Evolutionary Computing Applied to Stock Market using Technical Indicators

Transcription

1 Evolutionary Computing Applie to Stock Market using Technical Inicators Ariano Simões, Rui Neves, Nuno Horta Instituto as Telecomunicações, Instituto Superior Técnico Av. Rovisco Pais, Lisboa, Portugal. ABSTRACT This paper proposes a new a meium/long term investment strategy for stock markets base on a combination of Simple Moving Averages Crossover (SMAC) an Moving Average Derivate (MAD). This strategy is compare with the Buy an Hol, with the Moving Averages Crossover, an with the Moving Average Derivate strategy. The experiments show that the combination of SMAC an MAD outperforms the results of each strategy iniviually. The presente approach has an average return of investment of 9.0%, compare with the 2.6% return of the Buy an Hol, for the S&P500, FTSE00, DAX30 an NIKKEI225, between 2004 an General Terms Algorithms, Economics, Experimentation, Performance. Keywors Optimization, Technical Analysis, Evolutionary Algorithms, Financial Analysis, Moving Average.. INTRODUCTION The stuy of profitable traing rules in the stock market constitutes a wiely known problematic in financial markets. Although the existence of those rules still generate great controversy for many economists an acaemics [6]. On the other han, investor, traers, an other stakeholers of financial an investment firms, with large experience in the stock market, claim that it is possible to have excessive returns (compare with the Buy an Hol) using algorithmic traing [][4]. One investment technique commonly use is Technical Analysis, which forecasts the price of stocks base only on the price of the stock an the volume trae in the past. Momentum strategies base on the continuation in the evolution of a stock price on their recent history [0][8], have prove to be consistently more profitable than the inexes where those stocks were inclue. The founation of Technical Analysis is the Dow Theory, written by Charles Dow, founer of Wall Street Journal where the main ieas of the Dow Theory where publishe, in the en of the XIX century [][3] The main iea of this Theory is that stock markets move accoring to trens. These trens are more important with the longer the time-frame they ha been active, an can overlap. This means that in a large uptren small ownsizes of short term can occur, but the tren is not over until strong signals of reversal occur. In this paper we will concentrate on ientifying meium to long term trens. Although a theoretical explanation of why these meiums to long term trens occur is not the focus of this paper, several causes can be pointe out. The first an probably the more important is the economical cycles theory, which states that the economy has long perios (months or years) of growth followe by perios of ecline or stagnation. With this in min an knowing that the stock market reflects not only the current performance of companies, but also the expectations about the future it is possible to ientify a correlation between economic cycles an stock market cycles. Aitionally to the economic cycles are other factors that can contribute to the price fluctuation like share buyback, which mainly occurs when companies generate large profits (it woul be a o iea for a company in financial nees, to allocate money to stock repurchase), which implies that share buy backs are one most of the time in a uptren economical cycle, when the company generate excess profits. Other important factor is the money flow of the stock market (especially in countries like the U.S.A. where most citizens have investments in the stock market). The effect of the money flow can be foun even in companies or mutual funs with goo performance, as the aversion to risk increases to the public in the beginning of the Bear Markets, people ten to reirect their capital to more secure investments like bons, eposits (or even commoities as occurre in this Bear market). This ecapitalization of the stock market (an because the number of shares is the same) leas the stocks own following the simply rule of supply an eman: supply increase (as people try to sell) an eman stagnate or even ecrease (people change to ifferent markets). Genetic Algorithms are optimization techniques base on the principles of natural evolution. In [7] is provie a formal stuy of this subject. This paper presents a genetic algorithm for optimizing Technical Inicators parameters in orer to maximize returns. Other GAs have been previously use to optimize technical inicators parameters, in particular [7] an to evelop investment strategies base on technical inicators [] [8] [9] [20] [2]. In this sense, we propose the use of a GA to obtain the set of inicators an their parameters, which shoul be use to preict a aily market value. Initially we have applie GAs to fin the more suitable parameters of the SMAC an MAD inicator for meium an long term traing. After that we combine both strategies, so that a buy or short-sell signal is only mae when both strategies agree, again a GA is use to optimize the four Technical Inicators Parameters of the two strategies at the same time.

