Industries and Stock Return Reversals - EFA2012

Industries and Stock Return Reversals Allaudeen Hameed1 Department of Finance NUS Business School National University of Singapore E-mail: [email protected] G. Mujtaba Mian School of Accounting and Finance Hong Kong Polytechnic University Hong Kong E-mail: [email protected] Tel: (852) 6903 6215 Fax: (852) 2330 9845 This Draft: June 25, 2012

ABSTRACT This paper documents pervasive evidence of short-term intra-industry return reversals. Unlike a reversal strategy applied to all stocks, the intra-industry reversals are stronger in magnitude, persistent in time, robust to adjustments to market microstructure biases and common risk factors, and pervasive across stocks, including large, liquid and low volatility stocks. Our analyses suggest that the reversals are not due to overreaction to firm-specific information shocks or delayed reaction to industry information, and are more likely due to non-information shocks. Additionally, we show that the intra-industry reversals are linked to compensation for providing liquidity, and are stronger during volatile periods and for stocks that experience greater liquidity demand.

Keywords: Return reversals, Industry effects, Liquidity, Contrarian strategies, Industry momentum. JEL Classification: D14, D21, G24

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We would like to thank Tarun Chordia, Jennifer Conrad, Ro Guitierrez, Kewei Hou, Charles Lee, Ravi Jaganathan and Sheridan Titman and participants at Citi Quantitative Research Conference, Financial Integrity Research Network Forum, China International Conference in Finance, as well as seminar participants at City University of Hong Kong, University of New South Wales, University of Queensland, University of Sydney, University of Technology Sydney, and University of Texas at Austin for helpful comments. We especially thank Joshua Huang for contributing significantly to an earlier draft of the paper and Si Cheng for excellent research assistance. All remaining errors are ours.

I. Introduction The presence of short-term reversals in stock returns is well documented. Jegadeesh (1990) and Lehmann (1990) show that a contrarian strategy of buying stocks that underperformed the market (losers) and shorting stocks that outperformed the market (winners) yields economically significant returns. One plausible explanation for short term reversals is that these are related to compensation for providing liquidity. Campbell, Grossman and Wang (1993) present a model in which risk-averse market makers step in to address imbalances in the demand and supply for the security arising from liquidity shocks. If there is excess selling of a stock due to an exogenous shock, liquidity providers would step in to absorb the excess supply, but would do so only at a lower price and in expectation of a positive return. The subsequent reversal in the stock price, hence, reflects the premium required by liquidity providers. Conrad, Hameed and Niden (1994), and Llorente, Michaely, Saar and Wang (2002) provide supportive evidence that reversals are stronger for stocks that experience a large increase in volume, representing pressure emanating from liquidity shocks. Avramov, Chordia and Goyal (2006), however, argue that while return reversals are related to liquidity shocks, they are confined to a subset of illiquid stocks. An alternate view of short-term reversal is that it represents overreaction in stock prices to firm-specific information shocks stemming from behavioral biases (Lehmann (1990), Cooper (1999) and Subrahmanyam (2005)). Subrahmanyam (2005), for example, suggests that monthly return reversals are affected by reversion in investor beliefs. Conrad, Kaul and Nimalendran (1991), Conrad, Gultekin and Kaul (1997) and Jegadeesh and Titman (1995a), on the other hand, argue that short term reversals are plagued by market-microstructure related frictions such as the bid-ask bounce. As the debate on the existence and the sources of return reversals remains unresolved, a better understanding is of profound relevance for optimal portfolio investments. In this paper, we argue for benchmarking stock returns with the returns on peer firms in the industry to better identify short-term return reversals. First, we show that the traditional contrarian investment strategy can be analytically decomposed into two components. The first component is the within industry return reversals, where loser and winner stocks are defined 2

based on their performance relative to their industry portfolio. The second component is the inter-industry reversals which involve buying (selling) the industry portfolio that has underperformed (outperformed) the market portfolio. Given the evidence of inter-industry momentum in stock returns in Moskowitz and Grinblatt (1999), the traditional contrarian strategy is likely to underestimate reversals in stock returns. An intra-industry reversal strategy, on the other hand, isolates short-term reversals from across-industry momentum. Second, the decomposition of contrarian profits in Lo and MacKinlay (1990) shows that cross-sectional variation in expected returns in the contrarian portfolio significantly reduces the profits from a reversal strategy. Roll (1992) provides evidence that a large proportion of an individual stock’s return is explained by industry membership. Returns on stocks in the same industry are highly contemporaneously correlated as they are similarly affected by common shocks arising from shifts in demand and supply for their products and services, as well as from technological, regulatory and other macroeconomic changes. If return reversals represent deviations from fundamental values and subsequent convergence, as suggested by the alternate explanations, matching firms with similar fundamentals (or industries) provides a more natural framework to identify short-term reversals. Finally, an intra-industry contrarian strategy is also consistent with widespread market practice for fund managers to control risk by implementing their long-short strategies so that they are market as well as sector (industry) neutral. For example, “pairs trading” typically identifies pairs of stocks that experience temporary deviation in prices but have returns that are highly correlated, such as firms belonging to the same industry. The intraindustry reversal strategy may be viewed as the portfolio level equivalent of pairs trading, and therefore, provides a sharper focus on short-term reversals related to temporary deviations in stock prices. Consistent with this assertion, we find that the within industry reversal strategy of buying (selling) stocks that underperformed (outperformed) their industry benchmark in the previous month yields an economically significant equal-weighted (value-weighted), risk-adjusted return of 1.00 percent (0.54 percent) per month over the 1968-2010 period. The risk-adjusted return from the equal-weighted, unconditional (i.e. conventional) contrarian investment strategy is significantly lower at 0.69 percent, and the corresponding value-weighted return is insignificant

