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Answer: 1.77 years
The bond’s duration is the weighted average of the cash flow times, using each cash flow’s present value as the weight. From the table: - At 0.5 years: weight = 0.080 - At 1.0 years: weight = 0.074 - At 1.5 years: weight = 0.069 - At 2.0 years: weight = 0.776 So, \[ D = (0.5)(0.080) + (1.0)(0.074) + (1.5)(0.069) + (2.0)(0.776) \] \[ D = 0.040 + 0.074 + 0.1035 + 1.552 = 1.7695 \] Rounded, the duration is **1.77 years**. Because the yield is continuously compounded, Macaulay duration equals modified duration in this special case.
Author: Manit Arora
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Q-714.1. A very risky two-year bond with a face value of $100.00 pays a semi-annual coupon of 18.0% and has a yield (yield to maturity) of 15.0% with continuous compounding. Its price is therefore $104.032 as shown below. Please note that we could infer the price by translating the continuous rate into its semi-annual equivalent which is given by $2 * [\exp(0.15/2) - 1] = 15.577%104.03`2. The final column displays the weight of each cash flow's present value as a proportion of the bond's price.
Which is nearest to the bond's duration (please note that because the yield is continuously compounded, this is the special case where Macaulay duration is equal to modified duration so we don't really need to specify which!)?
A
1.77 years
B
1.85 years
C
1.93 years
D
2.00 years
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