Modigliani Risk-Adjusted Performance (M2, RAP)

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Written By
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Written By
Dan Buckley
Dan Buckley is an US-based trader, consultant, and part-time writer with a background in macroeconomics and mathematical finance. He trades and writes about a variety of asset classes, including equities, fixed income, commodities, currencies, and interest rates. As a writer, his goal is to explain trading and finance concepts in levels of detail that could appeal to a range of audiences, from novice traders to those with more experienced backgrounds.

The Modigliani Risk-Adjusted Performance (M2, RAP) is a performance measure for an investment or trading portfolio.

It extends the concept of the Sharpe Ratio by adjusting a portfolio’s returns for risk.

But it presents the results in a more intuitive, percentage-rate-of-return format.


Calculation and Components


M2 is calculated by first determining the Sharpe Ratio of the portfolio and then applying this ratio to the standard deviation of a benchmark to produce a risk-adjusted return.

The formula is:


M2 = (RpRf) × (SDb/SDp) + Rf



  • Rp is the average return of the portfolio.
  • Rf is the risk-free rate.
  • SDb is the standard deviation (a measure of risk) of the benchmark.
  • SDp is the standard deviation of the portfolio.

This formula adjusts the portfolio’s returns for risk, making it comparable to the benchmark.

The risk-free rate is added back to keep the scale of returns consistent.

Benchmark Standard Deviation

The standard deviation of the benchmark is used to scale the portfolio’s performance to the level of risk of the benchmark.



Risk-Adjusted Returns

M2 provides a clear measure of the risk-adjusted returns of a portfolio.

This allows traders/investors to compare the performance of portfolios with different risk levels on a like-for-like basis.

Performance Relative to Benchmark

It helps in assessing how much additional return a portfolio has generated per unit of risk compared to a benchmark.


For investors and portfolio managers, M2 can help in decision-making processes by providing a straightforward risk-adjusted performance metric.



Intuitive Interpretation

Unlike some other risk-adjusted metrics, M2 is expressed as a rate of return.

This can make it more intuitive and easier to understand.


It allows for direct comparison between portfolios or funds of differing risk levels by normalizing their performance to a common risk level.



Benchmark Dependency

The choice of benchmark is important in the calculation of M2.

An inappropriate benchmark can lead to misleading results.

Risk Measure

Like the Sharpe Ratio, M2 uses standard deviation as a measure of risk. This assumes that returns are normally distributed.

This may not fully capture the risk in portfolios with asymmetric return distributions.

Historical Data

M2 relies on historical data. This may not always be a reliable indicator of future performance.



The Modigliani Risk-Adjusted Performance (M2, RAP) evaluates and compares the performance of trading/investment portfolios by taking into account their respective risk levels.

By converting the Sharpe Ratio into an easily interpretable percentage return format, M2 offers an intuitive understanding of a portfolio’s risk-adjusted performance relative to a benchmark.

Nonetheless, its effectiveness is contingent on the appropriate selection of benchmarks and an understanding of its underlying assumptions and limitations.