Fire Sale Risk and Expected Stock Returns

Transcription

1 Fire Sale Risk and Expected Stock Returns George O. Aragon and Min S. Kim June 2017 Abstract We measure a stock s exposure to fire sale risk through its ownership links to equity mutual funds with investor outflows that are highly sensitive to systematic industry outflows. We find that more exposed stocks earn higher average returns: a portfolio that buys (shorts) stocks with the highest (lowest) exposure outperforms by 3-7% per annum. Our findings cannot be explained by several known determinants of average returns, including market or funding liquidity risks, or downside or skewness risks. Our results are consistent with the ex-ante pricing of the risk of future fire sales and suggest that stocks exposures to risks inherited from shareholders constraints have important implications for stock prices. JEL Classification Codes: G11, G12, G23. Keywords: Fire sales, stock returns, ownership, mutual fund, fund flows. George Aragon is with Finance Department, W.P. Carey School of Business Arizona State University, Tempe, AZ, U.S.A , ( george.aragon@asu.edu, Tel: , homepage: Min Kim is with School of Banking and Finance, UNSW Business School, University of New South Wales, Sydney, Australia, 2052 ( min.kim@unsw.edu.au, Tel: ). We thank Jonathan Cohn, Roger Edelen, Wayne Ferson, John Griffi n, Ehud Ronn, Clemens Sialm, Laura Starks, Sheridan Titman, and seminar participants at University of New South Wales, University of Southern California, University of Technology Sydney, and University of Texas at Austin for helpful comments and constructive suggestions.

2 1. Introduction Prior studies find that extreme outflows from equity mutual funds can lead to distressed selling that cause stock prices to temporarily fall below their fundamental values. These price effects are largest when distress is widespread and concentrated in a relatively few stocks (Coval and Stafford, 2007). An interesting question is whether stocks earn a risk premium, ex-ante, from being more exposed to the risk of such mutual fund fire sales. A possible channel is through a stock s ownership links to mutual funds that experience outflows when outflows are systematic to the industry. Such stocks become targets of distressed sales by mutual fund owners precisely when distressed selling is widespread. Stock market investors might demand higher expected returns in anticipation of realizing negative returns from fire sales during periods of industry distress. In this article we examine the relation between stock returns and fire sale risk using a novel measure of a stock s exposure to fire sales. We focus on a stock s ownership by equity mutual funds with a high flow beta the sensitivity of fund investor flows to systematic flows. In this way, our measure identifies stocks as having greater fire sale risk when they are held by mutual funds that experience outflows precisely when outflows are systematic within the industry. In our empirical analysis we extract common factors from quarterly U.S. equity mutual fund flows over We define systematic flows as the first common factor extracted from the principal component analysis of Connor and Korajczyk (1986). The quarterly time series of this flow factor is highly correlated with macroeconomic variables and financial market conditions (as in Ferson and Kim, 2012), an indication that our measure of fire sale risk captures a risk that matters for investors and, hence, could factor into asset pricing. Not surprisingly, we also find that systematic flows are highly correlated with asset-weighted equity fund flows (70%). However, in contrast to asset-weighted equity fund flows, systematic flows have distinct explanatory power for mutual funds net selling of assets beyond the equity fund sector, such as bond, municipal bond, 1

3 and hybrid funds. This suggests that our systematic flow factor captures a broader component of capital market flows beyond equities. Next we estimate a mutual fund s systematic component of flows (flow beta) by regressing its quarterly fund flows on the flow factor. In our analysis we focus on a stock s exposure to mutual fund fire sales (versus fire purchases). Therefore, when estimating flow betas, we partition our flow factor into negative (systematic outflows) and positive (systematic inflows) values, and separately estimate a fund s negative and positive flow beta, respectively. We use a recursive procedure to re-estimate the flow factor and flow betas each quarter so that only backward-looking information is used to construct our key exposure variable. We then calculate a stock s exposure to fire sales (purchases) as the ownership-weighted average of the negative (positive) flow betas of its mutual fund owners. Intuitively, a stock s fire sale exposure captures its ownership by mutual funds for which outflows are sensitive to systematic outflows. We find a positive relation between fire sale risk and average returns over our sample period ( ). A value-weighted portfolio of stocks with the greatest risk exposure earns annualized abnormal returns of 1.8% over the following month, while a portfolio of stocks with the lowest exposure earns only -1.6%. The difference, 3.4% per year, is significant. In contrast, we do not find a significant relation between average returns and a stock s exposure to fire purchase risk, as measured by a stock s ownership by mutual funds for which flows are sensitive to systematic inflows. In Figure 1 we plot the time series of monthly returns from a portfolio that buys (sells) stocks with highest (lowest) exposure to fire sale risk. The average difference of returns between the two groups of stocks is almost 0.6% per month, or, about 7% per year. Moreover, the portfolio experiences its lowest returns during periods when fire sales are likely (e.g., Tech bubble period, and Lehman bankruptcy). Taken together, our evidence shows that stock prices reflect a risk premium from exposure to the risk of fire sales. 2

