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IAI Actuarial Core Principles · Economic Modelling · Mean-variance portfolio theory

An equally weighted portfolio holds n assets, each with variance 0.04 and every pairwise covariance equal to 0.01. As n becomes very large, the portfolio variance tends to:

The portfolio variance tends to 0.01. Individual variance contributions fall as 1/n and vanish, while the average covariance term approaches its full value of 0.01. Diversification removes specific risk but cannot remove the risk arising from common covariance between the assets.

  1. A0
  2. B0.04
  3. C0.0025
  4. D0.01Correct
  5. 0.05

Explanation

Variance = (1/n)*0.04 + ((n-1)/n)*0.01. As n tends to infinity the first term vanishes and the second tends to 0.01, the average covariance. This is the undiversifiable (systematic) component.

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