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

UMI Number: 3098705

UMI

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© by David G Shrider, 2003 All Rights Reserved

To Betsy

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

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

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,

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

Table of Contents

Dedication iii

Acknowledgements iv

A bstract .vi

List of T ab les x

List of F ig u res xii

Chapter 1 - How Does Past Performance Affect Load Mutual Fund Investor Behavior? 1.1 Introduction 1

1.2 Mutual Fund In d u stry 6

1.3 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

1.4 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

1.5 R e su 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 T rading? 23

1.5.4 Regression Analysis - How does Performance Affect the Size of T rad es? 27

1.5.5 Robustness C h eck s 31

1.6 D iscussion 35

1.7 Sum m ary 37

1.8 References for Chapter 1 38

Chapter 2 - All Events Induce Variance: Analyzing Abnormal Returns When Effects Vary Across Firms 2.1 Introduction 75

2.2 A Simple Model of Cross-Sectional Variation 81

2.3 Unconditional Mean Abnormal Return Tests 84

2.3.1 Bias in Traditional and SPE Tests 84

2.3.2 Theoretically Robust T e s ts 86

2.4 Cross-Sectional Regression Tests of Conditional Means and Slopes 8 9 2.5 Data and Simulation Design 91 2.6 Empirical Results Q3

2.6.1 Unconditional Tests for Mean Abnormal R etu rn s 94

2.6.2 Cross-Sectional Regression Tests 96

2.7 Sum m ary 98

2.8 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

2.9 References for Chapter 2 102

List of Tables

1.1 Example Sales Charge and Commission Structure 42

1.2 Account Characteristics 43

1.3 Investor Demographics 45

1.4 Holdings by Asset Class 47

1.5 Transaction D ata 48

1.6 Redemptions by Return Deciles .49

1.7 Exchange Redemptions by Return D eciles 50

1.8 Purchases by Return Deciles 51

1.9 Exchange Purchases by Return Deciles .52

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 67

2.1 Variances and Mean Abnormal Return Test Statistics that Ignore Cross-Sectional Variation in Effect S iz e 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 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

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 l2.8 Summary Statistics for Mean Abnormal Return Test Statistics When

Mean Effect Size is Z ero 112

2.9 Empirical Rejection Frequencies for Mean Abnormal Return Test

Statistics 1132.10 Empirical Rejection Frequencies of Robust Test Statistics for

Conditional Mean Abnormal Return (Regression Intercept) 114

List of Figures

1.1 Proportion Redeemed - All Funds 69

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 .74

2.1 Estimation M ethods 115

2.2 Sample Size Cumulative Frequency .116

2.3 Cross-Sectional Heteroskedasticity Illustration 117

2.4 Type 1 Error R ates 118

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,

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

1 Many 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.

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

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

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

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

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 o f years (often

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

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

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 IssuesLess-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 no- load 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

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

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

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 averaging1.6 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

($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

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

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

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 three- year history in Momingstar, because I use three-year standard deviation of total returns as

1490, and 1220 observations are eliminated for redemptions, exchange redemptions, purchases and

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

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 1 0 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

fDR: = 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

f f

NP and DP are defined in a similar way for purchases

1, 1 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

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

XX DH,ft

feD it i _ 2 _ _

f i 1 , 1 for month t

PH^ = — = proportion of the value of shares held in decile k

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 (one- year performance compared against all funds as shown in Figure 1.1) has a proportion

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

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>t is 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 + (34 Expense f,t

+ P5 3Yr Std Dev + PglnTotalValuer + P7InTNAf>t + 23 Month Dummies + £f,t , f = 1 , , n (1)Winner f>t is 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

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>t is 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 InTotal Value 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 InTotal Value fjt is positive in all specifications Because InTotal Value 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

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

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

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: