4 - Bayesian estimation of risk premia in an APT context

Abstract

This chapter examines the problems of estimation error in computing risk premia via arbitrage pricing. The chapter provides a Bayesian methodology for estimating factor risk premia and hence equity risk premia for both traded and nontraded factors. The chapter also introduces the general Arbitrage Pricing Theory (APT) framework. Some illustrative calculations based on United Kingdom equity are also provided in the chapter. Using a sample of U.K. stocks from 1993–1998, evidence was found that suggests that a Capital Asset Pricing Model (CAPM) prior seemed to produce more data consistent results than an empirical Bayes approach. However, because CAPM prior still retains some empirical Bayes hyperparameters based on the APT is by no means conclusive. Results suggest that a Bayesian mixture of CAPM as prior and APT as the data generating process outperforms both classical cases of CAPM or APT alone. The chapter outlines the excess return generating process when factors are traded portfolios and suggests how a Bayesian estimation framework can be utilized in this case.