Heavy-math version of Investment Management 101. Same tools, but you're building optimizers, sizing factor bets, and stress-testing the Markowitz framework against real-world frictions (estimation error, regime change, transaction costs).
Quants, systematic-fund analysts, applied-stats grad students.
By the end you will…
Build a covariance matrix and run Markowitz with shrinkage estimators.
Construct multi-asset efficient frontiers under realistic constraints.
Apply CAPM and SML diagnostics to rank a 30-stock universe.
Stress-test risk decomposition under regime change.
Real-world scenarios that pull together the path. Each links back to the Labs you just used.
Case Study
When Markowitz breaks: estimation error eats Sharpe alive
Take a 25-asset universe. Run the optimizer with a sample-mean μ and sample-covariance Σ on the first 5 years; allocate per the tangency portfolio. Hold for next 5 years. Realized Sharpe usually disappoints by 30-50% versus in-sample. Why? Sample means have huge standard errors (μ_hat for stocks has σ ≈ 5-10% with 5y of data). Mitigations: (1) Black-Litterman with priors, (2) Ledoit-Wolf shrinkage on Σ, (3) max-weight constraints, (4) resampled efficiency. The Efficient Frontier Lab's constraint controls let you compare unconstrained vs constrained-and-shrunk versions side by side.
Building a low-correlation 12-asset portfolio: the multi-strat blueprint
Goal: maximize Sharpe with bounded leverage. Universe = SPY + QQQ + IWM + EFA + EEM + AGG + TLT + GLD + SLV + USO + BTC + ETH. Run the correlation matrix — most pairs in {0.4, 0.9}, but BTC-AGG ≈ 0.05, GLD-EEM ≈ 0.20. Tangency portfolio puts ~30% on BTC, ~15% gold, ~15% TLT, ~10% SPY, rest in EM and small bonds. Implementation note: BTC σ is 60%+, so your tangency weight will be tiny when you include realistic volatility constraints — but the diversification benefit is real. The Efficient Frontier Lab handles up to 15 assets simultaneously.