# P1.T3.21.9. Derivative payoffs

#### Nicole Seaman

##### Director of FRM Operations
Staff member
Subscriber
Learning objectives: Calculate and compare the payoffs from hedging strategies involving forward contracts and options. Calculate and compare the payoffs from speculative strategies involving futures and options. Describe arbitrageurs' strategy and calculate an arbitrage payoff. Describe some of the risks that can arise from the use of derivatives

Questions:

21.9.1. Ralph creates a portfolio with two positions: a short call and a short put with identical maturities on the same stock that has a current price, S(0) = $20.00. His short call with a strike price, K1 =$22.00 has a premium, c1 = $1.75. His short put with a strike price, K2 =$18.00 has a premium, p1 = $1.25. Both options are out-of-the-money by the same amount of$2.00. Recall that option profit is equal to the payoff net of the premium and we (typically) ignore the impact of discounting. On the future date with both options mature, under which future stock price scenario is Ralph's trade profitable?

a. If the stock price falls within $15.00 and$25.00
b. His portfolio will always generate a small profit
c. If the stock price is less than $18.00 or greater than$22.00
d. His portfolio will generate a small profit if volatility decreases

21.9.2. Peter creates a portfolio with the following two positions with identical maturities: a long forward contract with delivery price equal to K dollars; and a long European put option with a strike price equal to K + $3.00. Recall that the payoff excludes the premium. Which statement is TRUE about this portfolio's payoff? a. The payoff must be less than$3.00; i.e. maximum of $3.00 b. The payoff must be at least$3.00; i.e., minimum of $3.00 c. The payoff is equal to$3.00 regardless of the future asset price
d. We need the current asset price to answer the question

21.9.3. A new trader has $10,000.00 to invest in a stock or options on the stock. The current price of the stock is$20.00. She is interested in out-of-the-money European call options that mature in one year. The strike price is $28.00 and the call premium is$2.50; i.e., S(0) = $20.00, K =$28.00, and c = $2.50. Therefore, she can either purchase 500 shares or$10,000 ÷ $2.50 = 4,000 options. If we ignore the impact of discounting, what is the breakeven stock price for the two strategies? (Note: this is inspired by GARP's EOC Question 4.20). a.$18.43
b. $25.50 c.$32.00
d. \$47.72