Mutual Funds and the Sentiment-Related. Mispricing of Stocks

Mutual Funds and the Sentiment-Related Mispricing of Stocks Jiang Luo January 14, 2015 Abstract Baker and Wurgler (2006) show that when sentiment is high (low), difficult-tovalue stocks, including young stocks, risky stocks, unprofitable stocks, non-dividendpaying stocks, and growth stocks, are overpriced (underpriced). In this article, we test whether mutual funds cause this mispricing. We have two major findings. First, when sentiment is high, mutual funds tend to buy difficult-to-value stocks that have already been overpriced. Second, when sentiment is low, mutual funds heavy selling causes difficult-to-value stocks to be underpriced. Our additional tests suggest that fund managers play a more important role in causing this underpricing than fund investors do. Taken together, our findings suggest that mutual funds contribute to the sentiment-related mispricing of stocks, especially when sentiment is low. JEL Classification: G02; G12; G23 Keywords: Investor sentiment; Mutual fund; Stock price We thank Michael Brennan, David Hirshleifer, and Richard Roll for valuable comments. All errors are ours. Nanyang Business School, Nanyang Technological University, Singapore 639798. E-mail: luojiang@ntu.edu.sg. 1

1 Introduction An important finding in recent economic and financial research is that investor sentiment can cause stocks to be mispriced. In their seminal article, Baker and Wurgler (henceforth BW, 2006) construct a market-based investor sentiment index and show that when sentiment is high, difficult-to-value stocks, including young stocks, risky stocks, unprofitable stocks, non-dividend-paying stocks, and growth stocks, are overpriced relative to the benchmark. When sentiment is low, these stocks are underpriced relative to the benchmark. Other studies in a similar vein include Stambaugh, Yu, and Yuan (2012), Baker, Wurgler, and Yuan (2012), Ben-Rephael, Kandel, and Wohl (2012), Hwang (2011), Yu and Yuan (2011), etc. Yet, it remains unclear whose trades are related to sentiment, as measured by the BW (2006) investor sentiment index, and cause the sentiment-related mispricing of stocks. The literature usually argues that individual investors trades are related to sentiment and push stock prices away from fundamental values (e.g., DeLong, Shleifer, Summers, and Waldmann, 1990; BW, 2006). Recent studies of investors trading behavior (e.g., DeVault, Sias, and Starks, 2013; Cornell, Landsman, and Stubben, 2011) suggest that institutional investors trades, not individual investors trades, are related to sentiment. Specifically, they show that institutional investors tend to buy difficult-to-value stocks when sentiment is high, and sell difficult-to-value stocks when the BW sentiment is low. 1 In this article, we restrict our attention to mutual funds. We focus on the implication of mutual fund trades about the sentiment-related mispricing of stocks, not just their trading behavior. We are interested in mutual funds because after experiencing rapid growth in the 1 Institutional investors include hedge funds, investment managers (e.g., mutual funds, investment advisory firms, investment companies, and management subsidiaries of banks, brokers, and insurance companies), and other institutional investors (e.g., banks, brokers, insurance companies, pensions, and endowments). 2

past decades, mutual funds have become one of the most important players in the financial services industry. Toward the end of 2012, the total assets under management by the U.S. mutual fund industry reached $13 trillion, with 44.4% of households investing in mutual funds (Investment Company Institute, 2013). Mutual funds can have substantial impacts on consumers and financial markets. Our study sheds light on the impact of mutual funds on financial markets. We start our analysis by examining mutual funds trading behavior. We have two findings here. First, in general, mutual funds tend to trade (buy, hold, and sell) relatively big stocks, old stocks, safe stocks, profitable, and dividend-paying stocks. Second, depending on sentiment, which is measured using BW s (2006) investor sentiment index (we treat this index as a state variable), mutual funds can have a shift of trading behavior. For example, when sentiment is high, they tend to buy small stocks, whereas when sentiment is low, they tend to buy big stocks. However, this shift of trading behavior is neither very significant nor comprehensive. For example, there is no significant evidence that depending on sentiment, mutual funds prefer to buy stocks of different ages. This suggests that mutual funds may affect the pricing of some young stocks, but not all young stocks. We follow this logic in our test of the relation between mutual funds and the sentiment-related misplacing of stocks. Next, we test the relation between mutual funds and the sentiment-related mispricing of stocks. We focus our analysis on difficult-to-value stocks, including small stocks, young stocks, risky stocks, unprofitable stocks, non-dividend-paying stocks, and growth stocks. We have two major findings here. First, the overpricing of difficult-to-value stocks when sentiment is high, which BW (2006) has documented, is more pronounced among these stocks that mutual funds buy heavily than among these stocks that mutual funds sell heavily during this period. We further test whether mutual funds heavy buying causes 3

