Abstract

Most linear factor models used in portfolio risk management employ one of three basic estimation procedures: least squares regression on time-series data, (weighted) least squares regression on fundamental accounting variables, or factor analysis. These are often referred to as economic, fundamental, and statistical factor models. A variety of arguments have been offered as to why one approach or another is purportedly better than the others. We feel that each approach has merit for particular applications and that there may be advantages to building a model that combines all methods. We present an algorithm for estimating a combined linear model that incorporates the basic features of all three approaches in a single simultaneous estimation procedure. Under a set of appropriate assumptions, the resulting parameter values are maximum likelihood estimates. The simultaneous estimation procedure allows for some extensions of the linear model as well.

10.1 Introduction

Linear factor models are widely used for modeling portfolio risk. Three popular approaches most frequently used in modeling security returns are:

1. time-series regression with known factors, and estimated betas (assumed constant across observations),

2. cross-sectional regressions using known fundamental/technical variables as proxies for betas which may vary from period to period, and estimated factor values, and

3. factor analysis where factor values and betas are both missing and must be estimated (again beta is typically assumed to...