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Question
A statistician is currently trying to maximize his profit in the bond market. Four bonds are available for purchase and sale at the bid and ask prices shown in the table below. The statistician can buy up to 1300 units of each bond at the ask price or sell up to 1300 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 that are also shown in the table below. The statistician's goal is to maximize his revenue from selling bonds less his payments 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 sales of bonds) is nonnegative. His current cash position can depend on past coupons and that cash accumulated at the end of each year earns 12% annual interest. Determine how to maximize net profit from buying and selling bonds, subject to the constraints previously described.| Bid (for selling) and ask (for buying) prices of bonds | |||||
| Bond 1 | Bond 2 | Bond 3 | Bond 4 | ||
| Bid | $1,000 | $99 | $980 | $960 | |
| Ask | $1,020 | $1,015 | $1,002 | $184 | |
| Cash payments from seller to buyer | |||||
| Bond 1 | Bond 2 | Bond 3 | Bond 4 | ||
| Year 1 | $120 | $100 | $90 | $70 | |
| Year 2 | $140 | $130 | $110 | $90 | |
| Year 3 | $1,300 | $1,320 | $1,290 | $1,310 | |
Answer
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