Flow Reaction, Limited Attention, and Mutual Fund Window. Dressing. Xiaolu Wang 1. Iowa State University. November, 2014

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1 Flow Reaction, Limited Attention, and Mutual Fund Window Dressing Xiaolu Wang 1 Iowa State University November, I am grateful to Susan Christoffersen, Arnie Cowan, Truong Duong, Petri Jylha, Raymond Kan, Lisa Kramer, Wei Li, Travis Sapp, Kevin Wang, Fei Wu, Tong Yao, and seminar participants at University of Iowa, Shanghai University of Finance and Economics, Huazhong University of Science and Technology, the European Finance Association Annual Conference (2014), the Northern Finance Association Annual Conference (2014), and the China Finance Review International Conference (2014) for helpful comments and suggestions. Address correspondence to Xiaolu Wang, 3334 Gerdin Business Building, Iowa State University, Ames, IA 50011, xiaoluw@iastate.edu, Tel: (001) , Fax: (001) This paper was previously circulated under the title Mutual Fund Window Dressing: Prevalence, Flow Reaction, and Limited Attention.

2 Flow Reaction, Limited Attention, and Mutual Fund Window Dressing Abstract We show that mutual fund investors react positively to the performance of the top ten holdings of a disclosed mutual fund portfolio. In addition, a higher number of big stocks in the top-ten list exacerbates the positive response. These findings are consistent with the hypothesis that due to limited attention, investors focus on certain salient features of a portfolio to evaluate fund managers. Such investor behavior provides incentives for fund managers to window dress their portfolios. Our estimation results confirm the existence of the window dressing practice. Moreover, we show that managers are more likely to window dress when the performance of the top ten holdings is poor, and when they choose to window dress, they tend to load the top-ten list with more big stocks. These results suggest that managers realize investors behavior and manipulate their portfolios accordingly. JEL classifications: C14, G11, G23, G28 Keywords: limited attention, attention grabbing, window dressing, disclosure, portfolio holdings, false discovery rate

3 1 Introduction Mutual funds in the U.S. are required by the Securities and Exchange Commission (SEC) to disclose their complete portfolio holdings periodically so that investors have additional information to evaluate fund trading strategies and managers skills. However, a widely believed agency problem related to the disclosures is that fund managers engage in window dressing a practice that involves removing poorly performing stocks from and adding well performing stocks to the portfolio before the holdings information is released to the public to mislead investors. The belief that fund managers window dress presumes that mutual fund investors react positively to disclosed holdings. The existing literature, however, does not provide a clear answer to whether investors indeed do so. Even if fund investors, as expected, take into account the detailed holdings information when making investment decisions, it is still puzzling why they cannot recognize the inconsistency between actual fund returns and the returns of a window-dressed portfolio. This paper attempts to provide an answer to these questions. We conjecture that due to limited attention (e.g., Barber and Odean 2008), fund investors are unable to take into account all the information contained in disclosed holdings, and instead, they focus on certain salient and attention grabbing features of a disclosed portfolio to make investment decisions. 1 The cognitive constraint makes it difficult for investors to recognize the gap between actual fund returns and the returns of a disclosed portfolio. As a result, the window dressing practice is potentially efficacious. In other words, investors behavior resulting from limited attention can provide incentives for fund managers to manipulate their disclosed portfolios. We examine how fund flows respond to disclosed portfolios and find results consistent with our conjecture. Specifically, we show that fund flows react positively to the performance of the top ten holdings (i.e., the largest ten holdings, and H10 hereafter) of a disclosed portfolio instead of the performance of the entire portfolio. A one standard deviation increase in the performance of H10 will lead to 1.14% increase in annualized fund flow. As most financial websites (such as Yahoo Finance) report the top ten holdings of mutual funds, it is reasonable to expect that these holdings are more likely to draw attention from investors. Therefore, our findings are consistent with the limited attention and attention grabbing hypothesis. 1 Prior studies provide evidence that mutual fund investors are influenced by salient and attention grabbing information. For example, Barber, Odean, and Zheng (2005) find that investors are more sensitive to salient in-your-face fees, like front-end loads and commissions, than operating expenses. Solomon, Soltes, and Sosyura (2014) show that investors pay more attention to media covered holdings. 1

4 To further explore the role of investor attention in attracting fund flows, we investigate the effect of big stocks (defined as stocks with market value in the top 5% based on NYSE breakpoints) in H10 on the positive relation between fund flows and the H10 performance. Because big stocks are more likely to be featured in the media, they tend to attract more attention from investors. The attention hypothesis predicts that a higher number of big stocks in H10 should exacerbate the positive relation between fund flows and the H10 performance. Consistent with this prediction, we find a stronger flow reaction to H10 performance among funds with more than eight big stocks in the H10 list a one standard deviation increase in the performance of H10 is associated with 2.42% increase in annualized fund flow, more than doubled the effect in the whole sample. However, we do not find the number of big stocks in the next ten largest holdings (i.e., the eleventh to twentieth largest holdings, denoted as H20 hereafter) to change the flow reaction in any way, which indicates that big stocks only draw investors attention when they are in the H10 list. An alternative explanation for the positive flow reaction to H10 performance, which we label the information hypothesis, is that investors realize their cognitive constraints and rationally choose to focus on the most important information (e.g., information contanined in the largest holdings). We conduct two tests to examine this possibility, but test results do not support the information hypothesis. First, we show that fund flows do not react in any significant way to the performance of H20. As H20 is typically not reported in financial websites, these holdings are not expected to draw much attention from investors. The insignificant flow reaction is, therefore, consistent with the attention hypothesis. On the other hand, H20 constitutes 20% (based on dollar value) of a portfolio on average, 2 which suggests that decisions on H20 are critical to the value of a fund and the information contained in H20 should not be rationally ignored by investors. Thus, the information hypothesis predicts a positive flow reaction to H20 performance, but test result does not support this prediction. Our second test examines the effect of the size of H10 (as a proportion of the entire portfolio in dollar value) on the positive flow reaction to H10 performance. When the size of H10 is large, decisions on H10 are more important to the value of a fund, and we expect investors to put more weight on information in H10 if they rationally choose to focus on these largest holdings. That is, the information hypothesis predicts a stronger flow reaction among funds with larger size of H10. We test this prediction, but test results do not support the information hypothesis. The effect of the size of H10 on the flow reaction is insignificant. 2 As a comparison, H10 makes up 32% of a portfolio on average. 2

