Question

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 0.010, 0, and –0.010 — in order to understand how the variance of such a portfolio would react. Do the calculation for all three cases (0.010, 0, and -0.010), assuming an equal proportion of each stock in the portfolio.

Case 1, σ12 = 0.010: (Round answer to 4 decimal places, e.g. 0.0768.) Variance LINK TO TEXT

Case 2, ρ = 0.0: (Round answer to 4 decimal places, e.g. 0.0768.) Variance LINK TO TEXT

Case 3, σ12 = -0.010: (Round answer to 4 decimal places, e.g. 0.0768.) Variance

Answer 1

Case 1, σ₁₂ = 0.010: (Round answer to 4 decimal places, e.g. 0.0768.)

Variance = Weight of utility^2 * SD of utility^2 + Weight of Commodity^2 * SD of Commodity^2 + 2 * Weight of Commodity * Weight of Utility * covariance

Variance = 0.50^2 * 0.40^2 + 0.50^2 * 0.30^2 + 2 * 0.5 * 0.5 * 0.01

Variance = 0.0675

Case 2, σ₁₂ = 0.00: (Round answer to 4 decimal places, e.g. 0.0768.)

Variance = Weight of utility^2 * SD of utility^2 + Weight of Commodity^2 * SD of Commodity^2 + 2 * Weight of Commodity * Weight of Utility * covariance

Variance = 0.50^2 * 0.40^2 + 0.50^2 * 0.30^2 + 2 * 0.5 * 0.5 * 0

Variance = 0.0625

Case 3, σ₁₂ = -0.010: (Round answer to 4 decimal places, e.g. 0.0768.)

Variance = Weight of utility^2 * SD of utility^2 + Weight of Commodity^2 * SD of Commodity^2 + 2 * Weight of Commodity * Weight of Utility * covariance

Variance = 0.50^2 * 0.40^2 + 0.50^2 * 0.30^2 + 2 * 0.5 * 0.5 * -0.010

Variance = 0.0575

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