Trading rule discovery using technical analysis and a template matching technique for pattern recognition: Evidence from the Chinese stock market

4.1 Average return

Table 1 presents the average returns of the SEE index and the average returns yielded by the bull flag trading rule. These results vary depending on the length of fitting windows (p), holding periods (q) and threshold values (T) under consideration.

The first columns of the table reflect the results of a strategy that buys the SSE index in all tradable days, a trading policy advocated by the EMH. The columns on the right present the returns of a trading strategy guided by bull flag trading rules. For both strategies, it is possible to identify that each fitting window may have allocated five different holding periods, q = {20, 40, 60, 80 and 100}. In general, the longer the holding period, regardless of the length of the fitting window, the higher the average return generated by a given strategy. For example, as far as the buy everyday strategy is concerned, it generates an average daily market return of 1.58% for a fitting window and a holding period of 20 days. On the other hand, under the same conditions, a trading policy based on the bull flag is able to generate an average return per buy signal of 9.76% for a T = 3, which corresponds to the best template price fit of this study. This specific trading rule (Fit_k ≥ 3) delivered 1381 buy signals in a total of 7549 trading days.

Moreover, it is interesting to note that for the market-based strategy, each holding period corresponds to a single average return value, completely independent of the number of days chosen to compose the fitting window. This phenomenon can be explained by the intrinsic condition of the trading policy, which is to buy the index everyday, causing the fitting windows to be entirely composed of days in which an investment was made. Consequently, this neutralizes any effect on the return caused by varying the number of days each window covers. On the other hand, this same phenomenon is not observed when implementing the method based on technical analysis, as the buy signals are not triggered daily, but rather through a system of trading rules that integrate bull flag patterns. That is, bull flag returns are influenced by the quality of Fit_k, which naturally incorporates the value chosen as the p-trading day fitting window, as explained in the previous section. Instead, the implementation of conditional trading rules is associated with another event, which is related to the empirical result that, commonly, for holding periods of shorter duration and small fitting windows, the greater the number of p-days in the fitting window, the lower the average returns.

The average bull flag returns are categorized according to different threshold levels and can take the values of T = {0, 1, 2, and 3}. A threshold value can be defined, in this case, as being a lower bound of a hypothetical Fit_k measure from which conditional trading rules give a buy signal, that is, B_k = 1 if Fit_k ≥ T and B_k = 0, otherwise. On this sense, the empirical findings show the existence of another event related to the fact that there is a direct and positive relationship between the values assumed as threshold and the returns obtained, so that the higher the value of T, the greater the average return. For example, for a p = 20 and q = 20, the bull flag average returns were 2.60%, 3.75%, 6.87%, and 9.76% for increasing T values, respectively. These results are in agreement with other studies carried out in emerging markets, such as the Chinese Taiwan's stock market (Wang & Chan, 2007). In fact, increasing the threshold value makes the required level of Fit_k's quality also higher, which means that better degrees of template price fit lead trading rules to perform better, achieving higher average returns. On the contrary, the buy every day approach does not require the setting of any threshold as no condition prevents buying the index on any trading day.

It is also worth mentioning that each fitting window has an immutable number of days in which there was a buy indication, regardless of the holding period that can be chosen. This event occurs because each trading day is associated with a value of Fit_k, and the purchase of the index is decided based on the relationship of Fit_k's quality, on that trading day, with the threshold. Therefore, the number of days the investment is held has no impact on the quantity of signals captured by the trading rules. In addition, increasing the value assigned to the threshold causes the number of buy signals to decrease as higher Fit_k volumes are required, but on the other hand, as mentioned earlier, it improves the performance of the bull flag. However, if the method used is supported by the EMH, the methodological process is simpler, since the number of trading days that make up the sample period is equal to the number of times the index is bought.

