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)
Return.clean
. Current options are "none",
"boudt", or "geltner".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.
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, Lionel, and Volker Ziemann. Improved Forecasts of Higher-Order Comoments and Implications for Portfolio Selection. 2007. EDHEC Risk and Asset Management Research Centre working paper.
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")
# now use Gaussian
ES(edhec, p=.95, method="gaussian")
# now use modified Cornish Fisher calc to take non-normal distribution into account
ES(edhec, p=.95, method="modified")
# now use p=.99
ES(edhec, p=.99)
# or the equivalent alpha=.01
ES(edhec, p=.01)
# now with outliers squished
ES(edhec, clean="boudt")
# add Component ES for the equal weighted portfolio
ES(edhec, clean="boudt", portfolio_method="component")
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