Information Efficiency and Firm-Specific Return Variation - CiteSeerX

Information Efficiency and Firm-Specific Return Variation*

Patrick J. Kelly Arizona State University

Version: January 2005 Comments welcome

Special thanks to my dissertation committee John Griffin and Spencer Martin (co-chairs), Jeff Coles, and Federico Nardari. I would also like to thank Chris Anderson, Ana Balcarcel, George Cashman, Paul Irvine, Jennifer Juergens, Lidia Kelly, Paul Koch, Laura Lindsey, Felix Meschke, Laura Tuttle, Sriram Villupuram and seminar participants at Arizona State University and the University of Kansas for their insightful comments. I/B/E/S data are generously provided by Carr Bettis and Camelback Research. Patrick J. Kelly is a Doctoral Candidate in the Department of Finance at the W. P. Carey School of Business, Box 873906, Arizona State University, Tempe, AZ, 85287-3906, USA. E-mail: [email protected] tel: 480.965.8299, cell: 480.650.3268, fax: 480.965.8539 *

Information Efficiency and Firm-Specific Return Variation

This paper examines how a stock’s information environment affects its idiosyncratic volatility and market model R-square. West (1988) argues that rapid information incorporation reduces idiosyncratic volatility, thereby raising R-square, while Morck, Yeung, and Yu (2000) contend the opposite, and suggest that R-square is a measure of information efficiency inversely related to the rate of information incorporation. Consistent with West (1988), I find that low R-square stocks are smaller and younger with lower institutional ownership, analyst coverage, and liquidity than their high Rsquare counterparts. Low R-square stocks have greater transactions costs, more tightly binding short sale constraints, fewer informed trades, and the greatest degree of information asymmetry and sensitivity to past market returns. A low market model R-square is thus indicative of a poor information environment with greater impediments to informed trade. R-square is not a robust measure of information efficiency. In contrast, the breadth of institutional ownership is positively associated with the quality of the information environment in a manner consistent with a measure of information efficiency.

JEL classification: G12, G14

Roll (1988) observes that exposure to systematic risk, changes in the firm’s market environment, and the occurrence of value-relevant public information explains only a relatively small portion of stock return volatility. The average market model R-square in his study is only 20% using daily returns and 35% using monthly returns. He proposes that the remaining unexplained idiosyncratic return variance may be attributable to investors trading on private information. Recent cross-country evidence by Morck, Yeung, and Yu (2000) suggests that a low R-square is not merely indicative of private information incorporation in stock prices; it is also a reflection of traders rapidly impounding private information in stock prices. The authors find that the average market model R-square is higher in lesser-developed markets with greater impediments to informed trading due to the country’s legal and institutional structure. By contrast, in better developed countries with fewer impediments the market model R-square is lower. Citing this evidence, they propose that stocks with a low market model R-square have better price discovery and, as a result, are more informationally efficient. A growing body of research corroborates these findings internationally,1 and recent evidence within the United States suggests low R-square stocks have more informationally efficient stock prices.2 The hypothesis that rapid information incorporation results in greater idiosyncratic volatility and thus lower R-squares is not uncontested. West (1988), Leroy and Porter (1981), Shiller (1981), and Campbell, Lettau, Malkiel, and Xu (2001) argue that the rapid incorporation of firm-specific dividend information reduces volatility. Under a constant discount rate, the earlier future dividend changes enter expectations, the more heavily they are discounted. That is, if changes in dividends are known years before they occur, the discounting is so great that there is little impact on returns. On the other hand if changes in dividends are not revealed until the year of the change, the impact on returns and volatility is great (Shiller (1981)). 1Bris, 2

Goetzmann and Zhu (2003); Jin and Myers (2004); Li, Morck, Yang, and Yeung (2003); and Wurgler (2000). Durnev, Morck, Yeung, and Zarowin (2003) and Durnev, Morck, and Yeung (2004).

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This paper contributes to the debate by examining, at the stock level, whether the quality of the information environment, as captured by transactions costs, liquidity, cost of information, and investor attention, affects market model R-square. Specifically, I investigate the association between R-square and the following characteristics of the information environment surrounding stocks: a) the number of institutions and the percentage of institutional holdings as proxies for informed investor attention; b) size, age, and analyst coverage as proxies for the cost of information and level of attention; c) the Lesmond, Ogden, and Trzcinka (1999) estimate of implicit and explicit trading costs; d) volume, the percentage of zero-volume days, and (following Amihud (2002)) the average absolute return per unit of volume as proxies for liquidity; e) the change in breadth of institutional ownership, a proxy proposed by Chen, Hong, and Stein (2002), to measure the degree of short sale constraints; f) a measure of information delay in stock prices developed by Hou and Moskowitz (2004); and lastly, g) the probability of information-based trading (PIN) from a model developed by Easley, Hvidkjaer, and O’Hara (2002). The central finding of this paper is that stocks with greater impediments to informed trade have lower market R-squares than stocks with fewer impediments. That is, stocks have lower market model R-squares when they are held by fewer informed traders, are subject to higher information collection and transactions costs and greater short sale constraints, and are less liquid. Consistent with these findings, stocks with the lowest R-squares are on average those that are most sensitive to past market returns and are characterized by the greatest degree of information asymmetry as measured by PIN. By contrast, using the model developed by Easley, Hvidkjaer, and O’Hara (2002), I find that the arrival of informed trades and the probability of an information event is increasing in R-square. Together, these results are evidence that a low market model R-square is not indicative of rapid information incorporation. R-square is not a robust measure of information efficiency.

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The studies suggesting that a low market model R-square is the result of rapid information incorporation have attracted attention perhaps because of their implication that a simple to calculate measure, R-square, can capture the degree to which prices are informationally efficient.3 A measure of information efficiency is desirable because in market-based economies optimal resource allocation depends on informationally efficient prices; however, when information acquisition is costly, prices do not reflect all available information (Grossman and Stiglitz (1980)).

That is, traders will

optimally choose how much information to collect depending on the cost of information collection, the cost of trade, and, importantly, the ability of informed investors to trade without revealing their costly information (Grossman(1976)). As a result, stock prices may reflect information to differing degrees, and may be more or less informationally efficient. If assets that are more informationally efficient can be identified based on particular characteristics, then these characteristics proxy for the extent an asset’s price reflects its true risk-return tradeoff. This is valuable because informationally efficient prices present a clearer signal of the quality of managerial decisions while making the asset a better investment vehicle for uninformed investors. Conversely, a measure that can easily identify stocks with informationally inefficient prices would identify stocks that may yield a profit if a trader were to acquire costly information. I propose the breadth of institutional ownership as measure of information efficiency. Grossman (1976) argues that, in the absence of noise (liquidity) trading, prices reflect an informed trader’s information as soon as the informed investor attempts to trade. In order for traders to have an incentive to incur information collection costs there must be noise traders who prevent other market participants from immediately distinguishing informed from uninformed trades. That is,

Wurgler (2000); Durnev, Li, Morck, and Yeung (2003); Hamao, Mei, and Xu (2003); Huang (2004); Jin and Myers (2004); Chung (2003); Stahel (2002); Tong (2004); Veldkamp (2004); and Yuan (2001) cite Morck, Yeung and Yu (2000), as evidence that idiosyncratic return variation reflects the rate of information incorporation in stocks. 3

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informed trading is not enough to ensure informationally efficient prices. Without uninformed trading, no informed trader will be able to profitably trade on her information. Using the microstructure model developed by Easley, Hvidkjaer, and O’Hara (2002), I estimate the arrival rate of informed and uninformed trades and find that increased breadth of ownership is associated with both greater informed and uninformed trade flow. Thus, higher breadth means that both the level of informed trading and the means to conceal the trade are greater, so it is possible for informed traders to profit from information collection. Most directly, breadth of ownership is a proxy for the degree of information symmetry among traders, as evidenced by the negative association with PIN, and its positive correlation with the probability of an information event and the number of informed trades. I also find a negative association between the breadth of ownership and trading costs; illiquidity, as measured by volume and the number of zero volume days; and the degree to which short sale constraints are binding. Breadth is positively associated with size, age, analyst coverage, and institutional ownership. In short, high breadth of institutional ownership is associated with the quality of the information environment and, as such, it is a measure of the degree of information efficiency in prices. These findings contribute to the literature in several ways. First, they provide affirming evidence for the arguments of West (1988) and Campbell, Lettau, Malkiel, and Xu (2001); more rapid information leads to lower idiosyncratic return volatility, implying that market model R-square is not a robust measure of information efficiency. Second, the results of this paper show that trading frictions and other impediments to information incorporation significantly contribute to the crosssectional differences in R-square found by Roll (1988). Finally, this paper proposes an alternate measure of information efficiency: breadth of institutional ownership. The remainder of the paper proceeds as follows: Section I reviews the related literature. Section II motivates the choice of variables used to characterize the information environment

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surrounding stocks. Section III describes the construction of the information environment measures and the underlying data used to create them. Section IV examines the information environment surrounding stocks. Section V examines the relation between R-square and measures of weak form efficiency and information asymmetry. Section VI examines R-square in relation to several measures of risk. Section VII examines breadth of ownership as a proxy for information efficiency. Section VIII provides a brief discussion of the findings. Section IX concludes.

I. Related Literature Though the literature on market efficiency is voluminous (see Dimson and Mussavian (1998) for an overview), there has been little, if any, attempt to develop a broadly applicable measure of information efficiency. This perhaps explains the attention garnered by the proposition in Morck, Yeung, and Yu (2000) that the level of the market model R-square is inversely related to the rate of private information incorporation in stocks. Private information is key to informationally efficient pricing since, by definition, public information is incorporated in a stock’s price as soon as it is revealed. Recent studies make use of R-square as a measure of information efficiency, including work by Wurgler (2000); Durnev, Li, Morck, and Yeung (2003); Hamao, Mei, and Xu (2003); and Huang (2004).4 The hypothesis that idiosyncratic volatility is indicative of rapid information incorporation stems from the finding that, across countries, the average market model R-square is decreasing in the strength of private property rights and the extent of investor protection. Morck, Yeung and Yu 4

Others cite Morck, Yeung, and Yu (2000) as evidence of idiosyncratic return variation capturing the informational efficiency of stocks. These include Chung (2003), Stahel (2002), Tong (2004), and Yuan (2001). Veldkamp (2004) develops a model of the costliness of information, where cross-sectional differences in the cost of information impact the comovement of stocks. In low information cost countries stocks comove less, while in high information cost countries stocks comove more. Jin and Myers (2004) develop a model where greater company transparency results in less return comovement. Other studies have used the Morck, Yeung, and Yu (2000) measure as a measure of comovement in stocks. Such studies include Griffin, Nardari, and Stulz (2003) and Kaniel, Li, and Starks (2003).