5 Next, we examine whether fund managers realize investors behavior resulting from limited attention and window dress their portfolios accordingly. One challenge to study window dressing is that the manipulating trades of fund managers are not directly observable from available datasets. To this end, we propose a measure of window dressing, which is based on the difference in the momentum loading estimated using actual daily fund returns and the returns of a hypothetical portfolio comprised of the subsequently disclosed holdings over a period prior to the reporting day. 3 The intuition is that when a manager window dresses his portfolio before disclosure, the disclosed portfolio tends to contain more past winner stocks and fewer past loser stocks relative to the true portfolio held by the fund before disclosure. As a result, the momentum loading estimated using returns of the disclosed holdings is expected to be higher than that using actual daily fund returns. Of the 56,815 disclosed portfolios in our sample, 4,058 portfolios have positive window dressing measure (i.e., the momentum loading of the portfolio returns is higher than that of actual fund returns) with significant standard t-value (i.e., t 1.96). However, due to random sampling, simply counting the number of portfolios with significantly positive window dressing measure does not accurately reflect the prevalence of the practice in the sample. 4 We adopt an approach that specifically controls for false discoveries to obtain a better estimation of the prevalence. 5 Estimation results show that 9.88% of sample disclosures are window dressed, confirming the existence of the window dressing practice. More importantly, we find that the window-dressed proportion is higher among funds with poor H10 performance, and that funds with poor H10 performance tend to report more big stocks in the H10 list. These findings support the notion that fund managers realize investors behavior resulting from limited attention and window dress their disclosed portfolios accordingly. We conduct various robustness checks of our window dressing measure. First, we examine whether the momentum strategy of mutual funds drives our measure, and test results do not support this argument. Then, we provide evidence that our measure presents characteristics that are consistent with window dressing. Specifically, we find that funds are more likely to window dress towards fiscal year-ends, confirming the findings from prior studies of window dressing (e.g., 3 The reporting day is the last day of a reporting period. Mutual funds are required to disclose portfolio holdings as of the end of the reporting day. Our measure is motivated by other studies that compare these two return series, e.g., Kacperczyk, Sialm, and Zheng (2008). 4 There is always some probability that a significantly positive window dressing measure is coming from the null distribution, i.e., false discoveries. 5 See the Appendix for details. Barras, Scaillet, and Wermers (2010) and Bajgrowicz and Scaillet (2012) also provide an excellent discussion of the approach. 3

6 Elton, Gruber, Blake, Krasny, and Ozelge 2010). In addition, we show that funds are less likely to window dress when they are required to disclose their portfolios more frequently, consistent with the argument that more frequent disclosures increase the cost of window dressing, and therefore, lower the incentives for managers to window dress. Finally, we show that funds with poor past performance are more likely to window dress, and that window-dressed funds do not outperform other funds in the post-reporting-day periods. Our study contributes to the literature in multiple ways. First, we identify a new salient feature (i.e., H10) to which mutual fund investors pay attention to. We show that fund flows react positively to the H10 performance, and that big stocks attract more fund flows only if they are in the H10 list. These findings enhance our understanding on how mutual fund investors use available information to make investment decisions, complementing earlier studies about mutual fund investors behavior and adding new empirical evidence to the literature of limited attention. 6 In addition, these findings also offer a rationale for why fund managers may engage in window dressing. Because of limited attention, investors focus on certain salient features of a disclosed portfolio, and the gap between actual fund returns and the returns of the disclosed portfolio becomes less obvious to investors. This makes window dressing potentially efficacious. Second, our study confirms the existence of the window dressing practice and provides evidence that fund managers realize investors behavior resulting from limited attention and manipulate their disclosed portfolios in an expected way. These results provide useful information for investors and regulators to identify potential window-dressed funds, and add to the literature that investigates managers behavior as a result of agency conflict (e.g., Brown, Harlow, and Starks 1996; Chevalier and Ellison 1997; Musto 1997, 1999; Carhart, Kaniel, Musto, and Reed 2002; Pool, Sialm, and Stefanescu 2013; Lou 2014; Chen, Cohen, and Lou 2014). Finally, our finding that the likelihood of window dressing decreases when funds disclose the holdings more frequently provides some support for the regulatory change in May 2004, 7 and adds to the ongoing debate about the optimal disclosure frequency of mutual funds (e.g., Wermers 2001; Frank, Poterba, Shackelford, and Shoven 2004; Ge and Zheng 2006). 6 Studies about mutual fund investors behavior include, for example, Sirri and Tufano (1998), Jain and Wu (2000), Del Guercio and Tkac (2002, 2008), Nanda, Wang, and Zheng (2004), Pool, Sialm, and Stefanescu (2013), Agarwal, Gay, and Ling (2014), Harris, Hartzmark, and Solomon (2014), Sialm, Starks, and Zhang (2014), Sialm and Tham (2014), Solomon, Soltes, and Sosyura (2014). Studies of limited attention include, for example, Barber, Odean, and Zheng (2005), Barber and Odean (2008), Cohen and Frazzini (2008). 7 Mutual funds are required to disclose portfolio holdings quarterly after May 2004 as opposed to semi-annually before May

