Factor Selection

There are several commercially available factor models that provide useful insights into methodological differences regarding both estimation and factor selection. The BARRA, BIRR, and RAM multifactor models all offer a multidimensional view of risk analysis. BARRA was developed by Bar Rosenberg; BIRR by Burmeister, Ibbotson, Roll, and Ross, while RAM was a proprietary risk attribute model of Salomon Brothers. That is, each models asset returns as a function of several sources of risk, some emanating from macroeconomic sources, while for others, namely BARRA, company fundamentals.

BIRR and RAM are macroeconomic factor models motivated by arbitrage pricing theory. As we have just demonstrated, that theory maintains that factor sensitivities are determined in such a way as to preclude arbitrage opportunities. For example, in the single-factor CAPM model, estimated alpha and beta values must generate a relationship between excess returns to the asset and the market portfolio sufficient to eliminate riskless short-selling of one asset for a certain gain on the other. If it is believed that there are relatively few factors that account for the variation in asset returns, then a multifactor model will produce factor sensitivity estimates that meaningfully represent the pricing relationship to the factor in an arbitrage-free and hence, efficient, market. Of course, the objective is to determine what these factors are and no one has yet resolved this issue; hence, the multitude of proprietary models. For now, let us assume that each of these models is correctly specified.

The macroeconomic models offered by BIRR and RAM use historic stock returns and macroeconomic variables as descriptors. These are given next. More specifics can be found at their websites.

BIRR descriptors

Investor confidence (confidence risk)

Interest rates (time horizon risk)

Inflation (inflation risk)

Real business activity (business cycle risk)

A market index (market timing risk)

RAM descriptors

Change in expected long-run economic growth

Short-run business cycle risk

Long-term bond yield changes

Short-term Treasury bill changes

Inflation shock

Dollar changes versus trading partner currencies

Let's set up the RAM methodology, which uses a 3,500-stock universe. This method generalizes to BIRR and macroeconomic factor models in general. I describe the methodology in four steps and follow with an interpretation.