MANUEL MORENO 79Table 4.4Relative behavior of two portfolios with respect to a parallel
change in the yield curve
Yield Portfolio 1 Portfolio 2 Difference
Change (%)
Accumulated Yield Accumulated Yield
value (%) value (%)
5 81.632 −36.734 78.661 −42.677 −5.943
4.5 83.480 −33.038 80.802 −38.395 −5.356
4 85.398 −29.202 83.030 −33.938 −4.736
3.5 87.390 −25.219 85.349 −29.301 −4.081
3 89.459 −21.081 87.762 −24.474 −3.392
2.5 91.609 −16.780 90.275 −19.448 −2.668
2 93.847 −12.305 92.892 −14.215 −1.909
1.5 96.175 −7.648 95.617 −8.764 −1.115
1 98.600 −2.798 98.457 −3.085 −0.287
0.5 101.128 2.256 101.41 2.832 0.576
0 103.763 7.527 104.5 9 1.472
−0.5 106.513 13.027 107.714 15.429 2.402
− 1 109.385 18.770 111.066 22.133 3.363
−1.5 112.385 24.771 114.562 29.125 4.354
− 2 115.523 31.046 118.209 36.419 5.373
−2.5 118.806 37.612 122.014 44.029 6.417
− 3 122.243 44.487 125.985 51.971 7.483
−3.5 125.846 51.692 130.130 60.261 8.568
− 4 129.623 59.247 134.457 68.915 9.668
−4.5 133.588 67.176 138.976 77.953 10.776
− 5 137.751 75.503 143.696 87.392 11.888an increase (decrease) in interest rates implies that the final value of portfo-
lio 2 decreases (increases) more than that of portfolio 1 and, so, portfolio 1
performs better (worse) than portfolio 2. The difference between these gen-
eralized durations also implies that the longer the change in interest rates,
the bigger the difference in the portfolio yields.
Next, we analyse the effects of two alternative changes in the slope of
the yield curve. Results are shown in Tables 4.5 to 4.6 and Tables 4.7 to 4.8,
respectively.
The first non-parallel change implies a decrease in the slope of the
yield curve. Specifically, we assume that the change in the 5 (15) [20]-
year interest rate is equal to the change in the 10-year interest rate+1%
(−0.5%) [−1%].