thats all

(a) Consider a two-period consumption model consisting of now. I = 0 and next year, 1 = 1. There are two investors, Investor A who is patient and wants to wait and consume the maximum amount possible at = 1. and Investor B who is impatient and wants to consume the maximum amount possible now. Both investors have an income of $200.000 today and no income at t = 1. Both investors have access to a real investment opportunity costing $200,000 now and returning a guaranteed $215,000 at 1 = 1. They also have access to risk-free borrowing and lending at an annual rate of 10%. Explain the investment decisions taken by each investor (both real and financial) and the resultant cash flows and consumption, including a brief discussion of the optimality of the net present value (NPV) rule. (7 marks) (b) You have just purchased a house in Sydney for $2 million, using your own savings to make a down payment equal to 20% of the house's value, with the remainder financed via a 25-year mortgage. The mortgage has fixed monthly payments, with the first payment due in exactly one month. The stated annual interest rate on the loan is 6% with monthly compounding. How much of the loan principal will you repay in the first year of the loan, expressed as a percentage of your total annual mortgage payment? Will this percentage increase, decrease, or stay the same in subsequent years? Explain. (6 marks) (c) The term structure of interest rates is flat with all spot rates equal to 10%. Consider the following bonds Bond A: a ten-year 10% coupon bond with a face value of $100. Bond B: a four-year zero coupon bond with a face value of $100. Bond C: a four-year 5% coupon bond with a face value of $100. All coupons are paid annually. Using the bond duration concept, explain which bond will experience a smaller percentage price change if the term structure shifts upwards by 100 basis points (i.e. to 11%). (5 marks) (d) Comment on the validity of the following statements According to the CAPM, an in- the-money put option on a zero beta stock should have an expected retum equal to the risk-free rate (5 marks) (e) Suppose that in any given year, there is a 50% chance that a mutual fund will outperform the market simply by chance. If there are N mutual funds, what is the smallest number N such that the probability of observing at least one out of these N funds outperform the market for 10 consecutive years by chance exceeds 99%? Noting that there are around 8,000 mutual funds in the US, comment on the implication(s) of your answer for empirical tests of efficient markets. (5 marks) (1) Consider a forward contract to deliver, in two years' time, a two-year coupon bond with a face value of $100 and a coupon rate of 10%. The forward price F will be paid in year 2 while the bond payments occur in years 3 and 4. The current term structure of interest rates is given by: r, = 6%,r>= 5%, y = 4.5%, and r = 4%. Using a replicating portfolio approach, find the no-arbitrage forward price, F