4. (Future) A company has a 7,875,000RMB well diversified portfolio without dividend, named as P* with a beta of 1.8. The HS300 index is currently 3000. Each future contract is on 250 times the index. Risk-free rate is 10% per annum. (19%) 1) Can you construct another portfolio now with a future contract and borrowing/lending to replicate the position of P* at T in spot market, such that at time T they have the exact same payoff? (3%) 2) What should be the current six-month future index? (3%) 5 3) What is the optimal number of contracts? What direction should be taken in the future contracts to hedge the diversified portfolio? (3%) 4) Suppose that the CAPM model holds. Given the optimal hedging and assuming we will sell P* five months later (one month before expiration of the future contract), when the HS300 index is expected to be 2800. The future contract is also expected to be closed by then, what is the expected value of the hedger's position five months later? (6%) 5) Give an explanation about the purpose of hedging a diversified portfolio with an index future. (4%) E(r;)= r, + ,(E(r )r,) F, = S,(1+r,)