Laplace versus the Normal Distribution for Daily Stock Market Returns

Abstract

Daily stock market return distributions seem to have tails that are much fatter than Normal Distribution models. This paper examines the possibility of the Laplace Distribution as a better alternative for modeling daily stock returns. Visual inspection of Q-Q plots seem to confirm the Laplace Distribution better fit to the data. The Laplace Distribution also managed to outperform the Normal Distribution in the K-S statistical tests, while being rejected by A-D tests. Although it seems like an improvement on the Normal hypothesis, the Laplace Distribution remains far from a perfect fit for real world stock market daily returns.