SharpeRatio {PerformanceAnalytics} | R Documentation

## calculate a traditional or modified Sharpe Ratio of Return over StdDev or VaR or ES

### Description

The Sharpe ratio is simply the return per unit of risk (represented by variability). In the classic case, the unit of risk is the standard deviation of the returns.

### Usage

    SharpeRatio(R, Rf = 0, p = 0.95, FUN = c("StdDev", "VaR", "ES"),
      weights = NULL, annualize = FALSE, ...)

    SharpeRatio.modified(R, Rf = 0, p = 0.95, FUN = c("StdDev", "VaR",
      "ES"), weights = NULL, ...)

### 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
`p` | confidence level for calculation, default p=.95
`FUN` | one of "StdDev" or "VaR" or "ES" to use as the denominator
`weights` | portfolio weighting vector, default NULL, see Details in `VaR`
`annualize` | if TRUE, annualize the measure, default FALSE
`...` | any other passthru parameters to the VaR or ES functions

### Details

\frac{\overline{(R_{a}-R_{f})}}{√{σ_{(R_{a}-R_{f})}}}

William Sharpe now recommends `InformationRatio` preferentially to the original Sharpe Ratio.

The higher the Sharpe ratio, the better the combined performance of "risk" and return.

As noted, the traditional Sharpe Ratio is a risk-adjusted measure of return that uses standard deviation to represent risk.

A number of papers now recommend using a "modified Sharpe" ratio using a Modified Cornish-Fisher VaR or CVaR/Expected Shortfall as the measure of Risk.

We have recently extended this concept to create multivariate modified Sharpe-like Ratios for standard deviation, Gaussian VaR, modified VaR, Gaussian Expected Shortfall, and modified Expected Shortfall. See `VaR` and `ES`. You can pass additional arguments to `VaR` and `ES` via ... The most important is probably the 'method' argument/

This function returns a traditional or modified Sharpe ratio for the same periodicity of the data being input (e.g., monthly data -> monthly SR)

### Author(s)

Brian G. Peterson

### References

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

Laurent Favre and Jose-Antonio Galeano. Mean-Modified Value-at-Risk Optimization with Hedge Funds. Journal of Alternative Investment, Fall 2002, v 5.

### See Also

`SharpeRatio.annualized`
`InformationRatio`
`TrackingError`
`ActivePremium`
`SortinoRatio`
`VaR`
`ES`

### Examples

    data(managers)
    SharpeRatio(managers[,1,drop=FALSE], Rf=.035/12, FUN="StdDev")
    SharpeRatio(managers[,1,drop=FALSE], Rf = managers[,10,drop=FALSE], FUN="StdDev")
    SharpeRatio(managers[,1:6], Rf=.035/12, FUN="StdDev")
    SharpeRatio(managers[,1:6], Rf = managers[,10,drop=FALSE], FUN="StdDev")

    data(edhec)
    SharpeRatio(edhec[, 6, drop = FALSE], FUN="VaR")
    SharpeRatio(edhec[, 6, drop = FALSE], Rf = .04/12, FUN="VaR")
    SharpeRatio(edhec[, 6, drop = FALSE], Rf = .04/12, FUN="VaR" , method="gaussian")
    SharpeRatio(edhec[, 6, drop = FALSE], FUN="ES")

    # and all the methods
    SharpeRatio(managers[,1:9], Rf = managers[,10,drop=FALSE])
    SharpeRatio(edhec,Rf = .04/12)

[Package PerformanceAnalytics version 1.5.3 Index]