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.
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, ...)
| 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
|
| annualize | if TRUE, annualize the measure, default FALSE |
| … | any other passthru parameters to the VaR or ES functions |
$$\frac{\overline{(R_{a}-R_{f})}}{\sqrt{\sigma_{(R_{a}-R_{f})}}}$$
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 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)
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.
SharpeRatio.annualized
InformationRatio TrackingError
ActivePremium SortinoRatio
VaR ES
data(managers) SharpeRatio(managers[,1,drop=FALSE], Rf=.035/12, FUN="StdDev")#> HAM1 #> StdDev Sharpe (Rf=0.3%, p=95%): 0.3201889SharpeRatio(managers[,1,drop=FALSE], Rf = managers[,10,drop=FALSE], FUN="StdDev")#> HAM1 #> StdDev Sharpe (Rf=0.3%, p=95%): 0.308102SharpeRatio(managers[,1:6], Rf=.035/12, FUN="StdDev")#> HAM1 HAM2 HAM3 HAM4 #> StdDev Sharpe (Rf=0.3%, p=95%): 0.3201889 0.3057649 0.2610141 0.1522615 #> HAM5 HAM6 #> StdDev Sharpe (Rf=0.3%, p=95%): 0.02562009 0.3417545SharpeRatio(managers[,1:6], Rf = managers[,10,drop=FALSE], FUN="StdDev")#> HAM1 HAM2 HAM3 HAM4 #> StdDev Sharpe (Rf=0.3%, p=95%): 0.308102 0.2988608 0.2525301 0.1464385 #> HAM5 HAM6 #> StdDev Sharpe (Rf=0.3%, p=95%): 0.0354554 0.3785371data(edhec) SharpeRatio(edhec[, 6, drop = FALSE], FUN="VaR")#> Event Driven #> VaR Sharpe (Rf=0%, p=95%): 0.2710161SharpeRatio(edhec[, 6, drop = FALSE], Rf = .04/12, FUN="VaR")#> Event Driven #> VaR Sharpe (Rf=0.3%, p=95%): 0.1524982SharpeRatio(edhec[, 6, drop = FALSE], Rf = .04/12, FUN="VaR" , method="gaussian")#> Event Driven #> VaR Sharpe (Rf=0.3%, p=95%): 0.1909461SharpeRatio(edhec[, 6, drop = FALSE], FUN="ES")#> Event Driven #> ES Sharpe (Rf=0%, p=95%): 0.1289815# and all the methods SharpeRatio(managers[,1:9], Rf = managers[,10,drop=FALSE])#> HAM1 HAM2 HAM3 HAM4 #> StdDev Sharpe (Rf=0.3%, p=95%): 0.3081020 0.2988608 0.2525301 0.14643845 #> VaR Sharpe (Rf=0.3%, p=95%): 0.2306863 0.3970699 0.2504936 0.09553906 #> ES Sharpe (Rf=0.3%, p=95%): 0.1295014 0.1788256 0.2093343 0.06625013 #> HAM5 HAM6 EDHEC LS EQ SP500 TR #> StdDev Sharpe (Rf=0.3%, p=95%): 0.03545540 0.3785371 0.3142695 0.12558293 #> VaR Sharpe (Rf=0.3%, p=95%): 0.02399862 0.3022965 0.2737607 0.07957460 #> ES Sharpe (Rf=0.3%, p=95%): 0.01664487 0.2308450 0.1855867 0.05760917 #> US 10Y TR #> StdDev Sharpe (Rf=0.3%, p=95%): 0.05684359 #> VaR Sharpe (Rf=0.3%, p=95%): 0.03741555 #> ES Sharpe (Rf=0.3%, p=95%): 0.02610548SharpeRatio(edhec,Rf = .04/12)#> Convertible Arbitrage CTA Global #> StdDev Sharpe (Rf=0.3%, p=95%): 0.15339751 0.12558803 #> VaR Sharpe (Rf=0.3%, p=95%): 0.09469804 0.09337063 #> ES Sharpe (Rf=0.3%, p=95%): 0.03089192 0.07366957 #> Distressed Securities Emerging Markets #> StdDev Sharpe (Rf=0.3%, p=95%): 0.25179740 0.12736677 #> VaR Sharpe (Rf=0.3%, p=95%): 0.16804482 0.07720662 #> ES Sharpe (Rf=0.3%, p=95%): 0.07589603 0.03841453 #> Equity Market Neutral Event Driven #> StdDev Sharpe (Rf=0.3%, p=95%): 0.2963971 0.23372885 #> VaR Sharpe (Rf=0.3%, p=95%): 0.2352556 0.15249824 #> ES Sharpe (Rf=0.3%, p=95%): 0.0622208 0.07257669 #> Fixed Income Arbitrage Global Macro #> StdDev Sharpe (Rf=0.3%, p=95%): 0.06333844 0.2549431 #> VaR Sharpe (Rf=0.3%, p=95%): 0.03637036 0.2802548 #> ES Sharpe (Rf=0.3%, p=95%): 0.01508086 0.2187777 #> Long/Short Equity Merger Arbitrage #> StdDev Sharpe (Rf=0.3%, p=95%): 0.19962891 0.3090483 #> VaR Sharpe (Rf=0.3%, p=95%): 0.14572983 0.2321344 #> ES Sharpe (Rf=0.3%, p=95%): 0.09399888 0.1037628 #> Relative Value Short Selling Funds of Funds #> StdDev Sharpe (Rf=0.3%, p=95%): 0.25525305 0.015024743 0.14194452 #> VaR Sharpe (Rf=0.3%, p=95%): 0.17482979 0.011139811 0.10328569 #> ES Sharpe (Rf=0.3%, p=95%): 0.06890142 0.009175123 0.05597178