Review of Finance (2013) 17: pp. 1239–1278 doi:10.1093/rof/rfs026 Advance Access publication: October 25, 2012
What Does Stock Ownership Breadth Measure?* JAMES J. CHOI1, LI JIN2 and HONGJUN YAN3 1
Yale School of Management and NBER, 2Oxford University Saı¨d Business School and Peking University Guanghua School of Management, and 3 Yale School of Management
JEL classification: G02, G12, G14
1. Introduction What should we infer about future returns when we see a large number of investors buying a stock they had previously not owned, or a large number of investors completely liquidating their holdings of a stock? In this article, we test how changes in ownership breadth—the fraction of market participants with a long position in a given stock—predict the cross-section of stock returns.
*Choi and Yan received support from a Whitebox Advisors research grant administered through the Yale International Center for Finance, Jin received support from the Harvard Business School Division of Research, and Choi received support from the National Institute on Aging (grant P01-AG005842). We thank Yakov Amihud, Warren Bailey, Long Chen, Cam Harvey, David Hirshleifer, Harrison Hong, Christine Jiang, Ron Kaniel, Owen Lamont, Akiko Watanabe, and audience members at Berkeley, CICF Conference, Frontiers in Finance Conference, NYU Five Star Conference, Emory, Fudan, Goldman Sachs Asset Management, Harvard, HKUST, INSEAD, Michigan, Nanyang Technological University, National University of Singapore, Oxford, Peking University, Singapore Management University, SUNY Binghamton, University of Rochester, and Washington University in St Louis for their comments. We are indebted to Ben Hebert and Jung Sakong for their research assistance, and to Fenghua Wang and Dora Liu for their help in calculating all the breadth measures used in the article. ß The Authors 2012. Published by Oxford University Press on behalf of the European Finance Association. All rights reserved. For Permissions, please email: [email protected]
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Abstract. Using holdings data on a representative sample of all Shanghai Stock Exchange investors, we show that increases in ownership breadth (the fraction of market participants who own a stock) predict low returns: highest change quintile stocks underperform lowest quintile stocks by 23% per year. Small retail investors drive this result. Retail ownership breadth increases appear to be correlated with overpricing. Among institutional investors, however, the opposite holds: stocks in the top decile of wealth-weighted institutional breadth change outperform the bottom decile by 8% per year, consistent with prior work that interprets breadth as a measure of short-sales constraints.
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Most theoretical models find that short-sales constraints lead to overvaluation (e.g., Miller, 1977; Harrison and Kreps, 1978; Allen et al., 1993; Scheinkman and Xiong, 2003), but there are exceptions. For example, Diamond and Verrecchia (1987) argue that short-sales constraints do not bias stock prices on average when investors correctly anticipate that pessimistic investors are sitting on the sidelines. Bai et al. (2006) show that, depending on the relative importance of informed versus uninformed trading motives, short-sales constraints can increase, decrease, or have no impact on stock prices. 2 Cen et al. (2011) find that mutual fund breadth changes tend to negatively predict returns when the Baker and Wurgler (2006, 2007) sentiment index experiences large absolute movements. Lehavy and Sloan (2008) find that US mutual fund ownership breadth change is positively autocorrelated, and that controlling for future breadth changes, current breadth change negatively predicts future returns. 3 There were no equity derivatives prior to the end of 2005. From 2005 to 2007, eleven Shanghai Stock Exchange companies (out of over 800 total listed companies) were allowed to issue put warrants. See Xiong and Yu (2011) for more details on these warrants.
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Chen, Hong, and Stein (2002) (hereafter CHS) argue that in a market with short-sales constraints, when an investor holds no long position in a stock, he is likely to have negative information about the stock’s fundamental value. Due to short-sales constraints, this negative information is only partially incorporated into the stock’s price. Thus, when ownership breadth is low, there is a large amount of negative news missing from the stock’s price, and the stock’s future returns will be low.1 Empirically testing this theory is challenging because it requires a representative sample of all investors who face short-sales constraints, which is usually not available at high frequency. Previous empirical tests of ownership breadth have measured ownership breadth among US mutual funds, which are not representative of all US investors who face short-sales constraints. The mismatch between available data and theory may explain why the evidence on ownership breadth has been mixed to date. Because ownership breadth level is close to a permanent characteristic for a stock, CHS argue that focus should be placed on ownership breadth changes—essentially controlling for a stock fixed effect. CHS find that cross-sectionally, stocks that are held by fewer mutual funds this quarter than last quarter subsequently underperform stocks with mutual fund ownership breadth increases from 1979 to 1998. But Nagel (2005) expands the CHS sample by five years and finds that there is no relationship on average between mutual fund ownership breadth changes and future returns over the longer sample.2 We use a new holdings dataset from the Shanghai Stock Exchange (SSE) that is uniquely suited to testing the CHS theory. The investors in the data are a random, survivorship bias-free sample of all investors in the SSE. During our 1996 to 2007 sample period, short sales were strictly prohibited in China, and there was minimal equity derivatives activity.3 Therefore, our
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sample is also representative of all investors in the market who face short-sales constraints. We find, in sharp contrast to the CHS prediction, that high breadth change stocks subsequently underperform low breadth change stocks when we define ownership breadth as CHS do—the percent of all market participants who have a long position in a stock, giving equal weight to each investor. The annualized difference in the four-factor alpha between the highest and lowest quintiles of equal-weighted total breadth change (which is not public information) in the first month after portfolio formation is 23%, with a t-statistic of 9.7. Abnormal returns are present on both the long and short sides of the hypothetical zero-investment portfolio and persist for 5 months after portfolio formation. (Data on each stock’s monthly breadth portfolio assignments are available on the second author’s website.) This finding may be consistent with the lay theory recounted by Lewis (1989): “The first thing you learn on the trading floor is that when large numbers of people are after the same commodity, be it a stock, a bond, or a job, the commodity quickly becomes overvalued.” In other words, ownership breadth measures popularity among noise traders who are able to move prices. Indeed, the breadth measure we adopt from CHS is essentially a measure of breadth among retail investors in China, since retail investors vastly outnumber institutions in the market. Portfolios formed on equal-weighted breadth change among only retail investors have returns that are nearly identical to portfolios formed on equal-weighted total breadth change. Lewis is silent on when a commodity becomes popular and therefore overvalued. We find that equal-weighted retail breadth change’s contemporaneous correlation with a stock’s return is negative. Therefore, retail investors may be causing misvaluation by leaning against price movements and delaying full price adjustment to fundamental news. As we put more weight on sophisticated investors in our breadth measure, the results change. When we redefine total breadth so that investors are weighted by their lagged stock market wealth, the annualized four-factor alpha difference between the highest and lowest total breadth change portfolios attenuates to 5% (still statistically significant). Further restricting the population over which we calculate wealth-weighted breadth change to institutions only, we reproduce the original CHS result in a completely new sample: highest decile wealth-weighted institutional breadth change stocks outperform lowest decile wealth-weighted institutional breadth change stocks. The annualized difference in the four-factor alphas is 8%, with a t-statistic of 2.6. This last result suggests that when ownership breadth is measured within the population of all sophisticated investors that observe unbiased signals of
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the stock’s fundamental value but cannot short, it functions more in accordance with the CHS theory, primarily reflecting how much negative information is not in the stock price due to short-sales constraints. The CHS model does not have unsophisticated traders who observe no fundamental signals, which could be why it no longer applies once ownership breadth is measured over a population of predominantly unsophisticated retail investors. On average, institutional trades against retail investors are profitable before transactions costs; if a stock’s month-over-month change in the log fraction of shares owned by institutions is one standard deviation higher, its abnormal return in the subsequent month is 3.5% higher on an annualized basis. But the significance of institutional ownership percentage changes disappears once we control for equal-weighted retail breadth changes and wealth-weighted institutional breadth changes, while both breadth change measures remain significant return predictors. In other words, an institution buying shares from an individual positively predicts future returns only if the individual is completely liquidating his position or the institution previously had no position in the stock. This result indicates that how many shares in aggregate change hands between institutions and individuals does not matter as much as how many of each investor type start and end with holdings of the stock, thus demonstrating the value of disaggregated investor-level data for forecasting future returns. Because we only have ownership data from China, we have no direct evidence on the extent to which our results generalize to other countries, just as any empirical study using only US data cannot draw any conclusions about whether its results extend to non-US markets. We believe that even if our results were to apply only to China, they are of general interest given the significance of the Chinese stock market, which had 139 million investment accounts at year-end 2007 (China Securities Regulatory Commission, 2009) and the second largest market capitalization among all national stock markets at year-end 2010. Although much of our data come from a time when the Chinese stock market was quite young, all of our main results hold in the second half of our sample period, suggesting that they continue to apply to China’s market today. Nevertheless, similarities between China and other markets in retail investor behavior and stock return patterns give us some reason to think that ownership breadth operates in the same way outside of China. Chinese retail investors exhibit the disposition effect, excessive trading, home bias, and under-diversification, just as US investors do (Chen et al., 2007; Feng and Seasholes, 2008). Chen et al. (2010) test eighteen variables that have been shown to predict cross-sectional stock returns in the US market and find that in the 1995–2007 period, all eighteen variables’ point estimates in
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2. Data Description Our ownership breadth data come from the SSE. At the end of 2007—the last year of our sample period—the 860 stocks traded on the SSE had a total market capitalization of $3.7 trillion, making it the world’s sixth largest 4
These studies have adopted a number of proxies to measure short-sales constraints, such as analyst forecast dispersion (Diether et al., 2002; Yu, 2011), short interest (Asquith et al., 2005; Boehme et al., 2006), the introduction of traded options (Figlewski and Webb, 1993; Danielsen and Sorescu, 2001; Mayhew and Mihov, 2005), and lending fees (Jones and Lamont, 2002; D’Avolio, 2002; Reed, 2002; Geczy et al., 2002; Mitchell et al., 2002; Ofek and Richardson, 2003; Ofek et al., 2004; Cohen et al., 2007). 5 Examples include Lee, Shleifer, and Thaler (1991), Baker and Wurgler (2006, 2007), Cornelli et al. (2006), Kumar and Lee (2006), Qiu and Welch (2006), Tetlock (2007), Da et al. (2011), Hwang (2011), Baker et al. (2012), and Ben-Rephael et al. (2012). 6 See, for example, Gruber (1996), Daniel et al. (1997), Zheng (1999), Chen et al. (2000), Seasholes and Wu (2007), Frazzini and Lamont (2008), Kaniel et al. (2008), Barber et al. (2008), Campbell et al. (2009), Kelley and Tetlock (2012), and Barber, Odean, and Zhu (2012).
