Investor sentiment and the MAX effect

Accepted Manuscript Investor Sentiment and the MAX Effect Wai Mun Fong, Benjamin Toh PII: DOI: Reference:

S0378-4266(14)00167-8 http://dx.doi.org/10.1016/j.jbankfin.2014.05.006 JBF 4451

To appear in:

Journal of Banking & Finance

Received Date: Accepted Date:

7 April 2013 9 May 2014

Please cite this article as: Fong, W.M., Toh, B., Investor Sentiment and the MAX Effect, Journal of Banking & Finance (2014), doi: http://dx.doi.org/10.1016/j.jbankfin.2014.05.006

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Investor Sentiment and the MAX Effect

Wai Mun Fong1 and Benjamin Toh2

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Department of Finance NUS Business School National University of Singapore 15 Kent Ridge Drive Singapore 119245 2

Management Associate, Bunge Agribusiness Singapore Private Limited, 77 Robinson Road, Singapore 068896

Email: [email protected]

This version: May 2014

Abstract

Bali, Cakici and Whitelaw (2011) uncover a new anomaly (the “MAX effect”) related to investors’ desire for stocks with lottery-like payoffs. Specifically, stocks with high maximum daily returns (high MAX) over the past month perform poorly relative to stocks with low maximum daily returns (low MAX) over the past month. We show that the MAX effect is strongly dependent on investor sentiment and is mainly due to the poor performance of high MAX stocks rather than high returns of low MAX stocks. Investors’ desire to gamble in high MAX stocks is not limited to individual investors but is also present amongst some institutions. Controlling for past sentiment reduces the significance of the MAX effect. Our findings provide a behavioral underpinning to recent “optimal beliefs” theories (Brunnermeier, Gollier and Parker 2007) where investor optimism generates a preference for lottery-type securities Key words: MAX, lottery-like stocks, investor sentiment, investor optimism, market efficiency. JEL codes: G11, G23 

1.

Introduction Recent research has emphasized the potential role of gambling and speculation in

influencing stock returns. For example, Kumar (2009) shows that individual investors are attracted to “lottery-type” stocks with low prices, high idiosyncratic volatility, and high idiosyncratic skewness. These stocks earn significantly negative alphas on average. Preference for lottery-like assets is consistent with Cumulative Prospect Theory (Tversky and Kahneman, 1992) where errors in probability weighting cause investors to overvalue stocks that have a small probability of extreme positive returns. The propensity to gamble may also be reinforced by the tendency for less informed investors to seek attentiongrabbing stocks such as those with extreme one-day returns and abnormal trading volume (Barber and Odean 2008). Consistent with the attention effect, Bali, Cakici, and Whitelaw (2011) find that stocks with high daily maximum returns in the previous month (“high MAX stocks”) have anomalously low mean returns compared to stocks with low maximum daily returns (“low MAX stocks”) over the same period. They show that a MAX strategy that longs a value-weighted portfolio of high MAX stocks and shorts a value-weighted portfolio of low MAX stocks produces an average return of -1% per month and an even more negative alpha based on the four-factor model of Fama and French (1992, 1993) and Cahart (1997). Investor sentiment may also play a role in influencing the demand for high and low MAX stocks. One way to view investor sentiment is that it captures the propensity for investors to speculate. Consistent with this definition, Baker and Wurgler (2006) find that investor sentiment explains the cross-section of stock returns, with high sentiment being a significant predictor of the returns of more speculative stocks such as those of small firms, 1

young firms and highly volatile firms. When sentiment is high, subsequent returns to these stocks tend to be low and vice versa. Baker and Wurgler (2006) base their findings on a broad sentiment index which they construct from several underlying sentiment proxies, each orthogonalized for observable economic fundamentals. They show that fluctuations in their sentiment index line up well with important episodes of market booms and crashes. Investor sentiment may also reflect investors’ optimism or pessimism about stocks in general. This view of investor sentiment can be combined with Miller’s (1977) argument that due to short-sale constraints, the price of a stock reflects the views of the most optimistic investors. Empirical evidence by Stambaugh, Yu, and Yuan (2012) support this joint hypothesis. Using the Baker-Wurgler sentiment index, they find that many asset pricing anomalies are indeed stronger following periods of high sentiment. Moreover, longshort strategies designed to profit from sentiment are only profitable for the short leg of the strategies, consistent with the tendency for stocks to be overpriced when sentiment is high. In this paper, we examine the role of investor sentiment in explaining the MAX effect. Portfolio choice models based on Cumulative Prospect Theory suggest that marketwide sentiment should have a role in explaining extreme return anomalies like the MAX effect. For example, according to the optimal expectations theory of Brunnermeier, Gollier, and Parker (2007), investors maximize current utility by optimally overestimating future probabilities of good outcomes. This leads them to invest more in securities with highly skewed returns than investors with rational expectations. We conjecture that market-wide sentiment is an important cue that investors use when forming such beliefs. More specifically, we conjecture that when sentiment is high, investors are more optimistic about the future payoffs of high MAX stocks than when sentiment is low. We use the Baker2

Wurgler sentiment index (hereafter, the BW index) as our measure of market-wide sentiment. We use the BW index to test four hypotheses with regards to the MAX effect. The first hypothesis is that the mean monthly return of the long-short portfolio is negative only if the previous month’s sentiment is high. Following Baker and Wurlger (2007) and Stambaugh et al. (2012) we define a high-sentiment month as one in which the BW index is above the sample median, and a low-sentiment month as one in which the BW index is below the sample median. Hypothesis 1 is motivated by the theoretical models mentioned above. Our second hypothesis is that following high sentiment states, only high MAX stocks are overpriced. In other words, the short leg of the MAX strategy solely accounts for the MAX effect. This hypothesis is motivated by Miller’s (1977) theory. The third hypothesis is that accounting for the effects of sentiment reduces the significance and size of the MAX anomaly following high-sentiment states. Our fourth hypothesis is that sentiment affects both retail and institutional investors. While retail investors are often portrayed as prime examples of “noise traders” who are drawn to stocks with speculative features (Barber, Odean, and Zhu 2009; Kumar 2009), changes in institutional stock ownership in the U.S. over the last few decades suggest that riskier stocks have found their way into some institutional portfolios. In particular, Blume and Keim (2012) report that from 1980 to 2010, institutional investors allocated more of their assets to small capitalization stocks. Smaller institutions in general and hedge funds in particular recorded the steepest increase in ownership of these stocks. In light of these

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trends and given that high MAX stocks to belong to smaller and riskier firms, we conjecture that the MAX effect may also exist in stocks with significant levels of institutional ownership. We test this conjecture by forming institutional ownership quintiles using 13F holdings data. Our results support all four hypotheses. First, the MAX effect is significantly negative following high sentiment states, but is not significantly different from zero following low sentiment states. Indeed the former produces an average monthly return of 1.9%, more than twice as negative as the unconditional sample mean return. Consistent with Bali et al. (2011), adjusting for risk using the four-factor model amplifies the magnitude of the MAX effect. Second, the MAX effect exists only for the short leg of the strategy. This result is consistent with Miller’s hypothesis that due to short selling constraints, overpricing results because stock prices reflect the views of the most optimistic investors. Our results confirm that such overpricing affects only high MAX stocks and only during periods of high sentiment. Third, when we regress returns of the MAX strategy against lagged sentiment as a continuous variable, the coefficient for the lagged BW index is always significantly negative. Moreover, alphas following high-sentiment states are much less significant after accounting for lagged sentiment. We also perform the same test using a sentiment returns factor that captures the return spread between stocks with high and low sentiment loadings, producing essentially similar results. Fourth, consistent with the portfolio-based tests, firm-level cross-sectional regressions indicate that the MAX effect is amplified when past sentiment is high and in environments where gambling has greater religious acceptance. The latter result is consistent the findings of a recent study by Kumar, Page and Spalt (2011) on lottery-type stocks and suggests that a common gambling 4

motivation exists for lottery-type stocks and high MAX stocks. Finally, we show that the MAX effect is present in both low and moderately high institutional ownership portfolios, indicating that a broad spectrum of investors, not just retail investors, are attracted to high MAX stocks. The rest of this paper is organized as follows. Section 2 describes our data sources. Section 3 provides details of how MAX portfolios are formed, followed by a descriptive analysis of these portfolios in terms of their formation period returns, firm size, book-tomarket ratios, liquidity, and idiosyncratic risk. Section 4 reports post-formation returns of the MAX portfolios for the whole sample period. We also examine how these returns vary across high and low sentiment states. Section 5 extends the analysis by looking at the MAX effect in portfolios with different degrees of institutional ownership. We also report alphas of the long-short strategy following high sentiment states after controlling for the effects of lagged sentiment. Section 6 provides evidence on the impact of sentiment and the MAX effect on the cross-section of stock returns. The section ends with a discussion of the theoretical and practical implications of our findings. Section 7 concludes.

