  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.
