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

In mean-variance portfolio theory, which assumption about investor preferences is sufficient to justify ranking portfolios using only expected return and variance, even if returns are not normal?

Quadratic utility of terminal wealth. Its expected value depends only on the mean and variance of wealth, whatever the return distribution. Other utility forms need extra distributional assumptions such as normality, and risk-neutral investors ignore variance entirely.

  1. AQuadratic utility of terminal wealthCorrect
  2. BLogarithmic utility of terminal wealth
  3. CExponential utility of terminal wealth
  4. DRisk-neutral preferences
  5. Unbounded utility with increasing absolute risk aversion only

Explanation

With quadratic utility, E[U(W)] = E[W] - b(E[W]^2 + Var(W)), depending only on the mean and variance of wealth whatever the distribution. Log and exponential utility need normality or lognormality to reduce to mean-variance. Risk-neutral investors care only about the mean.

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