2.

Data Our sample includes common stocks traded on the New York Stock Exchange

(NYSE), American Stock Exchange (ANEX), and Nasdaq, downloaded from the Center for Research in Security Prices (CRSP) database for period from July 1965 to December 2007. We use daily stock returns to compute the maximum daily stock returns and other stock characteristics such as idiosyncratic volatility and market beta. We use the CRSP value5

weighted stock index as our proxy for the market portfolio. We use monthly data to calculate market capitalization and the Amihud (2002) illiquidity measure. We use book value of equity from COMPUTSTAT to compute book-to-market ratios. We obtain from Kenneth French’s online data library, daily and monthly risk-free rates (on one-month Treasury bills) and returns on risk factors which include MKT (market excess returns), SMB (small-minus-big firm returns), HML (high-minus-low book-to-market returns), and the UMD (up-minus-down, or winners-minus-losers returns). We use 13F filings from the Thomson Financial database to compute institutional ownership of equities. This data is quarterly and begins from March 1980. We download from Jeff Wurgler’s website, monthly data for the BW sentiment index from March 1980 to December 2007. We use the Michigan Consumer Sentiment Index (MCSI), compiled by the University of Michigan Survey Research Center as an alternative proxy for investor sentiment. From the website of the Federal Reserve Bank of Chicago, we obtain monthly values of the Chicago Fed National Activity Index (CFNAI) which is a weighted-average of 85 economic indicators covering broad categories of data such as output, income, employment, personal consumption, sales, inventories and orders. We use the CFNAI as a coincident indicator of national economic activity.

3.

Preliminary Data Analysis Every month, starting from July 1965 to December 2007, we sort stocks based on

their maximum daily returns (MAX) over the past month to form decile portfolios. Decile 1 (D1) is the portfolio with the lowest maximum daily returns in the past month, and D10 is 6

the portfolio with the highest maximum daily returns in the past month. Table 1 present summary statistics of our sample. Panel A shows that on average, there are nearly 500 firms in each MAX decile. As we shall see later, the MAX anomaly is concentrated on D9 and D10. Panel A shows that these two deciles comprise just 3% of the overall market capitalization across all deciles, indicating that the MAX effect is concentrated among small firms. Panel B reports typical firm characteristics of each MAX portfolio. Each characteristic is reported as the average (across months) of the median value of that characteristic1. MAX is the maximum daily return (in percent). Size refers to market capitalization and Price is stock price. The return spread between the high and low MAX decile is 8.93% a month. Size and price decrease as we go from low to high MAX deciles. Consistent with Panel A, median firm size and stock price decline monotonically as we go from low MAX to high MAX deciles. The average size and price for D1 is $226.8 million and $17.1 respectively, whereas the average size and price for D10 is $20.2 million and $4.08 respectively. Beta is the market beta of each portfolio. Beta increases as we move from low to high MAX deciles. BM refers to book-to-market ratio. The BM ratio is relatively stable across all MAX portfolios, suggesting that the MAX effect is not related to the book-tomarket factor, which is often interpreted as a firm distress factor (Fama and French 1992, 1993). Illiq (scaled by 105) is the Amihud illiquidity measure (Amihud 2002). Liquidity is high for MAX deciles 2 and 3, and decreases as we move to higher MAX deciles. Like size, this liquidity pattern makes the MAX phenomenon puzzling because stocks with 1

Variables construction follows the Bali et al. (2011, appendix) and are available on request from the author.

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lower liquidity should earn higher average returns than stocks that are more liquid. Finally, IVOL is idiosyncratic volatility, and is defined as the standard deviation of the residuals obtained from regressing a stock’s excess returns against the Fama-French (1992, 1993) three factors. We compute IVOL for month t using daily data for the previous month. Consistent with Kumar (2009), IVOL increases monotonically as we move from low MAX to more speculative high MAX stocks. [Table 1 about here]

4.

Returns of MAX Portfolios

4.1

The MAX Effect

Table 2 reports average returns of the MAX portfolios. All portfolios are value-weighted to minimize the effects of illiquidity. The second column shows average returns in excess of the one-month Treasury bill rate, while the column “FF4 Alpha” reports alphas with respect to the Fama-French-Cahart four factor model that includes the momentum factor of Cahart (1997). Table 2 confirms the results of Bali et al. (2011) that the high MAX portfolio (decile 10) has distinctly lower post-formation returns than the low MAX portfolio (decile 1). The mean monthly excess returns of these extreme portfolios are -0.44% and 0.33% respectively, giving a return spread of -0.8%. Adjusting for risk using the four-factor model magnifies the MAX effect to an alpha spread of -1.18% which is extremely significant (t-statistic: 5.01).

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[Table 2 about here] Although MAX is a salient variable for investors with high gambling propensity, it may be correlated with another gambling attribute, namely skewness. Skewness-seeking behavior is modeled by Barberis and Huang (2008) who show that securities with high idiosyncratic skewness are expected to earn lower mean returns because investors are willing to accept such low returns for the chance of earning lottery-like payoffs. Although Bali et al. (2011) show that the MAX effect is not subsumed by skewness, we control for idiosyncratic skewness (ISKEW) as a robustness check on our results. We do so using bivariate sorts, first on MAX, then on ISKEW. Following Harvey and Siddique (2000) and Bali et al. (2011), we define a stock’s ISKEW as the skewness that remains after controlling for the stock’s exposure to market risk. More specifically, a firm’s ISKEW for month t is estimated by regressing its daily excess returns in the previous month on the daily excess return of the market index and its square over the same period. The model is as follows: R i ,d − R f ,d = α i ,d + βi [R m ,d − R f ,d ] + λi [R m ,d − R f ,d ]2 + ε i ,d (1) where subscript i denotes a stock, subscript d denotes a day, R i is the return on stock i , R f is the risk-free rate (the one-month T-bill rate), and R m is the return on the market (the

CRSP value-weighted stock index). ISKEW for stock i in month t is the skewness of the residuals ε i ,d in month t − 1 .

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Each month, we sort stocks into MAX deciles as done previously. Next, stocks in each MAX decile are sorted into ISKEW deciles, where ISKEW1 (ISKEW10) denotes the decile with the lowest (highest) idiosyncratic skewness. We compute the value-weighted return spread between ISKEW10 and ISKEW1 across the MAX deciles and use this as our measure of the ISKEW effect. Finally, we subtract the ISKEW return spread from the MAX return spread. This skewness-adjusted MAX return spread and its t-statistic are shown in the last two rows of Table 2. While both the raw and risk-adjusted MAX return spreads are now smaller, they remain sizeable and statistically significant. This result is consistent with the findings of Bali et al. (2011) and confirms that the MAX effect is quite distinct from the ISKEW effect. 4.2

Investor Sentiment and the MAX Effect Recent studies show that investor sentiment affects stock prices. The sentiment

index most commonly employed in these studies is that of Baker and Wurgler (2006). The BW sentiment index is the first principal component of six underlying sentiment proxies: closed-end fund discount, the number and the first-day returns of IPOs, NYSE turnover, the equity share in total new issues, and the dividend premium. By construction, the BW index is a measure of market-wide sentiment. We use the version of the BW index in which each of the six sentiment proxies is orthogonalized to a set of business cycle variables described in Baker and Wurgler (2006). Following Baker and Wurgler (2007) and Stambaugh et al. (2012), we define a high (low) sentiment month as one in which the BW index is above

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(below) the sample median value, and denote these sentiment states by 1 and 0 respectively2. Baker and Wurgler (2006) show that stocks which are hard to value and difficult to arbitrage are affected more by changes in sentiment. Recent studies used the BW index to examine other issues related to stock market efficiency. Stambaugh et al. (2012) study eleven stock market anomalies and find that mispricing is more prevalent when sentiment is high. Yu and Yuan (2011) find that trading by sentiment investors during high sentiment periods undermines the mean-variance relation for the market portfolio. Moreover, they find that sentiment weakens the ability of business cycle variables to explain variations in aggregate risk aversion. As mentioned in the introduction, if the MAX effect is induced by investor optimism, this effect should be larger when market-wide sentiment is high. This conjecture is plausible if (a) we view high sentiment as reflecting high investor optimism about stocks in general and (b) investors who are more optimistic about future investment returns have greater propensity to gamble as predicted by the optimal expectations theory of Brunnermeier et al. (2007)3.

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Figure 1 in the Internet Appendix plots the high and low sentiment states from July 1965 to December 2007. The fluctuations in sentiment states correspond closely to anecdotal accounts of changes in investor sentiment over time. Investor sentiment was high during the late 1960s electronics bubble, fell during the 1973-74 oil crisis, recovered during the 1980s biotech bubble, and reached new highs during the Dot.com bubble in the new millennium. 3

There is also evidence from laboratory studies that investors are more optimistic and tend to overreact following good news than bad news even if they knew that these news signals are independently and identically distributed over time. This asymmetric reaction leads to greater overpricing of securities that are short-sale constrained. See Palrey and Wang (2012).

