3. (a) Three bonds A, B and C show the following year-on-year returns Rk (k = A, B, C) for 5 consecutive years: Year RA RB RC 1 20 15 5 2 -10 25 45 3 20 -15 -5 4 -15 10 10 5 -10 10 10 The relative weights of the bonds are given as A:B:C = (1:). i. Tabulate the asset returns in a 5-columned chart where the 1st column shows the year number, the 2nd column shows R, the 3rd column shows RB, the 4th column shows Rc and the 5th column shows the weighted portfolio entries. (6 marks) ii. Calculate the mean and variance of the combined portfolio from this chart. (4 marks) (b) A buyer agrees to buy a unit of each of these three bonds at different dates (i.e. 1 unit of A, 1 unit of B and 1 unit of C). A unit of bond A is priced at 1000 and is to be bought in 3 months' time from today, a unit of bond B is priced at 800 and is to be bought in 9 months' time from today while a unit of bond C is priced at 1500 and is to be bought in 10 months' time from today. If the bonds are charged at the rate of 6% interest compounded yearly and it is agreed to settle all dues in one single payment P at the end of 12 months, i. draw the relevant timeline chart for this problem, (2 marks) ii. derive the exact monthly interest rate starting from the given yearly rate of interest, (2 marks) iii. calculate the amount of this single payment P. (6 marks)