Blake Phillips, Kuntara Pukthuanthong, and P. Raghavendra Rau
Past performance may be an illusion: Performance, flows, and fees in mutual funds
Critical Finance Review | Volume 6, Issue 2 (2016), tbd

One of the most persistent and robust patterns documented in the mutual fund literature is return-chasing by investors. The finding that investors allocate wealth disproportionally to funds with prior superior performance transcends mutual fund asset classes, country boundaries, and investment objectives. In this paper, we examine a different type of return-chasing behavior, whether investors chase stale fund returns, returns arising from horizon effects in holding period returns (HPR). Specifically, when advertising past performance, Rule 482 of the Securities Act of 1933 requires investment companies to report past performance in the form of an HPR over horizons of 1, 5, and 10 years for funds in existence over those horizons. In addition, the 3 year horizon is also commonly reported but is not required.

The focus of our analysis is how investors interpret the change in reported HPRs. For example, consider the following 5 quarter return time series:

Period -1 -2 -3 -4 -5
Return –2% 3% 4% 5% –4%
The annual HPR for quarters -2 to -5 is 8% and the corresponding annual HPR for quarters -1 to 4 is 10%:   text{HPR}_{t-1} : =  :[(1+ : -0.02) cdot(1+ : 0.03) cdot(1+  : 0.04) cdot(1+ : 0.05)]-1 : =  : 0.102  HPR_{t-2} : =  :[(1+ : 0.03) cdot(1+  : 0.04) cdot(1+ : 0.05) cdot(1+ : -0.04)]-1 : =  : 0.079

Even though the fund experienced a negative return in the most recent period (t =  – 1), the HPR increased as the end-return which dropped from the sample was more negative. The change in the HPR is therefore a function of the most recent return (–2%) which enters the horizon and the end-return (–4%) which drops from the horizon. As all other intervening returns are common in the return sequences, they have no influence on the change in the HPR. Reacting to the new information conveyed in the most recent return is arguably rational to the extent it is related manager skill and future fund performance. In contrast, end-returns convey no new information and correspondingly should not influence rational investor preferences.

We study whether mutual fund investors differentiate between current and end-return influences on changes in reported mutual fund performance. We call investor reaction to end-returns the “stale return chasing” effect. We then examine the determinants of this behavior and the mechanisms by which mutual fund managers propagate and benefit from investor reaction to stale returns.

Investor Reaction to Stale Performance: Identification Strategy

Our data comes from the Center for Research in Security Prices (CRSP) Mutual Fund Database for the period of 1991-2010. To measure the stale performance effect, we relate proxies for investor allocation preferences to the first return lag plus successive return lags (n=2 : to : 73), in 72 separate regressions: Δ mt = α + β1Rt – 1 + βt – 1Rt – 1 + εt where n signifies the lag of the second return included as an independent variable in month t. The primary measure of investor preferences is the change in market share held by the fund, defined as: 
   Delta m_{i,t}=  frac{n_{i,t}}{ hat{N}_t} : -  frac{n_{i,t-1}}{ hat{N}_{t-1}}
where ni,t is total net assets under management for fund i in month t, and  hat{N}_t is aggregate total net assets for all funds in the sample at time t. We also cluster standard errors by fund and date (month-year). To motivate our use of the first equation, we note that the change in HPR has only two influences, the magnitude of the return in the current period and the magnitude of the end-return which drops from the calculation. These two returns have an equivalent impact on the HPR, though only the former is new information. Modeling investor response to the change in HPR, it then follows that Δ mt becomes a function of the new and end-return, linearly approximated by equation (1). All intervening returns are common between adjacent HPRs and have no influence on Δ HPR. If investors interpret the stale information component of the change in HPR as information regarding future fund performance, we expect the βn coefficient related to return observations at the end of standard HPR reporting periods to be negative. This relation follows from the inverse relation between the magnitude of the end return which drops from the sample and the change in the HPR.

Do investors chase stale returns?

The β n coefficients from our pooled, OLS regression series in the first equation show that they do. In particular, the magnitudes and signs of the variables of interest (the coefficients on the 13th, 37th, and 61st monthly return lag which are the end-returns related to the reported 1, 3, and 5 year HPR) are strikingly different from all the other variables. They are larger than all but one of the other coefficients. The average absolute value of these three coefficients is 0.35, twice the size of the absolute mean coefficient (significant at the 5% level). Almost none of the other coefficients are significantly different from both zero and the absolute mean of the coefficient sample (α = 10%). Interestingly, the magnitudes of return-chasing on the stale return chasing lags are of equal or greater magnitude to return-chasing on the first return lag. Investor asset allocations appear equally or more sensitive to the stale information reflected in HPR end-returns relative to the new information reflected in the most recent return. These relations are robust to a range of alternative specifications including alternative investor preference proxies, alternative adjustment of standard errors and inclusion of controls for investor preferences from the literature.

