Select and defend an asset allocation using the results of mean–variance optimisation
The idea
Screen efficient mixes against constraints, then rank the survivors. Utility is U = E(R) − 0.005 × λ × σ²; with λ = 4, a mix with 7% expected return and 12% volatility scores 7 − 0.005 × 4 × 144 = 4.12, while one with 9% and 18% scores 9 − 6.48 = 2.52, so the lower-risk mix is preferred. If the investor has a minimum return threshold, Roy's safety-first ratio (E(R) − RL) ÷ σ picks the mix with the lowest shortfall probability if returns are roughly normal: with RL = 2%, the ratios are (7 − 2) ÷ 12 = 0.42 and (9 − 2) ÷ 18 = 0.39, so the lower-risk mix wins again. A good justification also checks liquidity and concentration. The trap is picking the highest expected return that meets the target without testing the risk constraint.
Formulas
Roy's safety-first ratio
SFRatio = (E(R) − RL) ÷ σ
- E(R)
- the mix's expected return
- RL
- the minimum acceptable return
- σ
- the mix's standard deviation
Choose the mix with the highest ratio: with roughly normal returns it has the lowest chance of falling below RL. Use it when the client states risk as a return it must not fall below, rather than as volatility.
In the app: 2 practice questions on this outcome, a narrated walkthrough with diagrams, spaced review that brings it back before you forget it.
Take the free diagnostic →More in Principles of Asset Allocation
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- Explain what determines an appropriate rebalancing policy