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We begin by our analysis of sentiment and the MAX effect by examining differences in mean returns of each MAX portfolio across high and low sentiment states as defined earlier. Table 3 shows the results. [Table 3 about here] Panel A shows that following high sentiment periods, the high MAX portfolio performs poorly relative to the low MAX portfolio. Specifically, the high MAX portfolio’s mean monthly excess return is -1.32% compared to 0.58% for the low MAX portfolio. The return spread between these portfolios is -1.9%, which is highly significant, and much larger than the unconditional return spread of -0.77% shown in Table 2. The same pattern holds for the alpha spread which is now -2.04%, or nearly twice as negative as the unconditional alpha spread in Table 2. In fact, Table 3 shows that the difference in alphas between the less extreme speculative decile 9 and the low MAX portfolio is also an economically and statistically significant -0.79%. In short, conditioning on prior high sentiment greatly amplifies the MAX effect, supporting our hypothesis that high MAX stocks are more overpriced when sentiment is high. Panel B shows that following low sentiment periods, the high MAX portfolio has insignificant mean excess return and alpha. Interestingly, it is the low MAX portfolio which performs worst, with an alpha of -0.29% (t-statistic: 2.21), suggesting that investors switched to “safer” stocks during low sentiment periods. The return and alpha spread following low sentiment periods are 0.34% and -0.12% respectively. insignificant.

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Both are

There are two key takeaways from Table 3. First, the MAX effect is strongly driven by the high-sentiment state. Second the MAX effect following high-sentiment states is exclusively due to the subsequent poor returns of the most speculative portfolios (deciles 9 and 10). Put differently, it is the short leg of the MAX strategy that contributes to the MAX effect. This result supports Miller’s hypothesis that due to short selling impediments, stocks that attract the most optimistic investors will tend to be overpriced4. Although the BW index is orthogonalized with respect to many macroeconomic variables, one could argue that the index may still be picking up some aspects of the business cycle not accounted for by these variables. As such, it could be that the MAX effect following high sentiment periods is not directly due to noise-trader sentiment but because investors become too optimistic when the economy does well. From a purely empirical viewpoint, it matters little whether the MAX effect is driven by irrational sentiment or investor over-optimism in good times because the outcome is the same: high MAX stocks are overpriced relative to low MAX stocks. Nonetheless, the extent to which macroeconomic conditions can account for our findings is of some theoretical interest. Unfortunately, existing theories of stock gambling are essentially static and do not provide clear predictions about the relationship between changes in the economy and changes in investors’ propensity to gamble. Evidence from laboratory and empirical studies on this issue are also mixed. In a recent experimental study, Palfrey and Wang (2012) show that speculative securities tend to be more overpriced

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As a robustness check, we repeat our tests by defining a a high-sentiment (low-sentiment) month as one in which the BW index is above (below) its 12-month rolling median value up to t-1. The results of this test are qualitatively similar to the above findings using the full-sample BW index to define sentiment states (specifically, the MAX effect is statistically significant only following high sentiment periods). Details of the robustness test results are in the Internet Appendix (Table A1).

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when there are more good news than bad. On the other hand, using share ownership data from 1991 to 1996, Kumar (2009) shows that the demand for lottery-type stocks is higher in bad times, when the unemployment rate and bond default risk premium are high. In view of the conflicting evidence, we now provide a battery of tests using various macroeconomic indicators to see if our results are being conflated by the macroeconomic environment. We begin by refining our results in Table 3 using a two-way classification of the economy, one by the prior sentiment state, and the other, by the prior state of the economy. Following Bali, Brown, and Caglayan (2011), we use the Chicago Fed National Activity Index (CFNAI) as a broad measure of national economic activity. The CFNAI is a weighted average of 85 indicators of economic activity and inflationary pressure. Compiled by the Federal Reserve Bank of Chicago, the CFNAI is normally released towards the end of each calendar month. The 85 indicators are drawn from four broad categories of data: (a) production and income, (b) unemployment and hours, (c) personal consumption and housing, and (d) sales, orders, and inventories. Like the BW sentiment index, the CFNAI is standardized to have zero mean and a unit standard deviation. Thus, a positive index reading indicates that the economy is growing above trend and a negative index reading corresponds to growth below trend. We define two states of the economy by classifying periods with positive (negative) values of the CFNAI as periods of economic expansion (economic contraction). Together with the BW sentiment index, we now have four combinations of sentiment and economic states: low sentiment state with low or high economic activity and high sentiment state with low or high economic activity. If economy-based optimism rather than high sentiment

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drives the MAX effect, we should see a MAX effect only following periods of economic expansion, regardless of the level of investor sentiment. Similarly if investors are more attracted to high MAX stocks during bad times, a significant MAX effect should be observed only following a low CFNAI state. Table 4 shows the returns of selected MAX deciles following the above classification. To avoid clutter and because the MAX effect is about extreme returns, we only report MAX deciles 1 and 2 to represent low MAX portfolios and MAX deciles 9 and 10 to represent high MAX portfolios. We use a “0” to denote a low state and a “1” to denote a high state for each of the two variables. The results show that a significant MAX effect exists whenever sentiment in the prior month is high. This is the case whether or not the economy was in expansion or contraction. The FF4 alpha following a prior-month expansion is -2.2% a month and the alpha following a prior-month contraction is -2.42% a month. Both alphas are highly statistically significant. In contrast, there is no MAX effect when the prior-month sentiment is low, regardless of the economic state. These results suggest that sentiment states rather than economic conditions is a better predictor of the MAX effect. [Table 4 about here] Our results differ from Kumar (2009) who find that demand for lottery-type stocks increases when economic conditions are poor. Kumar’s result may be specific to lotterytype stocks and the short sample period he uses (1991 to 1996). Moreover, since Bali et al. (2011) show evidence that the MAX effect survives controls for idiosyncratic skewness and idiosyncratic volatility, it is possible that the MAX anomaly behaves differently with

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respect to changes in economic conditions as compared to lottery-type stocks. As a further check, we ran predictive regressions along the lines of Kumar (2009) using as dependent variable, returns on the long-short MAX portfolio.

We consider several sets of

macroeconomic predictors including (a) the previous month CFNAI value, (b) five macroeconomic variables used in the widely-cited Chen, Roll, and Ross (1986) study, and (c) the previous month unemployment rate, which Kumar (2009) finds to be a statistically significant predictor of the demand for lottery-type stocks. If bad times increase investors’ propensity to speculate in high MAX stocks, the coefficient of lagged unemployment coefficient should be significantly negative. Our results (Table A2 in the Internet appendix) show that although this coefficient is negative, it is not significant at any conventional significance level. Investors are also consumers. Some studies (e.g., Lemmon and Portniaguina, 2006) find that investor sentiment is correlated with consumer sentiment. To test the relative importance of investor versus consumer sentiment in driving the MAX effect, we perform a two-way classification of the data by using the BW index and the well known Michigan Consumer Sentiment Index (MSCI) to define sentiment states5. First, we orthogonalize the MCSI to macroeconomic factors using the same procedure as Baker and Wurgler (2006). Next, we define a high (low) consumer sentiment month as one in which the MCSI is above (below) the sample median value. This gives a total of four sentiment states: high

5

The MSCI is compiled by the Michigan Survey Research Center at the University of Michigan. The other widely used measure of consumer sentiment is the Conference Board Index of Consumer Confidence (CBIND) Both surveys poll U.S. households on their personal financial situation and outlook on the economy. The MCSI surveyors also ask households about their current propensity to buy major household items. Ludvigson (2004) gives details on the key differences between the CBIND and the MCSI. Most academic studies of consumer sentiment use the MSCI most likely because of its longer history.

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investor sentiment with high or low consumer sentiment, and low investor sentiment with high or low consumer sentiment. At first sight, consumer sentiment seems to have little to do with individuals’ optimism or pessimism about the stock market outlook. However, over our sample period, the MCSI has a positive, though modest correlation of 0.29 with the BW sentiment index, suggesting that there is some commonality between investor sentiment and individuals’ optimism or pessimism about the economy (see Ludvigson, 2004). The returns of MAX portfolios conditional on investor and consumer sentiment states are shown in Table 5. [Table 5 about here] Consistent with our earlier results in Table 3, there is a significant MAX effect only following high investor sentiment months. This is true even if consumer sentiment in the previous month is low. The FF4 alpha in this case is -1.97% a month. Conditioning on high prior-month consumer sentiment raises the MAX effect marginally to -2.12%. Interestingly, both alphas are close to the alpha obtained in Table 3 (-2.04%) where we condition returns only on investor sentiment. Taken together, the above results indicate that the MAX effect is mainly driven by investor sentiment rather than consumer sentiment.

