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FRM Part I · FRM Exam Part I · Modern Portfolio Theory (MPT) and the Capital Asset Pricing Model (CAPM)

An equally weighted portfolio holds N assets, each with variance 0.04 and every pairwise covariance equal to 0.01. What is the limit of the portfolio variance as N approaches infinity, and what does it represent?

The variance approaches 0.01, the average covariance. As N grows, the own-variance contribution shrinks as 0.04 divided by N, while the covariance term approaches 0.01. This residual is the market-wide component that diversification cannot remove.

  1. A0, because all risk is diversified away
  2. B0.04, because individual risk remains
  3. C0.01, the average covariance, representing non-diversifiable riskCorrect
  4. D0.005, half the average covariance

Explanation

Portfolio variance = (1/N)×0.04 + ((N−1)/N)×0.01. As N grows, the first term goes to 0 and the second goes to 0.01. This remaining part is the average covariance, which is the systematic, non-diversifiable component. Zero would apply only if covariances were zero.

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