CFA Practice Question

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CFA Practice Question

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.

User Contributed Comments 8

User Comment
mtcfa Is this really an arbitrage opportunity? If the price is $3 lower, you get $50 back from your $60 investment, which is a loss.
ronrun yes it is. This means if you repeat your strategy 1000 times then you will get profit without investing.
adenisov in addition - entering contract has higher risk and risk premium, as well.
LionHero Dont think it is a pure arbitrage opportunity since is still involves some degree of risk.
gazza77 Basically you have a 50% change of losing $10 and a 50% chance of making $40. No brainer really
gulfa99 well for me the question is not clear. if you are risk averse you would opt to deposit 60 at 5 pct..which is optimal for me...
the second option has a degree of risk where you can lose from your capital invested
Jordan2117 Where does the furtures contract come into this? If you decided the price was going up, it would give you a levered return wouldn't it?
As was said, this can depend on your preference for risk.
EEEEvia Agreed with Gulfa
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