Problem Set: You are required to do all calculations in EXCEL
You have been hired recently as a personal financial planner. Your first client is interested in a 12% coupon, 20 year bond that pays coupons semi-annually. The client's goal is to earn her expected returns on the investment, given that her holding period is equal to the duration of the bond. The current price of the bond is 100.
a) Calculate the duration of the bond and the expected return.
b) Prove to your client that even if interest rate should fall to 6% immediately after purchase and remain at 6% over the entire maturity of the bond, she will still reach her goal.
c) Prove to your client that if the interest rate should rise to 18% immediately after purchase and remain at that level from purchase to maturity, she will still reach her goal.
d) Calculate the realized return for a zero coupon bond of the same duration and yield at purchase as the 12% coupon bond, assuming rates follow the same path as in parts b and c above. Which bond performed best and why? Hint: What happened to duration as rates changed up and down and how did this impact realized return?
A financial institution has an asset portfolio worth $30 billion and has liabilities with a present value equal to $27 billion. The modified duration of its assets is 4 and the modified duration of its liabilities is 6. The convexity of its assets is 80 and the convexity of its liabilities is 40.
What are the bets the institution is making in terms of rates rising or falling and in terms of volatility? Explain.
Suppose that rates fall 200 basis points. Use the duration/convexity approximation to determine the change in the economic surplus as well as the new value of assets and present value of liabilities.