Distributionally robust mean-absolute deviation portfolio optimization using wasserstein metric

Area of Science:

• Quantitative Finance
• Optimization Theory
• Financial Modeling

Background:

• Data uncertainty significantly impacts portfolio selection accuracy.
• The classic mean-absolute deviation (MAD) model is widely used but sensitive to data variations.
• Robust decision-making is crucial for reliable investment strategies.

Purpose of the Study:

• To propose a novel distributionally robust mean-absolute deviation (DR-MAD) model using Wasserstein metrics.
• To address the non-convexity and infinite-dimensional challenges of robust optimization.
• To enhance portfolio selection under data uncertainty.

Main Methods:

• Developed a Wasserstein metric-based data-driven DR-MAD model.
• Transformed the non-convex problem into two finite-dimensional linear programs.
• Compared DR-MAD with 1/N, classic MAD, and mean-variance models using S&P 500 stocks.

Main Results:

• The DR-MAD model was successfully transformed into solvable linear programs.
• Portfolios from DR-MAD demonstrated superior profitability and stability versus benchmarks.
• Performance was evaluated across six different market settings.

Conclusions:

• The Wasserstein distributionally robust optimization framework effectively tackles data uncertainty in portfolio optimization.
• DR-MAD offers a computationally efficient and robust alternative to existing models.
• This approach provides enhanced performance in fluctuating market conditions.