Modigliani Squared (M2) Finance: A Risk-Adjusted Performance Measure

Modigliani Squared (M2), often simply called M-squared, is a risk-adjusted performance measure that builds upon the Sharpe ratio. Unlike the Sharpe ratio, which expresses risk-adjusted return as a ratio, M2 presents the performance in percentage terms, making it easier to interpret and compare across different investments. It addresses a perceived limitation of the Sharpe ratio – the challenge in intuitively understanding the magnitude of the risk-adjusted difference between, say, a Sharpe ratio of 0.5 and one of 0.8.

The core idea behind M2 is to create a hypothetical portfolio that has the same risk (measured by standard deviation) as the market or benchmark portfolio. This is achieved by leveraging or deleveraging the investment portfolio. By bringing the investment portfolio’s risk profile in line with the market, a direct comparison of their returns becomes more meaningful. In essence, M2 answers the question: “If this investment had the same risk as the market, what return would it have generated?”

The formula for calculating M2 is as follows:

M2 = (Sharpe Ratio of Portfolio * Standard Deviation of Market) + Risk-Free Rate

Where:

• Sharpe Ratio of Portfolio = (Return of Portfolio – Risk-Free Rate) / Standard Deviation of Portfolio
• Standard Deviation of Market = Volatility of the market benchmark
• Risk-Free Rate = Return on a risk-free asset, such as a Treasury bill.

Let’s break down how M2 works. First, the Sharpe ratio of the portfolio is calculated, quantifying the excess return per unit of risk. Then, this Sharpe ratio is multiplied by the standard deviation of the market. This scales the portfolio’s excess return to reflect the risk level of the market. Finally, the risk-free rate is added back to the product. This ensures that the M2 value is a total return, not just an excess return.

The interpretation of M2 is straightforward: it represents the return an investment would have generated if it had taken on the same level of risk as the market benchmark. A higher M2 value indicates better risk-adjusted performance relative to the market. For instance, if a portfolio has an M2 of 12% and the market returned 8%, the portfolio outperformed the market on a risk-adjusted basis. Conversely, an M2 lower than the market’s return signifies underperformance relative to the market’s risk level.

M2 is a valuable tool for investors and portfolio managers as it allows for easy comparison of investment performance across portfolios with different risk profiles. By expressing performance in percentage terms, it offers a more intuitive understanding of risk-adjusted returns than the Sharpe ratio alone. However, it’s important to remember that M2, like the Sharpe ratio, relies on historical data and the assumption of normally distributed returns. Therefore, it should be used in conjunction with other performance metrics and qualitative analysis for a comprehensive assessment of investment performance.