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at 0.22 percent.2 We also find strong intra-industry reversals of 1.72 percent per month (or 1.16 percent in value-weighted strategies) in stocks with non-extreme returns that are typically excluded or under-weighted in the unconditional contrarian strategies. The latter finding suggests that the intra-industry reversal strategy generates stronger returns partly by selecting pairs of similar stocks whose prices experience temporary divergence. Unlike the unconditional reversals, the intra-industry reversals survive a battery of robustness checks and are pervasive across time and sub-groups of stocks. Kaul and Nimalendran (1990) and Conrad, Gultekin and Kaul (1997) argue that short-term (weekly) reversals are dominated by reversals due to the bid-ask bounce. Similar to Jegadeesh (1990), we skip a day between the formation and holding months to account for any bid-ask effects and find that our intra-industry reversal profits remain significant. Avramov, Chordia and Goyal (2006) show that the unconditional return reversal is confined to illiquid stocks. While we find that reversals are clearly stronger in stocks that are exposed to greater market frictions and arbitrage costs, we obtain significant intra-industry reversals even among stocks that are large in market capitalization; have large institutional ownership; are liquid and have high turnover; and have low idiosyncratic volatility. The intra-industry reversals are also present in all sub-periods, including the recent decades which have recorded declines in transaction costs arising from changes in minimum tick size arrangements and increased turnover. In contrast, the profit from the unconditional reversal strategy is more fragile and does not survive these robustness tests. Our evidence of intra-industry reversals provides a fresh setting to reexamine the economic sources of the reversals. If return reversals are related to compensation for providing liquidity, collateral-based models in Garleanu and Pedersen (2007), Brunnermeier and Pedersen (2009), and others suggest that increases in market volatility also increases the expected return to supplying liquidity.3 In Brunnermeier and Pedersen (2009), for example, the market making sector faces capital constraints and obtain funding by pledging the securities they hold as collateral and posting margins. Declines in aggregate market valuations and increases in 2

In our empirical decomposition of unconditional contrarian profits, we find negative across-industry reversals of 1.0 percent per month, similar to the findings in Moskowitz and Grinblatt (1999). Our results are also consistent with a contemporaneous paper by Da, Liu and Schaumburg (2011), who report short-term return reversals within industries and momentum across industries. 3 Kyle and Xiong (2001), Vayanos (2004), Adrian and Shin (2010) and several others also develop theoretical models of time-variation in market illiquidity.

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volatility of asset prices lower the value of the securities pledged and increases the margin requirements (i.e. bigger haircuts), which in turn makes financially constrained liquidity providers less willing to make markets in volatile periods. Garleanu and Pedersen (2007) show that standard ‘value-at-risk’ risk management models used by financial intermediaries imply a tightening of their risk bearing capacity following an increase in asset volatility. Vayanos (2004) suggests that if transactions costs are higher during volatile times, return volatility would have a negative impact on liquidity. Hameed, Kang, and Viswanathan (2010) and Nagel (2011) use the conventional contrarian investment strategy to provide empirical evidence of higher returns to supplying liquidity during periods of market stress. Consistent with the predictions in these models, we find that intra-industry reversals are larger during volatile periods. We find a strong positive relation between the intra-industry reversals and implied market volatility (measured by VIX index of implied volatilities of S&P 500 index options). Additionally, when we decompose VIX into conditional realized volatility and volatility risk premium, the predictive effect on return reversals comes mostly from the realized volatility component. We also find a significant positive effect of conditional industry volatility on intra-industry reversals, suggesting that distress within industries also affects funding liquidity. These results are unaffected when we control for variations in aggregate liquidity levels due to decimalization, the effect of market declines in Hameed, Kang and Viswanathan (2010) or when we adjust for exposures to common risk factors. The evidence points to higher premium associated with liquidity provision when the market as well as industry returns are more volatile. We also explore the notion that the liquidity based explanation for intra-industry reversals necessarily involves a predictive relation between order flows and subsequent reversals. The return reversal predicted in Campbell, Grossman and Wang (1993), and others, represents a premium required by liquidity providers to absorb imbalances in the order flow emanating from liquidity demanders. We test the prediction that the liquidity provision ought to be more costly for stocks with a greater imbalance in the buy and sell order flows as these stocks have a bigger impact on the market makers’ inventory risks (see Chordia, Roll and Subrahmanyam (2001, 2005) for supportive evidence at daily and intra-day frequency). In particular, loser stocks with more sell than buy orders imply greater liquidity demand. Similarly, stronger reversals are 5

expected for winner stocks with greater buy orders. When we condition the loser and winner securities on the imbalance in their order flow during the previous month, we obtain stronger reversals. For the 1993-2008 NYSE sample, the risk-adjusted return on the intra-industry, equalweighted (value-weighted), reversal strategy of buying past losers with larger sell orders and selling past winners with greater buy orders is economically significant at 0.96 (0.61) percent per month. On the other hand, we do not find evidence of reversals among the within industry loser and winner stocks that do not experience similar price pressure, measured by imbalances in their order flows. Hence, the evidence suggests that short-term reversals are driven by variations in demand and supply of liquidity. We also examine if intra-industry reversals are related to overreaction in stock prices to firm-specific information shocks. We hypothesize that if overreaction to firm-specific information explains return reversals, we should see greater reversals following periods of more firm-specific news. Specifically, we examine the effect of earnings information on return reversals. After controlling for the drift in stock prices associated with the announcement of company’s quarterly earnings (Bernard and Thomas (1989)), we find that intra-industry loser (winner) stocks revert less after an earnings announcement, particularly after a negative (positive) earnings news. Our results suggest significantly lower, not higher, intra-industry reversals following the announcement of earnings news. Finally, we test if delayed reaction in stock prices to common (industry) information posited in Lo and MacKinlay (1990) is driving our findings. In particular, we investigate if losers and winners in the intra-industry reversal strategy react to lagged industry returns. Although stocks, on average, exhibit significant reaction to lagged returns on the industry portfolio (Hou (2007)), the intra-industry reversals do not vary with lagged industry returns. We, therefore, find insufficient evidence to conclude that reversals are related to identifiable information, whether industry-related or firm-specific. This implies that short-term reversals are likely to stem from non-informational shocks, again suggesting a link between reversals and returns to providing liquidity. The rest of the paper is organized as follows. Section 2 shows the decomposition of the unconditional contrarian strategy into intra-industry and inter-industry reversal strategies. Section 3 describes the data and methodology while Section 4 presents our main findings on

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short-term return predictability. Section 5 explores the sources of the intra-industry reversals. We provide our concluding remarks in Section 6.

