Empirical Tests for Differences in Equilibrium Risk Measures with Application to Downside Risk in Small and Large UK Companies

Several authors have proposed CAPM-style linear pricing models which utilise alternative notions of risk than the variance. The question then arises of whether these models produce equilibrium measures of risk, i.e. Betas, which are statistically different from that off the mean-variance CAPM. This paper surveys the models testing for such differences, a procedure involving making a distributional assumption for the excess return on the market portfolio which allows re-estimation of the model so that the maintained hypothesis is tested. This augmented procedure is then applied to a range of different datasets, including both emerging markets and small and large UK companies. The emerging markets data are found to be unsuitable for testing as the CAPM-style models are inapprop- riate for modelling extreme events while, for the UK data, smaller companies are more likely than larger ones to reject the mean-variance CAPM in favour of either the mean-semivariance CAPM or an unspecified alternative.