Portfolio of Automated Trading Systems: Complexity and Learning Set Size Issues

In this paper, we consider using profit/loss histories of multiple automated trading systems (ATSs) as $N$ input variables in portfolio management. By means of multivariate statistical analysis and simulation studies, we analyze the influences of sample size $(L)$ and input dimensionality on the accuracy of determining the portfolio weights. We find that degradation in portfolio performance due to inexact estimation of $N$ means and $N(N-1)/2$ correlations is proportional to $N/L$; however, estimation of $N$ variances does not worsen the result. To reduce unhelpful sample size/dimensionality effects, we perform a clustering of $N$ time series and split them into a small number of blocks. Each block is composed of mutually correlated ATSs. It generates an expert trading agent based on a nontrainable $1/N$ portfolio rule. To increase the diversity of the expert agents, we use training sets of different lengths for clustering. In the output of the portfolio management system, the regularized mean-variance framework-based fusion agent is developed in each walk-forward step of an out-of-sample portfolio validation experiment. Experiments with the real financial data (2003–2012) confirm the effectiveness of the suggested approach.