Two essays in finance

... gives information comparing investors in this sample to mutual fund investors in general Panel A of the table shows that in 2000, 83.2% of the holdings in my sample are in equity funds, 6.7% are in. .. avoid admitting that their original purchase decision was a mistake, so they avoid realizing losses and instead sell winning funds Shefrin and Statman (1985) call selling winners while holding losers... Fant and O’Neal (2000) find that individual investors buy top performing funds but hold underperforming funds These results suggest that buying and selling winners while holding poor performers is

Two Essays in Finance by David G. Shrider Bachelor of Science Miami University, 1992 Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in the Moore School of Business University of South Carolina 2003 mmittee Member Director of Dissertation Committee Member y / Committee Member Committee Member yiyl ^ Dean of The Graduate School Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UMI Number: 3098705 UMI UMI Microform 3098705 Copyright 2003 by ProQuest Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. ProQuest Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, Ml 48106-1346 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. © by David G. Shrider, 2003 All Rights Reserved ii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Dedication To Betsy. iii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Acknowledgements While the past four years have been challenging, I have thoroughly enjoyed my time at the University of South Carolina. There are a number of people that deserve thanks for their part in making my time in graduate school such a positive experience. Most importantly I would like to say thank you to Betsy and Ben. Without their infinite emotional support as well as their personal and financial sacrifice none of this would have been more than an unfulfilled dream. I would also like to thank the rest of my family for their support. In particular, thanks to my Mom and Dad who have fostered my self-confidence and encouraged my inquisitiveness for as long as I can remember. My Mother and Father also deserve credit, not only for their support of my graduate education, but also for their general and sometimes very specific academic advice. My chair, Greg Niehaus, has given me more than I can ever hope to repay. His ability to be ever fair, rational, logical, and of course scientific is a credit to academia and will remain my model of what I should attempt to become. I thank him most for the endless hours of his time that he freely gave throughout this entire process. Thanks to Mary Bange for putting up with me for eight straight semesters and for always having an answer to the countless questions I’ve posed over that time. Scott Harrington provided as much information as I could process in two excellent semesters of class work. However, I am most grateful to Scott for not only working with me and teaching me so much about the entire process of writing a paper, but for treating me as a peer rather than a student from beginning to end. Tim Koch deserves thanks for first introducing me to world of behavioral finance and showing me that all possible explanations must be explored. Thanks to Melayne Mclnnes for always finding iv Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. additional time to help me understand the economic intuition behind every derivative. I need to say thank you to others who had a major impact on my time in the program. Timo Korkeamaki acted as my big brother from my first weeks in Columbia by always giving me encouragement, motivation, and a perfect role model. Tom Smythe, despite graduating before I enrolled, helped me with data, had numerous conversations with me about mutual funds, provided specific comments on my papers, and always provided great advice on everything from how to buy a house in Columbia to how to pick a dissertation adviser. Steve Mann helped me survive the first semester and read my first attempt at a literature review on performance persistence in mutual funds. Ted Moore provided econometric help and most importantly gave me an opportunity to be a part of the PhD program at the University of South Carolina. Frank Fehle, Eric Powers, and D.H. Zhang gave me general advice throughout the program as well as specific comments on earlier drafts of my dissertation. My fellow graduate students Vladimir Zdorovtsov, Scott Brown, Ting Lu, Tim Michael, Tong Yu, D.K. Kim, Yoon Shin, and Chris McNeil provided guidance, encouragement, competition, laughter, and advice that not only helped me survive, but also made my time at South Carolina more enjoyable. Thank you to Barb Covington, who is vastly under appreciated solely because she does such an outstanding job of eliminating every administrative detail from the life of PhD students. Thanks to Charlie Conn, Bill Hutchinson, and especially the late Jeff Wyatt. Without their early advice and letters of support my transition to academia would simply not have been attainable. Finally thank you to God for giving me everything to make this experience possible. v Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Abstract Two Essays in Finance David G. Shrider How Does Past Performance Affect Load Mutual Fund Investor Behavior? I use a proprietary data set to provide evidence on how past performance affects the transaction decisions of a sample of load mutual fund investors by decomposing the overall effect into how past performance affects the probability investors will make a transaction and how past performance affects the size of the transactions made. I provide evidence on how mental accounting affects investors’ willingness to redeem poor performers as discussed in Shefrin and Statman (1985). Investors are more likely to purchase past winners and make larger purchases of past winners, which is consistent with representativeness and the findings of Barber, Odean, and Zheng (2000), Sirri and Tufano (1998), and Fant and O’Neal (2000). However, I find no evidence of loss aversion when it comes to the probability of redeeming poor performers. My results show that when investors do redeem a poor performer they are more likely to liqudate the entire position. Finally, I find evidence consistent with Shefrin and Statman’s (1985) hypothesis that investors are more willing to sell poor performers if the transaction is framed as a transfer rather than a sale. All Events Induce Variance: Analyzing Abnormal Returns When Effects Vary Across Firms Widely used test statistics for non-zero mean abnormal returns in short-horizon event studies ignore cross-firm variation in event effects. We use a simple model of event effects and simulations patterned after Brown and Warner (1980,1985) and Boehmer, vi Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Musumeci, and Poulsen (BMP, 1991) to highlight the resulting biases and the importance of using test procedures that appropriately allow for cross-sectional variation. We demonstrate analytically how cross-sectional variation produces “event-induced” variance increases and biases popular tests for non-zero mean abnormal returns. Our simulations provide evidence of that bias and of test power for several theoretically robust tests for non-zero means, including the standardized cross-sectional test statistic suggested by BMP, which we show equals the mean standardized prediction error divided by a heteroskedasticity-consistent standard error, and cross-sectional regression tests that condition on relevant regressors. Director of Dissertation - Gregory R. Niehaus vii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table of Contents Dedication...................... iii Acknowledgements.......................................... iv A bstract .......................................................................................................vi List of T ables................................................ x List of F igures..................................................................................................................xii Chapter 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 How Does Past Performance Affect Load Mutual Fund Investor Behavior? Introduction .......................................................................................1 Mutual Fund Industry...................................................................................6 Hypotheses ........................ 9 1.3.1 Load vs. No-Load Investors.......................................................... 9 1.3.2 Exchange Redemptions and Mental Accounting ........................11 1.3.3 How Past Performance Affects Transaction Size .............12 D a t a .............................................................................................................12 1.4.1 Account Information......................... 13 1.4.2 Demographic Information........................................................... 13 1.4.3 Transactions ................... 15 1.4.4 Performance M easures ................................................ 16 R esu lts.........................................................................................................18 1.5.1 Transactions by Performance Decile .................................. 18 1.5.2 Transactions Relative to Assets ................... 20 1.5.3 Logit Analysis - How does Performance Affect the Probability of Trading?........................................ 23 1.5.4 Regression Analysis - How does Performance Affect the Size of T rades?............................ 27 1.5.5 Robustness C hecks.......................................................................31 D iscussion.................................. 35 Sum m ary.....................................................................................................37 References for Chapter 1 ............... 38 Chapter 2 - All Events Induce Variance: Analyzing Abnormal Returns When Effects Vary Across Firms 75 Introduction........................................................................................ 2.1 81 A Simple Model of Cross-Sectional Variation ...................... ........... 2.2 84 Unconditional Mean Abnormal Return Tests .................................... 2.3 2.3.1 Bias in Traditional and SPE Tests ........................................... 84 2.3.2 Theoretically Robust T e s ts...................................................... 86 Cross-Sectional Regression Tests of Conditional Means and Slopes . ..8 9 2.4 91 Data and Simulation Design .............................................................. 2.5 Empirical Results ................................................................................. Q3 2.6 viii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.7 2.8 2.9 2.6.1 Unconditional Tests for Mean Abnormal R eturns.......................94 2.6.2 Cross-Sectional Regression Tests ................................................ 96 Sum m ary................................................................. 98 Appendix to Chapter 2 ............................................................................ 100 2.8.1 Robustness of Ordinary and Standardized C-S T ests............... 100 2.8.2 Simulation Results for k = Vi and k = 2 ...................................... 101 References for Chapter 2 ......................................................................... 102 ix Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. List of Tables 1.1 Example Sales Charge and Commission Structure............................................... 42 1.2 Account Characteristics 1.3 Investor Demographics............... 45 1.4 Holdings by Asset Class 47 1.5 Transaction D ata.................................................................................................... 48 1.6 Redemptions by Return Deciles 1.7 Exchange Redemptions by Return Deciles............................................................50 1.8 Purchases by Return Deciles..................................................................................51 1.9 Exchange Purchases by Return Deciles ...............................................................52 ......................................... ....................................... 43 .....................................................49 1.10 Logit Results - Redemptions.................................................................................53 1.11 Logit Results - Exchange Redemptions................................................................ 55 1.12 Logit Results - Purchases...................................................................................... 57 1.13 Logit Results - Exchange Purchases..................................................................... 59 1.14 Regression Results - Redemptions................................................... 61 1.15 Regression Results - Exchange Redemptions....................................................... 63 1.16 Regression Results - Purchases............................................................................. 65 1.17 Regression Results - Exchange Purchases................... 2.1 Variances and Mean Abnormal Return Test Statistics that Ignore Cross-Sectional Variation in Effect S ize.............. 67 105 2.2 Asymptotic Properties of Unconditional Estimation/Testing Procedures for Mean Abnormal Returns............................................................................... 106 2.3 Asymptotic Properties of Estimation Procedures for Cross-Sectional Models of Abnormal Returns.......................... x Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 107 2.4 Summary Statistics for Mean Abnormal Return Test Statistics When Effect Size is Z ero............................................................................................... 108 2.5 Empirical Rejection Frequencies for Mean Abnormal Return Test Statistics.......................... 109 2.6 Empirical Rejection Frequencies of Robust Test Statistics for Conditional Mean Abnormal Return (Regression Intercept)..............................110 2.7 Empirical Rejection Frequencies for Estimated Regression Slope Test Statistics...................................................................................................... I l l 2.8 Summary Statistics for Mean Abnormal Return Test Statistics When Mean Effect Size is Zero..................................................................................... 112 2.9 Empirical Rejection Frequencies for Mean Abnormal Return Test Statistics...............................................................................................................113 2.10 Empirical Rejection Frequencies of Robust Test Statistics for Conditional Mean Abnormal Return (Regression Intercept)..............................114 xi Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. List of Figures 69 1.1 Proportion Redeemed - All Funds.................. 1.2 Proportion Redeemed - Momingstar Categories .............................................. 70 1.3 Proportion Purchased - All Funds..................... 71 1.4 Proportion Purchased - Momingstar Categories................................................... 72 1.5 Accounts That Liquidate - Redemptions...............................................................73 1.6 Accounts that Liquidate - Exchange Redemptions 2.1 Estimation Methods..............................................................................................115 2.2 Sample Size Cumulative Frequency ...................................................................116 2.3 Cross-Sectional Heteroskedasticity Illustration............................................. 2.4 Type 1 Error R ates............................................................................................... 118 ...................................74 xii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 117 Chapter 1 How Does Past Performance Affect the Behavior of Load Mutual Fund Investors? 1.1 Introduction Despite the standard disclaimer on all mutual fund sales literature that past performance is not indicative of future results, investor decisions are clearly influenced by past performance. Barber, Odean, and Zheng (2000) find that no-load investors at a discount brokerage firm buy and sell the best performing funds, while holding poor performers. Using aggregate fund flow data, Ippolito (1992), Sirri and Tufano (1998), and Fant and O’Neal (2000) find that individual investors buy top performing funds but hold underperforming funds. These results suggest that buying and selling winners while holding poor performers is common at least among some investors. While this literature provides information on how past performance affects which funds investors buy and sell, it does not provide evidence on how past performance affects the size of the resulting transactions. The purpose of this paper is first, to determine whether the behavior of investors at a national full service brokerage firm is similar to no-load investors who buy and sell winners while holding losers, and second to examine how performance affects the size of the transactions that investors make. Since the early studies of Treynor (1965), Sharpe (1966), and Jensen (1968), there has been an ongoing debate surrounding the existence of performance persistence among mutual funds. While persistent winners are at best short-lived (Gruber (1996) and Carhart (1997)), many studies including Grinblatt and Titman (1992,1993), Hendricks, l Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Patel, and Zeckhauser (1993), and Brown and Goetzmann (1995) find that some mutual funds underperform both the market and their peers for extended periods of time.1 Sharpe (1996) states, “Perhaps the only safe conclusion is that there is little support for the thesis that within the group of funds, past losers ‘are due’ and likely to outperform past winners.” (pg. 6) Therefore, selling winners while continuing to hold poor performers hurts performance on average over time. To explain their findings with no-load investors Barber, Odean, and Zheng (2000) use ideas from the behavioral finance literature. They suggest that investors buy past winners because investors believe that past results are representative of future performance. However, once individuals own a fund, the representativeness heuristic is dominated by loss aversion as described by Kahneman and Tversky’s (1979) prospect theory. Loss aversion implies that investors want to avoid admitting that their original purchase decision was a mistake, so they avoid realizing losses and instead sell winning funds. Shefrin and Statman (1985) call selling winners while holding losers the disposition effect. Grinblatt and Kelohaiju (2001) show that Finnish investors’ behavior is consistent with the disposition effect. When combined, representativeness and the disposition effect give rise to investors buying and selling winners, while holding losers. There are at least three reasons why investors working with a financial adviser might exhibit different behavior than investors that don’t pay a load and make their own investment decisions.2 The first two reasons are related to the actions of the investor 1Many factors are associated with negative performance persistence. Grinblatt and Titman (1992), Kahn and Rudd (1995), and Elton, Gruber and Blake (1996) find that funds with high expenses tend to exhibit negative performance persistence. Volkman and Wohar (1995) provide evidence that both the very large and very small funds consistently underperform, while Kahn and Rudd (1995) and Sharpe (1996) show that investment style plays a role. 2 Funds may charge a 12b-l fee of up to 25 basis points and still be classified as no-load. 2 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. rather than the adviser. Wellman (2001) provides evidence that load fund investors trade less frequently than investors who buy no-load funds either because investors that have a higher propensity to trade self-select ex ante or because load investors trade less frequently because of the sales charges that they face ex post. Both of these effects would lead load investors to trade less often, but neither would affect investors’ decisions about which funds to buy and sell. A third reason that load and no-load investors might behave differently is because load investors get advice from trained professionals. If advisers better understand financial markets or are more objective, advisers can help investors avoid behavioral biases. Even if advisers fall prey to some of the same biases that plague investors, advisers are likely to be more objective, which could help investors avoid some of the behavioral biases that reduce performance. If advisers lead to better decisions, then relative to no-load investors, load investors would be more likely to sell losers and hold winners. Although the prior literature has examined how performance affects which funds to purchase or redeem, there is little if any evidence on the size of each purchase or redemption. When making purchase decisions, representativeness will cause investors to make larger purchases from the funds with the best track records, because they believe the superior past performance will be representative of future results. With redemptions, loss aversion implies that investors will avoid selling a loser, because they don’t want to admit that their decision to purchase was a mistake. However, once they admit their mistake and make a redemption, I hypothesize that the investor is more likely to sell the entire position and “wash their hands” of the mistake. 