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(2000) argue that these legal and institutional protections are implicit measures of the cost of arbitrage. Since private information is incorporated in stocks only through costly informed trading, the lower the cost of arbitrage the more rapidly informed traders impound private, firm-specific information in stock prices. The authors argue that the rapid incorporation of information is manifest in greater idiosyncratic return variance and lower market model R-squares, and that this results in prices that are more informationally efficient. A number of studies provide supporting evidence for this association between R-square and the legal and institutional structures that Morck, Yeung, and Yu (2000) propose facilitates informationally efficient prices. When average R-square is low, capital markets are more open (Li, Morck, Yang, and Yeung (2003)), short sales are less constrained (Bris, Goetzmann, and Zhu (2003)), capital is better allocated, and government ownership in the economy is less (Wurgler (2000)). Two studies conducted within the US examine whether R-square measures the degree of information efficiency in stock prices. Durnev, Morck, Yeung, and Zarowin (2003) and Durnev, Morck, and Yeung (2004) test this hypothesis by investigating the cross-sectional relation between a company’s market model R-square and indicators of information efficiency. The former study argues that if prices are more informationally efficient, then current returns should more rapidly and accurately reflect changes in future earnings. The study finds that the returns of low R-square stocks are more sensitive to future earnings innovations. The latter study notes that if prices are informationally efficient, then they present a clearer signal of the quality of managerial decisions and can serve as a better guide for corporate decision making. Durnev, Morck, and Yeung (2004) find that corporate investment is more efficient when R-square is low, consistent with the notion that low R-square stocks have more informationally efficient prices. An earlier literature uses measures of return volatility, not as evidence of efficient pricing, but rather as evidence against market efficiency. Shiller (1981), LeRoy and Porter (1981), and West

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(1988) model return volatility and present evidence that stock returns are significantly more volatile than the random arrival of new value relevant information would permit in an efficient market. They show that rapid information incorporation results in lower volatility, because when changes in expected firm value that are incorporated in a stock’s price sooner are more heavily discounted. West (1988) generalizes these models to show that return variance is greater anytime the information set expectations are based on is a subset of all available information.5 The idea that volatility reflects private information stems in part from the work of French and Roll (1986), who note that the key distinction between public and private information is that public information affects prices the moment it becomes known, while private information is only revealed through trading. Recognizing that trading can only impact volatility when the markets are open, French and Roll (1986) and Barclay, Litzenberger, and Warner (1990) contrast volatility over exchange holidays, which are not business holidays, with normal trading days. Both studies find that return volatility is lower over exchange holidays and argue that the greater portion of return volatility is due to the activity of private-information driven traders. Roll (1988) decomposes return variance further and proposes that idiosyncratic volatility is largely driven by private information. 6 Idiosyncratic volatility, and by extension R-square, may be driven by factors other than private information. In theory, price changes occur as a result of changes in the discount rate and expectations about future dividends. Campbell (1991) and Campbell and Ammer (1993) show that market level volatility is largely due to changes in the discount rate. At the firm level, Vuolteenaho (2002) shows that changes in cash flows explain the greater portion of volatility. Indeed, Irvine and Pontiff (2004) present evidence that the increases in idiosyncratic volatility found by Campbell,

Marsh and Merton (1986), Flavin (1983) and Kleidon (1985, 1986) point out several biases induced by Shiller’s (1981) empirical method. West (1988) corrects for these biases and still finds evidence of excess volatility. 6 The proposition that private information induces the greater portion of idiosyncratic return volatility is not entirely uncontested. Jones, Kaul, and Lipson (1994) present evidence that 20 to 30% of daily price movements are in the absence of trading. They argue this evidence is consistent with the incorporation of public information. 5

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Lettau, Malkiel and Xu (2001) are due to increases in the volatility of firm level cash flows. Cau, Simin and Zhao (2004) argue that increased exposure to growth options drives the increase in idiosyncratic volatility over time.

II. Variables Used To Characterize the Information Environment In this section, I discuss the motivation for the variables chosen to characterize the information environment. Malkiel (1992) defines efficiency in the following way: A capital market is said to be efficient if it fully and correctly reflects all relevant information in determining security prices. Formally, the market is said to be efficient with respect to some information set … if security prices would be unaffected by revealing that information to all participants. Moreover, efficiency with respect to an information set … implies that it is impossible to make economic profits by trading on the basis of [that information]. (as quoted by Campbell, Lo, and MacKinlay (1997) pp. 20-21)

In a frictionless world with rational agents, if all value-relevant information were public, then prices would be informationally efficient. With costly private information, perfect informational efficiency is unattainable (Grossman and Stiglitz (1980)); however, by admitting noninformation driven (noise) traders, some information can be imparted to the market. The informed trade can “hide” among liquidity (noise) trades so that prices do not adjust immediately upon an informed agent’s decision to trade, which could eliminate potential profit (Grossman (1976), Grossman and Stiglitz (1980)).7 Stocks with greater information efficiency in pricing should be those that: receive the attention of many informed investors; have a low cost of information acquisition; have a low cost to trade, including both explicit costs (e.g., bid-ask spread) and implicit costs (e.g., price pressure as the result of illiquidity); and be liquid. In short, the stocks should be in an environment Jackson (1991) observes that one solution to resolve the impossibility of informationally efficient pricing without the addition of noise trading is to relax the assumption that all agents are price takers. By allowing agents to recognize that their trades may impact the price of assets, under specific parameterizations, agents paying for costly information will be utility maximizing even though their revised demand schedule affects prices. 7

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where it is likely that the ex-ante expected returns from collecting information and trading on it are higher than the expected costs of doing so. In the subsections that follow, I motivate the choice of variables used to proxy for the characteristics of the information environment. Examining the impact of public news events on volatility, Roll (1988) finds that eliminating the days surrounding all public news events only marginally improves the fit of the market model he employs. These findings suggest that while public news events do impact volatility as one should expect, the impact is relatively small. For this reason, I focus on the characteristics necessary for the rapid and complete incorporation of private information: the attention of investors, the cost of information, the presence of informed traders, and the costs of trading. A. Attention and Cost of Information I use three measures to proxy for attention: analyst coverage, size, and age. Analyst coverage can also proxy for information costs. Analysts make their reports known to a range of investors; the accessibility of these reports lowers the cost of information acquisition for the companies that they cover. Work by Brennan, Jegadeesh, and Swaminathan (1993) finds that the returns on stocks followed by many analysts lead those of stocks followed by few analysts. Kim, Lin, and Slovin (1997), provide evidence that analysts promote the rapid incorporation of private information. According to Frankel and Li (2002) insiders profit less from their trades when there is greater analyst coverage.8 Hong, Lim, and Stein (2000) and Griffin and Lemmon (2002) find that momentum and book-to-market effects are concentrated in firms with few analysts and weaken dramatically with broad analyst coverage.

Other papers find problems with analysts. Abarbanell and Bernard (1992) show analysts underreact to recent earnings. Jegadeesh, Kim, Krische, and Lee (2004) find that higher consensus recommendations for stocks with unfavorable characteristics precedes lower returns. Trueman (1994) shows that analysts herd and that their forecasts are biased.

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Like attention, size and age have a dual role. In the Merton (1987) sense, few investors may follow small and young firms. If traders are unaware of a stock, then they cannot discover mispricing in the stock’s returns. Ho and Michaely (1988) argue that if information acquisition is more costly for small firms then, in equilibrium, investors may optimally choose to learn less about small companies. Even if the costs of learning about small stocks are no greater, the potential gains from small stock investment may be too low to justify the investment of time and money. When companies are young without a history of performance, there is often a great deal more uncertainty about the meaning of accounting statements and the nature of the firm. This uncertainty, though not an explicit cost, could translate into greater idiosyncratic return variance and a lower R-square. B. Informed Traders I use institutional investors as a proxy for informed traders. An extensive literature exists detailing the trading prowess of these large traders. Sias and Starks (1997) show that daily return autocorrelation is more prevalent among stocks with high institutional ownership, but that this autocorrelation is due to informed trading on the part of institutions increasing the speed of price adjustment to information. Chakravarty (2001) presents evidence that the relative price impact of institutional trades is greater than that of noninstitutional trades, which is indicative of informed trading. Cohen, Gompers, and Vuolteenaho (2003) find that institutions do not underreact to cashflow news, but individuals do. Sias (2004) suggests that institutions herd, but that they do as a result of inferring information from each other’s trades.9 In addition to trading skill, institutions arguably have a cost advantage relative to noninstitutional investors. This cost advantage increases the likelihood the decision to acquire information will be profitable. Finally, if there are fixed costs to information acquisition, then professional information aggregators may have a cost advantage. There is also evidence that institutions engage in uninformed trading or even trading that causes deviation of prices from the fundamental value of the firm. Cai, Fang, and Zheng (2004) show that institutions follow past returns, as do Griffin, Harris, and Topaloglu (2003), who find that intraday institutional trading is in the same direction as current and past prices. 9

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C. Costs of Trade The costs of trade are frictions that impact the speed of information incorporation in prices. They can be the result of market maker overhead, compensation for liquidity provision, and adverse selection costs. There may exist a bid-ask spread, even in the absence of overhead and liquidity costs, in order to compensate the market maker for the risk of trading against an informed trader (Gloston and Milgrom (1985)). When firms provide better disclosures, bid-ask spreads decrease (Helfin, Shaw, and Wild (2000)). Illiquidity and adverse selection costs are captured using several measures: the measure of trading cost developed by Lesmond, Ogden, and Trzcinka (1999); the Amihud (2002) illiquidity measure; and the percent of days with zero volume. Short sale constraints limit the ability to arbitrage. Diamond and Verrecchia (1987) argue that short sale constraints reduce the speed of information incorporation in prices. As a proxy for short sale constraints, I use change in the breadth of institutional ownership following Chen, Hong, and Stein (2002) who argue that reductions in the breadth of ownership signal that short sale constraints are more binding and that prices are higher relative to their fundamentals. Finally, Hou and Moskowitz (2004) develop a measure of delay, which is a measure of the sensitivity to past stock prices. I use this measure to capture the following characteristics of the stock’s information environment: attention, liquidity, and trading costs. If stocks are highly illiquid or if bid-ask spreads are wide, then stock prices may respond with delay to changes in systematic risk that in a costless world would be immediately observable (Rosett (1959) and Lesmond, Ogden and Trzcinka (1999)). Alternatively, this measure could be capturing the length of time it takes for a stock’s price to incorporate systematic information when attention is infrequent.

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III. Data and Methodology In this section, I describe the measures of the information environment characteristics and the data and procedures used to calculate them. Data are from the Center for research in Security Prices (CRSP), Compustat, Thomson Financial and I/B/E/S. In order to be included in this study, I require a security to have data available to calculate R-square, size, age, lagged analyst count, lagged institutional ownership, lagged breadth, lagged change in breadth, estimated trading costs, illiquidity, volume, turnover, and lagged book-to-market. This requirement restricts the dataset to the period from 1983 through 2003. All analyses are based on yearly measures or aggregates. Details are described in the discussion of data below. A. Market Model R-Square The market model R-square is created following Durnev, Morck, Yeung and Zarowin (2003) and Durnev, Morck and Yeung (2004) based on yearly regressions of Wednesday-to-Wednesday weekly ordinary, common equity returns from CRSP on the value-weighted market return and a value-weighted two-digit SIC industry portfolio of the following form: Ri ,t = α i + β Mkt ,i ,t RMkt ≠i ,t + β Indii ,t RIndi ≠i ,t + ε i ,t

(1)

RMkt ≠ i ,t and RIndi ≠ i ,t are the value-weighted market and industry portfolios excluding the firm under examiniation. Following Durnev, Morck, Yeung, and Zarowin (2003) and Durnev, Morck, and Yeung (2004), I exclude firms if they have fewer than 52 weeks of returns in a year. This is done to avoid problems with firms that experience IPOs, delisting, or trading halts. Also excluded are firms in financial or utilities industries (SIC codes 6000-6999 or SIC 4900-4999, respectively). B. Size, Age, Turnover, Volume, Illiquidity, and Delay Size and age are calculated at the end of each December. Size is price times shares outstanding. Age is measured as the number of years since the firm first appeared on the CRSP

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monthly tapes.10 Turnover, volume, and illiquidity are measures contemporaneous with the market model R-square. Turnover is the percentage of outstanding shares traded on a given day; and is averaged over the entire year to provided a yearly measure. The percentage of zero volume days is calculated as the percentage of days with non-missing price data where the volume is reported as zero by CRSP. Illiquidity is measured following Amihud (2002) and is the average of the absolute daily return divided by the daily dollar volume of trade over the year. Delay is a measure developed by Hou and Moskowitz (2004) and is analogous to a restricted/unrestricted least squares F-test that captures the improvement in R-square as a percent due to including four weekly lags of market returns. Delay is: Delay = 1 −

2 Rrestricted . 2 Runrestrict ed

(2)

This measure differs somewhat from the original methodology of Hou and Moskowitz (2004) in that regressions are run from January through December, instead of from July to June. C. Lesmond, Ogden, and Trzcinka (1999) Trading Costs Lesmond, Ogden and Trzcinka (1999) propose a model of trading costs which recognizes that the fundamental value of an asset is continuous while the realization is not, due to trading frictions.11 Measured returns of zero imply that the transactions costs are higher than any change in the fundamental value of the underlying asset. Observing the magnitude of returns needed to obtain a measurable nonzero return is indicative of the trading costs. Measured returns are the difference between true returns and the threshold trading cost. I follow Lesmond, Ogden and Trzcinka (1999) in estimation procedure and calculating trading costs as the difference between the upper and lower thresholds. See appendix A for estimation details. 10CRSP

began covering NASDAQ stocks in 1973. Since the majority of low R-square stocks are listed on NASDAQ, the correlation between Age and R-square is arguably biased upward. Examining the correlation between Age and R-square for NYSE alone results in a correlation coefficient of .17, versus the 0.29 correlation in Table II. 11 The model inspired by Rosett (1959)

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D. Book Equity, Size and Book-to-Market Factors. I gather book equity from Compustat and Moody's Industrial, Public Utility, Transportation, and Bank and Finance Manuals as calculated in Davis, Fama, French (2000). The Moody’s book equity data are made available on Ken French’s Dartmouth website.12 I calculate book equity following Cohen, Polk, and Vuolteenaho (2003). E. Probability of Information-Based Trading Easley, Hvidkjaer, and O’Hara (2002) develop a model using microstructure trade data to estimate the beliefs of the market maker regarding the probability that an information event has occurred and that a given trade is based on private information. I estimate the probability of information-based trading (PIN), probability of an information event, informed and uninformed order flow based on this model. Intraday trade data are from NYSE’s Trade and Quote System (TAQ). The data are available from 1993 only, so all analyses are for the eleven-year period from 1993 through 2003. Trades and quotes are matched and buy and sell trades are assigned by the algorithm suggested by Lee and Ready (1991). I follow Bessembinder (2004) when cleaning the trade and quote data.13 The PIN is estimated as the ratio of expected informed order flow informed to total order flow: PIN =

αµ , αµ + ε s + ε b

(3)

where α is the probability an information event occurs, µ is the arrival rate of informed trades, αµ is the expected arrive rate of informed trades, and εs and εb are the arrival rates of uninformed sells and buys respectively. See appendix B for estimation details.

