Portfolio Management Fundamentals

How do we measure investment outcomes, choose portfolio weights, and invest against future obligations? This course develops these decisions through calculations and Python examples.

Before You Begin

You should be comfortable with percentages, compound growth, averages, and basic Python. The examples use NumPy arrays and pandas tables with asset labels and date indexes.

The Learning Sequence

Work through the four chapters in order.

1. Understanding Returns and Assessing Risks with Value at Risk: distinguish compounded growth from average returns, measure volatility and drawdowns, and interpret Value at Risk and expected shortfall.
2. Fundamentals of Portfolio Optimization: combine expected returns and covariance, construct efficient portfolios, and examine how constraints and cash financing change the allocation.
3. Strategies Beyond Diversification: examine changing correlations, CPPI allocation rules, drawdown controls, and geometric Brownian motion simulations.
4. Fundamentals of Asset-Liability Management: calculate funding ratios, value bonds and liabilities, measure duration, and compare liability-driven investment strategies.

What You Should Be Able to Do

• Calculate compounded returns, volatility, drawdown, VaR, and expected shortfall.
• Construct a constrained portfolio and explain how covariance affects its risk.
• Explain how CPPI responds to changing wealth and where its protection can fail.
• Value a liability and assess a duration-matching strategy.

Working Through the Examples

Read the worked calculation, run the code, then change one assumption and explain the result. Keep units and return horizons consistent; distinguish historical observations from simulated outcomes.

Examples run in your browser. Within a lesson, run dependent cells in order: they share Python variables, and later examples often reuse earlier data and estimates. Reloading the page clears that Python session, although saved code edits remain. Use reset editor to return an edited cell to the lesson's current example.

Begin the Course

Start with Understanding Returns and Assessing Risks.

After these four chapters, continue with Derivatives, Options, and Structured Products, then Advanced Portfolio Construction and Analysis. The derivatives track applies financing and replication to contractual payments; the advanced portfolio course examines estimation uncertainty and its effect on allocations. Readers focused on allocation can also enter the advanced course directly after these foundations.

Carry the Conventions Forward

• Rates: effective 5% annual cash growth is the same as a continuous rate of $\log (1.05)\approx 4.8790\mathrm{\%}$. The number changes when the quotation convention changes, not the cash flow.
• Returns: portfolio arithmetic means, realized CAGR, and instantaneous GBM drift answer different questions. Deriving and Using Black–Scholes calculates their relationship on one common example.
• Risk and probability: historical VaR, simulated CPPI failure, and pricing-distribution exercise probability are not interchangeable. State the distribution and horizon. The CIR pricing examples explicitly use a pricing measure; their scenario frequencies are not forecasts of real-world failure.
• Budgets: portfolio weights describe invested capital. A derivative hedge may instead require asset quantities, borrowing, or zero-initial-value contracts. Always reconcile the cash account before calculating performance.