these stocks to be overpriced when sentiment is high. Although we cannot completely rule out this possibility, the evidence is more consistent with the notion that when sentiment is high, mutual funds chase momentum by buying these stocks that have already been overpriced. Second, the underpricing of difficult-to-value stocks when sentiment is low, which BW (2006) has documented, is more pronounced among these stocks that mutual funds sell heavily than among these stocks that mutual funds buy heavily during this period. We further test whether mutual funds heavy selling causes these stocks to be underpriced when sentiment is low. The evidence is consistent with this notion, although we cannot completely rule out the possibility that when sentiment is low, mutual funds chase momentum by selling these stocks that have already been underpriced. We also examine the pricing of easy-to-value stocks, including big stocks, old stocks, safe stocks, profitable stocks, dividend-paying stocks, and value stocks. We find that when sentiment is high, these stocks are fairly priced. When sentiment is low, these stocks can be underpriced, but this underpricing is concentrated in these stocks that mutual funds sell heavily during this period. Finally, we provide two additional tests on the relation between mutual funds and the sentiment-related mispricing of difficult-to-value stocks. In the first test, we conduct a subperiod analysis. We show that our above findings on this relation is particularly pronounced in the period of 1992-1998 and 2004-2010, during which investor sentiment is relatively stable. In the period of 1981-1991 and 1999-2003, during which investor sentiment has turbulent fluctuations, we find no significant evidence of a sentiment-related mispricing of difficult-to-value stocks. In the second test, we decompose the total mutual fund buying/selling into a passive component, which is driven by fund flows (e.g., Frazzini and Lamont, 2008; Pollet and 4

Wilson, 2008), and an active component, which is subject to fund managers discretion. We show that although both passive and active heavy selling are related to the underpricing of difficult-to-value stocks when sentiment is low, active heavy selling seems to be more related to this underpricing than passive heavy selling is. This suggests that fund managers play a more important role in causing this underpricing than fund investors do. Our study is related to two literatures. The first literature is on investor sentiment and stock prices. This literature usually argues that individual investors trades are related to sentiment and push stock prices away from fundamental values (e.g., DeLong, Shleifer, Summers, and Waldmann, 1990; BW, 2006). We find, however, that mutual funds can be a contributor to this mispricing. Particularly, mutual funds heavy selling causes difficultto-value stocks to be underpriced when sentiment is low. We also find that mutual fund managers play a more important role in causing this underpricing than fund investors do. Two related studies, DeVault, Sias, and Starks (2013) and Cornell, Landsman, and Stubben (2011), examine investors trading behavior. They find that institutional investors tend to buy difficult-to-value stocks when investor sentiment is high, and sell these stocks when investor sentiment is low, which suggests that institutional investors trades, not individual investors trades, are related to sentiment. We extend these studies in three ways. First, we restrict our attention to mutual funds. Second, our focus is on the implication of mutual funds on the pricing of stocks, not just their trading behaviors. Third, we further decompose mutual funds buying/selling into passive and active components. We find that the active component is more related to the mispricing of stocks, which suggests that mutual fund managers play a more important role in causing the mispricing than fund investors do. The second literature is on mutual funds. Previous studies in this literature provide evidence that mutual funds heavy buying and selling can cause stocks to be overpriced and 5

underpriced (e.g., Coval and Stafford, 2007; Frazzini and Lamont, 2008; Khan, Kogan, and Serafeim, 2012). Our focus is on whether mutual funds heavy buying and selling causes the mispricing of stocks related to the BW sentiment. We organize the rest of this article as follows. Section 2 describes the data. Section 3 presents our main results on mutual funds and the sentiment-related mispricing of stocks. Section 4 presents two additional tests. Section 5 concludes. 2 Data Our sample period is 1981 to 2010. Our sample starts from 1981 because a database we use to identify mutual funds, MFLINKS, starts from 1980. 2.1 Stock Data The firm-level stock data are obtained from the merged CRSP/Compustat database. We include in our sample all ordinary common stock (share codes 10 and 11). We further exclude penny stocks (stocks with a price below $1) and the 10% stocks with the smallest market equity, ME, in each year because Fama (1998) points out that common asset pricing models have difficulty explaining the returns of these stocks. [Insert Table 1 here.] Table 1 reports the summary statistics for accounting variables and stock returns used in our analysis. The unit is at the firm level. Panels A through D summarize accounting variables at the annual frequency. BW (2006) describe in detail the procedure to compute the accounting variables using CRSP/Compustat items. Panel A summarizes size, firm age, and total risk. Size is the market equity, ME. Firm age is the number of years from the firm s first appearance on CRSP to June 6

of calendar year y. Total risk, σ, is the standard deviation in monthly returns for the 12 months ending in June of calendar year y. Panel B summarizes profitability. Return on equity, E+/BE, is earnings, E, scaled by book equity, BE. It is positive if earnings, E, are positive, and 0 otherwise. The profitability dummy, E>0, is 1 if earnings, E, are positive, and 0 otherwise. Panel C summarizes dividend policy. Dividends to equity, D+/BE, is dividends, D, scaled by book equity, BE. It is positive if dividends, D, are positive, and 0 otherwise. The dividend payer dummy, D>0, is 1 if dividends, D, are positive, and 0 otherwise. Panel D summarizes growth opportunities. Book-to-market, BE/ME, is the ratio of book equity, BE, to market equity, ME. External finance, EF, is the change in assets less the change in retained earnings, scaled by book assets, BA. Sales growth, GS, is the percentage change in net sales. Comparing the means and medians of these accounting variables suggests that our sample stocks have an disproportionally large number of small stocks, young stocks, and non-dividend-paying stocks. This is consistent with the recent development in the stock market (e.g., Fama and French, 2001). Panel E summarizes stock returns at the monthly frequency. We follow Fama and French (1992) to match accounting variables for the fiscal year-end in calendar year y to monthly stock returns from July of year y through June of year y + 1. 2.2 Mutual Fund Data We obtain mutual fund holdings information from the Thomson Reuters CDA/Spectrum database. This information is collected from mutual funds filings with the Security and Exchange Commission (SEC) and their voluntary reports. Throughout our sample period 7

