Modigliani M² Measure
Computes Modigliani's M² measure (also M-squared or RAP), which translates the Sharpe ratio back into percentage points of return. The idea is plain: scale the portfolio to the market's volatility and ask what it would have returned under those conditions, M² = Rf + (Rp − Rf)·(σmarket/σportfolio). Unlike the Sharpe ratio, a bare number, M² compares directly against the benchmark's return. Above the market return, the portfolio beat the benchmark on a risk-adjusted basis. Enter the portfolio return and volatility, the risk-free rate and the market volatility.
Result
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Modigliani M² Measure
Computes Modigliani's M² measure (also M-squared or RAP), which translates the Sharpe ratio back into percentage points of return. The idea is plain: scale the portfolio to the market's volatility and ask what it would have returned under those conditions, M² = Rf + (Rp − Rf)·(σmarket/σportfolio). Unlike the Sharpe ratio, a bare number, M² compares directly against the benchmark's return. Above the market return, the portfolio beat the benchmark on a risk-adjusted basis. Enter the portfolio return and volatility, the risk-free rate and the market volatility.
The Sharpe ratio rewritten in plain numbers
The Sharpe ratio is great for ranking portfolios, but it has a communication flaw: it's a bare number with no units. Saying a fund has a Sharpe of 0.8 means almost nothing to someone who doesn't live in this world. To fix that itch, Franco Modigliani and his granddaughter Leah came up with the M² measure in 1997, which brings the comparison back to familiar ground: percentage points of return.
The trick is elegant. Picture taking your portfolio and adjusting its leverage until it has exactly the market's volatility. What would it have returned in that scenario? That's M². Since both now carry the same risk, you can compare them head to head: if M² beats the index return, the portfolio genuinely delivered more per unit of risk. If it falls short, it didn't pay off.
Enter the portfolio return and volatility, the risk-free rate and the market volatility. The maths behind it is simple: it rescales the portfolio's risk premium by the ratio of the two volatilities and adds back the risk-free rate. A result in percent is far easier to carry into a meeting than a naked Sharpe number.
Related Tools
Sharpe Ratio from Series
Computes the Sharpe ratio directly from a series of returns: the mean return minus the risk-free rate, divided by the sample standard deviation. It's the most practical way to get the Sharpe when you have the history at hand, without computing the mean and volatility separately. Remember the result comes in the frequency of the data entered — to annualize monthly returns, multiply by the square root of twelve. Enter the list of returns and the risk-free rate for the same period.
Burke Ratio
Computes the Burke ratio: the excess return over the risk-free rate divided by the square root of the sum of squared drawdowns. Unlike the Sharpe ratio, which penalizes all volatility, Burke focuses only on the falls, and by squaring each drawdown it punishes deep falls more than shallow ones. It's one of the tail-risk-adjusted performance metrics. Enter the portfolio return, the risk-free rate and the list of drawdowns in percent.
Sterling Ratio
Computes the Sterling ratio, a drawdown-adjusted performance measure. It divides return by a measure of how much the portfolio typically falls from peak to trough, rewarding strategies that deliver return without big drops. The tool shows two versions: the modern one, using excess return over the risk-free rate divided by the average drawdown, and the original Deane Sterling Jones form, which adds a ten percent constant to the denominator. Enter the annualized return, the risk-free rate and the average annual maximum drawdown.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.