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
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
G.E. Capital 5.50 26 September 4.33 10.10 1.38 101.66 101.52 1.18
LBK-Thuringen 4.25 29 September 4.34 10.08 1.06 99.85 99.99 1.19
KFW Intl 6.25 15 October 4.30 9.99 1.56 102.88 102.56 1.18
G.E. Capital 4.00 28 October 4.25 9.92 1.00 99.60 99.79 1.17
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%.