Consider a three-year bond with 11% annual coupon (paid semi-annually). Suppose the yield on the bond is 7% per year with continuous compounding. What is the duration of the bond (in years)?
(required precision: 0.01 +/- 0.01)
Following formula's are used to calculated duration of the bond;
Discount factor = e^(-0.07*t)
Face value = $1000
coupon = 5.5% of 1000 = $55
PV of coupon = discount factor*coupon
Price of bond = sum of PV of coupons = $1103.06
weight = PV of coupon/Price of bond
Duration = time in year of bond paid*weight
duration of bond = sum of duration of all coupon = 2.66 years
Year | discount factor | coupon | PV of coupon | Weight | duration |
0.5 | 0.9656 | $ 55.00 | $ 53.11 | 0.05 | 0.02 |
1 | 0.9324 | $ 55.00 | $ 51.28 | 0.05 | 0.05 |
1.5 | 0.9003 | $ 55.00 | $ 49.52 | 0.04 | 0.07 |
2 | 0.8694 | $ 55.00 | $ 47.81 | 0.04 | 0.09 |
2.5 | 0.8395 | $ 55.00 | $ 46.17 | 0.04 | 0.10 |
3 | 0.8106 | $ 1,055.00 | $ 855.17 | 0.78 | 2.33 |
Price | $ 1,103.06 | Duration | 2.66 |
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