The results observed in Table 1 illustrate that, in general, bull flag conditional trading rules can validly predict changes in the direction of the SSE index values regardless of the fitting window. Indeed, as the number of p-trading days increases, bull flag average returns tend to deteriorate, generating values below market returns on some occasions, mainly for shorter holding periods. As an example, this occurs for a p = 100, q = 20 and T = 0, in which the return obtained by the bull flag was 0.67%, being lower than the associated market average return, which was 1.58%.

These results are similar to those obtained by Wang and Chan (2007) when testing TAIEX, although, in this case, there was no indication of observations with worse performance than the market. The observed differences between our results and those obtained by Wang and Chan (2007) for the Chinese Taiwan's market may be attributed to several factors. First, the analysis periods are different: Wang and Chan (2007) focused on the period 1971–2004, while our article examines the period 1991–2021. Second, although both the Chinese mainland's and the Chinese Taiwan's stock markets can be considered emerging markets, there are significant differences between them. One noteworthy distinction is that the Chinese mainland's stock market has a significant presence of state-owned enterprises, which can impact market dynamics and investor sentiment, while in Chinese Taiwan, the proportion of state-owned companies is relatively lower. Additionally, the accessibility of the two markets to foreign investors presents significant differences. Historically, the Chinese mainland's stock market has had restrictions on foreign investor participation, with certain limitations on foreign ownership and investment channels. In contrast, the Chinese Taiwan's stock market has been relatively more accessible to foreign investors.

As a consequence of these empirical findings and considering only average returns, an investor interested in buying the Chinese index should follow strategies focused on the search for investment opportunities based on short fitting windows. Likewise, in Leigh et al. (2004), the bull flag strategies applied to the NYSE index with the shortest fitting windows are those that record the highest average returns for positive window price changes during the period from 1981 to 1999. In addition, Wang and Chan (2007) argue that an approach that uses shorter fitting windows can enhance the performance of technical analysis when applied to the NASDAQ and TAIEX indexes.

4.2 Excess profit after trading costs

Table 2 presents detailed evidence on other profitability indicators of both trading strategies, in situations in which the investor chooses to use a 20-day fitting window and simultaneously the best available price fit values, which occur when Fit_k ≥ 3.

The average daily return and the annualized return are two measures commonly used to infer the performance of a financial portfolio. However, in this case, it is necessary to make a distinction between the two. On the one hand, the average return is methodologically computed using a simple arithmetic average of the daily returns on the days indicated by the trading rules. Nonetheless, if one wants to retain some sort of conclusion regarding the performance of trading rules with different holding periods, it is important to resort to estimates expressed in annualized returns rather than average returns. In fact, this study is applied to an emerging market that has been expanding over the years. Thus, if we analyze only the average of the generated returns, it is quite natural that they are higher the longer the holding period. Thus, the annualized return calculates the average amount of money earned by a given investment on an annual basis that comprises 254 trading days and depends on the holding period of the assets. As a result, this measure allows the comparison of strategies based on trading rules with different holding periods (Wang & Chan, 2007). Henceforth, inferences about the performance of any trading approach are mainly supported by estimations of annualized returns.

The experimental results in Table 2 are circumscribed by 20-day fitting windows, as this is the only p capable of generating bull flag average returns higher than those of the buy everyday strategy, regardless of the holding period or threshold value, as seen in Table 1. Furthermore, due to the empirical fact highlighted above of better results in terms of bull flag performance for fitting windows with shorter days. In addition, the observations are restricted to the maximum threshold as the higher the value of T, the higher the average return yielded by the bull flag trading rule.