of 1981 to 2010, most mutual funds disclose their holdings quarterly, although they are required to disclose their holdings only semiannually. We compute the fund holdings at the end of a quarter using the latest report in that quarter. We assume that mutual funds trade at the end of the quarter. Our measure of mutual fund trades in a stock quarter, MF net purchase, is the quarterly change in the percentage of outstanding shares held by mutual funds. This measure has been used often in previous studies (e.g., Gompers and Metrick, 2001; Sias, Starks, and Titman, 2006). Sias, Starks, and Titman point out that this measure is proper when one studies the impact of institutional investors trades on stock prices. We also used other measures of mutual fund trades, such as the new dollar investment by mutual funds, and the change in the number of mutual funds holding the stock. There are two observations. First, these two measures are highly correlated with our measure of MF net purchase (the correlation coefficients are respectively 0.932 and 0.492), which suggests that they contain similar information. Second, the test results using these measures are almost identical to those using MF net purchase. We therefore report only the test results using MF net purchase. Panel F of Table 1 summarizes MF net purchase at the quarterly frequency. The mean and median of MF net purchase for a stock-quarter, 0.124% and 0.099%, are positive. This is consistent with Gompers and Metrick (2001), who show that as the mutual fund industry has grown rapidly in the past decades, mutual funds have been increasing their position in the stock market. In an average stock-quarter, mutual funds increase their total holdings by 0.124%, which seems small. However, the standard deviation of MF net purchase, 3.447%, is large, indicating that there is large cross-sectional dispersion in MF net purchase. 8

2.3 Investor Sentiment We use the monthly market-based investor sentiment index constructed by BW (2006) to measure investor sentiment. We treat this index as a state variable. BW compute this index, starting from July 1965, using the first principal component of six measures of investor sentiment, which have been orthogonalized to macroeconomic conditions. The six measures are the 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. The principal component analysis captures their common component. BW normalize this index to have mean 0 and standard deviation 1. [Insert Figure 1 here.] Figure 1 plots the BW sentiment index. It records all bubbles (the electronics bubble of 1968-69, the biotech bubble of the early 1980s, and the internet bubble of the late 1990s) and bursts. There are significant fluctuations in investor sentiment in the period of 1965-1991 and 1999-2003. Investor sentiment in the period of 1992-1998 and 2004-2010 is relatively stable. 2.4 Mutual Fund Trades Depending on Investor Sentiment In this section, we test whether mutual funds have different trading behaviors when investor sentiment is high or low. As mutual funds are assumed to trade at the end of each quarter, we use the BW sentiment index at the last month of the quarter to measure investment sentiment in the quarter. A quarter has high or low sentiment if this BW investor sentiment index is positive or negative. In each quarter, we sort stocks based on mutual fund trade information into four groups. The first group of stocks have no mutual fund holdings information. These stocks 9

are stocks that mutual funds don t trade (buy, hold, or sell). The second, third, and fourth groups of stocks have high (top 30%), medium (medium 40%), and low (bottom 30%) levels of MF net purchase. They are respectively stocks that mutual funds buy, hold, and sell. We use relative trade information, instead of absolute trade information such as MF net purchase >, =, and < 0, because BW (2007) show that mutual funds tend to be net buyers and sellers when sentiment is high and low. Using absolute trade information may complicate the interpretation of our findings. We assign rank information to each stock based on its characteristics. For example, a stock has size rank 1, 0, or -1 if it has high, medium, or low ME. The high, medium, or low ME is based on the top three, medium four, and bottom three NYSE decile breakpoints. We use the NYSE breakpoints to keep the meaning of the cutoff points consistent over time. We use rank information, instead of actual characteristics, because rank information is unlikely to be affected by sentiment. For example, small stocks remain to be small stocks even when sentiment is high. But their actual characteristics such as ME can be relatively large when sentiment is high (BW, 2006). Thus, using actual characteristics may complicate the interpretation of our findings. [Insert Table 2 here.] Table 2 reports the average rank information for stocks sorted based on mutual fund trades when sentiment is high. We have two notable observations. First, relative to the whole stock sample (Column 1), stocks that mutual funds don t trade (Column 2) have low ME and age, high σ, low E+/BE and D+/BE, high BM, and low EF and GS. This suggests that when sentiment is high, mutual funds tend to trade relatively big stocks, old stocks, safe stocks, profitable stocks, dividend-paying stocks, and value stocks. Second, Column 6 shows that relative to stocks with low MF net purchase, stocks with high MF 10

