Parallel Optimization of Sparse Portfolios with AR-HMMs

• Published in: Computational economics Vol. 49; no. 4; pp. 563 - 578
• Main Authors: Sipos, I. Róbert, Ceffer, Attila, Levendovszky, János
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.04.2017; Springer Nature B.V
• Subjects: Algorithms; Behavioral/Experimental Economics; Computer Appl. in Social and Behavioral Sciences; Economic Theory/Quantitative Economics/Mathematical Methods; Economics; Economics and Finance; High frequency trading; Markov analysis; Math Applications in Computer Science; Operations Research/Decision Theory; Optimization; Portfolio management; Program trading; Software; Studies; Time series; Portfolio optimization; High frequency algorithmic trading; Mean reversion; Financial time series; Hidden Markov models; GPGPU
• ISSN: 0927-7099; 1572-9974
• DOI: 10.1007/s10614-016-9579-y

In this paper we optimize mean reverting portfolios subject to cardinality constraints. First, the parameters of the corresponding Ornstein–Uhlenbeck (OU) process are estimated by auto-regressive Hidden Markov Models (AR-HMM), in order to capture the underlying characteristics of the financial time series. Portfolio optimization is then performed by maximizing the return achieved with a predefined probability instead of optimizing the predictability parameter, which provides more profitable portfolios. The selection of the optimal portfolio according to the goal function is carried out by stochastic search algorithms. The presented solutions satisfy the cardinality constraint in terms of providing a sparse portfolios which minimize the transaction costs (and, as a result, maximize the interpretability of the results). In order to use the method for high frequency trading (HFT) we utilize a massively parallel GPGPU architecture. Both the portfolio optimization and the model identification algorithms are successfully tailored to be running on GPGPU to meet the challenges of efficient software implementation and fast execution time. The performance of the new method has been extensively tested both on historical daily and intraday FOREX data and on artificially generated data series. The results demonstrate that a good average return can be achieved by the proposed trading algorithm in realistic scenarios. The speed profiling has proven that GPGPU is capable of HFT, achieving high-throughput real-time performance.