The empirical results show a positive and statistically significant annualized excess profit for all holding periods. These findings hold true even when considering the existence of transaction costs. This is an important aspect as it is a factor that makes the data analysis closer to reality. Indeed, the column in Table 2 referring to transaction cost relates to the theoretical value that the operating cost of a single transaction would need to have so that, in their entirety, the costs involved in buying and selling a given index on the days indicated by the trading rules, were able to offset the bull flag average gains. For example, for the bull flag average return with a trading rule that has a p = 20 and q = 20 to be offset by the associated transaction costs, the unit cost of a trading operation would have to be 4.88%. According to Leippold et al. (2022, p. 80), “25 bps might be a reasonable estimate of transaction cost in the Chinese mainland's stock market during normal times”. Thus, considering reasonable transaction costs, the bull flag approach continues to be profitable and with better results than the buy everyday strategy, since the theoretical costs indicated in Table 2 are shown to be fairly high.

The results displayed in Table 2 suggest that an increase in the holding period is associated with a decrease in excess profit. The bull flag annualized excess return when q = 20 was 103.83%, while for a q = 100 it was only 62.78%. So, based on this empirical observation, investors should hold index assets for the shortest possible time to maximize their possible gains, in this case, 20 days. In the literature, this trend is in agreement with the study by Wang and Chan (2007) for the NASDAQ and TAIEX Indices. However, according to Leigh et al. (2004), this investment policy is only viable when the market presents a positive window price change because if it is falling (usually connoted as a bear market), the opposite was true for the NYSE Index.

In this context, the standard deviation can be seen as a measure of investment risk as it determines the dispersion of the securities' returns around its average. Thus, the greater the movement of index values, the greater the market volatility, which increases the standard deviation. Relative to the Chinese index, the standard deviation associated with the bull flag is higher than that observed in the market for any q, but the average returns linked to trading rules are significantly higher. Thus, using the coefficient of variation that calculates an investment total risk per unit of return, it can be noticed that the underlying risk of the bull flag is lower than that of the buy everyday strategy, as shown in Table 3 (Reed et al., 2002).

Considering the variable referring to excess profits, and compared to other studies, it were obtained higher excess profits in the SSE index than in the emerging market of Chinese Taiwan analyzed by Wang and Chan (2007).

4.3 Market timing

The empirical results presented in Table 2 indicate that buy signals derived from bull flag patterns and captured by conditional trading rules generate the best performance when p = 20, q = 20, and Fit_k ≥ 3. Interestingly, among the displayed data, this is the observation where the annualized excess profit is maximum and, at the same time, the standard deviation is minimum. As in the previous section, this section is intended to provide additional detailed information on the performance of the aforementioned trading strategies, under the same conditions. In particular, it investigates the forecasting ability related to changes in the direction of the stock index series as shown in Table 4.

The statistics in Table 4, more specifically those attributed to the variable designated as Ratio, indicate the percentage of success allocated to the forecasting power of technical analysis by comparing predictions about changes in the direction of the index values, that is, whether the market will continue to rise or, instead, will have a decline in the future. This indicator is thus expressed by the number of buy signals that resulted in positive returns, in relation to subsequent actual changes in the market. Empirically, it is possible to observe that this quotient varies between 78.13% and 81.97%. In addition, these values are higher than those recorded by the buy everyday strategy, regardless of the holding period. As a result, based on these results, the bull flag strategy can accurately predict the movement of market prices, promptly signaling opportunities for price increases. This mechanism, in turn, improves the return associated with its investments, outperforming the market strategy.

As previously mentioned, for a p = 20 and Fit_k ≥ 3, the bull flag achieves its best performance when q = 20. In this case, in relation to the fraction of buys that resulted in a return greater than zero, this quotient is maximum when q = 40. However, it should also be noted that the existing figures for q = 20 and q = 40 are very close, which reinforces the results presented in Table 2. Likewise, Wang and Chan (2007) argue that technical analysis structured in bull flag conditional trading rules has an effectively higher degree of prediction than a buy everyday approach. Furthermore, the ratio between the number of buys with a positive return and the total number of buys reaches its maximum at 66.02% for the emerging market of Chinese Taiwan when q = 20 and 73.27% for the NASDAQ when q = 100 (Wang & Chan, 2007).

