FRB Finance and Economics Discussion Series Screen Reader Version The Economics of the Mutual

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FRB Finance and Economics Discussion Series Screen Reader Version The Economics of the Mutual

December 9, 2008

Board of Governors of the Federal Reserve System

Keywords: Mutual fund, scandal, market timing, late trading, asset management, dilution, alpha

Abstract:

I examine the economic incentives behind the mutual fund trading scandal, which made headlines in late 2003 with news that several asset management companies had arranged to allow abusive—and, in some cases, illegal—trades in their mutual funds. Most of the gains from these trades went to the traders who pursued market-timing and late-trading strategies. The costs were largely borne by buy-and-hold investors, and, eventually, by the management companies themselves.

A puzzle emerges when one examines the scandal from the perspective of those management companies. In the short run, they collected additional fee revenue from arrangements allowing abusive trades. When those deals were revealed, investors redeemed shares en masse and revenues plummeted; management companies clearly made poor decisions, ex post. However, my analysis indicates that those arrangements were also uneconomic, ex ante, because—even if the management companies had expected never to be caught—estimated revenue from the deals fell well short of the present value of expected lost revenues due to poor performance in abused funds.

Why some of the mutual fund industry’s largest firms chose to collude with abusive traders remains something of a mystery. I explore several possible explanations, including owner-manager conflicts of interest within management companies (between their shareholders and the executives who benefitted from short-term asset growth), but none fully resolves the puzzle. Management companies’ decisions to allow abuses that harmed themselves as well as mutual fund shareholders convey a broader lesson, that shareholders, customers, and fiduciary clients be cautious about relying too heavily on firms’ own self-interest to govern their behavior.

1 Introduction

The scandal that rocked the mutual fund industry beginning in late 2003 centered on abusive trades that reaped outsized returns for selected investors, particularly hedge funds, at the expense of buy-and-hold mutual fund shareholders. In a September 3, 2003 complaint, New York State Attorney General Eliot Spitzer alleged that several mutual fund firms had arrangements allowing trades that violated terms in their funds’ prospectuses, fiduciary duties, and securities laws. Subsequent investigations showed that at least twenty mutual fund management companies, including some of the industry’s largest firms, had struck deals permitting improper trading.

One common explanation for this behavior is that management companies had put self-interest ahead of fiduciary responsibilities to shareholders, since the deals that allowed abusive trades boosted revenues. In contrast, I find that, in facilitating trades that cut into their mutual funds’ performance, management companies acted against their own interests —even if they had thought that they would never be caught.

This conclusion arises from an exploration of the economics of the mutual fund trading scandal from the perspective of the management companies. I compare the expected present value of the revenues and costs associated with deals allowing abusive trades. Costs included the expected consequences of getting caught in violating fiduciary duties—official penalties, civil litigation outlays, and the loss of future fee revenues because investors would likely respond by redeeming shares—weighted by the likelihood of getting caught. But management companies incurred other costs that would have arisen even if the breach of fiduciary duties had never been detected, because, as I show, the trading abuses substantially impaired mutual fund returns. Subpar performance would diminish expected future fee revenues that are based on assets under management because lower returns would slow asset growth through capital gains and also reduce projected net inflows from investors.

I find that, in expected present-value terms, the performance-related costs of the trading abuses—costs that management companies would have incurred even if the wrongdoing had never been revealed—easily outweighed the revenues that these companies garnered by allowing abuses. Moreover, professional asset managers should have foreseen these revenues and costs when they struck deals to allow trading abuses. Thus, even if management companies had never expected to be caught, they made self-destructive decisions in allowing improper trading to hurt performance. Of course, the additional expected costs of getting caught should have made the ex ante decision even easier: Working with abusive traders would not pay.

My findings notwithstanding, state officials and the SEC have alleged that at least twenty firms, including some of the industry’s largest asset managers, elected to collude with abusive traders and share in the short-term gains they generated. That decision proved disastrous to many of those firms. Exactly why they made this choice remains something of a puzzle. Previous research has focused on fiduciary conflicts of interest between mutual fund investors and asset management firms, but by showing that these firms acted against their own interests, my results indicate that such conflicts alone cannot explain the scandal. Agency conflicts within asset management firms—between their owners and managers—may have been part of the problem, although that explanation falls short in some respects, as some principals with substantial ownership interests in their firms chose to allow and facilitate trading abuses that harmed their own interests. Myopia or impatience might have played a role, as the costs of the trading arrangements were incurred with some delay compared with the revenues they generated, but only very high discount rates would have rationalized collusion. It is worth noting that the decisions at issue were not merely the actions of rogue employees; official complaints and settlement documents indicate that senior executives at almost every firm (and board chairs, chief executive officers, or presidents at most) approved of deals with abusive traders, and in many cases, mutual fund executives aggressively sought such arrangements.

