(3) Options. Let A(0) = 100, A(T) = 110, S(0) = 25 dollars and let S(T) = 30 20 with probability 0.7 with probability 0.3 (a) Your initial wealth is $10,000. Design a portfolio that splits the money fifty-fifty between stock and bonds. Then compute the expected return and risk of this portfolio. (b) Construct a portfolio consisting only of risk-free assets and put options with strike $25 that has same final wealth as the portfolio in (a). (c) Construct a portfolio consisting only of shares of stock and call options with strike 25 and expiration T such that the value of this portfolio at time T, V(T), is 110 no matter whether the stock goes up or down. What is the price of the call option? (3) Options. Let A(0) = 100, A(T) = 110, S(0) = 25 dollars and let S(T) = 30 20 with probability 0.7 with probability 0.3 (a) Your initial wealth is $10,000. Design a portfolio that splits the money fifty-fifty between stock and bonds. Then compute the expected return and risk of this portfolio. (b) Construct a portfolio consisting only of risk-free assets and put options with strike $25 that has same final wealth as the portfolio in (a). (c) Construct a portfolio consisting only of shares of stock and call options with strike 25 and expiration T such that the value of this portfolio at time T, V(T), is 110 no matter whether the stock goes up or down. What is the price of the call option