5. MAX Effect and Institutional Ownership Because the MAX strategy is so simple, it is natural to assume that the MAX anomaly is mainly due to speculation by individual investors rather than institutions. After 17

all, individual investors are often portrayed as quintessential noise traders who trade for non-rational reasons (DeBondt, 1993; Kumar 2009). In particular, Kumar (2009) shows that individual investors are more attracted to lottery-type stocks than institutions. Relative to the market portfolio, individual investors overweight lottery-type stocks by 2.49% while institutional investors underweight them by 0.49%. We show that unlike the lottery-type stocks, the MAX anomaly is not confined to individual investors. To explore this, we use 13F filings with the Securities Exchange Commission (SEC) to sort stocks by institutional ownership and MAX. By law, any institution with discretionary managed portfolios of over $100 million in qualified securities is required to report those holdings quarterly to the SEC. Qualified securities include stocks listed on U.S. exchanges. Data on 13F institutional holdings for each stock is obtained from ThomsonReuters. The data starts from March 1980. A stock’s institutional ownership (IO) is computed as the fraction of its outstanding common shares that is owned by all 13F reporting institutions in a given quarter. Each month, we form double-sorted portfolios, first by IO into quintiles based on institutional ownership data in the previous quarter, then by each stock’s maximum daily return in the previous month into MAX deciles, giving a total of 50 portfolios. Table 6 reports summary statistics of the MAX portfolios sorted by IO quintiles. Panel A reports averages across months of the median maximum daily returns for each MAX portfolio for each month. Panels B and C report the average number of firms in each portfolio and their share of the overall market value (i.e., across all the portfolios). In every

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IO quintile, the maximum daily return increase monotonically as we move from the low MAX portfolio to the high MAX portfolio. The mean return spread between the high and low MAX portfolios is over 12% for Q1 and Q2, and decreases as we move from Q2 to Q5. [Table 6 about here] The relatively low return spread for Q5 (3.77%) is consistent with the fact that large institutions are governed by the prudent man rule which requires them to invest in high quality stocks (e.g., Badrinath, Gay, and Kale 1989; Del Guercio 1996). Thus, high institutional ownership appears to modulate otherwise intense demand for high MAX stocks. As we shall see, the MAX effect in the post-formation month is largely absent in Q5. At the other extreme, the large return spreads of Q1 and Q2 strongly suggests that demand for high MAX stocks in these IO quintiles come from retail investors and smaller institutions (those with assets under management of less than $100 million). More interesting perhaps are the intermediate IO quintiles, Q3 and Q4, which also exhibit high average return spreads of 9.23% and 6.12% respectively, again suggesting that many smaller institutions are attracted to high MAX stocks. The pattern of institutional ownership ratios (IOR) support our contention that smaller institutions are also represented in Q3 and Q4. The mean IORs for these quintiles are 0.26 and 0.41 respectively. These institutional ownership proportions are much higher those for Q1 and Q2 (0.03 and 0.12 respectively), though they are below the mean IOR for Q5 (0.61). That smaller institutions may be attracted to high MAX and other speculative stocks is also in line with evidence by Bennett, Sias, and Starks (2003) and Blume and Keim (2012) that in recent decades, U.S. institutional investors have increased their allocations to smaller and riskier firms and decreased their allocations to the largest firms. Panel C shows that collectively, the market 19

value share of high MAX stocks held by individuals and smaller institutions (Q1 to Q4) is 1.27%, on par with the proportion for Q5. We now turn to the post-formation performance of MAX portfolios by institutional ownership. Table 7 reports the post-formation FF4 alphas of MAX portfolios across the IO quintiles. The last panel shows that the MAX strategy yields economically and statistically significant alphas for all IO quintiles except Q5. Alphas range from 1.25% (Q3) to 3.1% (Q2). These results confirm that the MAX effect is also present in stocks with fairly high institutional ownership. It is also interesting to note that alphas for the high MAX portfolio are significantly negative for all IO quintiles except Q5, while alphas for the low MAX portfolio are mostly insignificant. Thus, the MAX effect is mainly driven by the short leg of the MAX strategy. [Table 7 about here]

5.

Sentiment, Institutional Ownership and the MAX Effect

Previous results show that the MAX effect only occurs following high sentiment states. We now examine how the MAX effect varies across sentiment states and level of institutional ownership. If investors are generally optimistic when sentiment is high, the MAX effect should be stronger across the board following high sentiment periods than low sentiment periods. To answer this question, we compute alphas of MAX portfolios for each institutional quintile conditional on prior-month high and low sentiment. As before, a high (low) sentiment state is one in which the Baker-Wurgler sentiment index is above (below) its sample median. Table 8 shows the results. Panel A reports alphas conditional on prior20

month high sentiment, while Panel B shows alphas conditional on prior-month low sentiment. Alphas which are significant at 5% are highlighted in bold. We report the profitability (alphas and t-statistics) of the MAX strategy in the last two columns of each panel. [Table 8 about here] A glance at the two panels clearly shows that the MAX effect exists only when prior-month sentiment is high. Moreover, Panel A shows that this effect is significant for all but the highest institutional ownership quintile (Q5). The mean alpha of the long-short strategy for IO quintiles Q1 to Q4 is -2.73%, which is both statistically and economically significant. The alpha for Q4 alone is a sizeable -2.5%. Consistent with our previous results, it is the short leg of the strategy that mainly accounts for the negative alphas. Finally, Panel B shows that there is no MAX effect for any IO quintiles following the low sentiment state. We conclude that investors have a greater propensity to speculate during high sentiment periods, leading to overpricing of high MAX stocks. Overpricing is not limited to individual investors. We now examine the impact of sentiment as a continuous variable instead of just discrete states. Specifically, we perform time series regressions where the dependent variable is the excess return on the MAX strategy, and the independent variables are the lagged BW index and the four risk factors. The regression approach allows us to conduct significance tests on the effects of investor sentiment while controlling for factors that are thought to be relevant for expected returns. If high sentiment leads to overpricing of high

21

MAX stocks, the coefficient on lagged sentiment should be negative. Moreover, if the effect of sentiment is pervasive, the coefficient should be negative across most IO quintiles. Table 9 reports the regression results. Consistent with the overpricing hypothesis, Panel A shows that high sentiment predicts lower excess returns one month later. Panel B shows that lagged sentiment remains significant even after controlling for the FF4 risk factors and the liquidity risk factor studied by Pastor and Stambaugh (2003). In general, the momentum and liquidity risk factors are the least significant among the five risk factors. Panel B shows that the coefficient on lagged sentiment is significantly negative for all IO quintiles except Q5, confirming the market-wide impact of sentiment on the pricing of MAX stocks. This result is robust to the inclusion of one-month lag values of the risk factors as well as one-month lag values of the Michigan consumer sentiment index. In untabulated results, we find that the coefficient on the lagged MCSI is insignificant for all IO quintiles, even at the 10% significance level. [Table 9 about here] Does sentiment account for the MAX effect? Since the MAX effect exists only following high sentiment periods, we focus our analysis on returns following this state. Specifically, we regress returns for this conditional sample on the lagged BW index and the risk factors. Panel C of Table 9 displays the regression intercepts and t-statistics. For the model without risk-adjustments, the intercepts are all insignificant. Thus, adjusting for lagged sentiment fully explains the MAX effect. This result is interesting in its own right

22

since many theories propose that investors who are drawn to lottery-like securities are riskseeking (e.g., Brunnermeier et al. 2007; Barberis and Xiong 2012)6. For risk-averse investors, we report alphas after controlling for lagged sentiment and the risk factors. The intercepts of this regression are shown in the last row of Panel C. These results should be compared with the highly significant alphas shown in Table 8. The key finding is that alphas are now much less significant after controlling for lagged sentiments. In particular, only one alpha (for Q1) is significant at 5%. Furthermore, the alphas are smaller for all IO quintiles. For example, the alpha for Q4 is 1.7% per annum compared to 2.50% in Table 8. We conclude that sentiment partially accounts for the riskadjusted return spread between high and low MAX stocks. An alternative test is to use a “sentiment factor” to predict MAX portfolio returns. To implement this factor-mimicking approach, we sort stocks by their estimated sentiment betas each month into deciles, where S1 and S10 denote the decile with the lowest and highest sentiment betas respectively. A stock’s sentiment beta in month t is the slope coefficient for sentiment from a rolling regression of the stock’s excess returns on the FF4 factors and monthly change in the BW index over the previous 36 months. The sentiment factor (SENT) for month t is the difference in returns between S10 and S1 in month t. We repeat the previous predictive regression by replacing the lagged BW index by SENT. To save space, we report the detailed results in the Internet Appendix (Table A4). The results 6

Although mainstream economics is based the assumption that agents are globally risk-averse, risk-seeking behavior also has a long history in economic discourse. Friedman and Savage (1948) were the first to propose that investors may be locally risk-seeking. Shefrin and Statman (2000) incorporate local risk seeking in their behavioral portfolio theory (BPT) in which investors hold multiple portfolios combining a desire for safety with the desire to get rich. Barberis and Xiong (2012) argue that highly volatile stocks appeal to certain risk seekers who maximize realized utility (the utility derived when extreme gains).

