2.1. The efficient markets hypothesis

Eugene Fama, proposed the EMH [4], suggesting that markets are rational and informationally efficient when the interaction among participants leads to an equilibrium situation where asset prices reflect all available information and quickly incorporate new information as it emerges into the price. These ideal trading conditions assume that no investor can beat the market by generating returns that could be considered unusual. Fama divides his hypothesis into three categories. Weak efficiency" is based entirely on the historical series of prices, where each asset sees reflected in its value all available information without the possibility of predicting future price behavior. The "semi-strong efficiency", in addition to the historical information, has the capacity to reflect all the new relevant information that becomes public. Finally, "strong efficiency", in addition to historical and public information, involves private information, which indicates that as efficiency goes from weak to strong, the possibilities of obtaining extraordinary and continuous returns over time are exhausted.

Now, in the stock markets there is evidence that asset prices do not follow the principles of efficient and rational markets, the three degrees of efficiency are not fully met as mentioned by Fama, the day-to-day stock market reflects those prices draw deviations to the guidelines previously proposed [9]. Such deviations are known as market anomalies since they are abnormalities that occur within perfect markets.

2.2. Market Anomalies

The EMH is antagonized by the model developed by Grossman and Stiglitz, which suggests that informationally efficient markets can never be efficient, i.e., that they are inefficient. This condition is the result of the imbalance generated by an asymmetry in information, which indicates that the flow of information does not reach all investors in the same way [3]. This means that not all participants are well informed and therefore prices reflect partial information, causing the profitability of each individual to vary according to the degree of advantage obtained in decision making. The model also clarifies that information travels with a lag from informed individuals to uninformed individuals, which means that the first can make more intelligent investment decisions.

Now, anomalies are the indicator of inefficient markets, everything that is not explained by the efficiency hypothesis is considered an anomaly, i.e., deviations that occur and do not follow the rules of perfect markets, some of them occur once, or a few times and disappear, while others are identified and recurrently remain over the years. According to Kuhn [10], an anomaly is systematic evidence of prolonged episodes with a regularly recurring structure and does not respond to isolated events, however, it does not find consistency with the basic theory. For their part, Tversky & Kahneman (1986) defined an anomaly as a deviation to currently accepted paradigms, which is too widespread to be ignored, too systematic to be dismissed as a random error and too fundamental to be accommodated at the cost of weakening the normative framework [11].

Therefore, if an unknown phenomenon occurs once or very rarely, even if it is initially classified as an anomaly, this condition is only ratified if it meets certain characteristics. According to Tua [12], for an anomaly to be considered an inefficient market sample, it must meet two requirements: persistence and opportunity to be exploited. Anomalies are classified into three categories, fundamental, calendar and technical. A fundamental anomaly is an irregularity where the return on the securities differs from the actual valuation of the asset. Calendar anomalies are those where the occurrence of certain events is directly related to specific times of the year and technical anomalies correspond to phenomena that are identified mainly through asset price charts where the aim is to predict future behavior based on events that have occurred with historical prices.

Classical authors have shared the research carried out in different stock markets delving into the subject of market anomalies and agree that the series of phenomena observed and analyzed in the different trading parks cannot be explained by market efficiency since they are unusual occurrences of prices. From these authors some early research emerge, from the calendar line we find Gultekin and Gultekin [13], Tversky and Kahneman [11], Ariel [14], Agrawal and Tandon [15], Smirlock and Starks [16]. For fundamental anomalies, Fama and French [4] and for technical anomalies, Brock, Lakonishok [17] stand out.

Gultekin and Gultekin [13] in their study found the existence of seasonality in the main stock markets of industrialized countries. Seasonality refers to the fact that there is a clear difference in average returns measured on a month-to-month basis. They used parametric and non-parametric methods for testing, but since the result between the methods was similar, they decided to report them with the non-parametric tests. The seasonality anomaly found was generally reflected in a significantly large average return at the end of the fiscal year.

