Quant Portfolio Construction

From Statistics to Markowitz to Factor Investing

The 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.

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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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الرحلة

المحطة 1، 25 دقيقة، Risk & Return

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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.

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مثال تطبيقي

10y annualized μ and σ for a 5-asset universe.

Asset	μ (ann.)	σ (ann.)	Sharpe
SPY	12.5%	16.2%	0.53
QQQ	16.8%	21.5%	0.60
IWM	9.1%	20.8%	0.25
AGG	2.4%	5.8%	0.07
GLD	5.5%	16.0%	0.09

المحطة 2، 30 دقيقة، Risk & Return

Correlation Matrix

Visualize how assets co-move; quantify diversification benefit.

Estimate the covariance matrix, and shrink it toward identity.

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مثال تطبيقي

Sample 5×5 correlation matrix (10y daily).

	SPY	QQQ	IWM	AGG	GLD
SPY	1.00	0.92	0.85	−0.18	0.05
QQQ	0.92	1.00	0.78	−0.15	0.07
IWM	0.85	0.78	1.00	−0.20	0.04
AGG	−0.18	−0.15	−0.20	1.00	0.18
GLD	0.05	0.07	0.04	0.18	1.00

المحطة 3، 20 دقيقة، 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.

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مثال تطبيقي

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)

المحطة 4، 45 دقيقة، Portfolio Construction

Efficient Frontier

Multi-asset Markowitz mean-variance optimization with tangency portfolio.

Markowitz quadratic programming with constraints + tangency portfolio.

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مثال تطبيقي

5-asset efficient frontier with 100 random Monte Carlo points.

المحطة 5، 30 دقيقة، 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.

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مثال تطبيقي

Asset βs vs market: full universe scatter.

المحطة 6، 30 دقيقة، 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.

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مثال تطبيقي

Top 5 alpha names from a 30-stock screen.

Ticker	β	Realized r	CAPM E(r)	α
NVDA	1.55	+28.5%	+13.3%	+15.2%
META	1.32	+18.1%	+11.9%	+6.2%
AAPL	1.20	+13.8%	+11.2%	+2.6%
JPM	1.05	+11.5%	+10.3%	+1.2%
KO	0.65	+ 8.1%	+ 7.9%	+0.2%

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دراسة حالة

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.

جرّب Efficient Frontier ←جرّب Correlation Matrix ←جرّب Risk Decomposition ←

دراسة حالة

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 sit between 0.4 and 0.9, but BTC-AGG ≈ 0.05 and 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.

جرّب Efficient Frontier ←جرّب Correlation Matrix ←جرّب Risk & Return Statistics ←