Efficient Market Hypothesis

EMH, developed by Eugene Fama [3], assumes that all the information in the market at a specific moment is reflected in the prices and therefore market participants cannot consistently perform better than the average market returns on a risk-adjusted basis. However, empirical findings have shown that the EMH may be questionable. Hasan et al. [4] find inefficiencies in the Dhaka stock market. They notice that factors like return, market capitalization, book-to-market ratio and market value influence the share returns. Moreover, similar features such as thin trading, volatility, small number of securities listed and investors’ attitude towards investment strategy characterize DSE, as well as other emerging markets.

Several studies find volatility in the level of efficiency over time and among different markets. Alvarez-Ramirez et al. [5] observe that the efficiency degree of financial markets changes over time. The relative efficiency of the US stock market varied over 1929–2012, with a decline in the late 2000s induced by the economic recession. The most efficient period was 1973–2003. Another study showing that the degree of inefficiency is not constant over time is made in [6]. IRR/USD market was inefficient over 2005–2010 and this may be caused by the negative long-range dependence, meaning that if the exchange rate is up it is likely to go down in the close future. A similar result is revealed by Kim et al. [7]. They provide evidence that supports time-varying return predictability of the Dow Jones Industrial Average index over the period 1900–2009. While the market seems efficient during market crashes, economic and political crises induce predictability in returns. The efficiency of the Asian stock markets varies with the level of equity market development [8]. The developed emerging markets are found to be weak-form efficient, while the secondary emerging markets are characterized by inefficiencies.

Dragota et al. [9] could not reject the weak-form EMH for the Bucharest Stock Exchange by applying Multiple Variance Ratio test to random walk hypothesis. For the same market, Armeanu and Balu [10] tested the efficiency of the Markowitz model, emphasizing the benefits of portfolio diversification. Charles et al. [11] evaluated the predictability of exchange rate returns and found that while they are unpredictable most of the times, return predictability may appear with coordinated central bank interventions and financial crises. The Chinese stock markets efficiency is investigated in [12]. The results show that Class A shares, which are generally available for domestic investors, seem efficient, while Class B shares, eligible for foreigners, are significantly inefficient. Trolle and Schwartz [13], using a database of 11 years of data for crude oil and natural gas futures and options traded on NYMEX, found that it is difficult to explain the variation and the level in energy variance risk premia using systematic factors such as the returns on commodities or equity market portfolios or specific factors such as inventories.

Technical Analysis

Most automated trading systems use several indicators in order to generate purchase and sale recommendations [14]. One found that the best indicator for companies with high capitalization is RSI and the best for small capitalization companies is Momentum. Moreover, indicators that do not give many trade signals, such as Momentum, are more suitable when the transaction costs are high. One research assessed the performance of technical analysis in the US equity market for some technical industry sectors and small caps, over the period 1995–2010 [15]. Results show that the strategies are capable of outperforming the buy-and-hold strategy after adjusting for data-snooping bias and without transaction costs in the first half of the sample period. However, the same strategies are not able to produce superior performance over the second half. Success in the period 1995–2002 is tempered when introducing transaction costs. Moreover, the forecast of short-term return became weaker in the recent years, this being consistent with the EMH in the equity market. A positive performance of technical analysis is generated by applying moving average trading rules on 16 European stock markets over the period 1990–2006 [16]. A moving average trading rule combined with a strategy that at buy signals recommends investing in the stock market, while at sell signals recommends investing in the money market outperforms the buy-and-hold strategy over the sample period.

In [17] is found that one can achieve performing returns using trading strategies only if he has full information of the stock price change for the future. However, if the future information is not accurate, it can be useless in increasing profits. Moreover, a search in a strategy space to get high profit is impossible and this is based on lack of future information of a company.

Trading strategies have been mainly based on technical analysis in the commodity futures market [18], [19], [20] and foreign exchange market [21], [22], [23], [24]. Evaluation of the technical analysis’ performance in the equity markets has generally been done using market indices such as Dow Jones Industrial Average [25], [26], S&P 500 [26], [27], NYSE and NASDAQ [26], [28], [29] or Russell 2000 [26], [27], [29]. Technical analysis has evolved beyond filter and moving averages rules, now including psychological barriers such us resistance and support levels [30]; [31].

