Problem 3 

You are managing interest rate risk in an investment portfolio.

Your liabilities consist of 250 bonds of type A. Each of these bonds has a face value of $1,000, pays coupons semiannually, and has two years to maturity. The annual coupon rate is 4%, and the YTM is 5% APR.

Your assets consist of cash and 180 bonds of type B. Each of these bonds has a face value of $1,000, has 4 years remaining until maturity, and pays coupons semiannually. The annual coupon rate is 5% and the YTM is 7% APR. The amount of cash in your portfolio is such that the current market value of assets is equal to the current market value of liabilities.

(a) What is the Macaulay duration of bonds A and B? What is the modified duration of bonds A and B?

(b) What is the modified duration of your assets and the modified duration of your liabilities?

(c) Using only modified duration, compute the approximate change in the value of your assets and the approximate change in the value of your liabilities (in % and in dollars) in response to a 200 bps upward shift in interest rates (YTMs) along the entire yield curve.

(d) Compute the actual change in the value of your assets and liabilities (in dollars) in response to a 200 bps upward shift in interest rates (YTMs) along the entire yield curve. Is the decrease in the value of assets and the decrease in the value of liabilities (in absolute terms) smaller or larger than that predicted by the duration approximation in part (c)? Explain why. How much capital do you need to contribute after the shift in YTMs so that the value of assets is again equal to the value of liabilities?