Portfolio construction, diversification and asset allocation
Portfolio construction turns return forecasts, risk estimates and constraints into weights. The exam tests whether you can compute the diversification benefit, explain the limits of optimisation, and design a strategic asset allocation that respects liabilities and regulation.
Mean-variance framework
Expected portfolio return is the weighted average; portfolio variance is wᵀΣw, so it depends on covariances, not just individual volatilities. The efficient frontier traces portfolios with the highest return for each risk level; adding a risk-free asset produces the capital market line and the tangency portfolio, which maximises the Sharpe ratio.
From theory to policy
The strategic asset allocation (SAA) is set from ALM and the investor's risk appetite, then implemented with a tracking-error budget; tactical asset allocation takes deliberate deviations within that budget. Constraints matter: liability hedging, Solvency II capital charges, tax, liquidity, concentration limits, governance budget and transaction costs.
Limitations
Mean-variance optimisation is an 'error maximiser': small changes in expected returns produce extreme weights. Correlations rise in crises exactly when diversification is needed. Returns are fat-tailed, so standard deviation understates tail risk. Practical responses: constraints, resampling, Black-Litterman, risk parity or equal-weight starting points.
Worked example: the diversification benefit
Two assets: expected returns 6% and 3%, volatilities 15% and 5%, correlation 0.2. At 60/40 the expected return is 0.6×6 + 0.4×3 = 4.8%. Variance = 0.6²×0.15² + 0.4²×0.05² + 2×0.6×0.4×0.15×0.05×0.2 = 0.0081 + 0.0004 + 0.00072 = 0.00922, so σ = 9.6%. The naive weighted-average volatility would be 0.6×15 + 0.4×5 = 11.0%; diversification saves 1.4 percentage points. The lower the correlation, the larger the saving, and at correlation 1.0 there is none.
Traps
Optimising on historical returns without adjusting for estimation error. Confusing arithmetic with geometric returns when setting assumptions. Setting an SAA with no reference to liabilities, then wondering why funding volatility is high.