Ariel has a direct impact on calendar anomalies [14], determining anomalous behavior for stocks, since they exhibit positive average returns only during the first half of the months, and show zero returns during the second half. His study focused on the U.S. stock market from 1963 to 1981. In turn, Agrawal and Tandon found two calendar anomalies, known as "the turn-of-the-month effect" and "the turn-of-the-year effect" [15]. In the first, during these four days that mark the change from one month to another, the yield is higher overall than that of the remaining days of the month. For the second anomaly describes the increase in stock prices in the last week of December and the first week of January.

From the point of view of technical anomalies, two of the most well-known technical analysis strategies, the moving average and the trading range breakout [18]. Applied to the Dow Jones between 1897 and 1986, they performed a statistical analysis with the bootstrap technique. They applied these tests on four models: the random walk, the AR (1), the GARCH-M and the exponential GARCH, concluding that the returns obtained when applying these two trading strategies with these models were not consistent. Sullivan took other popular analysis techniques, such as channel breaks, moving averages, supports and resistances, trading volume, chose measurement parameters for each, the objective was to establish as many rules as possible and determine which was the most profitable over a 100-year time span (1897-1996), and used the Dow Jones index [19]. They used Bootstrap to obtain the data that allowed them to quantify the performance of about 7,850 variables. The five-day moving average was the best rule with a 17.2% average annual return.

2.3. Nasdaq-100 Index

The technology Nasdaq-100 (NDX) is one of the three most representative stock indexes of the North American stock market, along with the SP500 and the Dow Jones. It brings together 100 of the largest non-financial companies in terms of market capitalization, both domestic and international [19]. No company in the index can have a weighting of more than 24%. The Nasdaq-100 is an index concentrated in the technology sector and it is there where the world's largest companies shine, it is also integrated by other large industries such as healthcare and consumer services. It is the world's fastest growing stock index by large capitalization, and since the 2008 crisis it has outperformed the SP500 index with higher annual returns and volatility (Nasdaq website). Observing that technology presents accelerated growth in the world and that its influence on companies is being decisive in obtaining better results and confirming through volatility calculations, the future of the Nasdaq-100 index is chosen to develop this research. Fig. 1 shows the composition of the Nasdaq-100 index by industry, a marked participation of technology companies is evident, which currently weigh 39%, and also shows an outstanding collaboration of the companies that make up the technology industries such as consumer services, health and consumer goods with weights of 24%, 14% and 11% respectively.

Figure 1: Nasdaq-100 Index Composition by Industry.

Source: Own Elaboration with data from Bloomberg (2020).

2.4. Strategy based on the Fast-Slow Pattern

The graphic pattern under study arises from the continuous observation of the price behavior of various financial assets, and it is through constant analysis that rules or guidelines have been defined that the retail trader must abide by and execute in order to obtain results close to or similar to those that the research will reveal. The pattern is also the response to the non-institutional trader's need to have a competitive advantage when positioning himself ahead of the market. The operator will have in front of him a future price chart of the Nasdaq-100 in the form of Japanese candlesticks, which will take direction to make investment decisions through the guidelines that will be detailed below, these allow the trader to begin the construction of his work chart that will be interpreted as he identifies that the rules of his action plan are being created.

The trader who wishes to use the strategy based on the short-term Fast-Slow Pattern (hereinafter PFS), should identify and execute the purchase or sale of the Nasdaq-100 index future at the moment when the following three rules occur strictly and in order:

1. Identification and marking on the chart of the trading zones, which correspond to: the maximum and minimum price of the most recent Asian, European and American sessions, as well as the highest and lowest price of the trading day of the immediately previous day.

2. Formation of the Fast-Slow pattern over at least one of the established trading zones (rule 1).

3. Formation of one of the established Japanese candlestick patterns, which will be the trigger for market entry.

It is important to emphasize that the essence of the strategy is the formation of the Fast-Slow pattern, however, this will only be important when it is formed over one of the established trading zones, therefore the zones are the first element (rule 1) to be identified and marked on the asset's price chart.

