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

In mean-variance portfolio theory, a risk-free asset is added to a set of risky assets. Which statement about the risk-free asset is correct?

The risk-free asset has zero variance and zero covariance with every risky asset, because its return is certain and never deviates from its mean. This is why mixing it with a risky portfolio changes risk in direct proportion to the weight held in the risky portfolio.

  1. AIts variance is positive but small, and it is positively correlated with all risky assets
  2. BIts return has zero variance and zero covariance with every risky assetCorrect
  3. CIts return has zero variance but a covariance of one with the market portfolio
  4. DIts standard deviation equals that of the market portfolio
  5. Its expected return must always exceed that of the market portfolio

Explanation

A risk-free asset has a certain return, so its variance is zero. Covariance with any asset is then zero because it never deviates from its mean. A covariance of one is impossible when one variable is constant, and its expected return is normally below that of the market portfolio.

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