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univariate Fama–MacBeth (1973) regressions have signs consistent with the US evidence, and five are statistically significant, compared with eight significant coefficients for the US markets during this same period. In addition to the literature on ownership breadth, our article is related to research that attempts to empirically detect the price impact of short-sales constraints,4 research on investor sentiment measures,5 and research on the portfolio performance of institutional versus individual investors.6 The remainder of the article is organized as follows. Section 1 describes our data, and Section 2 defines the variables we use in the analysis. Section 3 presents the main tests of ownership breadth’s ability to predict the cross-section of stock returns. Section 4 shows how returns, breadth, and institutional ownership behave around the formation date of portfolios sorted on breadth change, which gives us insight into the decisions that result in breadth changes and why breadth changes might be related to future returns. Section 5 explores the relationship between breadth changes and changes in institutional ownership percentages. Section 6 compares the return-predicting ability of retail breadth changes in months with and without earnings announcement to assess whether breadth changes reflect anything more than trading by investors with private information. Section 7 investigates the extent to which breadth changes predict future returns via a Merton (1987) investor recognition channel, and Section 8 discusses the different implications that ownership initiations versus discontinuations have for future returns. Section 9 concludes.
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Beginning in April 2005, nontradable shares began to be converted to tradable status, although the conversion process was slow enough that as of year-end 2007, 72% of total Chinese market capitalization remained nontradable. Converted tradable shares were subject to a one-year lockup, and investors holding more than a 5% stake were subject to selling restrictions for an additional 2 years. Dropping returns starting in May 2006 (the month after the first formerly non-tradable shares became liquid and thus begin to appear in our holdings data) does not qualitatively affect our breadth portfolio alpha estimates in Table V, except that in the shorter sample, the long-short wealth-weighted total breadth change portfolio’s three-factor alpha is significant at the 1% level, and the long-short wealth-weighted institutional breadth change portfolio’s one-factor alpha is significant at the 10% level and the four-factor alpha is significant at the 5% level. 8 Further details of the sampling process can be obtained from the authors.
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stock exchange behind NYSE, Tokyo, Euronext, Nasdaq, and London. Mainland China’s other stock exchange, the Shenzhen Stock Exchange, had a $785 billion market capitalization at year-end 2007. By year-end 2010, China’s stock market had the second largest market capitalization among all countries of the world, behind only the USA. Almost all SSE shares are A shares, which only domestic investors could hold until 2003. At year-end 2007, A shares constituted over 99% of SSE market capitalization. B shares are quoted in US dollars and can be held by foreign and (since 2001) domestic investors. Shares are further classified into tradable and nontradable shares. Nontradable shares have the same voting and cashflow rights as tradable shares and are typically owned directly by the Chinese government (“state-owned shares”) or by governmentcontrolled domestic financial institutions and corporations (“legal person shares”).7 We use the term “tradable market capitalization” to refer to the value of tradable A shares, and “total market capitalization” to refer to the combined value of tradable and nontradable A shares. During our sample period, about 27% of SSE market capitalization was tradable. To trade on the SSE, both retail and institutional investors are required to open an account with the Exchange, at which point they must identify themselves to the Exchange as an individual or an institution. Each account uniquely and permanently identifies an investor, even if the account later becomes empty. Investors cannot have multiple accounts. The data assembled by the Exchange for this article consists of the entire history of SSE tradable A-share holdings from January 1996 to May 2007 for a representative random sample of all accounts that existed at the end of May 2007. Since there are far fewer institutional accounts than retail accounts, the Exchange over-sampled institutional investors in order to ensure that a meaningful number of institutional accounts were extracted.8 The market-wide statistics computed from these account data are reweighted to adjust for the over-sampling of institutional investors. The sample contains
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Table I. Portfolio and position summary statistics This table reports (in RMB), separately for retail and institutional investors at the beginning of each year in our sample, the mean and median of investors’ individual stock position values and the mean and median of investors’ total stock portfolio value. Retail investors Individual position value
Total portfolio value
Individual position value
Total portfolio value
Mean
Median
Mean
Median
Mean
Median
Mean
Median
8,069 11,091 11,241 12,536 16,879 17,528 15,047 13,768 14,040 11,261 17,915 21,992
3,900 5,680 5,696 6,100 7,920 8,477 7,220 6,349 6,040 4,308 5,627 6,670
22,179 28,735 30,802 33,955 43,468 46,671 40,557 37,537 38,423 30,463 46,182 54,759
8,680 12,375 13,313 14,177 17,908 19,895 17,159 15,025 14,360 10,390 13,172 13,620
738,976 802,767 1,090,328 2,400,134 3,114,389 2,389,368 2,026,537 2,320,780 3,242,438 4,107,368 7,195,547 8,153,493
54,375 47,880 42,205 40,358 36,960 34,700 45,570 37,400 55,680 54,810 134,456 185,187
3,572,650 2,921,252 3,788,510 8,294,886 9,977,062 8,211,759 8,309,475 9,515,146 13,177,925 16,793,688 26,866,712 32,808,349
198,102 119,175 86,440 102,264 118,080 133,313 184,118 216,850 286,178 203,138 288,191 330,908
both currently active and inactive accounts, so there is no survivorship bias, and in expectation, a constant fraction of the accounts extant at any date are represented. The number of accounts in the sample grows from 36,349 retail accounts and 360 institutional accounts to 384,709 retail accounts and 20,727 institutional accounts from January 1996 to May 2007. Holdings data are aggregated at the Exchange into stock-level measures. The aggregation is carried out under arrangements that maintain strict confidentiality requirements to ensure that no individual account data are disclosed. Table I shows the mean and median value in renminbi (RMB) of an investor’s holdings in a single company, conditional on investing in the company, as well as the mean and median value of an investor’s total stock portfolio. For most of the sample period, the exchange rate was about 8.3 RMB per US dollar, but it then fell to 7.7 RMB per US dollar from July 2005 to May 2007. Retail investors start with a mean (median) stock position value of 8,069 (3,900) RMB and a mean (median) total portfolio value of 22,179 (8,680) RMB in 1996. By 2007, the last year of our sample, these values have increased to 21,992 (6,670) RMB and 54,759 (13,620) RMB, respectively. Even adjusting for the 16% rise in the Chinese consumer price index over this period, this represents a sizable increase in the position and portfolio values of retail investors. Institutions
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1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
Institutional investors
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3. Variable Definitions Following CHS, we define the equal-weighted total ownership breadth change of stock i in month t as follows. We first restrict the sample to investors who have a long position in at least one SSE stock at the end of both t 1 and t. This restriction ensures that the breadth change measure captures only the trading activity of existing market participants, rather than changes in the investor universe due to new market participants entering and institutions dissolving.9 Equal-weighted total ownership breadth change is the difference between the end of t 1 and the end of t in the fraction of these subsample investors who own stock i. We obtain equal-weighted retail breadth change and equal-weighted institutional breadth change by further restricting the investor subsample to retail investors or institutional investors. Stocks almost never have an empty set of retail owners in our sample, but zero ownership is more frequent within our institutional sample, particularly among small-cap stocks. At each time period, we do not calculate breadth change for stocks that have zero owners in the relevant subsample at either t 1 or t, since the breadth change measure we obtain would be censored. A stock’s equal-weighted total ownership breadth increases when one investor partially liquidates her position in the stock to sell to one or more investors who previously did not own the stock, or one investor completely 9
Portfolio returns are quite similar if we instead require that investors have a long position at either t 1 or t. When we construct wealth-weighted breadth change, described later in this section, using this alternative sample definition, we weight investors that are not in the market at t 1 by their stock market wealth at the end of t.
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start with a mean (median) stock position value of 738,976 (54,375) RMB, and a mean (median) total portfolio value of 3,572,650 (198,102) RMB in 1996. Their mean (median) stock position value increased to 8,153,493 (185,187) RMB and their total portfolio value increased to 32,808,349 (330,980) RMB by 2007. Institutional investors’ portfolio values grew much more quickly than retail investors’, particularly for the means. The median institutional investor portfolio is strikingly small throughout the sample period—far less than 100,000 USD—and the large difference between the mean and the median values indicates that the portfolio value distribution is extremely right-skewed. We obtain stock return, market capitalization, earnings announcement date, and accounting data from the China Stock Market & Accounting Research Database (CSMAR).
