Diverging from the Norm: An Examination of Non-Normality and its Measurement in Asset Returns

Abstract

This paper examines the normality of US equities and fixed income asset-class returns over 104 years. Analysis includes moment computations, hypothesis tests, and visual inspections. Findings indicate large cap equities are closer to normal distribution than small caps, and longer holding periods result in more normal returns across asset classes. While hypothesis tests suggest non-normality, their results are shown to largely depend on sample size. The practical implications of assuming normality are explored, revealing minimal effects on central estimates but significant variations in estimates of low-probability events.

Keywords: Asset returns, normal distribution, skew, kurtosis, Shapiro-Wilk, Anderson-Darling, Kolmogorov-Smirnov, stochastic forecast