Spot interest in January

Year 1 Spot interest 2%

Year2 Spot interest 2.25%

Year3 Spot interest 2.5%

Year4 Spot interest 3%

On January 11th there is a global economic shock and yields at all maturities fall by 50 basis points (0.5%)

1. What happens to the price of a 4 year bond paying a coupon of $5 a year and with a face value of $100? (4 marks)

2. Compare the change in the price of this bond calculated directly from the present value of its cash flows with what is predicted by a calculation based on the bonds duration. (6 marks)

3. What happens to the forward rate between years 3 and 4? (That is the forward rate that starts at 36 months from now and ends at 48 months from now) (5 marks)

4. Suppose that the global economic shock is so severe that it causes investors to think there is now a significant chance of default on the bond. Before the shock they did not believe this. How does that affect how you interpret the forward rate you have calculated (the 3 year ahead forwards rate) and its relation to the expectation of the 1 year rate in 36 months? (5 marks)