2.5. Trading Zones and Trading Sessions

Any price set by the financial asset can be negotiated (buy or sell), but a trader and especially a retailer cannot participate in the market at any price, that is to say, he cannot afford to buy and sell at the slightest variation in the quotation. Any trader using technical analysis will establish "his zone(s)" where he will seek to benefit from the fluctuations of the asset of his choice and from this choice derives much of his success. A trading zone (base zone) refers to a range of prices (several consecutive prices) and not to a specific one, this means that the final signal for the trader to participate in the market can occur at any price in the range. The size of the range is discretionary chosen by the trader. This study proposes to consider trading zones of which no previous research was found, and according to empirical evidence has an interesting potential to be explored.

Traditionally, the strategies that have within their components the identification of supports and resistances use the "price" factor for their plotting, that is, they will find for a certain reason a negotiation zone (price range) that allows them to define their entry to the market. The proposal presented in this document uses the price variable in a secondary place, the "time" variable has the leading role, since it is the time of the stock market day that will set the initial guideline for the drawing of the zone.

A trading day starts at 00.00 GMT and is divided into three trading days, the Asian, the European and the American. The Asian trading day starts and closes between 00.00-7.00 GMT, which is the trading hours when most of the stock exchanges of that continent are actively trading, and the other two sessions work in the same way, followed by the European stock exchanges from 7.00-13.30 and the American stock exchanges, with United States at the top, that start at 13.30 (summer time) or 14.30 (winter time), finishing operations at 20.00 or 21.00 depending on the time of the year. The period from 20/21.00-24.00 is considered a "dead" time as there is little or no trading activity. Each trading session is of high importance as it involves frantic competition between all types of participants. The listed time slots correspond to general trading ranges for each continent and to the opening and closing times of most stock exchanges, although there are some that, depending on their time of day, share activity with stock exchanges on other continents.

Fig. 2 shows the fluctuation of the price of the asset within the schedules of each of the sessions, which will mark and define clear and objective levels that will be used as trading zones, which correspond to the maximum and minimum prices of each band, i.e., each session will mark two zones. Also, the highest and lowest quote of the previous trading day are taken into consideration. According to the above, the trader will have eight potential objective trading zones in every moment, four tops (dark circles in the figure) and four bottoms (light circles in the figure). The most recent session of each time frame will always be used.

Figure 2: Trading Zones and Trading Sessions.

Source: Own Elaboration with Ninja Trader 8 Platform.

Having stated the above, the first rule of the strategy will be to have the potential trading zones defined at all times, and it will be on them that the observation of the price of the Nasdaq-100 index futures will be focused.

2.6. Fast-Slow Pattern (PFS)

The essence of the PFS focuses on the "time" that the price takes to develop the movements that make it up. For a correct understanding of the graphical pattern under study, it is important to clarify that the historical price chart of a financial asset is composed of two variables, time (X-axis) and price (Y-axis). Their characteristics are described below:

1. It is composed of two movements, which will always be comparable to each other and which go in opposite directions, that is a first upward movement (A-B) and a second downward movement (B-C), the order of which can be reversed, bearish-bullish.

2. The formation and identification of the PFS must necessarily take place over a trading zone, that is to say, it starts (point A) and ends (point C) its formation over a base zone and it is there where its validity to be traded is determined. It will not be valid when it is formed in zones other than those indicated.

3. In relation to the time variable, the displacement or segment B-C must be formed at least twice as long as it takes for the segment A-B to be formed. For example: A-B one hour, B-C two hours or more.

4. In relation to the price variable, the two advances will be of similar sizes.

In Fig. 3, the dynamics of the bullish and bearish PFS is observed, each scheme originates from point A which is located in a base zone, then moves in one direction until reaching the highest or lowest point (B), and thus concludes the first advance, finally it moves in the opposite direction to C, in at least twice the time it took the first journey, if it is triple or more, the empirical evidence shows a tendency to better results. So, in this way, the second rule of the proposed strategy is configured.