4 We show that the return spread associated with fire sale risk is distinct from the returns associated with several known stock return benchmarks, including the size, value, and market portfolios of Fama and French (1992), stock return momentum (Jegadeesh and Titman, 1993; Carhart, 1997), market liquidity risk (Pastor and Stambaugh, 2003), betting-against-beta risk (Frazzini and Pedersen, 2014), leverage constraint tightness (Boguth and Simutin, 2016), co-skewness risk (Harvey and Siddique, 2000), and downside risk (Ang, Chen, and Xing, 2006). We also reach similar conclusions when we implement Fama-MacBeth (1973) or pooled estimation procedures that control for several stock characteristics that may be correlated to our exposure variable, including the level of mutual fund ownership and illiquidity measures of Amihud (2002) and Sadka (2006). A potential alternative interpretation of our findings is that our measure of fire sale risk exposure captures ownership by relatively skilled mutual fund managers and, therefore, undervalued stocks that subsequently realize abnormally positive returns (rather than the pricing of fire sale risk). However, we do not find a strong relation between a mutual fund s flow beta and measures of manager skill, such as fund size or prior fund returns. In addition, we do not find any evidence of outperformance of mutual funds with a high flow beta after controlling for fund holdings exposure to fire sale risk or fund fixed effects. Rather, a major predictor of mutual fund performance is the proportion of most exposed stocks to fire sale risk in the fund holdings. Finally, we follow Bartram, et al. (2015) and use stock inclusion into the S&P 500 Index as a plausibly exogenous shock to mutual fund ownership and, hence, to a stock s exposure to fire sale risk. We find that changes in risk exposure following the listing are associated with higher returns on the underlying stock. Therefore, it seems unlikely that the positive relation between fire sale exposure and stock returns is driven by informed stock trading by mutual fund managers. Several papers find that distressed selling by institutional investors can negatively impact asset 3

5 prices. 1 The underlying mechanism is the generous liquidity provided by the fund to its investors under the open-end fund structure. By allowing investors to freely redeem funds shares on a daily basis, mutual funds face the risk that extreme outflows may force the fund to liquidate its portfolio assets at fire sale prices. However, much less is known about whether investors anticipation of fire sales affects risk premiums in asset prices, which is the subject of our analysis. One exception, Nanda, Wu, and Zhou (2016), use ownership by insurance companies as a proxy for fire sale risk in corporate bonds, and find that fire sale risk is related to higher bond yields. Our paper builds on this recent work by constructing an ownership-based measure of fire sale risk in equity markets and finding evidence of a fire sale risk premium. Massa, Schumacher, and Wang (2016) use the merger of BlackRock and Barclays Global Investors as an exogenous shock to ownership concentration in individual stocks. They find that stocks experiencing an increase in ownership concentration via the merger experience negative stock returns around the event. The authors attribute this finding to selling pressure from investors that anticipate future fragility and fire sales in those stocks, and are now trading strategically away from these stocks to avoid this risk. Our paper builds on this intuition and examines whether the risk of future fire sales has an impact on required stock returns. Our paper is also related to recent research on how commonality in the holdings of institutional investors can impact asset prices. Several recent papers find that commonality in mutual fund ownership increases co-movement in equity prices (Anton and Polk, 2014; Jotikasthira, Lundblad, and Ramadorai, 2012; Hau and Lai, 2016; Bartram, et al., 2016) and liquidity (Koch, Ruenzi, and Starks, 2016). Our paper provides evidence that commonality in ownership by mutual funds with 1 Evidence of institutional price pressure is found in U.S. equity markets (Coval and Stafford, 2007; Aragon and Strahan, 2012; Tang, 2013; Kang, Kondor, Sadka, 2014; and Hau and Lai, 2016), bond markets (Manconi, Masssa, and Yasuda, 2012), and international equity markets (Jotikasthira, Lundblad, and Ramadorai, 2012). Diamond and Dybvig (1983), Brunnermeier and Pedersen (2009), and Shleifer and Vishny (1992) present theoretical predictions on the effects of financial distress on asset values. Chen, Goldstein, and Jiang (2010) and Goldstein, Hao, and Ng (2016) find evidence that the investor flow patterns differ across mutual funds based on their exposure to illiquid assets. 4

6 high systematic flows is associated with greater stocks returns, because these stocks are exposed to greater fire sale risk. The rest of the paper is organized as follows: Section 2 discusses the data and construction of the key measure of exposure to fire sale risk. Section 3 discusses the main empirical results and robustness checks. Section 4 concludes. 2. Data and methodology 2.1. Flow betas of mutual funds We estimate mutual fund flow factors using the same data and method as those in Ferson and Kim (2012). The authors extract factors for U.S. equity mutual fund flows over the period from the fourth quarter of 1981 to the fourth quarter of 2009, applying the asymptotic principal components estimators in Connor and Korajczyk (1986). The data are from Morningstar Direct. Flows f it of fund i in quarter t are defined as the percentage change in the fund s assets net of returns by the following: f it = T NA it T NA it 1 (1 + r it ), where T NA it is total net assets of the fund i at the end of quarter t, and r it is returns in quarter t, which are continuously compounded monthly returns over the quarter. Table 1 presents descriptive statistics of equity mutual funds used to estimate the flow factors. Flows and returns are over the quarter and TNA ($ millions) and the number of years since the inception date are measured at the end of the quarter. 2 We use a recursive method to avoid a look-ahead bias in estimating the flow factor. The method uses data up to the first quarter of 1989 (30 quarters) and then extends one quarter at a time to 2 See Ferson and Kim (2012) for a detailed description of the estimation method for the flow factors. 5

