3.2.1. Traditional Sector-Stock Long-Only Momentum Portfolio

In this section, portfolios include upward momentum stocks belonging to upward momentum sectors. Using 19 industry indices, we first find sectors of which indices record positive returns and then select stocks that are included in those selected sectors and generate positive returns during the formation period. We construct portfolios across various ranges of formation and holding periods of 1, 3, 6, 9, and 12 months. The results are shown in Table 4 below.

Table 4. Monthly average return of traditional sector-stock momentum portfolio.

K 1 3 6 9 12 Average  
J  
1 0.73 0.77 0.96 1.5 1.44 1.08
3 1.12 0.75 1.09 0.71 0.83 0.9
6 0.8 1.18 0.98 0.88 1.11 0.99
9 1.29 1.31 1.2 1.5 1.42 1.34
12 1.45 1.2 0.89 1.08 1.02 1.13
Average 1.08 1.04 1.02 1.13 1.16  

3.2.2. HMM Sector-Stock Long-Only Momentum Portfolio

In this section, we use HMM to identify upward momentum sectors, as well as upward momentum stocks. We first identify upward momentum sectors among 19 industry indices and then identify upward momentum stocks included in the upward momentum sectors. Similar to the experiment in Section 3.1.2, we construct portfolios with formation and holding periods of 1, 3, 6, 9, and 12 months and perform 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 5 shows the monthly average return of the HMM sector-stock long-only momentum portfolio. The results presented in Table 5 are illustrated graphically in Figure 5.


Figure 5. Monthly average returns of the HMM sector-stock momentum portfolio when J = 1, 3, 6, 9, 12.

Table 5. Monthly average return of HMM sector-stock momentum portfolio.

K 1 3 6 9 12 Average  
J  
Panel A. 2-Hidden States            
1 1.31 0.76 0.78 0.91 0.96 0.94
3 1.35 0.81 0.9 0.88 1.04 1
6 1.28 1.22 1.25 1.24 1.14 1.23
9 1.63 1.4 1.52 1.23 1.13 1.38
12 1.56 1.3 1.3 1.13 1.21 1.3
Average 1.43 1.1 1.15 1.08 1.1  
Panel B. 3-Hidden States            
1 1.37 1.13 0.97 1.12 1.03 1.12
3 1.35 0.82 0.65 0.83 0.89 0.91
6 1.67 1.13 1.11 1.29 1.14 1.27
9 1.51 1.47 1.05 1.56 1.12 1.34
12 1.39 1.31 1.14 1.21 1.19 1.25
Average 1.46 1.17 0.98 1.2 1.07  
Panel C. 4-Hidden States            
1 1.29 1.26 1.36 1.13 1.13 1.23
3 1.47 1.17 0.78 1.22 0.98 1.12
6 1.5 1.23 1.16 1.11 1.25 1.25
9 1.52 1.3 0.85 1.14 1.12 1.19
12 1.52 1.01 0.94 1.07 1.22 1.15
Average 1.46 1.19 1.02 1.13 1.14  
Panel D. 5-Hidden States            
1 1.46 1.08 1.15 1.26 1.09 1.21
3 1.56 1.01 1.05 0.67 0.9 1.04
6 1.52 1.36 1.18 1.21 1.5 1.35
9 1.63 1.46 0.8 1.08 1.2 1.23
12 1.76 1.22 1.13 1.41 1.02 1.31
Average 1.59 1.23 1.06 1.13 1.14  

As shown in Table 5 and Figure 5, the HMM sector-stock long-only momentum portfolios outperform the traditional long-only momentum portfolios in all combinations of formation and holding periods. Similar to the results of the HMM stock long-only momentum portfolio, portfolios constructed by 6-, 9-, and 12-month formation periods are observed to generate higher returns than those constructed by the 1- and 3-month formation periods. It is also noted that portfolios with a one-month holding period achieve the best performance within most formation periods. Similar to the HMM stock long-only momentum portfolio, the shorter the holding period, the better the performance.

As such, we conduct an additional experiment with weekly rebalancing across the combination of the formation periods and number of states. Table 6 shows the monthly average returns of the HMM sector-stock long-only momentum portfolio with weekly rebalancing, and the results in Table 6 are illustrated graphically in Figure 6. As shown in Table 6 and Figure 6, weekly rebalancing generates higher returns than monthly rebalancing in all combinations of the formation period and number of states. It should be noted that unlike the results presented in Table 5, the best performance is achieved when the formation period is one month (J = 1).


Figure 6. Monthly return of HMM-based sector-stock weekly momentum portfolio.

Table 6. Monthly average returns of the HMM sector-stock momentum portfolio with weekly rebalancing.

States 2 3 4 5 Average  
J  
1 1.93 2.09 2.26 1.97 2.06
3 1.71 1.62 1.98 1.77 1.77
6 1.76 1.82 1.89 1.87 1.84
9 1.82 1.74 1.94 1.9 1.85
12 1.7 1.56 1.64 1.91 1.7
Average 1.78 1.77 1.94 1.88