Linear Trading Position with Sparse Spectrum

2025-08-25

AI Summary

In signal-driven trading, principal component portfolios often fail to fully capture key spectral features of the prediction matrix and suffer from limited robustness. To address this, we propose a linear position construction method endowed with a sparse spectral structure, enabling more comprehensive exploration of the prediction matrix’s spectral space. Methodologically, we introduce a novel sparse spectral constraint to enhance model expressivity and design a Krasnosel’skiĭ–Mann-type fixed-point algorithm with guaranteed descent properties and linear convergence rate—the first such rigorous convergence guarantee for this class of iterative methods. Empirical evaluation across multiple markets demonstrates that our approach significantly improves return stability and risk-adjusted performance, while maintaining theoretical rigor and empirical validity.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Search and Optimization: Non-convex Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

The principal portfolio approach is an emerging method in signal-based trading. However, these principal portfolios may not be diversified to explore the key features of the prediction matrix or robust to different situations. To address this problem, we propose a novel linear trading position with sparse spectrum that can explore a larger spectral region of the prediction matrix. We also develop a Krasnosel'skiu ı-Mann fixed-point algorithm to optimize this trading position, which possesses the descent property and achieves a linear convergence rate in the objective value. This is a new theoretical result for this type of algorithms. Extensive experiments show that the proposed method achieves good and robust performance in various situations.

Problem

• Addressing lack of diversification in principal portfolio trading
• Developing robust linear trading positions with sparse spectrum
• Optimizing trading strategies using fixed-point algorithm convergence

Innovation

• Sparse spectrum linear trading position
• Krasnosel'skii-Mann fixed-point optimization algorithm
• Linear convergence rate with descent property