3 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. One contribution of this research is that it sheds light on both the pervasiveness of behavioral biases among investor groups as well as the size of the biases. To do this I first provide evidence on whether investors working with a financial adviser react to past performance in a similar manner to no-load investors when deciding whether to purchase or sell mutual funds. While the existing literature has shown evidence of biases among certain classes of investors, it is not clear that these biases affect all investors in the same manner. If biases only impact the behavior of certain groups of investors then the implications for market prices are likely to be small. However, if biases affect different groups of investors in the same way, then these biases are more likely to impact prices. The second way I provide evidence regarding behavioral biases is to examine how past performance affects the size of the transactions given that a transaction is being made. The existing literature has explored how past performance affects the likelihood of buying and selling mutual funds, but it has not examined how past performance affects the size of the transactions that are made. If transaction size is positively related to performance then investors will be more likely to redeem and will make larger redemptions so that the combined effect will be large. However, if the transaction size effect mitigates the trading effect over time then the combined effect of individual behavior is less likely to have a measurable effect on market prices. Another contribution relates to the issue of mental accounting. Shefrin and Statman (1985) suggest that the way the idea of selling shares is framed by investors affects their willingness to sell poor performers. They specifically suggest that investors might frame a redemption that is part of an overall exchange differently than a redemption where the proceeds were not directly reinvested. 4 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Throughout the paper I define winners and losers using a number of relative performance measures. In particular, funds are ranked relative to other mutual funds within the universe of funds available to clients of the brokerage firm that provided the data and also ranked relative to other funds within the same Momingstar category that are available to investors in the sample. Funds are deemed winners (losers) if their performance ranks in the top (bottom) decile over the past one, three, or five years (each time period is considered independently). The results indicate that the load investors in my sample act in a manner similar to the no-load investors in Barber, Odean, and Zheng (2000) with respect to the probability of buying funds. That is, they are more likely to buy past winners. The evidence on the selling behavior are mixed. These investors are more likely to sell funds in the very best performance decile, but I do not find that investors are less likely to redeem funds in the worst performance decile than funds in performance deciles two through nine. Therefore, while there is evidence consistent with investors purchasing based on representativeness, this sample does not provide evidence that investors are more likely to hold losers as predicted by loss aversion. The results for tests of how much investors buy and sell indicate that transaction size is related to past performance. Individuals within this sample make larger purchases of past winners. Therefore, not only are investors more likely to buy past winners, but conditional on a purchase they invest larger amounts in past winners compared to other funds. The evidence on redemptions shows that conditional on a sale, investors sell relatively more of their losers when compared to funds with better performance. This 5 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. evidence is consistent with the idea that once investors admit to themselves that the purchase of a fund was a mistake, they are more likely to sell their entire position. Finally, the results provide support for Shefrin and Statman’s (1985) hypothesis that mental framing matters when investors make redemption decisions. The results show that these investors are more willing to redeem a poor performer when the redemption is part of an exchange than when the redemption is not part of an exchange. The paper proceeds as follows. In Section 1.2,1 provide an overview of the mutual fund industry. The reasons for differences between load and no-load investors and the hypotheses for the size of transactions are explained in Section 1.3. The data are described in Section 1.4 and results are discussed in Section 1.5. Section 1.6 discusses the implications of these results and I conclude with a short summary in Section 1.7. 1.2 Mutual Fund Industry Load funds have a sales charge and offer the investor professional advice, while no-load funds do not charge a fee and offer no assistance to the investor. Loads are used to compensate the adviser who sells the fund and can be in the form of up-front commissions, contingent deferred sales charges, or 12b-l fees. Rule 12b-1, which is an amendment to the Investment Company Act of 1940, allows mutual funds to charge an ongoing sales or distribution fee. The 12b-l fee is used to pay for marketing expenses either in the form of advertising or the compensation of intermediaries. Funds may charge a 12b-l fee of up to 25 basis points and still be classified as no-load. Fund share classes are defined by the structure of the sales charge. A typical multiple share class family that offers front-end load (A shares), back-end load (B 6 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. shares), and level-load (C shares) share classes is shown in Table 1.1. Traditional A shares have a substantial front-end load, no exit fee, and often a small 12b-l fee. B shares do not require an up-front sales charge, but have a declining contingent deferred sales charge that lasts from four to seven years, and a higher 12b-l fee. Finally, C shares, or level load classes, charge no up front sales charge, have a smaller contingent deferred sales charge that usually lasts for only one year, but also charge a 12b-l fee similar to those on B-shares. Adviser compensation also differs by fund class. A shares pay an up-front commission that includes most of the sales charge and some funds pay a small annual trailing commission. There is also an up-front commission and sometimes a trailing commission paid on B shares.3 C shares pay the adviser a smaller up-front commission, but a much larger annual trailing commission. The trailing commission is paid to the adviser of record for as long as the investor holds the fund. Fund families are a group of mutual funds all managed by the same sponsor. Sponsors usually try to make the family large enough to include a fund in all investment styles so the family will have a growth fund, value fund, fixed income fund, etc. Load fund families provide investors with additional benefits if they purchase within the same family. Investors can add all funds within the family to reach “break points” on A shares and earn a reduced sales charge. Furthermore, if investors exchange within the fund family, then no additional sales charge is paid on A shares and the contingent deferred sales charge is not incurred on funds with a redemption fee. 3 Most fund families now structure B shares so that they convert to A shares after a number of years (often seven or eight years). In these cases, the broker earns the lower A share trailer after conversion. 7 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. While no-load companies market their products directly to the public, load funds pay advisers to sell their funds. There are minor differences in load and commission structures, across fund families, but successful innovations in pricing are mimicked rapidly so there is little competition among fund families in this area. To convince advisers to sell their products to investors, mutual fund representatives, known as wholesalers, market their mutual funds directly to advisers. Wholesalers attempt to develop personal relationships with advisers both through periodic office visits and telephone calls. They try to help advisers increase business with sales ideas, sponsorship of client seminars, and names and phone numbers of potential investors. When advisers make a purchase in the fund family, wholesalers send thank you gifts such as golf balls, steaks, and apparel. Finally, the top producing advisers over the year are given larger gifts or all expenses paid due-diligence trips. Many brokerage firms, like the one that provided the data for this study, have approved lists of fund families. Brokerage firms claim that approved lists help advisers by giving them a smaller universe of pre-approved fund families from which they make recommendations to investors. Some firms wish to maintain a conservative image and therefore risky or unproven funds are not included on the approved list. Conflicts of interest can arise, as fund families often have to pay for the privilege of being on the list. Fund families included on the approved list get additional benefits beyond the brokerage firm’s seal of approval. They typically enjoy the benefits of having their fund data on the brokerage firm’s computer system, having wholesaler access to adviser offices (competitors may not have equal access), and having their funds fully supported on all internal systems so that trading and maintenance are easy. 8 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1.3 Hypotheses Kahneman and Tversky’s (1979) prospect theory posits that when making choices with uncertain outcomes people act as if they are maximizing a value function that is concave for gains but convex for losses. A gain or loss is defined relative to a reference point. Although the theory leaves reference points unspecified, Kahneman and Tversky (1979) hypothesize that individuals are likely to use performance of similar entities as reference points. Indeed, evidence suggests that mutual fund investors use the performance of other funds as reference points. Capon, Fitzsimons, and Prince (1996), for example, find that investors’ most important information source when making decisions is published performance rankings. If investors base decisions on fund rankings, then they would label a fund a loser if it has performed poorly against its peers even if the investor has an unrealized gain. Another possible reference point, used by Barber, Odean, and Zheng (2000), is the investor’s purchase price. My sample includes cost basis information only when funds are sold, which means that I cannot calculate unrealized gains and losses. I therefore use a variety of relative performance measures to define winners and losers. In particular, fund performance is measured against all other funds on the approved list or against funds on the approved list and within the same Momingstar category. I also examine performance using one, three, and five-year time horizons in order to check the robustness of the findings. 1.3.1 Load vs. No-Load Investors There are three reasons why load investors would exhibit different behavior from no-load investors: (1) the type of investors who select load funds might differ from those 9 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. who select no-load funds, (2) the sales charge on load funds can lead to different behavior, and (3) the input from advisers can influence investor behavior. It is also possible that the combined effect of these three reasons is not large enough to cause a noticeable difference in the behavior of load and no-load investors.4 1.3.1.1 Selection Issues Less-informed investors are likely to place a higher value on advice and therefore select load funds. However, this type of selection would only result in differences in trading behavior between load and no-load investors if the additional information provided by advisers was different from the information possessed by no-load investors. Self-selection can also occur if investors differ in their propensity to trade. Investors with a higher propensity to trade would be more likely to buy no-load funds than load funds. Consequently, load investors will hold funds longer than no-load investors.5 However, self-selection by propensity to trade does not imply any differences between load and no-load investors in the funds that they buy or sell. 1.3.1.2 Sales Charge Chordia (1996) shows that load mutual funds use front and back-end sales charges to discourage redemptions. Thaler (1980) and Arkes and Blumer (1985) find that sunk costs often influence individual decisions. If investors view the up-front sales charge paid, a sunk cost, as relevant, then they will be less likely to redeem A shares than noload funds. Because B shares have a contingent deferred sales charge, investors will also 4 The first two arguments may not hold if investors trade within a single fund family using free exchanges. 5 Self-selection by investors’ propensity to trade can also occur across load fund classes (A, B, and C). Investors who view themselves as frequent traders ex ante will avoid both A and B shares in order to avoid the sales charge they would incur by frequent trading. If load investors self-select between share classes by trading frequency, then A and B shares will have longer holding periods than C shares. 10 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. be more reluctant to sell B shares than no-load funds. C shares also have a contingent deferred sales charge, but only for one year. So, investors in C shares would be more reluctant to sell C shares than no-load funds, but only for the first year after purchases. Thus, sales charges imply that, all else equal, load investors will trade less often and have longer holding periods than no-load investors. Sales charges however, do not lead to any predictions about whether load investors are more likely to purchase or redeem winners or losers. These are the same predictions generated by the self-selection argument. 1.3.1.3 Adviser Influence Finally, if advisers steer investors away from behavioral biases, then load investors will differ from no-load investors in both redemption choices and holding periods. Load investors would be more likely to hold their best performing funds over long periods of time and more likely to sell their persistent poor performing funds. 1.3.2 Exchange Redemptions and Mental Accounting Shefrin and Statman (1985) provide a behavioral explanation, which relies on Thaler’s (1985) concept of mental accounting, of why investors are more willing to sell poor performers when the transaction is part of an exchange than when it is just a redemption. When investors purchase an investment they open a mental account. While simply selling a poor performing investment closes that mental account at a loss, exchanging from one fund to another changes the investment within the mental account without having to close the mental account at a loss. Shefrin and Statman (1985) cite Gross’ (1982) guide to selling intangibles as support for the concept. Gross (1982) says that many clients do anything to avoid selling at a loss, but that by using what he calls the “magic selling words” of “transfer your assets,” financial advisers can overcome many 11 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. client objections. Therefore, I examine the results from exchange redemptions separately from other redemptions to see whether investors are more willing to redeem poor performers when part of an exchange. 1.3.3 How Past Performance Affects Transaction Size Once investors have decided to make a transaction they must then make a decision about the size of the transaction. 1.3.3.1 Purchases The representativeness heuristic should affect the size of purchases in the same way it affects the decision regarding whether or not to purchase. If investors view past performance as representative of future results, then they will make relatively larger purchases as performance increases. 1.3.3.2 Redemptions While loss aversion would cause investors to hold poor performers, once the decision is made that buying a fund that ended up being a loser was a mistake, an investor is more likely to liquidate the entire position in order to eliminate all connection with the poor performer. In addition, since investors find selling losers to be painful, they will want to redeem the entire position so that they will only experience the pain once.6 1.4 Data The data are provided by a national full-service brokerage firm and include all mutual fund transactions during 2001 and 2002, a list of all funds in each account at year- 6 Grinblatt and Keloharju (2001) footnote the opposite effect from an unreported study. This study finds that equity investors sell smaller proportions of their position if the result of the sale is a capital loss. 12 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. end 2000,2001, and 2002 for all accounts with at least one mutual fund holding, demographic information for each investor, and the type of account. 1.4.1 Account Information Panel A of Table 1.2 gives descriptive statistics for all accounts as of December 31, 2000. Of the total accounts, 39.6% are single or joint accounts, 13.3% are custodial accounts, 38.9% are retirement accounts, and 8.2% are other non-individual accounts. In terms of value of holdings, 36.6% are single or joint accounts, 2.2% are custodial accounts, 42.1% are retirement accounts, and 19.1% are other non-individual accounts. On average, an account has 2.5 holdings, with the smaller custodial accounts averaging 1.6 holdings, single and joint accounts with 2.4 holdings, and retirement accounts averaging 3.0 holdings per account. New accounts are added to the data set throughout the sample period and the transactions from the new accounts are included in the analysis. As of year-end 2001, the number of accounts increased by 21.2% and the number of dollars invested in mutual funds increased by 6.4%, but the distribution of accounts across account types is similar to that at year-end 2000. Full descriptive statistics for accounts as of December 31, 2001 are given in Panel B of Table 1.2. 1.4.2 Demographic Information Table 1.3 gives basic investor demographic information. Panel A lists mean, median, and standard deviation for investor net worth, income, and age broken out by both account type and year. There is very little change in these numbers over time and little variation across account types (single, joint, retirement, and other accounts). The average (median), investor is 53 (53) years old, with a net worth equal to $350,969 13 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ($225,000), and an annual income of $49,526 ($40,000).7 As would be expected, custodial accounts, where the owner of the account is a minor, have lower average values of net worth, income, and age. Panel B of Table 1.3 gives investment experience and a breakout of age groups as a percentage of all investors with that account type. For the accounts held at the end of 2 0 0 0 ,9.6% of investors rated their investment experience as none when the account was opened, 36.7% as very limited, 40.8% as limited, 10.6% as moderate, and 2.3% as extensive. These numbers provide some evidence that these investors are seeking professional advice to make up for their perceived lack of experience as over 85% of them consider themselves to have limited, very limited, or no investment experience. 14.2% of the investors who held accounts at the end of 2000 were below the age of 20 when the accounts were opened, 17.2% between 20 and 39, 35.9% between 40 and 59, 27.2% between 60 and 79, and 5.5% over the age of 80. Table 1.4 gives information comparing investors in this sample to mutual fund investors in general. Panel A of the table shows that in 2000, 83.2% of the holdings in my sample are in equity funds, 6.7% are in fixed income funds and 10.1% are invested in balanced funds. The percentages for 2001 shown in Panel B are similar. The distribution of assets for investors in my sample is similar to how investors in general allocate assets. Considering the funds included in Momingstar as of December 31, 2000, load fund investors have 85.4% of their assets in equity funds, 9.4% in fixed income funds, and 7 Alexander, Jones, and Nigro (1998) report investor characteristics based on a survey of mutual fund investors. They find investors to be slightly younger but to have higher net incomes than the investors in my sample. Alexander, Jones, and Nigro’s (1998) load investors have a median age of 47 and median income of $67,600, while no-load investors have a median age of 44 and median income of $67,000. 14 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5.2% in balanced funds, while no-load fund investors have 84.1% in equity funds, 12.6% in fixed income, and 3.2% in balanced funds. 1.4.3 Transactions Table 1.5 gives descriptive information on the transactions within single and joint accounts, custodial accounts, retirement accounts, and other accounts between January 1, 2001 and December 31, 2002. I attempt to study only transactions where the investor made an explicit decision regarding that particular trade. Therefore I attempt to eliminate automated transactions and dividend and capital gains reinvestments by deleting all transactions with value less than $1,000. 8 By the use of this screen I include only 21% of the total transactions during the sample period, but these trades represent 8 6 % of the total dollars purchased and redeemed between January 1, 2001 and December 31, 2002. To include fund returns and characteristics in the analysis I also require each fund to be included in the Momingstar Principia Pro database. This screen eliminates 36% of the funds, but only 10 % of the total assets held in mutual funds at the firm. Panel A provides information on redemptions. The mean (median) redemption in my sample is $4,613 ($2,200) compared to the $13,914 ($5,893) found in Barber, Odean, and Zheng (2000). The true difference between the underlying samples is even larger since Barber, Odean, and Zheng (2000) do not exclude small trades. The purchase data in Panel B are similar to that found with the no-load investors in the sample used by Barber, Odean, and Zheng (2000). The mean (median) purchase size is $9,262 ($4,713) in my sample and $8,118 ($2,660) in their study of no-load investors. Without my 8 Thaler and Shefrin (1981), Shefrin and Thaler (1988), and Thaler and Benartzi (2001) discuss the use of automated investment plans as self-control mechanisms. The common theme of such plans is that dollars are automatically invested before individuals fall prey to the temptation to spend them on current consumption. Examining self-control mechanisms through automated trades is a subject of future research. 