Question

An investor is considering buying a put option for stock ABC with the following parameters:

Exercise price of the put option is $170, initial stock price $165, put option price $8.

A. Define payoff and profit function and provide payoff and profit formulae for the put option buyer at maturity with respect to stock price at expiration.  

B. Define payoff and profit function and calculate the payoff and profit for a protective put position at maturity when the stock price is $180 at expiration.  

C. Discuss why the stock owner should implement the protective put strategy as opposed to only buying the underlying stock.

Answer 1

A.

A put option pays off if the spot price at maturity (St) is lesser than the strike price (X)

If St > X, put option payoff = 0

If St < X, put option payoff = St-Strike price = St - 170

If St > X, profit function = -Put option price = -$8

If St < X, profit function = Strike price-St-Put option price = 170-8-St = $178 - St

B.

Protective put is when a long put option is combined with a long position in the stock

Since, Strike price is lesser than the stock price at maturity, the put option exercises out of the money

Payoff = 0 + (180-165) = $15

Profit = -Put option price - Initial stock price + Put option payoff + Stock price at maturity

Profit = -8-165+0+180 = $7

C.

Buying a protective put ensures that any downside in the stock price is hedged. If only a stock is buyed, there is a loss when the stock price goes below the purchase price. But if a put option is buyed at that strike price, any downside would lead a positive payoff by the put option, thus hedging the losses due to long call.