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

As the number of equally weighted, imperfectly correlated securities in a portfolio increases, the portfolio's standard deviation most likely:

Portfolio standard deviation declines toward a floor set by the average covariance among the securities. Diversification removes firm-specific risk, but the covariance terms, which reflect systematic risk, dominate as the number of holdings grows, so risk does not reach zero.

  1. Adeclines toward a level determined by the average covariance among the securitiesCorrect
  2. Bdeclines toward zero as firm-specific and market risk are both eliminated
  3. Crises because the number of covariance terms grows faster than the variance terms

Explanation

Portfolio variance has variance terms that shrink with n and covariance terms that approach the average covariance. Risk therefore falls toward a floor set by average covariance, which reflects systematic risk. It does not reach zero unless securities are uncorrelated with each other and the market is irrelevant.

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