Higher Moments Summary: Statistics and Stylized Facts

Summary of the higher moements and Co-Moments of the return distribution. Used to determine diversification potential. Also called "systematic" moments by several papers.

table.HigherMoments(Ra, Rb, scale = NA, Rf = 0, digits = 4,
  method = "moment")

Arguments

Ra

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

return vector of the benchmark asset
scale

number of periods in a year (daily scale = 252, monthly scale = 12, quarterly scale = 4)
Rf

risk free rate, in same period as your returns
digits

number of digits to round results to
method

method to use when computing kurtosis one of: excess, moment, fisher

References

Martellini L., Vaissie M., Ziemann V. Investing in Hedge Funds: Adding Value through Active Style Allocation Decisions. October 2005. Edhec Risk and Asset Management Research Centre.

See also

CoSkewness CoKurtosis BetaCoVariance BetaCoSkewness BetaCoKurtosis skewness kurtosis

Examples


data(managers)
table.HigherMoments(managers[,1:3],managers[,8,drop=FALSE])
#>                 HAM1 to SP500 TR HAM2 to SP500 TR HAM3 to SP500 TR
#> CoSkewness                0.0000           0.0000           0.0000
#> CoKurtosis                0.0000           0.0000           0.0000
#> Beta CoVariance           0.3906           0.3432           0.5572
#> Beta CoSkewness           0.5602           0.0454           0.5999
#> Beta CoKurtosis           0.4815           0.1988           0.5068
result=t(table.HigherMoments(managers[,1:6],managers[,8,drop=FALSE]))
rownames(result)=colnames(managers[,1:6])
require("Hmisc")
#> Loading required package: Hmisc
#> Warning: there is no package called ‘Hmisc’
textplot(format.df(result, na.blank=TRUE, numeric.dollar=FALSE,
         cdec=rep(3,dim(result)[2])), rmar = 0.8, cmar = 1.5,
         max.cex=.9, halign = "center", valign = "top", row.valign="center",
         wrap.rownames=5, wrap.colnames=10, mar = c(0,0,3,0)+0.1)
#> Error in format.df(result, na.blank = TRUE, numeric.dollar = FALSE, cdec = rep(3,     dim(result)[2])): could not find function "format.df"
title(main="Higher Co-Moments with SP500 TR")
#> Error in title(main = "Higher Co-Moments with SP500 TR"): plot.new has not been called yet