M2Sortino | R Documentation |
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_S = r_P + Sortino ratio * (\sigma_{DM} - \sigma_D)
where M^2_S
is MSquared for Sortino, r_P
is the annualised portfolio return,
\sigma_{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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