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A one-year call option on a stock with a strike price of $30 costs $3; a one-year put option on the stock with a strike price of $30 costs $4. Suppose that a trader buys two call options and one put option. The breakeven stock price above which the trader makes a profit is
A.$35
B.$40
C.$30
D.$36
A.$35
B.$40
C.$30
D.$36
Answer: A
When the stock price is $35, the two call options provide a payoff of 2×(35−30) or $10. The put option provides no payoff. The total cost of the options is 2×3+ 4 or $10. The stock price in A, $35, is therefore the breakeven stock price above which the position is profitable because it is the price for which the cost of the options equals the payoff.
When the stock price is $35, the two call options provide a payoff of 2×(35−30) or $10. The put option provides no payoff. The total cost of the options is 2×3+ 4 or $10. The stock price in A, $35, is therefore the breakeven stock price above which the position is profitable because it is the price for which the cost of the options equals the payoff.
Flashcard info:
Author: CoboCards-User
Main topic: Finance & Investment
Topic: Derivatives
Published: 27.10.2015
The trader buys:
- 2 call options with a strike price of $30 and a cost of $3 each
- 1 put option with a strike price of $30 and a cost of $4
Let's calculate the total cost of the trader's position:
- 2 call options: 2 × $3 = $6
- 1 put option: 1 × $4 = $4
Total cost: $6 + $4 = $10
Now, we need to find the breakeven stock price, which is the price at which the trader's total profit is zero.
The profit or loss from the call options can be calculated as:
- Profit from call options = (Stock price - $30) × 2, if stock price > $30
- Loss from call options = $6, if stock price ≤ $30
The profit or loss from the put option can be calculated as:
- Profit from put option = ($30 - Stock price) × 1, if stock price < $30
- Loss from put option = $4, if stock price ≥ $30
The total profit/loss http://quordle-game.io/ is the sum of the profits/losses from the call options and the put option.
To find the breakeven stock price, we need to set the total profit/loss equal to zero and solve for the stock price:
Total profit/loss = 0
(Stock price - $30) × 2 - $6 + ($30 - Stock price) × 1 - $4 = 0
3 × Stock price - $90 - $4 = 0
3 × Stock price = $94
Stock price = $31.33
Therefore, the breakeven stock price above which the trader makes a profit is $31.33.
The correct answer is C. $30.