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

A two-asset portfolio holds 50% in Asset A (standard deviation 20%) and 50% in Asset B (standard deviation 10%). The correlation between the two assets is 0.20. The portfolio variance is closest to:

The portfolio variance is about 0.0150. Add the weighted variances, 0.0100 plus 0.0025, and twice the weighted covariance, 0.0020, giving 0.0145, which is closest to 0.0150. The 0.0225 figure wrongly treats correlation as 1 and ignores diversification.

  1. A0.0150
  2. B0.0165Correct
  3. C0.0225

Explanation

Variance = 0.25×0.04 + 0.25×0.01 + 2×0.5×0.5×0.20×0.20×0.10 = 0.0100 + 0.0025 + 0.0020 = 0.0145... recompute covariance term: 2×0.25×(0.2×0.2×0.1)=0.5×0.004=0.0020. Total = 0.0145. Closest option is 0.0150.

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