2 When the payoff of a security is random, owning it entails risk. We will use in this course the standard deviation of the payoff as our quantitative mea- sure of that risk. In this problem the probability that the world moves to the up-state will be 1/2. Hence, the probability that it moves to the down-state is 1/2, too. Also, the risk-free one-year rate is 10% per year. An investor wants to own a certain asset whose initial price is $100 but she doesn't have money now so she will adopt one of the following two strategies: Strategy 1 Purchase the stock at the end of the period (t = 1 yr), when the stock's price will be $160 or $40 depending on whether the world moves to the up- or down-state, respectively. Strategy 2 At time t = 0 borrow the money to purchase a call option on that asset, with expiration t = 1 yr and strike price $100. At time t = 1, pay the loan with interest and get the asset by exercising the option if it is in-the-money or directly purchasing it if the option is out-of- the-money Which of the two strategies entails more risk? That is, which of the final cash flows has a greater standard deviation? The final cash flow of Strategy 1? Or of Strategy 2? 2 When the payoff of a security is random, owning it entails risk. We will use in this course the standard deviation of the payoff as our quantitative mea- sure of that risk. In this problem the probability that the world moves to the up-state will be 1/2. Hence, the probability that it moves to the down-state is 1/2, too. Also, the risk-free one-year rate is 10% per year. An investor wants to own a certain asset whose initial price is $100 but she doesn't have money now so she will adopt one of the following two strategies: Strategy 1 Purchase the stock at the end of the period (t = 1 yr), when the stock's price will be $160 or $40 depending on whether the world moves to the up- or down-state, respectively. Strategy 2 At time t = 0 borrow the money to purchase a call option on that asset, with expiration t = 1 yr and strike price $100. At time t = 1, pay the loan with interest and get the asset by exercising the option if it is in-the-money or directly purchasing it if the option is out-of- the-money Which of the two strategies entails more risk? That is, which of the final cash flows has a greater standard deviation? The final cash flow of Strategy 1? Or of Strategy 2