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«* * Lynch is from New York University and NBER and Musto is from University of Pennsylvania. We are grateful for comments from Franklin Allen, ...»

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How Investors Interpret Past Fund Returns

Anthony W. Lynch and David K. Musto*


Lynch is from New York University and NBER and Musto is from University of Pennsylvania.

We are grateful for comments from Franklin Allen, Stephen Brown, Jennifer Carpenter, Doug

Diamond, Ned Elton, Will Goetzmann, Gary Gorton, Bruce Grundy, Rudi Schadt, René Stulz, S.

Viswanathan and participants in the Corporate Finance and Friday lunchtime seminars at

Wharton, and also for research support from Dan Mingelgrin. Two anonymous referees get special thanks.

How Investors Interpret Past Fund Returns


The literature documents a convex relation between past returns and fund flows of mutual funds. We show this to be consistent with fund incentives, because funds discard exactly those strategies which underperform. Past returns tell less about the future performance of funds which discard, so flows are less sensitive to them when they are poor. Our model predicts that strategy changes only occur after bad performance, and that bad performers who change strategy have dollar flow and future performance that are less sensitive to current performance than those that do not. Empirical tests support both predictions.

How Investors Interpret Past Fund Returns Investors who condition open-end mutual fund allocations on past performance appear to be relatively indifferent among bad returns. Several recent papers (e.g., Sirri and Tufano (1998), Ippolito (1992)) show net new investment to be much less sensitive to past returns in the region of bad returns, as if all returns below some threshold send roughly the same signal to investors about future prospects. Brown, Harlow and Starks (1996) and Chevalier and Ellison (1997) interpret this pattern as the fund’s implicit compensation scheme and ask whether this induces the asset substitution associated with convex compensation; our goal here is to determine why the pattern occurs in the first place and provide empirical support for our explanation.

A mutual fund’s shareholders delegate its productive decisions to an investment advisor.

The shareholders and other investors can not usually observe these decisions directly, but they can infer them from the fund’s operating performance, and invest accordingly. The finance literature usually models this inference/investment process as: 1) estimating a fund’s past risk- adjusted expected return, and 2) investing on the assumption that the past risk-adjusted expected return will persist into the future (e.g. Ippolito (1992)). This paradigm has some intuitive appeal and empirical support, but it does not take into account the investment advisor’s option to disconnect past and future performance. We propose an explanation for the empirical results on fund flows by way of a model that incorporates this option.

The use of performance measures as estimates of future performance assumes (among other things) that the relevant personnel and management techniques carry forward from the past. Our point, building on the argument of Heinkel and Stoughton (1994), is that funds respond to bad - but not good - performance by replacing the personnel or techniques that

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replacements (Khorana (1996)) and mergers (Elton, Gruber and Blake (1996)) bears out this intuition. This abandonment option transforms the relationship between new investment and past returns, because if a bad return and a very bad return both mean that the next return will reflect a new strategy, the magnitude of their difference has little predictive power, and therefore little effect on investment decisions. With the exception of the very worst funds, this dynamic also fits the actual shape of performance persistence - flatter in the region of bad past returns.

Our model has several implications. First, strategy changes only occur after bad fund performance. Second, bad performers who change strategy have dollar flow and future performance that are less sensitive to current performance than those who do not. We test these implications using daily mutual fund returns from Micropal and manager-change dates from the CRSP mutual fund data set. We use three proxies for strategy change. The first two are based on a fund’s average absolute change in risk loading, where one proxy is the loading change itself, while the other takes those funds in the top quartile of loading changes for each fund type in each year to be those that changed strategy. Risk loadings are obtained from the four-factor model of Carhart (1997) and Busse (1999). Manager change is used as the third proxy.

To test the first implication, we define bad performance to be either negative or bottomquartile performance and we use two measures of performance, four-factor alpha and groupadjusted four-factor alpha. For all combinations of performance measure and bad-performance definition but one, we find a significantly greater incidence of both manager changes and top-quartile loading changes among bad performers than good performers, as well as a significantly higher average loading change. The only exception defines bad performance to be

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We then test the second implication by running piece-wise linear regressions of future performance or dollar flow on current performance, with a single breakpoint at zero. Thus, the sensitivity of the dependent variable to performance is allowed to differ between bad performers and good performers. Each of these sensitivities is also allowed to differ based on the value of the strategy-change proxy. The model predicts that the sensitivity of dollar flow to current performance for bad performers is lower for those bad performers who change strategy.

Consistent with the model, we always obtain this result, irrespective of which of the three strategy change proxies is used or whether performance is measured using absolute or relative four-factor alpha. Moreover, the difference is significant in five of the six cases. The model also predicts that the sensitivity of future performance to current performance for bad performers is lower for those bad performers who change strategy. But when future performance is used as the dependent variable in the regression, we are only able to confirm this prediction when we use manager change as the strategy change proxy. Considered together, these empirical results provide strong support for the model.

The rest of this paper is in six sections. In Section I we discuss the literature on performance persistence and fund flows, and outline our reasoning. Section II describes and solves a simple model which captures this reasoning, and in Section III we discuss the main implications of the model and their correspondence to the existing empirical literature. Section IV extends the model to allow for multiple funds. Our empirical testing of the model is described in Section V while Section VI summarizes and concludes.

