The price of a stock is $40. The price of a one-year European put option on the stock with a strike price of $30 is quoted as $7 and the price of a one-year European call option on the stock with a strike price of $50 is quoted as $5. Suppose that an investor buys 100 shares, shorts 100 call options, and buys 100 put options. Draw a diagram illustrating how the investor’s profit or loss varies with the stock price over the next year. How does your answer change if the investor buys 100 shares, shorts 200 call options, and buys 200 put options?
Question
The price of a stock is 30 is quoted as 50 is quoted as $5. Suppose that an investor buys 100 shares, shorts 100 call options, and buys 100 put options. Draw a diagram illustrating how the investor’s profit or loss varies with the stock price over the next year. How does your answer change if the investor buys 100 shares, shorts 200 call options, and buys 200 put options?
Solution
The investor's profit or loss can be illustrated using a payoff diagram. Here are the steps to create the diagram:
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Identify the different stock prices: The stock price can vary from 0 to $60.
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Calculate the payoff from the stock: The investor buys 100 shares. So, the payoff from the stock is the stock price minus the purchase price. The purchase price is 40) * 100.
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Calculate the payoff from the call option: The investor shorts 100 call options. So, the payoff from the call option is the maximum of zero and the difference between the stock price and the strike price of the call option. The strike price of the call option is 50)) * -100.
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Calculate the payoff from the put option: The investor buys 100 put options. So, the payoff from the put option is the maximum of zero and the difference between the strike price of the put option and the stock price. The strike price of the put option is 30 - stock price)) * 100.
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Calculate the total payoff: The total payoff is the sum of the payoff from the stock, the call option, and the put option.
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Plot the total payoff against the stock price: This will give you the payoff diagram.
If the investor buys 100 shares, shorts 200 call options, and buys 200 put options, the payoff from the call option and the put option will be doubled. So, the total payoff will be the sum of the payoff from the stock, twice the payoff from the call option, and twice the payoff from the put option. The shape of the payoff diagram will be the same, but the values will be different.
Similar Questions
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The investor buys a put option on a security with a strike price of $40 and a premium of $2; and buy a call option on a security with a strike price of $30 and a premium of $4. If price of security at maturity (ST) is $30, his profit will beSelect one:a. $3b. $4c. -$6d. -$4
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Consider a world in which some stock, S, can either go up by 25% or down by 20% in one year and noother outcomes are possible. The continuously compounded risk-free interest, r, is 5.5% and the current priceof the stock, S0, is $100.1. What are the possible stock values in one year’s time, ST ?2. What are the possible payoffs of a European call option written on stock S with a strike price, X, of$100 and time-to-expiration of 1 year, T = 1 ?3. Suppose you want to form a portfolio, P , consisting of short on one call option and long on somenumber, ∆, of the stock, such that the portfolio value in one year’s time, PT , does not depend on thevalue of the stock, ST . What would be the appropriate value of ∆, also called the hedge ratio or delta?4. What would be the (certain) portfolio value in one year’s time, PT ?5. What is the arbitrage-free value of the portfolio today, P0 ?6. What is the premium of the call option today, c0, if there is no arbitrage opportunity?7. Define p = (erT − d) /(u − d), and call this the risk-neutral probability that the stock price increases.What is the value of p ?8. What is the expected value of the stock in one year’s time, E (ST ), under the risk-neutral probabilities?9. At what continuous rate would the stock price have to grow to end up at the expected value?10. What would be the expected value of the call option in one year’s time, E (cT ), under the risk-neutralprobabilities?11. At what continuous rate would the call price have to grow to end up at the expected value?
A European option giving the right to sell a stock at $100 sells for $5. Under what circumstance will the buyer of the option make a profit? Select one: a. When the stock price at maturity is less than $95 b. When the stock price at maturity is less than $100 c. When the stock price anytime up to maturity is less than $95 d. When the stock price at maturity is greater than $100
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