A portfolio consists of a serial bond with the following terms: Face amount $10,000 Coupon rate 5.0% per year, payable annuallyRedemption At par in two equal installments: the first payable in 9 years; the second payable in 10 years.Yield to maturity 4.0% per year, compounded annuallyX = the modified duration of the portfolio.In what range is X?
A)Less than 7.40
B)7.40 but less than 7.60
C)7.60 but less than 7.80
D)7.80 but less than 8.00
E)8.00 or more

Question

Quizplus · Accepted Answer

The modified duration of a bond portfolio measures the portfolio's sensitivity to changes in interest rates, reflecting the weighted average time until the cash flows are received. In this case, the bond pays annual coupons and has a yield to maturity of 4.0%, with redemption in two equal installments at 9 and 10 years. Given these parameters, the modified duration will be influenced by the timing of these cash flows and the discount rate (yield to maturity). The modified duration will be less than the weighted average time to receipt of the cash flows because it accounts for the present value of these cash flows. Given the structure of the bond (coupon payments and the redemption at 9 and 10 years), the modified duration is likely to be less than the average maturity but still significant due to the relatively long-term nature of the bond. The correct range, considering the bond's characteristics and the yield to maturity, is between 7.40 and 7.60. This range reflects the bond's sensitivity to interest rate changes, considering both the timing of the cash flows and the discounting effect of the yield to maturity.

A Portfolio Consists of a Serial Bond with the Following