Liquidity, Price Behavior and Market-Related Events. A dissertation submitted to the. Graduate School. of the University of Cincinnati

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2 Liquidity, Price Behavior and Market-Related Events A dissertation submitted to the Graduate School of the University of Cincinnati in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Finance-Real Estate of Carl H. Lindner College of Business by Ran Lu B.A. Renmin University of China 2006 July 2011 Committee Chair: John L. Glascock, PhD

3 Abstract In this research, I investigate price behavior of stock market portfolios sorted by liquidity and/or size surrounding market-related events. Three liquidity measures are used (Amihud illiquidity measure, turnover and adjusted ILLIQ). Amihud illiquidity measure is the ratio between the absolute value of the daily stock return and the daily dollar trading volume. Turnover is measured by the ratio between the daily trading volume and the shares outstanding. Adjusted ILLIQ is based on Amihud illiquidity measure, considering the non-trading effect on stock liquidity. I also sort the portfolios by size (measured by market capitalization). The outcomes suggest that large, liquid stocks react in a stronger manner and faster to market-related shocks they also experience a faster reversal following the shocks than do illiquid and small stocks. My hypothesis is that large liquid stocks are more market related (with betas closer to or larger than one) while small illiquid firms tend to not be strongly market related (betas of less than one). The findings support this view. Additionally, I find that small illiquid stocks have more idiosyncratic risk (as measured by the variance of the error term) than liquid and large stocks. Overall, the results suggest that size and liquidity seem to identify the market relatedness of firms. ii

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5 Acknowledgments I am deeply indebted to my advisor, Dr. John Glascock for his guidance and advice throughout this PhD program and this research project. I would very much love to acknowledge his support and encouragement to me. His wise suggestions have enhanced my research in many ways. His kind heart has touched my life in many ways as well. I am deeply honored and extremely fortunate to work with him. In the meanwhile, I would also like to express my gratitude to Dr. Michael Walker and Dr. Yan Yu for their invaluable comments and suggestions on this dissertation. This work would not have been blossomed without them. I would also love to thank my parents in China. They have provided huge supports for my pursuit of this doctoral degree in Finance. I owe a great deal to them of my life, my success and my accomplishments. People say that I am a lucky kid. I agree. I have the best parents in the world to support my dreams. Last but definitely not least, I am also grateful to my (former) colleagues and close friends Qing Bai, Qingqing Chang, Doina Chichernea, Haim Kassa, Jie Wei and Yin Yu. For the past five years, my life would have been less enjoyable and productive without them. Together, we have experienced ups and downs, laughs and cries, excitements and depressions. Their companionships are one of the best things that have ever happened to me. I cannot imagine that this dissertation would have been produced without their intellectual and mental supports. iv

6 Table of Contents CHAPTER I: GENERAL INTRODUCTION... 1 CHAPTER II: LITERATURE REVIEW... 9 CHAPTER III: DATA AND METHODOLOGY DATA METHODOLOGY Define the market-related events Liquidity Measures Define stock returns Abnormal stock returns CHAPTER IV: EMPIRICAL TESTS CROSS-SECTIONAL TEST RESULTS i. Portfolios sorted on Liquidity ii. Portfolios sorted on Size iii. Portfolios sorted on Size and Liquidity LIQUIDITY AND MARKET RISK LIQUIDITY AND IDIOSYNCRATIC RISK CHAPTER V: CONCLUSION REFERENCES v

7 List of Tables and Figures FIGURE FIGURE FIGURE FIGURE TABLE 1 DESCRIPTIVE SUMMARY OF THE MARKET-RELATED NEGATIVE EVENTS. 82 TABLE 2 DESCRIPTIVE SUMMARY OF THE MARKET-RELATED POSITIVE EVENTS TABLE 3 PORTFOLIO ABNORMAL RETURNS SORTED BY LIQUIDITY SURROUNDING NEGATIVE EVENTS TABLE 4 PORTFOLIO ABNORMAL RETURNS SORTED BY LIQUIDITY SURROUNDING POSITIVE EVENTS TABLE 5 PORTFOLIO ABNORMAL RETURNS SORTED BY SIZE SURROUNDING NEGATIVE EVENTS TABLE 6 PORTFOLIO ABNORMAL RETURNS SORTED BY SIZE SURROUNDING POSITIVE EVENTS TABLE 7 PORTFOLIO ABNORMAL RETURNS SORTED BY SIZE AND LIQUIDITY SURROUNDING NEGATIVE EVENTS TABLE 8 PORTFOLIO ABNORMAL RETURNS SORTED BY SIZE AND LIQUIDITY SURROUNDING POSITIVE EVENTS TABLE 9 MARKET RISK ESTIMATION (NEGATIVE EVENTS) TABLE 10 MARKET RISK ESTIMATION (POSITIVE EVENTS) vi