23

in this table are qualitatively similar to those shown in Table 9. In particular, returns on the long-short MAX portfolios are negatively related to SENT for most institutional ownership quintiles, indicating that SENT captures sentiment movements that affect the pricing of the long-short portfolio. Moreover, controlling for SENT in the high-sentiment state leads to smaller and less significant alphas than the unconditional alphas.

6.

Cross-Sectional Regressions

So far, our analysis of the MAX effect has been at the portfolio level. Portfolio level analysis has the advantage of being non-parametric because we do not assume any functional relationship between the variables of interest. On the other hand, aggregating data into portfolios throws away potentially important firm-specific information. This final section complements our portfolio-level analysis by performing FamaMacBeth cross-sectional regressions using individual stock returns. We use this approach to test whether the MAX effect is mainly driven by sentiment and other proxies for the propensity to gamble. One interesting proxy for the propensity to gamble is religious beliefs, and in particular, the variation across regions in the ratio of Catholics to Protestants. This concept was first exploited by Kumar, Page, and Spalt (2011) in their study of the demand for lottery-type stocks. They find that U.S. counties with a higher ratio of Catholics to Protestants (CPRATIO) are more likely to legalize the sale of state lotteries and generate higher lottery sales per capita. More interestingly, Kumar et al. find that openness to state lotteries, as reflected by a high CPRATIO, is also positively correlated with investors’ propensity to speculate in lottery-type stocks. We map individual

24

firms’ CPRATIOs to the county where the firms are headquartered and use this variable to measure gambling propensity in our cross-sectional regressions. The dependent variable in our FM regressions is a stock’s monthly excess return. The key independent variables are (a) MAX, the maximum daily return of a stock over the previous month, (b) an interaction variable MAX x BW, where BW is a dummy variable with value equals to 1 if the BW sentiment index in the previous month is above the sample median and zero otherwise, (c) MAX x CPR, where CPR is a dummy variable with value equals to 1 if the CPRATIO for a firm headquartered in a particular county is above the median and zero otherwise, and (d) MAX x BW x CPR. Information to construct the CPRATIO is from the American Religion Data Archive (ARDA), which provides countylevel statistics on various religious composition profiles such as number of Judeo-Christian churches and number of church adherents by denominations for each church. This is the same data source used by Kumar et al. (2012). At the time of writing, the ARDA database contains information for the years 1980, 1990, 2000, and 2010. As in Kumar et al. (2012), we linearly interpolate the data to obtain values for the intermediate years. In addition to the above regressors, we include standard risk control variables in the form of factor exposures for market excess returns (MKT), the SMB factor, the HML factor, and the UMD factor, estimated contemporaneously following the approach suggested by Shanken (1992) and implemented by Ang, Hodrick, Xing, and Zhang (2009) in their analysis of idiosyncratic volatility. The complete regression model is as follows: Ri ,t = c i + λi ,0MAX i ,t −1 + λi ,1BWt −1 + λi ,2(MAX i ,t −1 ×BWt −1 ) + λi ,3CPRi ,t −1 + λi ,4(MAX i ,t −1 ×CPRi ,t −1 ) + λi ,5(MAX i ,t −1 ×BWt −1 ×CPRi ,t −1) + γ β ' βj ,t + εi ,t

(2) 25

where R i ,t ,t +1 is a stock’s excess return in month t, MAX i ,t −1 is the maximum daily returns of the stock in t-1, BWt −1 is the sentiment dummy variable in t-1, CPRi ,t −1 is the CPRATIO dummy variable in t-1, and β j ,t (j =1, ..,4) is the vector of FF4 risk factor loadings estimated over the same month as stock returns. The regression is estimated monthly for all firms sorted by institutional quintiles. All independent variables except for dummy variables are standardized to mean zero and unit standard deviation to facilitate interpretation of the results. Table 10 reports the mean slope coefficients for the above cross-sectional regression model. Panel A reports the coefficient estimates on MAX for a baseline model that does not include the interaction terms. This model is used to examine whether a MAX effect is evident for a typical firm within each institutional quintile. The results show that MAX coefficient estimate is significantly negative for IO quintiles Q1 to Q4, indicating that a firm-level MAX effect shows up in all but the highest institutional ownership quintile. [Table 10 about here] The rest of the table (Panel B) investigates the joint return impact of MAX and the two proxies for gambling propensity. We highlight five key results. First, the coefficient on the sentiment dummy is significantly negative at the 10% level for the three lowest IO quintiles, consistent with the hypothesis that returns of stocks that are dominated by individual investors and smaller institutional investors are more prone to sentiment shifts. Second, the coefficient for MAX x BW is significantly negative for Q1 to Q3, and marginally so for Q4. Thus, sentiment amplifies the stand-alone impact of MAX on stock 26

returns, except for stocks with very high institutional ownership. To give a sense of the size of the sentiment effect, consider quintiles Q1 to Q4, where the average coefficient for MAX x BW is -0.104. This number implies that if sentiment was high in the previous month, a one standard deviation increase in MAX translates to a current month annualized return that is 1.25% lower (-0.104 x 12) for the average firm in these quintiles, an impact which can considered to be economically significant. Third, similar to the effects of sentiment, the coefficient on CPR is significantly for Q1 to Q3, implying that stocks with low institutional ownership are more prone to speculation if the firms within these IO quintiles are headquartered in regions where gambling activities are more acceptable (i.e., counties with above median CPRATIOs). Fourth, a firm’s location in a high CPRATIO region amplifies the MAX effect on stock returns in the same way that high sentiment does. This can be seen in the coefficient estimates for MAX x CPR, which are significantly negative at 10% and below for Q1 to Q3. The average coefficient estimate for these quintiles is -0.038, which implies an additional underperformance of 0.46% a year due to the MAX effect for a high CPRATIO firm. The underperformance is higher for the two lowest IO quintiles, which are most likely dominated by retail investors. Based on the average MAX x CPR coefficient estimate for these two quintiles of -0.046, the underperformance is -0.55% per annum, which is more than twice that of Q3 and Q4. Finally, interacting MAX with both sentiment and the CPRATIO dummies leads to qualitatively similar results in that the effect of MAX on future returns is significantly amplified when above-average sentiment occurs in regions where the propensity to gamble is high. This result holds (at the 10% significance level) for the lowest four IO quintiles. 27

In the Internet Appendix, we report additional Fama-MacBeth regression results to provide more direct evidence on the role of institutional ownership level and institution type on the MAX effect. Unlike Table 10, these regressions treat institutional ownership as a continuous variable. Since our previous results show that the MAX-sentiment effect is concentrated in lower IO quintiles, we perform regressions on stocks in two institutional ownership groups: IO_LOW and IO-HIGH to increase the power of the tests. Specifically, we define IO_LOW as 1 minus the fractional institutional ownership of a firm in the lowest three institutional ownership quintiles and IO_HIGH as 1 minus the fractional institutional ownership of a firm in the top two institutional ownership quintiles. The regressions focus on whether (a) the level of a firm’s IO negatively predicts the cross-section of stock returns, (b) whether the strong MAX effect in low IO quintiles is simply due to investors clustering in regions with large financial counties (which also tend to have above-average CPRATIOs), and (c) whether the MAX effect differs across institutional types. Following Kumar et al. (2011), we hypothesize that the MAX effect is less pronounced among ‘conservative’ institutions such as banks and insurance and more pronounced among ‘aggressive’ institutions such as investment companies, independent investment advisors and other institution types. The results of these regressions are shown in Table A5 in the Internet Appendix where we also provide more details of the regression specifications. Here we give a summary of the main findings. The main results are: (1) geographical clustering does not explain the MAX effect. Specifically, the coefficient on a dummy variable that takes a value of one if a firm is located in one of the top 5 counties in terms of county-level institutional holdings and zero otherwise is not significant at any conventional level, (2) 28

lower institutional ownership increases the predictive power of the MAX-sentiment effect only within the IO_LOW group, (3) conditional on LOW_IO, a higher CPRATIO reinforces the MAX effect, but this effect is weaker than the institutional ownership effect, being significant only at the 10% level, and (4) the MAX effect is significant only among aggressive institutions, consistent with the results of Kumar et al. albeit in a somewhat different context (they consider lottery-type stocks). Overall, these results indicate that across a range of firms, institutional ownership plays a pivotal role in mediating the MAX effect. Furthermore, the influence of institutional ownership is independent of the CPRATIO and is also not mechanically induced by geographical clustering of investors in large financial counties. In summary, we find that the MAX effect is strongly sentiment-driven, and that smaller institutions, like individual investors appear to be important clienteles of high MAX stocks. There is also some evidence that the MAX effect among such investors is related to on the gambling-acceptance environment where firms and investors are located. At a broader level, our results have theoretical and practical implications for asset pricing and portfolio management. Existing theories of stock gambling such as the optimal expectations model of Brunnermeier et al. (2007) argue that investors are drawn to lotterylike securities because they are optimistic about the future payoffs of these securities. We provide a behavioral underpinning to their story by showing that investor optimism towards high MAX stocks is strongly dependent on sentiment. Our results suggest that investors should consider reducing their allocations to high MAX stocks during high-sentiment periods since these stocks have low subsequent returns. With the increasing participation of

29

institutional investors in smaller, riskier stocks, this message goes out to retail as well as institutional investors.

