Portfolio Optimization

From Markowitz to robust, cost-aware, validated construction.

Portfolio optimization turns forecasts about returns and risk into actual weights. This track moves from Markowitz mean-variance and the efficient frontier through CAPM and factor models, Black–Litterman views, risk parity and robust optimization, then down to earth: transaction costs, implementation, and out-of-sample validation that separates durable edges from backtest artifacts.

Mean-Variance

Markowitz Mean-Variance

A quadratic program over expected returns and covariances whose outputs inherit every flaw of its inputs.

The Efficient Frontier

The best risk-return trade-offs trace a hyperbola that a risk-free asset upgrades into a straight line.

Beyond Mean-Variance

CAPM & Factor Models

One beta prices risk in theory, multi-factor models in practice.

Black–Litterman

A Bayesian blend of market equilibrium with investor views that tames unstable mean-variance inputs.

Risk Parity

Allocate risk, not dollars: equalize each asset’s contribution to volatility, then lever to taste.

Robust & Constrained Optimization

Uncertainty sets and shrinkage make optimizers honest about estimation noise.

Doing It For Real

Transaction Costs & Implementation

Market impact and turnover mean the traded portfolio must be optimized, not just the theoretical one.

Out-of-Sample Validation

Walk-forward tests and deflated Sharpe ratios separate durable edges from tuned backtests.