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Optimal Stock Portfolio Selection with a Multivariate Hidden Markov Model

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Abstract

The underlying market trends that drive stock price fluctuations are often referred to in terms of bull and bear markets. Optimal stock portfolio selection methods need to take into account these market trends; however, the bull and bear market states tend to be unobserved and can only be assigned retrospectively. We fit a linked hidden Markov model (LHMM) to relative stock price changes for S&P 500 stocks from 2011–2016 based on weekly closing values. The LHMM consists of a multivariate state process whose individual components correspond to HMMs for each of the 12 sectors of the S&P 500 stocks. The state processes are linked using a Gaussian copula so that the states of the component chains are correlated at any given time point. The LHMM allows us to capture more heterogeneity in the underlying market dynamics for each sector. In this study, stock performances are evaluated in terms of capital gains using the LHMM by utilizing historical stock price data. Based on the fitted LHMM, optimal stock portfolios are constructed to maximize capital gain while balancing reward and risk. Under out-of-sample testing, the annual capital gain for the portfolios for 2016–2017 are calculated. Portfolios constructed using the LHMM are able to generate returns comparable to the S&P 500 index.

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Acknowledgements

The hardware used in the computational studies is part of the UMBC High Performance Computing Facility (HPCF). The facility is supported by the U.S. National Science Foundation through the MRI program (grant nos. CNS–0821258, CNS–1228778, and OAC–1726023) and the SCREMS program (grant no. DMS–0821311), with additional substantial support from the University of Maryland, Baltimore County (UMBC). See hpcf.umbc.edu for more information on HPCF and the projects using its resources. Reetam Majumder was supported by the Joint Center for Earth Systems Technology and by the HPCF as a Research Assistant.

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  1. University of Maryland Baltimore County, Baltimore, MD, USA

    Reetam Majumder & Nagaraj K. Neerchal

  2. Procter & Gamble, Cincinnati, OH, USA

    Qing Ji

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  1. Reetam Majumder
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Correspondence to Reetam Majumder.

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Qing Ji and Nagaraj K. Neerchal contributed equally to this work.

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Majumder, R., Ji, Q. & Neerchal, N.K. Optimal Stock Portfolio Selection with a Multivariate Hidden Markov Model. Sankhya B 85 (Suppl 1), 177–198 (2023). https://doi.org/10.1007/s13571-022-00290-5

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