net purchase have low ME and σ, high E+/BE, high BM, and low EF. This suggests that when sentiment is high, mutual funds tend to buy small stocks, safe stocks, profitable stocks, and value stocks. [Insert Table 3 here.] Table 3 reports the average rank information for stocks sorted based on mutual fund trades when sentiment is low. We have two notable observations. First, relative to the whole stock sample (Column 1), stocks that mutual funds don t trade (Column 2) have low ME and age, high σ, low E+/BE and D+/BE, high BM, and low EF and GS. This suggests that when sentiment is low, mutual funds also tend to trade relatively big stocks, old stocks, safe stocks, profitable stocks, dividend-paying stocks, and value stocks. Second, Column 6 shows that relative to stocks with low MF net purchase, stocks with high MF net purchase have high ME, low σ, and high D+/BE. This suggests that when sentiment is low, mutual funds tend to buy big stocks, safe stocks, and dividend-paying stocks. In sum, our analysis suggests that in general, mutual funds tend to trade (buy, hold, and sell) relatively big stocks, old stocks, safe stocks, profitable stocks, dividend-paying stocks, and value stocks. Moreover, depending on sentiment, mutual funds can have a shift of trading behavior. For example, when sentiment is high, they tend to buy small stocks, whereas when sentiment is low, they tend to buy big stocks. However, this shift of trading behavior is neither very significant nor comprehensive. For example, there is no significant evidence that depending on sentiment, mutual funds prefer to buy stocks of different ages. This suggests that mutual funds may affect the pricing of some young stocks, but not all young stocks. In what follows, we use this logic to test the relation between mutual funds and the sentiment-related misplacing of stocks. 11

3 Main Results In this section, we test the relation between mutual funds and the sentiment-related mispricing of stocks. We follow BW (2006) to identify the mispricing of a portfolio of stocks when sentiment is high or low (call it quarter 0) by looking at this portfolio s benchmark-adjusted return in the subsequent quarter (call it quarter 1), α H 1 or α L 1. The supscripts, H and L, indicate high sentiment and low sentiment for quarter 0; 1 indicate the number of lagged quarters. If, for example, α H 1 is significantly negative, then these stocks are overpriced during the high-sentiment quarter. If α H 1 is significantly positive, then these stocks are underpriced during the high-sentiment quarter. We use the approach suggested by Stambaugh, Yu, and Yuan (2012) to compute these benchmark-adjusted returns. Suppose that one is interested in the pricing of a portfolio of small stocks with high MF net purchase when sentiment is high (quarter 0). In order to obtain this portfolio s benchmark-adjusted return in quarter k, αk H, we run the following regression: R t R F,t = γ k + θ k BW q(t) k + β 1,k MKT t +β 2,k SMB t + β 3,k HML t + β 4,k UMD t + ɛ t. (1) In this regression, q(t) k indicates k quarters before month t. The portfolio is constructed based on firm size and MF net purchase in quarter q(t) k. BW q(t) k is a dummy variable indicating high sentiment (the BW sentiment index is above 0) for quarter q(t) k. The dependent variable is the portfolio return, computed by weighting all stocks in the portfolio equally, minus the risk-free rate in month t. We conduct the benchmark ad- 12

justment using the Fama-French (1993) three-factor model augmented by the momentum factor developed by Carhart (1997). MKT t is the return of the market portfolio minus the risk-free rate. SMB t is the average return of small-cap stocks minus the average return of large-cap stocks. HML t is the average return of high book-to-market stocks minus the average return of low book-to-market stocks. UMD t is the average return of high momentum stocks minus the average return of low momentum stocks. We run the regression at the monthly frequency in order to use the monthly information on stock returns and factor returns. α H k = γ k + θ k. In the case that one is interested in the pricing of a portfolio of small stocks with high MF net purchase when sentiment is low (quarter 0), its benchmarkadjusted return in quarter k is α L k = γ k. 3.1 Mutual Funds and the Pricing of Difficult-to-Value Stocks 3.1.1 When Sentiment is High We follow BW (2006) to form 8 bins of difficult-to-value stocks, including small (low ME) stocks, young (low age) stocks, risky (high σ) stocks, unprofitable (E 0) stocks, nondividend-paying (D=0) stocks, and growth (low BE/ME, high EF, and high GS) stocks. The high and low portfolios are based on the top three and bottom three NYSE decile breakpoints. [Insert Table 4 here.] In Table 4, Column 1 replicates BW s (2006) result on the overpricing of difficult-tovalue stocks when sentiment is high (quarter 0). Consistent with BW, most, 7 out of 8, portfolios of difficult-to-value stocks have a significantly (the p-value is less than 10%) negative α H 1. For example, α H 1 of the portfolio of young stocks equals -0.217%, indicating 13

