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CFA Level I · CFA Level I Exam · Portfolio Risk and Return: Part I

Asset X has a standard deviation of 20% and Asset Y has a standard deviation of 10%. The correlation between them is 0.20. A portfolio holds 50% in each. The portfolio standard deviation is closest to:

The portfolio standard deviation is about 12%, closest to 12.2%. Variance is 0.0145 from the two weighted variances plus the covariance term, and its square root is about 12.0%. The 15% simple average of standard deviations ignores the diversification from correlation below one.

  1. A10.5%
  2. B12.2%Correct
  3. C15.0%

Explanation

Variance = 0.25(0.04) + 0.25(0.01) + 2(0.5)(0.5)(0.2)(0.2)(0.1) = 0.01 + 0.0025 + 0.01 = wait: the covariance term is 0.5 x 0.2 x 0.1 x 0.2 x 0.5... computing: 2x0.25x0.2x0.20x0.10 = 0.002. Total = 0.01+0.0025+0.002 = 0.0145; square root = 12.04%, closest to 12.2%. The 15.0% option is the simple average of the standard deviations, which ignores diversification.

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