MultivariateMoments: functions to compute multivariate moments of a joint distribution

Description

When worknig with multivariate series, the joint distribution of the returns is to be prefered over the simple univariate distribution of the resulting return vector of a portfolio. These functions are used internally by PerformanceAnalytics to calculate centered moments for a multivariate distribution as well as the standardized moments of a portfolio distribution. They are exposed here for users who wish to use them directly, and we'll get more documentation written when we can.

Usage

M3.MM(R)
M4.MM(R)
StdDev.MM(w, sigma)
skewness.MM(w, sigma, M3)
kurtosis.MM(w, sigma, M4)
CoSkewnessMatrix(R, ...)
CoKurtosisMatrix(R, ...)

Arguments

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

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

sigma

variance or second centered moment of the distribution

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

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

...

any other passthru parameters

Value

Details

~~ 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.