that young stocks underperform the benchmark in the subsequent quarter by 12.7 basis points (bps) per month. Therefore, these stocks are overpriced when sentiment is high. The only exception is the portfolio of small stocks. It has an insignificant α1 H, suggesting that small stocks are fairly priced when sentiment is high. BW (2006) report a similar finding on small stocks. Column 2 considers the portfolios of difficult-to-value stocks that mutual funds don t trade (buy, hold, or sell). Most, 7 out of 8, portfolios of these stocks have a significantly negative α H 1, indicating that they are overpriced when sentiment is high. This finding suggests that the overpricing of a significant amount of difficult-to-value stocks when sentiment is high is not related to mutual fund trades. Columns 3 to 6 consider the portfolios of difficult-to-value stocks with high (top 30%), medium (medium 40%), and low (bottom 30%) MF net purchase. Column 3 shows that most, 6 out of 8, portfolios of these stocks with high MF net purchase have a significantly negative α1 H. In contrast, Column 5 shows that all portfolios of these stocks with low MF net purchase have an insignificant α H 1. Column 6 compares α H 1 between portfolios of these stocks with high MF net purchase and portfolios of these stocks with low MF net purchase. The differences are consistently negative, though the statistical significance is weak. In sum, our findings suggest that when sentiment is high, difficult-to-value stocks with high MF net purchase (mutual fund heavy buying) are more likely to be overpriced than those with low MF net purchase (mutual fund heavy selling). Testing Causality We now test whether high MF net purchase (mutual fund heavy buying) causes difficultto-value stocks to be overpriced when sentiment is high. [Insert Table 5 here.] 14

Table 5 focuses on portfolios of difficult-to-value stocks with high MF net purchase when sentiment is high (quarter 0). We report their benchmark-adjusted returns, αk H, in quarters k = 2 up to 2. Column 3 shows that all these portfolios have significantly positive α0 H, indicating that these portfolios outperform the benchmark when mutual funds make the high net purchase. Columns 1 to 2 show that all these portfolios have significantly positive α 2 H and α 1, H indicating that these portfolios outperform the benchmark even before mutual funds make the high net purchase. [Insert Figure 2 here.] Figure 2 plots for portfolios of difficult-to-value stocks with high MF net purchase when sentiment is high (quarter 0) their benchmark-adjusted returns, α H k, in quarters k = 2 up to 2. The evidence is broadly consistent with our above analysis. α H 2, α H 1, and α H 0 are mostly positive. α1 H are mostly negative. α2 H move close to zero. In sum, although we cannot rule out the possibility that high MF net purchase (mutual fund heavy buying) causes difficult-to-value stocks to be overpriced when sentiment is high, the evidence is more consistent with the notion that when sentiment is high, mutual funds tend to chase momentum by buying difficult-to-value stocks that have already been overpriced. 3.1.2 When Sentiment is Low In Table 6, Column 1 replicates BW s (2006) result on the underpricing of difficult-to-value stocks when sentiment is low (quarter 0). Consistent with BW, most, 5 out of 8, portfolios of difficult-to-value stocks have a significantly positive α1 L. For example, α1 L of the portfolio of young stocks equals -0.292%, indicating that young stocks outperform the benchmark in the subsequent quarter by 29.2 bps per month. Therefore, these stocks are underpriced 15

when sentiment is low. The exceptions are mainly portfolios of growth stocks. They have an insignificant α L 1, suggesting that growth stocks are fairly priced when sentiment is low. [Insert Table 6 here.] Column 2 considers the portfolios of difficult-to-value stocks that mutual funds don t trade (buy, hold, or sell). Most, 6 out of 8, portfolios of these stocks have an insignificant α1 L. Although the remaining 2 portfolios of these stocks have a significantly positive α1 L, the statistical significance is marginal. This indicates that these stocks are mostly fairly priced when sentiment is low. Columns 3 to 5 consider the portfolios of difficult-to-value stocks with high (top 30%), medium (medium 40%), and low (bottom 30%) MF net purchase. Column 3 shows that all portfolios of these stocks with high MF net purchase have an insignificant α L 1. In contrast, Column 5 shows that all portfolios of these stocks with low MF net purchase have a significantly positive α1 L. Column 6 compares α1 L between portfolios of these stocks with high MF net purchase and portfolios of these stocks with low MF net purchase. The differences are mostly significantly negative. In sum, our findings suggest that the overpricing of difficult-to-value stocks when sentiment is low is concentrated in those with low MF net purchase (mutual fund heavy selling). Testing Causality We now test whether low MF net purchase (mutual fund heavy selling) causes difficult-tovalue stocks to be underpriced when sentiment is low. [Insert Table 7 here.] 16

Table 7 focuses on portfolios of difficult-to-value stocks with low MF net purchase when sentiment is low (quarter 0). We report their benchmark-adjusted returns, αk, L in quarters k = 2 up to 2. Column 3 shows that all these portfolios have significantly negative α0 L, indicating that these portfolios underperform the benchmark when mutual funds make the low net purchase. Columns 1 to 2 show that most of these portfolios have insignificant α 2 L and α 1, L indicating that these portfolios perform similarly to the benchmark before mutual funds make the low net purchase. [Insert Figure 3 here.] Figure 3 plots for portfolios of difficult-to-value stocks with low MF net purchase when sentiment is low (quarter 0) their benchmark-adjusted returns, αk, L in quarters k = 2 up to 2. The evidence is broadly consistent with our above analysis. α 2 L and α 1 L are around zero. α0 L are negative. α1 L are positive. α2 L are also around zero. In sum, our findings are consistent with the notion that low MF net purchase (mutual fund heavy selling) causes difficult-to-value stocks to be underpriced when sentiment is low. We cannot rule out the possibility that mutual funds chase momentum by selling underpriced stocks within the low-sentiment quarter. Our data at the quarterly frequency do not allow us to address this possibility. 3.2 Mutual Funds and the Pricing of Easy-to-Value Stocks 3.2.1 When Sentiment is High We follow BW (2006) to form 8 bins of easy-to-value stocks, including big (high ME) stocks, old (high age) stocks, safe (low σ) stocks, profitable (E>0) stocks, dividend-paying (D>0) stocks, and value (high BE/ME, low EF, and low GS) stocks. The high and low portfolios are based on the top three and bottom three NYSE decile breakpoints. 17

