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 three 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 three 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 three 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 three months?

Quizplus · Accepted Answer

To calculate the expected profit of a naked put writer, first we need to find the probability of the stock's price movement based on the given information:

- Probability of stock price increasing by 10% = 60%
- Probability of stock price dropping by 5% = 30%
- Probability of stock price dropping by 20% = 10%

Then, we can use the following formula to calculate the expected profit of a naked put writer:
Expected Profit = Premium received - (Probability of exercise x (Strike price - Stock price at expiration))

Since it is a naked put, the writer does not own the underlying stock and therefore does not have a strike price. The premium received is $650 per contract.

Now, let's calculate the expected profit based on the given probabilities:

- Expected profit if stock price increases by 10%: $650 (premium received)
- Expected profit if stock price drops by 5%: $215 [($50 - $47.50) x 0.3 x 100]
- Expected profit if stock price drops by 20%: -$500 [($50 - $40) x 0.1 x 100] (negative because the writer will have to buy the stock at $40 and sell it at the lower market price of $50)

We can combine these expected profits using the given probabilities to get the final expected profit:
Expected Profit = (0.6 x $650) + (0.3 x $215) + (0.1 x -$500) = $390 + $64.50 - $50 = $404.50

Therefore, the expected dollar profit for a writer of a naked put at the end of three months is $404.50, which is closest to choice C ($475).

A Stock Is Trading at $50