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You are thinking of investing in two shares-A and B. The returns on these shares over the next year depends on the state of the economy, which could be described as "Boom", "Average", "Slow" or "Recession". The table below shows the probability of each of these states of the economy, and the expected return on each share given each possible state of the economy.
State of the economy
Probability
Share A return
Share B return
Boom
10%
15%
7%
Average
50%
8%
5%
Poor
20%
-2%
2%
Recession
-10%
-5%
The correlation between the two shares is 0.4. You construct a portfolio consisting of a 60% of your available funds invested in A and the balance invested in B. We will refer to this portfolio as Portfolio C.
a) What is the expected return on Share A?
b) What is the variance of returns on Share A (provide 6 decimal places)?
c) What is the expected return on Share B?
d) What is the variance of returns on Share B (provide 6 decimal places)?
e) What is the expected return on Portfolio C?
f) What is the variance of returns on Portfolio C (provide 6 decimal places)?
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