What is the minimum cost portfolio, consisting of up to 6 bonds, that provides enough cash flow to cover liabilities in each period? Interest Rate 7% Characteristics of bonds Bond 1 Bond 2 Bond 3 Bond 4 Bond 5 Face Value \$1,000 \$1,000 \$1,000 \$1,000 \$1,000 Coupon Payment \$100 \$125 \$150 \$200 \$75 Years to Maturity 3 5 6 4 6 Price \$1,078.73 \$1,225.51 \$1,381.32 \$1,440.34 \$1,023.83 Bond 1 Bond 2 Bond 3 Bond 4 Bond 5 Cost Number Purchased 10 10 10 10 10 \$61,497 Cash Flow Bond 1 Bond 2 Bond 3 Bond 4 Bond 5 Total Liability Year 1 \$1,000 \$1,250 \$1,500 \$2,000 \$750 \$6,500 \$32,000 Year 2 \$1,000 \$1,250 \$1,500 \$2,000 \$750 \$6,500 \$25,000 Year 3 \$1,000 \$1,250 \$1,500 \$2,000 \$750 \$6,500 \$22,000 Year 4 \$1,250 \$1,500 \$2,000 \$750 \$5,500 \$28,000 Year 5 \$1,250 \$1,500 \$750 \$3,500 \$25,000 Year 6 \$1,500 \$750 \$2,250 \$20,000 Problem In models BOND1 and BOND2 we saw a way for an investor to protect against interest rate fluctuations. Here, we'll look at another method. An investor wants to put together a portfolio consisting of up to 6 different bonds. He has certain cash- flow requirements in the future that the coupons of the bonds should cover. (For example, a pension fund must meet requirements for future pension payments.) These payments are independent of interest rate changes. How should the investor choose his portfolio to minimize the cost of the bonds, while making sure that the payments cover his future cash- flow requirements? Solution 1) The variables are the number of each bond to include in the portfolio. In worksheet BOND3 these are given the name Purchased_bonds. 2) The constraints are very simple. First we have the logical constraints: Purchased_bonds >= 0 via the Assume Non-Negative option Purchased_bonds = integer (We can not buy fractions of a bond) Then there is the constraint to make sure that the cash-flow requirements are met: Cash_flow >= Liabilities 3) The objective is to minimize the portfolio cost. This is given the name Total_cost. Remarks In this model we assume that money coming in from maturing bonds can not be used to cover the cash-flow requirements. Also, we do not account for excess money in one period that may be transferred to the next period. In model BOND4 we will account for this.