7 The rest of the paper is organized as follows. Section 2 reviews related literature. Section 3 describes our sample. Section 4 presents the flow reaction results. Section 5 examines when and how managers window dress their portfolios. Section 6 reports results of various robustness checks. Section 7 concludes. The Appendix describes the False Discovery Rate approach (FDR) that is used in this study. 2 Related Literature Our paper is linked to studies about how investors use available information to make capital allocation decisions, and in particular, how attention constraints affect investors behavior. Due to limited attention, investors tend to focus on certain salient features (e.g., Barber and Odean 2008; Chen, Cohen, and Lou 2014) and to behave in a biased or delayed way (Cohen and Frazzini 2008). In the mutual fund industry, effects of investor attention are documented in various studies. For example, Sirri and Tufano (1998) show that fund flows chase past fund performance in an asymmetric way, and this effect is most pronounced among funds with higher marketing effort. Jain and Wu (2000) report that mutual fund advertising significantly influences fund flows. Barber, Odean, and Zheng (2005) find that mutual fund investors are more sensitive to salient in-your-face fees, like loads and commissions, than operating expenses. Del Guercio and Tkac (2008) present evidence that the change in Morningstar ratings drives fund flows. Solomon, Soltes, and Sosyura (2014) show that media coverage of mutual fund holdings affects how investors allocate money across funds. Barber, Huang, and Odean (2014) find that among various risk factors, mutual fund investors only care about the widely reported market risk. We add to this strand of literature by documenting a new feature that tends to attract investors attention (i.e., H10) in the context of portfolio holdings. Given the rich information contained in disclosed holdings and the fact that H10 is widely reported, our setting is particularly suitable to test for investor attention. Our results also suggest a potential channel that contributes to the dumb money effect documented in Frazzini and Lamont (2008). Our study is also related to the broad literature that investigates managers behavior in response to investors cognitive biases, as a result of agency conflict. For example, Chevalier and Ellison (1997) and Brown, Harlow, and Starks (1996) document a risk-taking behavior of fund managers in response to the asymmetric relation between fund performance and future fund flows. Carhart, Kaniel, Musto, and Reed (2002) provide evidence that mutual fund managers are involved in portfo- 5

8 lio pumping a practice that managers move fund performance between periods with last-minute purchases in stocks already held as a result of the incentives provided by the flow-performance relation. Musto (1997, 1999) show that portfolio disclosures affect managers investment decisions in money markets, and Morey and O Neal (2006) find similar results among bond funds. Lou (2014) provides evidence that managers adjusts firm advertising to attract investor attention and to influence stock returns. Chen, Cohen, and Lou (2014) document an industry window dressing behavior of managers. We add to this literature by showing that equity mutual fund managers realize investors behavior as a result of limited attention and manipulate their disclosed portfolios in an expected way to exploit investors biased behavior. Our results suggest one potential mechanism that contributes to the finding in studies such as Kacperczyk and Seru (2007) and Fang, Peress, and Zheng (2014) that fund managers propensity to use public information is negatively related to managers skills. Our paper also adds to the window dressing literature. Prior studies present some evidence consistent with window dressing (e.g., Lakonishok, Shleifer, Thaler, and Vishny 1991; O Neal 2001; He, Ng, and Wang 2004; Ng and Wang 2004; Meier and Schaumburg 2006; Elton, Gruber, Blake, Krasny, and Ozelge 2010). 8 One critical assumption of window dressing is that investors react positively to holdings returns. An obvious puzzle associated with this assumption is that why investors cannot recognize the gap between actual fund returns and the returns of disclosed portfolios. Agarwal, Gay, and Ling (2014) offers a potential explanation assuming rational investors. They argue that investors use fund performance in the delayed period, i.e., the period from the reporting day to the day the holdings are publicly available, to interpret the inconsistency between actual fund returns and the returns of the disclosed portfolio, and only reward those funds with good performance in the delayed period. Fund managers, therefore, take a risky bet by window dressing the portfolios. We propose an alternative explanation based on investors cognitive bias, and show that our results are robust to the delayed-period-effect of Agarwal et al. (2014). In particular, we find that after controlling for the performance in the delayed period, the H10 performance continues to influence future fund flows (see Subsection 4.3), suggesting that at least some investors do not behave rationally and focus on the salient and attention grabbing features of disclosed portfolios to 8 Earlier studies (e.g., Haugen and Lakonishok 1988; Ritter and Chopra 1989) propose window dressing as a potential explanation for the turn-of-the-year effect. Studies such as Sias and Starks (1997), Poterba and Weisbenner (2001), and Grinblatt and Moskowitz (2004) show evidence inconsistent with this conjecture. More recently, Hu, McLean, Pontiff, and Wang (2014) examine transaction-level data of a sample institutions and find no evidence of window dressing on average. Our finding that only a minority of funds window dress offers a potential explanation for the mixed results in the literature. 6

