Is there a risk and return relation?

Traditional finance theory posits that the relation between the risk and return of stocks is positive. Equally, investment practice is often based on the contention that high (low) beta stocks earn higher (lower) returns. However, this fundamental relation is questioned by several researchers, who present mixed evidence. The purpose of this paper is to shed further light on this question by examining both market- and firm-level price data; employing a battery of tests, including individual market, panel and quantile regressions; analysing the nature of the relation during periods of high and low volatility and in bull and bear markets. The results indicate that there is no single robust relation between risk and return. Notably, the results suggest a positive relation when returns are high and during bear markets. Further, the finding of a positive relation is stronger at the market-level than the firm-level and over long time periods. However, a negative relation exists at low return levels, during bull markets and, even more so, at the individual firm level. Overall, the results suggest that the risk-return relation is switching in nature and is primarily driven by changing risk preferences. A positive relation exists when macroeconomic risk plays a larger role.