Textbook Problem

OPTIONS Audrey is considering an investment in Morgan Communications, whose stock currently sells for $60. A put option on Morgan’s stock, with an exercise price of $55, has a market value of $3.06. Meanwhile, a call option on the stock with the same exercise price and time until expiration has a market value of $9.29. The market believes that at the expiration of the options, the stock price will be $50 or $70 with equal probability.

1. a. What is the premium associated with the put option? The call option?
2. b. If Morgan’s stock price increases to $70, what would be the return to an investor who bought a share of the stock? If the investor bought a call option on the stock? If the investor bought a put option on the stock?
3. c. If Morgan’s stock price decreases to $50, what would be the return to an investor who bought a share of the stock? If the investor bought a call option on the stock? If the investor bought a put option on the stock?
4. d. If Audrey buys 0.6 share of Morgan Communications and sells one call option on the stock, has she created a riskless hedged investment? What is the total value of her portfolio under each scenario?
5. e. If Audrey buys 0.75 share of Morgan Communications and sells one call option on the stock, has she created a riskless hedged investment? What is the total value of her portfolio under each scenario?