Calculates Expected Shortfall(ES) (also known as) Conditional Value at Risk(CVaR) or Expected Tail Loss (ETL) for univariate, component, and marginal cases using a variety of analytical methods.
ETL(R = NULL, p = 0.95, ..., method = c("modified", "gaussian", "historical"), clean = c("none", "boudt", "geltner"), portfolio_method = c("single", "component"), weights = NULL, mu = NULL, sigma = NULL, m3 = NULL, m4 = NULL, invert = TRUE, operational = TRUE)
| R | a vector, matrix, data frame, timeSeries or zoo object of asset returns |
|---|---|
| p | confidence level for calculation, default p=.95 |
| … | any other passthru parameters |
| method | one of "modified","gaussian","historical", see Details. |
| clean | method for data cleaning through |
| portfolio_method | one of "single","component","marginal" defining whether to do univariate, component, or marginal calc, see Details. |
| weights | portfolio weighting vector, default NULL, see Details |
| mu | If univariate, mu is the mean of the series. Otherwise mu is the vector of means of the return series, default NULL, see Details |
| sigma | If univariate, sigma is the variance of the series. Otherwise sigma is the covariance matrix of the return series, default NULL, see Details |
| m3 | If univariate, m3 is the skewness of the series. Otherwise m3 is the coskewness matrix (or vector with unique coskewness values) of the returns series, default NULL, see Details |
| m4 | If univariate, m4 is the excess kurtosis of the series. Otherwise m4 is the cokurtosis matrix (or vector with unique cokurtosis values) of the return series, default NULL, see Details |
| invert | TRUE/FALSE whether to invert the VaR measure, see Details. |
| operational | TRUE/FALSE, default TRUE, see Details. |
The option to invert the ES measure should appease both
academics and practitioners. The mathematical definition of ES as the
negative value of extreme losses will (usually) produce a positive number.
Practitioners will argue that ES denotes a loss, and should be internally
consistent with the quantile (a negative number). For tables and charts,
different preferences may apply for clarity and compactness. As such, we
provide the option, and set the default to TRUE to keep the return
consistent with prior versions of PerformanceAnalytics, but make no value
judgement on which approach is preferable.
This function provides several estimation methods for the Expected Shortfall (ES) (also called Expected Tail Loss (ETL) or Conditional Value at Risk (CVaR)) of a return series and the Component ES (ETL/CVaR) of a portfolio.
At a preset probability level denoted \(c\), which typically is between 1 and 5 per cent, the ES of a return series is the negative value of the expected value of the return when the return is less than its \(c\)-quantile. Unlike value-at-risk, conditional value-at-risk has all the properties a risk measure should have to be coherent and is a convex function of the portfolio weights (Pflug, 2000). With a sufficiently large data set, you may choose to estimate ES with the sample average of all returns that are below the \(c\) empirical quantile. More efficient estimates of VaR are obtained if a (correct) assumption is made on the return distribution, such as the normal distribution. If your return series is skewed and/or has excess kurtosis, Cornish-Fisher estimates of ES can be more appropriate. For the ES of a portfolio, it is also of interest to decompose total portfolio ES into the risk contributions of each of the portfolio components. For the above mentioned ES estimators, such a decomposition is possible in a financially meaningful way.
Boudt, Kris, Peterson, Brian, and Christophe Croux. 2008. Estimation and decomposition of downside risk for portfolios with non-normal returns. 2008. The Journal of Risk, vol. 11, 79-103.
Cont, Rama, Deguest, Romain and Giacomo Scandolo. Robustness and sensitivity analysis of risk measurement procedures. Financial Engineering Report No. 2007-06, Columbia University Center for Financial Engineering.
Laurent Favre and Jose-Antonio Galeano. Mean-Modified Value-at-Risk Optimization with Hedge Funds. Journal of Alternative Investment, Fall 2002, v 5.