8 TABLE 11 MARKET RISK COMPARISON (NEGATIVE EVENTS) TABLE 12 MARKET RISK COMPARISON (POSITIVE EVENTS) TABLE 13 IDIOSYNCRATIC RISK COMPARISON (NEGATIVE MARKET-RELATED EVENTS) TABLE 14 IDIOSYNCRATIC RISK COMPARISON (POSITIVE MARKET-RELATED EVENTS) TABLE 15 SUMMARIZED RESULTS OF ALL EVENTS vii

9 Liquidity, Price Behavior and Market-Related Events Chapter I: General Introduction The United States stock market experiences persistent and significant extreme-event shocks. For example, between 1950 and 2008, there were twenty times that the stock market gained at least 4.5 percent and twenty-six times that the market lost at least 4.5 percent on a single day. In the 1980s there were seven such events and during the 1990s there were three such events. Some of these shocks were associated with market information events such as the collapse of a bank or political turmoil or a natural disaster, but many are what I label as statistical events. These statistical events are strong (in this case, I use five standard deviations of price movement as a benchmark) and occur frequently. For example in the 1980s there were seven times that the market reacted by over/under 4.5 percent and there was no known associated economic event. In this research, I examine the behavior of stock portfolios sorted by size (measured by market capitalization) and liquidity (measured by Amihud illiquidity, turnover and Adjusted ILLIQ measures) around these events. These events tend to be associated with price reversals. Campbell, Grossman and Wang (1993) suggest that after the movement away from fundamentals, the provision of liquidity induces price reversals. Empirically, I observe that prices reverse in the short run [Lehmann (1990), Jegadeesh (1990) and Avramov et al (2006)]. There are alternative explanations as to why stocks prices reverse. Some argue that it is uninformed and liquidity trading. Campbell, Grossman and Wang (1993) build a model which implies that noninformational trading will cause prices to deviate from their fundamental price. Risk-averse 1

10 market makers are attracted by the deviation from fundamentals and thus provide liquidity to non-informational traders. Therefore, the lack of liquidity in the first place will induce stock prices to move away from the fundamentals and the supply of liquidity from market makers will induce return reversals. Conrad, Hameed and Niden (1994) and Avramov, Chordia and Goyal (2006) confirm CGW s predictions. Others [Boudoukh, Richardson, and Whitelaw (1994)] argue that price reversals are induced by microstructure factors. Roll (1984) develops a model to show that bid-ask spreads can generate return reversals. Atkins and Dyl (1990) examine the relation between short-run return reversals and bid-ask spreads, and find that stocks with lowest bid-ask spreads have the smallest daily abnormal returns. Jegadeesh and Titman (1995) take into account the inventory imbalance of market makers when they explain the return reversals. Hendershott and Seasholes (2007) use a unique dataset to empirically test the relation between price reversals and dealers inventory positions. They find that market makers are compensated for inventory risk by return reversals. They show that long (short) inventories coincide with negative (positive) returns and forecast positive (negative) stock returns the next day. Regardless, whether it is an information story or a microstructure story, liquidity seems to play an important role in return reversals. Liquidity, or the lack of liquidity, will affect how prices behave surrounding event shocks, no matter whether they are market-wide event shocks or individual firm related shocks. Chordia, Roll and Subrahmanyam (2005, 2008) suggest that liquidity enhances the speed of convergence to efficiency. The improvement of liquidity speeds up the process of incorporating information into stock prices. Thus, if stocks prices move away from fundamentals, liquidity will influence how much and how fast prices reverse to some extent. 2

11 My hypothesis is that liquidity may act in separate ways depending upon what type event is involved. Since high liquidity stocks absorb new information faster than low liquidity stocks and they are less costly to trade than illiquid stocks, I expect to find that high liquidity stocks react faster or more intensely to market-related shocks and that it takes them a shorter time period to reverse than it would low liquidity stocks. In particular, I expect that large highly liquid stocks would be more market oriented than small illiquid stocks. My argument is that large firms with high liquidity are strongly market oriented and thus react to events that seem to be market wide. Small illiquid stocks would be more likely to be less market oriented and thus react less to market-wide events. My expectations are consistent with the findings in the previous studies around individual firm shocks. Numerous papers which study how return reversals behave surrounding individual event shocks [Atkins and Dyl (1990), Bremer and Sweeney (1991), Cox and Peterson (1994), and Benou and Richie (2003)] show that, on average, it takes two to three days for stock prices to reverse. Cox and Peterson (1994) find that smaller firms present larger return reversals than larger firms. Avramov, Chordia and Goyal (2006) show that highly illiquid stocks experience greater return reversals than highly liquid stocks. My argument is that these studies are consistent with my expectations in that a small firm with high idiosyncratic risk would be expected to react to a firm related event more significantly than a large firm that has less idiosyncratic risk. If an event is firm related, firms with strong firm related risk should react more. My expectations then are that such small illiquid firms should have less market risk as measured by beta and more individual risk as measured by the variance of the error term in a market model regression. 3