2 The next section will iscuss the relate work on the Genetic Algorithms an various traing strategies currently use in Technical Analyses. Section 3 explains the system architecture an the investment strategies use in this paper, the markets an years use to test those strategies. Also in this section the overall escription of the GA is shown, an the fitness, selection, crossover an mutation functions use. In section 4 the results are presente an a highlight of the most relevant results is mae. In section 5 the conclusions of this stuy are shown. 2. RELATED WORK One of the most use an olest strategies to ientify trens is the crossing of Moving Averages. This strategy consists of having two Moving Averages, one of long term, an other of meium term. A buying signal is generate when the Meium Moving Average crosses up the Long Moving Average, whenever the cross is ownwars a selling signal is generate. This strategy has been stuie by [2] an by []. This stuies conclue that from 90 to 2000 the Crossing of the Moving Average perform better than the Buy an Hol strategy, except for the perio from 980 to 2000 where the market exhibite a regular uptren, an no excess profits where possible as reporte in [5]. More complete stuies of other Technical Inicators has been mae, like the one in [3] who stuies the profitability of 76 Technical Inicators with robust results for some inicators. Many papers have been recently publishe on the use of GAs to optimize technical inicators like [7], which use GAs to optimize the parameter of a single Technical Inicator, the MACD (Moving Average Convergence-Divergence) with 3 parameters, an an extra parameter for the history winow size. Another solution base also on optimizing Technical Inicators parameters is the one use in [], where the chromosome is compose by the MACD, RSI an history winow size, also a comparison between single an multi-objective is mae. Besies GAs others optimization techniques has been applie to this area of stuy, like neural networks in [2], where the neural network uses for the inputs the price, volume, interest rate an foreign exchange rate. Also other more unexplore approaches like pattern recognition as been trie in [5] which explores a more visual approach to Technical Analysis. Other technical information has been stuie. The influence of volume as a preicting tool was stuie in [4] [6], the inicator is base in the suen increase of the volume to generate a buy signal. This stuy concentrates in the optimization of technical traing rules which has not been yet teste with GAs, like the SMAC an MAD strategies, an also, combines these two strategies in one chromosome trying to achieve better an soli returns than with the solo strategies. 3. METHODOLOGY The propose system consists on a Genetic Algorithm couple with a market return evaluation moule base on the return of the strategies in ifferent markets in specific time-frames. 3. SYSTEM ARCHITECTURE Figure System Overall Architecture. The complete process can be summarize as: The user starts by specifying the markets to analyze an next chooses the Technical Inicators use in the strategy. Finally, the user chooses the train an test perio. Afterwars, the Genetic Algorithm Kernel runs several number of times, optimizing the parameters of the strategy for the markets an training perio chosen. Finally for each run of the GA, its return on the test perio is calculate. Detail info is shown to the user isplaying the optimize strategy an the return for each market in the test an in the training perio. 3.. MODULES DESCRIPTION This section presents the overall escription of each moule an their main responsibilities. Technical Inicators: This moule is responsible for the creation an management of the technical inicators use by all the strategies. This unit calculates the value of the technical inicators for a specifie inex an time perio an stores it s calculation for later reuse. This moule is also responsible for calculating the strategies ecisions (if it shoul buy, short-sell or be out of the market). Train an Testing Perios: The Time Perio moule controls the time components of the Stock Inexes, in this unit the user can specify which time perios the Genetic Algorithm will use for optimization, an which time perio shoul be use for test, an its configuration (continuous, sliing winow, an others.) Stock Market Inexes: This moule is responsible for loaing the stock market inexes from the source (a.csv file) an giving access to the ata to the other parts, the store information inclues the close value, the open, high, low an the ate. Market Return Evaluation: In this block it is calculate the return an other metrics for evaluating the investment strategy (like the Sharpe Ratio, number of traes execute, ROI, an others.). The results can be evaluate

3 for several types of metrics, yearly or monthly an with simple or compoun average. Genetic Algorithm: The Genetic Algorithm Moule is the most important because it is the one who oes the core functions of the system. This moule uses ata from all the other moules to calculate the perfect strategy with the Technical Inicators specifie by the user for the specifie markets, in the training perio. The crossover is a onepoint crossover, an parents are chosen base on a roulette-wheel selection. Optimize Strategy: Finally this moule is responsible for showing the user the result of the optimization. Besie the best strategy obtaine, it also shows results from various runs of the Genetic Algorithm, so the user can test the average results an robustness of the solution. For each strategy it shows the return in the test an training perio, the yearly return an the Sharpe Ratio. 3.2 TRAIN AND TEST DATA SET The time perio chosen for training was from January 993 to 3 December 2003, eleven years of aily ata. This time perio was chosen for two main reasons. The first one is that the time perio shoul be big enough to be statically relevant an to avoi any kin of bias ue to a small sample perio. Seconly, the market ata shoul be similar in nature to the markets where the system is going to be applie. With the constant changes in the stock market in the last years, like online traing, algorithmic traing, high volume traing, an with the increase in the spee an amount of exchange information an short elays for new information to reach an change markets evolution, early an mi 20th century ata may be meaningless to current moels to preict stock markets behavior. The testing perio was from January 2004 to 3 December 2009, six years of testing. This perio was chosen to test the GAs in an almost real situation, simulating that the investor ha run the training in 993 to 2003, an applie these strategies until the present. Also, the fact that the markets ha been very stressful an that this has been a very ifficult perio for all the operators in the market, meaning that fining a successful strategy in this type of market is not an easy task. The markets teste where the S&P500 (USA), FTSE00 (Englan), DAX30 (Germany) an NIKKEI225 (Japan). They represent the main inexes of the main evelope economies. These are markets that behave in a stable an orerly fashion for long perios. They also inclue several big companies in ifferent sectors which gives an extra stability to them. They react mainly to company profits an major economic events. They also have high volume of transactions an are ifficult to manipulate ue to high stanars of regulation an size. 3.3 TECHNICAL INDICATORS For the strategies use the Simple Moving Average will be applie, which can be calculate using the following expression (): SMA n ( ) = n t= n+ P( t) () Where n is the time perio (in ays), is the ay where the moving average is calculate, P(t) is the value of the Inex at ay t. An example of this inicator for a SMA of 200 ays is presente in Figure 2. Figure 2 - Evaluation of the SMA(200) from 2000 to 200 in the S&P 500. The first strategy to be teste was the Simple Moving Averages Crossover (SMAC) which is compose by two Moving Averages (MA) with ifferent time perios. One of the MA is a long term MA, an the other is a short term MA. A buying signal is generate whenever the short term MA crosses over the long term MA, an a sell signal is generate whenever the short term MA crosses uner the long term MA. Following this strategy the investor will buy (or maintain) the Inex whenever Eq. (2) is higher than zero, an will short sell whenever Eq. (2) will be lower than zero. SMAC MAD n, g s, l ( ) = P( t) P( t) s t= s+ l t= l+ ( ) = t= n+ P( t) ng Where l is the time perio use for long term, s the time perio for short term, an P(t) the value of the Inex at ay t. An example of this inicator for a SMAC of 200 an 50 ays is presente in Figure 3. Another inicator that will be use in this paper is the Moving Average Derivate (MAD). It is an extene version of the MA Change escribe in []. In the original version it is calculate by subtracting e value of the current MA with the value of the MA in the previous ay. In mathematics this is simply the secant to the MA curve in the last two ays. In this way the Derivate of the MA can be calculate base on the efinition of Secant of the MA (Eq. 3). Where n is the time perio use to calculate the MA an g is the istance between the two ays to calculate the secant (the original strategy consists of a fixe g with value ). t= n+ P( t g) (2) (3)

