Should Benchmark Indices Have Alpha? Revisiting Performance Evaluation

Abstract

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 Russell 2000. We find that these alphas arise primarily from the disproportionate weight the Fama-French factors place on small value stocks, which have performed well, and from the CRSP value-weighted market index, which is historically a downward-biased benchmark for U.S. stocks. We propose small methodological changes to the Fama-French factors to eliminate the nonzero alphas, and we also propose factor models based on common and tradable benchmark indices. Both kinds of alternative models improve performance evaluation of actively managed portfolios, with the index-based models exhibiting the best performance.