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.

학습을 마치면…

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.

전체 6개 중 0개 Lab 탐색 완료

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학습 여정

1번째 스톱, 25분, Risk & Return

● 현재 위치

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.

랩 열기 →

풀이 예제

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

2번째 스톱, 30분, 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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풀이 예제

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

3번째 스톱, 20분, 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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풀이 예제

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)

4번째 스톱, 45분, Portfolio Construction

Efficient Frontier

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

Markowitz quadratic programming with constraints + tangency portfolio.

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풀이 예제

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

5번째 스톱, 30분, 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.

랩 열기 →

풀이 예제

Asset βs vs market: full universe scatter.

6번째 스톱, 30분, 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.

랩 열기 →

풀이 예제

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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사례 연구

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.

Efficient Frontier 체험하기 →Correlation Matrix 체험하기 →Risk Decomposition 체험하기 →

사례 연구

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.

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