9 make investment decisison. Such investor behavior can provide window dressing incentives to fund managers. 3 Data 3.1 Sample selection We merge the CRSP Survivor-Bias-Free US Mutual Fund Database with the Thomson Financial CDA/Spectrum holdings database using the MFLINKS file based on Wermers (2000) that is available through Wharton Research Data Services. The CRSP mutual fund database provides daily fund returns, total assets under management (TNA), fund expenses, fund styles, and other fund characteristics for each fund share class. We aggregate across share classes to compute fund-level variables based on a mapping file from MFLINKS. 9 The Thomson Financial CDA/Spectrum holdings database contains fund holdings in domestic common stocks at the end of a reporting period. The holdings data are collected both from reports filed by mutual funds with the SEC and from voluntary disclosures made by the funds. Daily stock returns, prices, and other stock characteristics are obtained from the CRSP stock database. Our sample covers the period from October 1998 to December Our analysis focuses on domestic equity funds because the holdings data are most complete and reliable for these funds. We use Lipper Objective Codes and Strategic Insight Objective Codes from the CRSP mutual fund database to identify equity funds. 11 To ensure that we mainly include domestic equity funds, we eliminate the disclosures with fewer than 20 stock holdings and the disclosures with less than 90% of the disclosed holdings matched to the CRSP stock database. We also eliminate disclosures if the combined CRSP TNA is above 120% or below 80% of the assets reported in Thomson Reuters. Since only managers of actively managed mutual funds have incentives to hide their true holdings, we exclude index funds from our analysis. Index funds 9 For most variables, fund level value is computed as the TNA-weighted average of the share class level value. Since TNA is only available at monthly frequency, daily fund returns are computed as the average daily returns across share classes of a given fund. As a further check for the accuracy of the mapping, we compute the correlation between daily returns of a share class and the corresponding daily fund returns, and only include those fund share classes with a correlation higher than 0.9. We exclude less than 1% of fund share classes due to this filtering. Fund age is equal to that of the oldest share class. 10 Daily fund returns are only available from October Lipper Objective Codes are available from Strategic Insight Objective Codes cover the earlier period of our sample period. We include funds with the following Lipper Objective Codes: CA, CG, CS, EI, FS, G, GI, H, ID, MC, MR, NR, RE, S, SG, TK, TL, and UT; and the following Strategic Insight Objective Codes: AGG, ENV, FIN, GMC, GRI, GRO, HLT, ING, NTR, RLE, SCG, SEC, TEC, and UTI. 7

10 are identified by checking both the index fund flag from the CRSP mutual fund database and the fund name. Elton, Gruber, and Blake (2001) identify a survivorship bias in the mutual fund database. This bias tends to be stronger for smaller funds. To partially address this bias, we exclude disclosures for funds with less than $5 million in assets under management on the reporting day. Evans (2010) shows an incubation bias in the mutual fund database. To address this concern, we eliminate disclosures made at a time when funds were younger than one year. Because our window dressing measure is constructed based on the comparison of daily fund returns and the hypothetical returns of the subsequently disclosed holdings, we only include days when both returns are available. For a disclosure to be included in our sample, we require at least 30 days with non-missing return data in the period from 60 days to three days before the end of a reporting period. 12 The resulting sample includes 2,860 distinct funds with 56,815 holdings disclosures. 3.2 Fund summary statistics For each disclosure in our sample, we obtain main attributes of the fund as well as the characteristics of the disclosed portfolio. Table 1 reports the mean, standard deviation, first quartile, median, and third quartile values. Panel A presents results of fund characteristics, and Panel B presents results of characteristics of disclosed portfolios. The number of funds ranges from 819 in the first quarter of 1999 to 1,775 in the third quarter of Panel A shows that the average fund size in our sample is $1,089.8 million and the median value is $201 million, suggesting that some funds are extremely large in size. The average and the median fund age are 11.5 years and 8.3 years respectively. As we focus on actively managed mutual funds, both the expense ratio and portfolio turnover are high in general. The average expense ratio is 1.34% per year, and the annual turnover for a typical fund in our sample is %. Using monthly fund returns from months m 36 to m 1 where month m is the last month of a reporting period, we calculate fund return volatility and alpha with respect to the Carhart four-factor model. The return volatility of a typical fund in our sample is 5.14% per month. The average alpha is slightly negative ( 0.03% per month), consistent with the finding from prior research that on average, mutual funds do not generate positive abnormal returns. Fund flow in the three-month period 12 We construct our window dressing measure using daily returns in this period as detailed in Section 5.1. We exclude the last two trading days before the end of a reporting period to partially control for the potential effect of portfolio pumping. See, for example, Carhart, Kaniel, Musto, and Reed (2002). 8