12 However, there is limited literature studying the price behavior around market event shocks and, thus, one of my contributions of this study is to enhance my ability to understand liquidity measures and event risk by including a sample of market related stock adjustments. There are two main reasons why I want to conduct studies around market-related event shocks. First of all, studying price behavior surrounding market-wide event shocks helps us to more deeply understand the mechanism behind the liquidity provision from market makers. When there is an individual stock shock, market makers will simply supply liquidity to the specific stock which is facing the lack of liquidity. In the contrast, market makers have to choose among stocks to which they provide liquidity when a market-wide event shock happens. Secondly, I can control for the characteristics of shocks when I study the price behavior of stocks around market-related events instead of individual stock events. Stocks have different frequencies of individual stock events, different magnitude of the shocks, different contexts of the individual events. A market-related event study can better control for these shock features. Since all the stocks in the market face the exactly same shock at the same time, their reactions will better reflect the influences from their stock characteristics, such as liquidity. Therefore, by controlling for the nature of the shocks, we can better understand what characteristics of stocks drive the different results surrounding different kinds of events. This effort examines the price behavior difference between large/liquid and small/illiquid stocks surrounding market-related events. I identify 26 extreme negative events and 26 extreme positive events. I perform cross-sectional tests to all the commons stocks 4

13 traded in NYSE\AMEX\NASDAQ around these events. Liquidity is measured by Amihud illiquidity [Amihud (2002)], turnover and adjusted ILLIQ measure. The definitions of Amihud illiquidity, turnover and adjusted ILLIQ measures are introduced in details at the methodology section. I find that liquid stocks react faster and more intensely to the market-related shocks than illiquid stocks. Surrounding negative events, the abnormal returns of liquid stocks on the event date (Day 0) are generally significantly negative, which means that, when a marketrelated negative event shock occurs, liquid stocks usually react immediately and their raw returns will fall below the average of the market. From the first day to the third day following the negative events, liquid stocks show substantially significant reversals. In contrast, the abnormal returns of illiquid stocks on the event date (Day 0) are significantly positive, which indicates that illiquid stocks raw returns are usually above the average of the market (in this case, it means that the raw returns are less negative). On Day 1, the prices of illiquid stocks continue dropping, which implies that it takes illiquid stocks more time to process the information imbedded in the market-related events. Surrounding positive events, the abnormal returns of liquid stocks on the event date (Day 0) are generally significantly positive. This indicates that, when a market-related positive event shock occurs, liquid stocks usually react immediately and their raw returns will rise above the average of the market. From the first day to the third day following the positive events, liquid stock show remarkably significant reversals. In contrast, the abnormal returns of illiquid stocks on the positive event date (Day 0) are generally negative. This implies that the raw returns of illiquid stocks are usually below the average of the market. On the days following the positive events, the prices of illiquid stocks started rising, which implies that it 5

14 takes illiquid stocks more time to process the information imbedded in the market-related positive events. To briefly summarize the results on the price behavior of liquid and illiquid stocks surrounding negative and positive events, I find that the direction of illiquid stocks return reversals is the opposite to the one of liquid stocks reversals. There is a substantially significant difference between the price behaviors of stocks sorted on liquidity. Next, I sort stocks by size on the previous day of the event shocks (Day -1). Surrounding 17 of 26 negative events, the value-weighted average abnormal returns of large stocks are generally significantly negative. This indicates that, similarly to liquid stocks, when a market-related negative event happens, large firms usually react faster and more intensely, and their raw returns are usually below the average of the market. On the days following the event shocks, I observe substantial return reversals. Oppositely, the abnormal returns of small firms are generally significantly positive on Day 0. Their raw returns are usually above the average of the market when a market-related negative event occurs. On average, it takes one day longer for small firms to react than for large firms. Surrounding 19 of 26 positive events, the value-weighted average abnormal returns of large stocks are generally significantly positive or significantly less negative. The abnormal returns of small firms are generally significantly negative on Day 0. This implies the same results as in negative events. Large firms usually react more immediately and more intensely than small firms to market-related events. The raw returns of large firms on Day 0 are usually above the average of the market. Following the positive events, there are remarkably return reversals. 6

15 When I control for both the liquidity effect and the size effect on stock returns, I find consistent and similar results which are liquid and large stocks react faster and more intensely to the market-related events than illiquid and small stocks. Liquid and large stocks reverse more and more immediately than illiquid and small stocks after the event shocks. These results hold for all the 26 negative market events using turnover and 22 of 26 negative market-related events using either Amihud illiquidity measure or adjusted ILLIQ measure. 19 out of 26 positive market-related events share these similar results using either Amihud illiquidity measure or adjusted ILLIQ measure, while these results hold consistently for 24 out of 26 positive events using turnover as liquidity measurement. My hypothesis is that liquid and large stocks have more market risk than illiquid and small stocks. When there is a market-related shock, since liquid and large stocks are more sensitive to the overall market (in another word, they are the market), they will react more intensely than the less sensitive illiquid and small stocks. My results confirm this hypothesis. Generally, liquid stock, indeed, have significantly larger betas than illiquid stocks. They are much more sensitive to the movements of the whole market than illiquid stocks. On the other hand, illiquid stocks have much more idiosyncratic risk than liquid stocks. I find evidence to support my hypothesis in the majority of market-related events in my research. When liquidity is measured by Amihud Illiquidity, betas of the portfolio of the illiquid and small stocks range from to ; while betas of the portfolio of the liquid and large stocks range from to When liquidity is measured by turnover, betas of the portfolio of the illiquid and small stocks range from to ; while betas of the portfolio of the liquid and large stocks range from to When liquidity is measured by adjusted ILLIQ, betas of the portfolio of the illiquid and small stocks range from 7

