Factor Models for Asset Returns

Abstract

Multifactor models can be used to predict returns, generate estimates of abnormal return, and estimate the variability and covariability of returns. This chapter focuses on the use of multifactor models to describe the covariance structure of returns¹. Asset return covariance matrices are key inputs to portfolio optimization routines used for asset allocation and active asset management. A factor model decomposes an asset’s return into factors common to all assets and an asset specific factor. Often the common factors are interpreted as capturing fundamental risk components, and the factor model isolates an asset’s sensitivities to these risk factors. The three main types of multifactor models for asset returns are: (1) macroeconomic factor models; (2) fundamental factor models; and (3) statistical factor models. Macroeconomic factor models use observable economic time series like interest rates and inflation as measures of pervasive or common factors in asset returns. Fundamental factor models use observable firm or asset specific attributes such as firm size, dividend yield, and industry classification to determine common factors in asset returns. Statistical factor models treat the common factors as unobservable or latent factors. Estimation of multifactor models is type-specific, and this chapter summarizes the econometric issues associated with estimating each type of factor model and gives illustrations using S-PLUS.