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

Which statement about a portfolio of two risky assets with a correlation of +1 is most accurate?

With perfect positive correlation, portfolio standard deviation equals the weighted average of the two assets' standard deviations. The variance formula collapses to the square of that weighted sum. Diversification gains require correlation below +1, and zero risk needs correlation of -1.

  1. APortfolio standard deviation is the weighted average of the asset standard deviationsCorrect
  2. BPortfolio standard deviation is below the weighted average of the asset standard deviations
  3. CPortfolio variance can be reduced to zero with suitable weights

Explanation

With correlation of +1, variance equals (w1σ1 + w2σ2)², so standard deviation is the weighted average of the individual standard deviations. Diversification benefits and zero variance need correlation below +1, with zero variance requiring -1.

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