A stock is trading at $50. You believe there is a 60% chance the price of the stock will increase by 10% over the next 3 months. You believe there is a 30% chance the stock will drop by 5%, and you think there is only a 10% chance of a major drop in price of 20%. At-the-money 3-month puts are available at a cost of $650 per contract. What is the expected dollar profit for a writer of a put at the end of 3 months? (Hint: remember how we calculated the expected return (E (r)) for stocks? Use the probabilities as the weights to calculate the weighted average profits in all scenarios.)

Question

Gina Santos

Business

18 October, 19:23

A stock is trading at $50. You believe there is a 60% chance the price of the stock will increase by 10% over the next 3 months. You believe there is a 30% chance the stock will drop by 5%, and you think there is only a 10% chance of a major drop in price of 20%. At-the-money 3-month puts are available at a cost of $650 per contract. What is the expected dollar profit for a writer of a put at the end of 3 months? (Hint: remember how we calculated the expected return (E (r)) for stocks? Use the probabilities as the weights to calculate the weighted average profits in all scenarios.)

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Answers (1)

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Laci Singh · Answer 1

The answer is $475.

Explanation:

We have the writer of the put contract has the obligation to buy the share at $50 (as the put is the at-the-money put) in 3 months time. The writer of the put also has received the premium at $650 for assuming the obligation to buy at the predetermined price.

Thus, the expected returns is calculated as below:

-[0.60 x 100 x Max[$0,$50 - ($50) (1.1) ] + 0.30 x 100 x Max[$0,$50 - ($50) (0.95) ] + 0.10 x 100 x Max[$0,$50 - ($50) (0.80) ] + $650 = - [0.6 x 100 x 0 + 100 x 0.3 x 2.5 + 0.1 x 100 x 10] + 650 = $475.