Simple Analysis for Trades

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for the n-day SMA rules are all higher than that from the FTP model. Since the price movements that Markov-Switching models detect are long term. As the information of market volatility is allowed to affect the generation of the SMA rule’s signals, in a sense that we make the SMA rule also to discover the short term price movements. As a result, the number of trades from the TVTP model is higher. Lastly, for each n-day SMA rule, the trades from the TVTP Markov-Switching model have higher cumulative return and annualized return no matter the transaction cost, compared to that from the FTP model. This result again verifies that the information of market volatility is valuable information in forecasting price movements for technical analysis.

3.4.3 Simple Analysis for Trades

Last section gives us the evidence that as we add the information of market volatility to the SMA rule, the profitability of the SMA rule will be improved. The theoretical benefits of the market volatility ratio in the moving average systems are to take better advantage of the price movement such as earlier/later trading or reducing losses from false trading signals. Thus, in this section, we further compare the trading signals generated from the FTP and TVTP Markov-Switching models one by one in order to investigate its empirical benefits in the moving average systems.

We choose the best results in Table 18, the case for the 250-day SMA rule. Then we compare their trading signals one by one according to their time point of generation. In our SPA tests, we cannot investigate how the information of market volatility affect the prediction for future price movements in technical analysis by comparing the trading signals of the best VMA and best SMA rule. Because these two best rule have different parameter settings and the time they generate trading signals are total different. Here, we focused on the trades for a particular n-day SMA rule and just allow the information of market volatility will affect dt’s probability of switching between states, not affect the value of d_t itself. Therefore, we expect the in-sample prediction from these two models will not be totally different.

According the time point the trading signals generated, we categorize these trades into four types: identical trades, similar trades, overlapping trades and different trades. The identical

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Table18:ComparisonsInProfitabilityOfTradesFromTheFTPandTVTPMarkov-SwitchingModels Thistablepresentstheperformanceofthen-daySMArules’tradingsignalsgeneratedfromrealtrading,fromthein-samplepredictionsoftheFixed-Transition-Probability(FTP)Markov- Switchingmodel,andfromthatoftheTime-Varying-Transition-Probability(TVTP)Markov-Switchingmodelinthefullsample.ThenumberofregimesswitchingintheFTPandTVTP Markov-Switchingmodelsindicatesthenumberoftradingsignalsobtainedfromthesetwomodels.Onebuyingsignalandonesellingsignalformatrade.Therefore,200tradingsignals implythenumberoftradeswillbe100.Cumulativereturnstandsforthetotalprofitofalltradesinthefullsample.AnnualizedReturniscomputedfromdividingthecumulativereturnby 81.5,thenumberofyearinthefullsample.Forthecostconcerns,theone-waytransactioncostissetas0.05%. n-dayModelNo.ofRegimeNo.ofCumulativeReturnCumulativeReturnAnnualizedReturnAnnualizedReturn SMASwitchingTrades(Withoutcost)(Withcost)(Withoutcost)(Withcost) n=5RealTrading24183.9661.5484.866%1.899% FTPMS2471237.1487.0248.770%8.619% TVTPMS4512257.8097.5839.581%9.304% n=20RealTrading11021.7820.6802.187%0.835% FTPMS2531267.1497.0238.772%8.617% TVTPMS5372687.8127.5449.586%9.256% n=40RealTrading7541.2490.4951.533%0.608% FTPMS2591297.4867.3579.130%9.027% TVTPMS5172587.8287.5709.546%9.288% n=75RealTrading5151.0010.4861.228%0.596% FTPMS2651327.3407.2089.006%8.844% TVTPMS5052528.0037.7509.819%9.510% n=100RealTrading4390.9780.5391.200%0.662% FTPMS2651327.2667.1348.770%8.753% TVTPMS5072537.8967.6439.581%9.377% n=250RealTrading2231.3551.1321.662%1.389% FTPMS2631317.2717.1398.921%8.760% TVTPMS4812408.1467.9059.995%9.700%

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Table 19: The Number Of Four Types Of Trades From The FTP And TVTP Markov-Switching Models

This table presents the number of four types of trades, the identical, similar, overlapping and different trades, generated from the FTP and TVTP Markov-Switching models for the 250-day SMA rule. The identical trades denotes that both the FTP and TVTP models generate exactly the same trades, while the similar trades represents those trades in which the prediction for the price movement from these two models is quite similar but a little difference. Compared to the FTP model, the TVTP model generates slightly earlier or later signals. The overlapping trades denote the situation that the FTP model forecasts an upward trend for 100 days. During this period, the TVTP model signals to trade three times. For the different trades, it means the FTP and TVTP model generate totally distinct signals. Total trades indicate how many trades the FTP and TVTP model suggest respectively in the full period.