Thank you to Ken French. Following footnote 7 of Bessembinder (2004) I eliminate trades that are in error, a correction, out of sequence, exchange acquisitions or distributions, or involve nonstandard settlement. I eliminate quotes that are non-positive, are associated with trading halts or designated order imbalances, or are non-firm. 12

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F. Institutional Ownership and Breadth of Ownership Data on the holdings of large institutions are from the 13f filings with the U.S. Securities and Exchange Commission (SEC) and distributed by Thomson (CDA/Spectrum). Each December the institutional ownership is calculated as the percentage of shares outstanding that are held by institutions with an asset value greater than a floating threshold.14 Breadth of ownership is calculated as the number of institutions with assets greater than the floating threshold holding a stock. Change in breadth of ownership is calculated analogously to the method used by Chen, Hong, and Stein (2002). When calculating the change in breadth of ownership for a stock at time t the count of managers is limited to those who are holding any stock in time t-1. The change is the difference between the number of institutions holding a stock in time t and those holding in time t-1 divided by number of managers in time t-1. Data on institutional ownership are available from 1980. G. Analyst Coverage Data on analyst forecasts are from I/B/E/S.15 Analyst coverage is the number of unique analysts issuing earnings forecasts during a given year for a given stock, where the entry date of the forecast in the I/B/E/S database is considered the earnings forecast date. The percent deviation of analyst count from the annual mean is used in regressions, in order to keep the interpretation of the coefficient estimates the same across years. Analyst count data are available from 1982.

IV. The Information Environment of Stocks by Degree of Market Model R-Square In the following sections, I examine the characteristics of the information environment surrounding stocks. The central question is whether there are consistent differences in the costs, Any firm with more than $100 million of securities under discretionary management must disclose holdings over $200,000 or 10,000 shares. Because the SEC does not adjust this $100 million dollar threshold, which was set in 1980, as the market has risen in value, the number of institutions required to report their holdings grows as the market rises. In order to adjust for the bias toward periods with higher market returns, the $100 million threshold is adjusted following Gompers and Metrick (1998, 2001). Each quarter, the threshold is increased by the growth in an index of all shares held by institutions. 15 I thank Carr Bettis and Camelback Research who generously provided the data. 14

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liquidity, and investor attention based on the level of R-square. To investigate these differences, Rsquare portfolio averages are presented, followed by simple correlations to understand if the patterns in the means mirror patterns at the observation level, and regressions to explore the incremental explanatory power of each of the variables and to see which information environment characters are most closely associated with differences in R-square. A. Sample Description To understand the nature of the information environment surrounding stocks and how it is associated with market model R-square, I begin with simple sorts of stocks into R-square16 sorted portfolios. To calculate portfolio averages I first sort all stocks into NYSE R-square deciles at the end of December each year. The average for each variable is calculated each year in the sample, and the time-series mean of the portfolio averages is presented in Panel A of Table 1. The number of stocks listed on each exchange is counted in December and the average of these yearly counts is presented in Panel B of Table 1. The dispersion of R-square across the portfolios is large. The average R-square for low and high portfolios is 0.027 and 0.567, respectively. Interestingly, the average R-square for the entire sample is 0.152 when based on weekly returns; this is lower than the average R-square of .20 in Roll (1988), which was calculated from daily returns. This low sample average R-square is consistent with the increase in idiosyncratic volatility documented by Campbell, Lettau, Malkiel, and Xu (2001). Consistent with the findings of Roll (1988), firm size is monotonically increasing in R-square (decreasing in idiosyncratic return variance). Given the small size of the low R-square stocks, it is not surprising to see that the vast majority (78%) of low R-square stocks trade on NASDAQ. Nearly all (74%) high R-square stocks trade on NYSE. R-square refers to the model fit coefficient from the market model regression used by Durnev, Morck, Yeung, and Zarowin (2003) and Durnev, Morck, and Yeung (2004). They use the term “synchronicity” for this same market model R-square. Idiosyncratic return variance is referring to the portion of return not explained by this market model and is measured as (1-R-square). 16

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Table 1, Panel A shows that relative to high R-square stocks, low R-square stocks tend to be young, small, illiquid, and have high trading costs. Average daily turnover for low R-square stocksis less than half that of high R-square stocks (0.31% versus 0.68%), while there are no trades for low R-square stocks on 15.5% of trading days in the year. The Amihud (2002) measure of illiquidity indicates that every million dollars in trade volume results in an average 17.95% return for low Rsquare stocks, compared to a 0.01% return for high R-square stocks. The average roundtrip trading cost is 12% for low R-square stocks and 0.4% for low R-square stocks. Low R-square stocks receive less attention from analysts and institutions. Fewer analysts cover low R-square firms; on average, two analysts cover low R-square stocks, whereas 23 cover high R-square stocks. Low R-square firms have 14.3% of the shares held by large institutions, as compared to 52% for high R-square stocks. Only 2.7% of all large institutions hold shares in the average low R-square company, but 32.6% of all institutions hold shares in the average high Rsquare company. These results are consistent with the notion that low R-square stocks, suffering from a poor quality information environment, face greater impediments to informed trade. B. Correlation Between R-square and Information Environment Characteristics I examine the simple correlation between R-square and the information environment of stocks. Table II presents the average of yearly cross-sectional Pearson correlation coefficients. In brief, the correlations are consistent with the associations between portfolio averages and the information environment characteristics seen in Table I. The correlations between R-square and each of the information environment characteristics are strong with the exception of the Amihud (2002) illiquidity measure where there is a correlation of -0.13. Notably, analyst coverage, percent of shares owned by institutions, and breadth of ownership have quite strong positive correlations with R-square – each over 0.50. Analyst coverage

17

and breadth of ownership are also highly correlated with size and volume; all four correlation coefficients are over 0.50. Each measure of attention, cost, and liquidity is associated with the market model R-square in a manner inconsistent with low R-square reflecting stocks with informationally efficient prices; however, consistent with the findings of Roll (1988), size and R-square are correlated, and each of the information environment measures are correlated with size. If large firms are more exposed to systematic risk than small firms for reasons not associated with the quality of the information environment, then it is important to control for this association with size. In the next section, I examine the characteristic averages of portfolios, sorted on size and dependently sorted on market model R-square. C. Average Size and R-square Portfolio Characteristics To control for the association between size and R-square, I sort stocks into NYSE deciles based on their prior December market capitalization, then dependently sort each size decile by the R-square from the current year’s market model regression.17 Table III presents the means of the highest and lowest R-square portfolios in each size decile and their difference, as are tests for the statistical significance of these differences. These sorts largely mitigate the relation between size and R-square for all but the bottom two deciles and the top size decile (the second panel, labeled “Size in Millions”). The differences between the extreme R-square portfolios for each of the information environment characteristics are statistically significant and in a direction consistent with the portfolio averages of Table I and the correlations of Table II for all characteristics except firm age and for nearly all size portfolios. These results suggest that even when controlling for the relation between size and each of the environment characteristics that a lower R-square corresponds with an 17

Independent sorts result in very few, if any, stocks in the extreme portfolios.

18

information environment less conducive to rapid information incorporation. Also notable from Table III is the extremely strong relation between size and each of the information environment characteristics. For each characteristic, with the exception of turnover, size is associated in a manner consistent with a better information environment for larger stocks. D. Regressions To examine the joint relation between R-square and the characteristics of the information environment, regressions are run on the information environment characteristics. In order to control for the fact the regressand, R-square, is bounded, I follow Durnev, Morck, and Yeung (2004), by using the following transformation in lieu of R-square:  R2 ln 2 1 − R

 . 

This transformation is identical to the log ratio of the explained variance to unexplained variance. In addition, all of the information environment variables undergo a log transformation. This allows the coefficients to be interpreted as elasticities. Because analyst count, institutional ownership, breadth, percent of zero volume days, and change in breadth can all have legitimate zero values, one is added to each variable prior to taking the log. This alters the interpretation slightly, but it does not change the sign of the coefficients. Each year, from 1983 through 2003, cross-sectional regressions are run of the log R-square ratio (R2/(1-R2)) on the log of the information environment characteristics. Table IV presents the time series average of the coefficients and the model fit statistics (R-squares). Newey-West (1987) corrected t-statistics test whether the time series coefficients are significantly different from zero.18 These regressions are consistent with the associations found in Tables I through III.

These results hold in pooled time-series cross-sectional regressions. In addition, the results are qualitatively the same whether I employ the log R-square ratio or R-square without any transformation, with and without using the log of the independent variables.

18

19

The signs on the coefficients are significant and consistent with the signs of the correlations in Table II with two exceptions. Incremental to the remaining information environment variables, volume possesses statistically insignificant explanatory power in Model (1); although, from models (2) through (5) and in (10) the coefficient on volume is statistically significant and of the correct sign. The coefficients on the Amihud (2002) illiquidity measure suggest that incremental to the other variables, contemporaneous illiquidity increases the R-square. This is most likely the result of the construction of this proxy for illiquidity, which is the absolute value of returns divided by volume. The rationale behind the measure is that the greater the volume needed to move returns the more liquid the stock is; however, if the market maker can recognize informed trades, then low volume could result in a high absolute value of returns and be measured as illiquidity using the Amihud (2002) measure. Differences in size, analyst coverage, breadth, trading cost, turnover, and change in breadth are associated with substantive differences in R-square. As an example, a firm with twice the market capitalization of the mean (mean =$1.1 billion) has an R-square ratio that is 18.2% higher, which translates in to an R-square that is 0.013 higher (an R-square of 0.175 versus the mean of 0.152). Doubling breadth of ownership from the mean of 8% to 16% of all institutions yields a 7.5% increase in the R-square ratio,19 which implies an R-square that is 0.009 greater than the mean (0.161). A decrease of roundtrip trading costs by half from 6.7% to 3.35% yields a similar increase in R-square of 0.01. A difference in turnover of 0.2% is associated with an R-square ratio, which is 4.4% greater, and a R-square which is 0.005 greater than the mean R-square.

The interpretation is a bit more challenging because a 1 is added before taking the log. For example, average breadth is 0.081 (8.1%), which means the value for the mean observation is ln(1.081). Doubling breadth to 0.162, means a 7.5% increase in the value 1.081 (0.075=0.081/1.081). To get the impact on the ratio, multiply 7.5% times the coefficient (0.909), to get a 6.8% increase in the R-square ratio. A 6.8% increase in the R-square ratio results in a 0.009 increase in R-square. 19

20

Annual cross-sectional regressions confirm the previously discussed associations between the environmental variables and market model R-square: high idiosyncratic return variance (low Rsquare) is associated with lower levels of institutional ownership, lower breadth of ownership, lower analyst coverage, lower turnover, higher transactions costs, greater illiquidity as proxied by the number of zero volume days, and more tightly binding short sale constraints. The results thus far suggest that the information environment surrounding stocks is an important contributor to the relative magnitude of the market model R-square. The analyses suggest that idiosyncratic return variance is associated with a poor information environment characterized by high transactions costs and low liquidity.

