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Ensembling Portfolio Strategies for Long-Term Investments: A Distribution-Free Preference Framework for Decision-Making and Algorithms

Duy Khanh Lam

TL;DR

The paper tackles the problem of ensembling multiple sequential portfolio strategies without relying on market-return distributions. It develops a distribution-free, time-consistent preference framework and a scalable online combinatorial strategy that, under a baseline comparison, is guaranteed to eventually surpass all component strategies. The method is analyzed for both small and large numbers of components, and validated through long-horizon CRSP data, showing superior cumulative wealth with acceptable Sharpe tradeoffs; accelerated variants further boost performance in practice. This work provides a theoretically grounded approach to robust, distribution-free portfolio ensembling with practical guidance for large-scale implementations.

Abstract

This paper investigates the problem of ensembling multiple strategies for sequential portfolios to outperform individual strategies in terms of long-term wealth. Due to the uncertainty of strategies' performances in the future market, which are often based on specific models and statistical assumptions, investors often mitigate risk and enhance robustness by combining multiple strategies, akin to common approaches in collective learning prediction. However, the absence of a distribution-free and consistent preference framework complicates decisions of combination due to the ambiguous objective. To address this gap, we introduce a novel framework for decision-making in combining strategies, irrespective of market conditions, by establishing the investor's preference between decisions and then forming a clear objective. Through this framework, we propose a combinatorial strategy construction, free from statistical assumptions, for any scale of component strategies, even infinite, such that it meets the determined criterion. Finally, we test the proposed strategy along with its accelerated variant and some other multi-strategies. The numerical experiments show results in favor of the proposed strategies, albeit with small tradeoffs in their Sharpe ratios, in which their cumulative wealths eventually exceed those of the best component strategies while the accelerated strategy significantly improves performance.

Ensembling Portfolio Strategies for Long-Term Investments: A Distribution-Free Preference Framework for Decision-Making and Algorithms

TL;DR

The paper tackles the problem of ensembling multiple sequential portfolio strategies without relying on market-return distributions. It develops a distribution-free, time-consistent preference framework and a scalable online combinatorial strategy that, under a baseline comparison, is guaranteed to eventually surpass all component strategies. The method is analyzed for both small and large numbers of components, and validated through long-horizon CRSP data, showing superior cumulative wealth with acceptable Sharpe tradeoffs; accelerated variants further boost performance in practice. This work provides a theoretically grounded approach to robust, distribution-free portfolio ensembling with practical guidance for large-scale implementations.

Abstract

This paper investigates the problem of ensembling multiple strategies for sequential portfolios to outperform individual strategies in terms of long-term wealth. Due to the uncertainty of strategies' performances in the future market, which are often based on specific models and statistical assumptions, investors often mitigate risk and enhance robustness by combining multiple strategies, akin to common approaches in collective learning prediction. However, the absence of a distribution-free and consistent preference framework complicates decisions of combination due to the ambiguous objective. To address this gap, we introduce a novel framework for decision-making in combining strategies, irrespective of market conditions, by establishing the investor's preference between decisions and then forming a clear objective. Through this framework, we propose a combinatorial strategy construction, free from statistical assumptions, for any scale of component strategies, even infinite, such that it meets the determined criterion. Finally, we test the proposed strategy along with its accelerated variant and some other multi-strategies. The numerical experiments show results in favor of the proposed strategies, albeit with small tradeoffs in their Sharpe ratios, in which their cumulative wealths eventually exceed those of the best component strategies while the accelerated strategy significantly improves performance.
Paper Structure (12 sections, 5 theorems, 27 equations, 12 figures, 3 tables)

This paper contains 12 sections, 5 theorems, 27 equations, 12 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Model settings and formalizations
  3. Preference relation and combination criterion
  4. A construction for combinatorial strategy
  5. The benchmark strategy
  6. Small scale of component strategies
  7. Arbitrarily large scale of component strategies
  8. Numerical experiments
  9. Data and testing strategies
  10. Experiments with small scales of component strategies
  11. Experiments with large scales of component strategies
  12. Summary and concluding Remarks

Key Result

Proposition 1

For any infinite sequence of assets' returns $x_{1}^{\infty}$, the preference relations established in Definition Definition of preference satisfy the following properties:

Figures (12)

  • Figure 1: Evolutions of component M-V strategies over time with different levels of risk aversion.
  • Figure 2: Final cumulative wealth plotted against discretization points and step sizes for approximating the combinatorial strategy with two component strategies.
  • Figure 3: Adjusted closing prices in USD of the stocks from December 31, 1992, to December 31, 2019.
  • Figure 4: Evolutions of the multi-strategies over time in Experiments 1, 2, 3, and 4 (from left-to-right and top-to-bottom order).
  • Figure 5: The constant combination $\lambda$ plotted against the final cumulative wealth with respect to the discretization. The best constant combinations in Experiment 1, 2, 3, and 4 are $\left(0.55,0.45\right)$, $\left(0.44,0,0.56\right)$, $\left(0.3,0.2,0,0.5,0\right)$ and $\left(1,0\right)$, respectively.
  • ...and 7 more figures

Theorems & Definitions (19)

  • Definition 1
  • Example 1
  • Definition 2
  • Proposition 1
  • proof
  • Definition 3
  • Proposition 2
  • proof
  • Remark
  • Claim 1
  • ...and 9 more