# Modigliani Risk-Adjusted Performance (M2, RAP)

Written By
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.
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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

### Formula

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

Where:

• 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.

## Significance

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.

### Decision-Making

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.

### Comparability

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

## Limitations

### Benchmark Dependency

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

### 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.

## Conclusion

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.

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