V. R-Square and Information Efficiency This paper has presented evidence that when stocks have greater idiosyncratic return variation, the information environment is less conducive to the rapid incorporation of firm-specific information. In this section, I shift focus from barriers to information efficiency to symptoms of information efficiency. The first section investigates whether stocks exhibit weak form efficiency using a measure of information delay proposed by Hou and Moskowitz (2002). The second section examines whether stocks differ by R-square in the probability of an information event, the rate of informed and uninformed trade flow, and the degree of information asymmetry as estimated from a microstructure model developed by Easley, Hvidkjaer, and O’Hara (2002). A. Weak Form Efficiency: Delay If stocks rapidly impound information then they should be at least weak form efficient. That is, past returns should hold no explanatory power over current returns. Hou and Moskowitz (2004) propose a measure of sensitivity to past market returns, which they simply call “delay.” The measure, similar to an F-test, is the percent decrease in R-square due to not including four lags of market

21

returns in the market model. The left panel of Table V presents the average delay measure by Rsquare portfolio. Delay is decreasing in the portfolio rank, except from the ninetieth percentile to the eightieth percentile. The average delay measure for the low R-square portfolio is 0.83, which means that the R-square from the model without four lags of market returns is 83% lower than the model with the lagged market returns. Inconsistent with stocks rapidly impounding information, low R-square stocks are more sensitive to past market return than high R-square stocks. The correlation between the delay measure and the market model R-square is –0.68. B. Asymmetric Information, the Probability of an Information Event, and Trade Flow Using a microstructure model developed by Easley, Kiefer, O’Hara, and Paperman (1996), Easley, Kiefer, and O’Hara (1997), and Easley, Hvidkjaer, and O’Hara (2002), I examine the relation among the probability of information events, informed trade flow, the probability of an information-based trade, and market model R-square. The probability of information-based trading (PIN) is estimated from a model of developed to capture the arrival of asymmetrically informed traders. The probability of an informed trade is calculated as PIN =

αµ , αµ + ε s + ε b

(3')

where α is the probability an information event occurs and µ is the arrival rate of informed trades, so that αµ is the expected arrival rate of information-based orders. εs and εb are the arrival rates of uninformed sells and buys respectively. Thus, PIN is the ratio of the expected number of informed trades to total trades. As such, PIN captures the probability that conditional on observing a trade, that trade is information driven. However, a high PIN does not necessarily mean that there are more informed trades. A high PIN can result from either a high expected arrival rate of informed trades or a low arrival rate of uninformed trades. So that there can be fewer informed trades, but a higher

22

PIN. As such, PIN is better characterized as a measure of information asymmetry: the greater the PIN the greater the likelihood that if you trade your counter party has more information than you do. Information efficiency is characterized by a symmetric distribution of information, because agents can infer information from the informationally efficient price; therefore, a high PIN is indicative of a worse information environment. On the other hand, higher informed trade flow and a higher probability of an information event are indicative of more information incorporation in prices. The right panel of Table V displays for 1993 through 2003 the average PIN, probability of an information event, informed trades, expected informed trades, probability of bad news (given that there is news), and uninformed buys and sells for stocks listed on NYSE.20 PIN is higher for low R-square stocks (19.1%) than for high R-square stocks (12.8%), indicating a greater degree of information asymmetry among traders of low R-square stocks. High R-square stocks have a greater probability of an information event (α) (38.1% versus 24.3%) and over two and a half times the number of expected informed trades (αµ) per day (25 versus 9). If information is to be incorporated into asset prices, uninformed traders are needed in the model of Grossman (1976); there are an estimated four times as many uninformed trades (εb+εs) for high R-square stocks (187) as there are for low R-square stocks (46). In short, low R-square stocks do not appear to be those with the superior information environment. On average, they have a greater degree of information asymmetry, a lower probability of an information event, and fewer informed and uninformed trades. The cross-sectional regressions of Table VI confirm the associations found in Table V. Informed and uninformed trade flow variables are highly correlated (the lowest correlation coefficient is 0.90). In Panel A, I combine uninformed buy and sell trades and leave out informed

In the model the market maker’s updates his or her beliefs based on the arrival of trades. The NYSE most closely matches the structure of the exchange assumed in the model. 20

23

and expected informed trade flow to avoid the problems associated with multicolinearity.21 Panel A shows that PIN, the probability of an information event and uninformed trade flow are incrementally associated with differences in R-square. The remainder of the information environment variables have coefficients consistent with Table IV, except breadth of ownership which has an unexpected negative and significant coefficient; a likely result of multicolinearity with PIN and its components.22 Table VI, Panel B shows that PIN is negatively correlated with R-square, while the probability of an information event has a positive association. Model (3) displays some unexpected signs on the flow coefficients, but this is likely due to the high correlation among all trade-flow variables, informed and uninformed.23 Differences in the PIN and the probability of an information event are associated with significantly different R-squares. As an example, in Model (6), a PIN (coefficient=-11) that is 3.2% higher than the mean PIN of 15.9% is associated with a 30% lower Rsquare ratio. This translates to an R-square which is 0.062 lower than the mean. The coefficient on the probability of an information event (4.965) implies that a firm with an information event probability of 38.1% (7.6% higher than the mean) has an R-square ratio that is 29% higher or an Rsquare that is 0.05 higher than the mean R-square. The results are consistent with the notion that stocks with high firm-specific return variation (low R-square) are in an environment that hinders rapid information incorporation. They also point to the fundamental problem in the information environment. High trading costs, low liquidity, and few informed traders do not merely make prices informationally inefficient; informational inefficiency also imposes risk on uninformed traders. Easley and O’Hara (2004) suggest that this

Using any of the trade flow variables yields results that are nearly identical. The second equation of Panel A is presented for comparison of the NYSE-only sample to the full sample in Table IV. 23 In unreported results, the lowest correlation between any two of these flow estimates is 0.85. 21

22

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information risk is undiversifiable and priced. If this is the case, then the incorporation of this priced firm-specific risk would further push prices away from the fundamental value of the firm.

VI. R-square and Risk Based on the evidence presented in this paper, a low R-square does not appear to be indicative of rapid information incorporation. However, there are other sources of idiosyncratic variance, with the most obvious of these being idiosyncratic risk. In this section, I use several simple measures to capture differences in non-beta, non-industry risk. These are: the book-to-market ratio, the debt-to-equity ratio, the percentage of stocks that delist from their traded exchange as an ex-post proxy for default risk, and the percentage of stocks that undergo a merger in the year following appearance in an R-square portfolio. Each of these measures may reflect risk not captured by the specification of the market model used in this study. High book-to-market may be riskier than other stocks because they have consistently lower earnings (Fama and French (1995)) and may be more susceptible to default (Vassalou and Xing (2004)).24 A greater debt-to-equity ratio makes the equity stake in the firm more option-like, more sensitive to systematic risk, and more susceptible to default. A higher debt to equity ratio will not only magnify the stock’s exposure to systemic risk, but it will also magnify its volatility due to idiosyncratic risk. The last measure is the percent of stocks in a given R-square portfolio that delist for undesirable reasons in the following year. Delisting reasons include corporate governance violations, bankruptcy, and insufficient capital, but do not include delistings because of a change of exchange, or because of an unspecified company request.25 Mergers are

Though there is considerable debate as to whether book-to-market represents any sort of risk (see for example Loughran (1997); Lakonishok, Shleifer, and Vishny (1994), and Daniel and Titman (1997)). Griffin and Lemmon (2002) argue that HML, the book-to-market factor does not capture default related risk.

24

25

Specifically, a delisting is counted if it has a CRSP share code (SHRCD) between 535 and 561 or between 572 and 591.

25

counted separately, and although mergers can be either value creating or destroying, they are likely to be idiosyncratic and not systematic in nature. Table VII presents average December-end book-to-market, debt-to-equity, and the percentage of stocks that delist and undergo mergers. Book-to-market and debt-to-equity ratios for the average low R-square stock are about double that of their high R-square brethren. In the year prior to the R-square calculation the average book-to-market ratio for low R-square stocks is 0.975, compared to 0.531 for high R-square stocks. Low R-squares stocks have an average debt-to-equity ratio of 0.828 in the year prior to portfolio formation, while high R-square stocks have an average debt-to-equity ratio of 0.395. These measures suggest that low R-square stocks are riskier than high R-square stocks. Nearly 6.8% of all low R-square stocks delist within one year of presence in the low Rsquare portfolio, whereas only 0.13% of high R-square stocks do. The percentage of firms that enter mergers in the year following presence in the low R-square portfolio is over twice (4.8%) that of high R-square portfolio stocks (2.2%). Ex-post, low R-square stocks appear to be riskier than high R-square stocks, and, this risk is likely to be magnified given the high debt-to-equity ratios of these firms. Table VIII examines whether book-to-market and debt-to-equity capture variation in Rsquare incremental to the remaining information environment variables. In univariate regressions (Models (1) and (2)) both book-to-market and debt-to-equity have the expected negative sign, but the remaining information environment variables (Model (10)) appear to capture the variation in Rsquare more completely. Overall, there is some indication that low R-square stocks are riskier.

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VII. Breadth of Ownership as a Measure of Information Efficiency An easy-to-calculate measure of information efficiency is desirable. If assets that more readily incorporate information into prices can be identified based on particular characteristics, then these asset prices would provide a better signal of the true risk-return tradeoff and serve as a better investment vehicle for uninformed investors. In addition, prices provide a more accurate signal to firm managers about their decisions when the price of their company’s stock is more informationally efficient. Breadth of ownership may serve as good proxy for the rate at which information may be incorporated in prices. When noise trading exists in the market, prices do not immediately reflect the information content of trades because there is some non-zero probability that any given trade is made purely for liquidity reasons (Grossman (1976)). This means that informed traders can profit by trading on information because their identity as an informed trader is not immediately revealed due to the presence of noise traders. At least theoretically, a desirable proxy for the degree of information efficiency is one that captures the extent to which there is informed and uninformed trading and few impediments to trade. Institutions as a group have the resources (and economies of scale, if there are fixed costs to information collection) to engage in informed trade, but many institutions must also engage in a large amount of liquidity trading; an example is when mutual clients idiosyncratically refund their shares. The key is that if informed trades can be matched to liquidity trades, then the impact of the information on prices is delayed, at least long enough for that informed trader to profit. Thus any proxy for the degree of information efficiency should also capture heterogeneity of information and liquidity driven demand (and supply). As such, breadth of institutional ownership is a candidate for a proxy of the degree of information efficiency.

27

Table IX examines the sub-sample of stocks for which the Easley, Hvidkjaer, and O’Hara (2002) PIN can be calculated. In this sample of NYSE stocks from 1993 through 2003, we see that (in Model (3)) the differences in breadth of institutional ownership are largely explained by the negative association with PIN and the positive association with the probability of an information event. Models (4), (5), (7), and (8) show that breadth of institutional ownership is also associated with the level of informed and uninformed trades.26

That is, stocks with high breadth of

institutional ownership have the high volume of informed and uninformed trades conducive to information incorporation in pricing and they have a high probability of an information event and a low degree of information asymmetry as measure by PIN. Consistent with an association between a better quality information environment and high breadth of ownership, Table X shows that lagged size, age, analyst coverage, institutional ownership, and change in breadth are positively correlated with breadth of ownership in Model (1), while trading costs and the percent of zero volume days are negative correlated. Comparing Model (6) to Models (4) reveals that size and analyst coverage are associated with much of the variation in breadth of ownership.27 Greater breadth of institutional ownership facilitates the incorporation of information both through informed trading and by providing liquidity trading that allows other informed traders to 26 The dependent variable, breadth of institutional ownership, is transformed in the same manner as R-square: ln(Breadth/(1-Breadth)). When calculating this log of breadth ratio, if breadth is zero, then 0.0001 is substituted in place of zero, because otherwise the ratio would be undefined. Deleting observations where breadth is zero results in qualitatively similar results. 27 It should be noted that analyst coverage is highly correlated with breadth of ownership. I use breadth because institutions are the agents who actually trade on information; in addition, to the empirical fact that the correlations with the information environment variables incremental to the impact of analyst coverage are largely of the expected sign. When regressing analyst coverage on the information environment variables, incremental to breadth of ownership (which is positively correlated with analyst coverage in all years), size, age, institutional ownership, and change in breadth have unexpected negative and significant coefficients; however, these unexpected results are probably due to multicolinearity with breadth. Without breadth, the coefficients have the expected signs, suggesting that breadth is a better proxy for these measures of the information environment. These results are available on request. Piotroski and Roulstone (2004) present evidence that suggests that institutional trading accelerates the incorporation of future firmspecific cash-flow information, while analyst forecast activity facilitates the incorporation of firm and industry information. The high correlation between breadth and analyst coverage indicates that either breadth or analyst coverage will capture the quality of the information environment.

