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Modigliani risk-adjusted performance: Explained

BY TIO Staff

|August 3, 2024

In the world of trading and investment, the Modigliani risk-adjusted performance (M2) is a key metric used to assess the risk-adjusted returns of an investment portfolio. Named after Franco Modigliani, a Nobel laureate in economics, this measure provides a comprehensive view of a portfolio's performance, taking into account both its returns and the risk associated with those returns.

The M2 measure is particularly useful in comparing the performance of different portfolios, as it adjusts for risk, allowing for a fair comparison between portfolios with different risk profiles. In this comprehensive glossary article, we will delve deep into the concept of Modigliani risk-adjusted performance, its calculation, its uses, and its limitations.

Understanding Modigliani risk-adjusted performance

The Modigliani risk-adjusted performance (M2) measure is a risk-adjusted measure of a portfolio's performance. It is derived from the Sharpe ratio, another popular risk-adjusted performance measure, but presents the results in a more intuitive manner. While the Sharpe ratio provides a dimensionless measure of risk-adjusted performance, the M2 measure expresses the risk-adjusted performance in terms of annual return percentage, which is easier for most investors to understand.

The M2 measure is calculated by adjusting the portfolio's returns for risk, using the risk-free rate of return as a benchmark. The risk adjustment is done by scaling the portfolio's returns to match the volatility of a benchmark portfolio. This allows the M2 measure to provide a fair comparison of different portfolios, regardless of their risk profiles.

Calculation of M2

The calculation of the M2 measure involves several steps. First, the excess return of the portfolio is calculated by subtracting the risk-free rate of return from the portfolio's return. This excess return is then divided by the portfolio's standard deviation, which is a measure of the portfolio's risk. The result is the Sharpe ratio of the portfolio.

Next, the Sharpe ratio is multiplied by the standard deviation of the benchmark portfolio, and the risk-free rate is added back in. The result is the M2 measure of the portfolio. This process effectively scales the portfolio's returns to match the risk level of the benchmark portfolio, allowing for a fair comparison of the two.

Interpretation of M2

The M2 measure provides a measure of a portfolio's risk-adjusted performance in terms of annual return percentage. A higher M2 measure indicates a better risk-adjusted performance. When comparing different portfolios, the one with the higher M2 measure is considered to have performed better, considering both its returns and its risk.

However, it's important to note that the M2 measure is a relative measure. It provides a comparison of the portfolio's performance against a benchmark, not an absolute measure of the portfolio's performance. Therefore, the choice of benchmark can significantly affect the M2 measure.

Uses of M2

The M2 measure is widely used in the field of investment management. It is particularly useful in comparing the performance of different portfolios, as it adjusts for risk, allowing for a fair comparison between portfolios with different risk profiles. By using the M2 measure, investors can identify which portfolios are delivering the best returns for a given level of risk.

Additionally, the M2 measure can be used to evaluate the performance of investment managers. By comparing the M2 measures of different managers, investors can identify which managers are delivering the best risk-adjusted performance. This can be a valuable tool in selecting investment managers and in monitoring their performance.

Portfolio comparison

One of the main uses of the M2 measure is in the comparison of different portfolios. By adjusting for risk, the M2 measure allows for a fair comparison of portfolios with different risk profiles. This can be particularly useful in the context of portfolio selection, where investors need to choose between different portfolios based on their risk and return characteristics.

For example, consider two portfolios, A and B. Portfolio A has a higher return than portfolio B, but also a higher risk. By calculating the M2 measures of the two portfolios, investors can determine which portfolio has a better risk-adjusted performance. If portfolio A has a higher M2 measure, it means that its higher return is enough to compensate for its higher risk, making it a better choice for investors.

Performance evaluation

The M2 measure can also be used to evaluate the performance of investment managers. By comparing the M2 measures of different managers, investors can identify which managers are delivering the best risk-adjusted performance. This can be a valuable tool in selecting investment managers and in monitoring their performance.

For example, consider two investment managers, X and Y. Manager X has a higher return than manager Y, but also a higher risk. By calculating the M2 measures of the two managers, investors can determine which manager has a better risk-adjusted performance. If manager X has a higher M2 measure, it means that his higher return is enough to compensate for his higher risk, making him a better choice for investors.

Limitations of M2

While the M2 measure is a powerful tool in assessing risk-adjusted performance, it is not without its limitations. One of the main limitations of the M2 measure is that it assumes that returns are normally distributed and that risk can be adequately captured by standard deviation. However, in reality, returns are often not normally distributed and risk can take many forms, not all of which can be captured by standard deviation.

Another limitation of the M2 measure is that it is a relative measure. It provides a comparison of the portfolio's performance against a benchmark, not an absolute measure of the portfolio's performance. Therefore, the choice of benchmark can significantly affect the M2 measure. If the benchmark is not representative of the portfolio's investment strategy, the M2 measure may not provide a meaningful assessment of the portfolio's performance.

Assumption of normal distribution

The M2 measure assumes that returns are normally distributed. This means that it assumes that returns are symmetrically distributed around the mean, with the majority of returns close to the mean and fewer returns further away. However, in reality, returns are often not normally distributed. They can be skewed, with more returns on one side of the mean than the other, or they can have fat tails, with more extreme returns than would be expected under a normal distribution.

This assumption of normal distribution can lead to inaccurate assessments of risk-adjusted performance. If returns are skewed or have fat tails, the standard deviation may not adequately capture the risk of the portfolio, leading to an over- or under-estimation of the M2 measure. Therefore, when using the M2 measure, it's important to be aware of this limitation and to consider other measures of risk and performance as well.

Reliance on benchmark

The M2 measure is a relative measure, meaning it provides a comparison of the portfolio's performance against a benchmark. Therefore, the choice of benchmark can significantly affect the M2 measure. If the benchmark is not representative of the portfolio's investment strategy, the M2 measure may not provide a meaningful assessment of the portfolio's performance.

For example, consider a portfolio that invests in high-risk, high-return assets. If the benchmark is a low-risk, low-return index, the M2 measure may overestimate the portfolio's risk-adjusted performance, as it compares the portfolio's returns to those of a less risky benchmark. Therefore, when using the M2 measure, it's important to choose a benchmark that is representative of the portfolio's investment strategy.

Conclusion

The Modigliani risk-adjusted performance (M2) is a valuable tool in the field of investment management. It provides a measure of a portfolio's risk-adjusted performance, allowing for a fair comparison of different portfolios and investment managers. However, like all performance measures, it is not without its limitations. It assumes that returns are normally distributed and that risk can be adequately captured by standard deviation, and it is a relative measure that depends on the choice of benchmark.

Therefore, while the M2 measure can provide valuable insights into a portfolio's performance, it should not be used in isolation. Investors should consider other measures of risk and performance as well, and should be aware of the limitations of the M2 measure. By doing so, they can make more informed investment decisions and better manage their portfolios.

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TIO Staff

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