16 to ; while betas of the portfolio of the liquid and large stocks range from to The differences between the betas of the two portfolios are highly significant all the time. I find evidence to confirm my hypothesis that liquid portfolios have larger betas than illiquid portfolios in 20 of 26 negative events and 18 out of 26 positive events when I use Amihud measurement and Adjusted ILLIQ measure. When I use turnover as a liquidity measure, all of the 26 negative market-related events and positive market-related events produce significant results. These results confirm that large\liquid stocks have more market risk than small\illiquid stocks. The comparisons of the idiosyncratic risk, measured by the variance or the standard deviation of the error terms from the market model regressions, are also consistent with my hypothesis. On negative events, when liquidity is measured by Amihud Illiquidity, the standard deviations of the error terms range from to for the small\illiquid stock portfolio and to for the large\liquid stock portfolio. The differences are highly significant across all the 26 negative market-related events. We find similar results with adjusted ILLIQ measure for the negative market-related events. On positive events, when Amihud illiquidity measure is used to measure liquidity, the standard deviations of the error terms range from to for the small\illiquid stocks portfolio and to for the large\liquid stock portfolio. The differences are highly significant across all the 26 positive market-related events. The tests to compare the market risks and idiosyncratic risks of large/liquid stocks and small/illiquid stocks help to reconcile the seemingly contradicting results from my market- 8

17 related event study and the prior individual-stock event studies. I propose that the results agree with each other once I control for the nature of the event shocks. The remainder of the paper is organized as follows. Chapter II reviews related literature. Chapter III describes data and methodology. Chapter IV provides the empirical test results and discussion. Chapter V concludes. Chapter II: Literature Review Liquidity is linked with return reversals in multiple dimensions. There are numerous papers which show that return reversals can be induced either by the lack of liquidity or some microstructure factors. Moreover, liquidity is also associated with market efficiency. Since return reversals impose a challenge towards market efficiency, it would be interesting to see how liquidity influences price behavior. This section reviews what has been studied in this area and explains, in detail, the rationale of my study around market event shocks. 9

18 Campbell, Grossman and Wang (1993) document that the first daily autocorrelation of stock returns is lower on high-volume days than on low-volume days. Furthermore, they develop a model to explain this phenomenon. Their model suggests that return reversals can be induced by the liquidity provision from risk-averse market makers. In their preliminary empirical exploration, they use the daily return on a valueweighted index of stocks traded on the NYSE and AMEX measured by CRSP as the main return series over the period July 3 rd, 1962 through December 30 th, Concerned about the influence of the stock market crash on October 19 th, 1987, they mainly focus on a shorter period from July 3 rd, 1962 through September 30 th, They also study the behavior of some other stock return series. They are particularly interested in the behavior of large stocks. Therefore, they use the Dow Jones Industrial Average in their study. They also examine the returns on 32 large stocks that were traded throughout the period, and were among the top 100 largest stocks on both the dates of July 2 nd, 1962 and December 30 th, They inter-act current stock returns with day-of-the week dummies (day dummies) and volume. And then they run regressions of the one-day-ahead stock returns on these interaction terms. Alternatively, they inter-act the current returns with day dummies and estimated conditional variance. Finally, they run a regression with current returns interacted with day dummies, volume, squared volume and conditional variance. They find that autocorrelations in stock returns on both a CRSP value-weighted index and thirty-two individual stocks from Top 100 largest stocks throughout the sample period are lower (more negative or less positive) on high-volume trading days than on low-volume 10

19 trading days. To explain this phenomenon, they propose a model relying on the idea that high trading volume occurs when the liquidity demand from non-informational traders are accommodated by risk-averse market makers. The intuition of their model is quite simple. Assume that one observes a decline in stock prices. This could be a result from either of the two following scenarios: 1) due to public information, all investors reduce their valuation of the stock market; 2) due to some exogenous selling pressure by non-informational traders. Campbell, Grossman and Wang (1993) argue that, in the former case, there is no reason why the expected return on the stock market should have changed. Since every trader s valuation is adjusted by the public information, this scenario should be accompanied by low trading volume. In the latter case, since market makers are risk-averse utility maximizers, they are willing to accommodate the needs of the non-informational traders as long as they can be rewarded in the form of a lower price and a higher expected stock return. Because the selling pressure from the liquidity or more generally non-informational traders is an exogenous shock to stock market, the requirement of higher expected stock returns from the risk-averse market makers is transitory. On subsequent days, stock prices tend to increase. The exogenous selling pressure must reveal itself in the form of unusually high trading volume. In other words, their model can be understood as follows. If a large subset of investors becomes more risk averse, and the rest of the economy does not change its attitudes towards risk, then the marginal investor is more risk averse, and in equilibrium, the expected return from holding the stocks must increase to compensate the marginal investor for bearing 11

