2.3.1. HMM Stock Momentum Strategy

The momentum investment strategy identifies upward momentum assets using their returns over a certain period in the past. In this study, we employ the HMM to identify upward momentum stocks to improve portfolio performance. The HMM is widely employed to describe a given time series, and it has recently been applied in the financial field. Stock prices have a trend that is a representative feature of the time series, and the trend changes as the regime shifts. The HMM has been proven to be an excellent model for this time series transition and trend. As mentioned earlier, the effectiveness of the momentum strategy has been proven in many studies. On the other hand, the effectiveness of the momentum strategy in a number of Asian countries, including Korea, is controversial. Therefore, in this study, we employ the HMM momentum investment strategy to examine its usefulness for Korean stock portfolios. We use a continuous HMM with a mixed normal distribution and adopt the momentum investment strategy used by Jegadeesh and Titman. We implement an upward momentum strategy of buying stocks in the rising state using the HMM and evaluate portfolio performance. To this end, we conduct a number of experiments with various ranges of the portfolio formation period (J) and holding period (K). Then, the utility of the upward momentum strategy with HMM is assessed by obtaining the portfolio returns and comparing returns from our portfolios with those from portfolios constructed by the existing momentum strategy.

In the HMM study for stock prediction, it is common to divide the state into three states: ascending, transverse, and falling. In this study, the state is divided into 2, 3, 4, and 5, and the effect of the number of states on stock price prediction is analyzed. As the stock prices are determined to be nonstationary time series, implying that trends and volatility are not constant, we use the series of stock price differences for the trend and the logarithmic stock prices for the volatility to normalize our time series data. In this study, we use the 1-month sliding window method for learning the HMM and depmixS4, which is the R package known to be the most suitable for HMM coding and experiments, to estimate the model.

2.3.2. HMM Sector-Stock Momentum Strategy

We extend the HMM stock momentum strategy by adding a procedure of identifying upward momentum sectors. The HMM is first used to identify upward momentum sectors and then identify upward moment stocks that belong to the upward momentum sectors. Using industry indices, we first identify upward momentum sectors within 19 industries and then identify upward momentum stocks included in the upward momentum sectors. In other words, we construct a portfolio that buys upward momentum stocks included in upward momentum sectors.

2.3.3. HMM Index Momentum Strategy

In this study, we propose an index momentum strategy using the HMM. The states of each sector and overall market are identified by the HMM, and the index momentum portfolios are constructed by the purchasing index in the rising states. We used 20 indices: 19 industry indices and the Korea Composite Stock Price Index (KOSPI). All indices are traded the same way as exchange traded funds (ETFs), and index returns are derived. All experimental models of this study are represented in Figure 2. The upper part of Figure 2, the traditional momentum portfolio, shows the process of constructing a traditional stock long-only momentum portfolio and a traditional sector-stock long-only momentum portfolio. The lower part of Figure 2, the HMM momentum portfolio, shows the process of constructing an HMM stock long-only momentum portfolio and an HMM sector-stock long-only momentum portfolio. As a last step, we compare the performance of the momentum strategy presented by Jegadeesh and Titman with the HMM momentum strategy developed in this study.


Figure 2. Experimental models for portfolio construction.