- CFA Exams
- CFA Level I Exam
- Study Session 2. Quantitative Methods (1)
- Reading 8. Probability Concepts
- Subject 6. Expected Value, Variance, and Standard Deviation of a Random Variable

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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. Buy $3 per bushel worth of corn futures

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

C. Invest $60 at 5% until the end of the year

**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.

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**User Contributed Comments**
2

User |
Comment |
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leo6fin |
how come the probabiliity of corn price equal to $3 is .5. my guess is it should be less than 0.5. am I missing something here |

steved333 |
That amount was stated in the question |