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CFA Level I · CFA Level I Exam · Portfolio Risk and Return: Part I

Two risky assets have a correlation of +1.0 between their returns. A portfolio is formed by combining them in positive weights. The standard deviation of the portfolio is most likely:

The portfolio standard deviation equals the weighted average of the two standard deviations. When correlation is +1.0, variance collapses to the square of the weighted sum of the standard deviations, so combining the assets gives no diversification benefit in risk reduction.

  1. Alower than the weighted average of the two standard deviations
  2. Bequal to the weighted average of the two standard deviationsCorrect
  3. Chigher than the weighted average of the two standard deviations

Explanation

With correlation of +1, portfolio variance equals (w1σ1 + w2σ2)^2, so portfolio standard deviation is the weighted average of the individual standard deviations. No diversification benefit arises. It cannot be lower (that needs correlation below 1) or higher (that is impossible for long positions).

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