Online Portfolio Selection: A Survey (1212.2129v2)

Abstract: Online portfolio selection is a fundamental problem in computational finance, which has been extensively studied across several research communities, including finance, statistics, artificial intelligence, machine learning, and data mining, etc. This article aims to provide a comprehensive survey and a structural understanding of published online portfolio selection techniques. From an online machine learning perspective, we first formulate online portfolio selection as a sequential decision problem, and then survey a variety of state-of-the-art approaches, which are grouped into several major categories, including benchmarks, "Follow-the-Winner" approaches, "Follow-the-Loser" approaches, "Pattern-Matching" based approaches, and "Meta-Learning Algorithms". In addition to the problem formulation and related algorithms, we also discuss the relationship of these algorithms with the Capital Growth theory in order to better understand the similarities and differences of their underlying trading ideas. This article aims to provide a timely and comprehensive survey for both machine learning and data mining researchers in academia and quantitative portfolio managers in the financial industry to help them understand the state-of-the-art and facilitate their research and practical applications. We also discuss some open issues and evaluate some emerging new trends for future research directions.

• The paper presents a comprehensive review of online portfolio selection methods, categorizing techniques into benchmarks, follow-the-winner/loser, pattern-matching, and meta-learning algorithms.
• It formulates portfolio selection as a sequential decision problem based on Capital Growth Theory, addressing challenges such as transaction costs and market liquidity.
• The survey underscores the need for adaptive algorithms by highlighting future research directions in predictive modeling, risk adjustments, and real-world trading constraints.

An Analytical Overview of "Online Portfolio Selection: A Survey"

The paper "Online Portfolio Selection: A Survey" by Bin Li and Steven C. H. Hoi provides an extensive review of online portfolio selection strategies, an essential problem in computational finance intersecting finance, statistics, artificial intelligence, machine learning, and data mining domains. The authors formulate online portfolio selection as a sequential decision problem, defining various state-of-the-art approaches and categorizing them into distinct classes, such as benchmarks, Follow-the-Winner, Follow-the-Loser, Pattern-Matching based techniques, and Meta-Learning Algorithms.

Core Framework and Algorithmic Perspectives

Within this survey, the authors effectively delineate online portfolio selection as a sequential decision-making challenge where a portfolio manager strategically reallocates wealth among multiple assets to maximize cumulative returns. The problem setup inherently aligns with both Mean Variance Theory and Capital Growth Theory, with the paper focusing primarily on the latter due to its sequential and multi-period nature.

1. Benchmarks: Benchmarks such as the Buy and Hold strategy, Best Stock, and Constant Rebalanced Portfolios (CRP) form baseline references. The Best CRP, in particular, serves as a hypothetical target, setting the upper bound for learning algorithms' performances.
2. Follow-the-Winner Approaches: These algorithms attempt to track the success patterns of past performers. Cover's Universal Portfolios exemplifies this category, achieving performance relativity to the Best CRP over individual sequences within theoretical bounds. Exponential Gradient (EG) methods offer a fast implementation with linear time complexities, strategically rewarding past winners.
3. Follow-the-Loser Approaches: The converse of Follow-the-Winner, these strategies are influenced by the mean reversion hypothesis. Techniques like Anti Correlation and Passive Aggressive Mean Reversion (PAMR) emphasize reallocating from historically successful assets to perceived undervalued ones.
4. Pattern-Matching Approaches: This category harnesses historical patterns to forecast future distributions. Employing methods like Nonparametric Kernel-based and Nearest Neighbor strategies, these approaches strive for universal consistency in non-stationary environments.
5. Meta-Learning Algorithms: These techniques combine insights from multiple strategy classes to refine asset allocation dynamically. Online Gradient and Newton Updates illustrate the adaptability of these methods, optimizing portfolio selection even amidst shifting market dynamics.

Theoretical and Practical Connotations

The exploration of Capital Growth Theory underscores a distinct theoretical foundation within the context of asymptotic growth rates. Methods aligning with this theory aim to maximize expected logarithmic returns iteratively, often through optimization frameworks reminiscent of convex formulations.

Practically, the authors assess challenges such as transaction costs, risk mitigation, and market liquidity, emphasizing the necessity to incorporate realistic market frictions into model parameters. While certain trading environments offer empirical robustness, theoretical guarantees remain constrained by these auxiliary market considerations.

Directions for Future Research

The survey identifies numerous avenues for advancing online portfolio strategies:

• Enhanced Predictive Models: Developing refined pattern-matching algorithms leveraging modern machine learning advancements could enhance prediction accuracy.
• Risk Adjustments: Including comprehensive risk metrics beyond simple variance or drawdown measures remains a critical challenge.
• Real-world Constraints: Overcoming practical issues such as market liquidity and transaction costs while maintaining computational feasibility is paramount.

In sum, the survey encapsulates the depth and diversity of online portfolio selection methodologies. It elucidates their connective threads to stochastic, pattern-based, and statistical approaches, encouraging ongoing research into adaptive algorithms that can nimbly respond to evolving financial landscapes. The comprehensiveness of the survey serves as a vital resource, both cataloging state-of-the-art strategies and provoking further inquiry into this financially and computationally significant field.