Paper: arXiv 2406.01199

Abstract

In this article, a geometric approach to incorporating investor views in portfolio construction is presented. In particular, the proposed approach utilizes the notion of generalized Wasserstein barycenter (GWB) to combine the statistical information about asset returns with investor views to obtain an updated estimate of the asset drifts and covariance, which are then fed into a mean-variance optimizer as inputs. Quantitative comparisons of the proposed geometric approach with the conventional Black-Litterman model (and a closely related variant) are presented. The proposed geometric approach provides investors with more flexibility in specifying their confidence in their views than conventional Black-Litterman model-based approaches. The geometric approach also rewards the investors more for making correct decisions than conventional BL based approaches. We provide empirical and theoretical justifications for our claim.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper introduces complex optimal transport theory (Wasserstein barycenters, McCann interpolants) with significant mathematical derivation, while the empirical section describes a backtesting methodology without presenting code or heavy implementation details.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Develop a geometric approach<br>to incorporate investor views<br>with more flexibility than BL model"] --> B["Data & Inputs"]
  
  subgraph B ["Data & Inputs"]
      B1["Asset Return Data"]
      B2["Statistical Estimates<br>Drifts & Covariance"]
      B3["Investor Views<br>Return Expectations"]
      B4["Confidence Level<br>Flexible/Parameterized"]
  end
  
  B --> C["Core Methodology<br>Generalized Wasserstein Barycenter"]
  
  C --> D["Computational Process<br>Combine Statistical Info + Views"]
  D --> E["Output: Updated<br>Drift & Covariance"]
  E --> F["Mean-Variance<br>Optimizer"]
  
  F --> G["Key Findings/Outcomes"]
  
  subgraph G ["Key Findings/Outcomes"]
      G1["Geometric Approach<br>provides more flexibility<br>in specifying confidence"]
      G2["Rewards investors more<br>for correct decisions<br>vs. BL model"]
      G3["Validated by<br>Empirical & Theoretical<br>justifications"]
  end

Cited References (22)

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  8. CVXPY: A Python-Embedded Modeling Language for Convex Optimization. (2016)
and 14 more
  1. Convex Optimization (2004) — link
  2. On the Bayesian interpretation of Black–Litterman (2016) — link
  3. Incorporating Trading Strategies in the Black-Litterman Framework (2006) — link
  4. The Black-Litterman Approach: Original Model and Extensions (2008) — link
  5. A rewriting system for convex optimization problems (2018) — link
  6. On the Bures–Wasserstein distance between positive definite matrices (2018) — link
  7. CVXPY: A Python-Embedded Modeling Language for Convex Optimization (2016) — link
  8. Bayesian methods in finance (2008)
  9. Advances in Financial Machine Learning (2018)
  10. Incorporating Trading Strategies in the Black-Litterman Framework (2006) — link
  11. Generalized Wasserstein barycenters between probability measures living on different subspaces (2023) — link
  12. Measure Theory (2007) — link
  13. Black-Litterman End-to-End (2023) — link
  14. Underperformance of Concentrated Stock Positions (2023) — link

0 of 22 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.