Estimate the 2-year, 5-year, and 10-year key rate durations of a 20-year bond ca

Question

Estimate the 2-year, 5-year, and 10-year key rate durations of a 20-year bond carrying a coupon of C1 percent on face value $100 paid semi-annually. The given term structure starts with C2 percent spot rate of interest at time zero and rises at a rate of 0.002 (.2%) per half year thereafter. Take a 20 basis point (.002) move in each key interest rate to calculate the key rate durations by the method done in class and given in textbook. Report answers for the following:

1.     Current fair price of the bond with the given term structure.

2.     Price change needed to calculate 2-year key rate duration.

3.     Price change needed to calculate 5-year key rate duration.

4.     Price change needed to calculate 10-year key rate duration.

C1 = 13.8
C2 = 9.4

Explanation / Answer

Solution:

1) Current fair Price = 202.58

2)

-0.10

3)

4)

Year Coupon Rate Spot Rate Discount factor for semi annual Cash Flow Present Value of Cash flow Yr C1 C2 Discount Factor =1/{(1+C2)^Yr} =C1*Discount Factor 0.5 13.8 9.4% 0.9561 13.1938 1 13.8 9.6% 0.9124 12.5912 1.5 13.8 9.8% 0.8692 11.9943 2 13.8 10.0% 0.8264 11.4050 2.5 13.8 10.2% 0.7844 10.8249 3 13.8 10.4% 0.7432 10.2559 3.5 13.8 10.6% 0.7028 9.6992 4 13.8 10.8% 0.6635 9.1563 4.5 13.8 11.0% 0.6252 8.6283 5 13.8 11.2% 0.5881 8.1162 5.5 13.8 11.4% 0.5522 7.6210 6 13.8 11.6% 0.5176 7.1432 6.5 13.8 11.8% 0.4843 6.6836 7 13.8 12.0% 0.4523 6.2424 7.5 13.8 12.2% 0.4217 5.8201 8 13.8 12.4% 0.3925 5.4169 8.5 13.8 12.6% 0.3647 5.0327 9 13.8 12.8% 0.3382 4.6676 9.5 13.8 13.0% 0.3132 4.3215 10 13.8 13.2% 0.2894 3.9941 10.5 13.8 13.4% 0.2670 3.6850 11 13.8 13.6% 0.2459 3.3940 11.5 13.8 13.8% 0.2261 3.1206 12 13.8 14.0% 0.2076 2.8643 12.5 13.8 14.2% 0.1902 2.6245 13 13.8 14.4% 0.1740 2.4007 13.5 13.8 14.6% 0.1589 2.1922 14 13.8 14.8% 0.1448 1.9984 14.5 13.8 15.0% 0.1318 1.8187 15 13.8 15.2% 0.1197 1.6523 15.5 13.8 15.4% 0.1086 1.4986 16 13.8 15.6% 0.0983 1.3569 16.5 13.8 15.8% 0.0889 1.2266 17 13.8 16.0% 0.0802 1.1069 17.5 13.8 16.2% 0.0723 0.9972 18 13.8 16.4% 0.0650 0.8969 18.5 13.8 16.6% 0.0584 0.8053 19 13.8 16.8% 0.0523 0.7219 19.5 13.8 17.0% 0.0468 0.6460 20 113.8 17.2% 0.0418 4.7598 Total Present Value 202.58

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