20 the risk. Meanwhile, risk is re-allocated from those people who become more risk averse to the rest of the market. The re-allocation is observed as a rise in trading volume. Recall that the rise in expected stock returns is a result of a fall in the current stock prices that causes a negative current return. Therefore, a large trading volume will be accompanied with a relatively large negative autocorrelation of stock returns. Therefore, in their model, if the stock market has heterogeneous investors, price changes accompanied by high volume will tend to be reversed. The provision of liquidity from risk-averse market makers induces stock return reversals in the next few days. Campbell, Grossman and Wang (1993) establish a strong link between stock liquidity and stock return reversals. There are several papers which follow Campbell, Grossman and Wang (1993) and test their implications. Conrad, Hameed and Niden (1994) find that high-transaction stocks have negative autocorrelations, but low-transaction stocks have positive autocorrelations. Two theoretical predictions are presented in their paper. Blume, Easley and O Hara (1994) conjecture that the relation between past volume and prices may be more pronounced for smaller, less widely followed firms (in another word, illiquid firms). However, Campbell, Grossman and Wang (1993) predict that price changes with high volume will tend to be reversed; this will be less true of price changes on days with low volume. They test the relation between lagged volume and prices suggested by these two models. They study the data for individual stocks in NASDAQ-NMS from CRSP between 1983 and The data consists of weekly returns and number of transactions for each individual stock. Stocks are included in the sample for week t if they have transactions in each 12

21 of the previous two weeks and if the most recent Wednesday-to-Wednesday return could be calculated. Because of the bid-ask bounce, returns are calculated using the midpoint of the bid-ask spread. By using Lehmann (1990) s contrarian portfolio strategy, Conrad, Hameed and Niden (1994) find a strong relation between lagged changes in weekly trading volume and weekly returns in individual stocks. Specifically, return autocorrelations are negative only for last period s highly traded stocks; autocorrelations in returns even become positive if trading volume declined last week. Their findings are consistent with the prediction from Campbell, Grossman and Wang (1993). Since high-transaction stocks are usually considered as liquid stocks, it suggests that liquid stocks experience return reversals while illiquid stocks do not. More recently, Avramov, Chordia and Goyal (2006) investigate the effects that trading volume and liquidity have on stock return autocorrelations. Their tests explicitly make a distinction between trading volume and liquidity. Turnover is used to proxy for trading volume; Amihud(2002) s illiquidity measure is used for liquidity. They show a strong relation between short-run reversals and stock illiquidity after controlling for trading volume. The largest reversals and potential contrarian trading strategy profits occur in high turnover, low liquidity stocks. Their study also follows the methodology proposed by Lehmann (1990). Portfolios are formed based on turnover and illiquidity on weekly and monthly frequencies. So their paper is not an event study, but a study about the difference in behavior in winner and loser stocks. The correlation between turnover and liquidity is only in their data. This facilitates their study to distinguish between turnover and liquidity. 13

22 They find that high turnover and low liquidity stocks face more price pressure in week t-1 and observe a greater fraction of that return reversed in the following week (week t) than low turnover, high liquidity stocks. Their results indicate that low liquidity stocks will reverse more and faster than high liquidity stocks. Following the framework aligned with Campbell, Grossman and Wang (1993), they conjecture that return reversals occur as liquidity providers absorb the order flows from non-informational traders, and since illiquid stocks are more sensitive to liquidity provision, the low liquidity stocks will reverse more than high liquidity stocks when liquidity is supplied. One particular paper that is worth of my attention is the one written by Pastor and Stambaugh (2003). They propose a new liquidity measure which relies on return reversals. Each stock s liquidity in a given month, estimated using that stock s within-monthly daily return and volume, represents the average effect that a given volume on day d has on the return for day d+1, when the volume is given the same sign as the return on day d. The basic idea is that lower liquidity is reflected in a greater tendency for order flow in a given direction on day d to be followed by a price change in the opposite direction on day d+1. Essentially, lower liquidity corresponds to stronger volume-related return reversals. Within this respect, Pastor-Stambaugh (2003) liquidity measure is aligned with the model implications and empirical evidence presented by Campbell, Grossman and Wang (1993). Methodologically, the liquidity measure for stock i in month t is the ordinary least squares estimate of, in the following regression:,,,,,,,,,,,,, 1,,, 14

