80 MANAGING INTEREST RATE RISK UNDER NON-PARALLEL CHANGESTable 4.5Relative behavior of the bonds included in the portfolio 1 with
respect to a decrease in the slope of the yield curve
Yield Bond A Bond B Bond C
Change
Accumulated Yield Accumulated Yield Accumulated Yield
value (%) value (%) value (%)
5 82.121 −35.757 78.042 −43.915 82.242 −35.514
4.5 83.631 −32.737 80.444 −39.110 84.648 −30.703
4 85.176 −29.646 82.974 −34.051 87.191 −25.616
3.5 86.757 −26.485 85.638 −28.722 89.883 −20.233
3 88.374 −23.250 88.447 −23.105 92.735 −14.529
2.5 90.029 −19.940 91.409 −17.181 95.758 −8.482
2 91.722 −16.554 94.534 −10.931 98.967 −2.064
1.5 93.455 −13.088 97.833 −4.333 102.376 4.752
1 95.229 −9.541 101.317 2.635 106 12
0.5 97.044 −5.911 105 10 109.856 19.713
0 98.901 −2.196 108.892 17.785 113.964 27.928
−0.5 100.803 1.606 113.010 26.021 118.343 36.687
− 1 102.75 5.5 117.369 34.738 123.017 46.034
−1.5 104.742 9.485 121.983 43.967 128.008 56.016
− 2 106.782 13.565 126.872 53.744 133.344 66.688
−2.5 108.871 17.743 132.053 64.107 139.054 78.108
− 3 111.010 22.020 137.547 75.095 145.168 90.337
−3.5 113.200 26.401 143.376 86.753 151.723 103.447
− 4 115.443 30.887 149.563 99.127 158.756 117.512
−4.5 117.740 35.481 156.133 112.267 166.308 132.616
− 5 120.093 40.186 163.113 126.227 174.424 148.849Table 4.5 shows the results for the bonds included in portfolio 1. The
first column shows the change in 10-year interest rates. The conclusions are
similar to those of the above change: an increase in interest rates leads to a
decrease in the bond yield and the highest (lowest) yields correspond to the
bond with the longest (shortest) maturity.
Table 4.6 includes the accumulated value and the yield for both portfolios.
As in Table 4.5, the first column shows the changes in the bond D. Results
are analogous to those obtained with a parallel change: portfolio 1 outper-
forms portfolio 2 if interest rates rise and vice versa if they fall. As above,
the difference between the generalized durations with respect to the short-
term interest rate in both portfolios implies that (a) in percentage terms, an
increase (decrease) in interest rates harms (benefits) portfolio 2 (1) more, and