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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Business

Ronan Horton

3 November, 19:57

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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Andrews · 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.