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. 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 S14. If the company does not do well, she earns S2. 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 Avvoltoio A 2 Return A 14 U 14 0.3 0.2 0.2 0.3 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, PAUc. Compute EIA l U-2] and E[A | U = 141. Explain in economic terms why EIA | U-2] > E[A 1 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 14 e. Compute the mean and the variance of the portfolio returns. Is the diversified portfolio preferable? Explain.

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Page No. Unctuous Relwn 0.2 + 0 8 4-0.3 (2-8) 00 3 (4-8) -8 (0-2) 2 6 0 on portlolio ! M E28 2Page No. Date: PREMIUM o KeturnBraba bi 0.2 4-S leralafa sinto

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