30

7. Conclusion The MAX effect documented by Bali et al. (2011) provides an interesting setting to test the effects of investor sentiment on stock returns. The weak form version of the efficient market hypothesis implies that past prices should contain no relevant information for predicting future prices. The MAX effect is a glaring counter-example to this principle. The effect is consistent with investors who are over-optimistic of extreme positive payoffs from buying high MAX stocks. We argue that investor optimism should be highly correlated with investor sentiment, and provide evidence that supports this conjecture. First, we confirm that the MAX effect exists based on a more recent sample than Bali et al. (2011), indicating that the anomaly has persisted over time. Second, consistent with the fundamental proposition in behavioral finance that sentiment affects asset prices, the MAX effect only exists following high investor sentiment states. Indeed, the MAX effect in this state is much larger than the unconditional MAX effect. Third, consistent with Miller’s (1977) hypothesis, the MAX effect following high sentiment states is largely due to the poor subsequent returns of high MAX stocks (the short leg of the MAX strategy). Furthermore, extensive tests show that unlike sentiment, macroeconomic variables have no predictive power for the MAX effect. Fourth, while the MAX effect is strongest for stocks with low institutional ownership, the anomaly is not limited to individual investors. On the contrary, we find that the MAX effect is also present in stocks with moderate institutional ownership. This result is consistent with Cornell, Landsman and Stubben (2011) who show that institutions increase holdings of difficult-to-arbitrage stocks when sentiment is high. Fifth, predictive 31

regressions show that accounting for lagged sentiment as well as a sentiment-based return factor reduces both the statistical significance and the size of the MAX effect. Finally, cross-sectional tests corroborate the time series test results by showing that the MAX effect exists at the firm level, and that this effect is amplified by environment factors such as high investor sentiment and religious beliefs that are more tolerant of gambling. Overall, our results provide a behavioral underpinning (sentiment) to models of stock gambling based on investor over-optimism and gambling attitudes. Our findings also imply that investors should consider reducing their investments in high MAX stocks when sentiment is high since it is precisely during such periods that such stocks are overpriced.

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Table 1. Descriptive Statistics of MAX Portfolios MAX portfolios are formed every month from July 1965 to December 2007 by sorting common stocks on NYSE, Amex and Nasdaq based on the maximum daily return (MAX) of each stock over the past month. Portfolio D1 (D10) is the portfolio of stocks with the lowest (highest) maximum daily returns in the last month. Panel A reports the average number of firms and average proportion of total market capitalization of each MAX decile. Panel B reports the average (across months in the sample), of median values of stock characteristics for each MAX decile: MAX (in percent), Size or market capitalization (in millions of dollars), stock price (in dollars), market beta, book-to-market ratio (BM), Amihud illiquidity measure, Illiq (scaled by 105) and idiosyncratic volatility over the past month, IVOL (in percentage). MAX Deciles D1

D2

D3

D4

D5

D6

D7

D8

D9

D10

Panel A. Portfolio Size No. of Firms % of Overall Market Value

497 14.8

495 21.9

496 19.2

496 14.5

496 10.6

496 7.5

497 5.0

496 3.4

496 2.1

496 1.1

Panel B. Firm Characteristics MAX (Percent) Size ($ Millions) Price Beta BM ratio

2.49 226.79 17.13 0.26 0.84

3.22 273.02 22.74 0.52 0.79

3.84 203.71 20.51 0.63 0.75

4.44 156.71 18.35 0.71 0.73

5.08 122.12 16.14 0.77 0.71

5.78 95.97 13.86 0.82 0.71

6.55 74.04 11.44 0.87 0.7

7.45 55.74 9.19 0.88 0.7

8.66 38.6 6.87 0.86 0.72

11.42 20.19 4.08 0.74 0.76

3.03 1.24

0.17 1.43

0.16 1.7

0.19 1.96

0.25 2.24

0.33 2.54

0.48 2.87

0.69 3.27

1.31 3.83

3.5 5.08

5

Illiq (10 ) IVOL

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Table 2. Returns and Alphas of MAX Portfolios MAX portfolios are formed every month from July 1965 to December 2007 by sorting common stocks on NYSE. Amex and Nasdaq based on the maximum daily return (MAX) of each stock over the past one month. The lowest (highest) decile contains stocks with the lowest (highest) MAX. Panel A reports mean excess returns and alphas of each portfolio one month after portfolio formation. Excess returns are returns in excess of the one-month Treasury bill rate. The FF4 Alpha column shows Fama-French-Cahart four-factor alphas and t-statistics. Panel B reports the MAX return spread (the difference in mean returns or alphas between MAX decile 10 and MAX decile 1), without and with controls for idiosyncratic skewness (ISKEW). See text for details of the ISKEW control procedure. All returns are expressed in percent per month. Newey-West (1987) adjusted t-statistics are shown in parentheses. Numbers in bold denote significance at 5% or better.

Panel A MAX Deciles Low MAX 2 3 4 5 6 7 8 9 High MAX Panel B

Excess Return 0.329 0.503 0.493 0.560 0.531 0.644 0.502 0.374 0.084 -0.440

FF4 Alpha Alpha -0.078 0.083 0.067 0.131 0.132 0.144 -0.011 -0.255 -0.533 -1.180

t-stat (-0.77) (1.05) (1.02) (1.74) (1.78) (1.71) (-0.10) (-1.90) (-2.99) (-5.01)

MAX Return Spread (10-1)

Control for ISKEW? -0.77 No (-2.24) -0.63 Yes (-2.31)

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-1.10 (3.73) -0.65 (-2.35)

Table 3. Returns and Alphas of MAX Portfolios Following High and Low Sentiment States This table reports monthly average excess returns and FF4 alphas of MAX portfolios following high and low investor sentiment. The sample period is from July 1965 to December 2007. Details of portfolio construction are given in Table 1. A highsentiment (low-sentiment) month is one in which the value of the Baker-Wurgler (BW) sentiment index is above (below) the sample median value. The Excess Return column shows mean returns in excess of the Treasury bill rate for each MAX decile. The FF4 Alpha column shows Fama-French-Cahart four-factor alphas and t-statistics. All returns are expressed in percent per month. The last row (“10-1”) reports average returns and alphas of a portfolio that longs the high MAX decile and shorts the low MAX decile. Newey-West (1987) adjusted t-statistics are shown in parentheses. Numbers in bold denote significance at 5% or better.

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Decile Low MAX 2 3 4 5 6 7 8 9 High MAX 10-1

Low MAX 2 3 4 5 6 7 8 9 High MAX 10-1

Panel A. High Sentiment Excess Return FF4 Alpha 0.583 0.136 0.687 0.211 0.726 0.237 0.571 0.136 0.507 0.177 0.548 0.077 0.169 -0.203 0.075 -0.355 -0.462 -0.930 -1.317 -1.906

t-stat [0.97] [1.68] [2.57] [1.27] [1.64] [0.63] [-1.12] [-1.61] [-3.43] [-5.68]

-1.90 -2.04 [-3.77] [-4.83] Panel B. Low Sentiment 0.077 -0.290 0.316 -0.073 0.255 -0.156 0.553 0.091 0.549 0.051 0.733 0.194 0.824 0.147 0.665 -0.165 0.613 -0.125 0.416 -0.412

[-2.21] [-0.86] [-2.04] [0.94] [0.57] [1.69] [1.08] [-1.18] [-0.64] [-1.33]

0.339 [0.81]

-0.123 [-0.32]

Table 4. Returns of MAX Portfolios: Sentiment versus Economic States This table reports monthly average excess returns and FF4 alphas of selected MAX portfolios using a two-way classification of sample months by investor sentiment (prior-month value of the Baker-Wurgler sentiment index) and macroeconomic condition (prior-month value of the Chicago Fed National Activity Index, CFNAI). The sample period is from July 1965 to December 2007. Details on portfolio construction are given in Table 1. A high-sentiment month (“BW=1”) is one in which the Baker-Wurgler (BW) sentiment index is above the sample median value. A low-sentiment month (“BW=0”) is one in which the BW index is below the sample median value. A high CFNAI month (“CFNAI=1”) is one in which the CFNAI is positive, and a low-CFNAI month (“CFNAI=0”) is one in which the CFNAI is negative. The Excess Return column shows mean returns in excess of the Treasury bill rate for each MAX decile. The FF4 Alpha column shows Fama-French-Cahart four-factor alphas and t-statistics. All returns are expressed in percent per month. The row (“10-1”) reports average returns and

40

alphas of the portfolio that longs the high MAX decile and shorts the low MAX decile. NeweyWest (1987) adjusted t-statistics are shown in parentheses.

