Variance, Covariance, and Correlation in Portfolio Analysis | CFA Level 1 Exam

Covariance Calculation for Lumber Providers and Smithson Homebuilders

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Question

Patrick Manning owns stock in Lumber Providers with a return variance equal to 16%. Manning is considering the addition of Smithson Homebuilders to his portfolio. The variance of returns for Smithson Homebuilders equals 25%, and its correlation of returns with Lumber Providers equals -0.60. The covariance of returns between Lumber Providers and Smithson Homebuilders is closest to:

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Explanations

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A. B. C.

C

To calculate the covariance between Lumber Providers and Smithson Homebuilders, we can use the following formula:

Covariance = Correlation × Standard Deviation of Lumber Providers × Standard Deviation of Smithson Homebuilders

Given information: Return variance of Lumber Providers = 16% Return variance of Smithson Homebuilders = 25% Correlation of returns between Lumber Providers and Smithson Homebuilders = -0.60

To calculate the standard deviation, we take the square root of the return variance. Therefore: Standard Deviation of Lumber Providers = √(16%) = 4% Standard Deviation of Smithson Homebuilders = √(25%) = 5%

Now we can substitute these values into the covariance formula:

Covariance = -0.60 × 4% × 5% = -0.60 × 0.04 × 0.05 = -0.012

Therefore, the covariance of returns between Lumber Providers and Smithson Homebuilders is -0.012, which is closest to -0.024 (option B) when rounded to three decimal places.

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