The Mathematics of Financial Modelingand Investment Management

21-Bond Portfolio Man Page 652 Wednesday, February 4, 2004 1:12 PM

652 The Mathematics of Financial Modeling and Investment Management

a forward-looking tracking error of zero or “very small”—indicates that

the manager is pursing a passive strategy relative to the benchmark

index. When the forward-looking tracking error is “large” the manager

is pursuing an active strategy.

Risk Factors and Portfolio Management Strategies

Since forward-looking tracking error indicates the degree of active portfo-

lio management being pursued by a manager, it is necessary to understand

what factors (referred to as “risk factors”) affect the performance of a man-

ager’s benchmark index. The risk factors affecting one of the most popular

broad-based bond market indexes, the Lehman Brothers U.S. Aggregate

Index, have been investigated by Dynkin, Hyman, and Wu.^6 A summary of

the risk factors is provided in Exhibit 21.1. They first classify the risk fac-

tors into two types: systematic risk factors and nonsystematic risk factors.

Systematic risk factors are the common factors that affect all securities in a

certain category in the benchmark bond market index. Nonsystematic fac-

tor risk is the risk that is not attributable to the systematic risk factors.

EXHIBIT 21.1 Summary of Risk Factors for a Benchmark

Systematic Nonsystematic

Risk Factors Risk Factors

Term Structure Nonterm Structure Issuer Issue

Risk Factors Risk Factors Specific Specific

Sector Risk

Quality Risk

Optionality Risk

Coupon Risk

MBS Sector Risk

MBS Volatility Risk

MBS Prepayment Risk

(^6) Lev Dynkin, Jay Hyman, and Wei Wu, “Multi-Factor Risk Factors and Their Ap-
plications,” in Frank J. Fabozzi (ed.) Professional Perspectives on Fixed Income
Portfolio Management: Volume 2 (Hoboken, NJ: John Wiley & Sons, 2001).