My results argue for a reinterpretation of the lessons of the mutual fund scandal; this was not a simple instance of self-interest trumping fiduciary duty. Shareholders, customers, and fiduciary clients should be cautious about relying too heavily on firms’ own self-interest to govern their behavior—for example, by assuming that firms will not engage in malfeasance if the expected present value of penalties outweighs any immediate benefit. One salient (and ironic) example of the consequences of overconfidence in private self-interest is the mutual fund scandal itself. According to a U.S. General Accountability Office (GAO) report that examined why the Securities and Exchange Commission (SEC) had not aggressively examined mutual fund companies for trading abuses prior to the New York Attorney General’s complaint:

Prior to September 2003, SEC did not examine for market timing abuses because agency staff viewed market timing as a relatively low-risk area and believed that companies had financial incentives to establish effective controls, that is, by maximizing fund returns in order to sell fund shares (U.S. Government Accountability Office, 2005 ). My analysis indicates that the SEC was correct about those incentives but not about their effects on behavior.

2 Background and literature: Market timing and late trading

An investor who purchases mutual fund shares for less than their fair value (a timer) gains the difference between the actual value and the price paid. 1 Because mutual fund shares are claims on a common pool of assets, the timer’s gain is just a transfer of wealth from other mutual fund shareholders. By creating new shares in the common pool and selling them for less than their proportional worth, the management company dilutes the value of existing shares. 2

The potential for dilution of mutual fund shareholders’ wealth has been understood at least since the 1930s, although dilution vulnerabilities and the mechanisms for exploiting them have changed over time. The Investment Company Act of 1940 included provisions intended to curb rampant exploitation—especially by brokers who sold mutual fund shares—of discrepancies between share prices and values that arose because mutual fund net asset values (NAVs) were typically set based on the previous day’s closing prices (U.S. Securities and Exchange Commission, 1940 ; United States v. National Association of Securities Dealers, Inc. et al. 1975 ). In 1968, the SEC adopted rule 22c-1, which mandated forward pricing, that is, funds had to execute transactions at the next net asset value calculated after the order was received, to eliminate investors’ ability to transact at stale prices that deviated from current market values (Barbash, 1997 ).

Yet, even with forward pricing, mutual fund NAVs can be stale if they are based on market prices of securities that have not recently traded. World equity funds are particularly vulnerable when they value foreign stocks at their most recent overseas-exchange market-close prices, which can be more than 12 hours old by 4 p.m. Eastern time when most U.S. mutual funds compute their NAVs. But prices for other types of funds, such as those that invest in domestic small-cap stocks or bonds that trade infrequently, can also be stale when the most recent transactions as of market close do not incorporate up-to-date information. Transactions in mutual fund shares to exploit these stale and predictable prices came to be known as market timing. 3

Investment management firms have recognized that dilutive trades are possible even with forward pricing at least since 1980, when the Putnam Funds sought and received from the SEC assurance that it would not take action against Putnam for using a fair value determination to value foreign stocks if some extraordinary event occurred between the daily closing of a foreign stock exchange and 4 p.m. Eastern time (U.S. Securities and Exchange Commission, 1981 ; Ropes & Gray, 1980 ). This would, according to Putnam, avoid the abuses which forward pricing, as set forth in Rule 22c-1, was intended to limit. SEC letters to the Investment Company Institute in 1999 and 2001 went a step further in urging funds to fair value securities to eliminate stale pricing and protect long-term fund investors from dilution (Scheidt, 2001 ,1999 ). By 2000, many mutual funds—including those in families that were later caught up in the scandal—had included prospectus language indicating that they prohibited market timing.

