Question 2: (13 marks) A market contains two stocks. Tomorrow, the state of the market could be Superb, Good, Bad or Ugly and this will affect the returns of the stocks denoted by R1 and R2 as shown in the table below.

State of market	Probability	R1	R2
Superb	0.2	12%	9%
Good	0.4	2%	3%
Bad	0.3	0%	0%
Ugly	0.1	-4%	-6%

Based on this information.

a) Write down the Joint Distribution of R1 and R2

b) Calculate (R1, R2) - the correlation of R1 and R2 (2 marks) (7 marks)

c) An investor sets up a portfolio in the two stocks with weights (w1, w2) = (0.6, 0.4). Let the random variable RP denote the return of the portfolio. Calculate the values and probabilities of RP. (2 marks)

d) Using the information from part c), calculate the expectation and standard deviation of RP (2 marks) You need to clearly show all steps in your calculation and the relevant formulas you are using.