Abstract

Recognizing the problems of estimation error in computing risk premia via arbitrage pricing, this chapter provides a Bayesian methodology for estimating factor risk premia and hence equity risk premia for both traded and non-traded factors. Some illustrative calculations based on UK equity are also provided.

4.1 Introduction

The calculation of factor-risk premia is one of the major contributions of Arbitrage Pricing Theory as espoused by Ross (1976) and Ingersoll (1987). In this literature, two cases are considered; when the factors are traded portfolios and when they are not (see, for example, Campbell et al. (1997)). While practitioner-oriented models focus on the former, the academic literature is more concerned with the latter (see Burmeister and McElroy (1988)). There are considerable problems in estimating factor-risk premia, as discussed in Pitsillis and Satchell (2001), Pitsillis (2002), and elsewhere. To alleviate some of the estimation problems, we consider a Bayesian approach to estimation, so that prior information can be utilized to improve accuracy. Many authors (see, for example, Polson and Tew (2000), Ericsson and Karlsson (2002)) have shown that Bayesian approaches to linear factor models and portfolio theory have been successful in reducing some of the excess variability in the data.

Regarding the choice of factors, interest rates, returns on broad based portfolios one of which, typically,...