Audrey is considering an investment in morgan communications, whose stock curren
ID: 2789045 • Letter: A
Question
Audrey is considering an investment in morgan communications, whose stock currently sells for 60$. A put option on Morgans 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.
a) What is the premium assocaited with the put option? The call option?
b) If Morgans Stock price increases to 70 what would be the return to an invesotr who bought a share of the stock? If the investor bought a call option? If the investor bought a put option?
c) If Audrey bought 0.6 share of Morgan Communications and sells one call option on her stock, has she created a riskless hedged investment? What is the total value of her portfolio under each scenerio?
e) If Audrey buys .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 scenerio?
Explanation / Answer
Premium of put=3.06
Premium of call=9.29
If 1 share is bought, return in case of price rise to 70 will be (70-60)/60=16.66%
If 1 call is bought, return in case of price rise to 70 will be (max(70-55,0)-9.29)/9.29=61.46%
If 1 put is bought, return in case of price rise to 70 will be (max(55-70,0)-3.06)/3.06=-100%
If she buys 0.6 share and sells one call, value in case of price rise will be 0.6*70-15=27
If she buys 0.6 share and sells one call, value in case of price decline will be 0.6*50-0=30
As the portfolio is impacted by price rise and decline that is it is not contant the riskless hedge is not created
If she buys 0.75 share and sells one call, value in case of price rise will be 0.75*70-15=37.5
If she buys 0.75 share and sells one call, value in case of price decline will be 0.75*50-0=37.5
As the portfolio is not impacted by price rise and decline that is it is contant the riskless hedge is created
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