Question

You plan to form a portfolio by investing in a 6-year zero-coupon bond and a 3-year 6% annual coupon bond with a yield to maturity of 10%. The target duration of this portfolio is 4 years. Therefore, ________ of the portfolio value should be allocated to the zero-coupon bond. A) 37.1% B) 62.9% C) 83.33% D) 24%

Answer 1

Duration of Zero Coupon Bond = Term = 6 years

weight of ZCB = w

weight of Coupon Bond = 1 - w

Portfolio weight = w * 6 + (1 - w) * 2.82

4 = w * 6 + 2.82 - w * 2.82

4 = w * 6 + 2.82 - w * 2.82

weight of ZCB = w = 37.1% Option A

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