A 10-year government bond has an annual coupon of 5%. Assume that it has a face value of $100 and that the spot rate curve is flat at 5% (annual compounding).

a) Suppose that you have a $100 million long position in the 10-year bond. You are trying to hedge the interest rate exposure on this position by selling 5-year bonds. Assuming that you rely on modified duration, how much of the 5-year bond should you sell?

b) After you have put on your hedge, the spot curve shifts down by 10 basis points across all maturities. What is the new price of the 10-year bond?

c) After you have put on your hedge, the spot curve shifts down by 10 basis points across all maturities. What is the profit/loss on the hedged portfolio?

Answer rating: 100% (QA)

To solve these questions we need to use the concept of modified duration which measures the sensitivity of a bonds price to changes in interest rates ... View the full answer