Martellini, L. and Ziemann, V., 2010. Improved estimates of higher-order comoments and implications for portfolio selection. Review of Financial Studies, 23(4):1467-1502.
Pflug, G. Ch. Some remarks on the value-at-risk and the conditional value-at-risk. In S. Uryasev, ed., Probabilistic Constrained Optimization: Methodology and Applications, Dordrecht: Kluwer, 2000, 272-281.
Scaillet, Olivier. Nonparametric estimation and sensitivity analysis of expected shortfall. Mathematical Finance, 2002, vol. 14, 74-86.
VaR SharpeRatio.modified
chart.VaRSensitivity Return.clean
data(edhec) # first do normal ES calc ES(edhec, p=.95, method="historical")#> Convertible Arbitrage CTA Global Distressed Securities Emerging Markets #> ES -0.048775 -0.04527143 -0.042725 -0.089225 #> Equity Market Neutral Event Driven Fixed Income Arbitrage Global Macro #> ES -0.018775 -0.0443375 -0.0423375 -0.0230375 #> Long/Short Equity Merger Arbitrage Relative Value Short Selling #> ES -0.043975 -0.024625 -0.0311 -0.110575 #> Funds of Funds #> ES -0.0390375# now use Gaussian ES(edhec, p=.95, method="gaussian")#> Convertible Arbitrage CTA Global Distressed Securities Emerging Markets #> ES -0.0348072 -0.04517756 -0.02976848 -0.07105359 #> Equity Market Neutral Event Driven Fixed Income Arbitrage Global Macro #> ES -0.01251258 -0.03010467 -0.02490408 -0.02731855 #> Long/Short Equity Merger Arbitrage Relative Value Short Selling #> ES -0.03782765 -0.01617616 -0.02042584 -0.1091181 #> Funds of Funds #> ES -0.03152384# now use modified Cornish Fisher calc to take non-normal distribution into account ES(edhec, p=.95, method="modified")#> Convertible Arbitrage CTA Global Distressed Securities Emerging Markets #> ES -0.09954768 -0.04284185 -0.06087217 -0.127887 #> Equity Market Neutral Event Driven Fixed Income Arbitrage Global Macro #> ES -0.04290042 -0.05909659 -0.05951833 -0.01983308 #> Long/Short Equity Merger Arbitrage Relative Value Short Selling #> ES -0.04709136 -0.03326371 -0.04888118 -0.09022777 #> Funds of Funds #> ES -0.04618555# now use p=.99 ES(edhec, p=.99)#> Convertible Arbitrage CTA Global Distressed Securities Emerging Markets #> ES -0.1009223 -0.05572595 -0.06533764 -0.1397195 #> Equity Market Neutral Event Driven Fixed Income Arbitrage Global Macro #> ES -0.04404136 -0.06385154 -0.05850228 -0.02437999 #> Long/Short Equity Merger Arbitrage Relative Value Short Selling #> ES -0.0695714 -0.03630211 -0.050531 -0.1697459 #> Funds of Funds #> ES -0.05500037# or the equivalent alpha=.01 ES(edhec, p=.01)#> Convertible Arbitrage CTA Global Distressed Securities Emerging Markets #> ES -0.1009223 -0.05572595 -0.06533764 -0.1397195 #> Equity Market Neutral Event Driven Fixed Income Arbitrage Global Macro #> ES -0.04404136 -0.06385154 -0.05850228 -0.02437999 #> Long/Short Equity Merger Arbitrage Relative Value Short Selling #> ES -0.0695714 -0.03630211 -0.050531 -0.1697459 #> Funds of Funds #> ES -0.05500037# now with outliers squished ES(edhec, clean="boudt")#> Error: requireNamespace("robustbase", quietly = TRUE) is not TRUE# add Component ES for the equal weighted portfolio ES(edhec, clean="boudt", portfolio_method="component")#>#> Error: requireNamespace("robustbase", quietly = TRUE) is not TRUE