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effectively hide their informed trades. The degree of information asymmetry is lower for high breadth of ownership stocks, as are information and trading costs, while liquidity and the probability of an information event are higher. In short, breadth of institutional ownership appears to be a strong candidate for a proxy for the degree of information efficiency.

VIII. Discussion Morck, Yeung, and Yu (2000) suggest that differences in R-square across countries are the result of differences in legal and institutional barriers to arbitrage which in turn affect the rate at which information is incorporated into prices. If this were true the increases in idiosyncratic variances in the US as documented by Campbell, Lettau, Malkiel, and Xu (2001) could be due to an improved flow of information. Confirming the arguments of West (1988) and Campbell, Lettau, Malkiel, and Xu (2001), the findings in this paper provide evidence that the differences in volatility are not due to better or cheaper information. Cross-sectionally, a higher quality information environment, characterized by the attention of more informed traders, a lower cost of information, greater liquidity, and a lower cost to trade, reduces idiosyncratic return volatility. An alternate possibility is that differences in R-square are the result of uninformed traders causing prices to deviate from their fundamentals; however, evidence from the cross-sectional examination of microstructure trade data (as discussed in Section V) suggests that uniformed trade flow is associated with higher R-square. Such a result is not a given. Grossman (1995) argues that increased allocational trading can cause deviations of stock prices from their discounted present value of cash flows, even in a market with rational agents. The findings in this paper show that greater uninformed trading is strongly associated with greater informed trading, arguably counter balancing the large volume of uninformed trade. This is empirical evidence consistent with the Grossman and Stiglitz (1980) argument that liquidity helps facilitate informed trades. The findings of

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this paper suggest that the explanation for the cross-sectional differences in R-square lie not in an improved ability to trade on information or an increase in uninformed trading, but elsewhere. Other possibilities are suggested by the work of Irvine and Pontiff (2004); Cao, Simin, and Zhao (2004); and Beck, Demirgüç-Kunt and Maksimovic (2004). Irvine and Pontiff (2004) find that firm-specific return variance in the US has increased in tandem with increases in the volatility of firm cash flows. Cao, Simin, and Zhao (2004), on the other hand, argue that an increased availability of growth options explains the increase in idiosyncratic volatility. Such an explanation lends itself to both the time series evidence of Campbell, Lettau, Malkiel, and Xu (2001) and the cross-country evidence of Morck, Yeung, and Yu (2000) because the legal and institutional structures that provide a better environment for investors may allow for smaller more specialized companies, which face greater competition or have greater growth opportunities. An intriguing possibility is that differences in average R-square across countries are due to the type or quality of firms in the market. Beck, Demirgüç-Kunt, and Maksimovic (2004) present evidence that financial and legal underdevelopment and corruption disproportionately impede the growth of small companies. If these are the same countries that Morck, Yeung, and Yu (2000) and others identify as countries with low investor protection, high short sale constraints, and less open capital markets, then it might be that these countries have stock markets that are biased toward “large” companies.28 In other words, these legal and institutional structure variables may capture the degree to which truly small (and risky) firms are present in the market. If this were the case, then one simple piece of evidence would be the portion of firms that have delisted in the country.29 Appendix Table 1 presents country average R-square from in Morck, Yeung, and Yu (2000) along with the percentage of all common equity listed on Datastream that has delisted. The greater

Even if these companies would fall in the lowest NYSE-size decile, they may posses the corporate structure, information environment, or proportion of economy that defines size related risk in developed countries. 29 Initial public offering and new listing data for countries would also be a signal. 28

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the number of delistings the lower the R-square. The Pearson’s correlation coefficient is -0.42. Though the evidence is only suggestive, the number of delisting may be indicative of the average quality of firms in the market. Markets that have easy entry and frequent exit, such as better developed markets, may have more unestablished firms, and hence more firms which are susceptible to failure; as a result such firms may have lower R-squares on average. In essence, it may be that the firms in high R-square countries are simply less idiosyncratically risky.

IX. Conclusion Recent studies have proposed that low market model R-squares are the result of rapid information incorporation in stock prices, and as a result, R-square is inversely related to the degree of information efficiency of a stock’s price. This contrasts with the work of West (1988) and Campbell, Lettau, Malkiel, and Xu (2001) who argue that better price discovery decreases idiosyncratic volatility. Consistent with these arguments this paper shows that a poor information environment surrounds stocks with low market model R-squares and that this environment is characterized by lower institutional holdings, lower breadth of institutional ownership, lower analyst coverage, higher transactions costs, lower liquidity, greater private information risk, fewer information events, and a lower flow of informed trades. R-square is increasing in the quality of the information environment and decreasing in the extent of trading fictions. In short, a low R-square is not the result of informed traders rapidly impounding firm-specific information in prices and it is not a robust measure of information efficiency. I propose breadth of institutional ownership as a measure of information efficiency. Widely held stocks are those that are larger, older, have more analyst coverage and more institutional ownership. They have lower trading costs, greater liquidity, are less sensitive to measures of delay, and have fewer short sale constraints. The models of Grossman and Stiglitz (1980) and Grossman

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(1976) suggest that information incorporation requires not only informed traders but also uninformed traders who camouflage the trades of the informed. High breadth of institutional ownership stocks are associated with both a high level of informed and uninformed trade. Stocks with a high breadth of institutional ownership have an information environment consistent with informationally efficient pricing. This paper suggests several avenues for future research. First, in the international empirical asset pricing literature, characteristics that identify a particular risk in the United States are often used to proxy for risk based factors in other countries. This paper finds the relation between Rsquare and impediments to trade across companies differs from that found across countries. If the differences in average R-square found by earlier studies are due to differences in exposure to risk (rather than information quality) these differences must be accounted for when developing international asset pricing models. Future research should investigate how information quality and risk differs by market. Second, a number of papers investigate the relation between institutional ownership and stock price behavior, but have focused on the percentage of the firm owned. The evidence from this paper (and the theoretical work of Grossman and Stiglitz (1980)) suggest that it may be the number of informed investors (proxied by institutional investors in this study) holding a particular stock that is more relevant to efficient pricing. There are a number of proposed factors in the asset pricing literature which appear to explain the cross-section of returns, but have yet to be undisputably associated with undiversifiable risk. Such factors include the Fama and French’s (1993) book-to-market factor and Carhart’s (1997) momentum factor. Using breadth of institutional ownership as a measure of information efficiency future work may examine whether these proposed factors are due to risk or mispricing. Finally, on a theory note, the evidence in this paper suggests that frictions impose constraints on our ability to estimate asset pricing models accurately. Lesmond, Ogden, and Trzcinka (1999) have developed a model to address the frictions associated with trading

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costs while Scholes and Williams (1977) have developed a model to correct for non-synchronous trading. The literature would benefit from an empirically implementable unified model.

Appendix A: Estimation of the Trading Cost Measure Lesmond, Ogden and Trzcinka (1999) propose a model of trading costs inspired by Rosett (1959) who recognizes that the fundamental value of an asset is continuous, however, the realization of its price in the market is discontinuous because of trading frictions. Trading costs are estimated by using the fact that zero returns, as measured from actual trade data, imply that the transactions costs are higher than any change in the fundamental value of the underlying asset. Observing the magnitude of returns needed to obtain a measurable nonzero return is indicative of the trading costs. Lesmond, Ogden and Trzcinka (1999) develop a model where true returns for stock i at time t, Rit* , follow:

Rit* = β i Rmt + ε it ,

(A1)

where Rmt is the return on the market and β i is the quantity of systematic risk associated with asset i. When there are a bid-ask spread and trading costs, such as in the presence of adverse selection, price pressure and sales commissions, measured returns (Rit) follow: Rit = Rit* − α Ni

if Rit* < α Ni

Rit = 0

if α Ni < Rit* < α Pi

Rit = Rit* − α Pi

if Rit* > α Pi ,

(A2)

where α Ni is the threshold return required to observe a non-zero return when true expected returns ( β i Rmt ) are negative, and α Pi is the threshold return required to observe a non-zero return when

33

true expected returns are positive. That is, the measured returns are lower in magnitude than true returns would be if there were no transactions costs. This is a limited dependent model in the spirit of Tobin (1958). To estimate costs the following likelihood function is maximized: L(α Ni ,α Pi , β i , σ i | Rit , Rmt ) =

1  Rit + α Ni − β i Rmt  φ  σi Rit ∈RN σ i  

∏

  α − β i Rmt   α − β i Rmt  − Φ Pi × ∏ Φ Pi σi σi Rit ∈0     1  R + α Pi − β i Rmt  × ∏ φ  it , σi Rit ∈RP σ i  

  

(A3)

where for asset i, α Ni and α Pi are defined as above, Rit is the observed return of asset i, σ i is the measured (observed) residual variance, β i is the quantity of systematic risk associated with asset i, Rmt is the return on the market, φ is the standard normal density function, Φ is the cumulative distribution function of a standard normal distribution. This likelihood functions is maximized for each year for each firm. The estimate of percentage trading costs used in this paper is α Pi - α Ni . Appendix B: Estimation of the Probability of Information Based Trading The probability of information based trading (PIN) is based on a model developed by Easley, Hvidkjaer, and O’Hara (2002) using microstructure trade data to estimate the beliefs of the market maker regarding the probability of an information event has occurred and that trade is based on private information. The model is estimated for NYSE only following Easley, Hvidkjaer, and O’Hara (2002) because the market structure of NYSE more closely resembles that of their model. In order to estimate the measure for each NYSE stock the following likelihood function is maximized, in which it is assume that trades arrive according to a Poisson distribution:

34

ε bB −ε s ε sS e B! S! S B −ε b ε b − ( µ +ε s ) (µ + ε s ) + αδe e B! S! B εS − ( µ + ε b ) (µ + ε b ) + α (1 − δ )e e −ε s s , B! S!

L(α , µ , ε b , ε s , δ | B, S ) = (1 − α )e −ε b

(A4)

where the first additive term represent the likelihood of the arrival of an uninformed trade, the second and third terms represent the likelihood of an informed trade to bad and good news respectively. In equation (5) α is the probability an information event occurs, µ is the arrival rate of informed trades, εs and εb are the arrival rates of uninformed sells and buys respectively, B and S are the number of buys and sell trades for the stock on a given day. For a factorization of this likelihood function that reduces estimation problems, see Easley, Hvidkjaer, and O’Hara (2004). Trades and quotes are matched and buy and sell trades are assigned by the algorithm suggested by Lee and Ready (1991). I eliminate trades which are in error, a correction, out of sequence, exchange acquisitions or distributions, involving nonstandard settlement. Quotes which are non-positive, are associated with trading halts or designated order imbalances, or are non-firm are eliminated following Bessembinder(forthcoming). The PIN is estimated as the ratio of expected informed order flow informed to total order flow: PIN =

αµ , αµ + ε s + ε b

(A5)

where αµ is the expected arrive rate of informed trades and the remaining parameters are defined as above.

35

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42

Table I Summary Statistics for Market-Model R-Square Portfolios To calculate R-square, the following regression is run for each stock in each year: R i ,t = α i + R Mkt ≠ i ,t + R Ind ≠ i ,t

where Rmkt ¹i, t and Rind i¹i,t is the i value weighted market return and company i 's two-digit SIC industry return excluding stock i in year t. Each year non-financial, non-utility stocks which are common ordinary shares and listed on NYSE, AMEX or NASDAQ with 52 weeks of weekly returns are sorted into ten NYSE-breakpoint portfolios based on R-square. For each data item from 1983 through 2003 averages are calculated for each R-square portfolio, for each year t . Company counts are in December of year t . The average across all 21 years is presented in the table below. Size is the market capitalization at the end of December in year t -1. Age is the number of days listed on CRSP at the end of December in year t -1 divided by 365. Analyst Count is the number of unique analysts issuing forecasts in year t -1 as reported by IBES. Institutions and their holdings are counted only if the institutions asset holdings as reported on their SEC 13f filing through Thomson (CDA/Spectrum) are larger than a threshold set following Gompers and Metrick (1998, 2001). The threshold is $100 million in 1980 and is grown by the increase in the market capitalization of all common equity stock ever held by any institution. Institutional Ownership is the percentage of shares outstanding held by institutions at the end of year t -1. Breadth is the number of unique institutions holding a stock at the end of year t -1 divided by the total number of unique institutions holding any stock, change in breadth is the change in the number of institutions holding a stock from year t -2 to year t -1 divided by the number of institutions in year t -2 conditional on the firm being counted as an institutional hold of stock for any stock in both year t -2 and t -1 (i.e. new institutions are not counted as part of the change in breadth). Trading cost is a measure for year t of percentage trading costs developed by Lesmond, Ogden and Trzcinka (1999) and its construction is described in the text. Illiquidity in year t is calculated following Amihud (2002) and is the average in year t of the absolute value of the daily return divided by the daily dollar volume for all stocks with non-missing, non-zero volume. Illiquidity is multiplied by 106. Zero Vol Days(%) is the percentage of trading days with non-missing volume equal to zero in year t . Avg. Daily Volume is the average volume over all trading days. Turnover is the year t average turnover, which is defined as the percentage of shares outstanding, traded on a given day. In order to be included all data must include each of the variables listed in this table and book-equity for the fiscal year ending in t -1 available from Compustat.

