Market Risk Analysis Volume II: Practical Financial Econometrics

II.1

Factor Models

II.1.1 INTRODUCTION

This chapter describes the factor models that are applied by portfolio managers to analyse the potential returns on a portfolio of risky assets, to choose the optimal allocation of their funds to different assets and to measure portfolio risk. The theory of linear regression-based factor models applies to most portfolios of risky assets, excluding options portfolios but including alternative investments such as real estate, hedge funds and volatility, as well as traditional assets such as commodities, stocks and bonds. Stocks and bonds are the major categories of risky assets, and whilst bond portfolios could be analysed using regression-based factor models a much more powerful factor analysis for bond portfolios is based on principal component analysis (see Chapter II.2).

An understanding of both multiple linear regression and matrix algebra is necessary for the analysis of multi-factor models. Therefore, we assume that readers are already familiar with matrix theory from Chapter I.2 and the theory of linear regression from Chapter I.4. We also assume that readers are familiar with the theory of asset pricing and the optimal capital allocation techniques that were introduced in Chapter I.6.

Regression-based factor models are used to forecast the expected return and the risk of a portfolio. The expected return on each asset in the portfolio is approximated as a weighted sum of the expected returns to several market risk factors. The weights ...