PerformanceAnalytics (version 2.0.8)

SharpeRatio: 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", "SemiSD"),
  weights = NULL,
  annualize = FALSE,
  SE = FALSE,
  SE.control = NULL,
  ...
)
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

SE

TRUE/FALSE whether to ouput the standard errors of the estimates of the risk measures, default FALSE.

SE.control

Control parameters for the computation of standard errors. Should be done using the RPESE.control function.

...

any other passthru parameters to the VaR or ES functions

Author

Brian G. Peterson

Details

$$\frac{\overline{(R_{a}-R_{f})}}{\sqrt{\sigma_{(R_{a}-R_{f})}}}$$

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 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/

Most recently, we have added Downside Sharpe Ratio (DSR) (see DownsideSharpeRatio), a short name for what Ziemba (2005) called the "Symmetric Downside Risk Sharpe Ratio" and is defined as the ratio of the mean return to the square root of lower semivariance:

$$\frac{\overline{(R_{a}-R_{f})}}{\sqrt{2}SemiSD(R_a)}$$.

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

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.

Ziemba, W. T. (2005). The symmetric downside-risk Sharpe ratio. The Journal of Portfolio Management, 32(1), 108-122.

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)