Avg. 2

R Portfolio Rank 1 2 3 4 5 6 7 8 9 10 All Portfolios

Avg. ln  R  2   R2  1 − R  0.027 -3.584 0.078 -2.471 0.119 -2.006 0.158 -1.677 0.198 -1.398 0.242 -1.142 0.292 -0.885 0.351 -0.616 0.427 -0.294 0.567 0.271 0.152 -1.717 2

Size (x 10 6 ) 131 260 296 564 786 1,093 1,832 3,186 5,101 8,085 1,122

Age 10 11 11 12 13 15 17 19 22 29 13

Analyst Count 2 3 4 5 6 8 10 13 17 23 6

Panel A Inst. Trading Zero Avg. Own. Breadth Cost Illiquidity Vol Days Daily 6 (%) (%) (%) (x 10 ) (%) Volume 14.3 2.7 12.0 0.1795 15.5 48,915 19.0 4.0 7.8 0.1255 10.3 69,011 22.6 5.3 5.6 0.0699 6.7 93,373 26.8 7.1 3.7 0.0409 4.5 160,384 30.4 8.9 3.1 0.0229 3.0 191,454 34.8 11.1 2.0 0.0246 2.0 240,791 38.8 14.3 1.5 0.0050 1.0 316,877 43.6 18.9 1.0 0.0031 0.5 501,223 47.3 24.0 0.7 0.0009 0.1 784,664 52.0 32.6 0.4 0.0001 0.0 972,275 25.3 8.1 6.7 0.0904 8.1 207,511

Turn Change in Over Breadth (%) (%) 0.31 0.3 0.37 0.4 0.42 0.6 0.48 0.8 0.52 1.0 0.56 1.3 0.59 1.7 0.63 2.0 0.68 2.5 0.68 2.8 0.45 0.9

Table I (continued ) Summary Statistics for Market-Model R-Square Portfolios

Panel B 2

R Portfolio Rank 1 2 3 4 5 6 7 8 9 10 Average per Year Total Observations

NYSE 91 91 91 91 91 91 91 91 91 89 908

Counts AMEX 112 65 48 35 27 20 12 8 5 3 336

NASDAQ 723 400 273 213 158 128 98 71 52 28 2,144

Average Total per Year Observations 927 19,462 556 11,679 412 8,657 340 7,136 276 5,798 239 5,010 201 4,219 170 3,561 148 3,111 120 2,523 3,388

19,071

7,053

45,032

71,156

44

Table II Average Cross-Sectional Correlation of Information Environment Variables and R-Square All variables are as defined in Table I. Cross-sectional Pearson's correlation coefficients are calculated each year from 1983 through 2003. The correlation coefficients are averaged across all 21 years.

0.39 0.36 0.54 -0.14 -0.05 -0.06 0.25 -0.13 -0.04

0.59 0.85 -0.25 -0.12 -0.28 0.60 0.17 0.15

r ve O rn Tu e m lu Vo l Vo ro Ze % ty di ui iq Ill st Co ing ad h Tr dt ea Br

t un Co

e Ag

Turnover Change in Breadth

0.34 0.50 0.20 0.64 -0.09 -0.04 -0.09 0.64 -0.01 0.09

n. Ow st. In

st aly An

Volume

0.30 0.31 0.57 0.51 0.60 -0.29 -0.13 -0.32 0.38 0.23 0.26

e Siz

2

R

Size Age Analyst Count Inst. Own. (%) Breadth Trading Cost Illiquidity Zero Vol (%)

0.64 -0.36 -0.18 -0.35 0.30 0.21 0.27

45

-0.27 -0.12 -0.28 0.64 0.11 0.26

0.44 0.49 -0.12 -0.19 -0.15

0.35 -0.06 -0.12 -0.06

-0.17 -0.32 -0.14

0.31 0.17

0.19

Table III Average of Information Environment Variables for Size and Dependent Sorted R-Square Portfolios In each year t stocks are sorted into NYSE-breakpoint size deciles based on the firm size at the end of year t -1. Within each size decile stocks are sorted into portfolios based on the R-square from the market model regression described in Table I. For each size and R-square portfolio stocks are pooled across all years and the equally weighted average is presented. All data and measures are as described in Table I. The row labeled "ten - one" is the difference between the high R-square portfolio and the low R-square portfolio. * indicates significance at the 5% level. e next to the t-stat, indicates that the variances of the first and tenth portfolios are insignificantly different using a folded-form F-statistic, and as a result the t-test is calculated using a pooled variance. Otherwise the variances are significantly different and the t-stat is calculated using unpooled variances.

R2 Rank 1 2 3 4 1 0.00 0.01 0.02 0.03 10 0.24 0.33 0.39 0.45 ten - one 0.24 * 0.32 * 0.37 * 0.42 t-stat (150.89) (88.32) (77.91) (71.67) p-value 0.000 0.000 0.000 0.000

R-Square NYSE Size Deciles 5 6 7 8 9 10 0.04 0.05 0.06 0.07 0.10 0.13 0.49 0.53 0.57 0.61 0.63 0.66 * 0.45 * 0.48 * 0.50 * 0.53 * 0.54 * 0.54 * (62.97) (64.97) (62.00) (65.88) (59.41) (60.98) 0.000 0.000 0.000 0.000 0.000 0.000

R2 Rank 1 1 22 10 40 ten - one 17 * t-stat (28.41) p-value 0.000

Size in Millions ($) 5 6 517 790 525 816 8 25 e (0.51) e (1.04) e 0.609 0.299

R2 Rank 1 10 ten - one t-stat p-value

1 9.1 9.4 0.4 (1.70) 0.089

e

R2 Rank 1 1 0.67 10 1.69 ten - one 1.02 * t-stat (21.30) p-value 0.000 2

R Rank 1 1 8.96 10 15.52 ten - one 6.56 * t-stat (19.91) p-value 0.000

2 114 121 7* (2.79) 0.005 2 10.1 9.4 -0.7 (-1.42) 0.156

e

2 2.88 4.18 1.30 * (7.83) 0.000 2 24.57 29.22 4.65 * (5.36) e 0.000

3 208 217 8 (1.56) 0.119 3 11.8 11.0 -0.8 (-1.24) 0.216

e

e

4 334 341 7 (0.76) 0.448 4 11.9 11.6 -0.2 (-0.29) 0.769

e

Age in Years 5 6 13.6 17.5 13.3 17.9 -0.3 0.4 (-0.29) e (0.31) 0.775 0.758

e

Analyst Count 5 6 7.14 9.24 10.74 13.72 3.60 * 4.48 * (7.19) e (6.90) 0.000 0.000

7 1,227 1,268 42 (1.03) 0.304

e

8 2,117 2,248 130 (1.64) 0.101

7 17.6 22.0 4.4 (3.06) 0.002

8 23.2 25.7 2.5 (1.45) 0.148

e

e

9 4,470 4,371 -99 (-0.46) 0.646 9 30.3 30.3 0.0 (-0.02) 0.983

e

e

10 20,516 34,067 13,551 * (3.41) 0.001 10 42.8 45.4 2.6 (1.14) 0.255

e

3 3.94 6.06 2.12 * (8.18) 0.000

4 5.54 7.96 2.42 * (6.56) 0.000

7 11.12 17.26 6.14 * (7.80) 0.000

8 15.59 21.92 6.33 * (7.05) e 0.000

9 21.54 26.51 4.97 * (5.10) e 0.000

10 30.89 34.79 3.90 * (2.91) e 0.004

3 31.59 37.59 6.00 * (5.28) 0.000

Institutional Ownership (%) 4 5 6 7 35.75 38.20 40.31 44.74 42.39 46.52 50.29 54.86 6.64 * 8.32 * 9.98 * 10.12 * (4.73) e (5.43) e (5.72) (5.70) 0.000 0.000 0.000 0.000

8 49.62 58.44 8.82 * (5.16) e 0.000

9 50.97 60.86 9.89 * (5.62) e 0.000

10 51.18 54.22 3.04 * (2.13) e 0.034

46

Table III (continued ) R2 Rank 1 1 1.2 10 2.1 ten - one 1.0 * t-stat (25.91) p-value 0.000 2

R Rank 1 10 ten - one t-stat p-value

1 17.4 5.0 -12.4 * (-18.2) 0.000

2 4.1 5.1 0.9 * (6.80) 0.000 2 3.4 1.7 -1.7 * (-8.3) 0.000

2

R Rank 1 2 1 0.280 0.011 10 0.057 0.002 ten - one -0.224 * -0.009 * t-stat -10.707 -10.752 p-value 0.000 0.000 R2 Rank 1 10 ten - one t-stat p-value R2 Rank 1 10 ten - one t-stat p-value

1 2 21.7 5.9 6.1 0.6 -15.6 * -5.2 * (-33.9) (-12.8) 0.000 0.000 1 24.3 63.2 38.8 * (2.72) 0.007

2 84.8 101.2 16.4 (0.77) 0.439

3 6.4 7.8 1.3 * (5.68) 0.000 3 2.1 1.2 -0.8 * (-7.6) 0.000 3 0.005 0.001 -0.004 * -5.101 0.000

4 8.8 10.3 1.5 (4.39) 0.000

Breadth (%) NYSE Size Deciles 5 6 11.0 14.3 13.0 16.7 * 2.0 * 2.4 * e (4.80) e (4.41) 0.000 0.000

7 17.9 21.1 3.2 * (5.09) 0.000

8 24.2 27.3 3.0 * (4.17) 0.000

9 33.3 35.3 2.0 * (2.27) e 0.024

10 53.3 58.5 5.2 * (4.10) e 0.000

4 1.6 1.0 -0.6 (-5.2) 0.000

Trading Cost (%) 5 6 1.4 1.2 0.9 0.6 * -0.6 * -0.6 * (-5.4) (-5.5) 0.000 0.000

7 0.8 0.4 -0.4 * (-4.2) e 0.000

8 0.5 0.2 -0.3 * (-3.3) 0.001

9 0.5 0.1 -0.4 * (-5.1) 0.000

10 0.3 -0.1 -0.4 * (-4.0) 0.000

Illiquidity (x 106) 4 5 6 0.002 0.001 0.001 0.000 0.000 0.000 -0.001 * -0.001 * -0.001 * -5.446 -5.827 -3.371 0.000 0.000 0.001

7 0.000 0.000 0.000 * -2.711 0.007

8 0.000 0.000 0.000 * -3.437 0.001

9 0.000 0.000 0.000 * -2.315 0.021

10 0.000 0.000 0.000 0.261 0.795

3 2.7 0.3 -2.5 * (-7.7) 0.000

Zero Volume Trading Days (%) 4 5 6 7 2.2 1.1 0.8 0.6 0.1 0.0 0.0 0.0 -2.1 * -1.1 * -0.8 * -0.6 * (-5.5) (-3.9) (-2.5) (-2.3) 0.000 0.000 0.012 0.022

8 0.1 0.0 -0.1 (-1.2) 0.247

9 0.0 0.0 0.0 (1.0) 0.318

10 0.0 0.0 0.0 (-0.0) 0.994

3 78.5 150.4 71.9 * (7.52) 0.000

Share Volume (in thousands) 4 5 6 7 114.6 151.4 204.1 361.7 203.6 267.5 348.3 466.6 89.0 * 116.1 * 144.2 * 104.9 (6.09) (5.37) e (4.40) (1.36) 0.000 0.000 0.000 0.174

8 472.5 840.6 368.1 * (3.62) 0.000

9 808.9 980.0 171.2 (1.45) 0.148

10 1,811.4 3,227.4 1416.1 * (2.67) 0.008

Turnover (%) 5 6 0.5 0.5 0.9 0.8 0.5 * 0.3 * (7.36) (5.57) 0.000 0.000

8 0.5 0.9 0.3 * (4.53) 0.000

9 0.5 0.7 0.2 * (3.42) 0.001

10 0.4 0.6 0.2 * (2.89) 0.004

8 2.3 2.9 0.6 (1.22) 0.222

9 1.9 3.2 1.3 * (2.94) e 0.003

10 1.5 3.8 2.3 * (3.62) e 0.000

R2 Rank 1 2 3 1 0.3 0.4 0.4 10 0.5 0.7 0.9 ten - one 0.2 * 0.3 * 0.4 * t-stat (20.07) (11.07) (10.29) p-value 0.000 0.000 0.000

4 0.5 0.9 0.4 * (8.57) 0.000

R2 Rank 1 10 ten - one t-stat p-value

Change in Breadth (%) 4 5 6 7 1.4 1.6 1.9 2.2 2.3 2.7 2.7 2.8 0.9 * 1.1 * 0.8 * 0.6 (3.76) e (4.03) (2.36) (1.52) 0.000 0.000 0.018 0.129

1 0.0 0.2 0.1 * (5.00) 0.000

2 0.7 1.1 0.4 * (4.10) 0.000

3 1.1 1.6 0.5 * (3.26) 0.001

47

7 0.5 0.8 0.3 * (4.28) 0.000

e

e

Table IV Time Series Average of Cross-Sectional Regressions of Market Model R-Square on Environmental Variables For each year t from 1983 through 2003 a cross-sectional OLS regression is run of ln(R-square/(1-R-square))on the environmental variables described in Table I. The time series average of the coefficients are presented below. t-stats are corrected for autocorrelation using the Newey-West (1987) correction. All independent variables are transformed by adding one and taking the natural log.

