The Theory and Practice of Investment Management: Asset Allocation, Valuation, Portfolio Construction, and Strategies, Second Edition

MODEL DESCRIPTION AND ESTIMATION

The basic relationship to be estimated in a multifactor risk model is

R_i–R_f = β_i,F1 R_F1 + β_i,F2 R_F2 + . . . + β_i,FH R_FH + e_i

where

Ri	=	rate of return on stock i
Rf	=	risk-free rate of return
βi,Fj	=	sensitivity of stock i to risk factor j
RFj	=	rate of return on risk factor j
ei	=	nonfactor (specific) return on security i

The above function is referred to as a return generating function.

Fundamental factor models use company and industry attributes and market data as “descriptors.” Examples are price/earnings ratios, book/price ratios, estimated earnings growth, and trading activity. The estimation of a fundamental factor model begins with an analysis of historical stock returns and descriptors about a company. In the Barra model, for example, the process of identifying the risk factors begins with monthly returns for 1,900 companies that the descriptors must explain. Descriptors are not the “risk factors” but instead they are the candidates for risk factors. The descriptors are selected in terms of their ability to explain stock returns. That is, all of the descriptors are potential risk factors but only those that appear to be important in explaining stock returns are used in constructing risk factors.

Once the descriptors that are statistically significant in explaining stock returns are identified, they are grouped into “risk indexes” to capture related company attributes. For example, descriptors such as market leverage, book leverage, ...