A stock market investor has $500 to spend and is considering purchasing 10 call

Question

A stock market investor has $500 to spend and is considering purchasing 10 call option contracts on 1,000 shares of Banana Computer stock. The shares themselves are currently selling for $28.50 per share. Banana is involved in a lawsuit, the outcome of which will be know within a month. If the outcome is in Banana's favor, analysts expect Banana's stock price to increase by $5 per share. If the outcome is unfavorable, then the price is expected to drop by $2.75 per share. The 10 call option contracts with a strike price of $30 per share and an expiration date in one month cost $500 right now. Besides purchasing the call options, the investor could : (i) do nothing and earn 8% per year compounded monthly on $500 (ii) purchase 17 shares of Banana stock right now and earn 8% per year compounded monthly on the rest of the money Suppose the probability that Banana wins the lawsuit is p, 0 < p < 1 . Assuming that the investor is risk-averse and his/her risk attitude is described by the exponential utiloty function U(x)=1-e^(-x/R), where R is the risk tolerance, R=2,500. What are the values of p that will make the investor choose to do nothing? What are the values of p that will make the investor choose to buy shares of Banana stock? What are the values of p that will make the invesstor choose to buy call options?

Explanation / Answer

If the investor believes that Apricot stands a 25% chance of winning the lawsuit, should he purchase the option? What if he believes the chance is only 10%? How large does the probability have to be for the option to be worthwhile?

Assuming 8% is the monthly interest rate and let p be the probability that Apricot will win the lawsuit

1) The expected monetary value associated with purchasing the option is:

EMV(Purchase Option) = 3,000p

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