15 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. exclusion of small trades the two purchase samples would likely be even more similar. The mean (median) trade size for exchange redemptions shown in Panel C is $12,482 ($6,180). For exchange purchases the mean (median) is $11,947 ($5,494) as shown in Panel D. 1.4.4 Performance Measures To conduct tests of how investor transaction decisions are related to past performance, I use several different performance measures. Del Guercio and Tkac (2 0 0 2 ) compare pension fund and mutual fund investors and find that mutual fund investors base their decisions on raw return numbers rather than risk-adjusted performance. Therefore, I measure performance with raw one, three, and five-year average annual total returns. Mutual funds are required by the NASD to cite one, three, and five-year average annual total returns on all marketing materials. Thus, these are the returns with which investors should be most familiar. While Jain and Wu’s (2000) results support the use of one-year return, I also use three and five-year returns because load investors have longer holding periods than no-load investors (Wellman (2001)). In order to be included in the multivariate tests I implicitly require funds to have a threeyear history in Momingstar, because I use three-year standard deviation of total returns as a measure of risk. 9 Because mutual fund investors are likely to use the performance of similar mutual funds as a reference point as discussed in Section n, I use two different measures of 9 Requiring funds to have a three-year standard deviation eliminates 2406 observations from the redemption and exchange redemption logit estimations, 2408 observations from the purchase logit estimation, and 2410 from the exchange purchase logit estimation. In the regression analysis 1269, 1403, 1490, and 1220 observations are eliminated for redemptions, exchange redemptions, purchases and exchange purchases respectively. 16 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. relative performance among the funds that are included on the approved list of the firm that provided the data. Since investors at the firm that provided the data effectively choose mutual funds only from the approved list, I use this list as the universe of funds for constructing relative performance measures. First, I assign funds to a percentile based on their performance among all funds on the approved list. Second, I rank funds against other funds on the list within each of Momingstar’s fund categories. There are 48 different categories, 28 for equity and balanced funds, and 2 0 for fixed income funds. For example, Momingstar divides domestic equity funds into nine categories based on the size of the equities they purchase (small, mid-cap, or large) and whether they focus on growth, value, or a blend. A potential problem arises when there are a small number of funds in a Momingstar category. When percentiles are assigned, the fund with highest return gets a value of 100 and the fund with the lowest return gets a value of 0. If there are no ties, then all other funds in the category get values that are evenly spaced between the two extremes. For example, in a category with five funds they would be assigned percentiles of 0,25, 50,75, and 100. Therefore, for categories with a small number of funds percentiles may not accurately represent performance and the winner and loser deciles are over-represented as these deciles are assigned funds from every category. To deal with this problem, I duplicate the tests using the category performance measure excluding categories with fewer than ten funds. These results are discussed in Section IV.2. 17 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1.5 Results I analyze all of the mutual fund transactions between January 1,2001 and December 31, 2002 at national full-service brokerage firm. 10 Redemptions and purchases are subdivided into two groups. I distinguish redemptions and purchases from exchange redemptions and exchange purchases. The latter transactions are those redemptions and purchases where the same account had a trade on the other side of the market on the same day and no sales charge was paid. 1.5.1 Transactions by Performance Decile I begin by examining transactions in a descriptive way. These results do not consider the assets invested in a given decile but simply illustrate whether conditional on a redemption (purchase) being made, investors are more likely to redeem (purchase) funds that fall into a particular performance decile. Thus, I use data on all redemptions (purchases) in a given month. To measure the likelihood of redeeming (purchasing) a fund within a performance decile, I use both the percentage of all redemptions (purchases) that fall in the performance decile and the ratio of the value of all redemptions (purchases) within a decile to the value of all redemptions (purchases). In algebraic terms, let r NR1 t = number of redemptions by investor i during month t of fund f. f DR: = dollar value of shares redeemed by investor i during month t of fund f. 1, I Dk= set of funds in decile k. 10 The only trades not included are trades of less than $1,000 and trades that could have been exchanges but instead the same account made both a purchase and a redemption on the same day and paid a sales charge. These potential exchanges might be the result of a conflict of interest between the client and the adviser but they amount to only 0.4% of the total transactions. 18 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. NP.f 1,1 and DP.f are defined in a similar way for purchases. 1, t Then, I compare the following numbers across deciles: Percentage of redemptions in decile k = Proportion of the value of shares redeemed in decile k = f i Again, similar ratios are calculated for purchases. Table 1 .6 gives the results for redemptions using the past one, three, and five-year total returns to create performance deciles. In Panel A, the largest numbers of redemptions are in deciles three through six using performance relative to all funds. However, with the other five performance measures, the number of redemptions increases with the level of performance, indicating that, like no-load investors, most of the funds sold by these load investors are top performers. Table 1.7 indicates that the results for exchange redemptions depend on the performance measure employed. Using one and three-year returns relative to all funds, investors are exchanging out of poor performers. However, using one and three-year returns relative to funds in the same Momingstar category, investors are exchanging out of good performers. With five-year total returns, regardless of the benchmark, investors are selling the best performers. The evidence for purchases (Table 1.8) is similar to the evidence for purchases that are part of an exchange (Table 1.9). With the exception of one-year performance relative to all funds, the other five performance measures indicate that funds that have the 19 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. best performance get the bulk of the new assets. Overall, this evidence is similar to that found in Barber, Odean, and Zheng (2000). 1.5.2 Transactions Relative to Assets A potential problem with the previous analysis is that it does not take into account that some funds are more widely held than others. For example, when looking at redemptions using five-year returns relative to all funds, the best performing decile (decile 10) has 42.7% of the dollars redeemed and the worst performing decile (decile 1) has 1.0%. But these numbers are similar to the total dollars invested in these deciles by investors. The best performing decile contains 42.3% of the dollars invested while the worst performing decile has only 1.2% of the total dollars invested. Therefore, instead of calculating percentages based on the number of redemptions (purchases) and the value of shares redeemed (purchased), I calculate the proportion of the value of shares redeemed (purchased) in each decile relative to the proportion of the total value of shares held in a given decile at the beginning of the month. Let f DR: = dollar value of shares redeemed by investor i during month t of fund f. 1,5t DFlf = total dollar value of shares held by investor i of fund f at the beginning i■ ,9t of month t. PR fk _ feDk i ^ = proportion of the value of shares redeemed in decile k — £ £ DRfi,t for month t. 20 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. PH^ = * XX DH,f t feD it i_________ 2 _ _ — = proportion of the value of shares held in decile k Y Y f i DHf 1 ,1 for month t. The total dollars held in a fund is calculated using the net asset value (NAV) of the most recent trade in that fund. Therefore, the most actively traded funds have the least amount of error. These funds also tend to have the largest holdings at the firm. Then I calculate the monthly average proportion of the value of shares redeemed in each decile relative to the proportion of the total value of shares held in a given decile: PR^ (1/T) £ 1 » PH^ Similar proportions and averages are calculated for purchases. If transactions occur not because of past performance but rather in proportion to the size of the funds in a given decile, then this ratio will be equal to one. If, on the other hand, investors purchase and redeem winners at a higher rate, then the ratio should be greater than one for the highest deciles. Similarly, if investors tend to hold the worst performers, then the ratio should be less than one for the lowest performing deciles. Figures 1.1 and 1.2 show the results for redemptions and exchange redemptions by deciles. Given the two different performance measures, and that each is calculated using one, three, and five-year returns, there are six different measures for redemptions and six different measures for exchange redemptions. There is very little evidence that investors are redeeming their best performers as only one out of the six measures (oneyear performance compared against all funds as shown in Figure 1.1) has a proportion 21 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. greater than 1 .2 in the highest decile for either redemptions or exchange redemptions. These results are quite different from Barber, Odean, and Zheng (2000). They use the same measure and find redemptions for the top performers reach a proportion of 2.9. In this sample, regardless of the performance benchmark, none of the graphs show a clear upward sloping line and most are flat to slightly downward sloping. While neither redemptions nor exchange redemptions exhibit a strong pattern, there is a difference between the two. When comparing redemptions to exchange redemptions, regardless of the performance measure, a greater proportion of poor performers are redeemed when the trade is part of an exchange. This result is consistent with Shefrin and Statman’s (1985) claim that investors are more willing to sell poor performers if the transaction is framed as transfer of assets rather than a liquidation as discussed earlier. Purchases are shown in Figures 1.3 and 1.4. Here, regardless of the performance measure, the proportion of the value of shares purchased in the top decile relative to the proportion of the total value of shares held in that decile is greater than one and also greater than the same proportion for the worst performers. The worst performers have a proportion of less than one in all six of the measures for purchases shown in Figures 1.3 and 1.4. The worst performers proportions are less than one for exchange purchases in all three performance measures comparing funds against all funds in Figure 1.3. Although the decile one performers have proportions greater than one for exchange purchases using both the one and five-year Momingstar category performance measures in Figure 1.4, neither of these graphs provide strong evidence that investors are buying losers. Overall, the graphs in Figures 1.3 and 1.4 are generally upward sloping, which 22 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. provides evidence that investors disproportionably purchase past winners. However, the evidence is not as strong as that found in Barber, Odean, and Zheng (2000). In only one of the twelve measures (including both purchases and exchange purchases) do I find a proportion for the top performing decile greater than 2. In contrast Barber, Odean, and Zheng (2000) report a number 4.7 for their top performing decile. 1.5.3 Logit Analysis - How does performance affect the probability of trading? To test how performance affects the probability that a fund experiences a redemption or a purchase, I estimate logit regression models. Using fund level data, the dependent variable, Redfjt (Purchfjt), is equal to one if a redemption (purchase) is made within fund f during month t and zero otherwise. Investors make a redemption (i.e. Redf>t is equal to one) in 44% of the fund-month observations for both the redemption and exchange redemption samples. Investors purchase a fund (i.e. Purchf>tis equal to one) in 45% (40%) of the fund-month observations for the purchase (exchange purchase) sample. The model has six variations because of the different performance measures used to define winners and losers, but it has the following general form: Redf,t (Purchf,t) = «o + Pi Winner f,t + P2 Loser f;t + P3 FundAge fjt + (34Expense f,t + P5 3Yr. Std. Dev. + PglnTotalValuer + P7 InTNAf>t + 23 Month Dummies + £f,t , f = 1 , . . . , n (1) Winner f>tis a binary variable equal to one if fund f is in the top performing decile ranked either against all funds or other funds in the Momingstar category and zero otherwise; Loser fit is a binary variable equal to one if fund f is in the bottom performing decile ranked either against all funds or other funds in the Momingstar category and zero otherwise; FundAge f,t is the age of fund f; Expense fit is the expense ratio for fund f at 23 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. time t; StdDev f;t is the standard deviation of monthly returns for fund f over the three years prior to time t; InTotalValue fit is the natural log of the total assets invested in the fund at the firm studied; and InTNA f,t is the natural log of the total net assets for fund f at time t. FundAge fit and InTNA f,t are included as control variables following Sirri and Tufano (1998) and Fant and O’Neal (2000). They find that older funds and larger funds tend to be better known by investors and, therefore tend to get larger net fund flows therefore I expect that the sign on the coefficients of these variables will be negative for redemptions and positive for purchases. Expense fit is included because Sirri and Tufano (1998) find that more expensive funds get larger flows. They argue this is because fees are likely to be correlated with advertising and broker compensation. The expected sign on the coefficient of Expense fjt is negative for redemptions and positive for purchases. StdDev f>tis included again following Sirri and Tufano (1998) as a measure of risk. If investors are risk averse then the sign should be positive on the coefficient of StdDev f_t for redemptions and negative for purchases. Finally, I include InTotalValue fit because some funds are more widely held than others among these investors, and therefore are more likely to experience transactions. The expected sign on the coefficient for InTotalValue fjt is positive in all specifications. Because InTotalValue and InTNA are correlated, these specifications were also estimated without InTNA. The results are qualitatively similar to those discussed here. The positive coefficient estimates on WINNER for redemptions in Table 1.10 and exchange redemptions in Table 1.11 are generally consistent with the findings in Barber, Odean, and Zheng (2000). Being a past winner (top decile) increases the likelihood that 24 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. it will be sold in five of the six performance definitions for redemptions shown in Table 1.10. The same is true in only two of the six specifications for exchange redemptions in Table 1.11. But, looking at the results from both Tables 1.10 and 1.11 there are no cases with a statistically significant negative coefficient on WINNER and thus no evidence to support the idea that these investors are more likely to hold funds that are in the top ten percent of funds based on past performance. The coefficients on all of the control variables except EXPENSE RATIO generally have the expected sign. Sirri and Tufano (1998) find that funds with higher expense ratios have greater net fund flows. However, since they only have aggregate fund flow data they can’t distinguish between purchases and redemptions. Sirri and Tufano (1998) argue that expense ratios are correlated with advertising and adviser compensation. If this connection has a larger impact on purchases than on redemptions then the sign on the coefficients in the redemption specifications is plausible. The results for the coefficient on LOSER in the redemption equations (Table 1.10) do not show that investors treat the worst performers any differently from funds in performance deciles two through nine, which is different from the findings in Barber, Odean, and Zheng (2000). In four of the six specifications the coefficient on LOSER is not statistically significantly different from zero at the 5% significance level. In the other two specifications, one coefficient is positive and statistically significant and one is negative and statistically significant. The results in Table 1.11 for exchange redemptions also differ from Barber, Odean, and Zheng (2000) and differ from those for redemptions. Three of the six specifications have coefficients on LOSER that are positive and statistically significant 25 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. while the coefficient on LOSER is negative and significant in only one case. This suggests that investors are more likely to redeem a poor performer than a fund from deciles two through nine when the trade is part of an exchange. This evidence supports Shefrin and Statman’s (1985) hypothesis that how redemptions are framed affects investor behavior. To determine what these results mean in terms of the probability of redeeming, I calculate the predicted value of the specification when the fund was a winner, loser, or neither a winner nor a loser using the coefficient estimates and the mean values from the sample for FundAge, Expense, 3Yr. Std. Dev., InTotalValue, and InTNA. For the five specifications for redemptions in Table 1.10 where the coefficient on WINNER is significant, the predicted probability of a redemption goes up by an average of 9.2% (a range of 4.3% to 13.1%), when the fund is a top performer. Turning to the poor performers with exchange redemptions in Table 1.11 and the three performance measures where the coefficient on LOSER is positive and significant, the predicted probability of redeeming goes up by between 3.7% and 13.0% when the fund is a poor performer. The evidence from purchases in Table 1.12 and exchange purchases in Table 1.13 are consistent with the findings of Barber, Odean, and Zheng (2000). In these two tables, eleven of the twelve specifications have positive coefficients on WINNER that are statistically significant at the 1% level. Indicating that investors are more likely to purchase funds that are in the top performance decile. For losers, I find that eight of the twelve specifications provide evidence at the 1% statistical significance level that these investors are less likely to purchase funds that are in the bottom decile. 26 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. On average in the eleven specifications where the coefficient on WINNER is positive and significant, investors are 13.2% more likely to purchase a fund that is in the top performance decile than a fund that is in deciles two through nine. For the eight specifications where the coefficient on LOSER is statistically significant, investors are 7.9% less likely to purchase a fund that is in the lowest performance decile compared to deciles two through nine. In the purchase and exchange purchase specifications the coefficients on all of the controls except FUND AGE and LOG TNA have the expected signs. Sirri and Tufano (1998) and Fant and O’Neal (2000) find that better known funds tend to get larger net inflows, but this is not the case for purchases by these investors during this time period. The month dummy variables show a strong pattern of negative and statistically significant coefficient estimates for 2001. This is because the holdout month is December of 2002 and there are more purchases and redemptions in 2002 than in 2001. 1.5.4 Regression Analysis - How does performance affect the size of trades? I now examine whether performance affects the size of trades given a purchase or redemption using regression “hurdle” analysis similar to Cragg (1971). I also use a Heckman (1979) two-step estimation procedure where the probability to trade was estimated using a probit regression. Inverse Mills ratios calculated from a probit estimation are then included as an explanatory variable in the second stage. The results from the Heckman procedure are similar to those reported in Tables 1.14-1.17. The dependent variable used in the analysis is the logit transformation of the proportion of fund holdings redeemed or purchased measured in dollar value of shares. The proportion of the value of shares redeemed in fund f during month t is defined as: 27 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (2) where: f DR. = dollar value of shares redeemed by investor i during month t of fund f. 1, I f DH: = total dollar value of shares held by investor i of fund f at the beginning 1, t of month t. The proportion of the value of shares purchased ($Pf,t) is defined similarly. The mean value for $Rf>t is 0.008 for redemptions and 0.020 exchange redemptions and the standard deviations are 0.002 and 0.053 respectively. For $Pfjt the mean values are 0.054 for purchases and 0.031 for exchange purchases with standard deviations of 0.013 and 0.005 respectively. The dependent variables in the regression analysis are the logit transformation of $Rf,t and $Pfjt: In ($Rf,t/(l - $Rf,t)) and In ($Pf,t/(l - $Pf>t)) (3) Since this analysis investigates how performance affects the size of a transaction, I only include funds where $Rf(t or $Pfjt is greater than zero and in no observation in the data set does $Rfjt or $Pf,t take on a value of one. However, the use of this dependent variable will likely give rise to heteroskedasticity because observations with small denominators give less precise estimates of the proportion of total trades.11 Therefore, I expect that the variance of the error terms is positively correlated with the inverse of the II With OLS, White’s (1980) test rejects the null of homoskedasticity with a p-value of less than 0.0001 in every specification. 