CFA Level I · CFA Level I Exam · The Return and Risk of a Financial Portfolio
Two risky assets have a correlation of +1.0 with each other. A portfolio is formed by combining them in positive weights. 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 two standard deviations. When correlation is +1.0, the variance formula collapses to a perfect square, so risk is linear in the weights and there is no diversification benefit.
- Alower than the weighted average
- Bequal to the weighted averageCorrect
- Chigher than the weighted average
Explanation
With a correlation of +1, portfolio variance equals (w1*s1 + w2*s2)^2, so the standard deviation is exactly the weighted average. No diversification benefit arises. Lower values would require a correlation below +1.
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