For 250 you can buy a call option on a stock you have studie

For $2.50 you can buy a call option on a stock you have studied carefully. The option will expire in one year, and has a strike price of $60. You believe there is a 50 % chance the stock will be worth $70 in one year and a 50 % change it will be worth less than $60 in one year. If you invest $1000 what is your expected return and what is the risk of your investment, as measured by the standard deviation? (For simplicity, assume you pay for the options at the end of the year.)

Solution

The option two payoff scenarios are:

Payoff ( St = 70) = (70-60) - 2.50 = 7.50 profit due to call option

or Payoff ( St < 60) = -2.50 loss due to call option

Thus,

expected payoff per option

= 0.5 (7.50) + 0.5(-2.50)

= 2.50 is the expected payoff per option

Now. number of options that I can buy = 1000 / 2.50 = 400 contracts

Thus, expected gain from the contract = 400 * 2.50 = 1000$ is the expected return.