Mutual Fund Performance at Long Horizons

Most research that considers investor outcomes reports on unconditional or conditional (as in “alpha” estimates) arithmetic means of returns that are measured over relatively short horizons, most often monthly. In contrast, investment and decision horizons can stretch to decades, and differ across investors. We posit that many investors are concerned with the compound returns that accrue over longer horizons, propose that empirical measures of investment performance should therefore consider a variety of return measurement horizons, and report on compound returns to U.S. equity mutual funds at the monthly, annual, decade, and full-sample horizons. We also shed light on the respective roles of return skewness and mutual fund expenses, and we tally the full-sample dollar gain or loss to mutual fund investors in aggregate, on both a fund-by-fund basis and in total. The results verify that compound long-horizon returns often contain important information that is not readily apparent in the distribution of short-horizon returns. For example, some funds with positive monthly performance estimates have negative long-horizon abnormal returns.

We study a broad sample of nearly 8,000 U.S. equity mutual funds during the 1991 to 2020 period. We show that the percentage of funds that outperform market benchmarks decreases with the horizon over which returns are measured. In the monthly data, fund returns exceed the matched-month return to the SPY Exchange Traded Fund (taken as a proxy for the overall market that investors could readily have captured) for 47.2% of observations. The percentage of sample funds that generate buy-and-hold returns that exceed buy-and-hold returns to the SPY decreases to 41.1% at the annual horizon, 38.3% at the decade horizon, and 30.3% at the full-sample horizon. In fact, over 20% of funds fail to even outperform one-month U.S. Treasury Bills at the full-sample horizon.

These results reflect a prominent dimension by which long-horizon returns contain different information than short-horizon returns: the cross-sectional distribution of long-horizon fund buy-and-hold returns is strongly positively skewed, while such skewness is not observable in monthly returns. This positive skewness in compound long-horizon returns is of substantial practical importance. Financial planning (e.g. at pension funds) is often based on assumptions regarding mean returns. Aside from the active debate as to whether the assumed mean returns are appropriate, in a positively skewed distribution a potentially large majority of possible future realizations are less than the mean outcome. Of course, while strong positive skewness implies that many funds underperform, some funds perform very well. Out of 7,883 sample funds, 442 delivered a positive full-sample compound return more than twice as large as the compound return to the SPY over the matched months, and 160 delivered compound returns three times as large as the SPY during the matched months of the full sample.

We assess the role of fund fees by considering long-horizon outcomes in pre-fee returns. Consistent with the short-return-horizon evidence reported by Berk and van Binsbergen (2015) and Fama and French (2010), we find that mean pre-fee mutual fund returns exceed returns to market benchmarks at long horizons. The cross-fund mean full sample pre-fee buy-and-hold return to sample funds is 394%, while the mean SPY buy-and-hold return over matched periods is 298%. Nevertheless, only a minority (45.2%) of individual funds outperform the SPY in the long run even in a comparison of pre-fee fund returns to SPY returns that are net of fees.

We also assess the potential effects of funds’ systematic risk exposures in explaining long-horizon outcomes. We rely on a simple single-factor market model because our main focus is on the effects of the compounding of random returns over long horizons, not on the widely-studied question of which benchmarks or factor models are most appropriate. In particular, we compute the excess of each actual compound fund return over the compound return to the market proxy that has been adjusted for the fund’s estimated beta. We find that the excess beta-adjusted compound return is negative for the majority of funds, and is negative for some funds where the “alpha” estimated from monthly returns is positive. Similarly, we show that about one of every six funds in our sample that has a positive monthly arithmetic mean market-adjusted return also has a negative lifetime market-adjusted buy-and-hold return. These outcomes reflect the well-known fact that the arithmetic mean exceeds the geometric mean in any return sample with positive volatility. Yet, the literature emphasizes conditional or unconditional arithmetic means of short-horizon returns, not only in the form of alpha estimates, but also when focusing on Sharpe ratios, fitted values from Fama-MacBeth or factor model regressions, and in comparisons of average returns across characteristic-sorted portfolios. We document the extent to which this emphasis can be misleading for long-term investors.

In addition to the effects of management fees and the role of positive skewness in the distribution of long- term fund returns, fund investors’ aggregate experience is affected by the timing of their investments and withdrawals (i.e. “flows”) to and from mutual funds. We show that investors’ “dollar-weighted” monthly returns, which reflect fund flow timing, average about nine basis points per month less than geometric mean returns, which pertain to buy-and-hold investors. The return differential attributable to investors’ flow timing is comparable in magnitude to the effect of fund fees.

While some funds perform very well, the net economic impact of fund underperformance is large. Relying on the return to the SPY to define the opportunity cost, and allowing estimates of fund betas, we estimate an aggregate wealth loss to investors in our fund sample of $1.02 trillion, measured as of the end of the 1991-2020 sample period. This wealth loss reflects the combined effect of mutual fund fees and investors’ timing decisions.

A central conclusion supported by our analysis is that inference regarding mutual fund performance differs when focusing on compound long-horizon returns rather than conditional or unconditional means of short-horizon returns. Our results imply that the evaluation of fund performance is intrinsically linked to return horizon, and that fund performance cannot be fully assessed independent of information regarding the return horizon that is most relevant to disparate investors

The complete paper is available at here.