Worked Examples
Portfolio theory is easier to argue about than to apply. These walk a single decision all the way through with real numbers — the inputs, the method, the output, and what the output does not tell you.
Adding Bitcoin to a 60/40 Portfolio
What 5%, 10%, and 15% Bitcoin actually does to a traditional 60/40 — expected return, volatility, Sharpe ratio, and the drawdown you would have had to sit through. Worked through with 2026 forward-looking assumptions.
Max Sharpe vs Risk Parity vs HRP
Three optimization methods, one set of inputs, three noticeably different portfolios. Why Max Sharpe concentrates, why Risk Parity spreads, and what Hierarchical Risk Parity does differently from both.