Should Benchmark Indices Have Alpha?
Martijn Cremers, Yale School of Management
Antti Petajisto, Yale School of Management
Eric Zitzewitz, Dartmouth College

Standard Fama-French and Carhart models produce economically and statistically significant nonzero alphas even for passive benchmark indices such as the S&P 500 and the Russell 2000. The authors find that these alphas primarily arise from the disproportionate weight the Fama-French factors place on small value stocks that have performed well, and from the CRSP value-weighted market index which is a downward-biased benchmark for stocks. They explore alternative ways to construct these factors as well as alternative models constructed from common and easily tradable benchmark indices. Such index-based models outperform the standard models both in terms of asset pricing tests and performance evaluation of mutual fund managers.

A very large fraction of institutional money is either indexed to-or evaluated relative to-market benchmark indices. Accordingly, the properties of these indices are of paramount importance to investment managers and investment sponsors. This research examines systematic performance characteristics of various indices in comparison to various market factors. The results help explain performance shortfalls and gains that may be due to the benchmark measures rather than to active (or in some cases, passive) strategies.


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