PerformanceAnalytics (version 1.1.0)

VaR: calculate various Value at Risk (VaR) measures

Description

Calculates Value-at-Risk(VaR) for univariate, component, and marginal cases using a variety of analytical methods.

Usage

VaR(R = NULL, p = 0.95, ...,
    method = c("modified", "gaussian", "historical", "kernel"),
    clean = c("none", "boudt", "geltner"),
    portfolio_method = c("single", "component", "marginal"),
    weights = NULL, mu = NULL, sigma = NULL, m3 = NULL,
    m4 = NULL, invert = TRUE)

Arguments

R

an xts, 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", "kernel", 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.

...

any other passthru parameters

Background

This function provides several estimation methods for the Value at Risk (typically written as VaR) of a return series and the Component VaR of a portfolio. Take care to capitalize VaR in the commonly accepted manner, to avoid confusion with var (variance) and VAR (vector auto-regression). VaR is an industry standard for measuring downside risk. For a return series, VaR is defined as the high quantile (e.g. ~a 95 quantile) of the negative value of the returns. This quantile needs to be estimated. With a sufficiently large data set, you may choose to utilize the empirical quantile calculated using 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 VaR can be more appropriate. For the VaR of a portfolio, it is also of interest to decompose total portfolio VaR into the risk contributions of each of the portfolio components. For the above mentioned VaR 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.

Denton M. and Jayaraman, J.D. Incremental, Marginal, and Component VaR. Sunguard. 2004.

Epperlein, E., Smillie, A. Cracking VaR with kernels. RISK, 2006, vol. 19, 70-74.

Gourieroux, Christian, Laurent, Jean-Paul and Olivier Scaillet. Sensitivity analysis of value at risk. Journal of Empirical Finance, 2000, Vol. 7, 225-245.

Keel, Simon and Ardia, David. Generalized marginal risk. Aeris CAPITAL discussion paper.

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.

Return to RiskMetrics: Evolution of a Standard http://www.riskmetrics.com/publications/techdocs/r2rovv.html

Zangari, Peter. A VaR Methodology for Portfolios that include Options. 1996. RiskMetrics Monitor, First Quarter, 4-12.

Rockafellar, Terry and Uryasev, Stanislav. Optimization of Conditional VaR. The Journal of Risk, 2000, vol. 2, 21-41.

See Also

SharpeRatio.modified chart.VaRSensitivity Return.clean

Examples

data(edhec)

    # first do normal VaR calc
    VaR(edhec, p=.95, method="historical")

    # now use Gaussian
    VaR(edhec, p=.95, method="gaussian")

    # now use modified Cornish Fisher calc to take non-normal distribution into account
    VaR(edhec, p=.95, method="modified")

    # now use p=.99
    VaR(edhec, p=.99)
    # or the equivalent alpha=.01
    VaR(edhec, p=.01)

    # now with outliers squished
    VaR(edhec, clean="boudt")

    # add Component VaR for the equal weighted portfolio
    VaR(edhec, clean="boudt", portfolio_method="component")