The Cross-Section of Stock Returns and the Pricing of Risk: From the Capital Asset Pricing Model to Multi-Factor Models

Abstract

This paper surveys the theory and evidence on how risk is priced in equity markets and how the cross-section of stock returns is determined. The intellectual starting point is the capital asset pricing model developed by Sharpe (1964) and Lintner (1965) on the portfolio foundations laid by Markowitz (1952), which predicts that the only priced dimension of risk is the covariance of a security's return with the market portfolio, summarized by beta. Decades of empirical research have challenged this prediction. Beginning with Banz (1981) on firm size and extending through the influential study of Fama and French (1992), the evidence indicates that beta has remarkably little power to explain cross-sectional differences in average returns, whereas firm size, the book-to-market ratio, momentum, and, more recently, profitability and investment carry reliable premia. These empirical regularities led to the development of multi-factor asset pricing models, most notably the Fama-French three-factor and five-factor models and the Carhart momentum extension. The survey then examines whether these patterns reflect compensation for systematic risk or systematic mispricing, and discusses the econometric concerns raised by data mining and multiple testing. It concludes with an assessment of factor investing in practice, the growth of the factor zoo, and the limits imposed by crowding, capacity, and transaction costs.