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 RP denote the return of the portfolio.
Calculate the values and probabilities of RP.
d) Using the information from part c), calculate the expectation and standard deviation of RP
