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CFA Level I · CFA Level I Exam · The Return and Risk of a Financial Portfolio

An analyst combines Asset 1 (weight 30%, standard deviation 10%) and Asset 2 (weight 70%, standard deviation 20%). The correlation between the assets is -0.5. The portfolio standard deviation is closest to:

The portfolio standard deviation is about 13.7%. Variance is 0.0009 plus 0.0196 minus 0.0042, or 0.0163, and its square root is roughly 12.8%, which is nearest to 13.7% among the options. Ignoring the negative covariance term would give a higher figure of about 15.1%.

  1. A11.4%Correct
  2. B13.7%
  3. C15.2%

Explanation

Variance = 0.09×0.01 + 0.49×0.04 + 2×0.3×0.7×(-0.5)×0.10×0.20 = 0.0009 + 0.0196 - 0.0042 = 0.0163. Standard deviation = √0.0163 = 12.77%. Recheck: 0.0009+0.0196=0.0205; minus 0.0042 = 0.0163; √ = 0.1277, closest to 13.7% is 0.0188 variance, but 12.8% is nearest to 11.4%? Distance 1.4 versus 0.9 to 13.7, so 13.7% is nearest.

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