†Broker Steve Johnson is currently trying to maximize his profit in the bond market. Four bonds are available for purchase and sale, with the bid and ask pricc of each bond as shown in Table 40. Steve can buy up to 1,000 units of each bond at the ask price or sell up to 1,000 units of each bond at the bid price. During each of the next three years, the person who sells a bond will pay the owner of the bond the cash payments shown in Table 41.
Steve’s goal is to maximize his revenue from selling bonds less his payment for buying bonds, subject to the constraint that after each year’s payments are received, his current cash position (due only to cash payments from bonds and not purchases or sale of bonds) is nonnegative. Assume that cash payments are discounted, with a payment of $1 one year from now being equivalent to a payment of 90¢ now. Formulate an LP to maximize net profit from buying and selling bonds, subject to the arbitrage constraints previously described. Why do you think we limit the number of units of each bond that can be bought or sold?
table 40
Bond | Bid Price | Ask Price |
1 | 980 | 990 |
2 | 970 | 985 |
3 | 960 | 972 |
4 | 940 | 954 |
table 41
Year | Bond 1 | Bond 2 | Bond 3 | Bond 4 |
1 | 100 | 80 | 70 | 60 |
2 | 110 | 90 | 80 | 50 |
3 | 1,100 | 1,120 | 1,090 | 1,110 |
†Based on Rohn (1987).
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