A share is trading at $50. You believe there is a 60% chance the price of the share will increase by 10% over the next three months. You believe there is a 30% chance the share 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 three months?
A)$300
B)$200
C)$475
D)$0

Question

A share is trading at $50. You believe there is a 60% chance the price of the share will increase by 10% over the next three months. You believe there is a 30% chance the share 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 three months?
A)$300
B)$200
C)$475
D)$0

Quizplus · Accepted Answer

To calculate the expected profit for a writer of a naked put, we need to calculate the expected stock price at the end of three months. 
Expected Value = (0.6 x $55) + (0.3 x $47.50) + (0.1 x $40) = $52.75
The writer of the put option must buy the stock at the strike price of $50. So, the profit will be:
Profit = Strike Price - Expected Stock Price - Premium
Profit = $50 - $52.75 - $6.50 = -$9.25
The negative sign indicates a loss for the writer. Thus, the expected dollar profit is -$925 per contract.
Therefore, the best choice is C, as it is the only option that matches the calculated expected dollar profit.

A Share Is Trading at $50