Risk-Adjusted Performance: The Correlation Correction

Current measures of risk-adjusted performance, such as the Sharpe ratio, the information ratio, and the M-2 measure, are insufficient for making decisions on how to rank mutual funds or structure portfolios. This article proposes a new measure, called the M-3, that accounts for differences in (1) standard deviations between a portfolio and a benchmark and (2) the correlations of mutual fund portfolios and their benchmarks for an investor's relative-risk target. This technique facilitates portfolio construction to optimally achieve investors' objectives by combining the risk-free asset, the benchmark, and mutual funds. A form of three-fund separation, this paradigm provides optimal mixes of active and passive management based on the ability of fund managers rather than on individual biases about market inefficiency. This article provides support for the claim that leverage may not be bad if it is used to structure portfolios to achieve the highest risk-adjusted performance. The mutual fund industry has experienced spectacular growth in assets and number of funds in the past two decades, and as this use of third parties to manage funds has increased, so has the need to measure the performance of these vendors-relative not only to their own benchmarks but also to their peers. A new methodology is presented here to measure the risk-adjusted performance of a mutual fund and to permit effective ranking among peers.The new measure, called the M-3, accounts for differences in (1) standard deviation between a portfolio and a benchmark and (2) the correlations of mutual fund portfolios and their benchmarks for an investor's relative-risk target. Correlations are important for two reasons: They serve both as measures of covariance with other assets for optimal portfolio selection and as forward-looking risk measures.The M-3 measure facilitates comparison of mutual funds and can be used to create optimal risk-adjusted portfolios. It is superior to the information ratio, the Sharpe ratio, and the M-2 measure (shown to be a special case of the M-3 measure), which may be inappropriate to adjust for risk. The information ratio by itself is not a useful measure of outperformance or for ranking portfolios. It is valid only when leverage is not permitted. The M-2 measure is appropriate only for reviewing historical performance or if one ignores the issues created when agents manage portfolios for others, and it fails the test on a forward-looking basis or when adding the benchmark can improve risk-adjusted performance. By exploiting the role of correlation as a measure of forward-looking risk, the proposed M-3 measure provides rankings of portfolios that are different from those of other techniques. Furthermore, the information ratio and Sharpe ratio are unable to indicate how portfolios should be structured to achieve a target tracking error.To demonstrate the superiority of the M-3 measure, I first applied the M-3 measure to 10 years of mutual fund data from a previous study. This exercise demonstrates the differences in rankings the three analytical methods provide. Next, I chose 10 mutual funds with high annualized absolute returns relative to the S&P 500 Index for the period September 1989 through August 1999 and compared these funds on a risk-adjusted basis. I show that when this technique is used to adjust for risk, the rankings of the mutual funds change from rankings provided by other measures. In fact, this comparison reveals that some of the funds that underperformed on a risk-adjusted basis when the M-2 method is used outperform when the M-3 method is used. I show that the M-2 measure or the Sharpe ratio can lead to incorrect rankings because they ignore correlations and thus are not forward-looking measures. They also ignore the possibility of investing passively in the benchmark to improve risk-adjusted performance. Leverage is found to be useful when it is used to structure portfolios of the highest risk-adjusted performance and when it can be created through shorting the risk-free asset or the benchmark.The M-3 technique provides an accurate measure of risk-adjusted performance by correcting for differences in standard deviations and for differences in correlations. The M-3 measure facilitates optimal portfolio construction to achieve investors' objectives by combining the risk-free asset, the benchmark, and mutual funds. This paradigm, a type of three-fund separation, provides an optimal mix of active and passive management based on the skill of fund managers rather than individual biases concerning market inefficiency. Furthermore, whereas the information ratio and Sharpe ratio are unable to indicate how portfolios should be structured to achieve a target tracking error, the M-3 measure provides such guidance. Thus, when agents manage portfolios on behalf of principals or principals are structuring their own portfolios, the M-3 measure is the most appropriate way to adjust for risk.