Final answer:
The payoff of a hedged portfolio created by purchasing stock, writing a call option, and buying a put option with the same exercise price and a net outlay will depend on the stock price at option expiration. The maximum loss is limited to the net outlay, and the potential gain occurs if the stock price is below the exercise price, limited to $1 per share.
Step-by-step explanation:
The scenario involves building a hedged portfolio by purchasing a share of stock, writing a 1-year call option, and buying a 1-year put option, all with the same exercise price of $55, and a net outlay of $54. The payoff of this portfolio will vary depending on the stock's price at the expiration of the options.
- If the stock's price is above $55, the call option will be exercised, and you will have to sell the stock at $55, leading to a capital gain equivalent to $55 minus the net outlay. However, since you are also holding the stock, any amount above $55 at which you could sell the stock is forfeited due to the call option.
- If the stock's price is below $55, the put option can be exercised, allowing you to sell the stock for $55 regardless of the lower market price. Your gain will be $55 minus the net outlay.
- If the stock's price is exactly $55, neither the call nor the put option will be exercised, and your position will be neutral, with the stock's value equal to the exercise price.
Thus, the payoff of this portfolio will be a maximum loss of the net outlay ($54) if the stock price is at or above the exercise price, and a potential gain if the stock price falls below the exercise price, limited to the difference between $55 and the $54 outlay.