Does Idiosyncratic Volatility Follow a Random-Walk? Evidence From U.S. Stocks

Authors

Zihan Cao, CUNY New York City College of TechnologyFollow
Ossama Elhadary, CUNY New York City College of TechnologyFollow

Document Type

Article

Publication Date

Fall 10-10-2025

Abstract

In asset pricing literature, idiosyncratic volatility (IVOL) measures the firm-specific risk that is not explained by broader market movements. In this study, I investigate whether the idiosyncratic volatility (IVOL) of individual stocks follows a random-walk. Using monthly residuals from the Fama-French three-factor model (Fama & French, 1993), I estimate IVOL for more than 11,000 U.S. stocks, and apply the Augmented Dickey-Fuller test (Said & Dickey, 1984) to determine whether IVOL behaves like a random-walk. While most stocks display random-walk behavior, the proportion varies across industries, with some sectors showing deviations from random-walk behavior. Stocks with different levels of average return exhibit varying distributions of random-walk properties. My analysis aims to reveal patterns in the predictability of firm-specific risk and how this predictability varies across different stock types and levels of average return.

Comments

This paper is based on Undergraduate Research conducted at New York City College of Technology from Fall 2024 to Fall 2025. Mentor: Ossama Elhadary (Computer Systems Technology).