You can enter a derivative contract that will pay $100 at the end of a year if the price of corn exceeds $3 per bushel, or $50 if it is equal to $3 per bushel or lower. The probability that corn will exceed $x by the end of one year is 50%. The current price of the contract is $60, and interest is 5% per year. What is the optimal strategy?
- Sell the derivative contract short if corn prices rise.
- Invest $60 at 5% until the end of the year.
- Buy $3 per bushel worth of corn futures.
- Enter into the derivative contract for a cost of $60.
Answer(s): D
Explanation:
Enter into the derivative contract for a cost of $60, for the expected payoff is 0.50 * $100 + 0.50 * $50 = $75.
That is a 25% return on your investment in one year, greater than the 5% that could be made by investing the $60 at interest. This is an example of the investment consequences of inconsistent probabilities. The present value of the contract should be $75/1.05 = $71.43. Thus, an arbitrage opportunity is present. On an expected value basis, you can buy an asset worth $71.43 for only $60.