PerformanceAnalytics (version 1.1.0)

Return.centered: calculate centered Returns

Description

the $n$-th centered moment is calculated as $$$$$$\mu^{(n)}(R) = E\lbrack(R-E(R))^n\rbrack$$

Usage

Return.centered(R, ...)
  centeredmoment(R, power)
  centeredcomoment(Ra, Rb, p1, p2, normalize = FALSE)

Arguments

R

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

Ra

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

Rb

an xts, vector, matrix, data frame, timeSeries or zoo object of index, benchmark, portfolio, or secondary asset returns to compare against

power

power or moment to calculate

p1

first power of the comoment

p2

second power of the comoment

normalize

whether to standardize the calculation to agree with common usage, or leave the default mathematical meaning

...

any other passthru parameters

Details

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.

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. Documentation Patches Welcome. ~~

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.

Examples

data(managers)
Return.centered(managers[,1:3,drop=FALSE])