announcement-drift payoffs over a short period around earnings announcement are lower than our earlier estimates over a six month holding period. The preceding analysis, therefore, raises the question: Why does a large fraction of the price adjustment occur around the subsequent earnings announcements after the SUE portfolios have been formed? We argue that prices adjust because of the information provided by the new earnings surprise around the subsequent announcements. In other words, specialists or other market makers adjust prices and quotes - prices do not move due to informed or arbitrage trading. To see this we examine the order imbalances and trade sizes around the next earnings announcements. Extreme order imbalances or large trade sizes around earnings announcements are likely to come from informed traders who are trying to exploit the earnings momentum phenomenon. Daily order imbalances are defined as buys minus sells during the day as a fraction of the total trades. The total trades, buys and sells are measured in both the number of trades and shares. The average trade size for a given stock, on a given day is calculated as the total number of shares bought or sold divided by the total number of buy or sell trades. Table 8 presents the average order imbalances and trade sizes for the highest and lowest SUE stocks around the subsequent earnings announcement dates. As before, the order imbalances and trade sizes are computed over t 2 to t + 1 relative to the same measures over the period t 10 to t 6 and t + 6 to t Focusing on the most illiquid stocks we find that buy trade size increased by an average of 85 shares and sell trade size by 51 shares over the three days around the subsequent earnings announcement relative to the weekly period before and after the earnings announcement. Since we expect informed traders to trade large sizes and because the trade size changes so little, it is unlikely that trades around earnings announcements come from traders attempting to exploit the drift. For the least liquid stocks, the order imbalance increases by 6.4% when measured in terms of number of trades and by 4.6% when measured in terms of shares traded. Not reported in the table, we find that for the highest SUE stocks, the average order 18