Genetic Algorithms

In recent years, individuals and companies have developed algorithms that try to improve profitability of trading rules. Genetic algorithms (GA) represent a class of optimization techniques that generate solutions to search problems and quickly adapt to changing environments. GA were developed by Holland [32] and they simulate the process of natural evolution. As the species evolve through genetic processes such as selection, crossover and mutation, GA create classes of solutions that evolve over some generations through analogous processes in order to generate one solution with the best fit to the specific problem [33]. Algorithms start by creating some strategies with specific parameters. In the following steps, they dynamically change their parameters in order to achieve higher profits.

In a natural evolution process, species change over time. New organisms are born by recombination between members. They inherit parents’ traits and are also influenced by environment conditions. The natural selection process comes from the fact that while the population grows, the organism need to struggle for resources. Therefore, only the organisms that possess well-suited characteristics for this struggle will bring more offspring to the new generation.

Holland [32] developed a way in which the natural evolution process might be imported into algorithms that offer solutions to search problems. GA are very suitable for managing financial markets because these represent a continuous changing environment and trading strategies need to adapt to the new conditions. The search problem is represented by finding a strategy that achieves positive excess returns when applied to a specific sample. GA generate many strategies and those well fitted (according to a specific function that can be mean return, Sharpe ratio or one that takes into account also environment conditions) are selected for passing in the new generation and for recombining to generate new strategies.

Mendes et al. [34] developed a system based on a genetic algorithm that optimizes a set of rules to obtain a profitable strategy to trade EUR/USD and GBP/USD. The system generates individuals defined by ten mandatory and optional rules, from which five of them decide whether opening a long/short position or not at current price in the market and the other five decide when to close an opened position. The rules contain 31 parameters that evolve in many generations through selection, crossover and mutation and, based on return and risk, the individual that had the highest performance is selected and tested in the next period. Results have shown that, considering transaction costs, the best individuals in the training series were often not able to achieve positive results in the out-of-sample test series. Dempster and Jones [2] created an adaptive trading system that uses genetic programming. They used USD/GBP spot foreign exchange tick data from 1994 to 1997. The algorithm is applied on out-of-sample data to provide new rules and a feedback system helps rebalancing the rule portfolio. The genetic algorithm is profitable even in the presence of transaction costs.

Another study about the performance of the genetic algorithms for FX markets has been developed in [35]. The authors show that the system often returned profit when the testing period was consecutive to the training period. They concluded that the success of the system depended on the similarity in the trends of the two periods. Also, genetic algorithms succeeded in finding performing trading rules for six exchange rates over the period 1981–1995 [36].

One bias that may appear when one tests a large number of strategies on the same sample is the data-snooping bias. As explained in [37], data-snooping bias appears when a set of data is used more than once for the purpose of model selection. Strategies that generate positive returns on a specific sample may be performing only due to luck and do not have a genuine predictive power. Therefore, when applied to a different sample, the results can be negative and investors may suffer important losses. A solution to this problem is the Bootstrap Reality Check developed by White [38] that relies on resampling the return series in order to give a reliable verdict regarding the genuine performance of the strategy.

The Individual Characteristics

In a genetic algorithm for setting a FX trading system, each individual is represented by a set of technical analysis rules. Each rule can be considered as a chromosome, while the parameters that define a rule are considered genes. Here we consider the individual as being defined by 6 chromosomes (rules) and 24 genes (parameters). The rules are divided in 4 rules that set the conditions for opening a position and the rest 2 rules are those that define the conditions for exiting the position. Each rule contains a Boolean gene that can activate or deactivate the rest of the rule’s genes.

Following, are described the rules (chromosomes).

Rules for Position Opening

Rule 1. Exponential Moving Average: EMA(n). Genes:

1. 1. Boolean_EMA –takes the values 0 or 1. Value 0 deactivates the rule, while value 1 activates it.
2. 2. Nr_periods_EMA, noted n, takes values between 5 and 90.

The rule generates trades as follows. If there is no current open position, then a long position is generated only if the close price is higher than EMA(n) and a short position is generated only if the close price is lower than EMA(n). If a position is currently open, then this rule is ignored.

