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, ...)

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

Author

Matthieu Lestel

Examples

data(portfolio_bacon)
MAR = 0.005
print(M2Sortino(portfolio_bacon[,1], portfolio_bacon[,2], MAR)) #expected 0.1035
#>                            portfolio.monthly.return....
#> Sortino Ratio (MAR = 0.5%)                    0.1034799

data(managers)
MAR = 0
print(MSquaredExcess(managers['1996',1], managers['1996',8], MAR))
#>            SP500 TR
#> SP500 TR 0.02027322
print(MSquaredExcess(managers['1996',1:5], managers['1996',8], MAR))
#>                                      HAM1 HAM2      HAM3        HAM4 HAM5
#> MSquaredExcess (Risk free = 0) 0.02027322   NA 0.1409545 -0.02546609   NA