Risk-Adjusted Performance: The Correlation Correction

Abstract

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.