- CFA Exams
- CFA Exam: Level I 2021
- Study Session 2. Quantitative Methods (1)
- Reading 8. Probability Concepts
- Subject 1. Introduction

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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?

B. Buy $3 per bushel worth of corn futures

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

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.

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**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 |