As early as 1995, however, several mutual fund management companies began colluding with market timers to permit extensive dilutive trades, often as part of quid-pro-quo arrangements. For example, asset management firm ABC might stipulate that a hedge fund seeking market-timing access to the ABC international equity fund must maintain a stable investment (sticky assets) in one of the ABC bond funds. The sticky assets would generate a steady stream of management fee revenue for ABC, and the hedge fund would obtain an agreed-upon timing capacity, that is, a maximum volume of market-timing transactions for a specified time period. Timing capacity was often a multiple of the sticky assets; multiples of five and ten were common. To improve the profitability of market timing in their mutual funds, some management companies also disclosed non-public portfolio composition data and waived redemption fees—which were designed in part to prevent market timing—for selected customers (see, for example, U.S. Securities and Exchange Commission (2003a ,2004c) ; Attorney General of the State of New York (2004a) ; U.S. Securities and Exchange Commission (2004b ,a) ; Attorney General of the State of New York (2005b ,a) ).

Worse yet, a handful of portfolio managers and mutual fund executives abusively traded their own mutual funds (U.S. Securities and Exchange Commission, 2003c ,2004c ; Massachusetts Securities Division, 2003 ; Tufano, 2005 ). And some mutual fund firms (and several brokers and transactions-processing firms) facilitated late trading, that is, transactions in mutual fund shares at previously -determined NAVs (see, for example, U.S. Securities and Exchange Commission (2007b) ; Attorney General of the State of New York (2005a) ). Late trading, like market timing, seeks to exploit stale prices and dilutes buy-and-hold investors’ wealth, but late trading also violates rule 22c-1, and is thus illegal.

Well before the scandal broke, researchers began documenting evidence of widespread market timing, particularly among world equity funds. Bhargava et al. (1998) described the profitability of simple market-timing strategies in international equity funds, and Chalmers et al. (2001) documented exploitable opportunities in small-cap domestic equity funds as well. Boudoukh et al. (2002) provided detailed strategies for market timing several specific international equity funds and noted: Currently, we know of at least 16 hedge fund companies covering 30 specific funds whose stated strategy is `mutual fund timing.’ Although Goetzmann et al. (2001) also documented stale prices in world equity funds, they found that market-timing flows were causing only minor dilution of returns. In contrast, Greene and Hodges (2002) found evidence of substantial dilution in international equity funds, particularly in those with high flow volatility. Zitzewitz (2003) provided estimates of dilution across a broader range of funds, including domestic mid- and small-cap equity funds and precious metals funds, as well as world equity funds. He argued that management companies’ sluggish response to a problem as costly and prevalent as abusive trading reflected an owner-manager conflict of interests between the companies and mutual fund shareholders. Moreover, foreshadowing the thesis of this paper, Zitzewitz provided a back-of-the-envelope calculation to suggest that management companies might be acting against their own interests in allowing abusive trades.

Even so, the extent of management companies’ collusion with abusive traders was apparently well-concealed before September 3, 2003. On that day, the New York Attorney General issued a complaint against a hedge fund, Canary Capital Partners, which had arrangements permitting extensive market timing and late trading at several mutual funds. The scandal broadened in the following months and eventually ensnared 21 mutual fund firms, which together managed 22 percent of industry assets in late 2003.

The scandal revelations prompted a flurry of research. Several papers surveyed the wrongdoing and offered explanations and remedies. Mahoney (2004). assuming that management companies had acted in their own interests in colluding with abusive traders, attributed the wrongdoing to basic conflicts of interest between mutual fund investors and the companies and individuals that organize, sell and provide services to mutual funds. Kadlec (2004) provided a brief overview of the vulnerabilities of mutual funds to market timing and a simple framework for addressing them. Greene and Ciccotello (2004) showed that the dilution losses of buy-and-hold investors depend on the cash management policies of portfolio managers, and Zitzewitz (2006) estimated the dilutive impact of late trading, which was not addressed in the academic literature before the scandal broke. Qian (2006) examined the relationship between wrongdoing and fund family attributes, such as governance, and found that families for which net flows were less sensitive to past performance were more likely to have been tainted by the scandal. 4 That conclusion is relevant to my analysis, as it suggests that ex ante costs of colluding might have been lower for families that chose to do so. Nonetheless, I find that even for the tainted fund families themselves, that choice was a very poor one.

