Return.centered {PerformanceAnalytics} | R Documentation

## calculate centered Returns

### Description

the n-th centered moment is calculated as

moment^n(R) = E[R-E(R)^n]

moment^n(R) = E[R-E(R)^n]

### 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
`...` | any other passthru parameters
`power` | power or moment to calculate
`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
`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

### 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. ~~

### Author(s)

Kris Boudt and Brian Peterson

### 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, L. and Ziemann, V., 2010. Improved estimates of higher-order comoments and implications for portfolio selection. Review of Financial Studies, 23(4):1467-1502.

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])

[Package PerformanceAnalytics version 1.5.3 Index]