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, ...)
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 |
M squared = Rp + SR * (Market risk - Portfolio risk) = (Rp - Rf) * Market risk / Portfolio risk + Rf
where r_P is the portfolio return annualized, σ_M is the market risk and σ_P is the portfolio risk
Matthieu Lestel
Carl Bacon, Practical portfolio performance measurement and attribution, second edition 2008 p.67-68
data(portfolio_bacon) print(MSquared(portfolio_bacon[,1], portfolio_bacon[,2])) #expected 0.10062 data(managers) print(MSquared(managers['1996',1], managers['1996',8])) print(MSquared(managers['1996',1:5], managers['1996',8]))
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