MS Model Identical Trades Similar Trades Overlapping Trades Different Trades Total Trades

FTP 13 58 53 7 131

TVTP 13 58 159 10 240

trades represents those trades in which their time to buy and sell suggested by the FTP and TVTP models are exactly the same. For example, both the FTP and TVTP models signal to buy the stock at the 51th day in the full period and sell it after 30 days. The similar trades is a little different to the identical trades. Both the FTP and TVTP models capture the same price movement, but the time they enter or quit the market has slight difference. In other words, the TVTP models may generate signals earlier or later, compared to those in the FTP models.

The FTP model suggests to buy the stock at the 43th day and sell it at the 58th day, while the TVTP model generates a buying signal at the 44th day and a selling signal at the 56th day. Both models suggest buying at the 188th day, but the FTP and the TVTP models suggest selling at the 203th and the 204th day, respectively.

The overlapping trades illustrate the situations that the FTP model predicts an upward trend for 40 days from the 2894th day to the 2933th day. While during this period, the TVTP model generates three trades from the 2894th day to the 2899th day, from the 2900th day to the 2922th day, and from the 2924th day to the 2931th day. Or the FTP model generates a buying signal at the 1945th day and a selling signal at the 2080th day, but the TVTP model advise to buy at the 1941th day, sell at the 2020th day, then buy at the 2022th day and sell at the 2078th day.

The different trades by definition denotes the trades that their time of generation are mutual

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Table 20: Comparisons In The Performance Of Trades Between The FTP and TVTP Model:

Similar Trades

This table presents the results that whether the TVTP Markov-Switching model has better performance than the FTP model in the case of similar trades. The similar trades represent those trades in which the prediction for the price movement from these two models is quite similar, but there is slightly difference in their time to enter or exit the market. We split up the similar trades into two groups as the improved group and the deteriorated group according to whether the TVTP model gets higher profit or incurs less loss than the FTP model.

The total excess return measures how much more profit the TVTP model gains as it suggests investors to buy or sell the stock earlier/later, compared to the suggestions from the FTP model. Days denotes how many extra days the TVTP has from its earlier and/or later signals, and the daily excess return means the average return gotten by the TVTP model in these extra days.

Performance Situation No. of Total Excess Days from Daily Excess Trades Return From Earlier/Later Return From

Earlier/Later Trades Trades Earlier/Later Trades

Improved More profit 27 0.618 131 0.472%

Less loss 7 0.160 40 0.400%

Deteriorated 24 -0.622 128 -0.486%

All 58 0.156 299 0.052%

distinct. For instance, the FTP model predicts the price rising from the 443th day to the 459th day. However, there exists no trading suggestion from the TVTP model in this period.

Table 19 reports the summary for the number of four types of trades between these two Markov-Switching models. The number of identical trades and similar trades for these two models are 13 and 58, respectively. For the overlapping trades, one trade from the FTP model is on average accompanied by three trades from the TVTP model. The FTP generates seven different trades, while the TVTP model generates tens. Since it doesn’t make sense to explore the performance of the identical trades between the FTP and TVTP Markov-Switching models, we do not report the related results and focus on making comparisons in the performance of their similar trades, overlapping trades and different trades, as shown in Table 20, Table 21 and Table 22 respectively.

Similar Trades For similar trades, we separate them into two groups. The first group includes those in which the TVTP model’s trading suggestion gets more profit or incurs less loss than the FTP models’. We label them as the improved group. In contrast, the second one is the

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deteriorated group denoting that the SMA rule does not gain more or lose less from embedding extra information, the market volatility ratio, in future price movement predictions. In Table 20, we report the total excess return that the TVTP model obtains and how many extra days it has from its earlier and/or later signals. For each similar trade, we calculate the excess re-turn that the TVTP model gains through the rere-turn of the TVTP model minus that of the FTP model.^{15, 16} Then we add those excess returns for all similar trades up and then see how much benefit the TVTP model enjoys for entering/exiting the market earlier/later. The extra days from earlier/later trades for the TVTP model are gotten as follows. If the FTP model signals to buy and sell at the 43th and the 58th day while the TVTP model’s signals are generated at the 44th and the 56th day, the extra days the TVTP model have are 3 days. Lastly, the daily excess return represents the average return gotten by the TVTP model in these extra days.

From the results in Table 20, we find that the information of market volatility will not always enhance the performance of the SMA rules for every similar trade. The proportion of the im-proved group to all similar trades is only 58.62%. However, the SMA rule does benefit from the information of market volatility in the entirety, since, on average, trading one day earlier/later will let investor acquiring more profit, 0.052% a day. In addition, the average of the extra days from the TVTP model’s earlier/later trades is 5 days a similar trade.

