Konstruksi Portofolio Kuantitatif

Dari Statistik ke Markowitz hingga Investasi Faktor

Versi matematika-berat dari Manajemen Investasi 101. Perangkat yang sama, tetapi Anda membangun optimizer, mengukur taruhan faktor, dan menguji ketahanan kerangka Markowitz terhadap friksi dunia nyata (galat estimasi, perubahan rezim, biaya transaksi).

Quants, systematic-fund analysts, applied-stats grad students.

Di akhir kamu akan…

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 dari 6 labs dijelajahi

TERSIMPAN DI PERANGKAT INI

Mulai jalur →

Perjalanan

Stop 1, 25 menit, Risk & Return

● Kamu ada di sini

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.

Buka lab →

Contoh penerapan

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

Stop 2, 30 menit, Risk & Return

Correlation Matrix

Visualize how assets co-move; quantify diversification benefit.

Estimate the covariance matrix, and shrink it toward identity.

Buka lab →

Contoh penerapan

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

Stop 3, 20 menit, 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.

Buka lab →

Contoh penerapan

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)

Stop 4, 45 menit, Portfolio Construction

Efficient Frontier

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

Markowitz quadratic programming with constraints + tangency portfolio.

Buka lab →

Contoh penerapan

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

Stop 5, 30 menit, 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.

Buka lab →

Contoh penerapan

Asset βs vs market: full universe scatter.

Stop 6, 30 menit, 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.

Buka lab →

Contoh penerapan

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%

Terapkan apa yang kamu pelajari

Studi Kasus

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.

Coba Efficient Frontier →Coba Correlation Matrix →Coba Risk Decomposition →

Studi Kasus

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.

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