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v2At
where Wv,t is the SSE stock portfolio value of investor v at month t’s market open, Vi,t is the set of subsample investors who held stock i at the end of month t, and At is the entire subsample of investors who owned at least one SSE stock at the end of both t 1 and t. Wealth-weighted retail breadth change and wealth-weighted institutional breadth change are defined analogously over their respective investor populations. Breadth change can be decomposed into the variables IN and OUT. Equal-weighted IN is the percent of subsample investors who had a zero position in stock i at the end of t 1 and a positive position at the end of t. Equal-weighted OUT is the percent of subsample investors who moved from a positive position to a zero position in stock i between the ends of t 1 and t. By construction, equal-weighted breadth change is equal-weighted IN minus equal-weighted OUT. Wealth-weighted IN and OUT are defined analogously. For example, wealth-weighted IN is the month t opening SSE stock portfolio value of subsample investors who moved from a zero position to a positive position in stock i between t 1 and t divided by the month t opening SSE stock portfolio value of all subsample investors. Our main cross-sectional analysis involves evaluating the return performance of portfolios formed on breadth changes. We estimate one, three, and four-factor alphas, where the factor portfolio returns capture CAPM beta, size, value, and momentum effects. The market portfolio return is the 10
Small investors have fewer resources with which to gather information. Natural selection arguments such as that of Friedman (1953) may also lead to rational individuals becoming overrepresented among wealthy investors. However, Yan (2008) shows that the natural selection mechanism does not robustly reduce irrational investors’ wealth share.
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liquidates her position by selling her shares to two or more investors who previously did not own the stock. Note that market clearing does not constrain a stock’s equal-weighted total ownership breadth change to be zero. To assess the extent to which unsophisticated investors drive the negative correlation between total ownership breadth change and future returns, we use an alternative measure of ownership breadth not found in CHS that de-emphasizes small investors by weighting investors by the value of their SSE portfolio at the beginning of the month.10 To calculate wealth-weighted total ownership breadth change at t, we again restrict the sample to investors who have a long position in at least one SSE stock at the end of both t 1 and t. Wealth-weighted ownership breadth change is P P Wv, t Wv, t v2Vi, t v2Vi, t1 P ð1Þ Wv, t
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Whenever possible, we use the book equity value that was originally released to investors. If this is unavailable, we use book equity that has been restated to conform to revised Chinese accounting standards.
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composite Shanghai and Shenzhen market return, weighted by tradable market capitalization. The risk-free return is the demand deposit rate. We construct size and value factor returns (SMB and HML, respectively) for the Chinese stock market according to the methodology of Fama and French (1993), but using the entire Shanghai/Shenzhen stock universe to calculate percentile breakpoints. We form SMB based on total (i.e., tradable plus nontradable) market capitalization and HML based on the ratio of book equity to total market capitalization, weighting stocks within component subportfolios by their tradable market capitalization.11 We construct the momentum factor portfolio MOM following the methodology described on Kenneth French’s website. We calculate the 50th percentile total market capitalization at month-end t 1 and the 30th and 70th percentile cumulative stock returns over months t 12 to t 2, again using the entire Shanghai/Shenzhen stock universe to calculate percentile breakpoints. The intersections of these breakpoints delineate six tradable market capitalization-weighted subportfolios for which we compute month t returns. MOM is the equally weighted average of the two recent winner subportfolio returns minus the equally weighted average of the two recent loser subportfolio returns. We control for other possible predictors of returns using Fama–MacBeth (1973) regressions, where the predictor variables are the stock’s breadth change (defined in various ways), log of total market capitalization, book-to-market ratio (the value at year-end 1 is used as the predictor from July of year through June of year þ 1), return during the last year excluding the prior month, return during the prior month, sum of monthly turnover during the prior quarter, change in the log percent of tradable A shares owned by institutions during the prior month (as measured in our ownership data), Amivest liquidity ratio (described further below) during the prior month, shadow cost of incomplete information, and two dummies for whether the stock’s share trading volume during the prior week was in the top tenth or bottom tenth of the ten most recent weeks (Gervais et al., 2001). We operationalize the Amivest liquidity ratio as the sum of the stock’s yuan trading volume over 1 month divided by the sum of the stock’s absolute daily returns over that month. Higher values of the liquidity ratio correspond to lower price impacts of trading, and hence higher liquidity. The shadow cost of incomplete information, l, captures abnormal returns due to Merton’s (1987) “investor recognition hypothesis” that investors neglect to hold stocks
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they are unaware of, causing the investors who do hold these neglected stocks to sacrifice diversification and hence demand a higher expected return. Investor recognition is closely related to ownership breadth changes, so it is important to explore the extent to which breadth changes predict returns through the investor recognition channel. We adopt the operationalization of l used by Bodnaruk and Ostberg (2009): it ¼ 2:5 it2 xit
1 Mit , Mit
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where 2.5 is an arbitrary constant representing aggregate investor risk aversion, it2 is the variance of the residuals from regressing stock i’s excess monthly returns on Chinese market excess returns from month t 35 to month t; xit is stock i’s tradable A-share market capitalization as a fraction of total Chinese tradable A-share market capitalization at month-end t; and Mit is the number of investors holding stock i at month-end t divided by the total number of investors at month-end t. In calculating Mit, we define “total number of investors” as all investors with at least one long SSE position at t (and do not condition on t 1 holdings). Table II displays summary statistics for the variables used in the cross-sectional analysis. Because the number of stocks listed on the SSE expanded rapidly during our sample period, we adopt the following procedure in order to keep later time periods from dominating the summary statistics. We calculate separately for each month the mean and standard deviation of each variable. The table reports the time-series average of these monthly mean and standard deviation series. The summary statistics for equal-weighted retail breadth change are nearly identical to those for equal-weighted total breadth change, since retail investors vastly outnumber institutions. Because institutions have disproportionately large stock holdings, wealth-weighted total breadth changes do not follow wealth-weighted retail breadth changes nearly as closely. Table III shows the mean and standard deviation of breadth changes separately for each year of our sample. The mean equal-weighted breadth changes are close to zero in every year; the largest magnitude occurs in 1996, when the mean equal-weighted institutional breadth change takes on a value of only 0.069%. The average wealth-weighted breadth changes experience considerably more variation, particularly among institutions. The average wealth-weighted institutional breadth change experiences two valleys of 0.446% and 0.525% in 1996 and 2003, respectively. The cross-sectional standard deviation of breadth changes generally falls as the sample period
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Table II. Summary statistics of variables used in cross-sectional analysis
Returni, tþ1 Equal-weighted total breadthi,t Equal-weighted retail breadthi,t Equal-weighted retail INi,t Equal-weighted retail OUTi,t Equal-weighted institutional breadthi,t Wealth-weighted total breadthi,t Wealth-weighted retail breadthi,t Wealth-weighted institutional breadthi,t Wealth-weighted institutional INi,t Wealth-weighted institutional OUTi,t li,t log(Institutional ownershipi,t) log(Total market capi,t) Book-to-marketi,t Returni,t 11 ! t 1 Prior quarter turnoveri,t Liquidity ratioi,t High relative volumei,t Low relative volumei,t
Mean
Standard deviation
1.944 0.002 0.002 0.067 0.069 0.009 0.031 0.025 0.114 0.542 0.656 0.011 0.009 14.562 0.409 17.413 1.105 0.936 0.124 0.145
9.422 0.051 0.051 0.074 0.075 0.194 0.265 0.115 2.123 1.558 1.684 0.039 0.806 0.786 0.193 37.316 0.603 1.387 0.275 0.271
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The cross-sectional means and standard deviations are calculated separately within each month. The table reports the time-series average of these means and standard deviations. Equal-weighted total breadth change is the change between month-ends t 1 and t in the number of investors holding stock i divided by the total number of investors. Wealthweighted total breadth change is like equal-weighted total breadth change, but weights investors by the value of their SSE stock portfolio at the open of month t. Institutional and retail breadth changes are defined analogously on the retail or institutional subsample. Equal-weighted retail IN is the percent of retail investors who held no position in the stock at t 1 but held a positive position in it at t. Equal-weighted retail OUT is the percent of retail investors who held a positive position in the stock at t 1 but held no position in it at t. Wealth-weighted institutional IN and OUT are defined analogously over institutions, weighting them by their SSE stock portfolio value at the open of month t. Breadth changes, IN, and OUT are expressed as percentages, so that a 1% value is coded as 1, rather than 0.01. The variable li,t is the Merton shadow cost of incomplete information defined in Equation (2), and log(Institutional ownershipi,t) is the change between month-ends t 1 and t in the log of the fraction of the stock’s tradable A shares held by institutions. Returni,t 11 ! t 1 is the stock’s cumulative return from month t 11 to t 1. Liquidity ratio is the sum of the stock’s yuan trading volume divided by the sum of the stock’s absolute daily returns during month t. High relative volume and low relative volume are dummies for whether the stock’s share trading volume during the prior week was in the top tenth or bottom tenth of the ten most recent weeks, respectively. The sample is stock-months where there are a positive number of individual investors and a positive number of institutional investors at both t and t 1.
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Table III. Mean and standard deviation of breadth change in each year This table shows the cross-sectional mean and standard deviation (in parentheses below the mean) of the six kinds of breadth change within each year. The means and standard deviations are calculated separately within each month, and we report the time-series average of these means and standard deviations within each year. Equal-weighted breadth change
1996
1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
Total
Retail
Inst.
Total
Retail
Inst.
