M-ratio

The M-ratio, also known as the Modigliani Risk-Adjusted Performance (MRAP) measure, is a measure of risk-adjusted return. It provides a percentage representation of excess return relative to the risk of a benchmark portfolio. Unlike the Sharpe ratio, which expresses return relative to the standard deviation of the portfolio, the M-ratio adjusts the portfolio's return to match the volatility of the market or a specified benchmark. This allows for a direct comparison of portfolios with different levels of risk to the market.

The M-ratio effectively creates a leveraged (or deleveraged) portfolio that has the same risk (standard deviation) as the market. The difference in return between this risk-adjusted portfolio and the risk-free rate is then compared to the market's excess return over the risk-free rate. This difference in return, scaled to the market's risk, is the M-ratio.

A higher M-ratio indicates better risk-adjusted performance, meaning the portfolio has generated a higher return for the same level of risk as the market. A negative M-ratio indicates underperformance relative to the market when adjusted for risk. The M-ratio is often preferred over the Sharpe ratio when comparing portfolios with significantly different levels of volatility to a specific benchmark.