7 estimate the factors at the end of each quarter. We focus on the first flow factor, which explains most of the variation in mutual fund flows. The flow factor represents systematic fund flow shocks to equity mutual funds. Variation in fund flows that are correlated with the flow factor represent exposures to systematic fund flow risks that cannot be mitigated by diversification across funds. In contrast, those variations that are uncorrelated with the flow factor are fund-specific and represent unsystematic or idiosyncratic fund flow risks. Following Ferson and Kim (2012), we scale the flow factor such that a 1% increase of the flow factor is associated with an average increase of 1% of the industry flow for U.S. equity mutual funds, where the industry flow is an asset (TNA)-weighted average across funds. The flow factor and industry flow variables have a significant sample correlation over 70%. This suggests that approximately half of the variation in industry flows is explained by the flow factor, while the remainder represents diversifiable fund flow risks. Panel A of Table 2 shows that, consistent with Ferson and Kim (2012), the flow factor is has significant explanatory power for macroeconomic conditions and financial market variables. For example, an increase in the flow factor is associated with improvements in overall U.S. economic conditions as determined by consumer opinion (changes in the University of Michigan Consumer Sentiment Index), appreciations in the U.S. dollar, stock market returns and volatility. Panel B shows that industry flows also has explanatory power, but mainly for the equity market variables like stock market volatility and return. Table 2 also shows that the flow factor has significant explanatory power for net purchases (purchases minus sales) of mutual funds as provided in the Financial Accounts of United States by the Board of Governors of the Federal Reserve System. 3 For example, the flow factor is positively and significantly related to the net purchases of equity funds, hybrid funds, municipal bond funds, 3 These data are available beginning in the first quarter of Edelen, Marcus, and Tehranian (2010) also use the Financial Accounts to measure the difference in portfolio allocations to risky assets between retail and institutional investors. 6

8 and a composite of all funds net purchases. In Panel B we find that industry flows are also significant in explaining these variables; however, the multivariate regression results in Panel C (i.e., when flow factor and industry flow appear together as explanatory variables) show that the explanatory power of industry flows is mainly limited to the trading activities of equity funds. In contrast, the systematic flow factor captures variation in trading activity both within and outside the equity fund market. We estimate the flow beta of individual mutual funds as the loading on the flow factor. We use a recursive method. At the end of each quarter from the first quarter of 1989 to the fourth quarter of 2009, we run a time series regression of quarterly flows on the first flow factor for each fund. We allow different loadings on the first factor when it is positive and negative. We define flow beta (+) and flow beta (-) as the loadings on positive value and negative value of the first factor, respectively. The time series regression for estimating flow betas of a fund i using data up to time T is given by f it = β + it F + t + β it F t + e it where f it is investors net money flows for a fund i in time t and F + t and F t are positive and negative value of the first flow factor in time t. In other words, F + t and F t are equal to F t, the first flow factor in time t, if F t is positive and negative, respectively. Otherwise, F + t and F t are equal to zero. The loadings β + it and β it define flow beta (+) and flow beta (-), respectively. The subscript T denotes the last time period used for the recursive estimation, i.e., t = 1, 2,..., T. For example, the first time-series regression uses data up to the first quarter of We estimate the flow betas of a fund only when the regression has at least 20 observations. We use Thomson-Reuters Mutual Fund Holdings database for mutual funds holdings of publiclytraded stocks. We only include in our sample mutual funds with objective codes representing aggressive growth, growth, or growth and income. Each fund in the holdings database is matched to 7

9 the one (aggregated across different share classes) in the CRSP (Center for Research in Security Prices) Survivor-Bias-Free US Mutual Funds Database Fund flow exposures of stocks Given mutual funds flow betas as described above, we estimate flow exposures of a stock j at the end of each quarter as a weighted-average of flow betas of mutual funds that own the stock. More weights are given to flow betas of funds that hold more shares. For instance, flow exposure (-) exp jt of a stock j at the end of quarter T is given by exp jt = K i=1 β it shr j it K, (1) i=1 shrj it where shr j it is the number of shares of the stock j that a fund i owns at the end of quarter T and K is the total number of mutual funds that hold shares of the stock j. The above method scale the weights using the total number of shares of the stock j that are held by mutual funds. We also estimate in a similar way exp + jt flow exposure (+), which captures fire purchase exposure; however, most of our analyses center on exp jt, which captures fire sale exposure and is the focus of our analysis. An alternative to Equation (1) would be to scale the weights by the stock s number of shares outstanding, which would be equivalent to an interaction term between exp jt and mutual fund ownership OW N jt of the stock j. However, this measure is highly correlated with mutual fund ownership and might underestimate a stock exposure to fire sales when a mutual fund s ownership is not a large part of the stock s shares outstanding but is a large part of the fund industry s investment in that stock. 4 Hence, we report empirical results using exp jt as the flow exposure (-) 4 For example, consider two stocks with exp jt equal to 10 and 1 and the mutual fund ownership equal to 10% and 100%, respectively. The first stock has a higher exposure to fire sales than the second stock given that 10% is sizable ownership. Nevertheless, the first stock has the same low exposure to fire sales as the second stock according to 8

10 measure in the subsequent sections. 5 We use CRSP s stock data for stock returns and other information such as market value and the number of shares outstanding. We include common stocks on NYSE/NASDAQ/AMEX in our sample. We exclude stocks if the prices are less than $5. These penny stocks are typically considered as speculative investments and involved with more market microstructure issues. They are also regulated by SEC. We group stocks into quintiles each quarter based on their flow exposure (-) and report the descriptive statistics of the stocks in Table 3. Stocks have flow exposure (-) of 5.35 on average and show substantial variations. The least exposed stocks to mutual funds flow factor have negative value of almost -5 on average. In contrast, the average flow exposure (-) of stocks in the highest quintile is almost 19. Both the lowest and the highest quintiles have higher flow exposure (+) than stocks in the middle quintiles. Other stock characteristics, such as market value, book-to-market ratio, prior 12-month returns, do not have systematic variations across the quintiles of flow exposure (-). Stocks with higher flow exposure (-) have higher mutual fund ownership and smaller number of mutual fund owners on average. A stock s breadth of ownership is the ratio of number of mutual funds that own the stock to the total number of mutual funds. We calculate change in breadth as the ratio with the total number of funds in the prior period, following Chen, Hong, and Stein (2002). Stocks that are least exposed to mutual funds flow factor have the smallest change in breadth on average. Panel (C) reports correlation coeffi cients of the variables. Most stock characteristics have significant correlations with flow exposure (-) at the significance level of 5% but the magnitudes are not large. The variables that are mostly correlated with flow exposure (-) are market beta and mutual = exp jt OW NjT. Also, mutual funds might still own a large quantity of shares despite a low percentage that these shares represent of the total number of shares outstanding. On the other hand, exp jt might overestimate a stock s exposure to fire sales when the level of mutual fund ownership is trivial. When we sort stocks by ownership, we find a positive relationship between exp jt and average returns in every ownership quintile except the lowest ownership quintile. 5 However, the results using the alternative measure exp OW N jt are qualitatively similar to the ones using exp jt. exp OW N jt 9

