calculate annualized Sharpe Ratio

The Sharpe Ratio is a risk-adjusted measure of return that uses standard deviation to represent risk.

SharpeRatio.annualized(R, Rf = 0, scale = NA, geometric = TRUE)

Arguments

R	an xts, vector, matrix, data frame, timeSeries or zoo object of asset returns
Rf	risk free rate, in same period as your returns
scale	number of periods in a year (daily scale = 252, monthly scale = 12, quarterly scale = 4)
geometric	utilize geometric chaining (TRUE) or simple/arithmetic chaining (FALSE) to aggregate returns, default TRUE

Details

The Sharpe ratio is simply the return per unit of risk (represented by variance). The higher the Sharpe ratio, the better the combined performance of "risk" and return.

This function annualizes the number based on the scale parameter. $$\frac{\sqrt[n]{prod(1+R_{a})^{scale}}-1}{\sqrt{scale}\cdot\sqrt{\sigma}}$$

Using an annualized Sharpe Ratio is useful for comparison of multiple return streams. The annualized Sharpe ratio is computed by dividing the annualized mean monthly excess return by the annualized monthly standard deviation of excess return.

William Sharpe now recommends Information Ratio preferentially to the original Sharpe Ratio.

References

Sharpe, W.F. The Sharpe Ratio,Journal of Portfolio Management,Fall 1994, 49-58.

See also

SharpeRatio InformationRatio TrackingError ActivePremium SortinoRatio

Examples

data(managers)
SharpeRatio.annualized(managers[,1,drop=FALSE], Rf=.035/12)
#>                                       HAM1
#> Annualized Sharpe Ratio (Rf=3.5%) 1.112293
SharpeRatio.annualized(managers[,1,drop=FALSE], Rf = managers[,10,drop=FALSE])
#>                                       HAM1
#> Annualized Sharpe Ratio (Rf=3.9%) 1.066795
SharpeRatio.annualized(managers[,1:6], Rf=.035/12)
#>                                       HAM1     HAM2      HAM3      HAM4
#> Annualized Sharpe Ratio (Rf=3.5%) 1.112293 1.059085 0.8854393 0.4512555
#>                                         HAM5     HAM6
#> Annualized Sharpe Ratio (Rf=3.5%) 0.01046591 1.194146
SharpeRatio.annualized(managers[,1:6], Rf = managers[,10,drop=FALSE])
#>                                       HAM1     HAM2      HAM3      HAM4
#> Annualized Sharpe Ratio (Rf=3.9%) 1.066795 1.033019 0.8539722 0.4292173
#>                                         HAM5     HAM6
#> Annualized Sharpe Ratio (Rf=3.9%) 0.04441162 1.333868
SharpeRatio.annualized(managers[,1:6], Rf = managers[,10,drop=FALSE],geometric=FALSE)
#>                                       HAM1     HAM2      HAM3      HAM4
#> Annualized Sharpe Ratio (Rf=3.9%) 1.067297 1.035284 0.8747901 0.5072777
#>                                        HAM5     HAM6
#> Annualized Sharpe Ratio (Rf=3.9%) 0.1228211 1.311291