Bayesian Variable Selection of Risk Factors in the APT Model

In this paper we use a probabilistic approach to risk factor selection in the arbitrage pricing theory model. The methodology uses a bayesian framework to simultaneously select the pervasive risk factors and estimate the model. This will enable correct inference and testing of the implications of the APT model. Furthermore, we are able to make inference on any function of the parameters, in particular the pricing errors. We can also carry out tests of efficiency of the APT using the posterior odds ratio and bayesian confidence intervals. We investigate the macroeconomic risk factors of Chen, Roll, and Ross (1986) and the firm characteristic factors of Fama and French (1992,1993). Using monthly portfolio returns grouped by size and book to market, we find that the economic variables have zero risk premia although some appear to have non zero posterior probability. The "Market" factor is not priced. An APT model with factors mimicking size (SMB), book to market equity (HML), value-weighted portfolio and Standard and Poor, is supported by a conditionally independent prior and offers a significant decrease in the pricing error over a two-factor APT with SMB and HML. The posterior probability and cumulative distributions functions of the average risk premia and the pricing errors are compared to the normal distribution. The results show that under certain conditions the distortions are very small.