M-Squared, often written as M^2, converts the Sharpe ratio into the return a portfolio would have if it carried the same volatility as a chosen benchmark, typically the market. It starts from the portfolio Sharpe ratio, Sharpe_p = (R_p - R_f) / sigma_p, and scales it by the benchmark's volatility sigma_m to yield M^2 = R_f + Sharpe_p × sigma_m. The result is the return corresponding to the benchmark's risk level, expressed in the same units as the portfolio's returns.
Analysts apply M^2 to compare risk-adjusted performance across portfolios with different risk profiles. By expressing performance at the benchmark's level of risk, it provides a common basis for comparison alongside other metrics. Practitioners interpret a higher M^2 as stronger risk-adjusted performance relative to the benchmark, assuming the inputs are estimated consistently.
M-Squared sits among risk-adjusted performance measures that translate volatility into an intuitive return reference. It relies on the Sharpe framework and the benchmark's standard deviation as the reference risk, using standard deviation as the risk metric. It is a comparative tool rather than a predictive one, and its usefulness depends on the quality of the input estimates.
If a portfolio has a Sharpe ratio of 0.75, a risk-free rate of 2%, and the market standard deviation is 15%, M^2 would be 2% + 0.75 × 15% = 12.25%, representing the hypothetical return at the market's risk level.
Sharpe ratio · Standard deviation · Risk-free rate · Benchmark (market index) · Beta · Risk-adjusted return · Modigliani-Modigliani (M^2)