PerformanceAnalytics (version 2.0.8)

OmegaExcessReturn: Omega excess return of the return distribution

Description

Omega excess return is another form of downside risk-adjusted return. It is calculated by multiplying the downside variance of the style benchmark by 3 times the style beta.

Usage

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

Arguments

Ra

an xts, vector, matrix, data frame, timeSeries or zoo object of asset returns

Rb

return vector of the benchmark asset

MAR

the minimum acceptable return

...

any other passthru parameters

Author

Matthieu Lestel

Details

$$\omega = r_P - 3*\beta_S*\sigma_{MD}^2$$

where \(\omega\) is omega excess return, \(\beta_S\) is style beta, \(\sigma_D\) is the portfolio annualised downside risk and \(\sigma_{MD}\) is the benchmark annualised downside risk.

References

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

Examples

data(portfolio_bacon)
MAR = 0.005
print(OmegaExcessReturn(portfolio_bacon[,1], portfolio_bacon[,2], MAR)) #expected 0.0805

data(managers)
MAR = 0
print(OmegaExcessReturn(managers['1996',1], managers['1996',8], MAR))
print(OmegaExcessReturn(managers['1996',1:5], managers['1996',8], MAR))