Optimizing Sparse Mean Reverting Portfolios with AR-HMMs in the Presence of Secondary Effects

• Published in: Periodica polytechnica. Electrical engineering and computer science Vol. 59; no. 1; pp. 1 - 8
• Main Authors: Sipos, I. Róbert, Levendovszky, János
• Format: Journal Article
• Language: English
• Published: Budapest Periodica Polytechnica, Budapest University of Technology and Economics 2015
• Subjects: Algorithms; Computer simulation; Electrical engineering; Mathematical models; Optimization; Profitability; Stochasticity; Time series
• ISSN: 2064-5260; 2064-5279
• DOI: 10.3311/PPee.7352

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 according to maximizing the mean return by the means of the introduced AR-HMM prediction algorithm. The optimization itself is carried out by stochastic search algorithms. The presented solutions satisfy the cardinality constraint thus providing a sparse portfolios which minimizes the transaction costs and maximizes the interpretability of the results.The performance has been tested on historical data obtained from S&P 500 and FOREX. The results demonstrate that a good average return can be achieved by the proposed AR-HMM based trading algorithms in realistic scenarios. Furthermore, profitability can also be accomplished in the presence of secondary effects.