Max Deciles 1 2 9 10

CFNAI = 0

Excess Returns 0.322 0.500 0.728 0.590

BW = 0 Alpha

t-stat

-0.363 -0.121 -0.331 -0.427

(-1.64) (-0.97) (-0.94) (-0.80)

10-1

0.268 (0.354)

-0.064 (-0.099)

1 2 9 10

-0.061 0.192 0.318 0.014

-0.145 -0.049 -0.215 -0.642

0.074 (0.12)

-0.498 (-1.27)

CFNAI = 1

10-1

(-0.83) (-0.47) (-1.10) (-1.97)

Excess Returns 0.795 0.714 -1.029 -1.747

BW = 1 Alpha

t-stat

0.310 0.240 -0.231 -2.110

(1.37) (1.55) (-4.29) (-5.00)

-2.54 (-3.33)

-2.42 (-4.66)

0.450 0.694 -0.071 -0.987

0.136 0.317 -1.002 -2.060

-1.44 (-2.36)

-2.20 (-3.28)

(0.88) (1.83) (-1.99) (-3.50)

Table 5. Returns of MAX Portfolios: Investor Sentiment and Consumer Sentiment This table reports monthly average excess returns and FF4 alphas of selected MAX portfolios using a two-way classification of sample months by investor sentiment (priormonth value of the Baker-Wurgler sentiment index) and consumer sentiment (prior-month value of the Michigan Research Survey Consumer Sentiment Index, MCSI). The sample period is from July 1965 to December 2007. Details of portfolio construction are given in Table 1. A high investor sentiment month (“BW=1”) is one in which the Baker-Wurgler (BW) sentiment index is above the sample median value. A low investor sentiment month (“BW=0”) is one in which the BW index is below the sample median value. A high consumer sentiment month (“MCSI=1”) is one in which the MCSI is above the sample median, and a low consumer sentiment month (“MSCI=0”) is one in which the MCSI is below the sample median. The Excess Return column shows mean returns in excess of the Treasury bill rate for each MAX decile. The FF4 Alpha column shows Fama-French-Cahart 41

four-factor alphas and t-statistics. All returns are expressed in percent per month. The row (“10-1”) reports average returns and alphas of a portfolio that longs the high MAX decile and shorts the low MAX decile. Newey-West (1987) adjusted t-statistics are shown in parentheses. Numbers in bold denote significance at 5% or better.

Excess Returns 0.016 0.185 0.490 -0.003

BW = 0 Alpha

t-stat

-0.400 -0.144 -0.060 -0.595

(-2.03) (-1.37) (-0.22) (-1.34)

10-1

-0.019 (-0.04)

-0.195 (-0.376)

1 2 9 10

0.234 0.552 0.472 0.695 0.462 (0.55)

Max Deciles 1 2 9 10

10-1

MCSI = 0

MCSI = 1

Excess Returns 0.474 0.513 -0.123 -1.042

BW = 1 Alpha

t-stat

0.250 0.263 -0.356 -0.796

(1.20) (1.46) (-3.82) (-4.12)

(-0.376)

-1.52 (-2.48)

-1.97 (4.42)

-0.028 0.011 -0.378 -0.002

(-0.17) (0.08) (-1.13) (-0.47)

0.664 0.810 -0.673 -1.456

0.046 0.230 -1.210 -2.079

0.026 (-0.342)

(-0.342)

-2.12 (-3.28)

-2.12 (-3.38)

42

(0.22) (1.28) (-3.07) (-4.45)

Table 6. Summary Statistics of MAX Portfolios by Institutional Ownership Institutional ownership (IO) quintiles are formed every quarter from April 1980 to December 2007 based on SEC 13-F filings. Q1 (Q5) consists of stocks in the lowest (highest) quintile of institutional ownership (IO). For each month within a quarter, MAX portfolios are formed by sorting common stocks from NYSE, Amax, and Nasdaq into deciles based on their maximum daily returns over the past month. Panel A reports for each portfolio, the average across months of the median maximum daily return (in percent) within each month, followed by return spread between the high Max and low MAX portfolio. Panel B reports the average number of firms in each portfolio, while Panel C reports the average ratio of each portfolio’s market value at the formation date to the market value of all the 50 portfolios.

43

Max Portfolios Low MAX 2 3 4 5 6 7 8 9 High Max 10-1 Low MAX 2 3 4 5 6 7 8 9 High Max Low MAX 2 3 4 5 6 7 8 9 High Max

Panel A. Q1 2.43 3.61 4.73 5.70 6.72 7.69 8.79 9.97 11.70 15.09

Mean Returns (%) Q2 Q3 2.34 2.49 3.78 3.60 4.94 4.44 6.06 5.20 7.17 5.99 8.21 6.71 9.30 7.48 10.50 8.24 12.23 9.29 16.22 11.71

12.66 Panel B. 128 120 107 111 110 111 111 111 110 110 Panel C. 0.16 0.17 0.28 0.22 0.11 0.12 0.08 0.06 0.05 0.03

13.88 9.23 6.12 Mean No. of Firms 113 114 115 113 114 115 114 114 115 113 114 115 113 114 115 114 114 115 114 114 115 113 114 115 113 114 115 113 114 115 Mean Proportion of Market Value (%) 2.00 2.93 5.60 1.74 3.60 7.05 1.15 3.21 6.64 0.59 2.27 5.32 0.47 1.80 4.28 0.33 1.23 3.51 0.25 0.84 2.57 0.20 0.56 1.90 0.13 0.52 1.29 0.12 0.32 0.81

Q4 2.60 3.37 3.93 3.93 4.95 5.46 6.06 6.59 7.31 8.72

Q5 3.00 3.46 3.72 3.99 4.25 4.56 4.93 5.36 5.92 6.77 3.77 115 116 116 116 116 116 116 116 116 115 5.20 5.76 5.10 4.21 3.94 3.46 2.74 2.21 1.67 1.22

Table 7. Returns of MAX Portfolios by Institutional Ownership Institutional ownership (IO) quintiles are formed every quarter from April 1980 to December 2007 based on SEC-13F filings. Q1 (Q5) consists of stocks in the lowest (highest) quintile of institutional ownership. Each month, MAX portfolios are formed within each IO quintile by sorting common stocks from NYSE, Amex, and Nasdaq into deciles based on their maximum daily returns over the past month. Panel A reports FF4 alphas (in percent) and Panel B reports their t-statistics. Panel C (“10-1”) reports for each IO quintile, the alpha and Newey-West t-statistic (in parentheses) of a portfolio that longs the low MAX portfolio and shorts the high MAX portfolio. Numbers in bold denote significance at 5% or better.

