# More on higher moments: rolling skewness of S&P 500 daily returns

October 15, 2011
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(This article was first published on DataPunks.com » R, and kindly contributed to R-bloggers)

In this post, Portfolio Probe explores a way to decide whether market kurtosis and skewness are predictable.

Market skewness, in naive financial modeling, is some kind of measure of (as-)symmetrical distribution of (daily) returns around the average market return. A higher skewness would tend to indicate a denser distribution of higher returns, compared to lower or negative returns.

In the cited example, skewness was estimated based on even partition of years since 2008. While is this is a neat idea, it seems like a good idea to study the evolution of a rolling skewness (skewness of returns of the preceding n days).

Below is a quick piece of R code to describe the distribution / fluctuation of a 30-day rolling skewness of the S&P 500 daily returns since 1980.

Surprisingly, the skewness is rather volatile, with sudden high negative values. The distribution of rolling skewness is negatively skewed as well.

 library(PerformanceAnalytics) library(quantmod) rm(list=ls()) getSymbols(c("^GSPC"), from="1980-01-01") part <- function(i) GSPC[i:(i+30)] part2 <- function(i) skewness(Return.calculate(Cl(part(i)))) skews <- unlist(lapply(1:(length(GSPC)/6-30), part2)) head(skews) plot(ts(skews), col='blue') hist(skews, breaks=50, col='cyan')

Photograph used with permission from mylittleshoebox.ca