Benchmarking Benchmarks: Much Ado About Nothing

Yuliya Plyakha

Universite du Luxembourg – School of Finance

June 28, 2013

Abstract:

We compare the performance of a wide variety of benchmarks: traditional, fundamentals-based and optimization-based. We find that for a set of all stocks of the S&P500 index during the period from February 1989 to December 2011 traditional and new benchmark portfolios perform similarly according to a variety of return, risk, turnover, and diversification performance metrics. Moreover, the difference between traditional value- or equal-weighted benchmark and new benchmark portfolios is not statistically significant. We identify a set of basis benchmarks, which span both the set of new and the set of traditional benchmarks. The first basis benchmark explains three quarters of the variation of all benchmark portfolios; correlation between this basis benchmark and systematic market factor is 96% for the last 10 years period. We conclude that the strongest driving force of all considered benchmark portfolios is the market factor. Irrespective of the benchmark portfolio, managers mainly track the market and do it in statistically sufficient way during the last 23 years. The difference in the performance of various benchmarks can be attributed to the skill to outperform the market. In the long run these skills are washed out. Our work has implications for big mutual, pension and hedge funds with fairly big number of stocks in their portfolios and long investment time horizon. For these funds the choice of the benchmark is not important.

Benchmarking Benchmarks: Much Ado About Nothing – Introduction

One of the most important questions in the area of investments is which benchmark to use when evaluating the performance of an investment strategy. The CAPM of Sharpe (1963) and Lintner (1969) suggests that this benchmark should be the market portfolio. Fama and French (1993) find that the benchmark should include other factors, in addition to the return on the market portfolio. Consequently, there is a large academic literature on empirical asset pricing that uses these benchmarks (see, for instance, the papers cited in Asparouhova, Bessembinder, and Kalcheva (2010)). The practitioner literature has proposed yet other benchmarks; for example, the Fundamental Index in Amott, Hsu, and Moore (2005), and the Equal-Risk Contribution benchmark in Demey, Maillard, and Roncalli (2010). Given the difficulty that active portfolio strategies and mutual funds have in outperforming these benchmarks, these benchmarks themselves are now widely marketed as investment strategies.

The main contribution of this paper is to evaluate the performance of a wide variety of benchmarks under the same test conditions. In undertaking this comparison, we are careful to account for the effect of microstructure noise in the calculation of returns. We distinguish among three groups of benchmarks: traditional, fundamentals-based, and optimization-based. Traditional benchmarks include cap-, price-, and equal-weighted; fundamentals-based are strategies that use different measures of company size, such as book value, cash  ow, sales, dividends, and a composite of these measures summarized in one; optimization-based strategies are equal risk contribution, minimum variance, and maximum Sharpe ratio portfolios.

First, we find that for a set of all constituents of the S&P500 index during the period from February 1989 to December 2011 traditional and new benchmark portfolios perform similarly according to a variety of return, risk, turnover, and diversification performance metrics. Moreover, the difference between traditional value- or equal-weighted bench- mark and new benchmark portfolios is not statistically significant. On a shorter time period preferred benchmarks are equal-weighted, dividends-based, equal-risk contribution, minimum-variance, and maximum Sharpe ratio constrained portfolio.

Second, we identify a set of basis benchmarks that span both the set of the new, and a set of long recognized benchmarks. The first basis benchmark (statistical factor) explains almost three quarters of the variation of all benchmark portfolios. We find that correlation between the first basis benchmark and systematic market factor is 91% for the period of the last 23 years and 96% for the last 10 years. All benchmark portfolios contain a very similar fraction of the aforementioned first basis benchmark. Difference in the performance of the benchmarks can be attributed to the skill of manager to outperform the market, the effect of skills will be washed out in the long run: more then 95% of the dynamic of the benchmarks is the market and the remaining 5% is alpha or skill.

Fund managers acquire knowledge and skills and, regardless of tracking a benchmark or not, they will be evaluated by investors according to some specific benchmark. Depending on reward structure of fund managers, they are interested in improving their relative performance (e.g., alpha relative to a benchmark) and/or raising funds for their trading strategy (e.g., in the case of at management fees). To earn alpha one needs skills, and to earn  at fees fund manager needs to hold a fraction of market portfolio. As a result, managers may continue pumping money into their fund (as discussed in Berk and Green (2004)) after making sure that they collect their alpha (stock picking).

benchmarks

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