28 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. total number of dollars invested in fund f. To mitigate the problems caused by heteroskedasticity I estimate a weighted least squares model known as the m inim um logit chi-square method (Berkson (1953) and Maddala (1983)).12 With this model the variance of the error terms is estimated as: Var(ef,t) = l/[(n$Rf>t(l- $Rf>t)], (4) where n is the total dollars invested in fund f at the firm. The model I use is a panel estimation with fixed-time effects and has the following form: 13 In ($Rf>t/(l - $Rf,t)) = oco + Pi Winner f;t + (32 Loser fjt + p3 FundAge f,t + P4 Expense^ + (3s 3Yr. Std. Dev. + InTNAf,t + 23 Month Dummies + £fjt , f = 1 , . . . , n, (5) where the variables are defined the same as in equation ( l ) . 14 Regression results for redemptions are found in Table 1.14 and the results of exchange redemptions are in Table 1.15. The results support the idea that these investors sell smaller proportions of the top performing funds. The sign of the coefficient on WINNER is negative and statistically significant at the 1% level in ten of the twelve specifications. The sign of the coefficient on LOSER is positive and statistically significant in eight of the twelve specifications, which suggests that investors sell larger 121 also estimate the all of the coefficients for the WINNER and LOSER variable using WLS with White (1980) robust standard errors. The results are qualitatively similar to those presented in Tables 1.14-1.17. 13 A model using fixed fund effects was estimated. With fixed fund effects the coefficient on LOSER was no longer statistically significant in some specifications because the fixed fund effect also picked up the loser characteristic. Examination of the cross-sectional observations shows a strong positive correlation between being a loser and the absolute value of the t-statistics for the fixed fund coefficients. 14 In addition to LogTNA I also use a size variable based on the percentage of total assets in all funds at the firm held in a given mutual fund. The results are even stronger than those presented here. 29 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. percentages of their positions in poor performers. While this finding only provides evidence that investors sell a larger percentage of poor performers, given that they make a redemption, it is consistent with investors being more likely to liquidate the entire position if they decide to sell a poor performer. I directly examine the liquidation issue with account level data in Section 1.5.5.1. To calculate economic significance, I calculate the predicted value of the equation using the mean values for FUNDAGE, EXPENSE, 3YRSTDDEV, and InTNA and the month equal to month 12 using Duan’s (1983) heteroskedastic consistent retransformation method. For the specification using three-year returns compared to all funds, the coefficient estimate on LOSER predicts that investors sell, on average, 4.3% more of the loser per year than when they sell funds in performance deciles two through nine. Of the four positive and statistically significant coefficients on LOSER in the redemption equations, the predicted effect ranges from 4.3% to 8.3% annually. Table 1.16 and Table 1.17 show the regression results for purchases and exchange purchases, respectively. These results are consistent with investors using the representativeness heuristic when making purchase decisions. In eleven of the twelve specifications, the sign of the coefficient on the WINNER variable is positive and statistically significant at the 1% significance level. This means that investors are purchasing proportionally more of the funds that are the top past performers. The economic significance is greater for purchases of winners than it is for redemptions of losers. The coefficient estimate of 0.47 for WINNER using five-year performance compared to all funds is close to the average coefficient on WTNNER in the six purchase specifications. Using the Duan (1983) retransformation, at the average 30 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. values of all the other variables in the model the coefficient estimate of 0.47 implies that to investors make 13.0% larger purchases per year of funds in the top performance decile as compared to the purchases they make in funds that are in deciles two through nine. The signs on the coefficients of the LOSER variable are negative and statistically significant in eight of the twelve specifications in Tables 1.16 and 1.17. This is further evidence that investors use the representativeness heuristic when buying funds because given a purchase is made, investors buy proportionally less of the worst performers. 1.5.5 Robustness Checks 1.5.5.1 Account Level Data The regression results in section 1.5.4 are consistent with the idea that once investors decide to sell a poor performer, they try to eliminate the entire position. However, the regression analysis is conducted at the aggregate fund level. To examine whether individual investor behavior also supports this idea, I examine account level data from 2002. The data from 2001 do not include the remaining balance after the transaction so 2001 transactions cannot be used. Figures 1.5 and 1.6 show the percentage of accounts that liquidate their entire position in a fund by performance deciles for redemptions and exchange redemptions respectively, where redemptions that leave less than $100 in the position are treated as a liquidation.15 The results in Figures 1.5 and 1.6 give further support to the idea that once the decision to redeem a loser has been made, 151 consider redemptions that leave less than $100 in the account as a full liquidation. I use this measure rather than requiring the account to have a balance of zero because when positions are liquidated it is common to have a small residual amount, usually from a partially accrued dividend, remain in the position. Given that the average holding size is over $7,000 for 96.6% of the assets in the study I know of no reason other than residual dividends or clerical error for selling all but $100 in a particular fund. 31 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. that investors are more likely to liquidate their entire position in the loser than if they were selling a non-loser. When performance is measured relative to all funds, over 34% (30%) of all investors that sell a fund that is in the bottom one-year (three-year) performance decile liquidate the entire position. The liquidation percentage steadily decreases as performance increases and reaches less than 7% (12%) for investors redeeming shares from a fund in the top performance decile measured over the last one (three) years. The redemptions that are part of an exchange transaction tell a similar story. However, investors making exchange redemptions are more likely to liquidate their position when compared to the redemptions discussed above, regardless of past performance. When performance is measured using one-year (three-year) returns, investors redeeming shares from the poorest performing decile liquidate over 87% (86%) of the time, while they liquidate their shares less than 44% (54%) of the time when performance in the highest decile. 1.5.5.2 Fund Performance Measures To determine whether the results depend on the definition of winners and losers, all of the regression tests shown in Tables 1.14-1.17 were also run with winners and losers defined as the top third and bottom third based on past performance. The results are qualitatively the same as those shown. The performance measure that uses Momingstar categories tends to over­ represent the winner and loser deciles because some categories have very few funds. Therefore, I also re-estimate all of the specifications that use the category performance measure after eliminating observations of funds that are in Momingstar categories where 32 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. there are less than ten funds in the sample. While this screen eliminates approximately one third of the observations across the logit and WLS estimations, the results are qualitatively similar to those already reported. The performance measure that compares fund performance to all other funds implicitly assumes that investors compare equity funds to bond funds, while the measure that uses Momingstar categories assumes that investors judge funds only against funds that are very similar. To examine an alternative between these two extremes I also calculate results similar to the univariate results in Tables 1.6-1.9 with a sample consisting only of equity funds. The results are similar to those shown here. 1.5.5.3 Retirement Accounts Because of differences in taxation and possible differences in investment time horizon I also ran tests separately for retirement and non-retirement accounts. There were no qualitative differences with regard to the relationships between past fund performance and investor transaction behavior. 1.5.5.4 Sample Selection Issues There are differences in the size and sign of the coefficients for the FUND AGE and EXPENSE RATIO variables in both the logit and WLS results between the one and three-year results and the five-year results. One explanation is that the samples differ because the younger funds that are not in the five-year sample have more C shares, which have higher expense ratios. To determine whether or not this sample selection changes the overall results, I also estimate these equations where the sample is restricted to funds 33 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. included in the five-year specifications.16,17 While this change leads to consistency across specifications for FUND AGE and other control variables, it has no qualitative effect on the coefficient estimates for LOSER. The coefficient estimates for WINNER also become more consistent across specifications. This is particularly true for the logit estimations for redemptions and exchange redemptions in Tables 1.10 and 1.11. With the restricted sample the coefficient on WINNER is positive and statistically significant in all twelve of the performance specifications in Tables 1.10 and 1.11. 1.5.5.5 Diagnostics I mn a variety of diagnostic tests on both the logit and the WLS estimations. To check for the extent to which multicollinearity is a problem, I calculate condition indices for each of the all fund performance specification design matrices.18 If two condition indices are greater than 30 in a given specification then collinearity may make estimation less precise. Across all logit and WLS design matrices tested, none have a condition index greater than 25 and none have a second condition index of greater than 12. I used three tests for influential observations for the all fund specifications of the logit models. These tests are the DFBetas, the change in Pearson chi-square, and the change in deviance as discussed in Hamilton (1992). Observations with DFBetas greater than two, changes in Pearson chi-square greater than four, or changes in deviance of more 16Several other methods were used to control for the differences in the samples. The funds in the one and three-year specifications are younger, have a greater proportion of C shares, and have higher expense ratios. However, control variables for these differences did not change the pattern of the coefficients on FUND AGE and EXPENSE RATIO. 17 Limiting the sample to funds in the five-year sample eliminates 3379-3385 observations for the various logit models and 1692,1664, 1895, and 1449 observations from the redemption, exchange redemption, purchase, and exchange purchase regression models respectively. 18 A few category specifications were chosen to see if the differences in the WINNER and LOSER variables change the results. The results are almost identical to those discussed above. 34 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. than four are potential influential observations. I re-estimate the logit specifications without observations that fail any of these tests and the results are similar to those reported in Tables 1.10-1.13. Similar tests for influential observations in the regression analysis define potentially problematic observations as those with an RStudent statistic of greater than 2 and a DFFit statistic of greater than 2(p/n)1/2,where p is the number of parameters in the model and n is the number of observations (Belsley, Kuh, and Welsch (1980)). As with the logit analysis regression, the results without these observations are similar to those discussed earlier. 1.6 Discussion This paper investigates how past performance affects individual investor behavior regarding the mutual funds that they purchase and redeem. Two separate effects are examined. Evidence on the first effect, how past performance affects whether investors make a transaction, is generally consistent with the prior literature. The load investors in this sample are more likely to purchase and redeem past winners, which is consistent with what Barber, Odean, and Zheng (2000) find using no-load account level data and consistent with what Ippolito (1992), Sirri and Tufano (1998), and Fant and O’Neal (2000) find using aggregate fund flow data. This behavior is consistent with investors making purchase decisions using the representativeness heuristic. However, in contrast to Barber, Odean, and Zheng (2000), I find no evidence that investors are less likely to sell past losers when compared to funds that are neither winners nor losers. In fact, with the sample of exchange redemptions I find some evidence that investors are more likely 35 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. to sell past losers. The difference in likelihood of selling a loser between the redemption and exchange redemption samples is consistent with Shefrin and Statman’s (1985) hypothesis that investors are more willing to sell past poor performers when the transaction is framed as an exchange or transfer rather than a sale. Since losers are the funds that are most likely to have an unrealized loss, then selling losers as part of an exchange could also be explained simply as a tax swap. Investors could sell a loser and buy a fund with a similar investment objective to establish a tax loss without significantly changing the growth prospects of their investment. However, while this might explain why investors are willing to redeem poor performers as part of an exchange, it does not explain why they are more willing to redeem poor performers as part of an exchange than when making other redemptions. The second effect is how past performance affects the size of transactions. I provide evidence that these investors purchase relatively more of past winners than they do of past losers, but that they redeem relatively more of past losers than they do of past winners. The purchase behavior is again consistent with representativeness. The redemption behavior is consistent with the idea that once investors decide to sell a poor performer, they are more likely to liquidate the entire position in order to forget the mistake they made in purchasing the fund initially. With purchases, investors are both more likely to purchase past winners and purchase relatively more of past winners than other funds. Therefore, it is not surprising that studies using aggregate fund flow data like Fant and O’Neal (2000) find large inflows into past winners. 36 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The behavior of these investors with regard to redeeming poor performers is also consistent with a fully rational investors where information is costly. When information costs prevent investors from knowing that a fund is a loser, they are not more or less likely to sell this fund when compared to other holdings. However, when investors periodically bear the cost of checking their portfolio, they discover the performance of the loser and liquidate the position. While this story is consistent with the redemption behavior of these investors, it does not explain why investors are more likely to sell their best performers. 1.7 Summary Prior research has found that no-load investors buy and sell past top performers while holding poor performers. The same pattern of behavior is found for the top performers in this sample of investors at a national full service brokerage firm. However, there is no evidence that investors hold poor performers and some evidence that they sell poor performers when the trade is part of an exchange. In addition, this is the first research to investigate how past performance affects the amount of investor transactions. These investors’ purchases are consistent with the representative heuristic. They are more likely to purchase a past top performer, and they purchase proportionally more of past top performers. When these investors sell they redeem proportionally more of the worst performers. This behavior is consistent with the idea that once an investor decides to sell a fund that they liquidate the entire position in order to remove the mistake from their portfolio. 37 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1.8 References for Chapter 1 Alexander, G., J. Jones, and P. Nigro, 1998, Mutual fund shareholders: characteristics, investor knowledge, and sources of information, Financial Services Review 7, 301316. Arkes, H. and C. Blumer, 1985, The psychology of sunk cost, Organizational Behavior and Human Decision Process 35, 124-140. Barber, B. and T. Odean, 2000, Trading is hazardous to your wealth: The common stock investment performance of individual investors, Journal of Finance 55, 773-806. Barber, B., T. Odean, and L. Zheng, 2000, The behavior of mutual fund investors, Working Paper. Belsley, D., E. Kuh, and R. Welsch, 1980, Regression Diagnostics, New York: John Wiley and Sons Inc. Berkson, J., 1953. A statistically precise and relatively simple method of estimating the bio-assay and quantal response, based on the logistic function, Journal of American Statistical Association 48, 565-599. Brown, K., W. Harlow, and L. Starks, 1996, Of tournaments and temptations: An analysis of managerial incentives in the mutual fund industry, Journal o f Finance 51, 85-110. Brown, S. and W. Goetzmann, 1995, Performance persistence, Journal of Finance 50, 679-698. Brown, S., W. Goetzmann, R. Ibbotson, and S. Ross, 1992, Surviviorship bias in performance studies, Review o f Financial Studies 4, 553-580. Capon, N., G. Fitzsimmons, and R. Prince, 1996, An individual level analysis of the mutual fund investment decision, Journal o f Financial Services Research 10, 59-82. Carhart, M., 1997, On persistence in mutual fund performance, Journal of Finance 52, 57-82. Chevalier, J.A. and G.D. Ellison, 1997, Risk taking by mutual funds as a response to incentives, Journal o f Political Economy 105, 1167-1200. Chordia, T., 1996, The structure of mutual fund sales charges, Journal o f Financial Economics 41, 3-39. Cragg, J., 1971, Some statistical models for limited dependent variables with application to the demand for durable goods, Econometrica 39, 829-844. 38 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Del Guercio, D. and P. Tkac, 2002, The determinants of the flow of funds of managed portfolios: Mutual funds versus pension funds, Journal o f Financial and Quantitative Analysis 37, 523-557. Del Guercio, D. and P. Tkac, 2001, Star power: The effect of momingstar ratings on mutual fund flows, Working Paper (Federal Reserve Bank of Atlanta). Duan, N., 1983, Smearing estimate: A nonparametric retransformation method, Journal of the American Statistical Association 2, 283-289. Elton, E., M. Gruber, and C. Blake, 1996, The persistence of risk-adjusted mutual fund performance, Journal o f Business 69, 133-157. Fant, L. and E. O’Neal, 2000, Temporal changes in the determinants of mutual fund flows, Journal of Financial Research 23, 353-372. Goetzmann, W. andN. Peles, 1997, Cognitive dissonance and mutual fund investors, Journal of Financial Research 20, 145-158. Grinblatt, M. and M. Keloharju, 2001, What makes investors trade? Journal o f Finance 56, 589-616. Grinblatt, M. and S. Titman, 1992, The persistence of mutual fund performance, Journal o f Finance 47,1977-1984. Grinblatt, M. and S. Titman, 1993, Performance measurement without benchmarks: an examination of mutual fund returns, Journal of Business 66, 47-68. Gross, L., 1982, The Art o f Selling Intangibles: How to Make Million($) by Investing Other People’s Money (New York: New York Institute of Finance). Gruber, M., 1996, Another puzzle: The growth in actively managed mutual funds, Journal o f Finance 51, 783-810. Hamilton, L.C., 1992, Regression With Graphics: A Second Course in Applied Statistics, (Belmont, California: Wadsworth, Inc.). Heckman, J., 1979, Sample selection bias as a specification error, Econometrica 47, 153161. Hendricks, D., J. Patel, and R. Zeckhauser, 1993, Hot hands in mutual funds: Short-run persistence of relative performance, 1974-1988, Journal of Finance 48, 93-130. Ippolito, R., 1992, Consumer reaction to measures of poor quality: Evidence from the mutual fund industry, Journal o f Law and Economics 35, 45-70. 