Design an investment of $20, 000 in a portfolio of duration 2 years consistingof two kinds of coupon bonds maturing after 2 years, with annual coupons, bond A with $20 coupons and $100 face value, and bond B with $5 coupons and $500 face value, given that the initial rate is 8%.

Question

Design an investment of $20, 000 in a portfolio of duration 2 years consisting of two kinds of coupon bonds maturing after 2 years, with annual coupons, bond A with $20 coupons and $100 face value, and bond B with $5 coupons and $500 face value, given that the initial rate is 8%. How much will this investment be worth after 2 years?

Accepted Answer

We first find the prices and durations of the bonds: [latex]P_A(y) ≅ 120.72[/latex], [latex]P_B(y) ≅ 434.95, D_A(y) ≅ 1.8471, D_B(y) ≅ 1.9894.[/latex] The weights [latex]w_A ≅ −7.46\%, w_B ≅ 107.46\%[/latex] give duration 2, which means that we have to buy 49.41 bonds B and issue 12.35 bonds A. After one year we shall receive $247.05 from the coupons of B and will have to pay the same amount for the coupons of A. Our final amount will be $23, 470.22, exactly equal to the future value of $20, 000 at 8%, independently of any rate changes.

Question 10.15: Design an investment of $20, 000 in a portfolio of duration ...

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