The Mathematics of Financial Modelingand Investment Management

19-EquityPort Page 580 Friday, March 12, 2004 12:40 PM

580 The Mathematics of Financial Modeling and Investment Management

EXHIBIT 19.6 Systematic-Residual Risk Decomposition

Source: Figure 4.3 in Barra, Risk Model Handbook United States Equity: Version

3 (Berkeley, CA: Barra, 1998), p. 34. Reprinted with permission.

Benchmark risk is defined as the risk associated with the benchmark

portfolio. Active risk or tracking error is the risk that results from the man-

ager’s attempt to generate a return that will outperform the benchmark. The

active risk is further partitioned into common factor risk and specific risk.

Active Systematic-Active Residual Risk Decomposition

There are managers who overlay a market-timing strategy on their stock

selection. That is, they not only try to select stocks they believe will out-

perform but also try to time the purchase of the acquisition. For a man-

ager who pursues such a strategy, it will be important in evaluating

performance to separate market risk from common factor risks. In the

active risk decomposition approach just discussed, there is no market

risk identified as one of the risk factors. Since market risk (i.e., system-

atic risk) is an element of active risk, its inclusion as a source of risk is

preferred by managers. When market risk is included, we have the

active systematic-active residual risk decomposition approach shown in

Exhibit 19.8. Total excess risk is again divided into benchmark risk and

active risk. However, active risk is further divided into active systematic

risk (i.e., active market risk) and active residual risk. Then active resid-

ual risk is divided into common factor risks and specific risk.