0.009 (0.177) 0.014 (0.113) 0.000 (0.069) 0.002 (0.054) 0.001 (0.069) 0.002 (0.025) 0.001 (0.014) 0.001 (0.018) 0.000 (0.020) 0.001 (0.012) 0.002 (0.034) 0.004 (0.068)
0.009 (0.177) 0.014 (0.113) 0.000 (0.069) 0.002 (0.054) 0.001 (0.069) 0.002 (0.025) 0.001 (0.014) 0.001 (0.018) 0.000 (0.020) 0.001 (0.012) 0.002 (0.034) 0.004 (0.068)
0.069 (0.486) 0.020 (0.296) 0.016 (0.200) 0.013 (0.159) 0.015 (0.188) 0.012 (0.130) 0.003 (0.129) 0.013 (0.207) 0.005 (0.222) 0.003 (0.192) 0.005 (0.220) 0.003 (0.148)
0.126 (0.455) 0.034 (0.221) 0.027 (0.198) 0.033 (0.295) 0.035 (0.295) 0.024 (0.168) 0.026 (0.214) 0.070 (0.286) 0.020 (0.286) 0.000 (0.329) 0.017 (0.450) 0.017 (0.569)
0.111 (0.461) 0.033 (0.224) 0.025 (0.133) 0.025 (0.097) 0.023 (0.106) 0.010 (0.044) 0.008 (0.035) 0.010 (0.061) 0.009 (0.051) 0.005 (0.054) 0.016 (0.104) 0.024 (0.112)
0.446 (2.505) 0.005 (1.508) 0.147 (4.509) 0.167 (5.160) 0.175 (3.884) 0.211 (2.503) 0.158 (2.536) 0.525 (2.246) 0.067 (1.607) 0.009 (1.291) 0.014 (1.452) 0.000 (1.474)
progresses, with the exception of institutional wealth-weighted breadth changes, which exhibits its greatest dispersion from 1998 to 2000, and total wealth-weighted breadth changes, whose dispersion follows a U-shaped path with respect to time. Table IV contains the correlations among the various breadth measures. Equal-weighted total and retail breadth changes are almost perfectly positively correlated with each other. Equal-weighted institutional breadth changes are mildly positively correlated (0.054) with equal-weighted retail breadth changes. Wealth-weighted retail breadth changes are strongly positively correlated with equal-weighted retail breadth changes, but the correlation coefficient of 0.643 indicates that there is still considerable divergence
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1997
Wealth-weighted breadth change
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Table IV. Correlation of breadth change measures with each other Each month, we calculate the cross-sectional correlation of each breadth measure with the other breadth measures. The table reports the time-series mean of these correlations, with the standard error (computed as the time-series standard deviation of the correlation divided by the square root of the number of months) in parentheses below. *Significant at the 5% level. **Significant at the 1% level. Equal-weighted breadth change Total
Retail
Inst.
Total
Retail
Inst.
1.000** (0.000) 1.000** (0.000)
0.058** (0.016) 0.054** (0.016) 1.000** (0.000)
0.128** (0.028) 0.127** (0.028) 0.294** (0.014) 1.000** (0.000)
0.643** (0.015) 0.643** (0.015) 0.141** (0.016) 0.347** (0.032) 1.000** (0.000)
0.117** (0.015) 0.117** (0.015) 0.305** (0.013) 0.811** (0.026) 0.030* (0.012) 1.000** (0.000)
Inst. Wealth-weighted Total breadth change Retail Inst.
between these two retail breadth change measures. Wealth-weighted institutional breadth change is negatively correlated with retail breadth change, and this negative correlation is stronger with equal-weighted retail breadth change (0.117) than with wealth-weighted retail breadth change (0.030). Wealth-weighted institutional breadth change exhibits only some positive correlation (0.305) with equal-weighted institutional breadth change, showing that large institutions behave differently from small institutions. 4. Main Return Prediction Tests 4.1 FORECASTING 1-MONTH-AHEAD RETURNS
We test the ability of breadth changes to predict the cross-section of returns by using breadth changes to form portfolios. Following CHS, at the end of each month t, we sort stocks into five groups based on tradable market capitalization (0th to 20th size percentile, 20th percentile to 40th size percentile, . . . , 80th percentile to 100th size percentile). Within each size quintile, we form five subportfolios based on breadth change during t, creating a total of 25 subportfolios. The breadth change breakpoints that determine the
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Equal-weighted Total 1.000** breadth change (0.000) Retail
Wealth-weighted breadth change
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12
The average of the long-only test portfolio alphas are not approximately zero mainly because the test portfolios contain only Shanghai Stock Exchange stocks, whereas our factor portfolios contain both Shanghai and Shenzhen Stock Exchange stocks. 13 Although the model of Bai et al. (2006) has only one risky asset and cannot be used to analyze cross-sectional returns directly, their intuition could potentially lead to the implication that ownership breadth increases should predict lower future returns through a
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subportfolio boundaries differ by size quintile, so that all 25 subportfolios contain the same number of stocks. We weight stocks by tradable market capitalization within each subportfolio. To form the “Quintile n” breadth change portfolio, we equally weight across size quintiles the five nth quintile breadth change subportfolios, and hold the stocks for 1 month before re-forming the portfolios at the end of month t þ 1. We adopt this sequential sorting methodology because the volatility of breadth change increases with firm size. If we sorted stocks by breadth change without considering size, very few small firms would be in the extreme quintiles of breadth change. Table V shows the breadth change portfolios’ raw excess returns and alphas generated by time-series regressions. The left half of Panel A shows that returns decrease monotonically with equal-weighted total breadth change. On a raw-return basis, the lowest quintile outperforms the highest quintile by 204 basis points per month, or 24.5% per year, with a t-statistic of 10.2. The lowest quintile has an annualized Sharpe ratio of 1.11, and a (noninvestable) zero-investment portfolio that holds the lowest quintile long and the highest quintile short has a Sharpe ratio of 2.97. In comparison, during this 137-month period, the Sharpe ratio of all SSE A shares weighted by tradable market capitalization was 0.77, and the Sharpe ratio of the US CRSP value-weighted index was 0.49. The return differential between the lowest and highest breadth change quintiles barely falls when we adjust the return using the CAPM, three-factor, and four-factor models: It is 202 basis points per month (24.2% per year) with a t-statistic of 9.6 when we adjust for CAPM beta risk, 197 basis points per month (23.6% per year) with a t-statistic of 9.4 when we additionally adjust for size and value effects, and 194 basis points per month (23.3% per year) with a t-statistic of 9.7 when we additionally adjust for size, value, and momentum effects.12 Abnormal returns come not only from underperformance in the highest total breadth change portfolio (which cannot be shorted), but also from outperformance in the lowest total breadth change portfolio, which has a significant positive four-factor alpha of 112 basis points per month (13.4% per year). These results are contrary to the CHS model, which predicts that future returns are increasing in ownership breadth, since high breadth means fewer investors with bad news are sitting on the sidelines.13 The remainder of this
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Table V. Monthly returns on breadth change portfolios
*Significant at the 5% level. **Significant at the 1% level. Equal-weighted breadth change Raw return
CAPM alpha
3-factor alpha
Panel A: Total breadth change portfolios Quintile 1 2.87** 1.01** 1.10** (lowest (0.77) (0.27) (0.21) breadth change) Quintile 2 2.41** 0.49 0.54** (0.79) (0.27) (0.19) Quintile 3 1.93* 0.13 0.26 (0.74) (0.26) (0.18) Quintile 4 1.80* 0.09 0.00 (0.78) (0.27) (0.21) 0.84 1.01** 0.87** Quintile 5 (0.76) (0.28) (0.22) (highest breadth change) 51 2.04** 2.02** 1.97** (0.20) (0.21) (0.21) Panel B: Retail breadth change portfolios Quintile 1 2.88** 1.02** 1.11** (lowest (0.77) (0.27) (0.21) breadth change) Quintile 2 2.46** 0.52 0.57** (0.79) (0.27) (0.19)
4-factor alpha
Wealth-weighted breadth change Raw return
CAPM alpha
3-factor alpha
4-factor alpha
0.52** (0.19)
1.12** (0.21)
2.18** (0.74)
0.37 (0.25)
0.49* (0.20)
0.58** (0.17) 0.28 (0.18) 0.04 (0.19) 0.83** (0.20)
2.16** (0.77) 1.91* (0.79) 1.70* (0.77) 1.82* (0.77)
0.28 (0.27) 0.03 (0.31) 0.15 (0.28) 0.08 (0.23)
0.32 (0.19) 0.11 (0.21) 0.06 (0.20) 0.08 (0.18)
0.35* (0.17) 0.15 (0.19) 0.03 (0.19) 0.10 (0.17)
0.45* (0.18)
0.41* (0.18)
0.42* (0.18)
1.94** (0.20)
0.36* (0.18)
1.13** (0.21)
2.59** (0.76)
0.73** (0.26)
0.86** (0.21)
0.88** (0.20)
0.61** (0.17)
2.18** (0.77)
0.31 (0.28)
0.36 (0.19)
0.40* (0.17) (continued)
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This table shows the raw return in excess of the risk-free rate and one, three, and four-factor alphas from portfolios that are formed based on the prior month’s equal- or wealth-weighted breadth change among the total, retail, or institutional investor sample. At the end of each month t, we first sort stocks into tradable market capitalization quintiles, and then calculate month t breadth change breakpoints within each size quintile. We value-weight stocks within each market cap breadth change subportfolio. For the total and retail investor samples, to form the “Quintile n” portfolio, we equally weight across the market cap quintiles the five nth quintile breadth change subportfolios, and hold the stocks for one month before re-forming the portfolios. The “5 1” return is the difference between the Quintile 5 and Quintile 1 portfolio returns. For institutions, to form the “
What Does Stock Ownership Breadth Measure?* JAMES J. CHOI1, LI JIN2 and HONGJUN YAN3 1
Yale School of Management and NBER, 2Oxford University Saı¨d Business School and Peking University Guanghua School of Management, and 3 Yale School of Management
JEL classification: G02, G12, G14
1. Introduction What should we infer about future returns when we see a large number of investors buying a stock they had previously not owned, or a large number of investors completely liquidating their holdings of a stock? In this article, we test how changes in ownership breadth—the fraction of market participants with a long position in a given stock—predict the cross-section of stock returns.