39 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Jain, P. and J. Wu, 2000, Truth in mutual fund advertising: Evidence on future performance and fund flows, The Journal o f Finance 55, 937-958. Jensen, M., 1968, The performance of mutual funds in the period 1945-1964, Journal of Finance 23, 389-416. Kahn, R. and A. Rudd, 1995, Does historical performance predict future performance? Financial Analysts Journal November-December, 43-52. Kahneman, D. and A. Tversky, 1979, Prospect theory: An analysis of decision under risk, Econometrica 46, 171-185. Maddala, G., 1983, Limited dependent and qualitative variables in econometrics, (Cambridge: Cambridge University Press). Odean, T., 1998, Are investors reluctant to realize their losses?, Journal of Finance 53, 1775-1798. O’Neal, E., 1999, Mutual fund share classes and broker incentives, Financial Analysts Journal September-October, 76-87. Sharpe, W., 1966, Mutual fund performance, Journal of Business 39,119-138. Sharpe, W., 1996, The styles and performance of large seasoned U.S. mutual funds. William F. Sharpe Web Page http://www.stanford.edu/~wfsharpe/art/ls 100. Shefrin, H. and M. Statman, 1985, The disposition to sell winners too early and ride losers too long: Theory and evidence, The Journal o f Finance 40, 777-790. Shefrin, H. and R. Thaler, 1988, The behavioral life cycle hypothesis, Economic Inquiry 87, 1190-1219. Sirri, E. and P. Tufano, 1998, Costly search and mutual fund flows, The Journal of Finance 53, 1589-1622. Smythe, T., 1999, Multiple share class funds: efficiency or exploitation, Unpublished Dissertation. Thaler, R., 1980, Toward a positive theory of consumer choice, Journal of Economic Behavior and Organization 1, 39-60. Thaler, R., 1985, Mental accounting and consumer choice, Marketing Science 4, 199-214. Thaler, R., and S. Benartzi, 2001, Save more tomorrow: Using behavioral economics to increase employee saving, Working Paper. 40 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Thaler, R., and H. Shefrin, 1981, An economic theory of self-control, Journal of Political Economy 89, 392-406. Treynor, J., 1965, How to rate management of investment funds, Harvard Business Review 43, 63-75. Volkman, D. and M. Wohar, 1995. Determinants of persistence in relative performance of mutual funds, Journal of Financial Research 43, 415-430. Wellman, J., 2001, High fees versus active trading: A study of load and no load funds and their investors. Working paper. White, H., 1980, A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity, Econometrica 48, 817-838. 41 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 1.1 Example Sales Charge and Commission Structure This is an example of sales charges and commissions paid to the adviser’s company for A, B, and C-shares. Front load is the percentage of the purchase amount paid by the investor at the time of purchase. Contingent deferred sales charge is the amount the investor pays if they redeem shares before the end of the year indicated. In this example B shares convert to A shares 8 years after date of purchase. Adviser commission is the percentage of the purchase price that is paid to the adviser’s firm. Adviser trail is the percentage of dollars invested that is paid to the adviser’s firm for each year the client holds the fund, beginning in the 13thmonth after purchase. While these numbers are not universal across all multiple share class fund families, they are typical. Equity Funds Class A, B, and C Shares Adviser Contingent Deferred Convert Sales Charge to A Commission 1 2 3 4 5 6 Share Class Front Load A* 5.25% 0% B 0% 5% C 0% 1% 4% 4% 3% 2% 1% Adviser Trail N/A 5% 0.25% 8 yrs. 4% 0.25% NO 1% 1.00% *This represents the sales charge and commission for purchases of less than $50,000. Sales charge and adviser commission both decrease as the purchase amount increases. 42 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 1.2 Account Characteristics Characteristics of accounts with mutual fund holdings from a national full service brokerage firm. Panel A gives information from accounts at the beginning of the sample period, December 31, 2000 and Panel B provides the same data as of December 31, 2001. Panel A Type of Account Percentage of Total Accounts Mean Acct Size Median Acct Size Std Dev of Acct Size Avg. Number of M.F. Holdings Perc. of Value Mean Holding Size Median Holding Size Std Dev of Holding Size Perc. of Total Value of M. F. Holdings Single 20.0% $35,947 $11,558 $82,458 2.4 19.4% $15,041 $7,580 $26,621 19.4% Joint 19.6% $32,285 $12,095 $73,925 2.3 17.1% $13,821 $7,242 $25,061 17.2% Custodian 13.3% $5,832 $1,899 $12,864 1.6 2.1% $3,753 $1,615 $6,715 2.2% Trust 6.6% $88,243 $38,066 $1,368,144 3.1 15.6% $28,291 $14,935 $209,572 15.6% Partnership 0.1% $157,372 $42,279 $388,435 3.4 0.4% $46,295 $20,331 $86,491 0.4% Invest. Club 0.0% $6,398 $1,700 $19,738 1.6 0.0% $4,091 $1,456 $7,406 0.0% Corporation 0.5% $98,011 $27,978 $343,091 2.7 1.3% $36,324 $15,029 $97,866 1.3% Church 0.1% $55,893 $19,506 $141,006 2.2 0.2% $24,918 $12,505 $44,425 0.2% Bank 0.0% $1,082,058 $50,733 $6,964,942 7.7 0.1% $141,242 $41,450 $330,442 0.1% Estate 0.1% $84,602 $39,419 $126,058 2.7 0.2% $31,556 $17,688 $44,139 0.2% 27.5% $51,610 $22,771 $89,796 3.3 38.4% $15,716 $8,791 $22,925 38.4% SEP IRA 2.0% $43,099 $15,536 $80,579 3.3 2.3% $13,168 $6,574 $21,571 2.3% Roth IRA 7.1% $5,448 $2,049 $17,842 1.9 1.0% $2,857 $1,303 $6,906 1.1% Simple IRA 2.3% $5,492 $2,805 $7,146 2.0 0.3% $2,729 $1,416 $3,822 0.3% Other 0.8% 3.0 1.3% 1.3% Total 100.0% 2.5 100% 100.0% Regular IRA Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 1.2 - Continued Panel B Type of Account Percentage o f Total Accounts Mean Acct Size Median Acct Size Std Dev of Acct Size Avg. Number of M.F. Holdings Perc. of Value Mean Holding Size Median Holding Size Std Dev of Holding Size Perc. of Total Value of M. F. Holdings Single 18.9% $32,563 $10,049 $75,625 2.5 19.0% $13,149 $6,166 $24,449 19.0% Joint 18.1% $29,297 $10,561 $67,796 2.4 16.3% $12,064 $5,876 $22,698 16.3% Custodian 12.6% $4,903 $1,540 $11,971 1.6 1.9% $3,062 $1,247 $6,170 1.9% Trust 6.2% $81,560 $35,203 $1,228,868 3.2 15.7% $25,339 $13,033 $183,791 15.7% Partnership 0.1% $149,133 $36,347 $368,935 3.5 0.4% $42,467 $17,849 $87,004 0.4% Invest. Club 0.0% $5,411 $1,522 $18,920 1.6 0.0% $3,448 $1,371 $7,272 0.0% Corporation 0.5% $93,014 $24,864 $349,886 2.7 1.3% $33,900 $12,854 $107,946 1.3% Church 0.1% $53,970 $19,105 $132,513 2.3 0.2% $23,368 $11,328 $41,039 0.2% Bank 0.0% $1,584,172 $45,273 $10,204,552 8.7 0.1% $181,625 $40,005 $439,827 0.1% Estate 0.1% $76,621 $33,611 $122,817 2.7 0.2% $28,600 $15,425 $43,671 0.2% 28.6% $44,974 $19,179 $80,139 3.4 39.6% $13,195 $6,965 $20,257 39.6% SEP IRA 2.0% $36,163 $12,422 $71,072 3.4 2.3% $10,657 $4,944 $18,916 2.3% Roth IRA 9.3% $4,323 $1,978 $13,377 2.1 1.2% $2,061 $974 $4,997 1.2% Simple IRA 2.7% $5,665 $3,003 $7,186 2.3 0.5% $2,511 $1,328 $3,522 0.5% Other 0.7% 3.1 1.2% 1.2% Total 100.0% 2.7 100% 100.0% Regular IRA Table 1.3 Investor Demographics At the time accounts are opened, investors self report demographic information including net worth, annual income, birth date, and investment experience. Panel A provides mean, median, and standard deviation for each variable as of year-end 2000 and year-end 2001 broken out by the individual account types in the study. Panel B gives the percentage of individuals by self-reported investment experience and age for each of the two years. Panel A: Net Worth, Income, and Age Mean Median Net Worth ($) - 2000 Single & Joint Custodial IRAs Combined* Net Worth ($)-2001 Single & Joint Custodial IRAs Combined* Income ($) - 2000 Single & Joint Custodial IRAs Combined* Income ($) - 2001 Single & Joint Custodial IRAs Combined* Age (yrs.) - 2000 Single & Joint Custodial IRAs Combined* Age (yrs.) - 2001 Single & Joint Custodial IRAs Combined* Std. Dev. 347,607 9,089 354,394 350,969 220,000 2,000 250,000 225,000 1,628,711 47,483 1,824,571 1,728,496 355,467 9,085 350,798 352,966 225,000 2,000 225,000 225,000 1,573,566 148,268 1,823,855 1,712,205 47,990 1,078 51,092 49,526 39,000 200 40,000 40,000 52,546 21,247 52,101 52,349 49,312 1,084 51,819 50,655 40,000 200 40,000 40,000 55,419 25,905 50,333 52,771 55 10 51 53 55 10 52 53 18 6 14 16 55 10 51 52 55 11 51 52 18 6 14 16 *All single, joint, and IRA accounts combined. 45 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 1.3 - Continued Panel B: Experience and Age Investment Experience None Very Limited 2000 9.6% 36.7% 2001 9.3% Age 2000 2001 Moderate 35.8% Limited 40.8% 41.3% 0-19 14.2% 20-39 17.2% 40-59 35.9% 13.7% 19.0% 37.3% 60-79 27.2% 25.4% 10.6% 11.1% 46 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Extensive 2.3% 2.4% 80+ 5.5% 4.6% Table 1.4 Holdings by Asset Class The first row of each panel gives the percentage of assets within the data set that is held in equity funds, fixed income funds, and balanced funds. The aggregate load and no-load rows list the percentage of assets invested in equity, fixed income, and balanced funds for all load and no-load funds listed in Momingstar. Sample Aggregate Load Funds Aggregate No-Load Funds Panel A: 2000 Equity Fixed Income 83.2% 6.7% 85.4% 9.4% 12.6% 84.1% Balanced 10.1% 5.2% 3.2% Sample Aggregate Load Funds Aggregate No-Load Funds Panel B: 2001 Fixed Income Equity 7.1% 80.7% 10.7% 82.5% 79.7% 17.6% Balanced 12.3% 6.7% 2.6% 47 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 1.5 Transaction Data Transactions from all accounts for 200land 2002 are shown. Panel A provides data for redemptions, Panel B provides data for purchases, Panel C provides data for redemptions are part of an exchange, and Panel D provides data for purchases that are part of an exchange. % Transactions is the percentage of total transactions included in the study. NAY is the net asset value at which trades took place.______________ Panel A: Redemptions % Transactions Mean Trade Size: Full Sample Joint & Single Custodial IRAs Other NAY 13.5% 4.6% 0.4% 6.9% 1.6% $4,613 $4,793 $3,156 $3,755 $8,554 $20.13 Median Std. Dev. $2,200 $2,500 $2,001 $2,001 $2,999 $18.92 $12,266 $11,572 $3,377 $6,786 $26,926 $8.72 Median Std. Dev. $4,713 $4,826 $2,412 $4,070 $6,393 $19.04 $20,862 $22,645 $5,020 $14,234 $38,718 $9.10 Panel B: Purchases % Transactions Trade Size: Full Sample Joint & Single Custodial IRAs Other NAY 66.3% 18.5% 1.4% 38.6% 7.7% Mean $9,262 $9,698 $3,923 $8,339 $14,386 $20.76 Panel C: Exchange Redemptions Median % Transactions Mean Trade Size: Full Sample Joint & Single Custodial IRAs Other NAY 10.3% 3.3% 0.3% 5.6% 1.1% $12,482 $12,160 $4,406 $11,312 $21,639 $16.97 $6,180 $6,321 $2,771 $5,931 $10,000 $14.79 Panel D: Exchange Purchases % Transactions Median Mean Trade Size: Full Sample Joint & Single Custodial IRAs Other NAY 9.9% 3.1% 0.3% 5.4% 1.1% $11,947 $11,981 $4,242 $10,503 $21,213 $17.89 $5,494 $6,000 $2,700 $5,000 $9,859 $15.53 48 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Std. Dev. $25,483 $22,633 $5,271 $19,112 $48,318 $8.61 Std. Dev. $26,402 $23,900 $5,497 $18,883 $52,178 $8.93 Table 1.6 Redemptions by Return Deciles Percentage of redemptions that are not part of an exchange between January 1, 2001 and December 31, 2002 at a national full-service brokerage firm by both number of trades and dollars and average total return by return deciles. Deciles are defined in two different ways. Performance relative to all funds means that funds were assigned to performance deciles ranked against all funds on the approved list of the brokerage firm that provided the data. Performance relative to category means that funds were ranked against funds on the approved list that share the same Morningstar category. Panel A ranks funds by their one-year total return, Panel B by their three-year total return, and Panel C by their five-year total return. _____________ Panel A; Redemptions by One-Year Return Deciles_____________ Performance Relative to AllFunds Performance Relative to Category %Trades %Dollars Mean Ret. Decile %Trades %Dollars Mean Ret. 11.7 24.9 24.2 -1.8 10 (Best) 8.7 9.3 8.0 8.2 8.1 -2.9 9 3.8 4.8 7.1 12.4 12.1 -6.2 8 3.0 3.8 14.1 4.9 13.7 -9.1 7 7.7 9.2 9.5 -0.8 9.6 -9.8 6 14.8 14.3 6.2 -6.6 6.3 -12.4 5 20.1 18.7 4 20.1 18.8 -12.9 6.9 7.7 -12.3 -18.7 9.2 9.3 3 10.4 -11.5 9.9 -26.0 6.7 6.5 -13.8 2 7.1 6.8 -35.0 2.2 2.6 1(Worst) 4.3 4.4 -18.0 Panel B: Redemptions by Three-Year Return Deciles Performance Relative to Category Performance Relative to All Funds Decile %Trades %Dollars Mean Ret. %Trades %Dollars Mean Ret. 12.2 24.6 10 (Best) 18.7 25.3 8.2 18.6 7.3 12.7 9 15.1 15.6 12.5 4.6 5.8 11.6 11.7 3.9 8 8.9 9.9 4.5 12.0 7 9.1 9.6 12.5 3.2 2.9 16.3 2.0 6 8.5 8.1 16.6 1.2 5.5 5.9 -0.2 5 16.9 15.9 4 8.2 -0.8 7.3 7.5 -0.8 8.7 4.1 -3.0 4.1 -0.8 3 5.5 5.2 2 -5.6 2.4 2.5 -4.4 5.0 4.9 -10.4 2.2 2.8 1(Worst) 3.8 4.0 -5.1 Panel C: Redemptions by Five-Year Return Deciles Performance Relative to All Funds Performance Relative to Category % Trades % Dollars Mean Ret. Decile % Trades % Dollars Mean Ret. 10 (Best) 41.6 12.7 27.7 26.9 12.2 42.7 9.5 19.3 9 16.6 16.6 19.7 10.4 7.9 20.0 8 9.9 10.8 20.7 9.6 5.9 6.4 9.6 9.5 8.2 7 5.4 5.4 6 7.1 6.3 6.3 7.9 7.0 4.7 3.5 5 5.1 5.1 3.6 6.2 5.0 3.8 5.7 4 5.2 6.3 5.7 3 2.9 3.7 4.1 3.9 3.7 5.8 1.0 2 3.2 3.4 2.0 2.0 3.6 -1.6 1.5 1.7 1(Worst) 1.0 0.9 2.9 49 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 1.7 Exchange Redemptions by Return Deciles Percentage of redemptions that are part of an exchange between January 1, 2001 and December 31, 2002 at a national full-service brokerage firm by both number of trades and dollars and average total return by return deciles. Deciles are defined in two different ways. Performance relative to all funds means that funds were assigned to performance deciles ranked against all funds on the approved list of the brokerage firm that provided the data. Performance relative to category means that funds were ranked against funds on the approved list that share the same Momingstar category. Panel A ranks funds by their one-year total return, Panel B by their three-year total return, and Panel C by their five-year total return. _________ Panel A; Exchange Redemptions by One-Year Return Deciles________ Performance Relative to All Funds Performance Relative to Category Decile % Trades % Dollars Mean Ret. % Trades % Dollars Mean Ret. 15.0 10 (Best) 3.4 4.8 11.8 19.1 -5.1 9 3.0 8.4 1.9 8.3 7.1 -5.5 8 13.0 1.8 2.7 7.1 12.5 -9.6 7 3.5 5.3 4.8 12.8 13.0 -14.2 6 10.5 -0.8 10.8 10.8 7.5 -15.2 5 15.4 -7.0 6.3 12.3 7.0 -16.3 4 -13.0 9.3 7.9 19.7 21.8 -17.6 3 10.8 9.1 17.5 15.2 -19.1 -19.4 8.6 2 13.0 10.1 18.7 -26.1 -24.7 -37.8 4.8 4.0 1(Worst) 13.9 8.3 -32.8 Panel B: Exchange Redemptions by Three-Year Return Deciles Performance Relative to All Funds Performance Relative to Category Decile % Trades % Dollars Mean Ret. % Trades % Dollars Mean Ret. 24.6 11.9 20.8 7.1 10(Best) 9.2 12.6 13.2 9 7.3 13.4 2.5 6.7 9.1 11.8 8 6.0 5.8 11.7 4.3 2.3 12.0 7 10.6 4.5 6.9 4.5 1.8 11.1 6 2.8 10.5 -0.4 7.7 9.3 6.4 5 19.2 1.2 6.6 -1.8 16.1 4 12.7 -0.9 6.3 5.5 -2.7 13.4 9.2 7.9 3 8.3 -3.1 -3.4 11.0 2 5.5 3.9 9.0 -5.7 -6.1 13.1 5.5 3.5 7.6 -10.8 -8.7 1(Worst) 14.0 Panel C: Exchange Redemptions by Five-Year Return Deciles Performance Relative to All Funds Performance Relative to Category % Dollars Mean Ret. % Trades % Dollars Mean Ret. Decile % Trades 27.6 10 (Best) 28.9 13.1 25.1 11.4 23.3 9 16.7 11.4 12.2 9.6 15.9 9.9 8 7.8 18.5 7.7 8.7 17.3 8.0 7 7.4 6.5 8.2 9.5 6.0 7.5 6 9.8 5.4 6.6 7.1 6.2 8.5 5 8.6 4.7 5.4 4.7 8.6 4.7 4 9.4 6.2 4.8 7.8 3.8 3.9 3 7.9 2.9 5.8 4.7 10.7 4.7 2 4.4 10.2 6.4 1.1 5.7 3.2 4.2 2.2 -3.2 3.3 2.6 1(Worst) 2.3 50 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 1.8 Purchases by Return Deciles Percentage of purchases that are not part of an exchange between January 1, 2001 and December 31,2002 at a national full-service brokerage firm by both number of trades and dollars and average total return by return deciles. Deciles are defined in two different ways. Performance relative to all funds means that funds were assigned to performance deciles ranked against all funds on the approved list of the brokerage firm that provided the data. Performance relative to category means that funds were ranked against funds on the approved list that share the same Momingstar category. Panel A ranks funds by their one-year total return, Panel B by their three-year total return, and Panel C by their five-year total return. _______________Panel A: Purchases by One-Year Return Deciles______________ Performance Relative to All Funds Performance Relative to Category Decile % Trades % Dollars Mean Ret. % Trades % Dollars Mean Ret. 10 (Best) 10.8 13.2 33.2 -1.9 9.2 34.7 9 8.9 -1.4 4.3 5.6 8.3 8.5 8 11.9 -3.6 3.2 4.2 7.1 11.6 7 10.7 13.0 4.8 12.3 11.5 -6.6 6 20.4 -0.7 9.7 9.2 -7.8 19.1 5 5.3 20.5 19.5 -6.6 4.9 -8.1 4 -12.8 4.3 -8.5 18.0 15.5 4.3 3 6.7 -18.7 7.6 -9.8 8.7 7.8 2 -25.9 5.6 -10.6 4.0 2.8 5.7 1(Worst) 1.5 -16.7 2.5 1.5 -34.8 1.5 Panel B: Purchases by Three-Year Return Deciles Performance Relative to All Funds Performance Relative to Category Decile % Trades % Dollars Mean Ret. % Trades % Dollars Mean Ret. 10 (Best) 36.3 28.0 25.5 13.3 35.9 9.9 9 16.7 7.3 12.7 13.2 6.8 15.1 8 8.9 10.4 5.8 11.7 11.6 5.6 7 11.7 13.7 4.5 11.9 11.8 4.3 6 2.9 9.3 9.7 16.0 16.1 2.9 5 16.6 15.7 1.2 3.4 3.3 1.2 4 3.9 -0.7 3.6 0.1 4.8 3.3 3 2.0 -2.9 2.6 1.1 2.6 2.9 2 2.0 -5.6 0.9 0.9 1.6 -2.0 1(Worst) 0.9 -2.0 1.0 0.7 -9.7 0.9 Panel C:: Purchases by Five-Year Return Deciles Performance Relative to All Funds Performance Relative to Category Decile % Trades % Dollars Mean Ret. % Trades % Dollars Mean Ret. 10 (Best) 56.9 54.0 13.2 38.5 37.2 13.3 9 14.9 15.8 9.6 19.7 19.5 10.7 8 22.1 7.2 7.6 7.9 20.6 9.9 7 5.6 6.7 6.5 8.1 8.5 8.8 6 5.9 5.4 5.0 5.1 8.9 5.5 5 4.2 2.4 3.9 4.7 2.4 7.0 4 3.0 3.0 3.8 2.7 2.5 6.3 3 1.7 1.6 2.9 1.7 6.7 1.5 2 1.0 0.8 1.0 0.6 0.5 4.1 1(Worst) 0.4 0.4 -1.1 0.7 0.6 3.5 51 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 1.9 Exchange Purchases by Return Deciles Percentage of purchases that are part of an exchange between January 1, 2001 and December 31, 2002 at a national full-service brokerage firm by both number of trades and dollars and average total return by return deciles. Deciles are defined in two different ways. Performance relative to all funds means that funds were assigned to performance deciles ranked against all funds on the approved list of the brokerage firm that provided the data. Performance relative to category means that funds were ranked against funds on the approved list that share the same Morningstar category. Panel A ranks funds by their one-year total return, Panel B by their three-year total return, and Panel C by their five-year total return. __________ Panel A; Exchange Purchases by One-Year Return Deciles__________ Performance Relative to All Funds Performance Relative to Category Decile % Trades % Dollars Mean Ret. % Trades % Dollars Mean Ret. 10 (Best) 8.8 11.3 14.0 25.1 26.7 -0.6 9 3.9 5.5 8.3 -0.8 8.5 9.3 3.2 4.7 13.9 -3.4 8 7.1 14.5 11.4 7 8.7 11.2 12.1 -5.6 4.8 6 18.3 19.3 8.4 8.0 -5.9 -0.9 17.6 6.6 5.9 -8.1 5 18.1 -6.6 4 16.7 14.2 7.2 -8.1 -12.9 7.8 10.8 8.2 -18.6 7.4 -10.4 3 7.9 8.4 5.5 2 -25.9 6.1 6.5 -12.2 1(Worst) 3.1 2.5 -34.7 3.1 3.7 -15.7 Panel B: Exchange Purchases by Three-Year Return Deciles Performance Relative to All Funds Performance Relative to Category Decile % Trades % Dollars Mean Ret. % Trades % Dollars Mean Ret. 19.5 10 (Best) 19.1 12.6 30.0 30.6 9.3 12.0 9 10.3 7.4 14.2 13.6 4.9 6.3 8.1 5.2 8 5.8 9.6 10.1 7 10.6 13.5 10.4 4.5 10.5 4.0 12.5 6 12.1 12.9 3.1 2.9 11.8 16.8 5 15.8 1.2 5.0 1.7 4.6 4 9.6 8.1 7.4 -0.8 8.5 0.0 5.4 3 7.0 -2.9 6.0 6.2 -0.5 2 4.9 3.2 -5.6 2.6 2.3 -2.0 3.2 1.9 1(Worst) -9.8 1.9 1.8 -1.7 Panel C: Exchange Purchases by Five-Year Return Deciles Performance Relative to All Funds Performance Relative to Category Decile % Trades % Dollars Mean Ret. % Trades % Dollars Mean Ret. 38.4 10(Best) 37.6 13.1 29.1 29.0 12.8 9 15.0 15.1 9.6 17.0 16.3 10.3 8.4 8 8.8 16.6 9.7 7.8 14.3 7 8.7 6.7 6.5 8.1 8.6 7.1 7.0 8.0 9.4 6 5.3 8.9 8.7 8.4 7.9 6.4 6.4 7.2 5 4.7 4 7.5 6.1 3.7 6.0 4.8 6.2 5.7 4.3 7.4 3 2.9 6.3 5.1 2 2.5 1.7 2.2 4.2 1.0 2.7 1(Worst) 1.1 0.9 -1.9 2.3 2.1 4.4 52 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 1.10 Logit Results - Redemptions The dependent variable is equal to one if there is a redemption of the mutual fund during the month and zero otherwise. The independent variables are a dichotomous variable equal to one if the fund is in the top performing decile of its Momingstar category and zero otherwise (Winner); a dichotomous variable equal to one if the fund is in the top performing decile of its Momingstar category and zero otherwise (Loser); the standard deviation of monthly returns for the fund over the three prior years (3 Yr Std Dev); the age of the fund in years (Fund Age); the expense ratio for the fund (Expense Ratio); the natural log of the total amount invested in a given fund at the brokerage firm that provided the data (Log Total Value); and the natural log of the total net assets of the fund (Log TNA). p-values are in parentheses. * and ** represent the 5 and 1 percent statistical significance levels respectively. 