PerformanceAnalytics (version 1.1.0)

M2Sortino: M squared for Sortino of the return distribution

Description

M squared for Sortino is a M^2 calculated for Downside risk instead of Total Risk

Usage

M2Sortino(Ra, Rb, MAR = 0, ...)

Arguments

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

Details

$$M^2_S = r_P + Sortino ratio * (\sigma_{DM} - \sigma_D)$$

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

References

Carl Bacon, Practical portfolio performance measurement and attribution, second edition 2008 p.102-103

Examples

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))