23 where,, is the return on stock i on day d in month t;,,,,,,, where,, is the return on the CRSP value-weighted market return on day d in month t; and,, is the dollar volume for stock i on day d in month t. In their paper, order flow is constructed as volume signed by the contemporaneous return on the stock in excess of the market. If the stock is not perfectly liquid, we expect the return will be partially reversed in the future. Hence,, is expected to be negative, and it is more negative when the stock is less liquid. The research of Pastor and Stambaugh (2003) is probably the most well-know paper which links liquidity with return reversals. Andrade, Chang and Seasholes (2008) test the implications of a multi-asset equilibrium model where a finite number of risk-averse liquidity suppliers accommodate noninformational trading imbalance. They find that these trading imbalances induce predictable stock return reversals. As in single-stock frameworks, such as Campbell, Grossman and Wang (1993), riskaverse liquidity providers are compensated via future price reversals. In this multi-stock framework, a demand shock for one stock also affects the prices of other stocks. The model implies that the effects depend on the correlation of their cash flows. A demand shock in one stock has greater impact on the prices of more correlated stocks. Provided that there are just two stocks in the market, if there is a non-informational order to buy the first stock and no orders to trade the second one, risk-averse liquidity providers become sellers of the first stock. Suppose the second stock s cash flow is positively correlated with the first stock s cash flow, then they can partially offset the position by buying the second stock. When there are a finite number of liquidity providers in the market, and the 15

24 market is competitive, the price of the second stock will be bid up because of the transmission from the demand shock of the first stock. The authors call this effect as cross-stock price pressure. Andrade, Chang and Seasholes (2008) test the implications from the framework above by using weekly data from Taiwan Stock Exchange. The exchange collects and publishes the number of shares of each stock held long in margin accounts at the end of every day. Margin accounts are owned by individual investors at local brokerage companies. Changes in margin account holdings are the proxy for the non-informational trading imbalances. The data include all 607 stocks from January 1994 to August Via regression analysis, they show that positive trading imbalances in stock i are linked to its price increasing and later reverting. When stocks are more cash-flow correlated, the cross-stock price pressure is higher. They use a sorting procedure to quantify the economic magnitude of the price pressure. Stocks are sorted on weekly trading imbalances. The prices of stocks in the highest quintile (buys) increase, while the prices of stocks in the lowest quintile (sells) fall. The difference between the two quintiles is 2.42%, on average, which is economically significant. Prices then revert to pre-sort levels over the next ten weeks. Their analysis indicates that a large number of buy (sell) orders during a given week increases the probability that prices end the week at the ask (bid) price. The results confirm that risk-averse liquidity providers are compensated for absorbing trading order imbalances. Liquidity is valuable, and agents with comparative advantages in liquidity provision can profit from doing so. 16

25 From the review of literature above, I draw the conclusion that liquidity is one of the major reasons that induce return reversals. Liquidity, or the lack of liquidity, can definitely influence how prices behave surrounding market-related events. There is another branch of literature which directly investigates the relationship between liquidity and return reversals. Roll (1984) suggests that return reversals can be generated by bid and ask prices if transactions occur at either bid or ask price. In a market where transactions are costly to effectuate, market makers must be compensated. One of such compensations is a bid-ask spread. If the market is informationally efficient, the underlying value fluctuates randomly. We assume that the underlying value is the midpoint of bid and ask prices. Thus, the bid-ask average fluctuates randomly in such market. However, if transactions occur at bid or ask price, observed prices changes are no longer independent. Given no new information about the stock, the underlying value of the stock remains the same, so if the transaction occurs at the bid (ask) price, the next price change cannot be negative (positive). Therefore, there is no probability of two successive price increases (decreases). Furthermore, Roll (1984) suggests that the effective bid-ask spread can be inferred from the first-order serial covariance of price changes. In his empirical work, the implicit percentage spread which is calculated by a constant of 200 multiplied by the square root of the inverse sign of the serial covariance of price changes. The implicit measure is estimated annually from daily and weekly returns of stocks listed on NYSE and AMEX between 1963 and The results show that the estimated effective bid-ask spreads are strongly 17

26 negatively related to firm size. Roll (1984) is probably the first one which points out that return reversals may be induced by bid-ask bounces. Thus, studies following Roll (1984) often control for the bid-ask bounces when they examine return reversals. Atkins and Dyl (1990) examine the behavior of common stock prices after a large change in price occurs during a single trading day. Atkins and Dyl (1990) investigate whether there is overreaction in stock markets by looking into price reversals. There is evidence that the stock market appear to have overreacted, especially in the case of price declines. Since part of price behavior can be explained by bid-ask spreads [Roll (1984)], they explore the relationship between short-run stock price reversals and bid-ask spreads when there are large individual stock price changes. They study daily abnormal returns on NYSE stocks from CRSP for the period from January 1975 through December They chose six common stocks during each of the 300 randomly selected trading days: three of those six stocks show the largest percentage loss in value and the other three stocks exhibit the largest percentage gain in value. Abnormal returns are measured via two different approaches. First, they use the meanadjusted returns model where they use the mean daily return earned by the stock during the 60-day period extending from the 31 st trading day after the stock experienced the large loss or gain to the 90 th trading day after the occurrence of the loss or gain as an estimate of the expected stock return. The abnormal returns are measured by the realized daily return net of the estimated expected daily return. Second, they also employ the market risk-adjusted model to measure the abnormal returns. The expected returns are estimated by simple CAPM 18