[Insert Table 8 here.] In Table 8, Column 1 replicates BW s (2006) result on the pricing of easy-to-value stocks when sentiment is high (quarter 0). Consistent with BW, all portfolios of these stocks have an insignificant α1 H, indicating that these stocks perform similarly to the benchmark in the subsequent quarter. Therefore, these stocks are fairly priced when sentiment is high. Columns 2 to 6 consider the portfolios of easy-to-value stocks with no mutual fund trades, and with high (top 30%), medium (medium 40%), and low (bottom 30%) MF net purchase. Most of these portfolios still have an insignificant α1 H, suggesting that these stocks are fairly priced when sentiment is high. The exception is these stocks with low MF net purchase. Column 5 shows that most, 5 out of 8, portfolios of these stocks with low MF net purchase have a significantly positive α1 H, suggesting that these stocks are underpriced when sentiment is high. 3.2.2 When Sentiment is Low In Table 9, Column 1 replicates BW s (2006) test on the pricing of easy-to-value stocks when sentiment is low. We find mixed evidence of underpricing. Specifically, one half, 4 out of 8, of portfolios of these stocks have a significantly positive α1 L. The other half, 4 out of 8, of portfolios of these stocks have an insignificant α1 L. [Insert Table 9 here.] Columns 2 to 6 consider the portfolios of easy-to-value stocks with no mutual fund trades, and with high (top 30%), medium (medium 40%), and low (bottom 30%) MF net purchase. Most of these portfolios have an insignificant α1 L, suggesting that these stocks are fairly priced when sentiment is low. The exception is these stocks with low MF net purchase. Column 5 shows that most, 7 out of 8, portfolios of these stocks with low MF 18

net purchase have a significantly positive α1 L, suggesting that these stocks are underpriced when sentiment is low. In sum, our findings suggest that easy-to-value stocks can be underpriced when sentiment is low. This underpricing is concentrated in those with low MF net purchase (mutual fund heavy selling). 4 Additional Tests In this section, we provide additional tests on the relation between mutual funds and the sentiment-related mispricing of difficult-to-value stocks. 4.1 Subperiods We consider two subperiods. The first subperiod includes 1981-1991 and 1999-2003. Figure 1 shows that investor sentiment has significant fluctuations during this period. We refer to this period as the turbulent subperiod. The second subperiod includes 1992-1998 and 2004-2010. Investor sentiment is relatively stable during the period. We refer to this period as the quiet subperiod. 4.1.1 The Turbulent Subperiod In Table 10, we use the turbulent subperiod to study mutual funds and the pricing of difficult-to-value stocks when sentiment is high (quarter 0). Unlike our previous analysis using the whole sample period, we find no significant evidence that in this subperiod, these stocks are overpriced when sentiment is high, even if these stocks receive high MF net purchase (mutual fund heavy buying). Specifically, Column 1 shows that all portfolios of these stocks have an insignificant α1 H. Column 3 shows that most, 7 out of 8, portfolios of these stocks with high MF net purchase have an insignificant α1 H. 19

[Insert Table 10 here.] In Table 11, we use the turbulent subperiod to study mutual funds and the pricing of difficult-to-value stocks when sentiment is low (quarter 0). Unlike our previous analysis using the whole sample period, we find no significant evidence that in this subperiod, these stocks are underpriced when sentiment is low, even if these stocks receive low MF net purchase (mutual fund heavy selling). Specifically, Column 1 shows that all portfolios of these stocks have an insignificant α1 L. Column 5 shows that most, 5 out of 8, portfolios of these stocks with low MF net purchase have an insignificant α1 L. [Insert Table 11 here.] In sum, we find no significant evidence that in the turbulent subperiod, there is a sentiment-related mispricing of difficult-to-value stocks. 4.1.2 The Quiet Subperiod In Table 12, we use the quiet subperiod to study mutual funds and the pricing of difficultto-value stocks when sentiment is high (quarter 0). The evidence is broadly consistent with our previous analysis using the whole sample period. Specifically, Column 1 shows that all portfolios of these stocks have a significantly negative α1 H. Even the portfolio of small stocks has an α H 1 of -0.362% per month, which is significant at the 5% level. This suggests that these stocks are overpriced when sentiment is high. Moreover, Column 3 shows that most, 7 out of 8, portfolios of these stocks with high MF net purchase have a significantly negative α1 H. In contrast, Column 5 shows that most, 7 out of 8, portfolios of these stocks with low MF net purchase have an insignificant α1 H. This suggests that these stocks with high MF net purchase (mutual fund heavy buying) tend to be overpriced when sentiment is high. 20