3-Year 1-Year 5-Year All Funds Category All Funds Category All Funds Category Intercept -0.334** (0.008) -0.298* (0.019) -0.305* (0.016) -0.358** (0.005) -1.357** (0.0001) -1.522** (0.0001) Winner 0.192** (0.001) -0.020 (0.746) 0.470** (0.0001) 0.224** (0.001) 0.595** (0.0001) 0.621** (0.0001) Loser -0.024 (0.752) -0.261** (0.0001) 0.568** (0.0001) 0.098 (0.091) 0.079 (0.295) -0.271 (0.529) Fund Age -0.014** (0.0001) -0.014** (0.0001) -0.014** (0.0001) -0.014** (0.0001) -0.002 (0.371) -0.002** (0.0001) Exp. Ratio 0.217** (0.0001) 0.231** (0.0001) 0.221** (0.0001) 0.238** (0.0001) 0.556** (0.0001) 0.664** (0.010) 3 Yr Std Dev 0.005* (0.015) 0.005** (0.010) -0.002 (0.240) 0.003 (0.071) -0.007** (0.003) -0.005** (0.0001) Log Total Value 0.645** (0.0001) 0.641** (0.0001) 0.650** (0.0001) 0.647** (0.0001) 0.625** (0.0001) 0.629** (0.0001) Log TNA -0.036* (0.017) -0.035* (0.022) -0.043** (0.005) -0.039** (0.010) 0.073** (0.0001) 0.077** (0.0001) PseudoR2 0.316 0.316 0.320 0.316 0.361 0.363 N 18804 18804 18765 18765 15419 15419 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 1.10 - Continued Jan/2001 Feb/2001 Mar/2001 Apr/2001 May/2001 Jun/2001 Jul/2001 Aug/2001 Sep/2001 Oct/2001 Nov/2001 Dec/2001 Jan/2002 Feb/2002 Mar/2002 Apr/2002 May/2002 Jun/2002 Jul/2002 Aug/2002 Sep/2002 Oct/2002 Nov/2002 1-year Category -1.999** (0.0001) -2.192** (0.0001) -2.061** (0.0001) -2.042** (0.0001) -2.075** (0.0001) -2.107** (0.0001) -2.132** (0.0001) -2.010** (0.0001) -2.162** (0.0001) -2.105** (0.0001) -2.053** (0.0001) -1.903** (0.0001) 0.294* (0.015) 0.237 (0.050) 0.096 (0.435) 0.291* (0.018) 0.183 (0.130) 0.034 (0.777) 0.188 (0.119) -0.016 (0.896) -0.107 (0.368) -0.004 (0.973) -0.046 (0.700) All Funds -1.996** (0.0001) -2.192** (0.0001) -2.059** (0.0001) -2.038** (0.0001) -2.071** (0.0001) -2.105** (0.0001) -2.132** (0.0001) -2.006** (0.0001) -2.158** (0.0001) -2.104** (0.0001) -2.049** (0.0001) -1.891** (0.0001) 0.302* (0.012) 0.245* (0.042) 0.105 (0.389) 0.302* (0.014) 0.191 (0.113) 0.041 (0.732) 0.190 (0.115) -0.011 (0.929) -0.105 (0.380) -0.001 (0.991) -0.042 (0.722) 3-Year Category -2.016** (0.0001) -2.211** (0.0001) -2.051** (0.0001) -2.032** (0.0001) -2.064** (0.0001) -2.097** (0.0001) -2.123** (0.0001) -1.998** (0.0001) -2.148** (0.0001) -2.096** (0.0001) -2.039** (0.0001) -1.889** (0.0001) 0.306* (0.011) 0.247* (0.040) 0.105 (0.391) 0.305* (0.014) 0.195 (0.106) 0.046 (0.699) 0.190 (0.114) -0.014 (0.907) -0.099 (0.407) 0.006 (0.962) -0.038 (0.752) All Funds -2.023** (0.0001) -2.212** (0.0001) -2.052** (0.0001) -2.032** (0.0001) -2.061** (0.0001) -2.104** (0.0001) -2.125** (0.0001) -2.010** (0.0001) -2.172** (0.0001) -2.107** (0.0001) -2.054** (0.0001) -1.906** (0.0001) 0.303* (0.012) 0.245* (0.043) 0.103 (0.400) 0.302* (0.014) 0.198 (0.101) 0.045 (0.710) 0.189 (0.118) -0.014 (0.910) -0.102 (0.394) 0.006 (0.958) -0.033 (0.785) 5-Year All Funds Category -2.590** -2.602** (0.0001) (0.0001) -2.680** -2.668** (0.0001) (0.0001) -2.621** -2.629** (0.0001) (0.0001) -2.542** -2.551** (0.0001) (0.0001) -2.617** -2.623** (0.0001) (0.0001) -2.627** -2.638** (0.0001) (0.0001) -2.502** -2.520** (0.0001) (0.0001) -2.387** -2.371** (0.0001) (0.0001) -2.512** -2.528** (0.0001) (0.0001) -2.410** -2.425** (0.0001) (0.0001) -2.405** -2.419** (0.0001) (0.0001) -2.447** -2.461** (0.0001) (0.0001) 0.408** 0.396** (0.002) (0.003) 0.342* 0.327* (0.011) (0.015) 0.150 0.139 (0.268) (0.306) 0.399** 0.394** (0.003) (0.004) 0.262* 0.254 (0.047) (0.055) 0.122 0.114 (0.352) (0.387) 0.280* 0.284* (0.033) (0.031) -0.020 -0.023 (0.877) (0.859) -0.075 -0.068 (0.561) (0.600) -0.012 -0.007 (0.925) (0.954) 0.004 -0.004 (0.976) (0.978) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 1.11 Logit Analysis - Exchange Redemptions The dependent variable is equal to one if there is a redemption of the mutual fund during the month and zero otherwise. The independent variables are a dichotomous variable equal to one if the fund is in the top performing decile of its Momingstar category and zero otherwise (Winner); a dichotomous variable equal to one if the fund is in the top performing decile of its Momingstar category and zero otherwise (Loser); the standard deviation of monthly returns for the fund over the three prior years (3 Yr Std Dev) ; the age of the fund in years (Fund Age); the expense ratio for the fund (Expense Ratio); the natural log of the total amount invested in a given fund at the brokerage firm that provided the data (Log Total Value); and the natural log of the total net assets of the fund (Log TNA). p-values are in parentheses. * and ** represent the 5 and 1 percent statistical significance levels respectively. 3-Year 1-Year 5-Year All Funds Category All Funds Category All Funds Intercept -0.964** (0.0001) -0.966** (0.0001) -0.942** (0.0001) -1.023** (0.0001) -2.256** (0.0001) -2.423** (0.0001) Winner -0.049 (0.426) -0.075 (0.238) 0.059 (0.346) 0.196** (0.002) 0.128 (0.084) 0.567** (0.0001) Loser -0.109 (0.165) -0.237** (0.0001) 0.650** (0.0001) 0.169** (0.005) 0.219** (0.004) -0.035 (0.600) Fund Age -0.005* (0.021) -0.005* (0.025) -0.005* (0.026) -0.005* (0.022) 0.006* (0.023) 0.007** (0.006) Exp. Ratio 0.834** (0.0001) 0.854** (0.0001) 0.836** (0.0001) 0.850** (0.0001) 1.317** (0.0001) 1.427** (0.0001) 3 Yr Std Dev 0.023** (0.0001) 0.022** (0.0001) 0.017** (0.0001) 0.021** (0.0001) 0.012** (0.0001) 0.012** (0.0001) Log Total Value 0.768** (0.0001) 0.766** (0.0001) 0.777** (0.0001) 0.771** (0.0001) 0.789** (0.0001) 0.791** (0.0001) Log TNA -0.175** (0.0001) -0.173** (0.0001) -0.180** (0.0001) -0.177** (0.0001) -0.065** (0.001) -0.072** (0.001) Pseudo R2 0.356 0.357 0.360 0.356 0.403 0.405 N 18769 18769 18730 18730 15389 15389 55 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Category Jan/2001 Feb/2001 Mar/2001 Apr/2001 May/2001 Jun/2001 Jul/2001 Aug/2001 Sep/2001 Oct/2001 Nov/2001 Dec/2001 Jan/2002 Feb/2002 Mar/2002 Apr/2002 May/2002 Jun/2002 Jul/2002 Aug/2002 Sep/2002 Oct/2002 Nov/2002 Table 1.11 - Continued 1--year 3-Year Category All Funds Category All Funds -2.431** -2.433** -2.427** -2.458** (0.0001) (0.0001) (0.0001) (0.0001) -2.550** -2.554** -2.589** -2.566** (0.0001) (0.0001) (0.0001) (0.0001) -2.509** -2.513** -2.525** -2.503** (0.0001) (0.0001) (0.0001) (0.0001) -2.596** -2.587** -2.593** -2.612** (0.0001) (0.0001) (0.0001) (0.0001) -2.680** -2.686** -2.690** -2.699** (0.0001) (0.0001) (0.0001) (0.0001) -2.724** -2.697** -2.705** -2.706** (0.0001) (0.0001) (0.0001) (0.0001) -2.880** -2.874** -2.877** -2.893** (0.0001) (0.0001) (0.0001) (0.0001) -2.571** -2.581** -2.603** -2.578** (0.0001) (0.0001) (0.0001) (0.0001) -2.410** -2.422** -2.451** -2.420** (0.0001) (0.0001) (0.0001) (0.0001) -2.408** -2.434** -2.401** -2.408** (0.0001) (0.0001) (0.0001) (0.0001) -2.506** -2.542** -2.516** -2.513** (0.0001) (0.0001) (0.0001) (0.0001) -2.300** -2.314** -2.336** -2.307** (0.0001) (0.0001) (0.0001) (0.0001) -0.442** -0.422** -0.430** -0.437** (0.001) (0.001) (0.001) (0.001) -0.521** -0.541** -0.528** -0.533** (0.0001) (0.0001) (0.0001) (0.0001) -0.130 -0.134 -0.118 -0.123 (0.352) (0.293) (0.331) (0.308) -0.115 -0.129 -0.127 -0.121 (0.367) (0.310) (0.319) (0.339) -0.295* -0.303* -0.310* -0.310* (0.017) (0.014) (0.012) (0.013) -0.256* -0.262* -0.249* -0.249* (0.039) (0.045) (0.044) (0.035) 0.348** 0.343** 0.339** 0.348** (0.006) (0.007) (0.007) (0.006) -0.013 -0.015 -0.021 -0.011 (0.917) (0.901) (0.865) (0.928) -0.220 -0.211 -0.216 -0.221 (0.087) (0.074) (0.077) (0.081) 0.168 0.167 0.171 0.165 (0.185) (0.181) (0.177) (0.169) 0.021 0.012 0.022 0.016 (0.864) (0.920) (0.858) (0.899) 5-Year All Funds Category -3.092** -3.104** (0.0001) (0.0001) -3.067** -3.079** (0.0001) (0.0001) -2.981** -2.989** (0.0001) (0.0001) -2.955** -2.962** (0.0001) (0.0001) -3.141** -3.145** (0.0001) (0.0001) -3.157** -3.163** (0.0001) (0.0001) -3.188** -3.201** (0.0001) (0.0001) -2.956** -2.965** (0.0001) (0.0001) -2.858** -2.867** (0.0001) (0.0001) -2.775** -2.783** (0.0001) (0.0001) -2.939** -2.928** (0.0001) (0.0001) -2.987** -2.995** (0.0001) (0.0001) -0.450** -0.451** (0.001) (0.001) -0.532** -0.535** (0.001) (0.001) -0.133 -0.133 (0.349) (0.353) -0.058 -0.057 (0.686) (0.689) -0.284* -0.280* (0.039) (0.042) -0.209 -0.208 (0.128) (0.130) 0.356** 0.362** (0.010) (0.009) 0.008 0.010 (0.956) (0.939) -0.242 -0.241 (0.072) (0.074) 0.152 0.157 (0.261) (0.247) 0.024 0.022 (0.861) (0.869) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 1.12 Logit Analysis - Purchases The dependent variable is equal to one if there is a purchase of the mutual fund during the month and zero otherwise. The independent variables are a dichotomous variable equal to one if the fund is in the top performing decile of its Momingstar category and zero otherwise (Winner); a dichotomous variable equal to one if the fund is in the top performing decile of its Momingstar category and zero otherwise (Loser); the standard deviation of monthly returns for the fund over the three prior years (3 Yr Std Dev); the age of the fund in years (Fund Age); the expense ratio for the fund (Expense Ratio); the natural log of the total amount invested in a given fund at the brokerage firm that provided the data (Log Total Value); and the natural log of the total net assets of the fund (Log TNA). p-values are in parentheses. * and ** represent the 5 and 1 percent statistical significance levels respectively. 1-Year All Funds Category 5-Year 3-Year All Funds Category All Funds Category Intercept 1.428** (0.0001) 1.533** (0.0001) 1.519** (0.0001) 1.466** (0.0001) 0.809** (0.0001) 0.646** (0.0001) Winner 0.480** (0.0001) 0.031 (0.621) 0.814** (0.0001) 0.355** (0.0001) 0.665** (0.0001) 0.711** (0.0001) Loser -0.309** (0.0001) -0.329** (0.0001) 0.127 (0.056) 0.066 (0.261) -0.326** (0.0001) -0.069 (0.300) Fund Age -0.011** (0.0001) -0.010** (0.0001) -0.010** (0.0001) -0.010** (0.0001) 0.001 (0.968) 0.001 (0.866) Exp. Ratio 0.113** (0.010) 0.145** (0.001) 0.133** (0.002) 0.157** (0.001) 0.390** (0.0001) 0.437** (0.0001) 3 Yr Std Dev -0.004 (0.083) -0.008** (0.0001) -0.014** (0.0001) -0.010** (0.0001) -0.020** (0.0001) -0.021** (0.0001) Log Total Value 0.860** (0.0001) 0.858** (0.0001) 0.868** (0.0001) 0.865** (0.0001) 0.858** (0.0001) 0.861** (0.0001) Log TNA -0.422** (0.0001) -0.428** (0.0001) -0.438** (0.0001) -0.433** (0.0001) -0.352** (0.0001) -0.340** (0.0001) Pseudo R2 0.337 0.335 0.340 0.335 0.373 0.373 N 18770 18770 18731 18731 15389 15389 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 1.12 - Continued Jan/2001 Feb/2001 Mar/2001 Apr/2001 May/2001 Jun/2001 Jul/2001 Aug/2001 Sep/2001 Oct/2001 Nov/2001 Dec/2001 Jan/2002 Feb/2002 Mar/2002 Apr/2002 May/2002 Jun/2002 Jul/2002 Aug/2002 Sep/2002 Oct/2002 Nov/2002 1-year All Funds Category -1.984** -1.981** (0.0001) (0.0001) -1.935** -1.933** (0.0001) (0.0001) -2.027** -2.027** (0.0001) (0.0001) -1.921** -1.919** (0.0001) (0.0001) -1.949** -1.949** (0.0001) (0.0001) -2.040** -2.037** (0.0001) (0.0001) -2.061** -2.070** (0.0001) (0.0001) -1.905** -1.909** (0.0001) (0.0001) -2.073** -2.066** (0.0001) (0.0001) -1.959** -1.967** (0.0001) (0.0001) -1.980** -1.977** (0.0001) (0.0001) -1.870** -1.852** (0.0001) (0.0001) 0.345** 0.357** (0.004) (0.006) 0.191 0.202 (0.127) (0.106) 0.272* 0.292* (0.034) (0.023) 0.514** 0.497** (0.001) (0.0001) 0.202 0.213 (0.106) (0.088) 0.145 0.152 (0.223) (0.247) 0.123 0.121 (0.332) (0.323) 0.200 0.205 (0.110) (0.100) 0.112 0.115 (0.369) (0.357) 0.044 0.041 (0.721) (0.738) 0.056 0.061 (0.655) (0.624) 3-Year All Funds Category -2.004** -2.000** (0.0001) (0.0001) -1.960** -1.957** (0.0001) (0.0001) -2.019** -2.020** (0.0001) (0.0001) -1.905** -1.915** (0.0001) (0.0001) -1.933** -1.942** (0.0001) (0.0001) -2.029** -2.030** (0.0001) (0.0001) -2.054** -2.053** (0.0001) (0.0001) -1.895** -1.896** (0.0001) (0.0001) -2.062** -2.054** (0.0001) (0.0001) -1.947** -1.951** (0.0001) (0.0001) -1.962** -1.964** (0.0001) (0.0001) -1.860** -1.861** (0.0001) (0.0001) 0.363** 0.355** (0.004) (0.005) 0.208 0.199 (0.096) (0.111) 0.278* 0.287* (0.030) (0.025) 0.499** 0.507** (0.001) (0.0001) 0.206 0.220 (0.079) (0.099) 0.157 0.151 (0.209) (0.228) 0.126 0.131 (0.295) (0.315) 0.211 0.202 (0.092) (0.106) 0.114 0.117 (0.348) (0.361) 0.044 0.051 (0.685) (0.721) 0.057 0.068 (0.588) (0.645) 5-Year All Funds -2.607** (0.0001) -2.470** (0.0001) -2.540** (0.0001) -2.326** (0.0001) -2.452** (0.0001) -2.479** (0.0001) -2.437** (0.0001) -2.274** (0.0001) -2.378** (0.0001) -2.278** (0.0001) -2.299** (0.0001) -2.447** (0.0001) 0.350* (0.011) 0.120 (0.379) 0.295* (0.037) 0.479** (0.001) 0.215 (0.114) 0.114 (0.399) 0.138 (0.307) 0.198 (0.139) 0.116 (0.383) 0.052 (0.692) 0.039 (0.770) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Category -2.627** (0.0001) -2.480** (0.0001) -2.545** (0.0001) -2.337** (0.0001) -2.454** (0.0001) -2.487** (0.0001) -2.448** (0.0001) -2.279** (0.0001) -2.383** (0.0001) -2.280** (0.0001) -2.299** (0.0001) -2.463** (0.0001) 0.339* (0.014) 0.107 (0.436) 0.282* (0.046) 0.472** (0.001) 0.204 (0.134) 0.102 (0.451) 0.132 (0.329) 0.192 (0.152) 0.124 (0.353) 0.054 (0.682) 0.030 (0.823) Table 1.13 Logit Analysis - Exchange Purchases The dependent variable is equal to one if there is a purchase of the mutual fund during the month and zero otherwise. The independent variables are a dichotomous variable equal to one if the fund is in the top performing decile of its Momingstar category and zero otherwise (Winner); a dichotomous variable equal to one if the fund is in the top performing decile of its Momingstar category and zero otherwise (Loser); the standard deviation of monthly returns for the fund over the three prior years (3 Yr Std Dev); the age of the fund in years (Fund Age); the expense ratio for the fund (Expense Ratio); the natural log of the total amount invested in a given fund at the brokerage firm that provided the data (Log Total Value); and the natural log of the total net assets of the fund (Log TNA). p-values are in parentheses. * and ** represent the 5 and 1 percent statistical significance levels respectively. 1-Year 3-Year 5-Year All Funds Category All Funds Category Intercept -0.611** (0.0001) -0.491** (0.001) -0.452** (0.001) -0.507** (0.001) All Funds Category -1.202** -1.394** (0.0001) (0.0001) Winner 0.692** (0.0001) 0.235** (0.001) 0.932** (0.0001) 0.497** (0.0001) 0.777** (0.0001) 0.696** (0.0001) Loser -0.385** (0.0001) -0.428** (0.0001) -0.004 (0.955) -0.210** (0.001) -0.312** (0.0001) -0.319** (0.0001) Fund Age -0.008** (0.001) -0.006* (0.013) -0.006** (0.008) -0.006* (0.011) 0.002 (0.345) 0.003 (0.277) Exp. Ratio 0.689** (0.0001) 0.740** (0.0001) 0.700** (0.0001) 0.763** (0.0001) 0.934** (0.0001) 1.017** (0.0001) 3 Yr Std Dev -0.003 (0.196) -0.009** (0.0001) -0.014** (0.0001) -0.012** (0.0001) -0.019** (0.0001) -0.019** (0.0001) Log Total Value 0.825** (0.0001) 0.821** (0.0001) 0.831** (0.0001) 0.829** (0.0001) 0.819** (0.0001) 0.820** (0.0001) Log TNA -0.182** (0.0001) -0.192** (0.0001) -0.202** (0.0001) -0.203** (0.0001) -0.112** (0.0001) -0.095** (0.0001) Pseudo R2 0.354 0.350 0.356 0.351 0.388 0.387 N 18748 18748 18709 18709 15369 15369 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Jan/2001 Feb/2001 Mar/2001 Apr/2001 May/2001 Jun/2001 Jul/2001 Aug/2001 Sep/2001 Oct/2001 Nov/2001 Dec/2001 Jan/2002 Feb/2002 Mar/2002 Apr/2002 May/2002 Jun/2002 Jul/2002 Aug/2002 Sep/2002 Oct/2002 Nov/2002 Table 1.13 - Continued 1-year 3-Year All Funds Category All Funds Category -2.599** -2.577** -2.602** -2.588** (0 .0001) -2.606** (0 .0001) -2.450** 5-Year All Funds Category -3.128** -3.138** (0.0001) (0 .0001) (0 .0001) (0 .0001) ( 0 .0001) -2.574** -2.572** -2.557** -3.034** -3.034** (0 .0001) (0 .0001) (0.0001) ( 0 .0001) (0 .0001) 2 . 868 * * -2.871** -2.437** -2.442** -2.430** - ( 0 .0001) (0 .0001) ( 0 .0001) ( 0 .0001) (0 .0001) ( 0 .0001) -2.548** -2.531** -2.528** -2.526** -2.912** -2.920** ( 0 .0001) (0 .0001) (0 .0001) ( 0 .0001) (0 .0001) ( 0 .0001) -2.778** -2.756** -3.191** -3.188** (0 .0001) -2.764** (0.0001) -2.775** -2.753** (0.0001) -2.790** (0 .0001) -2.828** (0 .0001) -2.676** (0 .0001) -2.518** (0 .0001) -2.487** (0 .0001) -2.525** (0 .0001) -2.229** (0 .0001) -1.032** (0 .0001) -1.067** (0 .0001) -0.547** (0 .0001) -0.461** (0.001) -0.492** (0 .0001) -0.487** (0 .0001) 0.199 (0 .112) -0.059 (0.636) -0.365** (0.003) 0.120 (0.334) -0.254* (0.041) (0 .0001) ( 0 .0001) ( 0 .0001) -2.760** -3.164** -3.169** - -2.762** (0.0001) (0 .0001) (0 .0001) ( 0 .0001) ( 0 .0001) -2.794** -2.804** -2.789** -3.079** -3.091** ( 0 .0001 ) (0 .0001) (0 .0001) ( 0 .0001) (0.0001) -2.653** -2.657** -2.645** -2.905** -2.913** ( 0 .0001) (0 .0001) (0 .0001) (0 .0001) ( 0 .0001) -2.502** -2.504** -2.488** -2.776** -2.784** ( 0 .0001) ( 0 .0001) (0 .0001) ( 0 .0001) (0 .0001) -2.467** -2.460** -2.457** -2.772** -2.775** ( 0 .0001) (0 .0001) (0 .0001 ) (0 .0001) (0 .0001 ) -2.508** -2.497** -2.491** -9 770 * * -2.780** (0.0001) (0 .0001) (0 .0001) (0 .0001) ( 0 .0001) -2.243** -2.231** -2.233** -2.778** -2.794** (0 .0001) (0 .0001) (0 .0001) (0 .0001) ( 0 .0001) -1.050** - 1. 022 * * -1.039** -1.145** -1.160** (0 .0001) (0 .0001) ( 0 .0001) (0 .0001) (0 .0001) -1.081** -1.058** -1.076** -1.141** -1.157** (0 .0001) (0 .0001) ( 0 .0001) (0 .0001) (0 .0001) -0.570** -0.555** -0.567** -0.545** -0.568** (0 .0001) (0 .0001) (0 .0001) ( 0 .001) (0 .0001) -0.480** -0.466** -0.484** -0.488** -0.504** ( 0 .001) (0 .001) ( 0 .001) ( 0 .001) ( 0 .001) -0.510** -0.484** -0.508** -0.645** -0.656** ( 0 .0001) (0 .0001) (0 .0001) ( 0 .0001) ( 0 .0001) -0.496** -0.481** -0.492** -0.454** (0 .0001) (0 .001) (0 .0001) ( 0 .001) 0.201 0.215 (0.087) -0.052 (0.677) -0.362** (0.004) -0.112 (0.366) -0.249* (0.046) 0.202 (0.107) -0.067 (0.590) -0.368** (0.003) -0.123 (0.322) -0.259* (0.037) 0.247 (0.070) -0.035 (0.794) -0.372** (0.005) -0.136 (0.304) -0.226 (0.087) -0.473** (0.001) 0.243 (0.075) -0.042 (0.756) -0.361** (0.007) -0.134 (0.313) -0.238 (0.073) (0.109) -0.068 (0.585) -0.368** (0.003) -0.124 (0.318) -0.263* (0.034) 60 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 1.14 Regression Results - Redemptions This table presents results from a weighted least squares model on the logit transformation of the proportion of the fund redeemed in terms of dollars as defined in equations 2 and 3. The weights come from the minimum logit chi-square method as defined in equation 4. The independent variables are a dichotomous variable equal to one if the fund is in the top performing decile of its Momingstar category and zero otherwise (Winner); a dichotomous variable equal to one if the fund is in the top performing decile of its Momingstar category and zero otherwise (Loser); the standard deviation of monthly returns for the fund over the three prior years (3 Yr Std Dev); the age of the fund in years (Fund Age); the expense ratio for the fund (Expense Ratio);and the natural log of the total net assets of the fund (Log TNA). Fixed time effects are included with month dummy variables, t-statistics are in parentheses. * and ** represent the 5 and 1 percent statistical significance levels respectively. 1-Year 5-Year 3-Year All Funds Category All Funds Category All Funds Category Intercept -5.23** (-69.26) -5.12** (-67.11) -5.11** (-67.33) -5.16** (-67.18) -5.25** (-59.33) -5.10** (-56.77) Winner 0.20** (7.88) -0.05** (-2.75) -0.09** (-4.73) -0.11** (-6.53) -0.23** (-12.96) -0.18** (-9.68) Loser 0.84** (20.60) 0.60** (13.74) 0.53** (14.11) 0.58** (14.21) -0.19** (-2.80) 0.07 (1.18) Fund Age 0.004** (8.91) 0.003** (6.83) 0.004** (7.73) 0.003** (6.00) 0.005** (9.20) 0.002** (4.33) Exp. Ratio 0.15** (4.70) 0.04 (1.12) 0.06* (2.02) 0.03 (0.86) 0.17** (4.62) 0.13 (3.33) 3 Yr Std Dev -0.02** (-17.92) -0.01** (-9.82) -0.01** (-11-95) -0.01** (-7.98) -0.01** (-5.60) -0.01** (-6.91) Log TNA -0.12** (-18.66) -0.13** (-20.16) -0.13** (-20.12) -0.12** (-19.15) -0.13** (-17.67) -0.13** (-17.72) Adj. R2 0.19 0.16 0.17 0.17 0.18 0.17 N 8578 8578 8549 8549 6886 6886 61 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 1.14 - Continued Jan/2001 Feb/2001 Mar/2001 Apr/2001 May/2001 Jun/2001 Jul/2001 Aug/2001 Sep/2001 Oct/2001 Nov/2001 Dec/2001 Jan/2002 Feb/2002 Mar/2002 Apr/2002 May/2002 Jun/2002 Jul/2002 Aug/2002 Sep/2002 Oct/2002 Nov/2002 1-year Category All Funds 0.44** 0.42** (9.67) (9.20) 0.14** 0.12* (2.86) (2.49) 0.41** 0.43** (9.23) (8.80) 0.37** 0.38** (8.02) (7.83) 0.14** 0.14** (2.76) (2.75) 0.07 0.06 (1.27) (1.38) 0.09 0.11* (1.87) (2.25) 0.24** 0.24** (4.97) (5.11) 0.23** 0.19** (4.76) (3.95) 0.12* 0.10 (1.87) (2.40) -0.01 -0.02 (-0.12) (-0.32) 0.29** 0.28** (5.91) (6.20) 0.24** 0.26** (5.78) (6.03) 0.03 0.05 (0.66) (1.05) 0.07 0.09 (1.51) (1.93) 0.14** 0.13** (3.30) (3.02) 0.04 0.03 (0.72) (0.93) 0.04 0.05 (0.82) (1.23) 0.23** 0.21** (5.45) (5.07) -0.04 -0.05 (-0.97) (-1.13) -0.12** -0.12** (-2.69) (-2.68) 0.04 0.01 (0.80) (0.18) -0.16** -0.15** (-3.39) (-3.18) 3-Year All Funds Category 0.45** 0.40** (9.88) (8.75) 0.19** 0.14** (3.87) (2.84) 0.47** 0.42** (10.05) (8.96) 0.42** 0.36** (7.59) (8.75) 0.18** 0.13** (3.60) (2.58) 0.11* 0.06 (2.09) (1-13) 0.10* 0.15** (2.05) (2.95) 0.25** 0.23** (5.28) (4.78) 0.21** 0.19** (4.34) (3.92) 0.11* 0.09 (2.21) (1.71) 0.00 -0.02 (0.05) (-0.32) 0.29** 0.28** (6.14) (5.96) 0.25** 0.25** (5.95) (5.86) 0.03 0.03 (0.57) (0.66) 0.06 0.08 (1.68) (1.45) 0.12** 0.13** (2.87) (2.97) 0.03 0.03 (0.76) (0.79) 0.04 0.05 (0.85) (1-10) 0.22** 0.22** (5.32) (5.27) -0.04 -0.05 (-0.81) (-1.10) -0.12** -0.13** (-2.58) (-2.71) 0.02 0.02 (0.42) (0.36) -0.15** -0.15** (-3.31) ..m e ) . 5-Year A ll Funds Category 0.50** 0.44** (9.88) (8.68) 0.27** 0.21** (4.87) (3.73) 0.55** 0.50** (9.59) (10.53) 0.49** 0.45** (9.30) (8.48) 0.26** 0.18** (4.68) (3.22) 0.18** 0.10 (3.29) (1.78) 0.17** 0.09 (3.09) (1.56) 0.30** 0.21** (5.66) (3.92) 0.26** 0.17** (4.90) (3.16) 0.15** 0.06 (2.67) (1-07) -0.04 0.05 (0.91) (-0.69) 0.37** 0.30** (7.07) (5.70) 0.32** 0.25** (6.96) (5.30) 0.10* 0.02 (1.96) (0.40) 0.13* 0.05 (2.65) (1.01) 0.20** 0.13** (4.34) (2.72) 0.12* 0.04 (2.44) (0.80) 0.12* 0.05 (2.45) (1.09) 0.23** 0.23** (4.95) (5.01) -0.04 -0.05 (-0.70) (-0.91) -0.15** -0.11 (-2.92) (-2.27) 0.02 0.02 (0.33) (0.37) -0.14** -0.15** (-2.70) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 1.15 Regression Results - Exchange Redemptions This table presents results from a weighted least squares model on the logit transformation of the proportion of the fund redeemed in terms of dollars as defined in equations 2 and 3. The weights come from the minimum logit chi-square method as defined in equation 4. The independent variables are a dichotomous variable equal to one if the fund is in the top performing decile of its Momingstar category and zero otherwise (Winner); a dichotomous variable equal to one if the fund is in the top performing decile of its Morningstar category and zero otherwise (Loser); the standard deviation of monthly returns for the fund over the three prior years (3 Yr Std Dev); the age of the fund in years (Fund Age); the expense ratio for the fund (Expense Ratio);and the natural log of the total net assets of the fund (Log TNA). Fixed time effects are included with month dummy variables, t-statistics are in parentheses. * and ** represent the 5 and 1 percent statistical significance levels respectively. 