The M² Measure (Modigliani–Modigliani) converts the Sharpe Ratio into an equivalent return — it shows what return the fund would have delivered if it had the same risk level as the benchmark, making risk-adjusted comparisons intuitive.
M² = Rf + Sharpe Ratio × σ(benchmark), where Rf is the risk-free rate and σ(benchmark) is the benchmark's standard deviation. It answers: 'What return would this fund have achieved if it were scaled to have exactly the same risk (standard deviation) as the benchmark?' This makes Sharpe Ratio comparisons concrete — instead of comparing abstract ratios, you compare hypothetical equal-risk returns. A fund with M² of 14% and a benchmark with actual return of 12% means: on a risk-adjusted basis, the fund outperformed by 2%.
Sharpe Ratio gives a dimensionless number that's hard to interpret intuitively. M² converts it into a familiar return percentage. It asks: 'If I levered up or de-levered this fund to match the benchmark's risk level exactly, what return would I get?' Fund M² = 14% vs Benchmark 12%: the fund delivered 2% extra return on an equal-risk comparison. It makes the Sharpe Ratio concrete and interpretable.
M² = Rf + (Sharpe Ratio of fund × Standard Deviation of benchmark).
Compare M² of the fund to the benchmark's actual return.
M² > benchmark return: fund outperformed on risk-adjusted basis.
M² < benchmark return: fund underperformed on risk-adjusted basis.
M² = Rf + Sharpe × σb