<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">\HeaderA{MultivariateRisk}{calculate common VaR and ES risk measures on a portfolio distribution}{MultivariateRisk}
\aliasA{GES.MM}{MultivariateRisk}{GES.MM}
\aliasA{GVaR.MM}{MultivariateRisk}{GVaR.MM}
\aliasA{mES.MM}{MultivariateRisk}{mES.MM}
\aliasA{mVaR.MM}{MultivariateRisk}{mVaR.MM}
\aliasA{SR.GES.MM}{MultivariateRisk}{SR.GES.MM}
\aliasA{SR.GVaR.MM}{MultivariateRisk}{SR.GVaR.MM}
\aliasA{SR.mES.MM}{MultivariateRisk}{SR.mES.MM}
\aliasA{SR.mVaR.MM}{MultivariateRisk}{SR.mVaR.MM}
\aliasA{SR.StdDev.MM}{MultivariateRisk}{SR.StdDev.MM}
\keyword{ts}{MultivariateRisk}
\keyword{multivariate}{MultivariateRisk}
\keyword{distribution}{MultivariateRisk}
\keyword{models}{MultivariateRisk}
\begin{Description}\relax
Functions to calculate Guassian and modified VaR and Expected Shortfall.

Note that these functions generally expect the moments to be passed in directly; this was done to eliminate repetitive calculations in a portfolio optimization context.  We'll write "friendly" wrapper functions that take the return vector when we have time.
\end{Description}
\begin{Usage}
\begin{verbatim}
GVaR.MM (w, mu, sigma, p)
mVaR.MM(w, mu, sigma, M3, M4, p)
SR.mVaR.MM (w, mu, sigma, M3, M4, p)
GES.MM (w, mu, sigma, p)
mES.MM(w, mu, sigma, M3, M4, p)
SR.mES.MM (w, mu, sigma, M3, M4, p)
SR.GVaR.MM (w, mu, sigma, p)
SR.GES.MM (w, mu, sigma, p)
SR.StdDev.MM (w, mu, sigma)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{w}] a vector of weights to be applied to each asset in trhe joint distribution 
\item[\code{mu}] mean or first centered moment of the distribution, normalley provided by  \code{\LinkA{Return.centered}{Return.centered}} 
\item[\code{sigma}] variance or second centered moment of the distribution 
\item[\code{M3}] The third mathematical moment of the joint distribution, provided by  \code{\LinkA{M3.MM}{M3.MM}} 
\item[\code{M4}] The fourth mathematical moment of the joint distribution, provided by  \code{\LinkA{M4.MM}{M4.MM}} 
\item[\code{p}] confidence level for calculation, default p=.99 
\end{ldescription}
\end{Arguments}
\begin{Details}\relax
These functions were first utilized in Boudt, Peterson, and Croux (2008), and have been subsequently used in our other research.

~~ Additional Details will be added to documentation as soon as we have time to write them. ~~
\end{Details}
\begin{Value}
~Describe the value returned
If it is a LIST, use
\begin{ldescription}
\item[\code{comp1 }] Description of 'comp1'
\item[\code{comp2 }] Description of 'comp2'
\end{ldescription}

...
\end{Value}
\begin{Section}{Warning}
....
\end{Section}
\begin{Note}\relax
~~further notes~~

~Make other sections like Warning with \section{Warning }{....} ~
\end{Note}
\begin{Author}\relax
Kris Boudt, Brian Peterson
\end{Author}
\begin{References}\relax
Boudt, Kris, Brian G. Peterson, and Christophe Croux. 2008. Estimation and Decomposition
of Downside Risk for Portfolios with Non-Normal Returns. Journal of Risk. Winter.

Martellini, Lionel, and Volker Ziemann. 2007. Improved Forecasts of Higher-Order Comoments and Implications for Portfolio Selection. EDHEC Risk and Asset Management Research Centre working paper.

Ranaldo, Angelo, and Laurent Favre Sr. 2005. How to Price Hedge Funds: From Two- to
Four-Moment CAPM. SSRN eLibrary.

Scott, Robert C., and Philip A. Horvath. 1980. On the Direction of Preference for Moments of
Higher Order than the Variance. Journal of Finance 35(4):915-919.
\end{References}
\begin{SeeAlso}\relax
\code{\LinkA{MultivariateMoments}{MultivariateMoments}}, \code{\LinkA{centeredmoment}{centeredmoment}}
\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
##---- Should be DIRECTLY executable !! ----
##-- ==&gt;  Define data, use random,
##--    or do  help(data=index)  for the standard data sets.

## The function is currently defined as
function (w, mu, sigma, M3, M4, p)
{
    skew = skewness.MM(w, sigma, M3)
    exkurt = kurtosis.MM(w, sigma, M4) - 3
    z = qnorm(1 - p)
    h = z + (1/6) * (z^2 - 1) * skew
    h = h + (1/24) * (z^3 - 3 * z) * exkurt - (1/36) * (2 * z^3 -
        5 * z) * skew^2
    return(-mean.MM(w, mu) - h * StdDev.MM(w, sigma))
  }
\end{ExampleCode}
\end{Examples}

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