11 before the end of a reporting period (i.e., months m 2 to m) is obtained. Monthly flow for fund i in month t is calculated as: flow i,t = T NA t T NA t 1 (1 + r i,t ) T NA t 1, (1) where T NA t and T NA t 1 are the total assets under management at the end of month t and t 1 for fund i, respectively, and r i,t is the after-fees fund return in month t. Fund flow over months m 2 to m (flow 2,0 ) is calculated as the average monthly fund flow in the period. Following previous studies (e.g., Huang, Sialm, and Zhang 2011), we winsorize the top and bottom 1% of fund flows to eliminate the effect of outliers. The average fund flow is 0.42% per month, and the median value is 0.39% per month. We also calculate fund returns in excess of S&P 500 (r fund, 2,0 ) over the three-month period before the end of a reporting period (i.e., months m 2 to m). The average fund performance in this period is 0.73% per quarter and the median value is 0.50% per quarter. Panel B presents the characteristics of disclosed portfolios. The average number of stock holdings (# holdings) disclosed is 109, indicating that mutual funds in our sample, in general, hold diversified portfolios. The average (hypothetical) portfolio return in excess of S&P 500 (r port, 2,0 ) over months m 2 to m is 4.59%, which is significantly higher than the fund return in the same period as shown in Panel A, consistent with the conjecture that fund managers window dress their disclosed portfolios. 13 CRSP TNA-weighted return in excess of S&P 500 over months m 2 to m of the largest ten holdings (i.e., r H10, 2,0 ) and the next largest ten holdings (i.e., r H20, 2,0 ) are also reported in the panel. The average performance is 8.19% for H10 and 5.23% for H20. The higher return of H10 is consistent with the notion that fund managers tend to window dress these holdings. H10 size ( H20 size ) is calculated as the combined CRSP TNA of H10 (H20) divided by the combined TNA of the disclosed portfolio. On average, H10 constitutes 31.93% and H20 constitutes 19.95% of the portfolio. We define stocks with market value in the top 5% based on NYSE breakpoints as big stocks. In our sample, all the big stocks have market value greater than $12 billion. # big in H10 and # big in H20 report the number of big stocks in H10 and H20, respectively. On average, a fund reports 4.5 big stocks in the top ten holdings (i.e., H10) and 3.6 in the next ten holdings (i.e., H20). 13 Similar results are also reported in Solomon, Soltes, and Sosyura (2014). 9

12 4 Flow Reaction to Disclosed Portfolios In this section, we examine how mutual fund flows react to disclosed portfolio holdings. In particular, we investigate whether and how mutual fund investors behavior provides window dressing incentives to fund managers. We show that instead of the disclosed portfolio, fund investors react positively to the performance of the largest ten holdings (i.e., H10) of the portfolio. Moreover, the positive relation between H10 performance and future fund flows becomes stronger when H10 contains more big stocks. Such results can be explained by limited attention of fund investors and the attention grabbing feature of H10. Because of limited attention, investors are less likely to identify the inconsistency between actual fund performance and a window-dressed disclosed portfolio, which provides incentives for fund managers to manipulate their portfolios to be disclosed. Table 2 reports results from pooled regressions. The dependent variable is fund flow over months m + 3 to m + 5, flow 3,5, where m is the last month of a reporting period. We choose flow 3,5 as the dependent variable because the SEC requires mutual funds to report their holdings within 60 days after the end of a reporting period and most funds choose to report right before the due date. As a result, investors do not have access to the holdings information in months m + 1 and m + 2. In addition, when funds disclose their portfolios quarterly, investors are exposed to information of an updated portfolio in month m Therefore, using flow 3,5 as the dependent variable helps us understand how investors react to the information contained in portfolios held by funds at the end of month m. We include in our regressions a set of control variables that are documented in prior studies to potentially affect future fund flows. Specifically, we include fund size, expense ratio, fund age, long-term past fund performance (captured by Carhart-alpha), past fund flow (flow 2,0 ), number of holdings disclosed, past fund return volatility, and portfolio turnover. The control variables are constructed in the same way as in Table 1. Finally, quarter-fund style fixed effects are included in all regressions. Standard errors are clustered by fund. 4.1 Positive reaction to the top ten holdings Panel A of Table 2 examines how investors respond to disclosed portfolios. First, we investigate whether fund flows react positively to disclosed portfolios as assumed in the literature to provide 14 Information of portfolio holdings as of the end of month m + 3 will be available to investors starting from month m

13 window dressing incentives. We measure performance of a disclosed portfolio as the return of the portfolio in excess of S&P 500 over the three-month period before the reporting day (i.e., from months m 2 to m), r port, 2,0. Model [1] in Panel A presents the results. The coefficient of r port, 2,0 is significantly positive, with t-value of This result seems to support the assumption taken in the existing literature. When r port, 2,0 increases by one standard deviation, the annualized fund flow will increase by 2.445% (= ). However, it is known that investors tend to chase past fund performance. In Model [2], we examine whether r port, 2,0 continues to contribute positively to future fund flows after controlling for past fund performance. We measure past fund performance as fund return in excess of S&P 500 over months m 2 to m, r fund, 2,0. Fund performance (r fund, 2,0 ) and portfolio performance (r port, 2,0 ) in the same period are highly correlated. To address the multicollinearity issue, instead of including r port, 2,0 and r fund, 2,0, we include the difference between the two excess returns (i.e., port, 2,0 = r port, 2,0 r fund, 2,0 ) and r fund, 2,0 in the regression. 15 Model [2] shows that the coefficient of port, 2,0 is significantly negative ( with t-value of 5.05), suggesting that investors do not reward a better-looking disclosed portfolio after taking into account the actual performance of the fund. This result does not seem to support the incentives of window dressing. A typical disclosed portfolio in our sample contains more than 100 stock holdings as shown in Table 1. We posit that due to limited attention, it is difficult for investors (especially retail investors) to process such rich information contained in the complete list of holdings. Instead, investors focus on certain salient features of disclosed portfolios to evaluate fund managers. The fact that most financial websites such as Yahoo Finance report the top ten holdings (i.e., H10) from the most recent disclosure of a mutual fund suggests that these holdings are more likely to grab investors attention. In Model [3], we examine how investors react to the performance of H10. The performance of H10 (r H10, 2,0 ) is calculated as the CRSP TNA-weighted stock return in excess of S&P 500 over months m 2 to m. Similarly, to deal with multicollinearity, instead of including r H10, 2,0, we include H10, 2,0 (= r H10, 2,0 r port, 2,0 ) in the regression. 16 Consistent with our prediction, Model [3] presents a significantly positive relation between H10, 2,0 and future fund flows. A one standard deviation increase in r H10, 2,0 will lead to 1.14% (= ) increase in annualized fund flow. This finding supports our conjecture that due to limited attention, investors pay attention to certain attention grabbing features (such as the largest ten holdings) of a 15 The correlation between r port, 2,0 and r fund, 2,0 is 0.789, and that between port, 2,0 and r fund, 2,0 is The correlation between r H10, 2,0 and port, 2,0 is The correlation between H10, 2,0 and port, 2,0 goes down to

