Subset second-order stochastic dominance for enhanced indexation with diversification enforced by sector constraints

Paper: arXiv 2404.16777

Abstract

In this paper we apply second-order stochastic dominance (SSD) to the problem of enhanced indexation with asset subset (sector) constraints. The problem we consider is how to construct a portfolio that is designed to outperform a given market index whilst having regard to the proportion of the portfolio invested in distinct market sectors. In our approach, subset SSD, the portfolio associated with each sector is treated in a SSD manner. In other words in subset SSD we actively try to find sector portfolios that SSD dominate their respective sector indices. However the proportion of the overall portfolio invested in each sector is not pre-specified, rather it is decided via optimisation. Our subset SSD approach involves the numeric solution of a multivariate second-order stochastic dominance problem. Computational results are given for our approach as applied to the S&P500 over the period 3rd October 2018 to 29th December 2023. This period, over 5 years, includes the Covid pandemic, which had a significant effect on stock prices. The S&P500 data that we have used is made publicly available for the benefit of future researchers. Our computational results indicate that the scaled version of our subset SSD approach outperforms the S&P500. Our approach also outperforms the standard SSD based approach to the problem. Our results show, that for the S&P500 data considered, including sector constraints improves out-of-sample performance, irrespective of the SSD approach adopted. Results are also given for Fama-French data involving 49 industry portfolios and these confirm the effectiveness of our subset SSD approach.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 6.0/10 (capped from 7.0: transaction costs not modelled; see penalty flags)
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced multivariate second-order stochastic dominance optimization with linear programming and cutting planes, showing high mathematical sophistication. It includes extensive out-of-sample backtests on S&P500 and Fama-French data over 5+ years, including pandemic stress periods, and makes datasets public, indicating strong empirical validation.

Research Flowchart

  flowchart TD
  A["Research Goal:<br/>Construct portfolio to outperform<br/>market index with sector constraints"] --> B{"Key Methodology:<br/>Subset Second-Order Stochastic Dominance<br/>(SSD)"}

  B --> C["Data & Inputs"]
  
  C --> C1["S&P 500 (2018-2023)<br/>+ Covid period context"]
  C --> C2["Fama-French 49 Industries"]

  C --> D["Computational Process<br/>Multivariate SSD Optimization"]
  
  D --> D1["Enforce Sector SSD<br/>Portfolio dominates sector index"]
  D --> D2["Optimize Sector Weights<br/>Non-pre-specified allocation"]
  D --> D3["Scale Approach<br/>Enhanced calculation method"]

  D --> E["Key Findings & Outcomes"]
  
  E --> E1["Scaled Subset SSD<br/>outperforms S&P 500"]
  E --> E2["Outperforms<br/>Standard SSD approach"]
  E --> E3["Sector constraints improve<br/>out-of-sample performance"]

Cited References (52)

1. The efficiency analysis of choices involving risk (1969) — link
2. Comparison methods for stochastic models and risks ({2002})
3. Optimization with multivariate stochastic dominance constraints (2015) — link
4. Portfolio selection ({1952}) — link
5. Enhanced indexation based on second-order stochastic dominance ({2013}) — link
6. Novel approaches for portfolio construction using second order stochastic dominance ({2017}) — link
7. Stochastic dominance and expected utility: survey and analysis ({1992}) — link
8. Dual stochastic dominance and related mean-risk models ({2002}) — link

1 of 52 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.