Explain how mean–variance optimisation is used to set an asset allocation and assess its strengths and weaknesses
The idea
Mean–variance optimisation uses expected returns, volatilities and correlations to trace the efficient frontier, then selects the portfolio that maximises utility, often written Um = E(Rm) − 0.005 × λ × σm² with returns in percent and λ the risk aversion coefficient. Its strength is a transparent, quantitative link between inputs and weights. Its weaknesses are serious: outputs are highly sensitive to expected return inputs, so the optimiser concentrates in a few asset classes and magnifies estimation error; it ignores liabilities and consumption; it is single-period; it treats risk as variance and ignores skewness and fat tails; and it ignores factor overlaps. Remedies include reverse optimisation, Black–Litterman views, resampling, and sensible constraints. The trap is accepting corner solutions uncritically.
Formulas
Risk-adjusted utility of an asset mix
U = E(R) − 0.005 × λ × σ²
- E(R)
- the mix's expected return, in whole percent
- λ
- the investor's risk aversion; higher means more averse
- σ
- the mix's standard deviation, in whole percent
Returns and volatility go in as whole percentages, which is why the factor is 0.005 rather than ½. Choose the efficient mix with the highest U: the more risk-averse the investor, the lower the volatility of the mix it picks.
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