1-Year 3-Year 5-Year All Funds Category All Funds Category All Funds Category -5.18** -5.08** (-48.89) (-47.20) Intercept -5.20** (-56.19) -4.84** (-52.12) -5.00** (-54.11) -4.90** (-52.25) Winner 0.53** (11.31) -0.17** (-6.89) -0.18** (-5.54) -0.08** (-3.22) -0.35** (-13.86) -0.14** (-5.87) Loser 0.62** (15.03) 0.24** (4.98) 0.40** (10.42) 0.06 (1.16) 0.03 (0.43) 0.16* (2.52) Fund Age -0.003** (-5.37) -0.004** (-7.09) -0.004** (-6.41) -0.004** (-6.37) -0.002** (-3.73) -0.004** (-6.32) Exp. Ratio 0.85** (23.66) 0.67** (18.07) 0.76** (21.10) 0.73** (19.57) 0.83** (19.95) 0.80** (18.77) 3 Yr Std Dev -0.003** (-2.65) 0.005** (4.59) 0.001 (L18) 0.01** (4.93) 0.01** (6.37) 0.01** (5.33) Log TNA -0.03** (-4.34) -0.06** (-7.56) -0.05** (-6.47) -0.06** (-7.78) -0.05** (-5.11) -0.05** (-5.33) Adj. R2 0.38 0.36 0.37 0.36 0.39 0.38 N 8083 8083 8055 8055 6419 6419 63 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 1.15 - Continued 1-■year Category A ll Funds Jan/2001 -0.70** -0.63** (-9.22) (-8.26) Feb/2001 -0.81** -0.71** (-9.93) (-8.58) Mar/2001 -0.59** -0.54** (-8.98) (-8.06) Apr/2001 -1.08** -1.02** (-12.33) (-11.53) May/2001 -1.28** -1.24** (-13.57) (-12.93) Jun/2001 -1.49** -1.45** (-15.20) (-14.53) Jul/2001 -1.27** -1.23** (-13.89) (-13.20) Aug/2001 -1.06** -1.04** (-13.47) (-13.01) Sep/2001 -0.34** -0.33** (-5.86) (-5.94) Oct/2001 -0.73** -0.72** (-10.12) (-10.50) Nov/2001 -0.91** -0.82** (-12.56) (-11.08) Dec/2001 -0.52** -0.47** (-9.06) (-7.95) Jan/2002 -0.57** -0.61** (-10.06) (-11.01) Feb/2002 -0.72** -0.71** (-12.47) (-12.01) Mar/2002 -0.52** -0.51** (-9.12) (-8.75) Apr/2002 -0.67** -0.66** (-11-95) (-11.54) May/2002 -0.68** -0.66** (-11.83) (-12.37) Jun/2002 -0.43** -0.41** (-9.02) (-8.40) Jul/2002 0.45** 0.45** (11.88) (11.52) Aug/2002 -0.39** -0.37** (-7.57) (-8.00) Sep/2002 -0.32** -0.34** (-6.70) (-7.00) Oct/2002 0.01 0.00 (0.31) (0.07) Nov/2002 -0.48** -0.45** (-8.70) (-9.47) 3-Year Category All Funds -0.62** -0.54** (-7.08) (-8.05) -0.59** -0.68** (-8.18) (-7.08) -0.41** -0.52** (-7.67) (-5.96) -0.95** -1.03** (-10.68) (-11.58) -1.17** -1.23** (-12.18) (-12.83) -1.40** -1.45** (-14.02) (-14.47) -1.14** -1.22** (-12.21) (-13.09) -1.04** -0.98** (-12.88) (-12.13) -0.27** -0.35** (-6.10) (-4.78) -0.68** -0.75** (-9.50) (-10.45) -0.85** -0.80** (-11.51) (-10.83) -0.49** -0.46** (-7.88) (-8.38) -0.58** -0.58** (-10.36) (-10.13) -0.71** -0.71** (-12.04) (-12.04) -0.52** -0.51** (-8.97) (-8.77) -0.67** -0.66** (-11.72) (-11-43) -0.68** -0.67** (-11.89) (-12.20) -0.44** -0.43** (-8.64) (-8.92) 0.45** 0.45** (11.73) (11.59) -0.37** -0.37** (-7.51) (-7.48) -0.34** -0.34** (-6.95) (-6.90) 0.02 0.01 (0.43) (0.27) -0.44** -0.45** (-8.62) (-8.62) 5-Year Category All Funds -0.62** -0.70** (-7.19) (-7.91) -0.50** -0.62** (-6.69) (-5.49) -0.29** -0.41** (-5.44) (-3.89) -0.88** -0.96** (-8.79) (-9.50) -1.06** -1.16** (-10.57) (-9.80) -1.28** -1.39** (-11-45) (-12.30) -1.14** -1.26** (-12.53) (-11.43) -0.95** -1.07** (-12.34) (-11.00) -0.17** -0.33** (-5.47) (-2.69) -0.62** -0.75** (-9.84) (-8.12) -0.72** -0.85** (-10.72) (-9.11) -0.34** -0.46** (-5.37) (-7.20) -0.53** -0.60** (-9.71) (-8.67) -0.65** -0.71** (-10.18) (-11.14) -0.47** -0.52** (-8.14) (-7.46) -0.61** -0.67** (-9.82) (-10.79) -0.61** -0.68** (-10.10) (-11.13) -0.34** -0.42** (-6.44) (-7.84) 0.49** 0.48** (11.71) (11.39) -0.33** -0.35** (-6.31) (-6.57) -0.36** -0.31** (-6.94) (-5.92) 0.04 0.06 (0.81) (1.19) -0.38** -0.42** (-6.95) (-7.58) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 1.16 Regression Results - Purchases This table presents results from a weighted least squares model on the logit transformation of the proportion of the fund purchsed in terms of dollars as defined in equations 2 and 3. The weights come from the minimum logit chi-square method as defined in equation 4. The independent variables are a dichotomous variable equal to one if the fund is in the top performing decile of its Morningstar category and zero otherwise (Winner); a dichotomous variable equal to one if the fund is in the top performing decile of its Morningstar category and zero otherwise (Loser); the standard deviation of monthly returns for the fund over the three prior years (3 Yr Std Dev); the age of the fund in years (Fund Age); the expense ratio for the fund (Expense Ratio);and the natural log of the total net assets of the fund (Log TNA). Fixed time effects are included with month dummy variables, t-statistics are in parentheses. * and ** represent the 5 and 1 percent statistical significance levels respectively. 1-Year 3-Year 5-Year All Funds Category All Funds Category All Funds Category Intercept -0.96** (-10.68) -1.16** (-13.37) -1.09** (-12.88) -1.52** (-17.89) -0.63** (-6.38) -1.02** (-10.23) Winner 0.20** (8.05) 0.39** (23.90) 0.57** (30.43) 0.53** (35.43) 0.47** (23.95) 0.39** (22.19) Loser -0.03 (-0.43) -0.22** (-3.62) -0.80** (-10.43) -0.53** (-7.92) -0.67** (-6.15) -0.68** (-7.05) Fund Age 0.003** (7.05) 0.007** (14.30) 0.002** (4.08) 0.006** (14.52) 0.001 (1.25) 0.006** (12.47) Exp. Ratio -0.71** (-17.93) -0.47** (-11.90) -0.64** (-17.40) -0.39** (-10.28) -0.77** (-17.47) -0.67** (-14.95) 3 Yr Std Dev -0.02** (-14.20) -0.02** (-20.97) -0.03** (-28.34) -0.03** (-28.65) -0.03** (-25.31) -0.03** (-22.87) Log TNA -0.23** (-30.84) -0.25** (-34.84) -0.20** (-28.27) -0.22** (-31.74) -0.24** (-29.83) -0.24** (-29.42) Adj. R2 0.22 0.26 0.30 0.32 0.30 0.29 N 8764 8764 8726 8726 6869 6869 65 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Jan/2001 Feb/2001 Mar/2001 Apr/2001 May/2001 Jun/2001 Jul/2001 Aug/2001 Sep/2001 Oct/2001 Nov/2001 Dec/2001 Jan/2002 Feb/2002 Mar/2002 Apr/2002 May/2002 Jun/2002 Jul/2002 Aug/2002 Sep/2002 Oct/2002 Nov/2002 Table 1.16 - Continued 5-Year 1-year 3-Year All Funds Category All Funds Category All Funds Category -0.09 0.13** -0.12* 0.02 -0.09 0.00 (2.74) (-2.17) (0.40) (-1.83) (-0.08) (-1.91) 0.04 -0.20** -0.27** -0.09 -0.17** -0.06 (-1.57) (-3.95) (0.88) (-4.47) (-3.12) (-1.08) 0.15** -0.12* -0.01 0.06 -0.18** 0.00 (-3.61) (3.17) (-2.05) (-0.24) (0.08) (1.16) -0.03 -0.17** 0.17** -0.13* -0.02 0.03 (-2.23) (-0.58) (-3.49) (3.47) (-0.47) (0.59) -0.12* 0.20** -0.10 0.08 0.04 0.09 (1.47) (-2.58) (4.19) (-1.78) (0.73) (1.78) -0.07 -0.22** 0.07 -0.25** -0.05 -0.09 (-4.41) (1.39) (-4.23) (-1.08) (-1.14) (-1.78) 0.00 0.02 -0.18** -0.30** -0.14** -0.12* (0.05) (-6.06) (0.43) (-3.22) (-2.41) (-2.71) 0.20** 0.04 0.22** -0.03 0.06 0.06 (3.75) (-0.65) (0.74) (4.73) (1.23) (1.14) -0.11* -0.30** -0.37** -0.09 -0.22** -0.26** (-1.97) (-1.80) (-6.29) (-5.77) (-3.94) (-4.76) 0.19** -0.02 0.22** 0.00 0.04 0.09 (-0.42) (3.59) (0.02) (4.58) (1.73) (0.73) 0.11 0.14** -0.11* -0.07 -0.05 -0.04 (1.92) (-1.96) (2.83) (-0.96) (-0.81) (-1.41) -0.02 -0.21** 0.00 -0.18** -0.14** -0.10 (-0.46) (-3.88) (-3.64) (0.00) (-2.73) (-1.93) 0.17** 0.00 0.23** 0.05 0.10* 0.13** (3.70) (-0.06) (5.62) (2.21) (2.92) (1.13) -0.16** 0.05 0.07 -0.08 -0.11* -0.01 (1.05) (-3.30) (1.68) (-2.58) (-1.71) (-0.22) 0.20** -0.01 0.22** 0.08 0.03 0.11* (4.30) (-0.12) (0.65) (5.33) (2.36) (1.80) 0.28** 0.06 0.31** 0.21** 0.17** 0.23** (6.08) (1.37) (5.09) (7.57) (5.22) (4.06) 0.14** -0.08 0.19** 0.06 0.06 0.12** (3.00) (-1.77) (4.68) (1.33) (1.33) (2.71) -0.08 -0.01 -0.27** -0.05 -0.13** -0.06 (-1.68) (-5.43) (-1.24) (-0.15) (-2.98) (-1.39) -0.07 0.00 -0.12* -0.05 -0.04 -0.06 (-2.44) (-1.22) (0.06) (-1.41) (-0.83) (-1.18) -0.03 0.04 -0.10* -0.02 -0.02 -0.02 (-2.02) (-0.68) (-0.45) (0.86) (-0.40) (-0.53) -0.09 -0.02 -0.03 -0.09* -0.08 -0.08 (-1.75) (-0.60) (-2.05) (-0.50) (-1.75) (-1.65) 0.08 0.13** 0.02 0.07 0.10* 0.07 (1.64) (0.32) (1.55) (3.06) (2.12) (1.61) 0.04 0.04 0.04 0.02 0.05 0.04 (0.90) (0.94) (0.84) ...(,Q.:.46)__ (1.02) (0.81) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 1.17 Regression Results - Exchange Purchases This table presents results from a weighted least squares model on the logit transformation of the proportion of the fund purchsed in terms of dollars as defined in equations 2 and 3. The weights come from the minimum logit chi-square method as defined in equation 4. The independent variables are a dichotomous variable equal to one if the fund is in the top performing decile of its Morningstar category and zero otherwise (Winner); a dichotomous variable equal to one if the fund is in the top performing decile of its Morningstar category and zero otherwise (Loser); the standard deviation of monthly returns for the fund over the three prior years (3 Yr Std Dev); the age of the fund in years (Fund Age); the expense ratio for the fund (Expense Ratio);and the natural log of the total net assets of the fund (Log TNA). Fixed time effects are included with month dummy variables, t-statistics are in parentheses. * and ** represent the 5 and 1 percent statistical significance levels respectively. 1-Year 3-Year 5-Year All Funds Category All Funds Category All Funds Category Intercept -2.11** (-18.36) -1.85** (-15.94) -2.04** (-17.88) -2.00** (-17.16) -1.87** (-14.27) -1.84** (-13.86) Winner 0.58** (14.68) 0.22** (8.11) 0.56** (18.25) 0.26** (10.31) 0.20** (7.12) -0.01 (-0.36) Loser 1.06** (12.83) 0.50** (7.99) 0.19* (2.26) -0.40** (-5.00) -0.52** (-4.39) -0.19* (-2.21) Fund Age 0.002** (3.37) 0.003** (4.65) 0.001 (1.74) 0.003** (4.25) 0.001 (1.12) 0.002* (2.13) Exp. Ratio 0.09 (1.85) 0.04 (0.73) 0.07 (1.57) 0.13** (2.69) 0.08 (1.53) 0.06 (0.99) 3 Yr Std Dev -0.03** (-19.66) -0.03** (-19.15) -0.04** (-21.87) -0.03** (-20.80) -0.04** (-19.72) -0.03** (-18.95) Log TNA -0.28** (-27.92) -0.32** (-31.79) -0.28** (-27.60) -0.31** (-30.64) -0.30** (-26.17) -0.30** (-26.22) Adj. R2 0.45 0.43 0.45 0.43 0.45 0.44 N 7170 7170 7140 7140 5721 5721 67 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Jan/2001 Feb/2001 Mar/2001 Apr/2001 May/2001 Jun/2001 Jul/2001 Aug/2001 Sep/2001 Oct/2001 Nov/2001 Dec/2001 Jan/2002 Feb/2002 Mar/2002 Apr/2002 May/2002 Jun/2002 Jul/2002 Aug/2002 Sep/2002 Oct/2002 Nov/2002 Table 1.17 - Continued 1-year 3-Year All Category All Funds Category -0.66** -0.65** -0.50** -0.47** (-7.88) (-6.06) (-7.99) (-5.65) -0.69** -0.84** -0.90** -0.65** (-9.67) (-7.26) (-9.00) (-6.87) -0.58** -0.39** -0.58** -0.36** (-4.74) (-7.03) (-7.08) (-4.38) -1.14** -1.01** -1.23** -0.97** (-12.05) (-10.54) (-12.91) (-10.20) -1.43** -1.32** -1.58** -1.30** (-14.17) (-12.88) (-15.49) (-12.72) -1.58** -1.45** -1.67** -1.42** (-13.41) (-14.83) (-15.57) (-13.20) -1.32** -1.17** -1.37** -1.11** (-13.26) (-11.62) (-13.79) (-11.13) -1.01** -0.90** -0.98** -0.85** (-9.94) (-11.29) (-10.95) (-9.41) -0.37** -0.37** -0.45** -0.30** (-4.84) (-4.92) (-5.99) (-3.89) -0.53** -0.55** -0.66** -0.48** (-7.04) (-7.08) (-8.66) (-6.25) -0.84** -0.77** -0.88** -0.71** (-9.52) (-10.47) (-11.00) (-8.83) -0.42** -0.32** -0.31** -0.27** (-4.74) (-4.94) (-6.44) (-4.09) -0.64** -0.67** -0.71** -0.57** (-10.88) (-10.27) (-11.54) (-9.24) -0.82** -0.90** -0.80** -0.78** (-12.18) (-13.54) (-11.56) (-12.11) -0.63** -0.72** -0.68** -0.57** (-9.78) (-10.61) (-11.24) (-8.82) -0.74** -0.69** -0.68** -0.66** (-10.59) (-10.65) (-11.53) (-10.21) -0.67** -0.67** -0.76** -0.64** (-10.63) (-10.34) (-11.87) (-9.96) -0.43** -0.43** -0.46** -0.40** (-7.20) (-7.79) (-7.27) (-6.70) 0.41** 0.43** 0.38** 0.47** (8.60) (7.82) (8.39) (9.65) -0.32** -0.32** -0.28** -0.26** (-5.69) (-4.87) (-5.81) (-4.61) -0.33** -0.34** -0.38** -0.30** (-5.64) (-5.69) (-6.57) (-5.12) -0.09 -0.06 -O.ll* -0.05 (-1.72) (-1.11) (-2.00) (-0.93) -0.44** -0.41** -0.43** -0.41** (-7.14) (-7.77) (-7.14) (-7.57) 5-Year All Funds Category -0.61** -0.55** (-5.86) (-6.57) -0.55** -0.63** (-5.27) (-6.03) -0.25** -0.32** (-3.42) (-2.66) -0.89** -0.97** (-8.25) (-9.01) -1.30** -1.20** (-11.31) (-10.49) -1.44** -1.34** (-11.87) (-11.10) -1.12** -1.20** (-11.19) (-10.45) -0.84** -0.93** (-9.60) (-8.66) -0.41** -0.33** (-4.01) (-4.99) -0.53** -0.62** (-7.40) (-6.38) -0.71** -0.81** (-9.28) (-8.23) -0.23** -0.32** (-4.46) (-3.25) -0.64** -0.59** (-9.53) (-8.79) -0.80** -0.85** (-11.00) (-11.75) -0.61** -0.66** (-8.80) (-9.48) -0.74** -0.80** (-11.35) (-10.56) -0.71** -0.78** (-11-16) (-10.21) -0.51** -0.46** (-7.95) (-7.09) 0.41** 0.45** (8.53) (7.70) -0.33** -0.29** (-5.42) (-4.81) -0.34** -0.34** (-5.38) (-5.27) -0.06 -0.09 (-1.65) (-0.99) -0.42** -0.41** (-6.92) (-6.65) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 1.1 - Proportion Redeemed - All Funds The proportion is the value of shares redeemed in each performance decile relative to the value of the share held in that decile at the beginning of each month. Red is redemptions that are not part of an exchange and Exch-Red is redemptions that are part of an exchange. Fund performance is relative to all funds available to investors of the firm that provided the data for the study. One-Year Performance 2.3 2.1 Red - - - Exch-Red 0.9 0.7 0.5 mm Three-Year Performance 1 2 3 4 5 6 7 8 9 10 Five-Year Performance 2.5 2.3 2.1 w— R ed - - Exch-Red 0.9 0.7 0.5 69 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 1.2 - Proportion Redeemed - Morningstar Category The proportion is the value of shares redeemed in each performance decile relative to the value of the share held in that decile at the beginning of each month. Red is redemptions that are not part of an exchange and Exch-Red is redemptions that are part of an exchange. Fund performance is relative to funds in the same Morningstar category available to investors of the firm that provided the data for the study. One-Year Performance 2.5 2.3 Red - - - Exch-Red 0.9 0.7 0.5 Three-Year Performance 2.5 -R e d - Exch-Red 0.9 0.7 0.5 Five-Year Performance 2.5 2.3 2.1 Red - - - Exch-Red 0.9 0.7 0.5 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 1.3 - Proportion Purchased - All Funds The proportion is the value of shares purchased in each performance decile relative to the value of the share held in that decile at the beginning of each month. Pur is purchases that are not part of an exchange and Exch-Pur is purchases that are part of an exchange. Fund performance is relative to all funds available to investors of the firm that provided the data for the study. One-Year Performance 2.5 Pur - - - Exch-Pur 0.5 Three-Year Performance 2.5 2.0 Pur - - - Exch-Pur 1.0 0.5 0.0 Five-Year Performance 2.5 2.0 Pur - - - Exch-Pur 0.5 0.0 71 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 1.4 - Proportion Purchased - Morningstar Category The proportion is the value of shares purchased in each performance decile relative to the value of the share held in that decile at the beginning of each month. Pur is purchses that are not part of an exchange and Exch-Pur is purchases that are part of an exchange. Fund performance is relative to funds in the same Morningstar category available to investors of the firm that provided the data for the study. One-Year Performance 2.5 r 2.0 4Pur - - - Exch-Pur Pi 0.5 0.0 Three-Year Performance 2.5 - 2.0 Pur 1.0 ■I - ;Exch-Pur 0.5 0.0 Five-Year Performance 2.5 2.0 Pur - - - Exch-Pur ill 0.5 0.0 1 2 3 4 5 6 7 8 9 10 72 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 1.5 - Accounts that Liquidate - Redemptions The percentage of redemptions that are not part of an exchange that leave less than $100 in the position is graphed by performance decile. All funds means that performance is relative to all funds available to investors at the firm that provided the data. Category means that performance is relative to funds in the same Morningstar category available to investors at the firm that provided the data. One-Year Performance “ c 0 .3 5 If 0.30 I a ■a o &£ 0.25 0.20 All Funds ®| 0.15 - - - Category 3 f 0.10 | is 0 05 a £ 0.00 Performance by Decile Three-Year Performance 0 .3 5 0 .3 0 \ 0 .2 5 \ I \ \ 0.20 All Funds - - - Category 0 .1 5 : 0.10 - 0 .0 5 - 0.00 Performance by Decile Five-Year Performance All Funds Category 1 2 3 4 5 6 7 8 9 10 Performance by Decile Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 1.6 - Accounts that Liquidate - Exchange Redemptions The percentage of redemptions that are part of an exchange that leave less than $100 in the position is graphed by performance decile. All funds means that performance is relative to all funds available to investors at the firm that provided the data. Category means that performance is relative to funds in the same Morningstar category available to investors at the firm that provided the data. One-Year Performance 0.90 0.80 0.70 -[ All Funds 0.60 Category 0.50 Performance by Decile Three-Year Performance 0.90 0.80 0.70 All Funds 0.60 - - - Category 0.50 0.40 Performance by Decile Five-Year Performance 0.90 0.80 0.70 All F unds • - - C ategory 0.60 -J 0.50 ISf 0.40 Performance by Decile 74 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 2 All Events Induce Variance: Analyzing Abnormal Returns When Effects Vary Across Firms19 2.1 Introduction Over 30 years following its introduction by Fama, Fisher, Jensen, and Roll (1969), the short-horizon event study remains a workhorse of empirical finance. Yet there are two troubling features of the econometric tests reported in many studies. First, widely used test statistics for non-zero mean abnormal returns ignore cross-firm variation in the effects of events. Second, cross-sectional regression analyses of abnormal returns often either ignore expected heteroskedasticity in model disturbances or ignore plausible implications of unexplained variation in effects for the structure of heteroskedasticity. We provide analytical and empirical evidence of the resulting biases and test power for a variety of theoretically robust (unbiased) tests for (1) non-zero mean abnormal returns and (2) non-zero regression coefficients in cross-sectional models of abnormal returns. Our analysis highlights that mean abnormal return tests that are robust to crosssectional variation in event effects should always be used in short-horizon event studies. The standardized cross-sectional test suggested by Boehmer, Musumeci, and Poulsen (BMP, 1991) is a good candidate for a parametric test. It is simple, more powerful than the ordinary cross-sectional test, and generally has power close to that of the more elaborate robust tests that we analyze. Our analysis also highlights that neither ordinary 19 With Scott Harrington. 75 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. least squares (OLS) nor weighted least squares (WLS) with conventional standard errors should be used to draw inferences from cross-sectional regression models of abnormal returns. WLS with robust standard errors and maximum likelihood estimation assuming non-proportional heteroskedasticity may represent useful supplements to OLS with robust standard errors. The typical short-horizon event study first calculates one or more sample mean abnormal returns using market model prediction (forecast) errors on the event day(s) and tests for significance with a t-test or asymptotic Z-test, most often either the “traditional” test (see Brown and Warner, 1980,1985) or the standardized prediction error (SPE) test (e.g., Patell, 1976, and Mikkelson and Partch, 1988). One or more cross-sectional regression models are then estimated to test hypotheses concerning the effects of firm or event characteristics on abnormal returns, generally using OLS, OLS with White standard errors, or WLS using either inverse market model residual standard deviations or forecast error standard deviations as weights (see Figure 2.1). Abundant theory and cross-sectional regression analyses of abnormal returns imply that the effects of most events will vary across firms. Increases in market model disturbance variances on event days are well known to bias conventional tests statistics for mean abnormal returns (e.g., Brown and Warner, 1985; Corrado, 1989; Sanders and Robins, 1991; Campbell and Wasley, 1993; and Cowan and Sergeant, 1996). BMP’s simulations show that “stochastic variation” in effects can badly bias the SPE and traditional tests. They discuss intuitively how cross-firm variation in effects can increase return variances and summarize prior empirical evidence that return variances increase on event days (pp. 254-255). Their introduction states (p. 254): “While we do not discuss 76 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the cause of event-induced variance in this paper, we show that it is necessary to control for variance changes to obtain appropriate tests of the null hypothesis that the average abnormal return is zero.” But the SPE and traditional tests remain prevalent, despite the ready availability of robust tests, such as the ordinary cross-sectional test analyzed by Brown and Warner (BW) and the standardized cross-sectional test proposed by BMP. Perhaps the absence of a model showing the cause of event-induced variance explains why researchers so often ignore it. We provide a model both to show that event-induced variance is always present when there is cross-sectional variation and to provide a sound analytical base for the standardized cross-sectional test.20 The model highlights that unbiasedness of the SPE and traditional tests depends on the twin assumptions that effect size does not vary across securities and that market model disturbance variances do not increase during event periods. Although the latter assumption may often be plausible, the former is not. But it is possible that many researchers regard event-induced variance increases the same as increases in market model disturbance variances on event days. With the exception of BMP, simulation studies of test statistic performance have followed BW (1985): (1) a constant is added to induce abnormal performance, and (2) variance increases are essentially induced by increasing market model disturbance variances (Sanders and Robins, 1991; Corrado and Zivney, 1992; Campbell and Wasley, 1993; and Cowan and Sergeant, 1996). While BMP discuss how cross-firm differences in effect size can increase variance, their abstract indicates that they simulate “stochastic 20 We focus throughout on short-horizon event studies and on parametric tests. Long-horizon studies usually employ cross-sectional standard errors or calendar-time methodologies that should be robust to cross-sectional variation. The available evidence is mixed as to whether non-parametric tests, such as Corrado’s (1989) rank test, are robust to variance increases. Corrado (1989), Corrado and Zivney (1992), Campbell and Wasley (1993), and Cowan and Sergeant (1996) provide evidence of test size and power for a number of non-parametric tests. 77 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. effects” without explicitly mentioning cross-firm variation, and most of the paper simply refers to event-induced variance. We derive the biases in the SPE and traditional tests analytically and show that the ordinary cross-sectional and standardized cross-sectional tests - motivated intuitively in prior work - have a rigorous statistical basis. The ordinary cross-sectional test statistic divides the mean abnormal return by a heteroskedasticity-consistent (HC1) standard error; the standardized cross-sectional test statistic divides the mean SPE by its HC1 standard error (see the Appendix and Davidson and MacKinnon, 1993, p. 554). Given that cross-sectional variation in effect size reduces test power, we also describe and analyze potentially more powerful parametric tests for non-zero means that are implied by the underlying statistical model of abnormal returns and have received little or no attention in prior work: (1) the WLS estimate of mean effect size divided by its HC1 (hereafter “White”) standard error, (2) a test based on maximum likelihood estimation (MLE) that allows for non-proportional heteroskedasticity, and (3) regression tests for non-zero means that condition on relevant explanatory variables. 