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.

Sau khi hoàn thành bạn sẽ…

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.

0 trong số 6 labs đã khám phá

ĐÃ LƯU TRÊN THIẾT BỊ NÀY

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Hành trình

Điểm dừng 1, 25 phút, Risk & Return

● Bạn đang ở đây

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.

Mở lab →

Ví dụ thực tế

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

Điểm dừng 2, 30 phút, Risk & Return

Correlation Matrix

Visualize how assets co-move; quantify diversification benefit.

Estimate the covariance matrix, and shrink it toward identity.

Mở lab →

Ví dụ thực tế

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

Điểm dừng 3, 20 phút, 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.

Mở lab →

Ví dụ thực tế

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)

Điểm dừng 4, 45 phút, Portfolio Construction

Efficient Frontier

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

Markowitz quadratic programming with constraints + tangency portfolio.

Mở lab →

Ví dụ thực tế

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

Điểm dừng 5, 30 phút, 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.

Mở lab →

Ví dụ thực tế

Asset βs vs market: full universe scatter.

Điểm dừng 6, 30 phút, 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.

Mở lab →

Ví dụ thực tế

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%

Áp dụng những gì bạn đã học

Tình huống thực tế

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.

Thử Efficient Frontier →Thử Correlation Matrix →Thử Risk Decomposition →

Tình huống thực tế

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.

Thử Efficient Frontier →Thử Correlation Matrix →Thử Risk & Return Statistics →