Suppose an investment manager holds a portfolio containing only one share of stock A. The price of stock A at time 0 is $100. In the time point 1 and 2, the stock price can be doubled or halved. The risk- free interest rate between every two-time point is 25%. Investment managers want their portfolio to be worth no less than $150 at time point 2. (1) Suppose an investor can buy a European put option that expires at the time point 2. What particular (strike price) put option should investors buy to achieve their goals? (don't forget the cost of buying options) (2) What kind of hedging strategy can investors use to replicate the options from the previous question? (3) Investors can only invest in stocks and bonds. In order to make that the portfolio value is no less than $150 at the time point 2, what kind of strategy should investors adopt?