Modern Portfolio Theory: Foundations, Analysis, and New Developments, + Website

Chapter 8

Index Models and Return-Generating Process

Index models are more than regressions that explain an investment's holding period returns, they are also important statements about the economic process that generates the returns. This chapter considers single-index models, two-index models, and multi-index models.

8.1 Single-Index Models

Single-index models are the simplest and most popular type of generating process used to explain what economic forces create investors' returns. They are also used to estimate a firm's undiversifiable systematic risk.

8.1.1 Return-Generating Functions

Preceding chapters suggested the single-period rate of return is the basic random variable of portfolio theory. As explained previously, for a share of common or preferred stock, a bond, a real estate investment, or other investments, this holding period return (HPR) is computed as follows.

or equivalently,

1.1

where , is the rate of return, or holding period return (HPR); P_t represents the market price at time t; and d_t stands for cash dividend income, or other source of income received during the holding period.

This chapter reviews the historical development of two similar, yet significantly different, ...