The Relation Between Expected Return and Beta: A Random Resampling Approach

Abstract

Theory predicts a certain positive cross-sectional relation between expected return and beta for individual stocks and portfolios. The preferred methodology in the empirical literature involves sorting the available cross-section of stocks into a number portfolios based on characteristics like market capitalization and book-to-market. However, any results obtained in this manner are subject to data snooping biases as well as various general biases in the data that are potentially correlated with the same variables. Moreover, the results do not necessarily carry over to different portfolios formed from the same universe of stocks that investors may hold. This paper proposes a method of randomly resampling portfolios from the population of individual stocks a large number of times to infer general population characteristics about the risk-return relationship, while being subject to few biases. Simulation evidence shows that the proposed procedure performs no worse than cross-sectional regressions based on individual stocks. In contrast to empirical evidence in the literature showing a zero or negative relation between expected return and beta this paper uncovers a positive association stronger than predicted by the CAPM regardless of time period.