What is the formula for M^2?

The formula for M^2, also known as the Modigliani-Modigliani measure, is indeed represented by the risk-free rate plus the Sharpe ratio multiplied by the standard deviation of the market. This measure is designed to calculate the risk-adjusted performance of an investment portfolio in comparison to a benchmark.

To dissect this further, the M^2 measure compares the excess return of a portfolio (which is the return over the risk-free rate) relative to the standard deviation (or risk) of the market. The Sharpe ratio, which measures the risk-adjusted return of an investment, reflects how much excess return is received for the extra volatility that is taken on by the portfolio.

By multiplying the Sharpe ratio by the standard deviation of the market, you essentially scale the risk-adjusted excess return of the portfolio to be on the same level of risk as the market. When you then add the risk-free rate to this value, it provides a way to assess how the portfolio’s performance stacks up against a benchmark, making it an useful tool in portfolio management and performance evaluation.

Other options do not adequately represent the M^2 calculation or confuse components of risk or return that are not in line with the appropriate formulation.