Momentum Investment

3.1.1. Traditional Stock Long-Only Momentum Portfolio

The traditional momentum investment strategy is typically implemented by buying past winners and selling (shorting) past losers under the assumption that past winners tend to continue to yield positive returns, while past losers tend to continue to yield negative returns. We construct a traditional long-only momentum portfolio that includes upward momentum stocks during the formation period and hold it during the holding period [5]. The performance of the portfolio is measured by the monthly average returns of individual stocks included in the portfolio, as described by the following equation:

$R_{P, T}=\frac{1}{n} \sum_{i=1}^{n} r_{i, T} \text { where } r_{i, T}=\frac{1}{T} \sum_{t=1}^{T} r_{i, t}$

where $R_{P, T}$ denotes the monthly average returns of a portfolio that includes n stocks during T months, $r_{i, T}$  is the monthly average returns of stock i during T months, and $r_{i, T}$ is the monthly returns of stock i in month t. The portfolio returns by (1) represents the returns of an equally weighted portfolio of stocks.

Table 1 shows the monthly average return of the traditional stock long-only momentum portfolio constructed across various ranges of formation and holding periods of 1, 3, 6, 9, and 12 months. The portfolio includes stocks whose J-month lagged returns are positive. After a portfolio is constructed, it is held for K months and rebalanced during the experimental period. The portfolio performance is evaluated by monthly average returns, ignoring slippage and trading cost.

Table 1. Monthly average returns of the traditional stock momentum portfolio.

3.1.2. HMM Stock Long-Only Momentum Portfolio

While the traditional momentum investment strategy is to buy only stocks that have shown positive past returns, the HMM momentum investment strategy uses past returns of stocks to determine the state of each stock using HMM and buys only stocks in the rising state. We construct portfolios with formation and holding periods of 1, 3, 6, 9, and 12 months and conduct the experiment with various numbers of hidden states, including 2, 3, 4, and 5. We use the 1-month sliding window method for learning the HMM. Table 2 shows the monthly average return of the HMM long-only momentum portfolio constructed across various ranges of formation and holding periods of 1, 3, 6, 9, and 12 months with 2, 3, 4, and 5 hidden states.

Table 2. Monthly average returns of the HMM stock momentum portfolio.

As shown in Table 2, the HMM long-only stock momentum portfolios outperform the traditional long-only momentum portfolios in all cases. Regarding the formation period (J), portfolios constructed by 6-, 9-, and 12-month lagged returns are found to generate higher returns than those constructed by 1- and 3-month lagged returns. It is also noted that portfolios held for one month exhibit the best performance within most formation periods. On the other hand, the number of states does not affect the portfolio performance. To summarize the results of the experiment, the HMM momentum investment strategy generates higher returns with formation periods of 6, 9 and 12 months and a 1-month holding period. The results in Table 2 are illustrated graphically in Figure 3.

Figure 3. Monthly average return of HMM stock momentum portfolio when J = 1, 3, 6, 9, 12 months.

As shown in Figure 3, portfolios perform best in the shortest holding period, that is, one month. In other words, the usefulness of HMM increases as the portfolio rebalancing period decreases. Therefore, we conduct an additional experiment with weekly rebalancing using the formation periods and number of states used in Table 2. Table 3 shows the monthly average returns of the HMM long-only momentum portfolio with weekly rebalancing, and the results in Table 3 are illustrated graphically in Figure 4. As shown in Table 3 and Figure 4, weekly rebalancing generates higher returns than monthly rebalancing in all combinations of formation periods and number of states. It should be noted that unlike the results in Table 2, the best performance is achieved when the formation period is one month (J = 1).

Figure 4. Monthly average returns of the HMM stock momentum portfolio with weekly rebalancing.

Table 3. Monthly average returns of the HMM stock momentum portfolio with weekly rebalancing.