Explanation:
For a zero-coupon bond, the Macaulay duration is exactly equal to its time to maturity. Therefore, the Macaulay duration = 8 years.
The modified duration is calculated as: Modified Duration = Macaulay Duration / (1 + y/m) Where: y = annual yield rate = 6% or 0.06 m = number of compounding periods per year = 2 (semi-annually)
Modified Duration = 8 / (1 + 0.06/2) = 8 / 1.03 = 7.76699 ≈ 7.77.
For an option-free zero-coupon bond, the effective duration is equal to its modified duration. The change in yield of four basis points is given as a distractor for this analytical relationship, though calculating the effective duration manually via price changes would yield approximately the same result.
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Q.48 A zero-coupon bond has a face value of USD 5,000 and a maturity of eight years. The 8-year yield rate is 6% compounded semi-annually. What is the value of the effective duration if the yield rate changes by four basis points?
A
7.77
B
6.78
C
6.45
D
7.45