Other research has focused on the penalties that markets and government officials imposed on mutual fund firms that were caught allowing abusive trading. Houge and Wellman (2005) found that in the three days following news of wrongdoing by a management company, its stock price (or that of its parent firm) dropped on average by more than five percent, and that, relative to their untainted competitors, tainted firms’ assets under management had fallen by 13 percent in the first six months following the scandal revelations. Choi and Kahan (2006) showed that stiffer official penalties and more press coverage were associated with larger net redemptions from tainted mutual fund families, and that within a year of the scandal revelations, net redemptions from tainted families had reached 19 percent of pre-scandal assets. According to Schwarz and Potter (2006). net outflows continued well into the second year after the scandal broke. Zitzewitz (2007b) found that the New York Attorney General’s involvement in settlement negotiations raised the ratio of penalties to dilution damage by roughly three- to four-fold.

I employed annual, monthly, and daily data from the Center for Research in Securities Prices U.S. mutual fund database (CRSP) to compute monthly fund flows, returns, and distributions from 1991 to 2007. To compute net new cash flow, that is, flows net of reinvested distributions, I also used data from the Investment Company Institute on the fractions of distributions reinvested by mutual fund investment objective. I obtained daily mutual fund assets information from TrimTabs and share-price and distribution data from CRSP and Yahoo! Finance to compute estimates of the dilution due to trading abuses. Data for calculations of management companies’ weighted average costs of capital came from Compustat and CRSP.

To identify the mutual funds that were subject to arrangements allowing market timing and late trading abuses, I used four types of sources. The first was published lists of firms that were tainted by the scandal, such as The Wall Street Journal’s Mutual Fund Scandal Scorecard, which tracked mutual fund complexes, investment advisers, brokers, hedge funds, and others who allegedly benefitted from trading abuses. Houge and Wellman (2005). Qian (2006). and Zitzewitz (2007b) also provide lists of the firms that were caught up in the scandal. The second, most important resource was state and SEC filings, including complaints, cease-and-desist orders, assurances of discontinuance, proposed plans of distribution, and other documents. These filings were essential in identifying the individual mutual funds that were subject to arrangements allowing abusive trades. A third resource was prospectus updates and published summaries of internal reviews regarding abusive trading that were provided by the mutual fund management companies themselves. Finally, I used press reports to identify an additional handful of funds not mentioned in official documents and to pin down the timing of the revelations about wrongdoing at different fund families.

4. 1 Abused and tainted mutual funds.

I label a mutual fund abused if, according to the sources listed above, its management company entered into an arrangement allowing the fund to be market timed or late traded or if the fund was abused by principals or employees at its management company. 5 Abused funds include those that were subject to abusive trades as part of quid-pro-quo arrangements that required investors to park sticky assets within the fund family—for example, at another mutual fund or a hedge fund. However, I do not label a fund abused if it received sticky assets or was on the other side of market-timing exchanges (that is, held temporarily between timing investments), but was not itself market timed or late traded.

I define as tainted any mutual fund that, according to my sources, was not itself abused but was operated by a mutual fund family that managed at least one abused fund. Tainted families are those that operated abused and tainted mutual funds. Hence, tainted funds and abused funds are two mutually exclusive sets whose union is all mutual funds operated by tainted mutual fund families. 6

Table 1 lists tainted mutual fund families, their assets under management at the end of August 2003 (at the eve of the scandal), the dates when they were publicly implicated for wrongdoing, the number of abused mutual funds they operated, and the assets under management in those funds. 7 In total, tainted families managed over $1 trillion in assets in long-term mutual funds—22 percent of the industry’s assets under management in long-term mutual funds at that time. 8 Combined, they managed 145 abused funds with $277 billion in assets—6 percent of the industry total. These funds spanned a broad range of investment objectives, including 81 domestic equity funds, 38 world equity funds, 3 hybrid funds, 14 taxable bond funds, and 9 municipal bond funds.

4. 2 Official penalties

The New York Attorney General’s complaint in September 2003 not only signaled a sweeping investigation of mutual fund management firms, broker-dealers, abusive traders, intermediaries, and others by his office, but also prompted inquiries by the SEC and states attorneys general from Massachusetts to Colorado. These official actions resulted in a slew of penalties assessed against management companies that were found to have facilitated and profited from trading abuses, as well as fines for many company executives and employees.