2. Unconditional and Intra-Industry Return Reversals In this section, we show the link between unconditional return reversals and intraindustry reversals by using the contrarian portfolio strategy employed in Lo and MacKinlay (1990). Following Lo and MacKinlay (1990), the portfolio weight assigned to security j at time t, wjt, is based on the past return of the security j (Rjt-1) relative to the returns on the market portfolio (Rmt-1): wjt = -(1/N) (Rjt-1 – Rmt-1), ∑

where

(1) and N is the number of securities in the market. The weights of the

unconditional reversal strategy imply buying the past loser securities and selling short the past winner securities. The profit for the zero-investment unconditional reversal strategy at time t, Pt, is given by: ∑

or ∑

.

(2)

To illustrate the effect of industry groupings, we subtract and add the return on the portfolio of stocks in industry I (RIt-1), where

⁄

∑

, NI is the number of

securities in industry I and I=1,…,L. ∑

(3)

Equation (3) can be rewritten as: ∑

∑

(4) 7

The first term in (4) represents the intra-industry reversal returns at time t, averaged across all securities in the market. It should be noted that the profits from the intra-industry reversal strategy is market and industry neutral as the portfolio weights on both long and short sides are distributed across all industries, consistent with common market practice to hedge market and sector exposures. The second term depicts the returns to a strategy of buying (selling) the portfolio of stocks in industry I if the industry underperformed (outperformed) the market portfolio. This is equivalent to implementing an across-industry reversal strategy of buying losing industry portfolios and selling winning industry portfolios. Hence, the unconditional reversal profits can be decomposed into two parts: profits from an intra-industry reversal strategy and the profits to an inter-industry reversal strategy. However, the evidence in Moskowitz and Grinblatt (1999) suggests that there is significant inter-industry momentum in monthly returns, where industries that performed well in the past month seem to continue to perform well in the following month. This implies that the unconditional reversal strategy is negatively affected by inter-industry momentum, and would understate the extent of short-term return reversals. Hence, forming portfolios at the industry level enables us to separate short term reversals from short-term industry momentum in stock returns.

3. Data and Methodology Our primary data consist of common stocks traded on the NYSE, AMEX and NASDAQ stock exchanges. Information on the common stocks, which have share codes 10 and 11, is obtained from the Center for Research on Security Prices (CRSP) database. To classify stocks into industries, we employ the widely used Fama and French (1997) system of classifying companies into 17 industry groups based on four-digit SIC codes. We also consider the FamaFrench 48 industry grouping to check for robustness of our results. The sample is obtained for the time period from January 1968 to December 2010.4

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Our start date for our main sample period is based on the availability of the Pastor-Stambaugh (2003) liquidity factor in CRSP. We obtain similar results if we extend the sample to earlier years.

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Table 1 provides the summary statistics of the monthly returns for the stocks in our sample in each of the 17 industry groups. We exclude stocks with a month-end price of below $5 to mitigate market microstructure effects associated with low priced stocks. The average number of stocks in an industry varies from 39 stocks in Mining to 808 (884) stocks in Financials (Other). Industry portfolio returns exhibit positive autocorrelations, ranging from 0.08 (Utilities) to 0.28 (Textiles and Apparel). The individual stock returns within each industry are more volatile, and autocorrelations are smaller and generally negative, averaging between 0.0 and 0.14. These return characteristics are consistent with those reported for earlier sample periods (see Lo and MacKinlay (1990), Boudoukh, Richardson and Whitelaw (1994), Moskowitz and Grinblatt (1999) and others). {Insert Table 1 here.} We start our analyses by computing returns from an unconditional zero-investment (longshort) contrarian strategy. At the end of each month t, we identify the top (winner) and bottom (loser) 30 percent of stocks based on their returns in month t. The contrarian strategy involves buying the loser stocks and selling the winner stocks. The monthly return from the loser minus winner portfolios in month t+1 produces our measure of monthly reversals. Besides reporting the equal- and value-weighted raw monthly returns, we also report the risk-adjusted returns, where raw monthly returns are regressed on several pre-specified common factors. We consider three factor-model specifications. First, we use the excess return on the value-weighted CRSP market index over the one-month T-bill return as the sole factor for the CAPM risk adjustment. In the second model, we add the small minus big return premium (SMB) and the high book-to-market minus low book-to-market return premium (HML) for the Fama-French risk adjustments.5 In the final model, we add the liquidity factor introduced in Pastor and Stambaugh (2003) as the fourth factor to arrive at the four-factor risk-adjusted returns.6 To obtain intra-industry reversal returns, the contrarian strategy is conditioned on industry membership. Specifically, we identify the winner and loser stocks within each industry 5

We thank Ken French for making available the time-series data for the Fama-French three factor model. These factors are described in Fama and French (1993). 6 The liquidity factor returns are also obtained from WRDS. For details on the construction of the liquidity factor, please refer to Pastor and Stambaugh (2003). We also obtain similar results when we use the liquidity measures in Sadka (2006) (available in WRDS); details are available from the authors upon request.

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as the top and bottom 30 percent of the stocks based on their returns in month t. We compute the equal-weighted and value-weighted returns of the loser and winner portfolios within each of the 17 industry groups for month t+1. The zero-investment intra-industry contrarian return is represented by the cross-sectional average of the within-industry contrarian returns and is industry-neutral since the strategy is invested in the long and short side within each industry.