Figure 3: Fast-Slow Pattern Bullish and Bearish.

Source: Own Elaboration with Ninja Trader 8 Platform.

2.7. Japanese Candlestick Formation

The Japanese candlestick (consisting of body and shadow) is one of the many ways to graphically represent the price of financial assets and the most popular among technical analysis traders. Since the focus of the research is the short term, the analysis of this rule will be performed on a chart with a periodicity of two minutes, i.e. each time this period elapses, a new candlestick will be drawn. The various price fluctuations determine the shape and size of each candlestick; therefore, it is essential to define the variants to be used in the strategy. A candlestick by itself does not transcend, that is why in the first two rules it is assigned a specific context.

The Japanese candlesticks constitute the third guideline of the strategy. These become the "trigger" that determines the "ideal" moment to execute the plan. The candles will only have protagonism when the two initial rules have been fully complied, that is, they must be formed in a trading zone and when the PFS is completed at point C, it is just at that moment that one of the formations must be drawn, if it is achieved, the trader must enter the market according to what the strategy determines, in case the first two patterns are generated and the candlestick pattern is not obtained, the entry will be canceled.

The most influential characteristic for identifying an adequate candle formation is its dimension or length, it means that this aspect is decisive for the validity of rule three. In general terms, the triggers are patterns that are characterized by outstand due to their size with respect to the preceding candles, when they do not stand out they are considered invalid. The study proposes formations with variants for the two directions that a market can take, when reference is made with respect to a bullish pattern it is indicated that the direction that is intended to be projected is ascending and the opposite is the case in a negative one. This document present three types of patterns: Envelope, Star and Pin Bar.

Enveloping Pattern: Consisting of two candles. It is characterized because the length of the body of the second candlestick wraps the body of the previous candlestick in its entirety. The two candles must have opposite directions.

Star Pattern: It is formed by a minimum of three candles and a maximum of five. It is characterized because the first and last candles go in opposite directions and their sizes are significant, the intermediate one(s) are generally of small length.

Pin Bar Pattern: It is composed of a candlestick. It is characterized by having a large shadow (upper in bearish pattern and lower in bullish) and a generally small body.

With the candlestick formation, regardless of which type occurs, what the trader projects is that the market generates a "twist" point, that is, in the context that the market goes in a downward direction and reaches point C of the PFS, when the candlestick pattern is drawn in that area, it causes a turn in the direction and from that moment begins a bullish path, likewise, it applies to a change from bullish to bearish. Fig. 4 illustrates the three types of formations for bullish and bearish market turns, equally, several examples are observed for each variant, the above plurality is important sinc markets are dynamic and small changes do not indicate that a formation is distorted.

Figure 4: Japanese Candlestick Patterns, Bullish and Bearish.

Fuente: Own Elaboration with Ninja Trader 8 Platform.

2.8. General Rules of the Strategy

In addition to the three main rules that make up the proposed strategy, there were other general rules that were used in the development of the strategy, which are listed below:

• Stop Loss: For buy/sell transactions the stop loss was placed four ticks (minimum price variation) below/above the minimum/maximum price of the candlestick pattern that generated the entry. Dynamic stops were not considered.

• Take Profit: The minimum profit ratio over risk that was handled in the totality of transactions is 1, i.e., profits of less than one unit are not accepted when the risk assumed is one unit.

• Entry at End of Session: No transactions were opened thirty minutes or less before the end of any of the trading sessions analyzed.

• News or Events: No trades were taken when there were sixty minutes or less to the release of U.S. unemployment rates or interest rates, as well as speeches of the nation's and Federal Reserve´s presidents. For other macroeconomic releases of lesser impact, no trades were taken when there were fifteen minutes or less before their release.