27 regressions, and abnormal returns are equal to the difference between realized daily returns and expected daily returns. They find that the magnitudes of daily abnormal returns are the smallest for the group with the lowest bid-ask spreads and largest for the group with the highest bid-ask spreads on both the event date and the following day. This means that when there is a large price decline (increase), low liquidity stocks prices drop (increase) more than high liquidity stocks. On the following day, the results imply that low liquidity stocks reverse more than high liquidity stocks. They interpret that the initial price change is an overreaction. The magnitude of the overreaction is much smaller for high liquidity stocks. Jegadeesh and Titman (1995) consider the relationship between return reversals and bid-ask spreads, taking into account the inventory imbalance of market makers. They show that to a large extent, the short-run return reversals can be explained by dealer-inventoryrelated market microstructure effects. They develop a simple model that builds on the framework of Ho and Stoll (1981). The model allows them to decompose the serial covariance of stock returns into four components: a component that relates to the decay of the temporary component of stock prices caused by the market makers inventory imbalances, a component that accounts for the effect of bid-ask bounces, and two additional components that relate to interactions between the order flow and the transitory components caused by inventory imbalances. Based on this simple model, Jegadeesh and Titman (1995) conduct empirical tests on NYSE stocks over the period 1963 to They find that most of the short-term return reversals can be explained by the way in which market makers set bid and ask prices. Since it 19

28 takes several days for market makers on the NYSE to work down their inventory imbalance [Madhavan and Smidt (1993)], return reversals are induced while market makers adjust their inventory by quoting bid and ask prices. Hendershott and Seasholes (2007) s story is consistent with the one of Campbell, Grossman and Wang (1993) that the liquidity suppliers are willing to accommodate trades only if they are able to buy (sell) at a discount (premium) relative to future prices. Thus, large liquidity-provider inventories should coincide with large buying or selling pressure, which causes price movements that subsequently reverse. They use a unique data sample of 11-year NYSE specialist inventories to test and confirm the hypothesis that specialists inventories are negatively correlated with contemporaneous stock returns at both market and individual stock levels. They find that market makers are compensated for inventory risk by return reversals. They show that long (short) inventories coincide with negative (positive) returns and forecast positive (negative) stock returns the next day. All the papers above are consistent with the suggestion in Boudoukh, Richardson and Whitelaw (1994) which indicates that microstructure factors are the most likely source of the autocorrelation patterns in stock returns. Boudoukh, Richardson and Whitelaw (1994) examine the autocorrelation patterns of short-run stock returns. They roughly divide the prevailing views on return autocorrelations into three schools of thought. The first school, the loyalists, believes that markets are rational. The large autocorrelations at short horizons are not due to fundamentals, but from market frictions. Specifically, the pattern and the magnitude of the return autocorrelations are consistent with 20

29 measurement error in data (e.g., non-synchronous trading, or bid-ask spreads), institutional structures (e.g., trading mechanism or trading/non-trading periods), or microstructure effects (e.g., changes in either inventory positions or the flow of information). The second school, the revisionists, believes that markets are efficient. However, they also believe that, even at a frictionless market, there could still be auto-correlated stock returns. They view that the autocorrelation patterns are consistent with time-varying risk premia. The third school, the heretics, believes that markets are irrational. Profitable trading strategies do exist. They argue that return correlation patterns occur because investors either overreact or only partially adjust to information arriving to the market. Thus, for rational investors, they can seek profit from these patterns. Boudoukh, Richardson and Whitelaw (1994) provide an ex ante test of the three schools implications. They study the relation between the autocorrelations of futures returns and the returns on the underlying spot index of two small-firms-weighted portfolios. They find that, although returns on small-firms-based indices exhibit significant autocorrelations, returns on the corresponding future contracts display almost none. This result suggests that there is evidence to support the first school (loyalists) explanation. Their analysis shows that institutional factors are the most likely source of the autocorrelation patterns in stock returns. Because microstructure factors, such as bid-ask spreads and inventory risk, usually reflect certain characteristics of stock liquidity, the literature which studies relationships between microstructure factors and return reversals help us to link liquidity with return reversals in another dimension. 21

