Stable Distributions and the Mixtures of Distributions Hypotheses for Common Stock Returns

Abstract

The form of the distribution underlying common stock returns has many implications for financial modeling. Among the frequently proposed models for stock return distributions is the family of stable distributions. Numerous studies of stock return distributions have also proposed various types of mixtures of normal distributions. This article examines the characteristics of several different combinations of mixtures of normal and stable distributions, and compares them with actual stock price distributions. The principal tests applied are based on the stability-under-addition property of stable distributions.

Key Words:

• Mixtures of normals
• Simulation
• Stable distribution
• Stability under addition
• Stock returns