Factor-Based Long-Short Portfolio Allocation under Beta Constraints

Fama-French Three-Factor Model · Portfolio Optimization · Long-Short Strategy · Risk Management · Python

FE-630 Final Project — MS Financial Engineering, Stevens Institute of Technology

Author: Swara Dave

Advisor: Prof. Papa Momar Ndiaye

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📌 Overview

This project constructs and compares two factor-based long-short portfolio allocation strategies under explicit beta constraints using the Fama-French three-factor model. Portfolios are rebalanced weekly over March 2007 – October 2025 across a 12-ETF global universe covering equities, commodities, currencies, and fixed income.

Two strategies compared:

1. Strategy I — Robust Utility Optimization: Low-beta, volatility-penalizing allocation targeting market de-correlation
2. Strategy II — Information Ratio Optimization: Benchmark-relative active strategy maximizing risk-adjusted excess returns over SPY

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📊 Key Results

Full-Sample Performance (S=90 days, λ=0.5)

Metric	Strategy I	Strategy II	SPY
Cumulative Return	17.96%	828.80%	535.62%
Annualized Volatility	17.51%	18.98%	19.91%
Sharpe Ratio	0.06	0.66	0.54
Max 10-Day Drawdown	-31.50%	-20.73%	-24.95%
CVaR (daily, 5%)	2.49%	2.94%	3.08%

Strategy II outperforms SPY on cumulative return (828.80% vs 535.62%) and Sharpe ratio (0.66 vs 0.54) while maintaining lower volatility (18.98% vs 19.91%).

Regime-Based Performance (S=90 days, λ=0.5)

Period	Strategy I Sharpe	Strategy II Sharpe	SPY Sharpe
Pre-Crisis	-1.31	-0.90	0.49
GFC 2008	0.30	-0.57	-0.84
Post-Crisis	0.26	1.04	1.03
COVID-19	-0.81	0.86	0.85
Post-COVID	-0.08	0.64	0.57

Strategy I excels during crisis periods (GFC Sharpe: 0.30 vs SPY's -0.84). Strategy II dominates during recovery and expansion phases.

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🗂️ Investment Universe

12 global ETFs covering major asset classes (Mar 2007 – Oct 2025):

ETF	Description
SPY	SPDR S&P 500 ETF (benchmark)
QQQ	Invesco NASDAQ-100 ETF
GLD	SPDR Gold Trust
USO	United States Oil Fund
DBA	Invesco DB Agriculture Fund
SHV	iShares Short Treasury Bond ETF
EWJ	iShares MSCI Japan ETF
FXE	CurrencyShares Euro Trust
XBI	SPDR S&P Biotech ETF
ILF	iShares Latin America 40 ETF
EPP	iShares MSCI Pacific ex-Japan ETF
FEZ	SPDR EURO STOXX 50 ETF

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⚙️ Methodology

Factor Model

• Fama-French 3-Factor Model: Market (MKT), Size (SMB), Value (HML)
• Factor loadings estimated via rolling time-series regressions
• Factor-based covariance: Σ = B·Ωf·Bᵀ + D (avoids noisy sample covariance)

Strategy I — Robust Utility Optimization

maximize: ρᵀω − λ·√(ωᵀΣω)
subject to: Σωi = 1, −2 ≤ ωi ≤ 2, −0.5 ≤ β_portfolio ≤ 0.5

Solved using CVXPY (convex optimization)

Strategy II — Information Ratio Optimization

maximize: (ρᵀω − rSPY) / TEV(ω) − λ·√(ωᵀΣω)
subject to: Σωi = 1, −2 ≤ ωi ≤ 2, −2 ≤ β_portfolio ≤ 2

Solved using SLSQP (SciPy nonlinear optimizer)

Sensitivity Analysis

• Risk aversion: λ ∈ {0.1, 0.5, 1.0}
• Estimation horizons: Short (40d), Medium (90d), Long (180d) for both returns and covariance
• Market regimes: Pre-Crisis, GFC, Post-Crisis, COVID-19, Post-COVID

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📁 Repository Structure

FactorPortfolio/
├── factor_portfolio_optimization.py    # Full implementation — factor model, optimization, backtesting
└── Plots/
    ├── CumulativePnL.jpeg              # Growth of $100: Strategy I vs II vs SPY
    ├── PerformanceSummary.jpeg         # Full performance summary table
    ├── PerformanceComparison.jpeg      # Side-by-side performance metrics
    ├── StrategyI.jpeg                  # Strategy I return distribution
    ├── StrategyII.jpeg                 # Strategy II return distribution
    ├── TermStructureSensitivity.jpeg   # Sensitivity to estimation horizons
    └── SensitivityAcrossLambda.jpeg    # Sensitivity to risk-aversion parameter

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🚀 How to Run

1. Clone the repo
2. Install dependencies:

pip install numpy pandas matplotlib scipy cvxpy statsmodels yfinance

3. Run the script:

python factor_portfolio_optimization.py

Note: Stock data is fetched automatically via yfinance. Fama-French factor data is downloaded from Ken French's Data Library. No manual data download required.

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👤 Author

Swara Dave — MS Financial Engineering, Stevens Institute of Technology