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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 has N assets, each with variance 0.04 and every pairwise covariance equal to 0.01. What is the limit of portfolio variance as N becomes very large?

Portfolio variance approaches 0.01, the average pairwise covariance. As N grows, the asset-specific variance term shrinks toward zero, but the covariance term remains. Diversification therefore removes idiosyncratic risk but not the common risk reflected in covariances.

  1. A0.00
  2. B0.01Correct
  3. C0.025
  4. D0.04

Explanation

Variance = (1/N)(0.04) + ((N-1)/N)(0.01). As N grows the first term goes to zero and the second goes to 0.01, the average covariance. This is the non-diversifiable part. Answer 0.00 wrongly assumes all risk diversifies away.

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