CFA Level I · CFA Level I Exam · Portfolio Risk and Return: Part I
Two risky assets have a correlation of +1.0. Compared with the weighted average of the two standard deviations, the standard deviation of a portfolio holding both assets in positive weights is most likely:
The portfolio standard deviation equals the weighted average of the two standard deviations. When correlation is +1.0, portfolio variance collapses to the square of the weighted sum of standard deviations, so combining the assets provides no risk reduction through diversification.
- ALower than the weighted average
- BEqual to the weighted averageCorrect
- CHigher than the weighted average
Explanation
With correlation of +1, portfolio variance equals (w1s1 + w2s2)^2, so portfolio standard deviation is exactly the weighted average of the standard deviations. No diversification benefit arises. Lower or higher results would require a correlation below or above +1, and the latter is impossible.
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