11 fund ownership. The correlation coeffi cients are and 0.054, respectively. Highly exposed stocks to the mutual fund flow factor tend to be less exposed to the market risk and have higher mutual fund ownership. Market beta and mutual fund ownership have a correlation coeffi cient of 0.19, suggesting that stocks with higher mutual fund ownership tend to have higher market risk. Flow exposure (-), on the other hand, has almost no correlation with changes in breadth. We also report correlation coeffi cients of mutual fund variables in Panel (D). Mutual funds with high flow beta (-) tend to be low-performing funds, younger funds, and more costly funds to investors (high expense ratio). These funds also belong to smaller fund families. In contrast, past winner funds and low-fee funds tend to have higher flow exposure (+). Ferson and Kim (2012) report more details about mutual funds flow betas. We examine how flow exposures of stocks are related to stock returns and characteristics. We run panel regressions of flow exposures on stock returns and characteristics in the prior quarter, such as size, book-to-market ratio, mutual fund ownership, change in breadth, market beta, and loadings on liquidity factors. We use four liquidity factors: non-tradable and tradable factors in Pastor and Stambaugh (2003) and variable permanent and fixed transitory factors in Sadka (2006). The regressions also include stock fixed effects and standard errors are clustered by quarter. Table 4 report the coeffi cient estimates and t-statistics. Size, mutual fund ownership, market beta, and loading on variable permanent liquidity factor are significant determinants of flow exposure (-). Stocks with smaller market value, higher mutual fund ownership, lower systematic risk, and more sensitivity to the variable permanent component of market illiquidity tend to more exposed to the negative mutual fund flow factor. Coeffi cient estimates on past three-month returns are marginally significant. These variables have sizable explanatory power with R-squared of around 37%. On the other hand, stock characteristics and returns appear less relevant for flow exposure (+). Only liquidity betas are significant determinants, such as Pastor and Stambaugh factors and the fixed 10

12 transitory liquidity factor. We sort stocks on flow exposure (-) at the end of each quarter and break them into three groups: bottom 30%, middle 40%, and top 30%. 6 The portfolios are re-balanced every quarter. We plot the difference of monthly value-weighted returns between the top group and the bottom group. Figure 1 shows that stocks that are most exposed to mutual fund flow risks outperform those that are least exposed on average. The average difference of the returns between the two groups of stocks is almost 0.6%, which is above 7% per year. The monthly difference of returns becomes most volatile during the dot-com bubble period. It ranges from -10.7% to 15.8% per month. It also drops sharply in September 2008 amid the Great Recession (lower than -8.1% per month). 3. Empirical results 3.1. Performance of trading strategies based on flow exposure (-) We form quintiles of stocks at the end of each quarter based on stock characteristics and flow exposures. Stock characteristics we use include size, book-to-market ratio, past one-year return, mutual fund ownership, and Amihud s illiquidity measure over the past 12 months. Trading strategy is to buy the top-quintile stocks and short-sell the bottom-quintile stocks 2 months after each quarter and rebalance the portfolio every three months. We only include stocks that are listed on NYSE/NASDAQ/AMEX and of which the prices are at least $5 at the time of rebalancing. 7 For example, stocks are grouped into 5 groups based on flow exposure (-) at the end of the fourth quarter of We buy non-penny stocks on NYSE/NASDAQ/AMEX in the highest quintile and short- 6 Fama and French (1993) and Carhart (1997) among many others also sort stocks on stock characteristics and examine returns on stocks in the top and the bottom 30%. 7 We report results without delisting returns, that is, the monthly return is zero after delisting. When we include delisting returns, all the results are virtually the same. The number of observations with delisting returns is only 0.5% of the total number of monthly observations (over 1 million). About 20% of the observations with delisting returns are for stocks with missing values of flow exposure (-). About 14-17% of the observations are for the stocks in each flow exposure (-) quintile. 11