30 The observation of return reversals has been widely documented despite some researchers claim that the reversion is just a statistical illusion [Miller, Muthuswamy and Whaley (1994)]. Return reversals have been recorded in various frequencies, such as daily, weekly and monthly. Short-run return reversals after extreme individual stock price declines have been an interesting research topic for decades. The phenomenon of return reversals has been considered as a challenge to market efficiency. Lehmann (1990) show significant weekly return reversals and claim there are arbitrage profits after controlling for bid-ask spreads and plausible transaction costs. He tries to find a strategy to test market efficiency. In order to do that, he forms portfolios weighted on the difference between the return of security i and the return on an equally weighted portfolio at different lags. A week was taken to be a sufficiently short period to apply the martingale model while the horizon of the portfolio strategy was set to twenty-six weeks. The evidence suggests that the winners and losers in one week experience sizeable return reversals the next week. Apparent arbitrage profits persist even after Lehmann (1990) controls for bid-ask spreads and other transaction costs. He concludes that this reflects inefficiency in the market for liquidity around large price changes. Jegadeesh (1990) examines the predictability of monthly returns on individual stocks. He finds negative serial correlation in the cross section of monthly stock returns and evident arbitrage profits. He claims that the predictable pattern of stock returns documented in his paper appears to be a pervasive phenomenon. Additionally, this paper shows that the extent to which stock returns can be predicted based on past returns is economically significant. Ten portfolios are formed based on returns 22

31 predicted using ex ante estimates of the regression parameters. The difference between the risk-adjusted excess returns on the extreme deciles is 2.49 percent per month over the period 1934 to 1987, 2.20 percent per month excluding January, and 4.37 percent per month when January is considered separately. Fehle and Zdorovtsov (2003) examine whether trading strategies based on short-term price reversals following large one-day losses have economically significant returns. They directly take transaction costs into account by calculating returns via the contemporaneous intraday bid and ask quotes. Also, they study the effects of over-reaction, liquidity pressure, and public information flow measures. They examine a trading strategy in which stocks with large one-day price decline during 2000 to 2001 are bought at the average of the ask quotes posted during the last 15 minutes of the event day and sold at the bid quotes observed at various points in time during the next trading day. Based on the cross-sectional results, simple refinements of the trading strategy have economically and statistically significant returns. For instance, buying large stocks with relative losses over 30% and high event-day trading volume could yield average overnight returns of 1.10%! In the cross-sectional analysis, they find evidence consistent with the over-reaction hypothesis to the extent that trading strategy returns increase in the absolute value of the event day loss. They find higher returns for events without concurrent public news releases. There is evidence that suggests price reversals be explained by temporary liquidity pressure, as implied by Campbell, Grossman and Wang (1993) and Jegadeesh and Titman (1995) that returns are 23

32 found to increase in event-day trading volume. The average overnight returns from the trading strategy on the large and high-volume stocks are robust to a number of alternative tests. However, Atkins and Dyl (1990) suggest that it is not profitable to arbitrage on return reversals once transaction costs are considered. Similarly, Avramov, Chordia and Goyal (2006) show the weekly and monthly return reversals and point out that the observation of the existence of return reversals does not propose a challenge toward efficient market and investors cannot benefit from return reversals. It is still a hot topic that whether stock return reversals impose challenges on efficient market hypothesis (EMH) in Fama (1970). The return reversal process presents a mechanism behind which stock prices incorporate new information. In other words, it reflects how fast stock prices will converge to efficiency. Chordia, Roll and Subrahmanyam (2005, 2008) use intraday data to examine the pattern of the predictability of order imbalance of stock returns and imply the role of liquidity in the convergence to market efficiency. Chordia, Roll and Subrahmanyam (2005) investigate how long it takes the market to achieve weak-form efficiency, i.e., how long it takes to remove return dependence. They use intraday data to find the answer. Their calculations cover 150 large stocks listed on NYSE for three years, 1996, 1999, and Small stocks are excluded because of the difficulty inherent in measuring serial dependence when trading is infrequent. The three years are chosen because, first, TAQ data are available, and second, they bracket significant changes in the minimum tick size, which was reduced from eighth to sixteenth during 1997, and was decreased again to one cent in January The sample is then split evenly into three size groups. 24

33 They find that it takes less than sixty minutes for order imbalance return predictability to disappear in the stock market in 1996, less than thirty minutes in 1999 and less than ten minutes in There is evidence that the market is not strong-form efficient over short intervals of a few minutes. Order imbalances are high positively dependent over both short and long horizons. And order imbalances predict future returns over very short horizons (e.g., about five minutes in 2002). They also find that the market for larger stocks is more efficient. They show evidence that the market designs, such as the progress in minimum tick size, actually push market into a more efficient direction. In another word, a more liquid market is more efficient. Chordia, Roll and Subrahmanyam (2008) argue that short-horizon return predictability should be diminished by arbitrage trading, which should be more extensive and effective during times in which the market is more liquid. They expand and further their study in Chordia, Roll and Subrahmanyam (2005) into three different market regimes: eighths regime, sixteenths regime and decimal regime according to the minimum tick size. Since regulatory reductions in the minimum tick size can be considered as exogenous decreases in bid-ask spreads, this paper addresses the question whether such increases in liquidity have enhanced market efficiency. Data of return, order flow, and liquidity for a large sample of NYSE stocks over the period 1993 to 2002 are used to address this issue. They show that stock market in the eighths regime is the least liquid and the least efficient one. Order imbalance shows high significant predictability of stock returns. Stock market in the decimal regime is the most liquid and the most efficient one. Order imbalance cannot predict stock returns in the decimal regime, 25