4. Reversal Strategies and Industry Membership 4.1 Profitability of Intra-industry Reversal Strategies The presence of short-horizon reversals in equity prices is well documented in the literature. Panel A1 of Table 2 reports the equal-weighted raw and risk-adjusted monthly returns for the loser, winner, and loser minus winner portfolios for the unconditional reversals. Consistent with the prior work, we find significant unconditional contrarian raw (four-factor risk-adjusted) returns of 0.82 (0.69) percent per month for our extended sample that includes the recent years. The risk-adjusted returns show that most of the contrarian profits come from the loser stocks outperforming the benchmark portfolios in the holding period. {Insert Table 2 here.} In Panel A2 of Table 2, we obtain substantially higher returns for the intra-industry reversal strategy. The raw (risk-adjusted) return on the loser minus winner portfolio based on within industry reversals is 1.12 percent (1.00) percent per month. As shown in Panel A3, the additional return of 0.3 percent per month from the intra-industry sorting is highly significant and is unaffected by adjustment for common risk factors. We plot the 12-month moving average of the monthly returns from the loser minus winner portfolios of the unconditional as well as the intra-industry strategy in Figure 1. These plots show that the profitability of the reversal strategies is not concentrated in any specific subperiods and appears to be related to periods of liquidity crisis. For example, the spikes in the reversal returns appear to coincide with episodes of illiquidity such as the oil crisis in November 1973, the stock market crash of October 1987, the LTCM crisis in 1998, the terrorist attacks of September 11, 2001 and the global financial crisis in 2008. In addition, the returns to the intra10

industry reversal strategy also appear to be less volatile and more reliably positive. The additional return from the industry sorting mechanism is, thus, more likely to be related to crosssectional differences rather than inter-temporal variation in the return reversals. {Insert Figure 1 here.} To verify if the intra-industry reversals are pervasive, we report the contrarian returns in each of the 17 industries. As shown in Figure 2, we find significant evidence of return reversals in every industry. The largest reversals are observed in the Fabricated Products industry, where the average reversal return is 1.42 percent per month. The smallest average reversal returns of 0.78 percent occur in the Mining industry. The significant contrarian returns within each industry contribute to a strong and consistent overall intra-industry reversal. {Insert Figure 2 here.} Fama (1998) and Fama and French (2008) show that the equal-weighted long-short portfolios have a potential problem of being dominated by microcaps (stocks with market capitalization below the 20th NYSE percentile). Consistent with this concern, we find that the unconditional reversals become insignificant when the hedge portfolios are value-weighted (see Panel B1, Table 2). This implies that the unconditional reversals are dependent on reversals among the smaller firms. More importantly, we continue to find significant value-weighted intraindustry reversal returns. The portfolio of buying within industry losers and selling within industry winners generates a significant return of 0.68 percent per month in Panel B2 of Table 2. These hedge returns are robust to adjustment for the common risk factors, and the profits come from both the loser and winner portfolios. 4.2 Empirical Decomposition of the Unconditional Contrarian Profits The intra-industry reversal strategy is designed to select pairs of stocks that are more likely to revert to similar fundamental values after an initial, non-informational return shock. On the other hand, it is also possible that the intra-industry strategy places greater weight on highly volatile stocks with extreme formation period returns. Moreover, removal of the inter-industry momentum effects of Moskowitz and Grinblatt (1999) may have strengthened the reversal returns we find. To shed light on these sources of reversal profits, we decompose the 11

unconditional reversal strategy by independently sorting stocks based on their returns relative to the industry as well as market portfolios. We sort stocks based on their past monthly returns relative to all other stocks in the market and classify the top and bottom 30 percent of stocks into market winners and market losers respectively. The middle 40 percent of stocks are labeled as market neutral stocks. In a similar way, we sort stocks based on past monthly returns within each of the 17 industries and classify the stocks into industry winners and industry losers if they are in the top and bottom 30 percent. The remaining 40 percent of the stocks are grouped as industry neutral stocks. The two-way independent sorting of stocks relative to market and industry portfolios gives us a total of nine portfolios based on the intersection of the sorted stocks along the two dimensions.7 This sorting scheme is used to build three non-overlapping reversal portfolios in Table 3. {Insert Table 3 here.} Table 3 reports the formation period and holding period returns (both equal-weighted and value-weighted) for the nine groups of stocks. We also report the four-factor risk-adjusted returns along with the number of securities in each portfolio. As expected, there is a large overlap in the classification of stocks under the two sorting methods—about 82 percent to 89 percent of the stocks that are classified as market winner, market neutral or market losers are also labeled in the same corresponding group based on industry sorts. The high degree of overlap between the two classification schemes raises the possibility that the unconditional (market) sorting produces reversals simply because it is capturing within industry reversals.

To understand the decomposition better, we direct our attention to the groups of stocks that are classified differently under the two strategies and find some striking observations. The unconditional reversal portfolio is constructed from buying market losers and shorting market winners. Among these stocks, the industry neutral stocks are those with returns that mimic the industry portfolio. Hence, the stocks which are market losers (winners) but are industry neutral represent industry portfolios that have underperformed (outperformed) the market portfolio. A strategy of buying market losers and selling market winners among these industry neutral stocks is closely related to an inter-industry reversal strategy in Section 2. As shown in Table 3, the

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Identifying winners and losers based on quintiles instead of top and bottom 30 percent produces similar findings.

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(equal-weighted) inter-industry reversal strategy generates significant negative risk-adjusted return of -1.0 percent per month, reflecting momentum in industry returns (Moskowitz and Grinblatt (1999)). However, the returns on this strategy become insignificant when we valueweight the portfolio, suggesting that the monthly industry momentum effect relies heavily on the small cap stocks. It should be noted that the intra-industry reversal strategy excludes these industry neutral stocks. In contrast, Table 3 reveals that stocks that are identified as industry winners and losers, but are market neutral, exhibit the strongest reversals. The equal-weighted intra-industry reversal strategy applied to these market neutral stocks yields a large 1.78 percent per month. The valueweighted, risk-adjusted returns are also large and significant at 1.16 percent per month, with significant contributions from both loser and winner portfolios. By construction, these stocks have less extreme formation period returns and hence are typically excluded (or under weighted) in the unconditional reversal strategies.8 For completeness, we also report the returns to the extreme returns reversal strategy (buying market and industry losers and selling market and industry winners). Here, the reversals are stronger in the loser portfolios than the winner portfolios. For example, the equal-weighted risk-adjusted return for the loser portfolio is 0.97 percent while the return is insignificant for the winner portfolio. Overall, the evidence in Table 3 highlights two sources for the higher intra-industry reversals compared to the unconditional reversals. First, the intra-industry strategy excludes the short-term industry momentum effect in Moskowitz and Grinblatt (1999), consistent with our decomposition shown in Equation (4). Second, a large portion of the intra-industry reversals come from the “non-extreme return reversal” strategy. In other words, stocks that have under or over performed their industry peers are more likely to reverse in the following period compared to stocks that simply experience extreme returns. The latter finding is consistent with short-term intra-industry reversals coming from selection of fundamentally correlated stocks that have experienced non-fundamental shocks in the formation period, rather than from overreaction in stock prices. We investigate this interpretation in detail in Section 5. 4.3 Robustness Checks 8

We place less attention on the stocks which are market winners (losers) but are industry losers (winners) due to the small number of stocks in these categories.