[Insert Table 12 here.] In Table 13, we use the quiet subperiod to study mutual funds and the pricing of difficult-to-value stocks when sentiment is low (quarter 0). Column 1 shows that most, 7 out of 8, portfolios of these stocks have an insignificant α1 L. This suggests that in the quiet subperiod, these stocks are generally fairly priced when sentiment is low. Column 5 shows that most, 5 out of 8, portfolios of these stocks with low MF net purchase have a significantly positive α L 1. This suggests that these stocks with low MF net purchase (mutual fund heavy selling) can still be underpriced when sentiment is low. [Insert Table 13 here.] In sum, our main results on mutual funds and the sentiment-related mispricing of difficult-to-value stocks are particularly pronounced in the quiet subperiod. 4.2 Passive vs. Active MF Net Purchase We decompose the total MF net puchase for a stock quarter into a passive component and an active component. The passive component is computed based on the assumption that after receiving a new money flow, a mutual fund scales up/down its investment in this stock according to its existing stockholdings (see, e.g., Frazzini and Lamont, 2008; Pollet and Wilson, 2008). It describes the MF net purchase that is driven by money flows from mutual fund investors. The active component captures the difference between the total MF net purchase and the passive component. It describes the MF net purchase that is subject to fund managers discretion. [Insert Table 14 here.] 21

Table 14 reports the descriptive statistics on the total, passive, and active MF net purchase. There are three notable observations. First, passive and active MF net purchases have a smaller number of observations, 288,121, than the total MF net purchase does, 384,513. The reason for this is that to we need to use fund flows (which equals the quarterly growth rate of fund TNA after adjusting fund quarterly return) to compute passive and active MF net purchases. We obtain fund TNA and return from the CRSP database. But after we link fund flows to MF net purchase, which is obtained Thomson Reuters CDA/Spectrum database, we lose a significant number of observations. For the same reason, the means of passive and active MF net purchases, 0.122% and -0.068, do not add up to the mean of total MF net purchase, 0.124%. Second, active MF net purchase has a lower mean but a higher standard variation than passive MF net purchase does. This suggests that mutual fund managers have a significant discretion over allocation. Third, total MF net purchase is highly correlated with active MF net purchase. The correlation is 0.982. This suggests that mutual fund trades are mainly determined by mutual fund managers. 4.2.1 Overpricing of Difficult-to-Value Stocks when Sentiment is High We now test whether high passive MF net purchase, or high active MF net purchase, or both are related to the overpricing of difficult-to-value stocks when sentiment is high (quarter 0). Table 15 reports the results. The evidence suggests that neither of them is related to this overpricing. Specifically, Columns 1 and 5 show that all portfolios of difficult-to-value stocks with high passive or active MF net purchase have an insignificant α1 H. [Insert Table 15 here.] 22

This finding is admittedly surprising. There can be two explanations. First, as discussed above, to obtain passive and active MF net purchase, we need to link Thomson Reuters CDA/Spectrum database to the CRSP database. This causes a significant loss of observations and can limit the power of our test. Second, it is possible that only the sum of passive and active MF net purchase is related to the overpricing of difficult-to-value stocks when sentiment is high. 4.2.2 Pricing of Difficult-to-Value Stocks when Sentiment is Low We now test whether low passive MF net purchase, or low active MF net purchase, or both are related to the underpricing of difficult-to-value stocks when sentiment is low (quarter 0). Table 16 reports the results. The evidence suggests that although both low passive MF net purchase and low active MF net purchase are related to this underpricing, low active MF net purchase seems to be more related to this underpricing. Specifically, Column 3 shows that most, 5 out of 8, portfolios of difficult-to-value stocks with low passive MF net purchase have a significantly positive α1 L. Column 7 shows that almost all portfolios of difficult-to-value stocks with low active MF net purchase have a significantly positive α1 L. [Insert Table 16 here.] In sum, our findings suggest that although both fund investors and fund managers contribute to the underpicing of difficult-to-value stocks when sentiment is low. Fund managers seem to play a more important role than fund investors do. 5 Conclusions It is generally accepted that when sentiment is high, difficult-to-value stocks, including young stocks, risky stocks, unprofitable stocks, non-dividend-paying stocks, and growth 23

stocks, are overpriced. When sentiment is low, these stocks are underpriced (e.g., BW, 2006 and 2007). However, it remains unclear who cause this mispricing. We test this question in this article. We restrict our attention to mutual funds. We have two major findings. First, when sentiment is high, mutual funds tend to buy difficult-to-value stocks that have already been overpriced. Second, when sentiment is low, mutual funds heavy selling causes difficult-to-value stocks to be underpriced. We also conduct additional tests to show that fund managers play a more important role in causing this underpricing than fund investors do. Taken together, our findings suggest that mutual funds contribute to the sentiment-related mispricing of stocks, especially when sentiment is low. 24

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Figure 1: The BW Monthly Investor Sentiment Index This figure plots the monthly market-based investor sentiment index constructed by BW (2006). They compute this index, starting from July 1965, using the first principal component of six measures of investor sentiment, which have been orthogonalized to macroeconomic conditions. The six measures are the 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. The principal component analysis captures their common component. BW normalize this index to have mean 0 and standard deviation 1. We use the sample period of 1981, which is indicated by the dashed line, to 2010. 3 2 1 0 1 2 3 1970 1975 1980 1985 1990 1995 2000 2005 2010 28