13 sell non-penny stocks on NYSE/NASDAQ/AMEX in the lowest quintile at the end of February 2001 and maintain the positions until May The portfolios are either equally weighted or value weighted by market value as of the trading time. The trading strategy has a two-month gap to ensure availability of required information to form the portfolio. Mutual funds holdings are publicly available within 60 days from each quarter. Other stock characteristics can also be easily obtained within 2 months. 8 We also use an one-year gap instead of two months. Table 5 shows annualized performance of the trading strategies based on exposures to the flow factor and the industry flow and t-statistics using Newey and West s (1987) adjusted standard errors. We use three kinds of exposures to the flow factor: flow exposure, flow exposure (-), and flow exposure (+). The strategies based on flow exposure (-) are significantly profitable. The equally- and value-weighted portfolios have about 5% and 9% returns per year, respectively. After controlling for Carhart s four factors, the annualized returns decrease to about 3% but are still sizable and statistically significant. On the other hand, the other flow exposure measures (i.e., flow exposure and flow exposure (+)) do not lead to profitable trading strategies. Exceptionally, the value-weighted portfolio of buying stocks in the top quintile and short-selling stocks in the bottom quintile of flow exposure has returns over 4% per year. Yet, the magnitude is much smaller when compared to the trading strategy based on flow exposure (-), and the returns are not different from zero after controlling for the four factors. We report performance of the trading strategies based on various stock characteristics and flow exposure (-) and t-statistics using Newey-West adjusted standard errors in Table 6. The strategies based on flow exposure (-) are significantly profitable. The equally- and value-weighted portfolios have about 5% and 9% returns per year, respectively. Performance of the strategies with a one-year gap is slightly lower: almost 4% and 8% when equally-weighted and value-weighted, respectively. 8 Note that, due to the backward-looking nature of our methodology, the trading strategy is feasible. Also, it does not incur high transaction costs because the portfolio is re-balanced only once every three months. The average number of stocks in each flow exposure (-) quintile is about 600 over our sample period. 12

14 We also adjust the performance by subtracting the returns of the stocks in the same quintiles of size, book-to-market ratio, and past one-year returns. The risk-adjusted returns are between 2% and 4% per year for equally- and value-weighted portfolios, respectively and still statistically significant at the 5% significance level. We also estimate flow exposure (-) differently and define it as flow exposure (-)*. Instead of estimating mutual funds flow betas using time-series regressions for each fund, we run panel regressions of individual mutual fund flows on the first flow factor, lagged fund characteristics and returns, and interaction terms between the first flow factor and lagged fund characteristics and returns. The coeffi cient estimates on the interaction terms are used to estimate expected flow betas in the following quarter conditional on fund characteristics and returns. Trading strategies according to flow exposure (-)* also significantly profitable even after controlling for the risks. Yet, the magnitudes are lower by about 1% per year than the trading strategies based on flow exposure (-) estimated by the time-series approach. Among the widely-used trading strategies, only the momentum strategy (Jegadeesh and Titman, 1993) is significantly profitable. The average returns on the equally- and value-weighted portfolios are about 8.7% and 7.3% per year, respectively. When trading on momentum after one year, the returns are not statistically different from zero. Amihud s illiquidity measure, on the other hand, does not lead to profitable trading. It is actually significantly negative. Other stock characteristics, such as size, book-to-market ratio, and mutual fund ownership, do not appear to lead to profitable trading strategies. Table 7 reports the results based on two-way sorting. It shows performance of the trading strategies based on flow exposure (-) of stocks in each quintile of widely-used stock characteristics, such as size, book-to-market ratio, momentum, and ownership. The two quintiles are grouped independently. Except for a few cases, flow exposure (-) are significant profitable even after controlling 13

15 for those stock characteristics. The results hold for equally- and value-weighted strategies and on a risk-adjusted basis. Given the results that flow exposure (-) leads to profitable trading strategies, we now run regressions of individual stock returns on flow exposure (-) and stock characteristics. We use Fama- MacBeth regressions and panel regressions with stock and time fixed effects. Table 8 reports the coeffi cient estimates and the standard errors adjusted by the Newey-West method from the Fama- MacBeth regressions. Only flow exposure (-) appear to be a significant determinant of stock returns over the following 3 months with a gap of 2 months. The magnitude is economically sizable. During the more recent period from 1998 to 2010, an increase of flow exposure (-) by one-standard deviation (about 10) increases 3-month returns by about 0.3%, i.e., 1.2% per year. The magnitude decreases to about 0.72% per year over the entire sample period of 1989 to Other stock characteristics are not statistically different from zero. Returns over the 2 months between sorting and trading time are not a significant determinant either. The average R-squared is between 4 and 6%. Table 9 shows the panel regression results using the entire sample period. Flow exposure (-) is still significant with a similar coeffi cient estimate to the one from Fama-MacBeth regressions. The results for other stock characteristics are consistent with previous studies. Stock returns over three months increase with book-to-market ratio, past one-year returns, and changes in breadth. These results support the literature on value premium and momentum premium and the findings by Chen, Hong, and Stein (2002). The authors show that change in breadth of ownership increase stock returns and argue that the variable proxies for short-sale constraints. Size and market beta have negative relationships with stock returns. Frazzini and Pedersen (2014) find a negative relationship between market beta and stock returns. Stocks that are more sensitive to Pastor-Stambaugh s (2003) tradable liquidity factor outperform those with lower sensitivity. Consistent with Table 6, higher illiquidity proxied by Amihud (2002) s liquidity measure over the prior one year predicts 14

