Advanced Portfolio Construction and Analysis

Portfolio Management Fundamentals introduced portfolio construction and basic historical estimates. How reliable are those estimates, and how do they affect allocations? This course examines factor exposures, risk and return estimates, and portfolio risk budgets.

Before You Begin

You should be able to calculate portfolio returns and volatility, distinguish total from excess returns, and work with long-only, fully invested constraints. Review Fundamentals of Portfolio Optimization if these ideas are unfamiliar.

The examples use pandas, covariance matrices, matrix multiplication, and basic regression. You should be able to explain an optimizer's objective and constraints without implementing the solver yourself.

The Learning Sequence

The recommended route reaches this course after Derivatives, Options, and Structured Products. That track is useful context, rather than a mathematical prerequisite for the allocation examples below. Keep these connections explicit:

• Expected returns: Black–Litterman views describe investment beliefs on the stated return basis. They do not replace the financing rate in Deriving and Using Black–Scholes.
• Replication: fitting historical returns with factors or style portfolios leaves residual risk. It does not establish the state-by-state payoff identity used to price a derivative.
• Risk inputs: covariance estimates describe specified return observations. A single GBM diffusion volatility is a different model input; nonlinear option risk can require full repricing rather than a fixed linear exposure.
• Self-financing: rebalances and fees are paid from the portfolio. The same budget discipline governs an option hedge, although that hedge can require borrowing and continuously changing quantities rather than long-only capital weights.

Work through four core chapters, then complete the capstone.

1. Style and Factor Exposures: interpret regression coefficients, alpha, style replication, and the effect of weighting rules.
2. Covariance Matrix Estimation for Portfolio Construction: compare sample, structured, and shrinkage estimates, then examine time-varying risk.
3. Black–Litterman: Reference Portfolios, Views, and Uncertainty: study mean uncertainty and shrinkage targets, then combine reference-implied returns with explicit views.
4. Robust Portfolio Construction: Diversification and Risk Budgets: distinguish capital from risk concentration and account for estimation sensitivity, turnover, and costs.
5. Comparing Portfolio Decisions: A Capstone: compare five allocation rules on one three-industry universe, including input sensitivity and rebalancing costs.

What You Should Be Able to Do

• Interpret factor exposures and explain the assumptions behind a covariance estimate.
• Compare sample-mean, equal-return, equal-Sharpe, factor-based, and reference-implied expected returns.
• Express views consistently and distinguish mean uncertainty from return risk.
• Calculate risk contributions and compare them with capital weights.
• Evaluate allocations using common dates, constraints, rebalancing rules, and costs.

Working Through the Examples

Read each worked calculation before running the code. Start each chapter with its setup cells and run dependent examples in order. Check return units and annualization before combining inputs.

Change one assumption at a time. Before moving a slider, predict what should change; then use the calculation to explain what happened.

Begin the Course

Start with Style and Factor Exposures.

After the capstone, continue with Fundamentals of Machine Learning: calculate predictions and errors, fit a line, and compare models on later observations. Machine Learning for Asset Management introduces the remaining four planned chapters.