The systematic risk estimation models: A different perspective

In practice, the capital asset pricing model (CAPM) using the parametric estimator is almost certainly being used to estimate a firm's systematic risk (beta) and cost of equity as in Eq. (1). However, the parametric estimators, even when data is normal, may not yield better performance compared with the non-parametric estimators when outliers existed. This research argued for the non-parametric Bayes estimator to be employed in the CAPM by applying both advance and basic evaluation criteria such as hypotheses/confidence intervals of the AIC/DIC, model variance, fit, and error, alpha, and beta and its standard deviation. Using all the S&P 500 stocks having monthly data from 07/2007–05/2019 (450 stocks) and the Bayesian inference, we showed the non-parametric Bayes estimator yielded less number of zeroed betas and smaller alpha compared with the parametric Bayes estimator. More importantly, this non-parametric Bayes yielded the statistically significantly smaller AIC/DIC, model variance, and beta standard deviation and higher model fit compared with the parametric Bayes estimator. These findings indicate the CAPM using the non-parametric Bayes estimator is superior compared with the parametric Bayes estimator, a contrast of common practice. Hence, the non-parametric estimator is recommended to be employed in asset pricing work.