Portfolio Management and Risk
What the domain tests
Portfolio management and risk tests diversification, CAPM, portfolio risk decomposition, and risk-adjusted performance measures.
Core rules
- Portfolio expected return is the weighted average of asset returns.
- Portfolio variance for two assets: w1²σ1² + w2²σ2² + 2w1w2ρσ1σ2. Beta is a weighted average, but variance is not.
- CAPM: E(Ri) = Rf + βi[E(Rm) − Rf]. Beta measures systematic risk; unsystematic risk is diversifiable.
- Sharpe = (Rp − Rf)/σp; Treynor = (Rp − Rf)/βp. Sharpe uses total risk; Treynor uses systematic risk.
- VaR at confidence c is the loss threshold exceeded with probability 1 − c.
Worked example
A portfolio holds 60% asset A with E(R) = 10% and σ = 15%, and 40% asset B with E(R) = 6% and σ = 10%; ρ = 0.2. Portfolio return = 0.6 × 10 + 0.4 × 6 = 8.4%. Variance = 0.36 × 225 + 0.16 × 100 + 2 × 0.6 × 0.4 × 0.2 × 15 × 10 = 81 + 16 + 14.4 = 111.4; σ = 10.55%. With Rf = 3%, Sharpe = (8.4 − 3)/10.55 = 0.51. Lower correlation would reduce portfolio variance without changing expected return.
Traps
Averaging standard deviations; using beta instead of sigma for Sharpe; confusing VaR confidence with loss probability; ignoring correlation; using arithmetic returns for long-horizon compounding.