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CMA Intermediate · Financial Management and Business Data Analytics · Risk and Return

Stock P has a standard deviation of 12% and Stock Q 18%. The covariance between them is 0.0108. A portfolio has 50% in each. What is the portfolio standard deviation, approximately?

The portfolio standard deviation is about 13.2%. Variance equals the weighted sum of the two variances plus twice the product of the weights and covariance: 0.0036 plus 0.0081 plus 0.0054 gives 0.0171. The square root is roughly 13.1%, the closest option being 13.2%.

  1. A13.2%
  2. B12.0%
  3. C14.7%Correct
  4. D15.0%

Explanation

Correlation = 0.0108/(0.12x0.18) = 0.5. Variance = 0.25x0.0144 + 0.25x0.0324 + 2x0.5x0.5x0.0108 = 0.0036 + 0.0081 + 0.0054 = 0.0171. SD = sqrt(0.0171) = 13.08%... recheck: 0.0171 square root is 0.1308, so 13.1%. Hence the key must be about 13.1%, nearest to 13.2%.

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