Table 2 lists these penalties. They included $2.3 billion in civil penalties and disgorgement levied by the SEC and state officials against mutual fund management companies and their parent firms (columns 1 and 2). An additional $47 million in penalties was self-imposed by four fund families that initiated their own shareholder restitution programs (column 3). 9 Several top executives—management company chairmen, chief executive officers, and presidents—paid a total of about $220 million in disgorgement and civil penalties (columns 4 and 5). Aggregate penalties for other less-senior employees were less than $5 million (columns 6 and 7). Finally, New York Attorney General Eliot Spitzer negotiated very large management fee reductions as part of his settlements with several mutual fund companies. He explained his rationale to The Wall Street Journal :

. [I]n a context where a company has violated its fiduciary duties and failed to protect shareholders by acquiescing to fees higher than a market permits, a rollback should be an appropriate part of the remedies imposed on a company (Solomon, 2003 ). The New York Attorney General’s settlements mandated that the fee reductions occur over five years. Cumulative fee reductions for all tainted firms totalled $1.1 billion (column 8). Aggregate penalties, including civil penalties, disgorgement, restitution, and fee reductions, sum to $3.7 billion (column 9).

5. 1 Previous estimates of losses

FRB Finance and Economics Discussion Series Screen Reader Version The Economics of the Mutual

Previous studies of the costs of market timing and late trading for buy-and-hold investors fall into two categories. First, in papers mostly completed before the scandal broke, researchers estimated dilution due to trading abuses without any specific knowledge of the funds that were harmed by trading-abuse arrangements. These papers identified investment objectives in which dilution was most problematic, and typically argued for policy changes—by mutual fund management companies and regulators—that would reduce or eliminate dilution due to market timing. A second group of papers, written after the scandal first made headlines in September 2003, focused more specifically on tainted mutual fund families and either estimated dilution in those families or compared the returns of their mutual funds to those of untainted funds to ascertain the costs to investors of the abusive-trading arrangements.

As shown in table 3, papers written before September 2003 employed measures of dilution to estimate losses to buy-and-hold investors. Greene and Hodges (2002) used daily data on fund flows and returns and estimated that dilution in world equity funds with above-median flow volatility averaged 0.94 percentage point of assets per year in the period from February 1998 to March 2001. Their estimates of dilution in other investment objectives were small. Zitzewitz (2003) used futures data to identify timing opportunities more precisely and found substantial dilution in world equity funds, with the worst problems in regionally-focused (Pacific, Japan, and European) equity funds, where annual dilution averaged 1.60 percentage points from 1998 to 2001. General international equity and precious-metals funds also suffered substantial dilution. Zitzewitz’s (2006) estimates of dilution due to late trading were considerably smaller than those he computed for market timing, although the late-trading losses are averaged over much broader categories of funds.

After the scandal broke, researchers turned their attention to the tainted fund families. Based on mutual funds’ share turnover rates, Zitzewitz (2007b) found average dilution of about one-half percentage point per year from 2000 to 2003 among all (both abused and tainted) international equity funds in tainted families—with predicted dilution exceeding three percentage points in a couple of complexes. Other researchers examined differences in fund returns to estimate losses to investors. Houge and Wellman (2005) estimated that simple average returns from 2000 to 2003 for funds at scandal-tainted complexes were 0.15 percentage point per year below those of funds at non-tainted families, but they also did not distinguish funds that were subject to abusive trading and those that were not, and their calculation does not control for the investment objectives and risks of the funds offered at different complexes. Schwarz and Potter (2006) estimated that the risk-adjusted returns of domestic equity funds at tainted complexes lagged those of their peers by an average of 0.83 percentage point from 2000 to 2003. Again, their calculation did not differentiate mutual funds that were subject to dilutive trades and those that were not. Qian (2006) sought to distinguish tainted and abused mutual funds and estimated that abused funds suffered performance penalties of roughly two percentage points from January 2001 through August 2003.

5. 2 New estimates of losses

Because the effects of abusive trading on mutual fund performance are central to the thesis of this paper, and since estimates of these effects in previous research have been motivated by questions different from those addressed here, I computed new estimates of the performance losses among abused funds. I used a two-stage approach: First, I computed the risk-adjusted relative performance for every mutual fund in my sample, using methods discussed below; and second, I tested whether the adjusted returns of abused and tainted funds were significantly different from those of other funds in the years before and after the scandal broke.

5. 2. 1 Stage 1: Estimating each fund’s annual risk-adjusted relative performance.

