Jerchern Lin and Wayne Ferson
Alpha and Performance Measurement: The Effects of Investor Disagreement and Heterogeneity
Journal of Finance | Volume 69, Issue 4 (August 2014), 1565–1596

Finance researchers have an easy familiarity with alpha, the most well-known measure of the expected abnormal return of an investment. Studies refer to CAPM alpha, three-factor alpha or four-factor alpha, assuming the reader hardly requires a definition. Investment practitioners discuss their strategies in terms of the quest for alpha. Alpha can be active, conditional or portable. The number of investment firms with alpha in their names is staggering.

Despite the apparent familiarity with alpha, the current literature too often fails to think rigorously about how alphas can be interpreted. The literature has provided examples and counterexamples, leading to the conclusion that, given a fund with a positive traditional alpha, an investor would not necessarily wish to buy the fund.

In this paper, we propose a client-specific alpha that unambiguously signals the attractiveness of a fund to a client. We also derive and estimate an upper bound on the extent to which a client is likely to disagree with a traditional alpha about a fund's performance. We find that disagreement based on client preferences is likely to be of a similar economic magnitude as the errors in the estimation of alpha, and roughly as important as the choice of the performance benchmark. We provide empirical proxies for the expected disagreement with a traditional alpha and for heterogeneity, which is the variation in disagreement across a fund's investors. We study empirically the relation of disagreement and heterogeneity to investor flows of new money in and out of mutual funds. We find that investor flows do respond to disagreement and heterogeneity, and conclude that disagreement and heterogeneity are economically important issues for mutual funds.

A General Model for a Client's Alpha

We incorporate client preferences in a portfolio optimization problem to derive a client-specific alpha without the assumption in utility functions and normally distributed returns. We then study how the client adjusts consumption and portfolio choices when facing a new investment. We analytically show that the client optimally buys (sells) a fund with a positive (negative) client-specific alpha.

Investor Disagreement and Heterogeneity

Investors will not in general agree about the “right” alpha, so the same fund may look attractive to one investor but not to another. We thus define a measure of the expected disagreement a client will have with a traditional alpha and derive bounds on its magnitude. We also define heterogeneity as the variance of disagreement across investors. We investigate the implications for mutual fund flows of the expected disagreement and heterogeneity.

Main Results

Our results are summarized as follows. First, we derive a well-specified alpha using a multi-period model under general returns distributions, and show that the client-specific alpha does provide a reliable buy or sell indication. Second, we find that disagreement with traditional alphas can be similar in importance to the choice of the performance benchmark or to the statistical imprecision in estimates of alphas. Third, investor disagreement and heterogeneity are economically significant in the behavior of fund investors. Funds whose clients' alphas are expected to be larger than a traditional alpha have positive average disagreement. We find that such funds experience larger inflows, controlling for the traditional alpha, than funds with low average disagreement. Funds with a large cross-sectional variance of investor disagreement have greater investor heterogeneity. We find that funds with more heterogeneity across investors experience lower average flows. These effects are separate from uncertainty about the true value of the traditional alpha.


The importance of investor disagreement with traditional alphas and investor heterogeneity are likely to be greater than our empirical results indicate, because we abstract from important sources of additional disagreement and heterogeneity. For example, we do not consider differences in investor beliefs, taxes or institutional setting. If investors disagree enough, then even a fund with a negative traditional alpha can thrive. A fund with a positive traditional alpha can find itself spurned in the marketplace. These results are potentially important in practice. If our empirical results are conservative, the economic magnitudes of disagreement and heterogeneity for funds and investors might be larger than the benchmark choice decision and the uncertainty in estimates of traditional alphas. These two issues have received much research, but the effects of disagreement and heterogeneity have been little explored in the literature.