Figure 2: Difficult-to-Value Stocks with High MF Net Purchase when Sentiment is High: Performance in the Surrounding Quarters We form 8 bins of difficult-to-value stocks, including small (low ME) stocks, young (low age) stocks, risky (high σ) stocks, unprofitable (E 0) stocks, non-dividend-paying (D=0) stocks, and growth (low BE/ME, high EF, and high GS) stocks. The high and low portfolios are based on the top three and bottom three NYSE decile breakpoints. We consider portfolios of stocks in each bin that have high (top 30%) MF net purchase when sentiment is high (quarter 0; the BW sentiment index at the end of the quarter is positive). This figure plots the portfolios benchmark-adjusted returns in quarters k = 2 up to 2, αk H in % per month. A portfolio s return is computed by weighting all stocks in the portfolio equally. We compute its αk H using Eq. (1). The sample period is 1981 to 2010. 1.4 1.2 1 α k H (% per month) 0.8 0.6 0.4 0.2 0 0.2 0.4 3 2 1 0 1 2 3 Quarter k 29

Figure 3: Difficult-to-Value Stocks with Low MF Net Purchase when Sentiment is Low: Performance in the Surrounding Quarters We form 8 bins of difficult-to-value stocks, including small (low ME) stocks, young (low age) stocks, risky (high σ) stocks, unprofitable (E 0) stocks, non-dividend-paying (D=0) stocks, and growth (low BE/ME, high EF, and high GS) stocks. The high and low portfolios are based on the top three and bottom three NYSE decile breakpoints. We consider portfolios of stocks in each bin that have low (bottom 30%) MF net purchase when sentiment is low (quarter 0; the BW sentiment index at the end of the quarter is negative). This figure plots the portfolios benchmark-adjusted returns in quarters k = 2 up to 2, αk L in % per month. A portfolio s return is computed by weighting all stocks in the portfolio equally. We compute its αk L using Eq. (1). The sample period is 1981 to 2010. 0.6 0.4 0.2 α k L (% per month) 0 0.2 0.4 0.6 0.8 1 3 2 1 0 1 2 3 Quarter k 30

Table 1: Summary Statistics: Accounting Variables, Stock Returns, and Mutual Fund Trades This table reports the time-series average of cross-sectional summary statistics for stock returns, accounting variables, and mutual fund trades. The unit is at the firm level. Panels A through D summarize accounting variables at the annual frequency. Accounting variables for the fiscal year-end in calendar year y are matched to monthly stock returns (summarized in Panel E) and quarterly mutual fund trades (summarized in Panel F) from July of year y through June of year y + 1. Panel A summarizes size, firm age, and total risk. Size is the market equity, ME. Firm age is the number of years from the firm s first appearance on CRSP to June of calendar year y. Total risk, σ, is the standard deviation in monthly returns for the 12 months ending in June of calendar year y. Panel B summarizes profitability. Return on equity, E+/BE, is earnings, E, scaled by book equity, BE. It is positive if earnings, E, are positive, and 0 otherwise. The profitability dummy, E>0, is 1 if earnings, E, are positive, and 0 otherwise. Panel C summarizes dividend policy. Dividends to equity, D+/BE, is dividends, D, scaled by book equity, BE. It is positive if dividends, D, are positive, and 0 otherwise. The dividend payer dummy, D>0, is 1 if dividends, D, are positive, and 0 otherwise. Panel D summarizes growth opportunities. Bookto-market, BE/ME, is the ratio of book equity, BE, to market equity, ME. External finance, EF, is the change in assets less the change in retained earnings, scaled by book assets, BA. Sales growth, GS, is the percentage change in net sales. Panel E summarizes stock returns at the monthly frequency. Panel F summarizes mutual fund trades at the quarterly frequency. MF Net Purchase for a firm is the quarterly change in the percentage of outstanding shares held by mutual funds. The sample period is 1981 to 2010. 31

Obs Mean Median Min Max SD Panel A: Size, Age, and Risk ME ($mils) 144,329 1,191.328 190.788 16.892 26,234.240 3,212.427 Age (yrs) 144,329 13.647 9.167 0.000 65.967 14.027 σ 133,480 0.133 0.115 0.030 0.490 0.077 Panel B: Profitability E+/BE 138,195 0.076 0.024 0.000 0.564 0.106 E>0 138,195 0.560 0.833 0.000 1.000 0.493 Panel C: Dividend Policy D+/BE 104,071 0.016 0.002 0.000 0.155 0.029 D>0 111,413 0.369 0.100 0.000 1.000 0.471 Panel D: Growth Oportunities BM 102,792 0.723 0.630 0.035 2.832 0.496 EF 119,700 0.131 0.063-0.424 1.266 0.256 GS 113,579 0.275 0.109-0.676 5.901 0.765 Panel E: Monthly Stock Return Return (% per month) 1,667,165 1.013 0.213-75.273 202.078 14.812 Panel F: Quarterly Mutual Fund Trades MF Net Purchase 384,513 0.124 0.099-12.772 12.874 3.447 (% per quarter) 32