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4.3.1

January seasonality It is well documented that there are strong return reversals in the month of January and

several papers argue that this turn-of-the-year effect is due to tax-loss selling (see Grinblatt and Moskowitz (2004), George and Hwang (2004) and others). We separately examine the returns from the unconditional and intra-industry strategies in January and the remaining months of February to December. Consistent with the presence of a strong January seasonal, Table 4 shows that both the unconditional and intra-industry strategies yield large risk-adjusted returns of 2.2 and 2.5 per cent, respectively, during the month of January. More importantly, though, we find that the intra-industry strategy continues to produce economically significant returns in the nonJanuary months. {Insert Table 4 here.} 4.3.2 Do microstructure effects explain intra-industry reversals? Several researchers, including Kaul and Nimalendran (1990), Lo and MacKinlay (1990), Boudoukh, Richardson and Whitelaw (1994) and Jegadeesh and Titman (1995a), have pointed out that short-term return reversals are plagued by microstructure biases such as the bid-ask bounce. To address this possibility, we examine the effect of skipping one day between the portfolio formation period and the holding period, similar to Jegadeesh (1990). Specifically, we rank stocks based on their month t returns and examine the contrarian returns during month t+1 with a one-day delay (i.e. we exclude the first trading day in month t+1). This approach purges the negative autocorrelation in contiguous returns induced by the bid-ask bounce.9 The return reversals reported in Table 4 after skipping a trading day show a reduction in the abnormal returns from both the unconditional and intra-industry reversal strategies. In particular, the unconditional reversals decline from 0.82 percent per month to 0.34 percent. Moreover, this profit figure goes down further, and becomes statistically insignificant, after adjusting for common risk factors. This confirms the previous conclusion in the literature that the

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We obtain similar results when we skip the last trading day in month t or skip two days between formation and holding periods. While helpful in eliminating the effect of the bid-ask bounce, the procedure of skipping a day also discards potentially useful information contained in the first trading day, and can, thus, overstate the effect of the bid-ask bounce on reversals (Jegadeesh (1990)).

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(unconditional) short-term reversals are fragile and are driven by market frictions and illiquidity (Avramov, Chordia and Goyal (2006)). For intra-industry reversals, however, even though there is a reduction in the quantum of returns, we continue to observe an economically and statistically significant 0.49 percent risk-adjusted return per month. This indicates that the intra-industry reversals remain strong after adjusting for the effects of bid-ask bounce. 4.3.3 Robustness across size, institutional ownership, idiosyncratic volatility and liquidity The higher profitability of the intra-industry contrarian strategy appears to come from selection of fundamentally correlated stocks that initially diverge in value, possibly in response to liquidity shocks, and subsequently converge to their fundamental values. Prior evidence suggests that a large portion of the unconditional short-run reversals may be attributed to stocks that are illiquid (Avramov, Chordia and Goyal (2006)). To examine if the intra-industry reversals are economically meaningful, we check if the intra-industry contrarian strategy tilts the portfolio exclusively towards stocks that have higher trading frictions, or greater transaction and arbitrage costs. We investigate the robustness of our findings by applying the contrarian strategies separately within subsample of firms sorted on firm characteristics that have been shown to be related to market frictions and arbitrage costs. These characteristics include firm size, institutional ownership, idiosyncratic volatility and liquidity. In Panel A of Table 5, we report the return reversals associated with the large and small stocks. Large (small) stocks are those that, at the end of the formation month, fall among the largest (smallest) 30 percent of the stocks in terms of market capitalization using the NYSE breakpoints. As expected, both the intra-industry and unconditional contrarian strategies yield lower (higher) returns for large (small) stocks. Nevertheless, the risk-adjusted monthly return associated with the intra-industry strategy for the large stocks is highly significant at 0.61 percent. This confirms that the intra-industry reversals are pervasive, even among the larger stocks. {Insert Table 5 here.} Greater institutional ownership could lead to more efficient pricing of stocks; for example, by facilitating more informed institutional trading (Boehmer and Kelley (2009)) and by 15

increasing the supply of loanable shares and mitigating constraints on short-selling (Asquith, Pathak and Ritter (2005)). To examine whether greater institutional shareholding eliminates return reversals, we sort stocks on institutional ownership and group the top and bottom 30 percent of stocks into high and low institutional ownership stocks, respectively. As reported in Panel B of Table 5, we find that both the unconditional and the intra-industry contrarian strategies remain profitable for the stocks with high institutional ownership. Interestingly, the large intra-industry contrarian profit among stocks with high institutional ownership suggests that institutional trading consumes liquidity and hence, contributes to short-term return reversals (Kaniel, Saar and Titman (2008) and Campbell, Ramadorai, Schwatrz (2009)). Pontiff (1996) and Shleifer and Vishny (1997) predict that stocks with the largest arbitrage costs have the largest mispricing. Pontiff (1996) argues that arbitrage activity is limited when idiosyncratic risk is high because arbitrageurs cannot effectively hedge their positions. To design a stricter test of the role of arbitrage constraints, we double sort stocks (independently) on idiosyncratic volatility and size, and create two sub-groups. Idiosyncratic volatility for each stock is measured as the standard deviation of the residuals from the standard market model regression of daily stock returns on the returns on the CRSP value-weighted market portfolio in the formation month t. The first group includes stocks that have low idiosyncratic volatility (bottom 30 percent) and large market capitalization (top 50 percent using NYSE breakpoints), whereas the second group includes stocks that have high idiosyncratic volatility (top 30 percent) and small capitalization (bottom 50 percent using NYSE breakpoints). We report the return reversals in the two groups separately in Panel C of Table 5. We find that return reversals are pervasive even among the large and low volatility stocks—the intra-industry reversal strategy yields a significant return of 1.08 percent per month for this group of stocks. Our final robustness check follows Avramov, Chordia and Goyal (2006), who find that unconditional return reversals are limited to illiquid stocks. We employ two measures of illiquidity—Amihud’s measure and turnover—and examine whether the cross-sectional differences in illiquidity across stocks are responsible for the profits we report. Amihud’s (2002) measure of illiquidity is defined as [1/n ∑ {|Rj,d| / (Pj,d * Nj,d)}], where n is the number of trading days in each month, |Rj,d| is the absolute return of stock j on day d, Pj,d is the daily closing price of stock j and Nj,d is the number of shares of stock j traded during day d. The greater the change 16

