Bayesian Selection of Risk Factors and Estimation of Factor Betas and Risk Premiums in the APT model

This paper provides a Bayesian analysis of the historical risk premium in the US monthly portfolios returns. The study investigates the importance of non-traded economic risks in the pricing of securities. Incorporating model uncertainty in the post-selection inference is very important as it has implications in addressing crucial issues such as: (1) what sources of risks investors should track and hedge against? (2) the sign and magnitude of risk premia commanded by economic and financial risks. The study uses an approximate linear factor model to allow for cross sectional correlation in the estimation of the return sensitivities to the market-wide risk and in measuring the market reward for each priced risk. Posterior distributions of functions of risk premia and factor betas provide exact statistical tools to assess the link between predictability and risk and to study the time series behavior of market reward for holding economic risk. The results show that expected compensation for bearing different sorts of risk is changing with the business cycle with an evidence for higher reward during recessions and financial distress and higher returns for the month of January. The article also provide strong evidence for ’Economic’ risk measured by unanticipated inflation and lagged Unemployment rate. Inflation risk commanded on average a negative risk premia with a positive reward for periods of economic contraction. However, the results show no support for Fama & French factors {Market, SMB, HML} as risks factors that are pervasive for the pricing of securities. JEL Classification: C1, C22, C52