4.4 Robustness of empirical results for several nonoverlapping subperiods

The main objective of this section is to test the robustness of the results expressed in Table 2, particularly, the trading rule that had the best performance. To this end, the overall sample period is divided into five nonoverlapping subperiods of equivalent duration for the SSE index. Subsequently, in Table 5, these time horizons are investigated individually in terms of their average and annualized returns. Consequently, this information makes it possible to assess whether the bull flag's performance is due to the good results of a certain subperiod or if, on the contrary, it is explained by a generalized trend.

The five subperiods defined for the SSE are 01/02/1991 to 30/12/1996, 31/12/1996 to 24/04/2003, 25/04/2003 to 17/07/2009, 20/07/2009 to 12/10/2015, and 13/10/2015 to 31/12/2021. For all these subperiods, the empirical results inherent to the bull flag trading rule, characterized by a 20-day fitting window, 20-day holding period and maximum threshold, show positive average and annualized returns. It is also noteworthy that the returns from the buy everyday strategy are positive for all time intervals but on a much smaller scale.

According to Table 5, technical analysis achieves positive and significant annualized excess profits for the five subperiods of each index, relative to the market's trading strategy. Therefore, these results are statistically consistent with the data presented in Table 2, reinforcing its robustness. In fact, the excess profit found for this trading rule is the result of a greater predictive power translated during the entire sample period, an result that does not change when the investigation is carried out considering nonoverlapping subperiods. In addition, it is noted that subperiods with a better level of performance, related to higher annualized returns, are linked to a greater number of buy signals detected by the trading rules.

4.5 Performance of the “buying run” approach

According to Leigh et al. (2004), the empirical results presented in Tables 2 and 5 may be incorrect. It is argued that the statistical computation of applied significance tests is more likely to calculate probabilities that represent lower bounds rather than what those values might truly be. To this end, the authors identify two assumptions in the decision-making process with inconsistent dependencies regarding the use of the t-test as a mechanism to calculate the significance of the difference between the average returns of both strategies for all trading rules. First, the fact that the commitment to buy at the beginning of the next trading day is established after the market has closed on the previous day and, finally, the circumstance that the price change to any fitting window of p-days after a trading day is closely related to that same change for the next trading day. Consequently, to establish an upper bound, this article also suggests using probabilities measured through t-tests that only incorporate the first trading day of each buying run. This means that the remaining buy signals arising from the bull flag-conditioned trading rules are completely ignored. In fact, buy recommendations normally occur during consecutive days, which gives rise to a concept called buying runs.

Table 6 reveals the bull flag performance adjusted to the concept of buying runs for a 20-day fitting window and Fit_k ≥ 3. At this point, instead of the quantity of buy signals, only the number of buying runs that can be identified during the whole period under analysis is measured. For instance, there were 111 trading days that culminated in consecutive index purchases. Note also that the average run length is approximately 11 days. Furthermore, with the exception of the 20-day holding period, trading rules are capable of generating positive average returns for both indices and, in particular, it appears that the annualized return is higher the smaller the holding period associated with it. In turn, when compared with a market approach, the bull flag manages to produce significant annualized excess profits in four out of five observations. For a q = 20, there is an insignificant loss of performance of technical analysis relative to the buy everyday strategy of −7.99%. Thus, in general the empirical results presented in this section corroborate the result expressed in Tables 2 and 5, where trading rules seem to perform better than the market strategy, even in situations where buying runs are considered.

In the literature, when bull flag trading rules are conditioned to situations of buying runs on the Chinese Taiwan's stock market, technical analysis has shown to be an instrument with “great forecasting power” (Wang & Chan, 2007, p. 314). For instance, considering buying runs with an average run length of roughly 4 days, the excess return from the bull flag when q = 20 was 22.74% and with q = 40 it was 13.93% for the TAIEX. On the contrary, for both the NASDAQ and the NYSE, bull flag trading rules often produce insignificant excess profits when only buying runs are considered (Leigh et al., 2004; Wang & Chan, 2007).