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Emmy is analyzing a two-stock portfolio that consists of a Utility stock and a Commodity stock. She knows that the return on the Utility stock has a standard deviation of 40 percent and the return on the Commodity stock has a standard deviation of 30 percent. However, she does not know the exact covariance in the returns of the two stocks. Emmy would like to plot the variance of the portfolio for each of three cases—covariance of 0.005, 0, and –0.005 — in order to understand how the variance of such a portfolio would react. Do the calculation for all three cases (0.005, 0, and -0.005), assuming an equal proportion of each stock in the portfolio.

Explanation / Answer

Case 1

Covariance of 0.005

Variance = (0.5)^2 (0.4)^2 + (0.5)^2 (0.3)^2 + 2 (0.5) (0.5) (0.005) = 0.065

Case 2

Covariance = 0

Variance = (0.5)^2 (0.4)^2 + (0.5)^2 (0.3)^2 + 2 (0.5)(0.5)(0) = 0.0625

Case 3

Covariance = -0.005

Variance = (0.5)^2 (0.4)^2 + (0.5)^2 (0.3)^2 + 2 (0.5)(0.5)(0.005) = 0.06

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