Question 2

Let y denote the current year. A municipality sends you the following liability stream (in million dollars):

(a) Determine the current term structure of treasury rates, and find the present value, dollar duration, and dollar convexity of the stream of liabilities. Please explain the main steps (interest rates, discount factors, compounding, etc.) followed in your calculations. You can find current data on numerous websites such as

http://finance.yahoo.com/bonds

http://fixedincome.fidelity.com/fi/FILanding 

(b) Identify at least 30 fixed-income assets that are suitable for a dedicated portfolio. Use assets that are considered risk-free, e.g., US government noncallable treasury bonds, treasury bills, or treasury notes. Display a succinct summary of the main characteristics of the bonds you chose (prices, coupon rates, maturity dates).

(c) Formulate a linear programming model to find the lowest-cost dedicated portfolio that covers the stream of liabilities. To eliminate the possibility of any interest risk, assume a 0% reinvestment rate on cash balances carried from one date to the next. Assume no short sales are allowed. What is the cost of your portfolio? What is the composition of your portfolio?

(d) Use the linear programming sensitivity information to determine the term structure of interest rates implied by the portfolio. Use a plot to compare it with the current term structure of treasury rates.

(e) Formulate a linear programming model to find the lowest-cost portfolio that matches the present value, dollar duration, and dollar convexity of the stream of liabilities. Assume no short sales are allowed. What is the cost of your portfolio? How much would you save by using this immunization strategy instead of dedication? Is your portfolio immunized against non-parallel shifts in the term structure? Explain why or why not.

(f) Combine a cash matching strategy for the liabilities during the first three years and an immunization strategy based on present value, duration and convexity for the liabilities during the last five years. Compare the cost of this portfolio with the cost of the two previous portfolios.

(g) The municipality would like you to make a second bid: What is your best dedicated portfolio of risk-free bonds you can create if short sales are allowed? Did you find arbitrage opportunities? Did you take into consideration the bid–ask spread? Did you set limits on the transaction amounts? Discuss the practical feasibility of your solution.