44

IO Quintiles: Low MAX 2 3 4 5 6 7 8 9 High Max Low MAX 2 3 4 5 6 7 8 9 High Max 10-1 t stat

Panel A. Alphas Q1 Q2 Q3 -0.13 0.11 0.27 0.12 0.24 0.41 0.13 0.07 0.00 -0.18 0.01 0.09 0.20 -0.02 0.00 -0.80 -0.06 -0.16 -1.15 -0.92 -0.16 -1.18 -0.67 -0.67 -0.99 -1.84 -0.72 -2.02 -3.00 -0.98 Panel B. t-statistics -0.70 0.54 1.61 0.81 1.30 2.46 0.46 0.33 0.02 -0.91 0.05 0.46 0.71 -0.06 0.00 -2.41 -0.19 -0.57 -3.12 -2.68 -0.48 -3.36 -2.06 -1.59 -4.44 -2.03 -1.82 -3.50 -4.78 -2.18 Panel C. Difference in Alphas 1.89 3.10 1.25 [-3.02] [-4.65] [-2.46]

45

Q4 0.38 0.39 0.54 0.44 0.22 0.26 0.17 -0.26 -0.46 -1.14

Q5 0.01 0.05 0.03 0.00 0.04 0.09 -0.02 0.03 -0.12 0.02

2.58 3.50 3.51 2.29 1.30 1.39 0.85 -1.19 -1.84 -3.34

0.10 0.36 0.27 -0.01 0.34 0.70 -0.12 0.21 -0.62 0.11

1.52 [-3.65]

-0.01 [0.03]

Table 8. Returns of MAX Portfolios by Institutional Ownership and Investor Sentiment Institutional ownership (IO) quintiles are formed every quarter from April 1980 to December 2007 based on SEC 13F filings. Q1 (Q5) consists of stocks in the lowest (highest) quintile of institutional ownership. Each month, MAX portfolios are formed within each IO quintile by sorting common stocks from NYSE, Amex, and Nasdaq into deciles based on their maximum daily return over the past month. The table reports FF4 alphas for MAX portfolios conditional on high and low prior-month sentiment states. A high-sentiment (low-sentiment) state is one where the Baker-Wurgler sentiment index is above (below) its median value. Panel A reports FF4 alphas of each MAX portfolio, the difference in alphas between the Low and high MAX portfolio (column labeled 10-1) and Newey-West t-statistics of this difference. Numbers in bold denote significance at 5% level or better. Institutional Ownership Quintiles Q1 Q2 Q3 Q4 Q5

Low MAX -0.14 0.50 0.37 0.61 0.26

2 0.21 0.48 0.59 0.50 0.16

3 0.02 0.16 0.12 0.76 0.08

4 -0.36 -0.14 0.11 0.49 0.05

Q1 Q2 Q3 Q4 Q5

-0.20 -0.26 0.15 0.10 -0.22

-0.11 0.09 0.23 0.16 -0.15

0.02 0.03 -0.18 0.15 -0.11

-0.14 -0.01 0.34 0.39 -0.11

Panel A. High Sentiment States MAX Deciles 5 6 7 -0.02 -1.07 -1.80 -0.22 -0.49 -1.03 0.27 -0.18 -0.37 0.42 0.60 0.02 -0.03 -0.07 -0.28 Panel B. Low Sentiment States 0.42 -0.36 -0.15 0.23 0.48 -0.66 -0.28 -0.09 0.22 -0.06 -0.16 0.38 0.06 0.15 0.30

46

8 -1.50 -0.70 -0.93 -0.57 0.13

9 -1.40 -2.60 -0.94 -0.54 -0.44

-0.56 -0.35 -0.29 0.12 -0.04

-0.31 -0.81 -0.25 -0.41 0.24

Long-Short Portfolio High MAX 10-1 t-stat -2.73 -2.58 [-3.67] -3.68 -4.19 [-3.92] -1.27 -1.64 [-2.42] -1.89 -2.50 [-4.38] -0.26 -0.52 [-1.15] -0.71 -2.09 -0.55 -0.03 0.30

-0.51 -1.83 -0.70 -0.13 0.52

[-0.54] [-3.24] [-1.12] [-0.30] [1.41]

Table 9. Regressions of Long-Short MAX Returns on Lagged Sentiment This table reports the results of regressing excess returns of the long-short MAX portfolio against the lagged Baker-Wurgler (BW) sentiment index for each institutional ownership (IO) quintile. IO quintiles are formed every quarter from April 1980 to December 2007 based on SEC 13F filings. Q1 (Q5) consists of stocks in the lowest (highest) quintile of institutional ownership. Each month, MAX portfolios are formed within each IO quintile by sorting common stocks from NYSE, Amex, and Nasdaq into deciles based on their maximum daily return over the past month. The long-short portfolio longs the High MAX portfolio and shorts the Low MAX portfolio. Panel A reports regression results with the lagged BW index as the regressor, with Newey-West t-statistics in parentheses. Panel B reports regression results which include contemporaneous values of the FamaFrench-Cahart four factors plus the liquidity risk factor (ILLIQ) of Pastor and Stambaugh (2003). Results in both Panels A and B are based on the whole sample period. Panel C reports the intercepts for above regressions conditional on high sentiment in the previous month.

c Lagged BW Adj Rsq c MKT SMB HML UMD ILLIQ Lagged BW Adj Rsq Risk-adjustment: None Yes

Panel A. Returns on Lagged Sentiment Q1 Q2 Q3 Q4 Q5 -0.009 -0.017 0.0058 -0.0042 0.0038 (-1.35) (-2.86) (0.51) (-0.98) (1.12) -0.025 -0.029 -0.0226 -0.025 -0.0118 (-2.86) (-3.77) (-1.79) (-3.18) (-1.95) 0.020 0.029 0.0132 0.0401 0.0128 Panel B. Returns on Lagged Sentiment and Risk Factors -0.014 -0.027 -0.014 -0.010 -0.001 (-1.91) (-3.52) (-2.33) (-1.68) (-0.40) 0.833 0.797 1.023 0.816 0.552 (3.40) (3.27) (4.55) (4.05) (4.10) 0.645 0.527 0.364 0.296 0.318 (2.23) (1.97) (1.23) (1.13) (2.05) -0.538 -0.296 -0.245 -0.217 -0.496 (-1.81) (-0.75) (-0.73) (-0.82) (-2.46) 0.034 0.224 -0.003 -0.078 -0.042 (0.09) (0.49) (-0.01) (-0.28) (-0.19) 0.008 -0.078 -0.178 -0.006 -0.098 (0.08) (-0.54) (-2.12) (-0.08) (-1.66) -0.014 -0.022 -0.013 -0.018 -0.004 (-2.23) (-3.62) (-2.85) (-3.11) (-1.05) 0.250 0.184 0.292 0.285 0.333 Panel C. Regression Intercepts: High Sentiment States -0.012 (-0.81) -0.023 (-2.01)

-0.015 (-0.85) -0.026 (-1.43)

47

0.008 (0.65) -0.010 (-1.02)

-0.005 (-0.46) -0.017 (-1.79)

-0.006 (-0.77) -0.010 (-1.67)

Table 10. Sentiment and the MAX Effect: Estimates from Cross-Sectional Regressions This table reports estimates from Fama-MacBeth regressions of stock excess returns in which the dependent variable is monthly stock excess returns for firms in each institutional ownership quintile. Q1 (Q5) is the quintile with the lowest (highest) institutional ownership based on 13F filings. The sample period is April 1980 to December 2007. The key independent variables are (a) MAX, the maximum daily return of a stock over the previous month, (b) an interaction variable MAX x BW, where BW is a dummy variable with value equals to 1 if the Baker-Wurgler sentiment index in the previous month is above the sample median and zero otherwise, (c) MAX x CPR, where CPR is a dummy variable with value equals to 1 if the ratio of Catholics to Protestants (CPRATIO) for a firm headquartered in a particular county is above the median and zero otherwise, and (d) MAX x CPR x BW. The regression also includes exposures to the FF4 risk factors estimated contemporaneously to stock returns. Panel A reports estimates of the MAX coefficient from a baseline model that excludes the interaction terms. Panel B reports the results of the full regression model. Numbers in parentheses are Newey-West-adjusted t-statistics. Variable

-0.152 (-2.22)

Firms in Institutional Quintiles Q2 Q3 Q4 Panel A. Baseline Model -0.175 -0.163 -0.094 (-2.58) (-2.27) (-2.10)

-0.042 (-1.32)

-0.069 (-1.72) -0.058 (-2.34) -0.120 (-2.12) -0.064 (-2.27) -0.041 (-2.69) -0.103 (-2.34) 1.020 (5.20) 0.19 (1.47) -0.528 (-3.05) 0.126 (2.17)

Panel B. Full Model -0.082 -0.094 (-1.83) (-1.96) -0.079 -0.048 (-1.68) (-1.75) -0.133 -0.098 (-2.30) (-2.30) -0.049 -0.057 (-1.99) (-1.79) -0.050 -0.023 (-2.51) (-1.77) -0.118 -0.078 (-2.47) (-2.32) 0.931 0.984 (4.82) (5.37) 0.255 0.165 (1.20) (1.52) -0.600 -0.521 (-3.44) (-3.18) 0.104 0.104 (1.83) (2.06)

-0.070 (-1.82) -0.015 (-1.43) -0.064 (-1.64) -0.031 (-1.43) -0.014 (-1.58) -0.071 (-1.83) 1.020 (5.33) 0.085 (0.80) -0.447 (-2.39) 0.071 (2.30)

-0.026 (-0.71) -0.006 (-0.58) -0.027 (-0.97) 0.013 (0.54) -0.005 (-0.75) -0.029 (-1.32) 0.990 (4.94) 0.086 (0.38) -0.297 (-1.76) 0.060 (1.36)

0.057

0.056

0.034

0.040

Q1 MAX tstat Full Model: MAX BW MAX x BW CPR MAX x CPR MAX x CPR x BW MKT beta SMB beta HML beta UMD beta

Adj Rsq

0.050

48

Q5