14 disclosed portfolio to evaluate fund managers. This behavioral bias makes the gap between actual fund performance and that of the disclosed portfolio less obvious to investors, and therefore, it is more difficult for investors to recognize potential manipulating behavior of fund managers, which provides incentives for fund managers to window dress their portfolios. 4.2 The information hypothesis Instead of investor attention, one potential alternative explanation for the positive relation between H10 performance and future fund flows is that investors realize their cognitive constraints and rationally choose to focus on the largest holdings. Because the largest holdings represent the most important decisions a manager made, these holdings tend to contain the most important information to evaluate the manager. We call this alternative hypothesis the information hypothesis, and conduct two tests to examine this possibility. Test results, however, do not support the information hypothesis, and are more consistent with the prediction of the attention story. First, we examine how investors react to the performance of the next ten largest holdings of a portfolio (i.e., H20). Table 1 shows that on average, H10 constitutes 32% and H20 constitutes 20% of a portfolio. Therefore, managers decisions on H10 and H20 are both critical to the value of the portfolio, and both H10 and H20 contain important information to evaluate managers. The information hypothesis predicts that investors should also react positively to the performance of H20 (probably to a lesser degree relative to that of H10). The attention hypothesis, on the other hand, does not predict any significant relation between fund flows and the performance of H20 because H20 is typically not reported in websites such as Yahoo Finance, and therefore, we do not expect them to draw attention from investors. Models [4] and [5] in Panel A report test results. The performance of H20 (r H20, 2,0 ) is calculated as the CRSP TNA-weighted stock return in excess of S&P 500 over months m 2 to m. Similarly, instead of r H20, 2,0, we include in the regressions H20, 2,0 which is the difference between r H20, 2,0 and r port, 2,0 to deal with multicollinearity. Test results show an insignificant negative coefficient of H20, 2,0, with t-value of 1.28 in Model [4] and with t-value of 0.89 in Model [5], suggesting that investors do not react in any significant way to the performance of H20. These results are, therefore, consistent with the attention hypothesis but inconsistent with the information hypothesis. Our second test examines the effect of H10 size on the positive relation between H10 performance 12

15 and fund flows. When H10 constitutes a larger portion of the portfolio, managers decisions on H10 are more important to the value of the fund. If investors rationally choose to focus on these important decisions to evaluate a manager (i.e., the information hypothesis), then they should put more weights on the performance of H10 when the size of H10 is large. To test this prediction, we sort our sample into terciles based on H10 size. I H10size is a dummy variable that equals to one when a disclosure is in the highest tercile, and zero otherwise. We include I H10size and its interaction with H10, 2,0 in the regression. The information hypothesis predicts a significantly positive coefficient on the interaction term. Model [6] of Panel A shows that the coefficient of the interaction term is insignificantly negative ( with t-value of 0.17), a finding inconsistent with the information hypothesis. 4.3 Performance in the delayed period Agarwal, Gay, and Ling (2014) propose a rationale for window dressing assuming rational investors. They argue that investors are more likely to attribute the gap between actual fund performance and a window-dressed portfolio to manager s improved security selection strategy if fund performance is good in the period between the reporting day and the day the holdings information is publicly available (i.e., the delayed period), and only reward funds with good delayed-period performace with higher fund flows. In Model [7] of Panel A, we examine whether this delayed-period-performance effect will take away the identified positive relation between H10 performance and future fund flows. We define a delayed-period-good-performance dummy (I delay ) which equals to one when a fund s return is higher than the S&P 500 return in the delayed period, and zero otherwise. We include I delay and the interaction term between I delay and port, 2,0 into the regression. The delayedperiod-performance effect predicts a significantly positive coefficient of the interaction term. Consistent with the findings in Agarwal et.al (2014), Model [7] shows that the interaction term between I delay and port, 2,0 is positive (0.013 with t-value of 1.58), suggesting that fund performance in the delayed period affects how investors allocate their money. However, H10, 2,0 remains significantly positive (0.007 with t-value of 1.96) after including the good performance dummy (I delay ) and the interaction term ( port, 2,0 I delay ). Therefore, our finding is not driven by the delayed-period-performance effect. At least some investors do not seem to behave rationally and focus on the attention grabbing feature of a disclosed portfolio to evaluate managers. 13