*Choi and Yan received support from a Whitebox Advisors research grant administered through the Yale International Center for Finance, Jin received support from the Harvard Business School Division of Research, and Choi received support from the National Institute on Aging (grant P01-AG005842). We thank Yakov Amihud, Warren Bailey, Long Chen, Cam Harvey, David Hirshleifer, Harrison Hong, Christine Jiang, Ron Kaniel, Owen Lamont, Akiko Watanabe, and audience members at Berkeley, CICF Conference, Frontiers in Finance Conference, NYU Five Star Conference, Emory, Fudan, Goldman Sachs Asset Management, Harvard, HKUST, INSEAD, Michigan, Nanyang Technological University, National University of Singapore, Oxford, Peking University, Singapore Management University, SUNY Binghamton, University of Rochester, and Washington University in St Louis for their comments. We are indebted to Ben Hebert and Jung Sakong for their research assistance, and to Fenghua Wang and Dora Liu for their help in calculating all the breadth measures used in the article. ß The Authors 2012. Published by Oxford University Press on behalf of the European Finance Association. All rights reserved. For Permissions, please email: [email protected]
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Abstract. Using holdings data on a representative sample of all Shanghai Stock Exchange investors, we show that increases in ownership breadth (the fraction of market participants who own a stock) predict low returns: highest change quintile stocks underperform lowest quintile stocks by 23% per year. Small retail investors drive this result. Retail ownership breadth increases appear to be correlated with overpricing. Among institutional investors, however, the opposite holds: stocks in the top decile of wealth-weighted institutional breadth change outperform the bottom decile by 8% per year, consistent with prior work that interprets breadth as a measure of short-sales constraints.
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1
Most theoretical models find that short-sales constraints lead to overvaluation (e.g., Miller, 1977; Harrison and Kreps, 1978; Allen et al., 1993; Scheinkman and Xiong, 2003), but there are exceptions. For example, Diamond and Verrecchia (1987) argue that short-sales constraints do not bias stock prices on average when investors correctly anticipate that pessimistic investors are sitting on the sidelines. Bai et al. (2006) show that, depending on the relative importance of informed versus uninformed trading motives, short-sales constraints can increase, decrease, or have no impact on stock prices. 2 Cen et al. (2011) find that mutual fund breadth changes tend to negatively predict returns when the Baker and Wurgler (2006, 2007) sentiment index experiences large absolute movements. Lehavy and Sloan (2008) find that US mutual fund ownership breadth change is positively autocorrelated, and that controlling for future breadth changes, current breadth change negatively predicts future returns. 3 There were no equity derivatives prior to the end of 2005. From 2005 to 2007, eleven Shanghai Stock Exchange companies (out of over 800 total listed companies) were allowed to issue put warrants. See Xiong and Yu (2011) for more details on these warrants.
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Chen, Hong, and Stein (2002) (hereafter CHS) argue that in a market with short-sales constraints, when an investor holds no long position in a stock, he is likely to have negative information about the stock’s fundamental value. Due to short-sales constraints, this negative information is only partially incorporated into the stock’s price. Thus, when ownership breadth is low, there is a large amount of negative news missing from the stock’s price, and the stock’s future returns will be low.1 Empirically testing this theory is challenging because it requires a representative sample of all investors who face short-sales constraints, which is usually not available at high frequency. Previous empirical tests of ownership breadth have measured ownership breadth among US mutual funds, which are not representative of all US investors who face short-sales constraints. The mismatch between available data and theory may explain why the evidence on ownership breadth has been mixed to date. Because ownership breadth level is close to a permanent characteristic for a stock, CHS argue that focus should be placed on ownership breadth changes—essentially controlling for a stock fixed effect. CHS find that cross-sectionally, stocks that are held by fewer mutual funds this quarter than last quarter subsequently underperform stocks with mutual fund ownership breadth increases from 1979 to 1998. But Nagel (2005) expands the CHS sample by five years and finds that there is no relationship on average between mutual fund ownership breadth changes and future returns over the longer sample.2 We use a new holdings dataset from the Shanghai Stock Exchange (SSE) that is uniquely suited to testing the CHS theory. The investors in the data are a random, survivorship bias-free sample of all investors in the SSE. During our 1996 to 2007 sample period, short sales were strictly prohibited in China, and there was minimal equity derivatives activity.3 Therefore, our
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sample is also representative of all investors in the market who face short-sales constraints. We find, in sharp contrast to the CHS prediction, that high breadth change stocks subsequently underperform low breadth change stocks when we define ownership breadth as CHS do—the percent of all market participants who have a long position in a stock, giving equal weight to each investor. The annualized difference in the four-factor alpha between the highest and lowest quintiles of equal-weighted total breadth change (which is not public information) in the first month after portfolio formation is 23%, with a t-statistic of 9.7. Abnormal returns are present on both the long and short sides of the hypothetical zero-investment portfolio and persist for 5 months after portfolio formation. (Data on each stock’s monthly breadth portfolio assignments are available on the second author’s website.) This finding may be consistent with the lay theory recounted by Lewis (1989): “The first thing you learn on the trading floor is that when large numbers of people are after the same commodity, be it a stock, a bond, or a job, the commodity quickly becomes overvalued.” In other words, ownership breadth measures popularity among noise traders who are able to move prices. Indeed, the breadth measure we adopt from CHS is essentially a measure of breadth among retail investors in China, since retail investors vastly outnumber institutions in the market. Portfolios formed on equal-weighted breadth change among only retail investors have returns that are nearly identical to portfolios formed on equal-weighted total breadth change. Lewis is silent on when a commodity becomes popular and therefore overvalued. We find that equal-weighted retail breadth change’s contemporaneous correlation with a stock’s return is negative. Therefore, retail investors may be causing misvaluation by leaning against price movements and delaying full price adjustment to fundamental news. As we put more weight on sophisticated investors in our breadth measure, the results change. When we redefine total breadth so that investors are weighted by their lagged stock market wealth, the annualized four-factor alpha difference between the highest and lowest total breadth change portfolios attenuates to 5% (still statistically significant). Further restricting the population over which we calculate wealth-weighted breadth change to institutions only, we reproduce the original CHS result in a completely new sample: highest decile wealth-weighted institutional breadth change stocks outperform lowest decile wealth-weighted institutional breadth change stocks. The annualized difference in the four-factor alphas is 8%, with a t-statistic of 2.6. This last result suggests that when ownership breadth is measured within the population of all sophisticated investors that observe unbiased signals of
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the stock’s fundamental value but cannot short, it functions more in accordance with the CHS theory, primarily reflecting how much negative information is not in the stock price due to short-sales constraints. The CHS model does not have unsophisticated traders who observe no fundamental signals, which could be why it no longer applies once ownership breadth is measured over a population of predominantly unsophisticated retail investors. On average, institutional trades against retail investors are profitable before transactions costs; if a stock’s month-over-month change in the log fraction of shares owned by institutions is one standard deviation higher, its abnormal return in the subsequent month is 3.5% higher on an annualized basis. But the significance of institutional ownership percentage changes disappears once we control for equal-weighted retail breadth changes and wealth-weighted institutional breadth changes, while both breadth change measures remain significant return predictors. In other words, an institution buying shares from an individual positively predicts future returns only if the individual is completely liquidating his position or the institution previously had no position in the stock. This result indicates that how many shares in aggregate change hands between institutions and individuals does not matter as much as how many of each investor type start and end with holdings of the stock, thus demonstrating the value of disaggregated investor-level data for forecasting future returns. Because we only have ownership data from China, we have no direct evidence on the extent to which our results generalize to other countries, just as any empirical study using only US data cannot draw any conclusions about whether its results extend to non-US markets. We believe that even if our results were to apply only to China, they are of general interest given the significance of the Chinese stock market, which had 139 million investment accounts at year-end 2007 (China Securities Regulatory Commission, 2009) and the second largest market capitalization among all national stock markets at year-end 2010. Although much of our data come from a time when the Chinese stock market was quite young, all of our main results hold in the second half of our sample period, suggesting that they continue to apply to China’s market today. Nevertheless, similarities between China and other markets in retail investor behavior and stock return patterns give us some reason to think that ownership breadth operates in the same way outside of China. Chinese retail investors exhibit the disposition effect, excessive trading, home bias, and under-diversification, just as US investors do (Chen et al., 2007; Feng and Seasholes, 2008). Chen et al. (2010) test eighteen variables that have been shown to predict cross-sectional stock returns in the US market and find that in the 1995–2007 period, all eighteen variables’ point estimates in
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2. Data Description Our ownership breadth data come from the SSE. At the end of 2007—the last year of our sample period—the 860 stocks traded on the SSE had a total market capitalization of $3.7 trillion, making it the world’s sixth largest 4
These studies have adopted a number of proxies to measure short-sales constraints, such as analyst forecast dispersion (Diether et al., 2002; Yu, 2011), short interest (Asquith et al., 2005; Boehme et al., 2006), the introduction of traded options (Figlewski and Webb, 1993; Danielsen and Sorescu, 2001; Mayhew and Mihov, 2005), and lending fees (Jones and Lamont, 2002; D’Avolio, 2002; Reed, 2002; Geczy et al., 2002; Mitchell et al., 2002; Ofek and Richardson, 2003; Ofek et al., 2004; Cohen et al., 2007). 5 Examples include Lee, Shleifer, and Thaler (1991), Baker and Wurgler (2006, 2007), Cornelli et al. (2006), Kumar and Lee (2006), Qiu and Welch (2006), Tetlock (2007), Da et al. (2011), Hwang (2011), Baker et al. (2012), and Ben-Rephael et al. (2012). 6 See, for example, Gruber (1996), Daniel et al. (1997), Zheng (1999), Chen et al. (2000), Seasholes and Wu (2007), Frazzini and Lamont (2008), Kaniel et al. (2008), Barber et al. (2008), Campbell et al. (2009), Kelley and Tetlock (2012), and Barber, Odean, and Zhu (2012).
