What is the duration of the $80 million in new securities

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Q1 You are an investor purchasing the 8-year maturity, annual coupon rate of 4% bond. The par value is $1,000 and market value upon purchase is $1,000. The Macaulay duration is 7.0 years.
One day after purchasing the bond, interest rates increase to a 6% annual rate and remain at this level until bond maturity. Assume bond coupons can be re-invested at a 6% annual rate.
1. Calculate the following immediately after the fourth coupon payment:
(1) The accumulated value of re-invested coupons,
(2) The market value of the bond, and
(3) The total annual return. Show all work.
2. Explain the relationship between the total annual return after the fourth coupon payment and the yield-to-maturity when the bond was purchased.

Question 2. A bank has two, 3-year commercial loans with a present value of $70 million. The first is a $30 million loan that requires a single payment of $37.8 million in 3 years, with no other payments till then. The second is for $40 million. It requires an annual interest payment of $3.6 million. The principal of $40 million is due in 3 years.
(a) What is the duration of the bank's commercial loan portfolio?
(b) What will happen to the value of its portfolio if the general level of interest rates increased from 8% to 8.5%?

Q3. The duration of a $200 million portfolio is 10 years. $80 million in new securities are added to the portfolio, increasing the duration of the portfolio to 12.5 years. What is the duration of the $80 million in new securities?

Reference no: EM133430587

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