16 4.4 Effect of the number of big stocks in H10 So far, we have presented results consistent with the argument that mutual fund investors pay attention to H10 performance due to the attention grabbing feature of these holdings. To provide further support to the attention story, we examine whether other attention grabbing feature of stocks in H10 will affect the positive relation between H10 performance and future fund flows. In particular, we investigate the effect of the size (in terms of market value) of the stocks. Big stocks are more likely to be featured in the media, and therefore, are more likely to draw attention from investors. The attention grabbing hypothesis predicts a stronger positive relation between future fund flows and H10 performance when there are more big stocks in the H10 list. To investigate the effect of the number of big stocks among H10, we define a dummy variable (I nonbig10 ) that equal to one when a disclosure has less than eight big stocks in the H10 list, and zero otherwise. 17 We include this dummy and its interaction with H10, 2,0 in our regression. Test results are reported in Model [1] of Panel B of Table 2. The coefficient of H10, 2,0 now captures the relation between H10 performance and fund flows among funds with more than eight big stocks in their H10 list. Compared to the whole sample result as reported in Model [3] of Panel A, the magnitude of the positive relation between H10 performance and fund flows is more than doubled (0.017 with t-value of 2.56). The significantly negative coefficient of the interaction term ( with t-value of 1.84) suggests that the H10 performance-flow relation among funds with fewer than eight big stocks in the H10 list is much weaker. These results are consistent with the attention grabbing hypothesis. Next, we examine whether the number of big stocks outside H10 affects investors decision similarly. In particular, we investigate the effect of the number of big stocks in H20. We define a dummy variable (I nonbig20 ) that equals to one when H20 contains less than eight big stocks and zero otherwise. 18 We include I nonbig20 and its interaction with H20, 2,0 in regression. Test results are reported in Models [2] and [3] of Panel B. We can see that the coefficient of H20, 2,0 remains insignificantly negative, and the coefficient of the interaction term ( H20, 2,0 I nonbig20 ) is also insignificant. These results indicate that big stocks in H20 do not seem to affect investors decisions in any significant way. In sum, Panel B suggests that big stocks only draw investors attention when they are in the H10 list. Therefore, reporting stocks in places easily accessible to investors seems to be a necessary 17 A third of our sample disclosures (19,067 out of 56,815) have more than eight big stocks in their H10 list. 18 About 20% of our sample disclosures (11,219 out of 56,815) have more than eight big stocks in their H20 list. 14

17 condition to grasp investors attention. Stocks outside H10 (e.g., H20), typically not reported, draw much less attention from investors, and the number of big stocks in H20 does not significantly affect how investors allocate their money. 5 Mutual Fund Window Dressing In the previous section, we provide evidence that limited attention influences how mutual fund investors allocate their money. In particular, we show that instead of the disclosed portfolio, investors react positively to the top ten holdings (H10) of the portfolio, and that a higher number of big stocks in the top ten list exacerbates the positive relation. Such investor behavior can provide incentives for fund managers to manipulate their portfolios. In this section, we examine whether managers indeed window dress accordingly. 5.1 The measure One challenge to study window dressing is that we cannot directly observe the manipulating trades conducted by fund managers in the databases currently available. To this end, we propose a measure of window dressing. The construction of the measure is based on the following intuition. When a fund manager window dresses his portfolio, the disclosed portfolio tends to contain more past winner stocks and fewer past loser stocks relative to the actual portfolio held by the fund before the reporting day. As a result, the momentum loading estimated using actual fund returns in the period before the reporting day tends to be lower than that estimated using hypothetical portfolio returns in the same period. Our window dressing measure is, therefore, constructed as the difference between the two momentum loadings. We present steps to obtain the measure in the following. Let t denote the reporting day of fund i. We obtain daily returns of the disclosed portfolio in a period prior to day t: n RH i,t,τ = w j,τ 1 R j,τ, (2) j=1 where n is the number of holdings disclosed, R j,τ is the return of stock j on day τ with τ < t, and w j,τ 1 is the weight of stock j at the beginning of day τ. 19 The weight w j,τ 1 depends on the 19 The difference between the market value of all disclosed stock holdings and the asset under management of the fund at the reporting date is assumed to be cash. Cash is expected to earn the risk-free rate that is proxied by the 15

18 number of shares held by the fund at the end of day t (N i,t,j ) and the stock price at the end of day τ 1 (p j,τ 1 ): w j,τ 1 = N i,t,j p j,τ 1 n j=1 N i,t,jp j,τ 1. (3) Further, stock prices and the number of shares are adjusted for stock splits and other share adjustments between day τ 1 and day t. We compare the obtained portfolio daily return RH i,t,τ with the actual fund return on the same day. Since the CRSP Mutual Fund database only reports the after-fees daily fund returns, we add back daily expense ratio to make the daily fund returns comparable to the obtained returns of the disclosed portfolio: 20 RF i,τ = r i,τ + e i /250, (4) where RF i,τ and r i,τ are the before- and after-fees returns of fund i on day τ respectively, and e i is the annual expense ratio of fund i. We then obtain the return difference on day τ: RD i,t,τ = RH i,t,τ RF i,τ. (5) Trades related to window dressing occur before the reporting day t. However, when exactly these trades take place is an empirical question. We posit that a two-month window before the reporting day t should capture most of these trades, and therefore, our window dressing proxy is calculated using daily returns in this window. For each day τ from 60 days to three days before the reporting day, i.e., t 60 τ t 3, we obtain the return difference RD i,t,τ and run the Carhart four-factor model using these daily return differences: RD i,t,τ = α i,t + β i,t,mkt r MKT,τ + β i,t,smb r SMB,τ + β i,t,hml r HML,τ + β i,t,umd r UMD,τ + ɛ i,t,τ, (6) where r MKT,τ, r SMB,τ, r HML,τ, and r UMD,τ are returns of the market factor, size factor, value factor, and momentum factor on day τ. β i,t,mkt, β i,t,smb, β i,t,hml, and β i,t,umd are the corresponding factor loadings. Our focus is β i,t,umd. If a manager window dresses before a disclosure, rate of one-month Treasure bill. 20 Because fund expense ratio is unlikely to change over a short-term period, the expense ratio add-back will have limited effect on the estimated momentum loading. Therefore, a window dressing measure based on the difference in momentum loading is less sensitive to the expense ratio adjustment than a measure based on return or alpha difference. 16