Rule 2. Moving Average Convergence Divergence: MACD(p,q,m). Genes:

1. 3. Boolean_MACD – takes the values 0 or 1. Value 0 deactivates the rule, while value 1 activates it.
2. 4. Periods_short_MA, noted p takes values between 5 and 90
3. 5. Periods_long_MA, noted q - takes values between 10 and 100, with the restriction q >p
4. 6. Periods_signal_MACD, noted m - takes values between 5 and 25 and is the moving average of the difference between the short and the long moving average.
5. 7. Boolean_signal - takes the values 0 or 1. Value 0 sets the value for the signal to 0. Basically, it transforms the MACD in a simple rule of moving averages crossover. Value 1 activates the signal. For the 0 value is attached a probability of occurrence of 25%, while for value 1 the probability is set to 75%

The trades are generated by this rule as follows. Firstly, if a position is already open, the rule is ignored. If there is no currently open position, then, if the Boolean_signal has the null value, the rule takes into consideration only the short and the long moving averages. Therefore, a long position is opened when the short moving average is higher than the long one and a short position is opened otherwise. If the Boolean_signal takes the value 1, the rule proceeds as follows. If the difference between the short moving average and the long one is higher than the value of the signal, then a long position is opened, while otherwise is opened a short position.

Rule 3. Relative Strength Index: RSI (n). Genes:

1. 8. Boolean_RSI – takes the values 0 or 1. Value 0 deactivates the rule, while value 1 activates it.
2. 9. Periods_RSI, noted n, takes values between 5 and 50.
3. 10. Oversold_signal_RSI, noted p, takes values between 15 and 35.
4. 11. Overbought_signal_RSI, noted q, takes values between 65 and 85.
5. 12. Boolean_signal_RSI - takes the values 0 or 1. The use of this gene is described below.

The rule generates trades only if currently there is no open position. The trades are generated based on the Boolean_signal_RSI value as follows. When it takes the value 0, a long position is opened when the RSI value drops under p and a short position is opened when the RSI value rises over q. When it takes the value 1, a long position is opened when the RSI value rises over p and a short position is opened when the RSI value drops under q.

Rule 4. Filter(n). Genes:

1. 13. Boolean_Filter –takes the values 0 or 1. Value 0 deactivates the rule, while value 1 activates it.
2. 14. Periods_Filter, noted n, takes values between 1 and 15.
3. 15. Increase_signal_Filter, noted p, takes values between 50 and 100 pips.
4. 16. Decrease_signal_Filter, noted q, takes values between 50 and 100 pips.
5. 17. Boolean_trader_type_Filter - takes the values 0 or 1.

This rule respects the same restriction as the rest of the three opening rules: if there is already a currently open position, the rule is ignored. The trades are generated based on the Boolean_ trader_type_Filter value as follows. Value 0 signals a trend follower (enters long if the price increases more than p pips or short if the price decreases more than q pips). Value 1 signals that the trader will enter long if the price decreases more than q pips or short if the price increases more than p pips.

For the above, a great importance have the Boolean genes that activate or deactivate the rules: 1, 3, 8 and 13. When all of them take the value 0, this means that the individual will never open a position (because no opening rule is active). In order to avoid such situations, that have a probability of occurrence of 6.25%, we proceed the following way. If these genes take all value 0, then we randomly change the value for one of them.

Moreover, if two or more of these genes take simultaneously the value 1, then a position is opened only if all the active rules give the same trading signal (to buy or to sell). Therefore, it is more probable that an individual that has only one active rule to trade more than an individual that has all the rules active.

As important as the rules that define the conditions to open a position are the rules used to exit that position, in order to take the profit or to cut the losses. Following are described these rules.

Rules for Exiting the Position

Rule 5. Fixed exit levels (p,s). Genes:

1. 18. Boolean_fixed_exit –takes the values 0 or 1. Value 0 deactivates the rule, while value 1 activates it.
2. 19. TP_fixed, noted p, takes values between 15 and 150 pips
3. 20. SL_fixed, noted s, takes values between 10 and 100 pips

Opposite to the opening rules, the rules for exiting the position are active only when a position is opened. The above rule exits a long position if the price rises at least p pips (take profit) or drops at least s pips (stop loss). Accordingly, the rule exits a short position if the price drops at least p pips (take profit) or rises s pips (stop loss).

