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 naked put at the end of 3 months?

Question

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 naked put at the end of 3 months?

Quizplus · Accepted Answer

E[Profit] = −{.60Max [$0, $50 − ($50)(1.1)] + .30Max [$0, $50 − ($50)(0.95)] + .10Max [$0, $50 − ($50)(.80)]} (100) + $650 = − [.6(0) + .3(250) + .1(1,000)] + 650 = $475

A Stock Is Trading at $50