19 then there is a high likelihood for us to observe β i,t,umd > 0. This is because when the manager window dresses, he tends to add winner stocks to and/or unload loser stocks from his portfolio. As a result, the momentum loading of the disclosed portfolio (RH) would be higher than that of the actual fund returns (RF ). One may argue that our measure picks up the momentum trading of a fund instead of window dressing. We do not believe this is the case. In the case of momentum trading, it is reasonable to assume that the buying-winners-and-selling-losers trades are more uniformly distributed over time, whereas those of window dressing are more likely to occur close to the end of a reporting period. Notice that when these trades occur at a time closer to the end of a reporting period, the momentum loading estimated using actual fund returns (RF ) in the estimation window (i.e., [t 60, t 3]) is lower than otherwise would be, which leads to a larger β i,t,umd in Eq.(6). Therefore, our measure is higher in the case of window dressing than that of momentum trading, and it is more likely to pick up window dressing than momentum trading. In Subsection 6.1, we conduct additional tests to further support that our measure captures window dressing instead of momentum trading. 5.2 The prevalence Of the 56,815 disclosures in our sample, 27,900 show a positive window dressing measure, and 4,058 of which have a significant standard t-value (i.e., t 1.96). However, due to random sampling, a significantly positive β i,t,umd does not necessarily mean window dressing. To obatin a more accurate estimation of the prevalence of window dressing, we adopt the False Discovery Rate (FDR) approach. This approach controls for false discoveries due to random sampling in multiple hypothesis testing, and is a natural choice in our setting. Specifically, we assume that our sample contains observations from both the null distribution and alternative distributions: i) the null group (i.e., β i,t,umd = 0), ii) the window-dressed group (i.e., β i,t,umd > 0), and iii) the decreasing momentum group (i.e., β i,t,umd < 0). The FDR approach provides a way to estimate the proportion of each group in the sample. Our focus is the window-dressed proportion, which we denote as π +. Details about the FDR approach are provided in the Appendix. This approach is also adpoted in Barras, Scaillet, and Wermers (2010) and Bajgrowicz and Scaillet (2012). Table 3 reports estimation results. Panel A shows that of the 56,815 disclosures, 9.88% present evidence of window dressing. This result confirms the existence of the window dressing practice, and the relatively low window-dressed proportion provides a potential explanation for the weak 17

20 evidence of window dressing in the existing literature. Panel B of Table 3 examines the proportion of funds that choose to window dress in the right tail (i.e., ˆβi,t,UMD > 0) of the cross-sectional distribution. We examine four significance levels (κ = 0.05, 0.10, 0.15, and 0.20). Column Ŝ+ reports the percentage of the sample disclosures with p-value lower than a given significance level. For example, when κ = 0.05, 6.76% of the disclosures in our sample show a positive window dressing measure with a two-sided p-value smaller than However, significant p-value does not necessarily mean window dressing. Column ˆT + presents the proportion after controlling for false discoveries (see the Appendix for details). When κ = 0.05, the corrected window-dressed proportion is 4.80% (= 6.76% 78.02% 2.5%). The last two columns of Panel B present the percentage of disclosures that are window-dressed in various segments of p-values. For disclosures with p-values smaller than 5%, 71.13% are window dressed. The percentage number goes down dramatically as p-value increases. For disclosures with p-values between 0.15 and 0.20, for example, the window-dressed percentage decreases to 25.73%. The results in Table 3 suggest that the usual practice of comparing p-values to a given level of significance (e.g., κ = 0.05) is likely to lead to an inaccurate window-dressed prevalence estimation. The FDR approach not only considers the information contained in the tails of the cross-sectional distribution but also leverages the information in the center of the distribution, and therefore, more accurately captures the true window-dressed proportion. 5.3 Window dressing and the performance of the lagged H10 If fund managers realize that investors pay more attention to the largest ten holdings of a disclosed portfolio, then those managers with poorly performing H10 will have more incentives to window dress. Notice that the portfolio that a manager wants to window dress is the one held by the fund before the reporting day, but holdings information about this portfolio is not publicly available. Therefore, we use holdings from the lagged disclosure as a proxy. If the H10 performance of this lagged portfolio turns out to be poor, then the manager will have more incentives to window dress before the reporting day. As a result, we expect a higher window-dressed proportion among funds with poor lagged H10 performance. Table 4 examines this prediction. We identify the largest ten holdings of the lagged disclosed portfolio (lagged H10) using stock prices at the end of the current reporting period, and calculate the performance of lagged H10 as CRSP TNA-weighted stock returns in excess of S&P 500 over the 18