Portfolio Construction and Risk Management
Construction
Mean-variance optimisation uses expected returns, a covariance matrix and constraints to trace the efficient frontier; the tangency portfolio maximises the Sharpe ratio. Know factor models (CAPM, multi-factor, commercial risk models), covariance shrinkage and robust estimation, Black-Litterman for blending views with equilibrium, and resampling. Risk budgeting and risk parity allocate by risk contribution rather than by capital.
Risk measurement
Volatility, beta, tracking error, VaR, expected shortfall, drawdown, stress testing and scenario analysis. VaR is not subadditive and says nothing about the magnitude of losses beyond the threshold; expected shortfall is coherent. Know parametric, historical and Monte Carlo VaR, and the conditions under which scaling by sqrt(t) is valid.
Traps
- Optimisers are error maximisers: small changes in expected returns produce extreme weights.
- VaR at 95% is not a worst case, and portfolio VaR can exceed the sum of component VaRs.
- Scaling one-day VaR by sqrt(t) ignores autocorrelation and volatility clustering.
- Correlations assumed by the covariance matrix break down in stress.
- Confusing tracking error (active risk) with total volatility.
Worked example
Weights 60/40, volatilities 15% and 5%, correlation 0.2. Variance = 0.36(0.0225) + 0.16(0.0025) + 2(0.6)(0.4)(0.15)(0.05)(0.2) = 0.0081 + 0.0004 + 0.00072 = 0.00922, so volatility is about 9.6%, below the weighted-average 11%.