(1) Mean (t-stat) p-value

(2) Mean (3)

(t-stat) p-value Mean

(4) Mean (5) Mean (6) Mean (7) Mean (8) Mean (9) Mean (10) Mean

Const.

Size

-6.825 ** (-24.70) 0.00 -4.065 (-15.17) 0.00 -7.785 (-36.66) 0.00 -8.219 (-30.94) 0.00 -7.611 (-38.23) 0.00 -7.149 (-21.81) 0.00 -6.632 (-32.06) 0.00 -5.927 (-30.87) 0.00 -7.258 (-36.52) 0.00 -6.996 (-32.50) 0.00

Age

0.182 ** (13.48) 0.00

0.037 ** (4.60) 0.00

0.261 (29.46) 0.00 0.236 (14.02) 0.00 0.235 (13.35) 0.00 0.208 (14.61) 0.00 0.215 (18.12) 0.00 0.172 (16.23) 0.00 0.162 (9.83) 0.00 0.221 (16.71) 0.00

0.033 (4.02) 0.00 0.057 (7.20) 0.00 0.048 (8.15) 0.00 0.046 (6.70) 0.00 0.040 (4.66) 0.00 0.005 (0.52) 0.61 0.018 (2.08) 0.05 0.038 (4.56) 0.00 0.025 (3.50) 0.00

**

**

**

**

**

**

**

**

**

**

**

**

**

**

**

**

**

**

**

Analyst

Inst.

Count

Own.

Trade Breadth

**

Volume

Volume

Turn

∆

Over

Breadth

R2

0.628 ** (5.38) 0.00

0.909 ** (2.89) 0.01

-2.482 ** (-3.14) 0.01

0.419 * (2.46) 0.02

-0.714 ** (-3.97) 0.00

0.052 (1.99) 0.06

21.936 ** (6.35) 0.00

3.019 ** 0.368 (5.91) (17.01) 0.00 0.00

0.153 ** (11.24) 0.00 0.162 ** (11.29) 0.00

0.899 ** (5.77) 0.00

2.563 ** (7.53) 0.00

-3.630 (-3.47) 0.00 -2.171 (-3.01) 0.01 -2.573 (-3.06) 0.01 -2.821 (-3.04) 0.01

0.194 (1.16) 0.26 0.515 * (2.76) 0.01 0.475 * (2.68) 0.01 0.458 * (2.60) 0.02 0.112 (1.26) 0.22 0.110 (0.97) 0.34

-0.778 (-4.11) 0.00 -0.983 (-6.36) 0.00 -0.432 (-2.45) 0.02 -0.839 (-4.39) 0.00 -0.912 (-4.50) 0.00

0.098 ** (4.21) 0.00

9.072 (2.84) 0.01 31.350 (6.78) 0.00 17.156 (6.37) 0.00 29.338 (6.17) 0.00 27.133 (5.93) 0.00

3.826 (6.82) 0.00 3.550 (6.26) 0.00 2.794 (4.80) 0.00 2.903 (5.04) 0.00 3.075 (6.14) 0.00 3.454 (6.48) 0.00 3.709 (6.91) 0.00 3.458 (6.78) 0.00 2.877 (5.57) 0.00

0.875 ** (6.64) 0.00

**

**

Illiq.

0.112 ** (9.62) 0.00

**

**

Zero

Cost

0.115 (9.52) 0.00 0.158 (10.78) 0.00 0.142 (11.18) 0.00 0.113 (9.21) 0.00 0.134 (11.13) 0.00

**

**

**

**

**

0.658 (6.22) 0.00 0.639 (4.17) 0.00 0.645 (4.27) 0.00 0.736 (5.87) 0.00 0.539 (3.96) 0.00

**

**

**

**

**

1.589 (5.11) 0.00 0.851 (2.56) 0.02 0.935 (3.48) 0.00 1.416 (5.50) 0.00 0.363 (1.34) 0.20 1.037 (3.46) 0.00

**

**

**

**

**

*

**

**

**

-2.582 (-3.64) 0.00 -1.571 (-2.95) 0.01 -2.158 (-3.43) 0.00 -1.831 (-3.27) 0.00

**

**

**

**

**

**

*

**

**

0.098 ** (4.54) 0.00 0.045 (1.64) 0.12 0.027 (1.07) 0.30

*

**

**

**

**

-1.211 ** (-10.43) 0.00 0.136 ** (8.17) 0.00 34.958 ** (5.99) 0.00

** 0.360 (17.27) 0.00 ** 0.361 (16.85) 0.00 ** 0.363 (16.88) 0.00 ** 0.361 (17.43) 0.00 ** 0.365 (16.81) 0.00 ** 0.351 (15.26) 0.00 ** 0.357 (15.43) 0.00 ** 0.363 (16.71) 0.00 ** 0.360 (16.68) 0.00

Table V Average Sensitivity to Past Returns and Asymmetric Information by R-Square Portfolios R-square is calculated as in Table I. Each year non-financial, non-utility stocks which are common ordinary shares and listed on NYSE, AMEX or NASDAQ with 52 weeks of weekly returns are sorted into ten NYSE-breakpoint portfolios based on R-square. For each data item averages are calculated for each R-square portfolio, for each year t . The average across all years is presented in the table below. In the left panel data are used from 1983 through 2003 consistent with Table I. Delay is calculated following Hou and Moskowitz (2004) as follows: firm returns are regressed on market returns and four lags of the market to obtain an unrestricted R-square; then a second regressions is run, restricting the coefficients on lagged returns to zero. The delay measure is then calculated using 2 2 Runrestrict the following equation: Delay = 1 − Rrestricted ed The right panel is for NYSE stocks only from 1993 through 2003. Using a model by Easley, Hvidkjaer, and O'Hara (2002) the following data items are estimated: The probability of an informed trade (PIN), Probability of an Information Event (α), Informed Trades (µ), Expected Informed Trades (αµ), Uninformed Buys(εb), Uninformed Sells (εs), Prob. Bad News (δ).

Full Sample 2

R Portfolio Rank 1 2 3 4 5 6 7 8 9 10 All Portfolios

Delay 0.833 0.626 0.508 0.424 0.360 0.306 0.253 0.213 0.188 0.196 0.531

PIN (%) 19.1 18.2 17.5 16.6 16.1 15.4 14.8 14.0 13.4 12.8 15.9

Pr. Info. Event (%) (α) 24.3 26.3 27.5 28.2 29.4 30.9 32.1 34.0 36.3 38.1 30.5

NYSE Only 1993-2003 Info. Exp. Info. Pr. Bad Trades Trades News (%) (µ) (αµ) (δ) 33 9 39.9 38 11 40.0 43 13 40.9 47 14 41.6 49 16 42.1 53 17 42.3 57 19 42.0 64 23 43.6 65 24 44.7 69 25 43.1 52 17 42.0

49

Uninf. Buys (εb) 22 29 35 42 47 53 61 75 79 89 52

Uninf. Sells (εs) 24 31 37 44 50 56 66 80 88 98 57

Table VI Time Series Average of Cross-Sectional Regressions of Market Model R-Square on Asymmetric Information Variables For each year t from 1983 through 2003 a cross-sectional OLS regression is run of ln(R-square/(1-R-square)) on the environmental variables described in Table I and the estimates of probability of an informed trade (PIN), Probability of an Information Event (α), Informed Trades (µ), Expected Informed Trades (αµ), Uninformed Buys(εb), Uninformed Sells (εs), Prob. Bad News (δ) as described in Table V. The time series average of the coefficients are presented below. t-stats are corrected for autocorrelation using the Newey-West (1987) correction. Independent variables are transformed by adding one and taking the natural log.

(1) Mean (2)

PIN

Pr. Inf.

Uninf.

α

ε

Size

0.119 ** (3.56) 0.00

0.113 * (2.21) 0.04 0.170 * (2.52) 0.02

-4.612 ** 2.390 ** (t-stat) (-7.16) (8.80) p-value 0.00 0.00 Mean (t-stat) p-value

Panel A Inst.

Analyst Age 0.050 ** (4.25) 0.00 0.073 ** (5.51) 0.00

Count

Own.

0.145 ** (7.11) 0.00 0.181 ** (7.86) 0.00

(3) (4)

Mean (t-stat) p-value Mean

(5)

Mean

(6)

Mean

(7)

Mean

(8)

Mean

-2.273 (-4.75) 0.00 -0.167 (-0.87) 0.39 -2.878 (-16.53) 0.00 -1.336 (-7.33) 0.00 -1.992 (-6.85) 0.00 -2.242 (-5.20) 0.00

PIN **

Cost

-1.483 ** -11.375 ** (-3.21) (-10.08) 0.00 0.00 -0.782 -14.411 ** (-1.16) (-10.97) 0.26 0.00

Panel B Inf. Exp. Inf. Pr. Bad Trades Trades News

Pr. Inf. Event Const.

0.240 * (2.38) 0.03 0.445 * (2.62) 0.02

Brdth

Trade

α

µ

αµ

1.080 ** -0.724 ** -0.184 (2.98) (-3.50) (-1.96) 0.01 0.00 0.06

δ

Zero

4.680 (11.40) 0.00 ** -11.012 ** 4.965 (-29.75) (11.77) 0.00 0.00 ** -8.606 ** 3.552 (-10.71) (10.59) 0.00 0.00 ** -6.958 ** 3.559 (-5.27) (10.04) 0.00 0.00

Vol.

Over

4.298 (1.74) 0.10 4.362 (1.32) 0.20

-1.535 (-1.54) 0.14 -2.822 * (-2.66) 0.01

0.038 (0.77) 0.45 0.108 * (2.25) 0.04

18.086 * (2.54) 0.02 20.108 * (2.23) 0.04

Uninf. Buys

Uninf. Sells

εb

εs

R2

0.106 (0.72) 0.48

0.305 (12.55) 0.00 0.135 (5.08) 0.00 0.113 (9.79) 0.00 0.262 (9.81) 0.00 0.300 (12.64) 0.00 0.304 (12.81) 0.00

-0.476 ** 0.994 ** (-2.89) (12.46) 0.01 0.00

**

**

0.304 ** (3.92) 0.00 -0.243 (-1.68) 0.11

Brdth

Vol.

**

**

∆

Illiq.

