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Sharpe ratio in percentage points instead of unitless numbers. The "what would this look like at S&P 500 risk?" lens.
Modigliani-squared (M²) converts Sharpe ratio into a directly comparable percentage return. It rescales a portfolio's return to match the volatility of a benchmark, then subtracts the benchmark's actual return. Where Sharpe is unitless and abstract, M² answers in dollars: if you levered this portfolio to match the S&P 500's volatility, what return would it produce?
M² = Sharpe · σ_benchmark + RfM² = Sharpep · σbenchmark + RfThink of it as scaling your portfolio up or down until its volatility equals the benchmark's, then asking what return it would produce. The answer is in percentage points, directly comparable to the benchmark itself.
Sharpe ratio is mathematically beautiful but practically hard to interpret. Is a Sharpe of 0.8 a lot? M² answers the question by translating Sharpe into a return percentage at a known volatility level. If the benchmark has 15% volatility and your M² is 11.5%, that is a direct comparison: a benchmark-volatility version of your portfolio would have returned 11.5%.
Your portfolio has Sharpe of 0.75. The benchmark (S&P 500) had volatility of 15.5%, and the risk-free rate was 4.5%.
M² = 0.75 · 15.5% + 4.5% = 11.625% + 4.5% = 16.1%
If the benchmark itself returned 12%, then your M² of 16.1% says your portfolio is a 4.1% improvement at the same risk level.
Compare M² directly to the benchmark's nominal return. If M² > benchmark return, your risk-adjusted performance beats the benchmark. The magnitude is in percentage points — easy to interpret.
Sharpe Ratio · Lo-Adjusted Sharpe · Treynor Ratio · Volatility
When explaining risk-adjusted return to non-quants. M² is in percentage points, which is easier to grasp than Sharpe's unitless scale.
Franco Modigliani and his granddaughter Leah Modigliani in 1997. Hence "Modigliani-squared."
Yes — if Sharpe is negative (you underperformed the risk-free rate), M² will be less than Rf.
Yes — alongside Sharpe and the other risk-adjusted ratios. M² is shown against multiple benchmarks (S&P 500, VT, etc.) for direct visual comparison.
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