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	10%	9%
Good	0.4	5%	3%
Bad	0.3	0%	0%
Ugly	0.1	- 2%	- 5%

 

(Note: The minus sign when market is Ugly)

Based on this information.

a) Write down the Joint Distribution of R1 and R2                        

b) Calculate ρ(R1, R2) - the correlation of R1 and R2                  

c) An investor sets up a portfolio in the two stocks with weights (w₁, w₂) = (0.6, 0.4). Let the random variable R_P denote the return of the portfolio.

Calculate the values and probabilities of R_P.                                                           

d) Using the information from part c), calculate the expectation and standard deviation of  R_P