The Mathematics of Financial Modelingand Investment Management

19-EquityPort Page 582 Friday, March 12, 2004 12:40 PM

582 The Mathematics of Financial Modeling and Investment Management

Summary of Risk Decomposition

The four approaches to risk decomposition are just different ways of

slicing up risk to help a manager in constructing and controlling the risk

of a portfolio and for a client to understand how the manager per-

formed. Exhibit 19.9 provides an overview of the four approaches to

carving up risk into specific/common risks, systematic/residual risks,

and benchmark/active risks.

Portfolio Construction and Risk Control

The power of a multifactor risk model is that given the risk factors and

the risk factor sensitivities, a portfolio’s risk exposure profile can be

quantified and controlled. The three examples below show how this can

be done so that the a manager can avoid making unintended bets. In the

examples, we use the Barra E3 factor model.^17

EXHIBIT 19.9 Risk Decomposition Overview

Source: Figure 4.6 in Barra, Risk Model Handbook United States Equity: Version

3 (Berkeley, CA: Barra, 1998), p. 38. Reprinted with permission.

(^17) The illustrations are taken from Frank J. Fabozzi, Frank J. Jones, and Raman
Vardharaj, “Multi-Factor Risk Models,” Chapter 13 in Frank J. Fabozzi and Harry
M. Markowitz (eds.), The Theory and Practice of Investment Management (Hobo-
ken, NJ: John Wiley & Sons, 2002).