Question

5.1. A one-year call option on a stock with a strike price of $45 costs $3; a one-year put option on the stock with a strike price of $45 costs $5. Suppose that a trader buys five call options and three put option. What is the breakeven stock price above which the trader makes a profit?

Answer 1

Call option is the right to buy a share at the specified price and put option is the right to sell a share at the specified price

Premium paid = 5*3+3*5 = $30

Breakeven stock price assuming that put will not be exercised and shares will be sold in the market = 45 + 30/5 = $51

At this price, call option will be exercised and sold in the market. Put option will lapse. Profit = (51-45)*5 - 30 = $0. Profit will be earned if the price rises above $51

Another break even stock price assuming that call will not be exercised and put will be exercised = 45 - 30/3 = $35

At this price, 3 shares will be bought from the market and sold using put option. Profit will be earned if this price falls further.

Since the question asks the price above which the trader makes a profit, the answer is $51