Rule 6. Trailing exit levels (p,s,q). Genes:

1. 21. Boolean_trailing_exit - takes the values 0 or 1. Value 0 deactivates the rule, while value 1 activates it. This gene is conditioned by gene number 18. If gene 18 takes value 0, then gene 21 takes value 1 and if gene 18 takes value 1, then gene 21 takes value 0.
2. 22. TP_trailing, noted p, takes values between 15 and 150 pips
3. 23. SL_trailing, noted s, takes values between 10 and 100 pips
4. 24. Trailing_level, noted q, takes values between 10 and 100 pips, under the restriction that q<p.

The above rule can be active only if a position is already open and rule 5 is not active. If a long position is already open and the price rises at least q pips, but less than p pips, the take profit and stop loss levels are updated, by increasing them with q pips. Continuing, if the price rises another q pips, but the new take profit level is not reached, then the stop loss and take profit levels are updated again, by increasing them with another q pips. The same procedure is followed until the stop loss is reached or during one period the take profit is hit. In the case of a short position, same methodology is used, with the difference that the stop loss and take profit levels are updated by decreasing them with q pips.

The Genetic Algorithm

After defining the individual, characterized by the rules for entering into position (based on the technical analysis indicators) and by the exit rules (take profit and stop loss), we proceed to the genetic algorithm, which consists in the following steps:

1. A population of 100 individuals is randomly generated.
2. We compute the profit or loss generated by each individual over the training period. Each individual is evaluated based on this measure.
3. The individuals are ranked based on the generated profit or loss.
4. The new generation is created by the following procedures:
   1. Elitism. The most profitable individual is automatically passed to the new generation
   2. Selection of parents. The probability of a given individual to become a parent for the new generation is based on its ranking. In order to increase the computational speed, we divided the individuals in 10 classes of fitness (profitability). First class contains the first 10 best-ranked individuals, the second class contains the individuals ranked 11th to 20th, while the 10th class contains the last 10 ranked individuals (Table 1). For the individuals of the same class, we attach the same probability. In addition, the probability is higher for classes that contain better-ranked individuals (e.g. the first class will have attached a higher probability than the 10th class).
   3. Crossover. Using the selection criteria described above, pairs of two parents are randomly chosen. Each pair of parents will create a new individual. In order to choose what genes from what parent will be passed to the new individual, a number n (where 1<n<24) is randomly generated. The new individual will receive the genes 1 to n from one parent and the genes n+1 to 24 from the other parent. The gene 21 will still depend on the gene 18. This way 80 individuals from the new generation are obtained.
   4. Introduction of migrants. In order to increase the diversity and to avoid fast convergence, we randomly generate 19 individuals in the new generation.
5. The new generation becomes the actual generation and the steps 2–4 are repeated.
6. We repeat the procedure from steps 2–5 until we reach 30 such iterations.

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Table 1. Probabilities of individuals to become parents.

https://doi.org/10.1371/journal.pone.0078177.t001

By executing the genetic algorithm, is obtained one individual, the result of the evolution. We repeat the genetic algorithm for 100 times in order to obtain 100 such individuals (sets of trading rules). Then, these 100 best individuals from the training period will be evaluated on the testing period. The evaluation procedure consists in assessing the profit or loss (expressed in pips) generated by the each individual in the testing period. The results obtained are attached in the Supporting Information file.

GA was developed under Eclipse Integrated Development Environment (IDE) version Helios Service Release 1 using Java Development Kit (JDK) version “1.7.0_21″. Three Java Archive (JAR) libraries have been added to the project: JFreeChart (http://sourceforge.net/projects/jfreechart/files/1.%20JFreeChart/1.0.14/) and JCommon (http://sourceforge.net/projects/jfreechart/files/3.%20JCommon/1.0.17/), both used to plot the cumulative profits of strategies and CSV_JAR ((http://www.java2s.com/Code/JarDownload/opencsv/opencsv-2.3.jar.zip)) used to read the data from comma-separated values (CSV) files.