Does fund advertising take advantage of stale return chasing behavior?

We use two proxies for fund marketing expenditures, the 12b – 1 expenditure of the fund and investment company advertising data compiled by Kantar Media. We then relate the change in annual fund-specific advertising expenditures to determinant variables. We focus on advertising that reports HPR related information, either the actual return or analyst rating by holding period. We show that funds spend more money advertising HPRs the year after the 1, 3, and 5 year HPRs are individually higher, consistent with funds seeking to draw attention to prior strong performance. We also partition the sample into quartiles by the 1-year HPR which dropped from the sample (i.e. the HPR_{T-4}^{1 Year} or HPR_{T-6}^{1 Year} for the 3 and 5 year HPR, respectively). If funds are preferentially advertising stale performance, we expect greater spending on HPR advertising when the return which dropped from the sample is small (more negative), resulting in an increase in the reported HPR. That is precisely what we find. Funds indeed spend a greater amount on HPR related advertising when reported HPRs are higher due a low return dropping from the horizon of assessment.

What does stale performance chasing depend on?

To explore the determinants of stale performance chasing at the fund-level, we next estimate the first equation by fund and year, producing an annual time series of βn coefficients for each fund. We then relate the fund-level β13, β37, and β61 coefficient time series to determinant variables using a pooled, cross-sectional panel. We find that stale performance chasing tends to be lower for larger (greater TNA) and older funds and funds from larger families (greater family TNA). Funds from families which offer a larger number of funds also tend to have less return-chasing, though the relation is not significant at conventional levels. Stale performance chasing tends to be higher for funds with greater value uncertainty as proxied by the standard deviation of mutual fund returns over the prior year. Advertising broadly increases stale performance chasing, both at the fund and family-level. Ads that report HPR info induce the largest investor response to stale performance signals, followed by advertising that features analyst ratings. The magnitude of the response of investors to ads that feature HPR info is typically twice that of ads that feature analyst rating with no reference to HPR info. Finally we examine how investor sophistication affects the stale return chasing behavior. Sophisticated investors should understand the mechanical influence of time on HPRs and recognize that HPR signals provide no new information in excess of the most recent return observation. As a proxy for investor sophistication, we contrast retail with institutional funds. Institutional funds are marketed to high net worth individuals and large pension funds managed by professionals who are often viewed as being more sophisticated than retail investors. Across all three stale return horizons we find that, if anything, institutional investors are more prone to stale return chasing than retail investors.

Do mutual funds change their fees to take advantage of stale performance chasing?

Our final analysis examines the implications of stale performance chasing for fees. Mutual fund fees are set in a competitive environment. Funds that wish to increase fees are likely to time the increase to special situations. For example, Bris-Gulen-Kadiyala-Rau (RFS 2007) show that mutual funds choose to raise fees at points in time when they close their funds to new investors. Thus, stale performance chasing may provide mutual funds with the opportunity to increase fees, in essence cashing in on the mechanical effects of HPRs.

To test this hypothesis, we relate fees to our return-chasing estimates. We find that funds with higher stale return-chasing in the prior period typically charge higher fees as a percentage of TNA. Although contractual fees are typically time invariant and may only be changed with shareholder consent, mutual funds routinely voluntarily waive fees during periods of poor performance in order to retain performance-sensitive investors (Christoffersen [JF 2001]). We obtain fee waiver data from Morningstar, which reports the percentage of TNA waived from fees in a given year. We then relate the change in waived fees to the stale performance chasing estimates and control variables. The stale performance chasing coefficients are all positive and significant, suggesting that funds reduce waived fees on the heels of stale performance chasing flow. The absolute sizes of the coefficient estimates across the model sets are highly similar, suggesting that adjustment to waivers explains the majority of the change in fees associated with stale performance chasing. Thus, our results suggest a channel by which managers are able to realize opportunities to return fees to prior levels without having to generate exceptional returns, i.e. by waiting for mechanical increases in HPRs realized as time passes.