in stock price for a given trading volume, the higher would be the value of the Amihud illiquidity measure. Turnover is computed for each month by dividing the number of shares traded during the month by the shares outstanding. We focus on a stricter test for the effect of illiquidity by double sorting (independently) stocks on Amihud illiquidity and turnover.10 As the reporting mechanism for trading volume differs between NYSE/AMEX and NASDAQ stock exchanges (Atkins and Dyl (1997)), we sort stocks traded in each exchange separately. Specifically, we sort the stocks into liquid (illiquid) group if they belong to the bottom (top) 30 percent based on Amihud illiquidity measure and we do this separately for NYSE/AMEX and NASDAQ stocks. Similarly, stocks are classified as high (low) turnover stocks if they are among the top (bottom) 50 percent traded on the NYSE/AMEX and NASDAQ exchanges. The sorting of stocks into the two groups—liquid, high turnover and illiquid, low turnover groups—is updated at the end of each formation month. Panel D of Table 5 reports the returns to the unconditional and intra-industry reversal strategies applied to these two groups. Consistent with the findings of Avramov, Chordia and Goyal (2006), we find that the unconditional reversals are strong, and in excess of 1.3 percent per month, for stocks that have low turnover and low liquidity, but become insignificant for the high turnover high liquidity stocks. The raw return for intra-industry reversals, on the other hand, remain significant at 0.49 per cent per month (t-statistic = 3.15) for the high turnover, high liquidity stocks, though the return declines to 0.3 per cent (t-statistic = 1.91) once we adjust for the common risk factors. Overall, while turnover and the level of illiquidity jointly seem to have significant effect on return reversals, we find that even the most liquid stocks experience significant intra-industry reversals.11 4.3.4 Robustness to alternative industry classification schemes and across time To examine if our findings are robust across time periods and across alternative industry classification schemes, we examine the intra-industry reversals for four sub-periods: 1963-1979, 1980-1989, 1990-1999 and 2000-2009 for the finer 48-industries classification scheme of FamaFrench. To the extent that the contrarian profits are due to market frictions, such as bid-ask 10

In untabulated results, when we sort stocks into top and bottom 30 percent based on only one characteristic— turnover or Amihud Illiquidity—we find robust intra-industry reversals in all sub-groups. 11 The t-statistics for the differences between the intra-industry reversals and unconditional reversals are all significant in each panel and each sub-group in Table 5.

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bounce, improvements to the trading mechanisms in the stock market arising from regulatory reforms and technological enhancements might lead to a monotonic decline in the reversal profits across time. Table 6 reports the returns for the unconditional and intra-industry strategies for the Fama-French 48 industries over the full sample period and the four sub-periods. In Panel A, the equal-weighted intra-industry reversal is present in each of the sub-periods, and the riskadjusted returns hover around 1 percent per month. For example, the intra-industry reversal strategy continues to generate a significant 1.09 percent during the recent period of 2000-2010, suggesting that trading frictions alone may not be the primary reason for the existence of reversals. Moreover, most of the profits seem to come from the reversals in the loser portfolio, particularly in the later sub-periods. Although smaller in magnitude, the unconditional reversal is significant in each sub-period, except during 1990-1999. We report the value-weighted portfolio returns in Panel B of Table 6. Except for the 1968-1979 sub-period, the value-weighted unconditional contrarian profit is not different from zero in the full sample period and in most sub-periods. The value-weighted intra-industry strategy, on the other hand, yields significant returns in each of the four sub-periods, with a return of 0.56 percent in 2000-2010. Hence, intraindustry reversals seem to be robust to the alternative industry classification scheme and across sub-periods.12 {Insert Table 6 here.} To summarize, in this section we report returns to both unconditional and intra-industry short-term contrarian strategies across various sub-groups of stocks and across time. The unconditional strategy generates returns that are consistent with the established evidence that short-term reversals are not so conspicuous and are generally confined to a subset of stocks that are likely to be affected by market frictions and illiquidity. The intra-industry reversals that we document in this paper, however, are economically significant, and are pervasive among subsamples of large, liquid and high turnover stocks, and are also persistent over time. We investigate the sources of the intra-industry reversals in the following section.

5. Economic Sources of Short-Term Reversals 12

In additional analysis, we find that our results remain robust when we classify stocks into industries using the four-digit Global Industry Classification Standard (GICS) scheme.

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5.1 Intra-Industry Reversals and Liquidity Provision Short-term stock return reversals may be related to the return to providing liquidity as shown by Grossman and Miller (1988) and Campbell, Grossman and Wang (1993). In these models, the risk-averse market makers require compensation for providing liquidity and immediacy to accommodate imbalances in the demand and supply for the security. The return to supplying liquidity is reflected in the price pressure generated by the liquidity motivated trades and the subsequent adjustment in prices as they revert to fundamental values. Recent theoretical models posit that the cost of supplying liquidity increases during periods of market distress due to either an increase in aggregate demand for liquidity or a decrease in the market making sector’s ability to absorb liquidity shocks or both. For example, in Brunnermeier and Pedersen (2009), liquidity providers obtain financing by posting margins and pledging their inventory of securities as collaterals. During periods of high market volatility, falling asset values and binding margin requirements generate a “liquidity spiral” which tightens funding constraints, and restricts the market’s capacity to supply liquidity. Garleanu and Pedersen (2007) show that tightening of risk bearing capacity due to heightened market volatility, which is a standard feature of risk management models, lowers funding liquidity during market stress.13 Vayanos (2004) suggests that if transactions costs are higher during volatile times, the impact of market volatility on liquidity would be even stronger. Consistent with the central predictions in these models, Hameed, Kang and Viswanathan (2010) and Nagel (2011) find that the profit from the unconditional return reversal strategy is higher during bad times, i.e. when funding constraint is likely to be binding. We expand our analyses by exploring the relation between intra-industry reversals and market and industry volatilities. Following Nagel (2011), we use the implied volatility of S&P 500 index options (VIX) to proxy for periods of market turmoil. Since VIX measures the risk neutral implied aggregate volatility, it would be useful to decompose VIX into two components— the physical volatility measure (VOLmkt) and the variance risk premium. As shown in Bollerslev, Gibson and Zhou (2011), for example, the difference between implied and realized volatilities (VIX-VOLmkt) reflects a volatility risk premium (or risk aversion index) that appears to respond to 13