The mutual funds that were abused in the trading-abuse scandal covered the full range of investment objectives and included domestic equity, world equity, taxable bond, municipal bond, and hybrid funds. However, standard measures of risk-adjusted mutual fund performance, such as that employed by Carhart (1997). are generally applicable only to U.S. equity funds and would only be useful for a subset of abused funds. To make industry-wide comparisons, I used three measures of risk-adjusted relative performance that are applicable across all types of mutual funds.

My primary method employs asset-weighted mean returns for different categories of mutual funds as risk factors; that is, it controls for the degree of category-specific risk (as well as broader market risks) that each fund exhibits. I computed two additional measures of risk-adjusted returns to show that my estimates of the losses due to trading abuses are robust to different methods of adjusting returns for risk. One is just the difference between a fund’s return and the average return of all other funds in its category. The other method uses a set of standard market-risk factors.

1. Relative return. A simple, if primitive, measure of risk-adjusted returns is a fund’s return less the average return of funds sharing its investment objective. I define a mutual fund’s category return as the asset-weighted mean return of all funds that share its S&P investment objective, 10 and its relative return as its total return less its category return.

2. Alphas based on category-return risk factors. A second method adjusts relative return for risk by employing three risk factors for each fund: The fund’s own category excess return, the asset-weighted mean excess returns of all funds sharing its broader asset class, and the asset-weighted mean excess return of all mutual funds. 11 A mutual fund’s loading onto the category-return risk factor is a measure of its sensitivity to the risk common to all funds that share its specific investment objectives, while loading onto the returns of its broader asset class picks up exposure to risks from related fund categories due, for example, to a management strategy that encompasses multiple objectives or to misclassification by S&P. And loading onto the returns of all funds indicates a fund’s exposure to general market risk, controlling for its comovement with its narrower asset classes. I estimated risk-adjusted return, . in the following regression:

(A- 1 )

Here, is fund ‘s excess return (return less the mean money market fund yield) in month . is the asset-weighted excess mean return for ‘s category, is the excess mean return of fund ‘s broader asset class, and is the excess mean return of all long-term mutual funds. (Relative return is estimated in equation (1 ) subject to the constraints that and

3. Alphas based on market risk factors. I also computed risk-adjusted performance using a common set of more-standard risk factors, namely: (1) the S&P 500 index return, (2) the Russell 2000 index return less the S&P 500 index return (a size premium), (3) the Nasdaq index return less the S&P 500 index return (a technology premium), (4) the MSCI excluding-US value-weighted index return, (5) changes in constant-maturity off-the-run 10-year Treasury bond yields, and (6) changes in spreads on 10-year BBB corporate bonds over Treasuries (a credit spread).

In general, the category-return risk factors explain slightly more of the variance in mutual fund returns over the sample periods I studied. For example, the median adjusted R 2 from the category-return risk-factor regressions described by equation (1 ) for the three years ending August 2003 is 0.92, while that for the standard risk-factor regressions is 0.87. For the three years following the scandal revelations, the median adjusted R s are 0.92 and 0.88 respectively.

Gross and net returns. Because mutual fund investors earn returns net of fees, rather than gross returns, fund performance is usually reported net of fees, and most research focuses on net returns. However, the effects of trading abuses on performance should be seen most clearly in gross returns, because variation in net returns would reflect not only the effects of trading abuses but also any differences in fee structures. 12 Hence, I used gross returns in my baseline calculations of risk-adjusted performance, but I also report results using net returns.

Sample periods. To estimate the losses to the shareholders of abused and tainted mutual funds, I initially examined the performance of these funds in the three years before the scandal broke (September 2000 through August 2003) and in the three years afterward (January 2004 through December 2006) relative to that of untainted mutual funds. While there is evidence that some abusive-trading arrangements were in effect well before September 2000, I did not find (as discussed below) statistical evidence of an aggregate performance loss among abused funds prior to 2000.

5. 2. 2 Stage 2: Estimating the effects of trading abuses on risk-adjusted annual performance.

To capture the performance effect of the trading abuses, I estimated a cross-sectional regression of each fund’s alpha (from stage 1) on two dummies—one for abused funds and a second for tainted funds. I also included the natural log of each fund’s assets under management in the regression, because other researchers have predicted or found that risk-adjusted excess returns, timing-related dilution, and the likelihood of collusion with abusive traders varied with fund size. 13


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