Shares of company A cost $10 per share and give a profit of X%. Independently of A, shares of company B cost $50 per share and give a profit of Y%. Deciding how to invest $1,000, Mr. X chooses between 3 portfolios:
(a) 100 shares of A,
(b) 50 shares of A and 10 shares of B,
(c) 20 shares of B. The distribution of X is given by probabilities:
P{X = -3} = 0.3, P{X = 0} = 0.2, P{X = 3} = 0.5.
The distribution of Y is given by probabilities:
P{Y = -3} = 0.4, P{Y = 3} = 0.6.
Compute expectations and variances of the total dollar profit generated by portfolios (a), (b), and (c). What is the least risky portfolio? What is the most risky portfolio?