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

An equally weighted portfolio holds N assets, each with variance 0.04 and every pairwise covariance equal to 0.01. As N increases without limit, the portfolio variance most likely approaches:

Portfolio variance approaches 0.01, the average pairwise covariance. Individual variance terms shrink toward zero as N grows, but the covariance term remains, representing systematic risk that cannot be diversified away by adding more assets.

  1. A0.00
  2. B0.01Correct
  3. C0.04

Explanation

Variance = (1/N)(0.04) + ((N-1)/N)(0.01). As N grows, the first term goes to zero and the second approaches 0.01, the average covariance. Option 0.00 wrongly assumes all risk diversifies away; 0.04 ignores diversification.

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