16 lower returns over 3 months with a gap of 2 months. Among Sadka s liquidity factors, loadings on the fixed transitory factor have a positive relationship with returns. We also look at alphas to estimate risk-adjusted profitability of the trading strategy based on flow exposure (-), i.e., buying the stocks in the top quintile and shortselling the stocks in the bottom quintile two months after each quarter and re-balancing the portfolio every three months. We run time-series regressions of monthly returns on the portfolio on various factors, including Carhart s four factors and Pastor-Stambaugh s tradable liquidity factor. Data for these factors are obtained on Kenneth French s website. We also control for the factors suggested by more recent studies. Frazzini and Pedersen (2014) argue that stocks with high market beta have lower expected returns because of high demand of constrained investors. The authors find consistent results that low market beta stocks outperform stocks with high market beta and construct the betting-againstbeta (BAB) factor. Given that flow exposure (-) is negatively correlated with market beta, we also control for the BAB factor in the regression (data provided on Frazzini s website). Boguth and Simutin (2016), on the other hand, show that market beta of aggregate mutual fund holdings predicts returns on the BAB portfolio. The results suggest that the mutual funds market beta proxies for tightness of leverage constraints. Following the authors, we use the change in the market beta (MFB) as another factor in the regressions. Previous studies also find that stocks with low coskewness have higher expected returns because investors prefer right-skewed portfolios to left-skewed ones (e.g., Harvey and Siddique (2000)). Downside risk is related to coskewness but different. Ang, Chen, Xing (2006) find that stocks that are more sensitive to downside market movements outperform stocks with low sensitivity to them. We use the trading strategies based on coskewness and sensitivity to downside market movements and construct the coskewness factor and the downside risk factor, respectively. Table 10 reports the estimates of alphas and factor loadings of the time-series regressions of 15

17 monthly returns on the flow exposure (-) portfolios. Panel (A) and (B) report the results for value- and equally-weighted portfolios. The first rows represent annualized alphas, i.e., the alpha estimates times 12. The results show that outperformance of stocks with high flow exposure (- ) is partially attributable to the value, momentum, and liquidity factors. The CAPM alpha of the value-weighted portfolio is about 9.5% per year. Carhart s four factors seem to contribute to about 30% of the risk-adjusted returns. The alpha decreases to 6.7% after controlling for the four factors. When Pastor-Stambaugh s (2003) tradable liquidity factor is also included in the regression, an additional 1% of the alpha is reduced. On the other hand, leverage constraints do not appear relevant to the risk captured by the mutual fund flow factor. Both the BAB factor and the mutual funds aggregate market beta are not statistically significant and the alpha stays the same. Similarly, the coskewness factor is irrelevant for the flow exposure (-) premium. In contrast, the downside risk explains the premium. The flow exposure (-) portfolio s alpha is reduced to 5%. On the other hand, the premium is much smaller when the portfolio is formed by equal weights. The CAPM alpha is 5.8%, which is reduced to 3.5% after controlling for Carhart s (1997) four factors, Pastor-Stambaugh s liquidity factor, and the downside risk factor. The regressions described above use the data for the entire sample period. We also use a recursive method and a rolling method to estimate alphas of the trading strategy based on flow exposure (-). When using the recursive method, we use the data up to December 1991 for the first estimation (30 months) and obtain alpha and factor loadings estimates for the period until December Then we extend the data by one month at a time and construct time-series of the estimates from January 1992 to May The alphas represent the risk-adjusted returns that investors could have earned if they had followed the trading strategy from the first quarter of The rolling method, on the other hand, uses the most recent 7 years (or fewer if the data are not enough) to estimate the alphas and the factor loadings. 16

18 Figure 2 plots the time-series of Carhart s (1997) 4-factor alpha estimates by the recursive method. The alpha estimates increase dramatically in January 2001 and then stay at high levels before the middle of the Great Recession, the second half of Figure 3 shows the results by the rolling method. In particular, the trading strategy based on flow exposure (-) was highly profitable, starting in January 2001 until June Carhart s 4-factor alpha was between 9% to 15% (annualized). The trading strategy achieves a monthly alpha of 0.76% in January 2001, much higher than 0.43% in December trading strategy based on flow exposure (+). Figure 4 and 5 show the alpha estimates of the The magnitudes are small and the estimates are not statistically significant. Other results for flow exposure (+) are similar, economically and statistically insignificant. Hence, we do not report the results. We also control for Pastor and Stambaugh s (2003) tradable liquidity factor and Frazzini and Pedersen s (2014) Betting-Against-Beta factor and estimate the time-series alphas using the recursive and the rolling methods. For example, Figure 6 shows the results by the rolling method. The estimates are slightly lower than Carhart s (1997) 4-factor alpha estimates but very similar. We also estimate alphas similarly after controlling for other factors, such as coskewness and downside risk factors. The time-series look almost the same as Figure 6 with a slight decrease in the magnitude (not plotted) Mutual fund performance The positive relationship between flow exposure (-) and future stock returns could be a result of stock picking skills of mutual funds with high flow betas (-). If mutual funds, of which money flows are more sensitive to the flow factor, tend to invest in under-valued stocks, these stocks will have higher flow exposure (-) than other stocks with all other things equal. As a consequence, 9 This is because the strategy outperforms the momentum factor despite having a positive loading on momentum (Table 10) and a -25% return on the momentum factor in January

19 more exposed stocks to the flow factor are likely to have higher returns. In such cases, we should also observe a positive relationship between mutual funds flow beta (-) and fund performance. We examine this hypothesis by regressing mutual fund returns on mutual fund flow betas. We also estimate how funds returns are related to funds holding exposures. Given stocks flow exposure (-), a fund s holding exposure (-) is an average flow exposure of stocks that are held by the fund. The average is calculated using weights equal to the portfolio weights of the fund. We estimate funds holding exposure (+) in a similar way. Another variable in interest is funds proportion of investments in stocks in the top quintile of flow exposure (-). The panel regression results are reported in Table 21. Panel (A) and (B) show regressions with no fixed effects and with clustering by either time or fund. The results suggest that flow beta (-), holding exposure (-), and portfolio weights in the most exposed stocks predict higher fund returns when each of them is separately included in the regressions, i.e., model (1) to (3). However, funds flow beta (-) becomes insignificant when holding exposure (-) is controlled for. Also, when all three variables are included in the regressions and standard errors are clustered by time, only the top exposure (-) weight is significant. These results show that the main determinant of fund returns is not funds exposure to the flow factor but their holdings of most risky stocks proxied by flow exposure (-). In fact, funds flow betas and holding exposure (-) are not statistically significant determinants of fund returns once funds fixed effects are controlled for (see Panel (C)). In particular, funds flow beta (-) have serial correlations of about 0.7. When unobservable time-invariant effects are considered in the regressions, the coeffi cient on flow beta (-) is not statistically different from zero even without other proxies for risks arising from systematic mutual fund flows. Only funds weights in the most exposed stocks to the flow factor are significant determinants in the presence of fund fixed effects. 18

