There are two stocks in an economy. If you buy a share of stock A, you have a 60% chance of getting $50 next year and a 40% chance of getting $30. Stock B has a 10% chance of getting $200 and a 90% chance of getting $31. Assume both stocks cost the same today.
a) If the consumer must buy exactly 2 shares of the same stock, which one will they buy if their utility = U(W) = W^(1/2) . Use the expected income of each stock and how the person feels about risk to justify why B is a riskier stock.
b) If the probabilities of the two stocks are completely unrelated (This means the probabilities for stock A are unaffected by the outcome of stock B and vice versa. Mathematically, the covariance between stock A and B is 0), show that buying 1 share of each stock is better than your result in (a). (Note: With one share of each stock, there are 4 possible outcomes a year from now. Also remember that the probability of two independent events happening is the product of their probabilities.)