Portfolio management and asset allocation
Portfolio management and asset allocation tests whether you can combine assets, measure risk-adjusted performance and map client constraints to a policy portfolio.
Core rules
- Portfolio expected return is the weighted average of asset returns; portfolio risk is not, because covariance matters.
- Two-asset variance = w1²σ1² + w2²σ2² + 2w1w2ρσ1σ2. Lower correlation reduces risk without reducing return.
- CAPM: E(R) = rf + β(E(Rm) − rf). Beta measures systematic risk only; unsystematic risk is diversifiable.
- Sharpe ratio uses total risk (σ); Treynor uses beta. Use Sharpe for a stand-alone portfolio and Treynor for a well-diversified sleeve.
Worked example
60% in an asset with σ = 20%, 40% in one with σ = 10%, correlation 0.2. Variance = 0.36 × 400 + 0.16 × 100 + 2 × 0.6 × 0.4 × 0.2 × 20 × 10 = 144 + 16 + 19.2 = 179.2, so σ = 13.4%. Reasoning: the weighted-average volatility is 16%, so diversification removes 2.6 percentage points. With ρ = 1 the portfolio σ would be exactly 16%.
Traps that cost marks
- Averaging volatilities instead of using the variance formula.
- Using standard deviation in Treynor or beta in Sharpe.
- Ignoring rebalancing, liquidity needs and taxes when setting the policy portfolio.
- Treating a high-risk-tolerance score as permission to ignore capacity for loss.