PerformanceAnalytics (version 1.1.0)

ETL: calculates Expected Shortfall(ES) (or Conditional Value-at-Risk(CVaR) for univariate and component, using a variety of analytical methods.

Description

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.

Usage

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)

Arguments

R

a vector, matrix, data frame, timeSeries or zoo object of asset returns

p

confidence level for calculation, default p=.95

method

one of "modified","gaussian","historical", see Details.

clean

method for data cleaning through Return.clean. Current options are "none", "boudt", or "geltner".

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 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 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.

...

any other passthru parameters

Background

This function provides several estimation methods for the Expected Shortfall (ES) (also called Expected Tail Loss (ETL) orConditional 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.

References

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, 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.

See Also

VaR SharpeRatio.modified chart.VaRSensitivity Return.clean

Examples

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")