M squared for Sortino of the return distribution
M squared for Sortino is a M^2 calculated for Downside risk instead of Total Risk
M2Sortino(Ra, Rb, MAR = 0, ...)
Ra |
an xts, vector, matrix, data frame, timeSeries or zoo object of asset return |
Rb |
return vector of the benchmark asset |
MAR |
the minimum acceptable return |
... |
any other passthru parameters |
M^2 (Sortino) = Rp + Sortino ratio * (DownsideRiskBenchmark - DownsideRiskPortfolio)
where M^2_S is MSquared for Sortino, r_P is the annualised portfolio return, σ_{DM} is the benchmark annualised downside risk and D is the portfolio annualised downside risk
Matthieu Lestel
Carl Bacon, Practical portfolio performance measurement and attribution, second edition 2008 p.102-103
data(portfolio_bacon) MAR = 0.005 print(M2Sortino(portfolio_bacon[,1], portfolio_bacon[,2], MAR)) #expected 0.1035 data(managers) MAR = 0 print(MSquaredExcess(managers['1996',1], managers['1996',8], MAR)) print(MSquaredExcess(managers['1996',1:5], managers['1996',8], MAR))
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