-10.362 ** (-20.91) 0.00 **

Turn

0.255 ** (3.52) 0.00

R2

1.650 * 0.345 (2.82) (14.63) 0.01 0.00 1.851 ** 0.322 (3.21) (16.40) 0.00 0.00

Table VII Average Book to Market, Debt to Equity, and Percent of Companies Delisting or Merging by R-Square Portfolio R-square is calculated as in Table I. Each year non-financial, non-utility stocks which are common ordinary shares and listed on NYSE, AMEX or NASDAQ with 52 weeks of weekly returns are sorted into ten NYSE-breakpoint portfolios based on R-square. For each data item averages are calculated for each R-square portfolio, for each year t . The average across 1983 through 2003 is presented in the table below. Book to Market is calculated as the ratio of fiscal year end Compustat book equity to December-end market capitalization. Book equity is calculated following Cohen, Polk, and Vuolteenaho (2003). Debt to Equity is calculated as the ratio of [Long Term debt (Data 9) + Current Liabilities (Data 34)] to December-end market capitalization. Delisted is the percentage of firms which delist in the year following presence in the given portfolio. Delistings are counted only if the CRSP delisting code (DLSTCD) is in the range from 535 through 591, except 570. Mergers are CRSP delisting codes from 200 through 290, none are excluded.

2

R Portfolio Rank 1 2 3 4 5 6 7 8 9 10 All Portfolios

Book to Market 1.076 0.982 0.892 0.802 0.739 0.663 0.621 0.582 0.526 0.541 0.852

Prior Dec. Book to Market 0.975 0.881 0.825 0.745 0.682 0.632 0.580 0.544 0.511 0.531 0.789

Debt to Equity 1.139 0.962 0.909 0.721 0.728 0.490 0.448 0.424 0.389 0.406 0.828

51

Prior Dec. Debt to Equity 0.828 0.679 0.676 0.589 0.525 0.444 0.388 0.390 0.365 0.395 0.628

Delisted within 1 Yr (%) 6.78 4.40 3.65 2.52 2.04 1.27 0.88 0.69 0.19 0.13 3.80

Merger within 1 Yr (%) 4.81 4.82 4.88 4.89 4.26 3.74 3.79 3.87 3.37 2.20 4.65

Table VIII Time Series Average of Cross-Sectional Regressions of Market Model R-Square on Book to Market, Debt to Equity, and Information Environment Variables For each year t from 1983 through 2003 a cross-sectional OLS regression is run of ln(R-square/(1-R-square)) on the environmental variables described in Table I and book to market and debt equity as described in Table VII. The time series average of the coefficients are presented below. t-stats are corrected for autocorrelation using the Newey-West (1987) correction. All independent variables are transformed by adding one and taking the natural log. lag

(1) Mean

Const.

lag

BTM DEME

Size

Age

Analyst

Inst.

Count

Own.

Trade Brdth

Cost

Zero Illiq.

Vol.

Vol.

Turn

∆

Over

Brdth

-1.905 ** -0.834 ** (t-stat) (-16.48) (-10.79) p-value 0.00 0.00

(2) Mean

-2.209 ** (t-stat) (-20.20) p-value 0.00 (3) Mean -1.907 ** (-16.47) 0.00 (4) Mean -9.847 ** (-39.18) 0.00 (5) Mean -9.782 ** (-50.12) 0.00 (6) Mean -9.855 ** (-39.16) 0.00 (7) Mean -5.839 ** (-21.28) 0.00 (8) Mean -7.229 ** (-36.79) 0.00 (9) Mean -3.088 ** (-32.58) 0.00 (10) Mean -6.930 ** (-21.75) 0.00

-0.351 ** (-9.51) 0.00 -0.808 ** -0.035 (-8.46) (-0.78) 0.00 0.44 0.038 (0.81) 0.43 -0.002 (-0.06) 0.95 0.050 -0.013 (1.07) (-0.55) 0.30 0.59 -0.033 (-0.90) 0.38 -0.007 (-0.30) 0.77 -0.213 ** 0.013 (-9.04) (0.57) 0.00 0.57 0.042 0.000 (1.71) (-0.02) 0.10 0.98

R2 0.042 (4.64) 0.00

0.411 (26.11) 0.00 0.408 (29.70) 0.00 0.411 (26.07) 0.00 0.168 (11.55) 0.00 0.160 (9.69) 0.00

** ** ** ** **

0.187 ** (11.51) 0.00

0.018 (2.13) 0.05 0.039 (4.70) 0.00 0.019 (2.19) 0.04 0.037 (4.46) 0.00

*

0.144 (11.37) 0.00 ** 0.114 (9.54) 0.00 * 0.204 (15.43) 0.00 ** 0.112 (10.30) 0.00

** ** ** **

0.661 (4.70) 0.00 0.738 (5.76) 0.00 0.967 (4.74) 0.00 0.605 (5.22) 0.00

**

1.441 ** -1.569 ** (5.26) (-2.95) 0.00 0.01 ** 0.373 -2.143 ** (1.37) (-3.44) 0.19 0.00 ** 3.380 ** -3.491 ** (15.06) (-3.80) 0.00 0.00 ** 0.871 * -2.471 ** (2.71) (-3.12) 0.01 0.01

-1.193 ** (-10.71) 0.00 0.136 ** (8.42) 0.00

0.412 * (2.42) 0.02

-0.719 ** (-4.06) 0.00

0.052 (2.04) 0.06

31.529 ** (6.05) 0.00 22.398 ** (6.38) 0.00

3.648 (6.97) 0.00 3.474 (6.85) 0.00 3.397 (5.88) 0.00 3.103 (6.17) 0.00

0.014 (4.10) 0.00 0.044 (4.96) 0.00 0.325 (15.67) 0.00 0.323 (15.70) 0.00 0.325 (15.67) 0.00 ** 0.358 (15.51) 0.00 ** 0.363 (16.73) 0.00 ** 0.348 (17.01) 0.00 ** 0.369 (17.02) 0.00

Table IX Time Series Average of Cross-Sectional Regressions of Breadth of Institutional Ownership on Asymmetric Information Variables For each year t from 1983 through 2003 a cross-sectional OLS regression is run of ln(B/(1-B)), where B is Breadth of Institutional Ownership, on the estimates of probability of an informed trade (PIN), Probability of an Information Event (α), Informed Trades (µ), Expected Informed Trades (αµ), Uninformed Buys(ε b), Uninformed Sells (εs), Prob. Bad News (δ) as described in Table V. B is set to 0.0001 if B is zero, otherwise B is Breadth. The time series average of the coefficients are presented below. t-stats are corrected for autocorrelation using the Newey-West (1987) correction. All variables are transformed by adding one and taking the natural log.

(1) Mean (t-stat) p-value (2) Mean

(3) Mean (4) Mean (5) Mean (6) Mean (7) Mean (8) Mean

Const. 0.661 (11.49) 0.00 -3.333 (-39.73) 0.00 -1.005 (-29.33) 0.00 -2.422 (-5.44) 0.00 -1.809 (-7.98) 0.00 -1.134 (-6.98) 0.00 -2.284 (-5.98) 0.00 -2.327 (-5.58) 0.00

PIN **

**

**

**

**

**

Inf. Trades

α

µ

Exp. Inf. Trades

Pr. Bad News

Uninf. Buys

Uninf. Sells

αµ

δ

εb

εs

-15.678 ** (-25.10) 0.00

**

**

Pr. Inf. Event

-16.600 (-20.90) 0.00 -13.595 (-29.14) 0.00 -13.380 (-31.97) 0.00 -16.237 (-24.24) 0.00 -11.090 (-10.96) 0.00 -11.257 (-10.09) 0.00

**

**

**

**

**

**

6.864 (15.80) 0.00 7.279 (12.87) 0.00 7.030 (14.60) 0.00 5.406 (23.47) 0.00 7.151 (13.40) 0.00 5.402 (22.23) 0.00 5.438 (19.49) 0.00

**

**

**

0.317 ** (3.17) 0.00

**

0.379 ** (3.35) 0.00

**

0.260 (0.77) 0.45

**

0.329 ** (3.19) 0.00

**

0.320 ** (3.08) 0.01

53

R2 0.364 (10.00) 0.00 0.304 (30.16) 0.00 0.701 (32.33) 0.00 0.775 (72.97) 0.00 0.778 (73.29) 0.00 0.710 (36.59) 0.00 0.783 (60.70) 0.00 0.775 (71.64) 0.00

Table X Time Series Average of Cross-Sectional Regressions of Breadth of Institutional Ownership on Environmental Variables For each year t from 1983 through 2003 a cross-sectional OLS regression is run of ln(B/(1-B)), where B is Breadth of Institutional Ownership, on the enviromental variables described in Table I. B is set to 0.0001 if B is zero, otherwise B is Breadth. The timeseries average of the coeffiecients are presented below. t-stats are corrected for autocorrelation using the Newey-West (1987) correction. All variables are transformed by adding one and taking the natural log.

Year

(1) Mean

(t-stat) p-value

(2) Mean (3)

(t-stat) p-value Mean

(4) Mean (5) Mean (6) Mean

Const.

Analyst

Inst.

Trade

Count

Own.

Cost

Size

Age

-14.512 ** (-28.68) 0.00

0.523 ** (18.48) 0.00

0.096 ** (13.67) 0.00

0.063 ** (6.39) 0.00

-16.125 (-21.59) 0.00 -17.372 (-26.59) 0.00 -16.164 (-21.69) 0.00 -5.726 (-27.29) 0.00 -5.862 (-13.99) 0.00

0.640 ** (15.59) 0.00 0.699 ** (19.05) 0.00 0.634 ** (16.09) 0.00

0.130 (16.96) 0.00 0.140 (16.21) 0.00 0.131 (16.31) 0.00 0.218 (10.86) 0.00 0.382 (11.87) 0.00

0.172 ** (9.98) 0.00

** ** ** ** **

** ** ** ** **

0.172 ** (9.29) 0.00 0.824 ** (25.53) 0.00

2.535 ** (13.64) 0.00

Illiq.

-2.786 ** (-4.26) 0.00 -3.252 (-3.99) 0.00 -3.422 (-3.85) 0.00 -3.233 (-4.22) 0.00 -7.746 (-4.19) 0.00 -12.654 (-3.67) 0.00

Turn

∆

Volume

Over

Breadth

0.029 (1.81) 0.09

6.785 (1.20) 0.24

-0.014 (-0.98) 0.34 0.013 (0.76) 0.45

26.761 (3.11) 0.01 26.583 (3.11) 0.01 22.965 (3.46) 0.00 16.724 (1.88) 0.07 37.843 (3.42) 0.00

Zero

** ** ** ** **

-0.290 (-1.19) 0.25 -0.183 (-0.79) 0.44 -0.115 (-0.52) 0.61 -0.184 (-0.83) 0.42 -0.675 * (-2.38) 0.03 -0.254 (-0.75) 0.46

Volume -1.258 ** (-7.11) 0.00 -1.357 (-8.05) 0.00 -1.306 (-8.30) 0.00 -1.295 (-9.98) 0.00 -2.878 (-8.09) 0.00 -5.327 (-25.87) 0.00

** ** ** ** **

R

2

0.867 ** 0.817 (2.85) (154.20) 0.01 0.00 ** ** **

**

0.799 (135.93) 0.00 0.795 (142.68) 0.00 0.798 (137.36) 0.00 0.671 (46.46) 0.00 0.503 (31.17) 0.00

Appendix Table 1 Average Country R-Square and Percent of Delisted Companies Average Country R-squares are from Morck, Yeung and Tu (2000) Table 2. The percent delisted is based on a count of all companies list in Datastream and noted as a delisting, exluding financial companies, warrents, preferred shares, unit trusts and stocks listed on foreign markets.

Australia Germany Belgium Brazil Columbia China Chile Canada Czech Denmark Spain Finland France Greece Hong Kong Indonesia India Ireland Italy Japan Korea Mexico Malaysia Holland Norway New Zealand Austria Peru Philippines Pakistan Poland Portugal South Africa Sweden Singapore Taiwan Thailand Turkey U.K. United States Correlation

Average Country 2 R 0.064 0.114 0.146 0.161 0.209 0.453 0.209 0.062 0.185 0.075 0.192 0.142 0.075 0.192 0.150 0.140 0.189 0.058 0.183 0.234 0.172 0.290 0.429 0.103 0.119 0.064 0.093 0.288 0.164 0.175 0.569 0.068 0.197 0.142 0.191 0.412 0.271 0.393 0.062 0.021 -0.425

55

Percent Delisted (%) 0.096 0.202 0.213 0.294 0.031 0.008 0.015 0.207 0.000 0.321 0.203 0.177 0.161 0.156 0.063 0.472 0.072 0.072 0.282 0.089 0.109 0.095 0.104 0.204 0.357 0.244 0.327 0.006 0.046 0.082 0.000 0.379 0.331 0.289 0.036 0.066 0.257 0.043 0.061 0.064