Credit Risk: From Transaction to Portfolio Management

added to the other elements of return including the accrued interest

on the bond, which is always positive. This is simply the interest that

accrues due to the bond bearing a coupon. Finally we have the ‘pull-to-

par’ which is the change in value due to the effect of maturity. (This is

a distinct effect and is dependent upon the bond yield.) This effect can

either work for the portfolio manger or against depending on whether the

bond is priced above or below par. If above there will be a loss because

the bond must redeem at par. In Tables 1.21 and 1.22 we examine the

total return for a variety of bonds, and a sample of the optimized output,

sharing the characteristic of being priced of the same Bloomberg Fair

Market Curve.

Marginal measures of risk

Rather than the explicit use of quadratic optimizers, many managers

control risk through the use of ‘risk plots’ illustrated in Figure 1.43.

These display the portfolio relative to contours of equal risk. These are

formed by isolating the risk contribution of each position into a product

of its sensitivity and the exposure. The contour then represents the

exposure which would give equal risk contributions. This allows two

ways of managing the risks annotated as shown in Figure 1.43.

78 Credit risk: from transaction to portfolio management

Table 1.21 Comparison of benchmarks.

Issue Coupon Maturity Yield Roll Carry Price Clean Return

end (%)

G.E. Capital 5.50 26 September 4.33 10.10 1.38 101.66 101.52 1.18

2003

LBK-Thuringen 4.25 29 September 4.34 10.08 1.06 99.85 99.99 1.19

2003

KFW Intl 6.25 15 October 4.30 9.99 1.56 102.88 102.56 1.18

Finance 2003

G.E. Capital 4.00 28 October 4.25 9.92 1.00 99.60 99.79 1.17

2003

Table 1.22 The linear optimization output.*

Issue Duration Return (%) Holding (%) Weighted return (bps)

G.E. Capital 2.3 1.32 5 6.6

KFW Intl Finance 2.2 1.28 0 0

G.E. Capital 2.3 1.30 0 0

Rabobank 2.3 1.33 5 6.65

*Constraints: duration 4; holding 5%.