Kyle and Xiong (2001), and others build models based on limits-to-arbitrage to show that the market maker’s ability to provide liquidity is limited during market distress due to binding capital constraints with mark-to-market losses.

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economic state variables. Garleanu, Pedersen and Poteshman (2009) find that the market makers’ ability to accommodate demand pressures from end-users in the options market is reflected in the variance risk premium. To explore the relative importance of the two components that drive the relation between VIX and reversals, we obtain monthly realized volatility from Bollerslev, Gibson and Zhou (2011), who show that VOLmkt is efficiently estimated by summing five-minute squared returns on the S&P 500 index within the month.14 The monthly volatility of industry returns is measured by the volatility of daily returns on the (value-weighted) portfolio of stocks in industry I within month t, VOLI,t. Our empirical specification takes the following form: (

) (5)

where PIt is the intra-industry reversal returns for industry I in month t, for I=1,2,,,,17 FamaFrench industries; the value of VIX is lagged one month, and controlst-1 is a vector of control variables that captures institutional changes and other factors that may affect market liquidity and are observable in month t-1. These control variables include a January dummy; a predecimalization dummy to denote the change in the tick size to decimals in April 2001; and the lagged one-month returns on the value-weighted CRSP index, to account for the effect for market state in Hameed, Kang and Viswanathan (2010). We also consider the effect of controlling for common risk factors (Ft) via the four risk factors described in Section 2. The system of 17 equations in (5) is estimated via Seemingly Unrelated Regressions (SUR), allowing the intercept to differ across industries. Our sample period is limited by the availability of data on VIX from 1990 to 2010. Results of our estimation of Equation (5) are presented in Table 7. We find that the reversal profits are significantly larger prior to the switch to decimalization of tick size, are higher in January, and are greater following market declines.15 The salient finding in Table 7 is 14

We thank Hao Zhou for making available the data on his website at http://sites.google.com/site/haozhouspersonalhomepage. We obtain similar results if we use the realized volatility measured using daily returns on the S&P 500 index within the month, 15 The difference between the three-month Eurodollar deposit rate minus the three-month US Treasury bill rate (TED spread) suggested in Garleanu and Pedersen (2011) to capture funding costs also does not explain our findings. The coefficient for TED spread takes on a negative sign when we include the volatility measures in the regressions.

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that industry and market volatilities are positively related to the reversal profits. As shown in the table, the effect of VIX (market distress) on reversal profits is fully captured by the variations in realized market volatility and industry volatility, leaving an insignificant role for volatility risk premium (VIX-VOLmkt). The estimated coefficients of VOLI,t-1 and VOLmkt,t-1 indicate a bigger industry effect. A one percent increase in industry (market) volatility predicts a significant 0.22 (0.10) per cent increase in the risk-adjusted reversal profits per month (see Model 4 in Table 7). Given the results in Table 2, it is not surprising that the estimated coefficients do not change much when we control for the common risk factors. To the extent that high values of VIX are associated with market stress and liquidity constraints as in Brunnermeier, Nagel and Pedersen (2008), and Nagel (2011), our findings suggests that intra-industry reversals are related to liquidity dry-ups during volatile times. {Insert Table 7 here.} 5.2 Reversals and Order Flow Imbalances The liquidity provision explanation necessarily involves a predictive relation between order flows and subsequent reversals. In Campbell, Grossman and Wang (1993), for example, return reversals represent compensation to risk-averse liquidity providers for absorbing imbalances in order flows emanating from liquidity demanders. Constraints on the risk bearing capacity of the market making sector or funding constraints can also limit the ability to fully accommodate order imbalances and, hence, generate significant return reversals (e.g. Brunnermeier and Pedersen (2009), and Garleanu and Pedersen (2007)). The reversal profits in these models represent the premium required by liquidity providers to absorb the imbalance in the demand and supply for the security. Chordia, Roll and Subrahmanyam (2001, 2005) and Hendershott and Seasholes (2007) argue that the return reversals are related to inventory effects, where the market makers demand a risk premium for bearing inventory risk, which in turn depends on the order flow. Chordia, Roll and Subrahmanyam (2001,2005) provide empirical evidence that order flows induce price pressure and reversals in intra-day and daily returns.

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Subrahmanyam (2005) finds that monthly order flow imbalances predict returns next month.16 We turn to high frequency data to measure order flow imbalance and gauge its relation to return reversals. We rely on NYSE Trades and Automated Quotations (TAQ) database to obtain high frequency transactions data for the period 1993 to 2008. The data filters and computation methods used in extracting the intraday transactions records to compute daily measures of order imbalance and bid-ask spreads correspond to those in Chordia, Roll and Subrahmanyam (2001, and 2005).17 For example, the sign of each trade (i.e. buy or sell initiated trade) is decided by the Lee and Ready (1991) algorithm, which matches a trade to the most recent quote preceding the trade by at least five seconds.18 For each stock, the intra-day buy and sell orders are aggregated to obtain the daily buyer and seller initiated trades. Following Chordia, Roll and Subrahmanyam (2005), we use two measures of order imbalance. The first measure, OIBP, is defined as the monthly dollar value of buyer initiated trades less the monthly dollar value of seller initiated trades divided by the total value of trades during the month. The second measure, OIBN, is the difference in the number of buyer and seller initiated trades during the month divided by the total number of trades. The monthly observations of buyer and seller initiated trades are constructed by summing the corresponding daily values over the month, for each stock. While the OIBN measure ignores the size of the trade, OIBP places greater weight on larger dollar value trades. To provide an idea of the liquidity and transaction costs associated with the securities in our portfolio, we use two measures of bid-ask spread for each stock using the TAQ database. PQSPR, the proportional quoted spread, is defined as the difference between the bid and ask quotes divided by the midpoint of the bid-ask prices, averaged across all trades during the trading day. The proportional effective spread, or PESPR, is obtained as two times the absolute difference between the transaction price and the midpoint of the prevailing bid and ask quotes, again averaged over the day. Both daily PQSPR and PESPR measures follow those reported in

