Portfolio of automated trading systems: complexity and learning set size issues

Area of Science:

• Quantitative Finance
• Computational Finance
• Financial Engineering

Background:

• Automated trading systems (ATSs) are increasingly used in portfolio management.
• Accurate portfolio weight determination is crucial for optimizing investment strategies.
• The influence of input dimensionality and sample size on portfolio performance requires investigation.

Purpose of the Study:

• To analyze the impact of sample size (L) and input dimensionality (N) on the accuracy of portfolio weights derived from ATS profit/loss histories.
• To develop a novel approach for mitigating the negative effects of high dimensionality and limited sample size in portfolio management.
• To validate the proposed method using real-world financial data.

Main Methods:

• Multivariate statistical analysis and simulation studies to assess the relationship between N, L, and portfolio weight accuracy.
• Clustering of N time series to group correlated ATSs into blocks.
• Development of expert trading agents using a 1/N portfolio rule and diverse training set lengths.
• Fusion agent development within a regularized mean-variance framework for out-of-sample validation.

Main Results:

• Portfolio performance degradation due to inexact estimation of means and correlations is proportional to N/L.
• Estimation of N variances does not significantly worsen portfolio results.
• The proposed clustering and fusion agent approach effectively reduces sample size/dimensionality effects.
• Experiments with 2003-2012 financial data confirm the approach's effectiveness.

Conclusions:

• The study provides a robust method for enhancing portfolio management with multiple ATSs, particularly under high dimensionality and limited data.
• The findings offer practical insights for optimizing the selection and weighting of ATSs in investment portfolios.
• The developed fusion agent framework demonstrates superior performance in out-of-sample validation, highlighting its real-world applicability.