We can interpret the measure as the difference between the scaled excess return of our portfolio P and that of the market, where the scaled portfolio has the same volatility as the market.
It is derived from the widely used Sharpe ratio, but it has the significant advantage of being in units of percent return (as opposed to the Sharpe ratio – an abstract, dimensionless ratio of limited utility to most investors), which makes it dramatically more intuitive to interpret.
[1] Sharpe originally called it the "reward-to-variability" ratio before it began being called the Sharpe ratio by later academics and financial operators.
[3] They originally called it "RAP" (risk-adjusted performance).
They also defined a related statistic, "RAPA" (presumably, an abbreviation of "risk-adjusted performance alpha"), which was defined as RAP minus the risk-free rate (i.e., it only involved the risk-adjusted return above the risk-free rate).
Thus, RAPA was effectively the risk-adjusted excess return.
be the excess return of the portfolio (i.e., above the risk-free rate) for some time period
is the average risk-free rate for the period in question.
and rearrange: The original paper also defined a statistic called "RAPA" (presumably, an abbreviation of "risk-adjusted performance alpha").
The M2 measure is used to characterize how well a portfolio's return rewards an investor for the amount of risk taken, relative to that of some benchmark portfolio and to the risk-free rate.
Thus, an investment that took a great deal more risk than some benchmark portfolio, but only had a small performance advantage, might have lesser risk-adjusted performance than another portfolio that took dramatically less risk relative to the benchmark, but had similar returns.
Further, it is difficult to directly compare the Sharpe ratios of several investments.
M2 has the enormous advantage that it is in units of percentage return, which is instantly interpretable by virtually all investors.
Thus, for example, it is easy to recognize the magnitude of the difference between two investment portfolios which have M2 values of 5.2% and of 5.8%.
The difference is 0.6 percentage points of risk-adjusted return per year, with the riskiness adjusted to that of the benchmark portfolio (whatever that might be, but usually the market).
It is not necessary to use standard deviation of excess returns as the measure of risk.