PerformanceAnalytics (version 0.9.7.1)

MultivariateRisk: calculate common VaR and ES risk measures on a portfolio distribution

Description

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.

Usage

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)

Arguments

w

a vector of weights to be applied to each asset in trhe joint distribution

mu

mean or first centered moment of the distribution, normalley provided by Return.centered

sigma

variance or second centered moment of the distribution

M3

The third mathematical moment of the joint distribution, provided by M3.MM

M4

The fourth mathematical moment of the joint distribution, provided by M4.MM

p

confidence level for calculation, default p=.99

Value

• ~Describe the value returned If it is a LIST, use
• comp1
  Description of 'comp1'
• comp2
  Description of 'comp2'
• ...

Details

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. ~~

References

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.

See Also

MultivariateMoments, centeredmoment

Examples

##---- Should be DIRECTLY executable !! ----
##-- ==>  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))
  }