The Mathematics of Financial Modelingand Investment Management

21-Bond Portfolio Man Page 663 Wednesday, February 4, 2004 1:12 PM

Bond Portfolio Management 663

EXHIBIT 21.6 Tracking Error Summary

Passive Portfolio versus Aggregate Index, 9/30/98

Tracking Error (bp/year)

Isolated Cumulative Change

Tracking error term structure 7.0 7.0 7.0

Nonterm structure 9.6

Tracking error sector 7.4 10.5 3.5

Tracking error quality 2.1 11.2 0.7

Tracking error optionality 1.6 11.5 0.3

Tracking error coupon 2.0 12.3 0.8

Tracking error MBS sector 4.9 10.2 −2.1

Tracking error MBS volatility 7.2 11.1 0.9

Tracking error MBS prepayment 2.5 10.3 −0.8

Total systematic tracking error 10.3

Nonsystematic tracking error

Issuer-specific 12.4

Issue-specific 3.0

Total 12.7

Total tracking error return 16

Systematic Nonsystematic Total

Benchmark sigma 417 4 417

Portfolio sigma 413 13 413

Source: Exhibit 16 in Lev Dynkin, Jay Hyman, and Wei Wu, “Multi-Factor Risk

Models and Their Applications,” in Frank J. Fabozzi (ed.) Professional Perspec-

tives on Fixed Income Portfolio Management: Volume 2 (New Hope, PA: Frank

J. Fabozzi Associates, 2001).

make a single payment to a policyholder at a specified date with a guaran-

teed interest rate); and (3) municipal governments for prerefunding munic-

ipal bond issues (i.e., creating a portfolio that replicates the payments that

must be made for an outstanding municipal government bond issue), and,

for states, payments that must be made to lottery winners who have

agreed to accept payments over time rather than a lump sum.

There are two types of solutions to the problem of liability funding

currently used by practitioners: (1) numerical/analytical solutions based

on the concept of duration and convexity and (2) numerical solutions