Question

An investor has an opportunity to buy stock in two publicly traded companies: Avvoltoio Airlines and
Unctuous Energy. If the investor puts her money in a stock, and the company does well, she earns a return of
$14. If the company does not do well, she earns $2. Avvoltoio tends to do well when oil prices are low;
Unctuous tends to do well when oil prices are high. The returns are therefore negatively correlated.
Returns have the following probability distribution.

Unctuous Return
U = 2 U = 14
Avvoltoio A = 2 0.2 0.3
Return A = 14 0.3 0.2

a. For each stock, compute the mean return and the variance of the return. Are you computing a
population mean, or a sample mean?
b. Compute the covariance of the returns, Cov(A, U), as well as their correlation, ρAU.

c. Compute E[A | U = 2] and E[A | U = 14].
Explain in economic terms why E[A | U = 2] > E[A | U = 14].
d. Suppose a risk averse investor decides to diversify by putting half of her money in each of the two
stocks. The 2-stock portfolio has three possible returns: 2, 8, and 14. Why?
Write down the distribution of returns for the 2-stock portfolio by completing the table below.
Hint: The investment in each stock is halved, so the return from each stock is only half the amount in the
table above. Also, from the table there are four possible outcomes, but two of them yield the same total
return, so there are only three different total returns.

RETURN PROBABILITY
2 ______
8 ______
14 ______

e. Compute the mean and the variance of the portfolio returns. Is the diversified portfolio preferable? Explain

Answer 1