Unit exposures to Country,Industry and World factors in Fundamental Factor Risk Models

Question

I may have what can be called a rudimentary question about Fundamental Factor models for Risk (ala Barra).

Why is the exposure to World,Countries,Industries set to 1 instead of a real number. The standard explanation given is that the security's membership determines the binary nature of the exposure. But specification of a structural model measuring the relationship between return of security and some concomitant factors should be driven by the sensitivity of the return with the proposed factor rather than membership (??)

May be part of my confusion stems from not being an financial economist privy to the philosophical evolution of the asset pricing framework. Nevertheless just from a model building approach makes this kind of binary exposure fixing rather arbitrary to me.

Any references or pointers are greatly appreciated.

Answer 1

The Barra Fundamental Factor models date back to the 70s, and a commonly cited paper by Rosenberg & Marathe ("The Prediction of Investment Risk", Proceedings of the Seminar on the Analysis of Security Prices, Univ. of Chicago, 1976). I've never actually read the paper, and it's hard to find a link on the web. The closest I've come is reading "Modern Portfolio Theory" (Rudd & Clasing, 1982). The book is a comprehensive overview of Barra models, but may be a bit out-of-date now! It's tough to find more modern links, but here is the book at Amazon (https://www.amazon.com/Modern-Portfolio-Theory-Andrew-Rudd/dp/0870941917)

Rudd & Clasing have this to say about the use of 1-0 Industry membership variables "The assignment of a company wholly to a single industry is traditional in investment research but quite clearly wrong. A more defensible (and accurate) approach would be to assign a company to industries on the basis of its sales or earnings within those industries. Fortunately, databases containing the breakdown of corporate sales, assets, and earnings across industries are now becoming available, so the preferred approach is now possible".

So, I think it's fair to say that the original builders of these models saw the shortcomings, but had little choice at the time. For what it's worth, the advantages of using the 1-0 binary indicator are that (a) it reduces the number of estimated parameters which is likely to help with the stability of the final model, and (b) it is easy to build & determine the industry factor - just look up industry membership and you are done.

People have attempted to remove this assumption over time. For example, I believe the UBS PAS model used a more inductive model that used industry membership to determine whether a security had exposure to a particular industry factor. The actual exposure was determined during the model fitting process.