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The information content of fund returns is one of the oldest and most popular topics in finance. A large portion of the academic literature has considered how to measure it, and much of the popular press has tried to report it. It is not surprising in this context that the relation between new investment and past returns is positive. What is surprising is that the relation is qualitatively different for lower and higher past returns. Ippolito (1992), Sirri and Tufano (1998) and Chevalier and Ellison (1997) all find a small positive slope in the lower region and a considerably larger slope in the higher region. Goetzmann and Peles (1996) find a significant relation between flows and past returns only for the top quartile of past returns.

The asymmetric flow-response pattern is consistent with investors expecting a relation between past and future performance with a convex shape. That is, investors put slightly less cash into bad funds than mediocre ones because bad funds’prospects are slightly worse than those of mediocre funds, whereas they put considerably more cash into good funds than mediocre ones because good funds’ prospects are considerably better than those of mediocre funds. This fits the published results on performance persistence, with the notable exception of the very worst funds. Hendricks, Patel and Zeckhauser (HPZ) (1993) estimated the past return/future performance relationship with a sample of fund returns covering 1974 to 1988 by sorting funds at each quarter-end into octile portfolios by their total returns over the past year,1 then measuring the portfolios’ performance over the following quarter. Brown and Goetzmann (BG) (1995) ran the same test on a sample covering 1976 to 1988, except they rebalanced every year-end and held for a year. Carhart (1997) ran this test over the period 1963 to 1993, using decile portfolios and calculating monthly returns. Figure 1 reports the returns net of the risk-free

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(i.e. Jensen’s alphas). The HPZ quarterly numbers are multiplied by four and the Carhart numbers are multiplied by 12 to approximate the scale of the annual BG numbers. Setting aside the worst group, these point estimates reproduce the fund-flow pattern, where the slope of flows on performance is flatter on the left than on the right. This result is not sensitive to the choice of risk-adjustment; Gruber (1996) forms and evaluates portfolios of funds using intercepts from regressions on four factors2 and finds the same pattern, as reproduced in Figure 3. However, notice that some risk adjustment is important since the pattern is less discernable in Figure 1 using excess returns than in the other two figures using risk-adjusted performance.

The correspondence between the fund-flow and persistence patterns begs two questions.

The first is how to explain the continued investment in the worst performers, a puzzle already noted by BG, Gruber (1996) and others. We do not attempt to resolve these investors’ behavior with rational decision-making, which, evidence suggests, may be futile in any case. For example, Goetzmann and Peles (1996) document biases in investor information sets which could encourage bottom-fund investors to stay put, and Sawaya (1992), Brandstrader (1992) and Rukeyser (1996) argue that many bottom-fund investors may be dead. Gruber (1996) posits the existence of a “disadvantaged clientele,” which includes investors who are either locked into bad funds by institutional restrictions (e.g. pension plan menus) or accrued capital gains, or who follow the advice of advertisements or brokers, and Christoffersen and Musto (2002) provide evidence that bottom-fund investors are relatively less sensitive to performance and price. The population of bottom-fund investors appears, in any case, to be small; Goetzmann and Peles (1996) estimate the fraction of mutual fund investors in bottom-octile funds at two to three

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The other question raised by the empirical results is the source of the asymmetry. Our response is that the investment advisor, like most other enterprises, holds an option to replace its production method. Heinkel and Stoughton (1994) (HS) argue that “a manager is retained if his performance is ‘good enough’ relative to an alternative for the client.” In the equilibrium of their two-period model with a risk-neutral investor and a risk-neutral manager with unknown skill, the manager must outperform a threshold return in the first period to keep his job for the second. This analysis delivers several predictions about the design and purpose of management contracts, but not about fund flows, since the risk-neutral investor simply invests all his money with whatever manager he hires. We modify and extend the HS analysis to study the fund flows, and find that it predicts the observed convex relationship.

HS model the situation where an investor delegates the choice between asset-selection algorithms to a portfolio manager. The fund-flow results refer to open-end mutual funds, which insert an additional layer of delegation: investors delegate the choice of a portfolio manager to an investment advisor (e.g. Fidelity Management Corporation), and the portfolio manager (e.g.

Peter Lynch) chooses the asset-selection algorithm. By the same logic as in HS, retail investors can expect that the investment advisor will retain exactly those managers whose performance is “good enough” compared to other potential managers.3 As a consequence, a fund’s realized returns convey two facts to investors: the expected future performance of the same manager, and whether or not the manager will actually persist. If a fund’s past return is below the retention threshold, investors know the next return will reflect a new manager so it hardly matters just how bad the past return was. If the return signals that last period’s manager will be next period’s

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risk-averse consumers, are consequently more sensitive to past returns above the threshold.

Our reasoning applies to more than just the investment advisor’s choice between retaining and replacing his manager. The manager himself can retain or replace his assetselection algorithm, and this decision also hinges on the past return. A manager deploys an algorithm (momentum, book-to-market, etc.) with some prior belief about its value, but has some residual uncertainty that its realized returns can help resolve. As in HS, there will be a threshold past return that determines whether or not the manager’s past algorithm persists in the future, and investors can invest on the knowledge that the manager must have abandoned his old algorithm without actually observing him do it.

The argument is based on the idea that underperforming managers and algorithms are abandoned. For managers, this is obvious: a portfolio manager is either retained or replaced.

But in the portfolio-selection context there is the possibility of short-selling. A manager may, depending on transactions costs, be able to transform a money-losing strategy into a moneymaking strategy by selling it short in the next period. If mutual funds could short-sell, they might be expected to reverse, rather than abandon, underperforming strategies. But for practical purposes this is not an issue, because mutual funds can not (see the Investment Company Act of 1940, section 18) engage in meaningful short-selling.

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