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

A portfolio holds 60% in Asset 1 (standard deviation 10%) and 40% in Asset 2 (standard deviation 20%). The correlation between the assets is -0.25. The portfolio standard deviation is closest to:

The portfolio standard deviation is about 8.7%, closest to 8.9%. Portfolio variance is 0.0036 plus 0.0064 plus the negative covariance term of minus 0.0024, giving 0.0076, whose square root is roughly 8.7%. The negative correlation reduces risk below the weighted average.

  1. A8.9%Correct
  2. B10.7%
  3. C12.4%

Explanation

Variance = (0.6×0.10)² + (0.4×0.20)² + 2(0.6)(0.4)(−0.25)(0.10)(0.20) = 0.0036 + 0.0064 − 0.0024 = 0.0076. Standard deviation = √0.0076 = 8.7%, so the closest option is 8.9%. Ignoring the sign of the correlation gives 0.0124, or 11.1%; ignoring covariance gives 0.0100, or 10%, both wrong.

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