Mean-Variance Optimization

Portfolio Ch. 12 — Markowitz & CML

Asset Expected Returns (%)

Equities

Fixed Income

Real Estate

Commodities

Asset Volatilities (%)

Equities

Fixed Income

Real Estate

Commodities

Correlation Matrix

Constraints

Risk-Free Rate (%)

Max Weight (%)

Min Weight (%)

Frontier Points

Tangency Portfolio

Expected Return—

Volatility—

Sharpe Ratio—

Optimal Weights

Risk Contribution

min w'Σw s.t. w'μ = μ_target, w'1 = 1
SR = (μ_p − r_f) / σ_p

Ch. 12 — Markowitz Mean-Variance Ch. 12 — Capital Market Line Ch. 12 — Euler Risk Decomposition