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 $3 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?

A. Invest $60 at 5% until the end of the year
B. Buy $3 per bushel worth of corn futures
C. Enter into the derivative contract for a cost of $60

Correct Answer: C

Enter into the derivative contract for a cost of $60; 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.