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Several papers such as Campbell, Grossman and Wang (1993), Conrad, Hameed and Niden (1994), Pastor and Stambaugh (2003) and Avramov, Chordia and Goyal (2006) use changes in (unsigned) trading volume to measure liquidity shocks. We use order imbalance to measure variations in demand for liquidity. 17 Chordia, Roll and Subrahmanyam (2005) explain the filter rules used to eliminate anomalous records in the intraday data in the TAQ database. We thank Tarun Chordia for generously sharing the daily data extracted from the TAQ database. 18 The Lee and Ready (1991) method classifies a trade as a buyer (seller) initiated order if a transaction occurs at a price that is closer to ask (bid) quote. If the trade is at the quote midpoint, it is signed according to the tick test; i.e. the trade is classified as a buyer (seller) initiated if the price is higher (lower) than the previous trade.

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Chordia, Roll and Subrahmanyam (2005), which we average over each month to obtain monthly indicators of liquidity and transaction costs. We reconstruct the intra-industry reversal strategy for the NYSE-TAQ merged dataset for the period 1993 to 2008. We apply the same methodology and $5 price filter as in Table 2. As shown in Table 8, we obtain significant reversal profits for this sample, both in terms of raw profits as well as four-factor risk-adjusted returns. For example, we obtain a risk-adjusted contrarian return of 0.62 (0.42) per cent per month when the reversal strategy is based on equalweighted (value-weighted) portfolios. Table 8 also reports greater seller initiated orders (low OIBP and OIBN) associated with the loser portfolio in the formation period, indicating that the loser stocks experience significant selling pressure. Similarly, we observe greater buy pressure in the winner portfolios, when compared to the middle group of industry neutral stocks. Interestingly, the average buyer minus seller initiated orders across the loser, neutral and winner portfolios become smaller during the subsequent month (the holding period), implying that the imbalances are not persistent. {Insert Table 8 here} To the extent that the intra-industry reversals that we document are related to liquidity provision, the returns from the strategy would be greater for stocks that also experience larger imbalances in the order flow. To verify this prediction, we sort stocks in the industry loser and winner portfolios in Table 8 into two equal groups, based on OIBP in the formation month. The liquidity provision strategy implies buying loser securities that also face selling pressure (low OIBP) and shorting winner securities that exhibit greater buying pressure (high OIBP). Panel A of Table 9 reports the returns to the equal-weighted reversal strategy. The strategy of buying industry losers with low OIBP and selling industry winners with high OIBP increases the raw returns to 1.07 percent per month. The risk-adjusted return on this reversal strategy that takes offsetting position in stocks that experience imbalances is significant at 0.96 percent. These returns are also economically large when compared to the one-way transaction costs estimate (PESPR) of between 0.36 to 0.46 percent. Moreover, PESPR is likely to overstate trading costs

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for institutions and market makers, who may adjust their trades to minimize actual costs.19 We arrive at a similar conclusion when the strategy places greater weight on larger firms. The valueweighted (risk-adjusted) return on the reversal strategy is 0.74 (0.61) per month, compared to the average PESPR of between 0.16 to 0.21 percent.20 On the other hand, the intra-industry reversal strategy applied to stocks that do not face the price pressure does not generate significant riskadjusted profits. For instance, the profits from the value-weighted strategy of buying industry losers with low selling pressure (high OIBP) and shorting winners with low buying pressure (low OIBP) is an insignificant 0.23 percent per month. Hence, these findings provide further support to the proposition that return reversals reflect compensation for liquidity provision, even at the monthly horizon. {Insert Table 9 here}

5.3 Are Reversals Related to Overreaction to Earnings Information? So far, the evidence points to return to liquidity provision as a likely source of intraindustry reversals. An alternative explanation of the short-term return reversals is that it is linked to overreaction to information (e.g. Lehmann (1990) and Subrahmanyam (2005)). To explore this possibility, we examine if intra-industry reversals are related to the release of earnings information. If investors overreact to firm-specific earnings information, followed by correction in prices in the following period, we expect reversals to be stronger following the announcement of earnings news. On the other hand, if intra-industry reversals arise from non-informational (liquidity) shocks, we expect the reversals to be unrelated to (or weaken by) the release of firm specific information. Our proxy for the arrival of firms’ earnings news is the incidence of quarterly earnings announcements. Besides being themselves informative about firm’s future fundamentals, earnings announcements are often accompanied by other firm level news from corporate managers (e.g., the announcements of future earnings targets, dividends and splits) and analysts 19

In a recent paper, Groot, Huij and Zhou (2012) show that the net returns to unconditional weekly reversal strategies increase, and become economically significant, once trading costs are carefully managed. 20 We obtain qualitatively similar results if we use OIBN instead of OIBP.

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(e.g., revisions in forecasts of future earnings and recommendations). We compute a three-day, size, and book-to-market adjusted cumulative abnormal return (CAR), over the days -1 to +1, around the earnings announcement date (day 0). The abnormal return on stock j on day d is computed by subtracting the return on size and book-to-market matched portfolios from the contemporaneous return on stock j. The construction of the size and book-to-market benchmark portfolios follows the methodology in Fama and French (1992).21 We separate the positive and negative earnings information using the CAR calculated in the formation month, depending on whether CAR>0 (denoted as PosCAR) or CAR