21 Some papers that mention possible bias in abnormal return tests from cross-sectional variation in effect size focus on test properties in the presence of cross-sectional dependence in abnormal returns (e.g., Collins and Dent, 1984; Sefcik and Thompson, 1986; Karafaith, 1994; but also see Morse, 1984, and Dyckman, Phibrick, and Stephan, 1984). That focus tends to obscure the implications of cross-sectional variation for studies without such dependence. Similarly, although regulatory event studies (e.g., Binder, 1985) often consider and test for possible cross-sectional variation in effect size, the statistical procedures again emphasize cross-sectional dependence. 22 Greene (1997, p. 569) suggests using WLS with robust standard errors given uncertainty concerning the appropriate weights in heteroskedastic regression models when disturbance variance is plausibly related to a particular variable. Naranjo, Nimalendron, and Ryngaert (2000) use WLS with White standard errors in their cross-sectional regression analysis of ex-dividend day returns. Barth and Kallapur (1996) examine the method’s performance in the context of scaling firm variables in cross-sectional regressions with accounting data. BMP analyze a potentially robust test based on the method of moments estimator proposed by Froot (1989), but their simulations suggest that the test is biased. Savickas (2002) proposes a GARCH test for non-zero mean abnormal returns when increases in return volatility during event periods vary across firms and presents evidence that the test is more powerful than the standardized cross sectional test when average effect size increases with volatility. 78 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The prevalence of studies that report the use of OLS without indicating the use of robust standard errors is likewise surprising.23 Cross-firm variation in market model disturbance variances will generally produce heteroskedastic errors in cross-sectional regression models of abnormal returns (see, e.g., Sefcik and Thompson, 1986; Campbell, Lo, and MacKinlay, 1997, p. 174). OLS standard errors will therefore be biased if market model disturbance variances are related to any regressor, such as market capitalization or any other variable related to firm size. With unexplained cross-sectional variation in effect size, we show that the disturbances in cross-sectional regression models may plausibly be characterized by heteroskedasticity that is not proportional to inverse market model forecast error variances (sometimes called “mixed” heteroskedasticity in the econometrics literature; see Goldfeld and Quandt, 1972, and Kennedy, 1985). If so, conventional weighting procedures will not produce homoskedasticity, and WLS standard errors will generally be biased. We conduct BW and BMP type simulations to demonstrate empirically the Type 1 error rates and power of alternative tests for mean abnormal returns in the presence of cross-firm variation in effect size. We analyze 250 samples of 50 stocks and 200 stocks. The simulations confirm severe bias in conventional tests when effect size varies across firms. They indicate very low power for robust tests when the mean effect is 1 percent, much greater power when the mean effect is 2 percent, and excellent power when the mean effect is 2 percent and the sample size is 200. The WLS (White) and MLE tests 23 Published studies often contain little or no discussion of why a particular estimation method was chosen. It’s possible that some studies may neglect to indicate specifically that robust standard errors were used. For studies that report the use of “White” standard errors, it’s seldom clear whether they used the “HC1” version, which divides by degrees of freedom, or the “HC0” version initially proposed by White (1980), which divides by sample size. We use HC1 standard errors throughout (retaining the familiar “White” moniker). 79 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. generally are more powerful than the standardized cross-sectional test, but the power difference generally is not large. Conditioning on a relevant regressor often increases test power, but the increase is only material when the regressor explains a substantial proportion (e.g., 50 percent) of the underlying variation in effect size (i.e., in variation in an event’s impact apart from random noise in estimated abnormal returns). Finally, we provide simulation evidence of Type 1 error rates and power of alternative tests for a non-zero slope in a simple regression model with heteroskedastic errors due to cross-firm variation in both effect size and market model disturbance variances, allowing the regression slope to vary across experiments. The simulations confirm that both OLS and WLS standard errors are biased when we generate disturbances with variances related to the regressor. The theoretically robust procedures analyzed (OLS with White standard errors, WLS with White standard errors, and MLE assuming non-proportional heteroskedasticity) appear biased but much less so than OLS and WLS, especially for 200-firm samples. They have reasonable power to reject the null hypothesis correctly for 50-firm samples and excellent power for 200-firm samples. Tests based on WLS with White standard errors and MLE tend to be more powerful than OLS with White standard errors, especially for the 50-firm samples. Section 2.2 presents a simple model of cross-sectional variation in effect size. Section 2.3 uses the model to illustrate the theoretical bias in conventional tests for mean effects and analyzes theoretically robust tests. Cross-sectional regression tests for mean effects and non-zero slopes are described in Section 2.4. Section 2.5 describes the data and design of our simulations of test size and power; results are presented in Section 2.6. Section 2.7 concludes. 80 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.2 A Simple Model of Cross-Sectional Variation Assume that the market model describes security returns on days without an event: Rjt =(Xj + P j R Mt + £jt ( 1) where Rjt is the day t return for security j (j = 1, 2 , . . . , N), a,- and fy are security specific parameters, R m i is the market return, and Ej is a mean zero disturbance with time invariant variance &l. on non-event days. Security j ’s return on the event day T equals: Rjt = aj +P j R M T+ u j (2) + e jT where Uj is the event’s effect and Ejt is mean zero with variance a j . The abnormal return is: Aj = RjT - & j - Pj^MT where dj (2) and fij are OLS estimates of otj and As t —>oo, d j and converge to aj and . . If uj is a constant, fi, for all j, the abnormal return converges to: Aj = h + £ ]T ~(At,cr£2jT) . (4) If disturbance variance increases on event days, a le]T > a El j , so that a A\ j > a Ejl . Prior J simulation studies document that the SPE and traditional test statistics are biased in that case. A simple and natural assumption that incorporates cross-sectional variation in effect size (and for now focuses on the unconditional distribution of uj) is that uj is drawn from a population with mean jj, and variance cr^., is uncorrelated across firms, and is uncorrelated with e for all j and t (see Morse, 1984). With those assumptions, A j converges to: Aj = ^ J +eJT~(ji,tTli + a ^ ) . (5) As before, if the event-day variance of a security’s market model disturbance is greater than on non-event days, a\, > a \,even if - 0, and test procedures that ignore the variance increase will be biased towards rejecting Ho: = 0. If, however, Uj varies 81 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. across securities so that then a I, > 0, g a , > a 2, even with no event-day increase in market model disturbance variances, i.e., even if a j = a \, for all j. Test procedures that ignore cross-sectional variation in effect size will therefore be biased towards rejecting Ho even if a t2J T = a 2 t j . Given this framework, cross-sectional variation in effect size and event-day increases in market model disturbance variances are qualitatively equivalent. Although there may be little a priori expectation of event-day increases in market model disturbance variances, event day variance increases due to cross-sectional variation in effect size should be pervasive, a point which most studies have overlooked. We focus on the implications of cross-sectional variation in what follows by assuming that g 2t = a e2, for all j . Given that assumption, < = < + < • j = 1, 2, . . . , N (6) Expression (6) indicates that abnormal returns are heteroskedastic, because, at a minimum, market model disturbance variances differ across securities. Although a 2u , may also differ across firms, it could be homoskedastic (i.e., uj is simply a draw from a common distribution with mean assumption that and variance is linearly related to 2 gu 2 ). If g 2. encompasses is heteroskedastic, an the non-proportional (or “mixed”) heteroskedastic error structure examined in the econometric literature (see Goldfeld and Quandt, 1972, and Kennedy, 1985). With that assumption, = Y+ S o2 e. (7) where y and d are parameters. Three special cases of (7)and thus (6) are: 1. y = 0 and8 > 0 =>g 2a . = (1 + 8) 2a .= y + 2. y > 0 and 8 =0 =>g 3. y 0 and 8 >0 => g a = y + (1 + 8) > g 2, g 2, g 2, 82 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Case 1 represents proportional heteroskedasticity: A/s variance is proportional to security j ’s market model disturbance variance. This case is analogous to one considered by BMP (the event-day variance increase is k a j with k constant) and is empirically equivalent to a constant effect size with a proportional increase in market model disturbance variances on the event day (the case considered by BW and Sanders and Robins, 1991). Cases 2 and 3 represent non-proportional heteroskedasticity. A/s variance is linearly related but not proportional to market model disturbance variance. Case 2 encompasses the second case considered by BMP (the variance increase, y, equals k a j ). Because cross-sectional variation in effect size will be plausibly related to firms’ economic characteristics, there is little or no reason to assume that a U j : will be proportional to a j , . Non-proportional heteroskedasticity, or 5 = 0 with y varying across firms, are intuitively more plausible. The implications of predictable variation in effect size can be simply illustrated by assuming that uj is linearly related to a single explanatory variable: Uj = p + k X j' + Vj , (8) where x /is the value of xj for security j minus the mean value of x for the given sample, and vj is a mean zero disturbance uncorrelated with x and e. The abnormal return is then: Aj — p + AXj' + ej (9) where: ( 10) Because x{ is the deviation of xj from the sample mean, E(A/ = p : the intercept in equation (9) is the unconditional mean abnormal return. The expression for a j is analogous to equation (6) for the unconditional variance of Uj. Analogous to (7), if a j y + 8 a j , then a ej j = y + (1 + 8) a cjI . (11) 83 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. As before, special cases of (11) include proportional heteroskedasticity (y = 0) and non­ proportional heteroskedasticity (y > 0). 2.3 Unconditional Mean Abnormal Return Tests 2.3.1 Bias in Traditional and SPE Tests The traditional test statistic for mean abnormal returns is the ratio of the sample mean abnormal return to its estimated standard deviation. The SPE test statistic equals the average ratio of the market model prediction error to its estimated standard error.24 Given the preceding assumptions, it is easy to show how cross-sectional variation biases the SPE and traditional tests. Table 2.1 summarizes the results. 2.3.1.1 Traditional Test The traditional test is based on the sample mean abnormal return: where the variance follows from expression (6). The following statistic will therefore be asymptotically standard normal under Hq: ( 12) 24 Patell (1976) introduced the SPE test. Collins and Dent (1984) and Sanders and Robins (1991) show that the SPE test is equivalent to testing the significance of a weighted mean abnormal return where the weight for security j is the inverse of its market model forecast error standard deviation. For a single event day, the traditional and SPE tests are equivalent to Campbell, Lo, and MacKinlay’s (1997, p. 162), 7; and J2 tests, respectively. Simulations generally suggest that the traditional test is less powerful than the SPE test (BW, 1980, 1985; BMP, 1991). Some studies calculate the SPE and traditional tests using market model residual standard deviations rather than forecast error standard deviations. We use forecast error standard deviations throughout. 84 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. where a l and a l are the sample (cross-sectional) averages of a l and a \ ' . The traditional test statistic, which is assumed to be asymptotically standard normal in applied work, is: Z r^ V V -jL (13) ] 0. If returns are not normally distributed, thenumerator and denominator ofZTrad are not independent (see, e.g., Marais, 1984). Although the finite sample properties of ZTrad are unknown absent an explicit distributional assumption, as t —» °° it converges to: ZM = W - ^ . (14) ZTrad has zero expectation under the null hypothesis, but its variance is: 1 ' (15) With cross-sectional variation in effect size {of, > 0), the traditional test statistic will Uj have greater variance than a standard normal variate and is therefore biased towards rejecting Ho. The larger cr„ is in relation to cr| , the larger are the variance and bias. Table 2.1 shows 0zrarf for a U 2j = y + S a 2Ej and for the special cases considered by BMP. 2.3.1.2 Standardized Prediction Error (SPE) Test Given cross-sectional variation in effect size, the following statistic is asymptotically standard normal: 85 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. whereas the SPE test statistic, which is assumed to be asymptotically standard normal in applied work, is: ( \ 1 y Aj N j °e, (17) where Ajl a e is the standardized prediction error and a £ is the market model forecast error standard deviation. As t —» °°, zs converges to: ' l y A ' N j1° eeJ ( 18) with mean zero under Ho and variance: OZ = 1 + N ; cr > 1 (19) Z— is thus biased towards rejecting Ho when cr„ . > 0. The larger is in relation to a l ,, the larger are the variance and bias. Comparing expressions (15) and (19), the SPE test statistic’s bias will tend to be more severe than the traditional test statistic’s bias, because Jensen’s inequality implies that E (l/a l ,) > 1/ E (a l )• Table 2.1 shows fT |_ for a l. = 7 + 0 and a ^ > 0, the robust (unbiased) tests that consider variation in across securities generally are more powerful than the ordinary cross-sectional test, which does not. However, power for the robust tests when (A = 1% is quite low for samples of size 50, especially in the plausible case of non-proportional heteroskedasticity (middle panel). For samples of 50 (200) firms, a mean effect size of 1%, and non­ proportional heteroskedasticity, the standardized cross-sectional test correctly rejects the null hypothesis at the 5% significance level only 24% (63%) of the time. The robust tests are considerably more powerful when the mean effect size is 2%. With non-proportional heteroskedasticity, the null hypothesis is correctly rejected at the 5% significance level in 65% (99%) of the 50-firm (200-firm) samples. The corresponding rejection rates for the intuitively less plausible case of proportional heteroskedasticity are 94% and 100%. 95 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.6.2 Cross-Sectional Regression Tests 2.6.2.1 Conditional Tests for Mean Abnormal Returns Table 2.6 shows empirical rejection frequencies for the theoretically robust test statistics for conditional mean abnormal returns at a nominal test size of 5% when disturbance variance is unrelated to the regressor. OLS and WLS results are not reported because they might be misleading. While OLS and WLS standard errors are unbiased when heteroskedasticity is unrelated to the regressors, that assumption generally will not be satisfied. When the mean effect size is zero, all of the tests are reasonably well specified. The results for R2 = 0 are naturally nearly identical to those for the corresponding unconditional tests shown in Table 2.5. When the mean effect size is 1% and a 2_= (T2 , there generally is no increase in power (rejection rates) as the model R2 increases from 0 to 10%. The rejection rate declines in some instances, presumably due to imprecise estimation of the relatively small slopes. There generally is some increase in test power as the model R2 increases from 0 to 25%. When heteroskedasticity is non-proportional, the greatest power increase is for the WLS (White standard errors) and MLE tests for samples of size 200, where, for example, the rejection frequency for WLS (White) is 70% when R2 = 25% compared with 63% for R2 = 0 (and for the unconditional WLS test; see Table 2.5). When the mean effect size is 1%, a 2. = a 2 , and/?2 = 50%, power is materially greater than when R2 = 0 (e.g., 82% vs. 63% for WLS with White standard errors and 200-firm samples). When the mean effect size is 2% and the sample size is 200, conditioning on xj is irrelevant because the power is near 1 for the unconditional tests. Otherwise, and as was true for the related unconditional tests, the WLS (White) and MLE tests, which consider a 2,, generally are materially more powerful than OLS (White). The results suggest that conditional tests for mean abnormal returns will likely be more powerful than unconditional tests in applications where a material proportion of cross-sectional variation in effect size is predictable with a well-specified model. The 96 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. potential power increase in practice may often be modest, however, given the relatively low power increase for the simulations when the model R2 is no more than 25%. i?2s for variations in effect sizes in applied work may often be relatively small. Any benefits from using conditional tests would also hinge on the assumption that the cross-sectional model is well specified. 2.6.2.2 Regression Slope Tests The first panel of Table 2.7 shows empirical rejection frequencies of test statistics for the estimated regression slope (A) at a nominal test size of 5% when disturbance variance is unrelated to the regressor and /r = 1%. Using /t = 0 and fi = 2% produced similar results. When = [...]... gives information comparing investors in this sample to mutual fund investors in general Panel A of the table shows that in 2000, 83.2% of the holdings in my sample are in equity funds, 6.7% are in fixed income funds and 10.1% are invested in balanced funds The percentages for 2001 shown in Panel B are similar The distribution of assets for investors in my sample is similar to how investors in general... aversion implies that investors want to avoid admitting that their original purchase decision was a mistake, so they avoid realizing losses and instead sell winning funds Shefrin and Statman (1985) call selling winners while holding losers the disposition effect Grinblatt and Kelohaiju (2001) show that Finnish investors’ behavior is consistent with the disposition effect When combined, representativeness... allocate assets Considering the funds included in Momingstar as of December 31, 2000, load fund investors have 85.4% of their assets in equity funds, 9.4% in fixed income funds, and 7 Alexander, Jones, and Nigro (1998) report investor characteristics based on a survey of mutual fund investors They find investors to be slightly younger but to have higher net incomes than the investors in my sample Alexander,... fund investors use the performance of other funds as reference points Capon, Fitzsimons, and Prince (1996), for example, find that investors’ most important information source when making decisions is published performance rankings If investors base decisions on fund rankings, then they would label a fund a loser if it has performed poorly against its peers even if the investor has an unrealized gain... rise to investors buying and selling winners, while holding losers There are at least three reasons why investors working with a financial adviser might exhibit different behavior than investors that don’t pay a load and make their own investment decisions.2 The first two reasons are related to the actions of the investor 1Many factors are associated with negative performance persistence Grinblatt... relative to other funds within the same Momingstar category that are available to investors in the sample Funds are deemed winners (losers) if their performance ranks in the top (bottom) decile over the past one, three, or five years (each time period is considered independently) The results indicate that the load investors in my sample act in a manner similar to the no-load investors in Barber, Odean, and... entire position in order to eliminate all connection with the poor performer In addition, since investors find selling losers to be painful, they will want to redeem the entire position so that they will only experience the pain once.6 1.4 Data The data are provided by a national full-service brokerage firm and include all mutual fund transactions during 2001 and 2002, a list of all funds in each account... of buying funds That is, they are more likely to buy past winners The evidence on the selling behavior are mixed These investors are more likely to sell funds in the very best performance decile, but I do not find that investors are less likely to redeem funds in the worst performance decile than funds in performance deciles two through nine Therefore, while there is evidence consistent with investors... Sirri and Tufano (1998), and Fant and O’Neal (2000) find that individual investors buy top performing funds but hold underperforming funds These results suggest that buying and selling winners while holding poor performers is common at least among some investors While this literature provides information on how past performance affects which funds investors buy and sell, it does not provide evidence... to define winners and losers, but it has the following general form: Redf,t (Purchf,t) = «o + Pi Winner f,t + P2 Loser f;t + P3 FundAge fjt + (34Expense f,t + P5 3Yr Std Dev + PglnTotalValuer + P7 InTNAf>t + 23 Month Dummies + £f,t , f = 1 , , n (1) Winner f>tis a binary variable equal to one if fund f is in the top performing decile ranked either against all funds or other funds in the Momingstar