Labs/Paths/Quant Portfolio Construction
Curated learning path
Advanced
3 hr · 6 labs

Quant Portfolio Construction

From Statistics to Markowitz to Factor Investing

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.
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The journey

6 stops · 3 hr of focused work · Advanced

1
Stop 1 · 25 min · Risk & Return
Risk & Return Statistics
Compute E(r), σ², σ, Sharpe, skew, kurtosis from probabilistic or historical data.
Build the inputs: μ vector and σ vector for every asset in the universe.
Open lab →
Worked example
10y annualized μ and σ for a 5-asset universe.
Assetμ (ann.)σ (ann.)Sharpe
SPY12.5%16.2%0.53
QQQ16.8%21.5%0.60
IWM9.1%20.8%0.25
AGG2.4%5.8%0.07
GLD5.5%16.0%0.09
2
Stop 2 · 30 min · Risk & Return
Correlation Matrix
Visualize how assets co-move; quantify diversification benefit.
Estimate the covariance matrix — and shrink it toward identity.
Open lab →
Worked example
Sample 5×5 correlation matrix (10y daily).
SPYQQQIWMAGGGLD
SPY1.000.920.85−0.180.05
QQQ0.921.000.78−0.150.07
IWM0.850.781.00−0.200.04
AGG−0.18−0.15−0.201.000.18
GLD0.050.070.040.181.00
3
Stop 3 · 20 min · Portfolio Construction
Two-Asset Portfolio
Sliders for weights and correlation; see how σ shifts.
Sanity-check the optimizer: 2-asset case has a closed-form solution.
Open lab →
Worked example
Minimum-variance weights for SPY/AGG with ρ = −0.2
w*₁ = (σ²₂ − ρσ₁σ₂) / (σ²₁ + σ²₂ − 2ρσ₁σ₂)
= (0.01 − (−0.2)(0.20)(0.10)) / (0.04 + 0.01 + 0.008)
w*₁ = 0.21 (MVP weight on stock leg)
4
Stop 4 · 45 min · Portfolio Construction
Efficient Frontier
Multi-asset Markowitz mean-variance optimization with tangency portfolio.
Markowitz quadratic programming with constraints + tangency portfolio.
Open lab →
Worked example
5-asset efficient frontier with 100 random Monte Carlo points.
MTRfσ (vol) →↑ E(r)
5
Stop 5 · 30 min · Asset Pricing Models
CAPM Calculator
Live β regression, expected return via Capital Asset Pricing Model.
Run β regressions on the universe and validate vs realized α.
Open lab →
Worked example
Asset βs vs market — full universe scatter.
SPYQQQIWMβ →↑ E(r) %α > 0 (above SML)α < 0 (below SML)
6
Stop 6 · 30 min · Asset Pricing Models
Security Market Line
Plot the SML; find under and overpriced assets via Jensen's α.
Rank the universe by Jensen's α and look for cross-sectional bets.
Open lab →
Worked example
Top 5 alpha names from a 30-stock screen.
TickerβRealized rCAPM E(r)α
NVDA1.55+28.5%+13.3%+15.2%
META1.32+18.1%+11.9%+6.2%
AAPL1.20+13.8%+11.2%+2.6%
JPM1.05+11.5%+10.3%+1.2%
KO0.65+ 8.1%+ 7.9%+0.2%

Apply what you learned

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.

Case Study

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.

Free for any classroom or self-study use. Each Lab works standalone too — this path is one suggested ordering of the foundations.