Is There a Risk and Return Relation?

Abstract

Traditional finance theory posits that the relationship between the risk and return of stocks is positive. Furthermore, investment practice is often based on the central contention of the Capital Asset Pricing Model (CAPM) that high (low) beta stocks earn higher (lower) returns. However, this fundamental return and risk relationship is questioned by a several researchers who assert that the relationship is, in fact, negative. Consequently, a growing body of research examines the nature of the stock return-risk relationship using both market- and firm-level data. The results of this research are mixed. The purpose of this paper is to shed further light on this relationship by (i) examining both market- and firm-level price data; (ii) employing a battery of tests, including individual market, panel and quantile regressions; and (iii) analysing the nature of the relationship during periods of high and low volatility and in bull and bear markets. The results indicate that there is no single robust relationship between risk and return. Of note, our results suggest a positive relationship when returns are high and during bear markets. Furthermore, the finding of a positive relationship is stronger (i) at the market-level than the firm-level; and (ii) over long time periods. However, the analysis indicates that a negative relationship exists at low return levels, during bull markets and, more so, at the individual firm level. Overall, the results suggest that the risk-return relationship is switching in nature and is primarily driven by changing risk preferences. Notably, a positive relationship exists when macroeconomic risk plays a larger role.

Keywords: Stocks, Return, Risk, Volatility, Quantile, Bull v’s Bear, Index, Firm-Level

JEL Classification: C22, C23, G11, G12