Performance

M² (Modigliani-Modigliani)

M² (Modigliani-Modigliani) rescales the Sharpe Ratio to the benchmark's volatility, expressing risk-adjusted return in percentage points directly comparable to the benchmark.

Also known as: Modigliani risk-adjusted performance · M2 · RAP

M² (Modigliani-Modigliani Risk-Adjusted Performance), introduced by Franco and Leah Modigliani in 1997, takes the Sharpe Ratio and rescales it back into percentage-point return space at the benchmark's volatility. The advantage is communication — a number like "M² = 8.4%" is intelligible to non-technical investors in a way "Sharpe = 0.92" is not.

Formula

M² = ( Sharpe_p × σ_b ) + R_f
    = ( ( R_p − R_f ) / σ_p ) × σ_b + R_f

Interpretation: if I leverage the portfolio up or down until its volatility equals the benchmark's, what annual return would it have produced? M² > benchmark return → outperformed on a risk-adjusted basis; M² < benchmark → underperformed.

When M² is useful

·Communicating fund performance to a non-technical audience.
·Ranking funds with very different volatility profiles against a common benchmark.
·Pension-board reporting where everything must be expressible as a percentage.

How MEDGE Capital uses M²

M² is reported in the Compare module next to Sharpe when a benchmark is selected — gives readers a direct "how many percentage points of return did the active risk buy" answer.