The Distribution of S&P 500 Index Returns

Abstract:     
This paper examines the fit of three different statistical distributions to the returns of the S&P 500 Index from 1950-2005. The normal distribution is a poor fit to the daily percentage returns of the S&P 500. The lognormal distribution is a poor fit to single period continuously compounded returns for the S&P 500, which means that future prices are not lognormally distributed. However, sums of continuously compounded returns are much more normal in their distribution, as would be expected based on the central limit theorem. The t-distribution with location/scale parameters is shown to be an excellent fit to the daily percentage returns of the S&P 500 Index.

Keywords: S&P 500 index, stock returns, continuously compounded returns, normal distribution, skewness, kurtosis, lognormal distribution, risk, t-distribution

Working Paper Series