20 3.3. S&P 500 inclusion events An exogenous event that changes stock ownership dramatically is inclusions to the S&P 500 index. This event leads to S&P 500 index funds that follow the index to buy the newly added stocks and other funds to sell the stocks in their holdings. We examine how stocks flow exposure (-) prior to the inclusion event and changes in the exposure around the event are related to abnormal returns of stocks. More precisely, we look at two variables. One is flow exposure (-) four quarters prior to the inclusion event. The other is changes in flow exposure (-) relative to that level. The changes are estimated in each of the event quarters, which are three quarters prior to the event and 20 quarters (5 years) after the event. Then we use dummy variables to represent the quarters before and until one year after the event and the quarters between 2 years and 5 years after the event. The inclusion event is often announced ahead of actual inclusion day and mutual funds might delay their trading to minimize price impacts and funding liquidity effects after the event. As a result, the one-year period before and after the event could be involved with frequent trading of mutual funds and subsequent changes of their ownership. We also define other ownership-related variables, such as mutual fund ownership and breadth of ownership, in a similar way. Panel (1), (2), and (3) in Table 12 show the results for flow exposure (-), mutual fund ownership, and breadth of mutual fund ownership, respectively. Consistent with the positive relationship between flow exposure (-) and future returns, stocks with higher flow exposure (-) at the beginning of the event period tend to outperform other stocks with everything else equal. Changes in flow exposure (-) over the quarters between two years and five years after the inclusion event also have significant, positive relationships with abnormal stock returns. On the other hand, changes in mutual fund ownership is significant only during the time around the inclusion event. This is consistent with temporary price pressure induced by index funds purchases of the stocks newly added in the index. After one year of the event, stocks with high mutual fund ownership prior to 19

21 the event underperform other stocks. Changes in breadth of ownership are consistent with Chen, Hong, and Stein (2002). Increases in the breadth predict higher returns throughout the quarters. The effects of flow exposure (-) changes around the S&P 500 inclusion still hold after controlling for the effects of stock ownership and breadth of ownership, as shown in Panel (4) to (6). 4. Conclusions We construct a measure of a stock s exposure to fire sale risk through its ownership links to mutual funds with high systematic outflows ( flow betas ). We find that stocks with significant flow beta ownership subsequently earn higher average returns. A long/short portfolio that buys (sells) stocks with largest (smallest) exposure to fire sale risk earns about 7% per year. We interpret this as evidence that investors demand a return premium for bearing the risk of future fire sales during periods of systematic outflows. We also find that systematic outflows are related to macroeconomic variables and financial market conditions, including the net selling activity of the broader equity, bond, and hybrid mutual fund universe. This help corroborate our conclusions that systematic outflows appears to be a state variable that matters in the pricing of stocks. We also show that the higher returns on more exposed stocks cannot be fully explained by several other known contributors to expected returns, including market or funding liquidity risk, downside or co-skewness risk, or the level of (overall) institutional ownership. In addition, we do not find empirical support for an alternative explanation in which the higher returns on more exposed stocks reflect stock ownership by mutual fund managers with a greater capacity for informed trading. Overall, by showing that investors demand a risk premium in anticipation of future fire sales, our findings build on existing research documenting significant negative stock returns upon the realization of fire sales. Our evidence also contributes to a broader literature showing that the risk exposures or characteristics of stocks are inherited from the risk exposure of the holders. 20

22 References [1] Amihud, Y., 2002, Illiquidity and Stock Returns: Cross-section and Time-series Effects, Journal of Financial Markets 5, [2] Ang, A., J. Chen, and Y. Xing, 2006, Downside Risk, Review of Financial Studies 19, [3] Anton, M., and C. Polk, 2014, Connected stocks, Journal of Finance 69, [4] Aragon, G. and P. Strahan, 2012, Hedge Funds as Liquidity Providers: Evidence from the Lehman Bankruptcy, Journal of Financial Economics 103, [5] Baker, W. and J. Wurgler, 2006, Investor Sentiment and the Cross-section of Stock Returns, Journal of Finance 61, [6] Bartram, S., J. Griffi n, T. Lim, and D. Ng, 2015, How Important Are Foreign Ownership Linkages for International Stock Returns? Review of Financial Studies. [7] Ben-Rephael, A., S. Kandel, and A. Wohl, 2012, Measuring Investor Sentiment with Mutual Fund Flows, Journal of Financial Economics 104, [8] Boguth, O. and M. Simutin, 2016, Leverage Constraints and Asset Prices: Insights from Mutual Fund Risk Taking, Rotman School of Management Working Paper No [9] Brunnermeier, M. and M. Pedersen, 2009, Market Liquidity and Funding Liquidity. Review of Financial Studies 22, [10] Carhart, M., 1997, On Persistence in Mutual Fund Performance, Journal of Finance 52, [11] Chen, J., H. Hong, and J. Stein, 2002, Breadth of Ownership and Stock Returns, Journal of Financial Economics 66, [12] Chen, Q., I. Goldstein, and W. Jiang, 2010, Payoff Complementarities and Financial Fragility: Evidence from Mutual Fund Outflows, Journal of Financial Economics 97, [13] Chen, Y. and N. Qin, 2014, The Behavior of Investor Flows in Corporate Bond Mutual Funds, Working Paper. 21