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univariate Fama–MacBeth (1973) regressions have signs consistent with the US evidence, and five are statistically significant, compared with eight significant coefficients for the US markets during this same period. In addition to the literature on ownership breadth, our article is related to research that attempts to empirically detect the price impact of short-sales constraints,4 research on investor sentiment measures,5 and research on the portfolio performance of institutional versus individual investors.6 The remainder of the article is organized as follows. Section 1 describes our data, and Section 2 defines the variables we use in the analysis. Section 3 presents the main tests of ownership breadth’s ability to predict the cross-section of stock returns. Section 4 shows how returns, breadth, and institutional ownership behave around the formation date of portfolios sorted on breadth change, which gives us insight into the decisions that result in breadth changes and why breadth changes might be related to future returns. Section 5 explores the relationship between breadth changes and changes in institutional ownership percentages. Section 6 compares the return-predicting ability of retail breadth changes in months with and without earnings announcement to assess whether breadth changes reflect anything more than trading by investors with private information. Section 7 investigates the extent to which breadth changes predict future returns via a Merton (1987) investor recognition channel, and Section 8 discusses the different implications that ownership initiations versus discontinuations have for future returns. Section 9 concludes.
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7
Beginning in April 2005, nontradable shares began to be converted to tradable status, although the conversion process was slow enough that as of year-end 2007, 72% of total Chinese market capitalization remained nontradable. Converted tradable shares were subject to a one-year lockup, and investors holding more than a 5% stake were subject to selling restrictions for an additional 2 years. Dropping returns starting in May 2006 (the month after the first formerly non-tradable shares became liquid and thus begin to appear in our holdings data) does not qualitatively affect our breadth portfolio alpha estimates in Table V, except that in the shorter sample, the long-short wealth-weighted total breadth change portfolio’s three-factor alpha is significant at the 1% level, and the long-short wealth-weighted institutional breadth change portfolio’s one-factor alpha is significant at the 10% level and the four-factor alpha is significant at the 5% level. 8 Further details of the sampling process can be obtained from the authors.
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stock exchange behind NYSE, Tokyo, Euronext, Nasdaq, and London. Mainland China’s other stock exchange, the Shenzhen Stock Exchange, had a $785 billion market capitalization at year-end 2007. By year-end 2010, China’s stock market had the second largest market capitalization among all countries of the world, behind only the USA. Almost all SSE shares are A shares, which only domestic investors could hold until 2003. At year-end 2007, A shares constituted over 99% of SSE market capitalization. B shares are quoted in US dollars and can be held by foreign and (since 2001) domestic investors. Shares are further classified into tradable and nontradable shares. Nontradable shares have the same voting and cashflow rights as tradable shares and are typically owned directly by the Chinese government (“state-owned shares”) or by governmentcontrolled domestic financial institutions and corporations (“legal person shares”).7 We use the term “tradable market capitalization” to refer to the value of tradable A shares, and “total market capitalization” to refer to the combined value of tradable and nontradable A shares. During our sample period, about 27% of SSE market capitalization was tradable. To trade on the SSE, both retail and institutional investors are required to open an account with the Exchange, at which point they must identify themselves to the Exchange as an individual or an institution. Each account uniquely and permanently identifies an investor, even if the account later becomes empty. Investors cannot have multiple accounts. The data assembled by the Exchange for this article consists of the entire history of SSE tradable A-share holdings from January 1996 to May 2007 for a representative random sample of all accounts that existed at the end of May 2007. Since there are far fewer institutional accounts than retail accounts, the Exchange over-sampled institutional investors in order to ensure that a meaningful number of institutional accounts were extracted.8 The market-wide statistics computed from these account data are reweighted to adjust for the over-sampling of institutional investors. The sample contains
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Table I. Portfolio and position summary statistics This table reports (in RMB), separately for retail and institutional investors at the beginning of each year in our sample, the mean and median of investors’ individual stock position values and the mean and median of investors’ total stock portfolio value. Retail investors Individual position value
Total portfolio value
Individual position value
Total portfolio value
Mean
Median
Mean
Median
Mean
Median
Mean
Median
8,069 11,091 11,241 12,536 16,879 17,528 15,047 13,768 14,040 11,261 17,915 21,992
3,900 5,680 5,696 6,100 7,920 8,477 7,220 6,349 6,040 4,308 5,627 6,670
22,179 28,735 30,802 33,955 43,468 46,671 40,557 37,537 38,423 30,463 46,182 54,759
8,680 12,375 13,313 14,177 17,908 19,895 17,159 15,025 14,360 10,390 13,172 13,620
738,976 802,767 1,090,328 2,400,134 3,114,389 2,389,368 2,026,537 2,320,780 3,242,438 4,107,368 7,195,547 8,153,493
54,375 47,880 42,205 40,358 36,960 34,700 45,570 37,400 55,680 54,810 134,456 185,187
3,572,650 2,921,252 3,788,510 8,294,886 9,977,062 8,211,759 8,309,475 9,515,146 13,177,925 16,793,688 26,866,712 32,808,349
198,102 119,175 86,440 102,264 118,080 133,313 184,118 216,850 286,178 203,138 288,191 330,908
both currently active and inactive accounts, so there is no survivorship bias, and in expectation, a constant fraction of the accounts extant at any date are represented. The number of accounts in the sample grows from 36,349 retail accounts and 360 institutional accounts to 384,709 retail accounts and 20,727 institutional accounts from January 1996 to May 2007. Holdings data are aggregated at the Exchange into stock-level measures. The aggregation is carried out under arrangements that maintain strict confidentiality requirements to ensure that no individual account data are disclosed. Table I shows the mean and median value in renminbi (RMB) of an investor’s holdings in a single company, conditional on investing in the company, as well as the mean and median value of an investor’s total stock portfolio. For most of the sample period, the exchange rate was about 8.3 RMB per US dollar, but it then fell to 7.7 RMB per US dollar from July 2005 to May 2007. Retail investors start with a mean (median) stock position value of 8,069 (3,900) RMB and a mean (median) total portfolio value of 22,179 (8,680) RMB in 1996. By 2007, the last year of our sample, these values have increased to 21,992 (6,670) RMB and 54,759 (13,620) RMB, respectively. Even adjusting for the 16% rise in the Chinese consumer price index over this period, this represents a sizable increase in the position and portfolio values of retail investors. Institutions
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1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
Institutional investors
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3. Variable Definitions Following CHS, we define the equal-weighted total ownership breadth change of stock i in month t as follows. We first restrict the sample to investors who have a long position in at least one SSE stock at the end of both t 1 and t. This restriction ensures that the breadth change measure captures only the trading activity of existing market participants, rather than changes in the investor universe due to new market participants entering and institutions dissolving.9 Equal-weighted total ownership breadth change is the difference between the end of t 1 and the end of t in the fraction of these subsample investors who own stock i. We obtain equal-weighted retail breadth change and equal-weighted institutional breadth change by further restricting the investor subsample to retail investors or institutional investors. Stocks almost never have an empty set of retail owners in our sample, but zero ownership is more frequent within our institutional sample, particularly among small-cap stocks. At each time period, we do not calculate breadth change for stocks that have zero owners in the relevant subsample at either t 1 or t, since the breadth change measure we obtain would be censored. A stock’s equal-weighted total ownership breadth increases when one investor partially liquidates her position in the stock to sell to one or more investors who previously did not own the stock, or one investor completely 9
Portfolio returns are quite similar if we instead require that investors have a long position at either t 1 or t. When we construct wealth-weighted breadth change, described later in this section, using this alternative sample definition, we weight investors that are not in the market at t 1 by their stock market wealth at the end of t.
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start with a mean (median) stock position value of 738,976 (54,375) RMB, and a mean (median) total portfolio value of 3,572,650 (198,102) RMB in 1996. Their mean (median) stock position value increased to 8,153,493 (185,187) RMB and their total portfolio value increased to 32,808,349 (330,980) RMB by 2007. Institutional investors’ portfolio values grew much more quickly than retail investors’, particularly for the means. The median institutional investor portfolio is strikingly small throughout the sample period—far less than 100,000 USD—and the large difference between the mean and the median values indicates that the portfolio value distribution is extremely right-skewed. We obtain stock return, market capitalization, earnings announcement date, and accounting data from the China Stock Market & Accounting Research Database (CSMAR).