Overlapping Trades Table 21 presents the comparisons in the performance of the overlap-ping trades between the FTP and TVTP models. As discussed before, one trade from the FTP model is on average accompanied by three trades from the TVTP model. As matter of fact that, as the FTP model predicts an upward trend for m days (one trade), the maximum and minimum number of trades the TVTP model generates are 13 and 2 during these m days. The above fact in a sense coincides with what we have discussed in section 3.4.2. That is, the price movements

15Excess return for an investment in the literature is often defined as the return of that investment minus its cost.

Here, we define the excess return as the return of the TVTP model minus that of the FTP model in order to see whether the TVTP model has better predictability for price movements.

16There is no need to report the total return of these two Markov-Switching models with cost concerns. Because when we deduct the transaction cost from the return of the TVTP model, the return of the FTP model will be lower by the same amount.

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Table 21: Comparisons In The Performance Of Trades Between The FTP and TVTP Model:

Overlapping Trades

This table presents the comparisons in the performance of the overlapping trades between the FTP and TVTP models in the full sample.

Total return stands for the total profit from all overlapping trades in the full sample. Annualized Return is computed from dividing the total return by days, the number of total days those overlapping trades last. For the cost concerns, the one-way transaction cost is set as 0.05%.

MS Model No. of Trades Days Total Return Total Return(cost) Daily Return Daily Return(cost)

FTP 53 13245 5.022 4.969 0.0379% 0.0375%

TVTP 159 13025 5.590 5.431 0.043% 0.042%

Difference 220 0.568 0.462 0.258% 0.210%

the FTP Markov-Switching model for the SMA rule almost detects are long term. The infor-mation of market volatility enables it not only to detect the long term price movements but also to discover the shorter term ones. This may be the reason why the total days the FTP model’s trades have are 13245 days, higher than the TVTP model’s with 220 days, as shown in Table 21. Although the total days the investors stay in the market are less due to taking the trading suggestions from the TVTP model, its daily return with cost concerns is higher than that from the FTP model with 0.004% (i.e., 0.042%-0.0375%) a day. Further, those 200 days the TVTP model suggests investors to withdraw from the market are found to bring less loss to investors.

On average, the reduced daily loss over these days is 0.210%.

Different Trades In Table 21, we compare the performance of different trades between the FTP and TVTP Markov-Switching model. The FTP Markov-Switching model makes seven predictions for price movements. Over the periods of these seven trades, the TVTP Markov-Switching model does not generate any signal. In contrast, there exists no trading suggestion from the FTP Markov-Switching model for ten trades of the TVTP Markov-Switching model.

The ratio of different trades to total trades is the least, compared to other type of trades. These different trades also have the smallest average day. On average, one trade from the FTP Markov-Switching model will last for 8 days, while the TVTP Markov-Markov-Switching model’s will last

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Table 22: Comparisons In The Performance Of Trades Between The FTP and TVTP Model:

Different Trades

This table reports the comparisons in the performance of the different trades between the FTP and TVTP models in the full sample. Total return stands for the total profit from all different trades in the full sample. Annualized Return is computed from dividing the total return by days, the number of total days those different trades last. For the cost concerns, the one-way transaction cost is set as 0.05%.

MS Model No. of Trades Days Total Return Total Return(cost) Daily Return Daily Return(cost)

FTP 7 58 -0.035 -0.042 -0.060% -0.072%

TVTP 10 41 0.117 0.107 0.285% 0.261%

for 4 days. We can observe that the performance of the seven trades in the FTP Markov-Switching model is not good with the negative daily return no matter the cost. However, we can gain 0.261% a day on average by the trades in the TVTP Markov-Switching model. We further investigate the performance for each trade in the FTP Markov-Switching model and find that there are four trades that investors will incur losses from them in seven trades. In ten trades from the TVTP Markov-Switching model, the number of trades with positive return is seven. For the results in the similar and overlapping trades, the proportion of trades incurring losses to total trades in the FTP Markov-Switching model are 32.76% and 21.28%, which are relatively lower than that in the different trades (i.e., 57.14%). In the case of the TVTP Markov-Switching model, the ratio for the similar and overlapping trades are 32.76% and 19.15%. Its ratio for the different trades is 30%. The above results imply that the ability of the FTP Markov-Switching model to detect the shorter term price movements is worse than that to forecast long term ones. Furthermore, they also denote that the detection for shorter term price movements can be improved as we use the information of market volatility in forecasting.

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3.5 The Future Way of Exploring Explanations for Higher Profits Gained