New approximate stochastic dominance approaches for Enhanced Indexation models

Paper: arXiv 2401.12669

Abstract

In this paper, we discuss portfolio selection strategies for Enhanced Indexation (EI), which are based on stochastic dominance relations. The goal is to select portfolios that stochastically dominate a given benchmark but that, at the same time, must generate some excess return with respect to a benchmark index. To achieve this goal, we propose a new methodology that selects portfolios using the ordered weighted average (OWA) operator, which generalizes previous approaches based on minimax selection rules and still leads to solving linear programming models. We also introduce a new type of approximate stochastic dominance rule and show that it implies the almost Second-order Stochastic Dominance (SSD) criterion proposed by Lizyayev and Ruszczynski (2012). We prove that our EI model based on OWA selects portfolios that dominate a given benchmark through this new form of stochastic dominance criterion. We test the performance of the obtained portfolios in an extensive empirical analysis based on real-world datasets. The computational results show that our proposed approach outperforms several SSD-based strategies widely used in the literature, as well as the global minimum variance portfolio.

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 6.0/10 (capped from 8.5: transaction costs not modelled; see penalty flags)
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents advanced mathematical constructs like new approximate stochastic dominance rules (CSESD) and OWA operator generalizations with proofs, indicating high mathematical density. It is empirically rigorous with extensive backtesting on multiple real-world datasets (FTSE100, NASDAQ100, S&P500, Fama-French) and comparisons to established benchmarks, demonstrating strong data/implementation focus.

Research Flowchart

  flowchart TD
  A["Research Goal:<br>Select EI portfolios dominating<br>benchmark with excess return"] --> B["Methodology: Introduce<br>Approx. Stoch. Dominance &<br>OWA Operator"]
  B --> C["Linear Programming Model<br>Solution Process"]
  D["Data Inputs:<br>Real-world return datasets<br>Benchmark index"] --> B
  B --> C
  C --> E{"Empirical Testing"}
  E --> F["Key Outcomes:<br>Outperforms SSD-based<br>strategies & GMV portfolio"]
  
  style F fill:#d4edda,stroke:#155724
  style A fill:#cce5ff,stroke:#004085

Cited References (259)

1. Diversified minimum-variance portfolios (2015)
2. Norm constrained minimum variance portfolios with short selling (2023)
3. Comparing SSD-efficient portfolios with a skewed reference distribution (2022)
4. Robust performances hypothesis testing with the variance (2011)
5. How to use security analysis to improve portfolio selection (1973)
6. Maximum entropy aggregation of expert predictions (1996)
7. Between first-and second-order stochastic dominance (2017)
8. Fractional degree stochastic dominance (2020)

0 of 259 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.