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v2At
where Wv,t is the SSE stock portfolio value of investor v at month t’s market open, Vi,t is the set of subsample investors who held stock i at the end of month t, and At is the entire subsample of investors who owned at least one SSE stock at the end of both t 1 and t. Wealth-weighted retail breadth change and wealth-weighted institutional breadth change are defined analogously over their respective investor populations. Breadth change can be decomposed into the variables IN and OUT. Equal-weighted IN is the percent of subsample investors who had a zero position in stock i at the end of t 1 and a positive position at the end of t. Equal-weighted OUT is the percent of subsample investors who moved from a positive position to a zero position in stock i between the ends of t 1 and t. By construction, equal-weighted breadth change is equal-weighted IN minus equal-weighted OUT. Wealth-weighted IN and OUT are defined analogously. For example, wealth-weighted IN is the month t opening SSE stock portfolio value of subsample investors who moved from a zero position to a positive position in stock i between t 1 and t divided by the month t opening SSE stock portfolio value of all subsample investors. Our main cross-sectional analysis involves evaluating the return performance of portfolios formed on breadth changes. We estimate one, three, and four-factor alphas, where the factor portfolio returns capture CAPM beta, size, value, and momentum effects. The market portfolio return is the 10
Small investors have fewer resources with which to gather information. Natural selection arguments such as that of Friedman (1953) may also lead to rational individuals becoming overrepresented among wealthy investors. However, Yan (2008) shows that the natural selection mechanism does not robustly reduce irrational investors’ wealth share.
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liquidates her position by selling her shares to two or more investors who previously did not own the stock. Note that market clearing does not constrain a stock’s equal-weighted total ownership breadth change to be zero. To assess the extent to which unsophisticated investors drive the negative correlation between total ownership breadth change and future returns, we use an alternative measure of ownership breadth not found in CHS that de-emphasizes small investors by weighting investors by the value of their SSE portfolio at the beginning of the month.10 To calculate wealth-weighted total ownership breadth change at t, we again restrict the sample to investors who have a long position in at least one SSE stock at the end of both t 1 and t. Wealth-weighted ownership breadth change is P P Wv, t Wv, t v2Vi, t v2Vi, t1 P ð1Þ Wv, t
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11
Whenever possible, we use the book equity value that was originally released to investors. If this is unavailable, we use book equity that has been restated to conform to revised Chinese accounting standards.
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composite Shanghai and Shenzhen market return, weighted by tradable market capitalization. The risk-free return is the demand deposit rate. We construct size and value factor returns (SMB and HML, respectively) for the Chinese stock market according to the methodology of Fama and French (1993), but using the entire Shanghai/Shenzhen stock universe to calculate percentile breakpoints. We form SMB based on total (i.e., tradable plus nontradable) market capitalization and HML based on the ratio of book equity to total market capitalization, weighting stocks within component subportfolios by their tradable market capitalization.11 We construct the momentum factor portfolio MOM following the methodology described on Kenneth French’s website. We calculate the 50th percentile total market capitalization at month-end t 1 and the 30th and 70th percentile cumulative stock returns over months t 12 to t 2, again using the entire Shanghai/Shenzhen stock universe to calculate percentile breakpoints. The intersections of these breakpoints delineate six tradable market capitalization-weighted subportfolios for which we compute month t returns. MOM is the equally weighted average of the two recent winner subportfolio returns minus the equally weighted average of the two recent loser subportfolio returns. We control for other possible predictors of returns using Fama–MacBeth (1973) regressions, where the predictor variables are the stock’s breadth change (defined in various ways), log of total market capitalization, book-to-market ratio (the value at year-end 1 is used as the predictor from July of year through June of year þ 1), return during the last year excluding the prior month, return during the prior month, sum of monthly turnover during the prior quarter, change in the log percent of tradable A shares owned by institutions during the prior month (as measured in our ownership data), Amivest liquidity ratio (described further below) during the prior month, shadow cost of incomplete information, and two dummies for whether the stock’s share trading volume during the prior week was in the top tenth or bottom tenth of the ten most recent weeks (Gervais et al., 2001). We operationalize the Amivest liquidity ratio as the sum of the stock’s yuan trading volume over 1 month divided by the sum of the stock’s absolute daily returns over that month. Higher values of the liquidity ratio correspond to lower price impacts of trading, and hence higher liquidity. The shadow cost of incomplete information, l, captures abnormal returns due to Merton’s (1987) “investor recognition hypothesis” that investors neglect to hold stocks
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they are unaware of, causing the investors who do hold these neglected stocks to sacrifice diversification and hence demand a higher expected return. Investor recognition is closely related to ownership breadth changes, so it is important to explore the extent to which breadth changes predict returns through the investor recognition channel. We adopt the operationalization of l used by Bodnaruk and Ostberg (2009): it ¼ 2:5 it2 xit
1 Mit , Mit
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where 2.5 is an arbitrary constant representing aggregate investor risk aversion, it2 is the variance of the residuals from regressing stock i’s excess monthly returns on Chinese market excess returns from month t 35 to month t; xit is stock i’s tradable A-share market capitalization as a fraction of total Chinese tradable A-share market capitalization at month-end t; and Mit is the number of investors holding stock i at month-end t divided by the total number of investors at month-end t. In calculating Mit, we define “total number of investors” as all investors with at least one long SSE position at t (and do not condition on t 1 holdings). Table II displays summary statistics for the variables used in the cross-sectional analysis. Because the number of stocks listed on the SSE expanded rapidly during our sample period, we adopt the following procedure in order to keep later time periods from dominating the summary statistics. We calculate separately for each month the mean and standard deviation of each variable. The table reports the time-series average of these monthly mean and standard deviation series. The summary statistics for equal-weighted retail breadth change are nearly identical to those for equal-weighted total breadth change, since retail investors vastly outnumber institutions. Because institutions have disproportionately large stock holdings, wealth-weighted total breadth changes do not follow wealth-weighted retail breadth changes nearly as closely. Table III shows the mean and standard deviation of breadth changes separately for each year of our sample. The mean equal-weighted breadth changes are close to zero in every year; the largest magnitude occurs in 1996, when the mean equal-weighted institutional breadth change takes on a value of only 0.069%. The average wealth-weighted breadth changes experience considerably more variation, particularly among institutions. The average wealth-weighted institutional breadth change experiences two valleys of 0.446% and 0.525% in 1996 and 2003, respectively. The cross-sectional standard deviation of breadth changes generally falls as the sample period
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Table II. Summary statistics of variables used in cross-sectional analysis
Returni, tþ1 Equal-weighted total breadthi,t Equal-weighted retail breadthi,t Equal-weighted retail INi,t Equal-weighted retail OUTi,t Equal-weighted institutional breadthi,t Wealth-weighted total breadthi,t Wealth-weighted retail breadthi,t Wealth-weighted institutional breadthi,t Wealth-weighted institutional INi,t Wealth-weighted institutional OUTi,t li,t log(Institutional ownershipi,t) log(Total market capi,t) Book-to-marketi,t Returni,t 11 ! t 1 Prior quarter turnoveri,t Liquidity ratioi,t High relative volumei,t Low relative volumei,t
Mean
Standard deviation
1.944 0.002 0.002 0.067 0.069 0.009 0.031 0.025 0.114 0.542 0.656 0.011 0.009 14.562 0.409 17.413 1.105 0.936 0.124 0.145
9.422 0.051 0.051 0.074 0.075 0.194 0.265 0.115 2.123 1.558 1.684 0.039 0.806 0.786 0.193 37.316 0.603 1.387 0.275 0.271
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The cross-sectional means and standard deviations are calculated separately within each month. The table reports the time-series average of these means and standard deviations. Equal-weighted total breadth change is the change between month-ends t 1 and t in the number of investors holding stock i divided by the total number of investors. Wealthweighted total breadth change is like equal-weighted total breadth change, but weights investors by the value of their SSE stock portfolio at the open of month t. Institutional and retail breadth changes are defined analogously on the retail or institutional subsample. Equal-weighted retail IN is the percent of retail investors who held no position in the stock at t 1 but held a positive position in it at t. Equal-weighted retail OUT is the percent of retail investors who held a positive position in the stock at t 1 but held no position in it at t. Wealth-weighted institutional IN and OUT are defined analogously over institutions, weighting them by their SSE stock portfolio value at the open of month t. Breadth changes, IN, and OUT are expressed as percentages, so that a 1% value is coded as 1, rather than 0.01. The variable li,t is the Merton shadow cost of incomplete information defined in Equation (2), and log(Institutional ownershipi,t) is the change between month-ends t 1 and t in the log of the fraction of the stock’s tradable A shares held by institutions. Returni,t 11 ! t 1 is the stock’s cumulative return from month t 11 to t 1. Liquidity ratio is the sum of the stock’s yuan trading volume divided by the sum of the stock’s absolute daily returns during month t. High relative volume and low relative volume are dummies for whether the stock’s share trading volume during the prior week was in the top tenth or bottom tenth of the ten most recent weeks, respectively. The sample is stock-months where there are a positive number of individual investors and a positive number of institutional investors at both t and t 1.
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Table III. Mean and standard deviation of breadth change in each year This table shows the cross-sectional mean and standard deviation (in parentheses below the mean) of the six kinds of breadth change within each year. The means and standard deviations are calculated separately within each month, and we report the time-series average of these means and standard deviations within each year. Equal-weighted breadth change
1996
1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
Total
Retail
Inst.
Total
Retail
Inst.
