|
When Benchmark Indices Have Alpha: Problems with Performance Evaluation Authors: Martijn Cremers, Antti Petajisto, Eric Zitzewitz Source: Working Paper Date: April 2008 |
Cremers, Petajisto, and Zitzewitz note that passive indices, such as the S&P 500 or the Russell 2000, widely used as benchmarks in portfolio management, exhibit abnormal statistically significant returns – whether positive or negative – relative to the Carhart four-factor model. In their view, these abnormal returns suggest that this model does not correctly take into account all the factors that explain asset returns. As a result, the alpha from this model will not correctly evaluate managers’ portfolio performance: they will be credited for performance stemming from their exposure to passive indices or they will be penalised for it. The authors suggest that unbiased evaluation of managerial performance would require adjusting for the alpha of the benchmark index or using a benchmark model that does not produce such biases across common benchmarks.
To explain the sources of the non-zero alpha of passive indices, the authors look into alternative methods of constructing the two Fama-French factors (small minus big and high minus low book-to-market) that are part of the Carhart model. These two factors are constructed as equal-weighted differences of value-weighted style portfolios. The authors suggest calculating value-weighted versions of the factors. For the S&P 500 and the Russell 2000, the indices they look at, they find that the Carhart factor model, including these two alternative factors, leads to alpha that is lower by approximately 50%. In addition, they find that all S&P 500 alpha and 80% of the Russell 2000 alpha are explained by the indices’ exposure to the 10×10 Fama-French portfolios.
As an alternative to the four-factor Carhart model, they use the S&P 500, Russell Midcap, and Russell 2000 as well as their value and growth components to construct index-based factor models. They find that these models can improve asset pricing relative to the Carhart model by improving cross-sectional explanatory power, as well as by significantly reducing pricing errors. They also show that adding the index-based factors to the four-factor Carhart model can substantially improve asset pricing. They test the robustness of their model by analysing different sets of value-weighted portfolios formed on size and book-to-market.
Concerning performance evaluation, their analysis reveals that the benchmark alpha has an impact of about 5% per year on Fama-French and Carhart alpha of funds and that it can fully reverse the conclusions about skill between small- and large-cap funds. Using all equity mutual funds invested in the US market and with significant net assets, they find that the best model that produces reasonable alpha estimates across all mutual fund groups of their sample – constructed by size and value dimensions – and regardless of the benchmark index, is a seven-factor model based entirely on benchmark indices, including the S&P 500, Russell Midcap, Russell 2000, a separate value-minus-growth factor for each index, and a momentum factor. In addition, they find that, compared to the Carhart four-factor model, this model leads to reduced tracking-error for individual funds.
In concluding, the authors state that the purpose of their study is first to outline the weakness of existing models, not to examine alternative models. They thus encourage further research in the development of these alternatives.
Related links