23 [14] Connor, G. and R. Korajczyk, 1986, Performance Measurement with the Arbitrage Pricing Theory: a New Framework for Analysis, Journal of Financial Economics 15, [15] Coval, J., and E. Stafford, 2007, Asset Fire Sales (and Purchases) in Equity Markets, Journal of Financial Economics 86, [16] Diamond, D. and P. Dybvig, 1983, Bank Runs, Deposit Insurance, and Liquidity, Journal of Political Economy 91, [17] Edelen, R., A. Marcus, and H. Tehranian, 2010, Relative Sentiment and Stock Returns, Financial Analysts Journal 66, [18] Fama, E. and K. French, The Cross-section of Expected Stock Returns, Journal of Finance 47, [19] Fama, E., and J. MacBeth, 1973, Risk, Return, and Equilibrium: Empirical tests, Journal of Political Economy 81, [20] Ferson, W. and M. Kim, 2012, The Factor Structure of Mutual Fund Flows, Int. J. Portfolio Analysis and Management 1, [21] Frazzini, A., and L. Pedersen, 2014, Betting Against Beta, Journal of Financial Economics 111, [22] Goldstein, I., H. Jiang, and D. Ng, Investor Flows and Fragility in Corporate Bond Funds, Journal of Financial Economics, forthcoming. [23] Harvey, C. and A. Siddique, 2000, Conditional Skewness in Asset Pricing Tests, Journal of Finance 55, [24] Hau H. and S. Lai, 2016, The Role of Equity Funds in the Financial Crisis Propagation, Review of Finance. [25] Jegadeesh, N. and S. Titman, 1993, Returns to Buying Winners and Selling Losers: Implications for Stock Market Effi ciency, Journal of Finance 48, [26] Jotikasthira, C., C. Lundblad, and T. Ramadorai, 2012, Asset Fire Sales and Purchases and the International Transmission of Funding Shocks, Journal of Finance 67,

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25 Figure 1. Time-series of monthly flow exposure (-) factor Figure 1 plots time-series of the flow exposure (-) factor from 1989 April to 2010 March. The flow exposure (-) factor is monthly returns on the trading strategy of buying a portfolio of stocks in the top 30% and shortselling a portfolio of stocks in the bottom 30% after sorting stocks based on flow exposure (-). Each portfolio is formed with weights equal to market value of equity. Only stocks with the closing price of at least $5 on the trading day are included in the portfolio. The position is held for three months and is rebalanced every three months. A stock s flow exposure (-) is an average of flow beta of mutual funds that own the stock with weights proportional to the number of shares that each mutual fund owns. Flow beta (-) of mutual funds is estimated by time-series regressions of fund flows on the flow factors for each fund. See Table 3 for the estimation method for flow exposure (-). Highlighted areas in yellow represent recession periods according to the National Bureau of Economic Research (NBER). 24

26 Figure 2. Carhart alpha of High-Low flow exposure (-) quintile portfolio by a recursive estimation Figure 2 plots time-series of estimates of Carhart alpha of the trading strategy of buying a portfolio of stocks in the top quintile and shortselling a portfolio of stocks in the bottom quintile after sorting stocks based on flow exposure (-). See Table 5 for the details. Given time-series of returns on the trading strategy, Carhart alpha is defined as the estimate of the intercept of the regressions of the returns on Carhart s four factors. Alpha is estimated in each month from January 1998 to May 2010 using the time-series of the returns up to that month (recursive estimation). The left axis represents alpha estimates (solid line) and the right axis the t-statistics (dashed line). The horizontal line is equal to the critical value at the 10% significance level. Highlighted areas in yellow represent recession periods according to the National Bureau of Economic Research (NBER). 25

27 Figure 3. Carhart alpha of High-Low flow exposure (-) quintile portfolio by a rolling estimation Figure 3 is the same as Figure 2 except that the alpha is estimated in each month using the time-series of the returns for the past 7 years (rolling estimation). 26

28 Figure 4. estimation Carhart alpha of High-Low flow exposure (+) quintile portfolio by a recursive Figure 4 plots time-series of estimates of Carhart alpha of the trading strategy of buying a portfolio of stocks in the top quintile and shortselling a portfolio of stocks in the bottom quintile after sorting stocks based on flow exposure (+). See Table 5 for the details. Given time-series of returns on the trading strategy, Carhart alpha is defined as the estimate of the intercept of the regressions of the returns on Carhart s four factors. Alpha is estimated in each month from January 1998 to May 2010 using the time-series of the returns up to that month (recursive estimation). The left axis represents alpha estimates (solid line) and the right axis the t-statistics (dashed line). The horizontal line is equal to the critical value at the 10% significance level. Highlighted areas in yellow represent recession periods according to the National Bureau of Economic Research (NBER). 27

29 Figure 5. Carhart alpha of High-Low flow exposure (+) quintile portfolio by a rolling estimation Figure 5 is the same as Figure 4 except that the alpha is estimated in each month using the time-series of the returns for the past 7 years (rolling estimation). 28

30 Figure 6. BAB alpha of High-Low flow exposure (-) quintile portfolio by a rolling estimation Figure 6 is the same as Figure 3 except that the alpha is defined as the estimate of the intercept of the regressions of the returns on Carhart s four factors and the betting-against-beta factor (Frazzini and Pedersen (2014)). 29