0.009 (0.177) 0.014 (0.113) 0.000 (0.069) 0.002 (0.054) 0.001 (0.069) 0.002 (0.025) 0.001 (0.014) 0.001 (0.018) 0.000 (0.020) 0.001 (0.012) 0.002 (0.034) 0.004 (0.068)
0.009 (0.177) 0.014 (0.113) 0.000 (0.069) 0.002 (0.054) 0.001 (0.069) 0.002 (0.025) 0.001 (0.014) 0.001 (0.018) 0.000 (0.020) 0.001 (0.012) 0.002 (0.034) 0.004 (0.068)
0.069 (0.486) 0.020 (0.296) 0.016 (0.200) 0.013 (0.159) 0.015 (0.188) 0.012 (0.130) 0.003 (0.129) 0.013 (0.207) 0.005 (0.222) 0.003 (0.192) 0.005 (0.220) 0.003 (0.148)
0.126 (0.455) 0.034 (0.221) 0.027 (0.198) 0.033 (0.295) 0.035 (0.295) 0.024 (0.168) 0.026 (0.214) 0.070 (0.286) 0.020 (0.286) 0.000 (0.329) 0.017 (0.450) 0.017 (0.569)
0.111 (0.461) 0.033 (0.224) 0.025 (0.133) 0.025 (0.097) 0.023 (0.106) 0.010 (0.044) 0.008 (0.035) 0.010 (0.061) 0.009 (0.051) 0.005 (0.054) 0.016 (0.104) 0.024 (0.112)
0.446 (2.505) 0.005 (1.508) 0.147 (4.509) 0.167 (5.160) 0.175 (3.884) 0.211 (2.503) 0.158 (2.536) 0.525 (2.246) 0.067 (1.607) 0.009 (1.291) 0.014 (1.452) 0.000 (1.474)
progresses, with the exception of institutional wealth-weighted breadth changes, which exhibits its greatest dispersion from 1998 to 2000, and total wealth-weighted breadth changes, whose dispersion follows a U-shaped path with respect to time. Table IV contains the correlations among the various breadth measures. Equal-weighted total and retail breadth changes are almost perfectly positively correlated with each other. Equal-weighted institutional breadth changes are mildly positively correlated (0.054) with equal-weighted retail breadth changes. Wealth-weighted retail breadth changes are strongly positively correlated with equal-weighted retail breadth changes, but the correlation coefficient of 0.643 indicates that there is still considerable divergence
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1997
Wealth-weighted breadth change
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Table IV. Correlation of breadth change measures with each other Each month, we calculate the cross-sectional correlation of each breadth measure with the other breadth measures. The table reports the time-series mean of these correlations, with the standard error (computed as the time-series standard deviation of the correlation divided by the square root of the number of months) in parentheses below. *Significant at the 5% level. **Significant at the 1% level. Equal-weighted breadth change Total
Retail
Inst.
Total
Retail
Inst.
1.000** (0.000) 1.000** (0.000)
0.058** (0.016) 0.054** (0.016) 1.000** (0.000)
0.128** (0.028) 0.127** (0.028) 0.294** (0.014) 1.000** (0.000)
0.643** (0.015) 0.643** (0.015) 0.141** (0.016) 0.347** (0.032) 1.000** (0.000)
0.117** (0.015) 0.117** (0.015) 0.305** (0.013) 0.811** (0.026) 0.030* (0.012) 1.000** (0.000)
Inst. Wealth-weighted Total breadth change Retail Inst.
between these two retail breadth change measures. Wealth-weighted institutional breadth change is negatively correlated with retail breadth change, and this negative correlation is stronger with equal-weighted retail breadth change (0.117) than with wealth-weighted retail breadth change (0.030). Wealth-weighted institutional breadth change exhibits only some positive correlation (0.305) with equal-weighted institutional breadth change, showing that large institutions behave differently from small institutions. 4. Main Return Prediction Tests 4.1 FORECASTING 1-MONTH-AHEAD RETURNS
We test the ability of breadth changes to predict the cross-section of returns by using breadth changes to form portfolios. Following CHS, at the end of each month t, we sort stocks into five groups based on tradable market capitalization (0th to 20th size percentile, 20th percentile to 40th size percentile, . . . , 80th percentile to 100th size percentile). Within each size quintile, we form five subportfolios based on breadth change during t, creating a total of 25 subportfolios. The breadth change breakpoints that determine the
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Equal-weighted Total 1.000** breadth change (0.000) Retail
Wealth-weighted breadth change
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12
The average of the long-only test portfolio alphas are not approximately zero mainly because the test portfolios contain only Shanghai Stock Exchange stocks, whereas our factor portfolios contain both Shanghai and Shenzhen Stock Exchange stocks. 13 Although the model of Bai et al. (2006) has only one risky asset and cannot be used to analyze cross-sectional returns directly, their intuition could potentially lead to the implication that ownership breadth increases should predict lower future returns through a
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subportfolio boundaries differ by size quintile, so that all 25 subportfolios contain the same number of stocks. We weight stocks by tradable market capitalization within each subportfolio. To form the “Quintile n” breadth change portfolio, we equally weight across size quintiles the five nth quintile breadth change subportfolios, and hold the stocks for 1 month before re-forming the portfolios at the end of month t þ 1. We adopt this sequential sorting methodology because the volatility of breadth change increases with firm size. If we sorted stocks by breadth change without considering size, very few small firms would be in the extreme quintiles of breadth change. Table V shows the breadth change portfolios’ raw excess returns and alphas generated by time-series regressions. The left half of Panel A shows that returns decrease monotonically with equal-weighted total breadth change. On a raw-return basis, the lowest quintile outperforms the highest quintile by 204 basis points per month, or 24.5% per year, with a t-statistic of 10.2. The lowest quintile has an annualized Sharpe ratio of 1.11, and a (noninvestable) zero-investment portfolio that holds the lowest quintile long and the highest quintile short has a Sharpe ratio of 2.97. In comparison, during this 137-month period, the Sharpe ratio of all SSE A shares weighted by tradable market capitalization was 0.77, and the Sharpe ratio of the US CRSP value-weighted index was 0.49. The return differential between the lowest and highest breadth change quintiles barely falls when we adjust the return using the CAPM, three-factor, and four-factor models: It is 202 basis points per month (24.2% per year) with a t-statistic of 9.6 when we adjust for CAPM beta risk, 197 basis points per month (23.6% per year) with a t-statistic of 9.4 when we additionally adjust for size and value effects, and 194 basis points per month (23.3% per year) with a t-statistic of 9.7 when we additionally adjust for size, value, and momentum effects.12 Abnormal returns come not only from underperformance in the highest total breadth change portfolio (which cannot be shorted), but also from outperformance in the lowest total breadth change portfolio, which has a significant positive four-factor alpha of 112 basis points per month (13.4% per year). These results are contrary to the CHS model, which predicts that future returns are increasing in ownership breadth, since high breadth means fewer investors with bad news are sitting on the sidelines.13 The remainder of this
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Table V. Monthly returns on breadth change portfolios
*Significant at the 5% level. **Significant at the 1% level. Equal-weighted breadth change Raw return
CAPM alpha
3-factor alpha
Panel A: Total breadth change portfolios Quintile 1 2.87** 1.01** 1.10** (lowest (0.77) (0.27) (0.21) breadth change) Quintile 2 2.41** 0.49 0.54** (0.79) (0.27) (0.19) Quintile 3 1.93* 0.13 0.26 (0.74) (0.26) (0.18) Quintile 4 1.80* 0.09 0.00 (0.78) (0.27) (0.21) 0.84 1.01** 0.87** Quintile 5 (0.76) (0.28) (0.22) (highest breadth change) 51 2.04** 2.02** 1.97** (0.20) (0.21) (0.21) Panel B: Retail breadth change portfolios Quintile 1 2.88** 1.02** 1.11** (lowest (0.77) (0.27) (0.21) breadth change) Quintile 2 2.46** 0.52 0.57** (0.79) (0.27) (0.19)
4-factor alpha
Wealth-weighted breadth change Raw return
CAPM alpha
3-factor alpha
4-factor alpha
0.52** (0.19)
1.12** (0.21)
2.18** (0.74)
0.37 (0.25)
0.49* (0.20)
0.58** (0.17) 0.28 (0.18) 0.04 (0.19) 0.83** (0.20)
2.16** (0.77) 1.91* (0.79) 1.70* (0.77) 1.82* (0.77)
0.28 (0.27) 0.03 (0.31) 0.15 (0.28) 0.08 (0.23)
0.32 (0.19) 0.11 (0.21) 0.06 (0.20) 0.08 (0.18)
0.35* (0.17) 0.15 (0.19) 0.03 (0.19) 0.10 (0.17)
0.45* (0.18)
0.41* (0.18)
0.42* (0.18)
1.94** (0.20)
0.36* (0.18)
1.13** (0.21)
2.59** (0.76)
0.73** (0.26)
0.86** (0.21)
0.88** (0.20)
0.61** (0.17)
2.18** (0.77)
0.31 (0.28)
0.36 (0.19)
0.40* (0.17) (continued)
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This table shows the raw return in excess of the risk-free rate and one, three, and four-factor alphas from portfolios that are formed based on the prior month’s equal- or wealth-weighted breadth change among the total, retail, or institutional investor sample. At the end of each month t, we first sort stocks into tradable market capitalization quintiles, and then calculate month t breadth change breakpoints within each size quintile. We value-weight stocks within each market cap breadth change subportfolio. For the total and retail investor samples, to form the “Quintile n” portfolio, we equally weight across the market cap quintiles the five nth quintile breadth change subportfolios, and hold the stocks for one month before re-forming the portfolios. The “5 1” return is the difference between the Quintile 5 and Quintile 1 portfolio returns. For institutions, to form the “
