M squared of the return distribution

M squared is a risk adjusted return useful to judge the size of relative performance between differents portfolios. With it you can compare portfolios with different levels of risk.

MSquared(Ra, Rb, Rf = 0, ...)

Arguments

Ra

an xts, vector, matrix, data frame, timeSeries or zoo object of asset return
Rb

return vector of the benchmark asset
Rf

risk free rate, in same period as your returns
…

any other passthru parameters

Details

$$M^2 = r_P + SR * (\sigma_M - \sigma_P) = (r_P - r_F) * \frac{\sigma_M}{\sigma_P} + r_F$$

where \(r_P\) is the portfolio return annualized, \(\sigma_M\) is the market risk and \(\sigma_P\) is the portfolio risk

References

Carl Bacon, Practical portfolio performance measurement and attribution, second edition 2008 p.67-68

Examples


data(portfolio_bacon)
print(MSquared(portfolio_bacon[,1], portfolio_bacon[,2])) #expected 0.10062
#>                      benchmark.return....
#> benchmark.return....              0.10062

data(managers)
print(MSquared(managers['1996',1], managers['1996',8]))
#>           SP500 TR
#> SP500 TR 0.2544876
print(MSquared(managers['1996',1:5], managers['1996',8]))
#>                               HAM1 HAM2      HAM3      HAM4 HAM5
#> MSquared (Risk free = 0) 0.2544876   NA 0.4028725 0.1982483   NA