The Mathematics of Financial Modelingand Investment Management

21-Bond Portfolio Man Page 657 Wednesday, February 4, 2004 1:12 PM

Bond Portfolio Management 657

sidered in the “Isolated” calculations are the correlations between the

risk factors. For example, the 14.7 basis points for the tracking error for

quality considers only the mismatch between the portfolio exposure and

benchmark exposure due to quality and taking into consideration the

correlations only of quality exposure for the different quality ratings.

The tracking error for the portfolio is 52 basis points and the tracking

error for the systematic and nonsystematic risk is 45 basis points and

26.1 basis points, respectively. Because the tracking errors represent

EXHIBIT 21.3 Tracking Error Breakdown for Sample Portfolio

Sample Portfolio versus Aggregate Index, 9/30/98

Tracking Error (bp/year)

Isolated Cumulative

Change in

Cumulative

Tracking error term structure 36.3 36.3 36.3

Nonterm structure 39.5

Tracking error sector 32.0 38.3 2.0

Tracking error quality 14.7 44.1 5.8

Tracking error optionality 1.6 44.0 −0.1

Tracking error coupon 3.2 45.5 1.5

Tracking error MBS sector 4.9 43.8 −1.7

Tracking error MBS volatility 7.2 44.5 0.7

Tracking error MBS prepayment 2.5 45.0 0.4

Total systematic tracking error 45.0

Nonsystematic tracking error

Issuer-specific 25.9

Issue-specific 26.4

Total 26.1

Total tracking error 52

Systematic Nonsystematic Total

Benchmark return standard deviation 417 4 417

Portfolio return standard deviation 440 27 440

Source: Exhibit 2 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).