CFA Level I · CFA Level I Exam · Portfolio Risk and Return: Part I
An analyst combines two risky assets with the same weights and a correlation of +1.0 between them. Compared with the weighted average of the two assets' standard deviations, the portfolio standard deviation is most likely:
The portfolio standard deviation equals the weighted average of the asset standard deviations. With a correlation of +1, portfolio variance becomes the square of the weighted sum of the standard deviations, so there is no diversification benefit. Lower correlations would push risk below the weighted average.
- Alower than the weighted average
- Bequal to the weighted averageCorrect
- Chigher than the weighted average
Explanation
With a correlation of +1, the portfolio variance is (w1σ1 + w2σ2)², so the portfolio standard deviation equals the weighted average of the standard deviations. No diversification benefit arises.
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