How is β related to asset returns?

Existing empirical evidence for the relevance of the β in modelling asset returns is mixed. Drawing on conditional tests of β first proposed by Pettengill, Sundaram and Mathur (1995) and extended by Bollen (2010), empirical evidence employing monthly data is presented that indicates that β is highly related to variability of asset returns but not to the level of asset returns. This result is consistent with the predictions of the market model but not with the predictions of the CAPM. It is concluded that β remains a useful construct in financial economics but may have a differing role in financial economics than the conventional wisdom asserts.