This question has confused me a little, I understand the basic premise of the protective put but its the payoff that’s confusing me.
You own a share worth $431. You forecast that the price in a year is expected to decline. The forecast will decline to $367. At the time call options trade at $10 and put options trade at $7. You decide to purchase a put option at the money ( ie. X= $431), thereby creating a protective put strategy.
The question now asks what is the profit and payoff to the strategy if the price is $400 on expiry?
I obviously understand that the put is in the money, but do you just consider the payoff to the put?
You are correct the put option is in the money. Hence, X is greater than St. I would say the payoff would be 431-400= $31 and since you paid $7 for the option your profit is 31-7= $24.
The “payoff” depends whether you are looking at the option alone, or the combination of option and stock. Since the question refers to “the strategy”, I’d assume that it means the latter - a protective put implies the put AND the stock.
At any price at or below $431 the payoff to the put negates any decreases in value in the stock. So, for ANY price below $431, your payoff to the strategy is 431, and your profit is -7 – you break even on the portfolio (it still pays off $431, but this is less the $7 premium.
Chris Luyckx93 your answer was correct according to the memo. However, Busprof your answer logically seems more correct. They asked for the profit and payoff to the strategy. Surely this includes the stock you already own?
Payoff is typically the value of the strategy given the holdings (exercise value of the put and change in asset price), “gross”. Profit includes the option premium, “net”.