4 market or in short-sell, an issues a short-sell signal when both inicators avise to short-sell. Other inicators were teste like Relative Strength Inex (RSI) an Moving Average Convergence Divergence (MACD) [3]. The RSI inicator is a momentum oscillator use to compare the magnitue of a stock s recent gains to the magnitue of its recent losses, in orer to etermine overbought or oversol conitions. The formula use on its calculation is: 00 RSI n ( ) = 00 Ups ( n) + Downs ( n) (4) Figure 3 - Evaluation of the SMAC(200, 50) from 2000 to 200 in the S&P 500. Figure 4 - Evaluation of the MAD(200, 50) from 2000 to 200 in the S&P 500. In this way the value of the MAD reflects the current value of the Inex. As mentione the strategy consists of buying when the MAD is larger than zero an short sell when it is less than zero. The strategy introuce in this paper is the MAD (Moving Average Derivate) an consists on having only one MA. The iea behin this strategy is to buy the Inex when the Derivate of the MA is positive (meaning that the Inex will go up), an short sell when the Derivate is negative. An example of the calculation of this Inicator with the parameters, 200 for the long Moving Average, an 50 for the gap, can be seen in Figure 4, where is shown the evolution of the S&P 500 from 2000 to 200 an the respective values of the MAD. This inicator gives a buy orer when the MAD crosses the zero in an ascening slope an a sell orer when it crosses the zero in a escening slope. Besie this two inicators a new inicator is create, calle SMAC & MAD that inclues the two inicators mentione above (SMAC an MAD) that signals a buy when both the inicators are buying, oes nothing when one of the inicators is out of the Where n is the time perio (in ays), is the ay where the inicator is calculate. Ups is the sum of gains over the n perio an Downs is the sum of losses over the n perio. When calculate, the RSI line forms a signal between 0 an 00, which specifies etermine overbought or oversol conitions when its value is above or below specific levels. The Moving Average Convergence Divergence (MACD) inicator constitutes one of the most reliable inicators within the market. It is a tren following momentum inicator that exhibits the relation between two istinct moving averages. Essentially, it efines two lines; the MACD line which correspons to the ifference between a 26-week an 2-week EMA an a trigger line which correspons to an EMA of the MACD line. The ifference between the former lines allows us to obtain a histogram which can be easily analyze an offering us perspectives on price evolution PARAMETERS OF TECHNICAL INDICATORS After efining the strategies it is necessary to efine the parameters to use both in the SMAC an in the MAD strategies. As both strategies have two parameters, with similar meanings: The first parameter is similar to both strategies, the time perio of the long term MA. The secon parameter in one strategy is the time perio of a short term MA an in the other strategy is the istance between the two points use to calculate the secant. Both this parameters shoul be a meium term perios. The new Inicator (SMAC & MAD) has four parameters, two for the SMAC an two for the MAD. These parameters represent the parameter of the unerlying strategies. 3.4 GENETIC ALGORITHM KERNEL 3.4. GENETIC ENCODING The chromosome create must represent the Technical Inicators use, in this way the SMAC chromosome is represente by two genes, one for the shortest MA other for the longest MA in ays (natural numbers), the interval of this values is between an 250 (this value is above the largely use MA for long term analysis: 200 ays). The same rule applies to the MAD chromosome, where one of the parameters is the gap an the

5 other the number of ays of the MA. In Table it is shown a representation of a possible chromosome for the SMAC & MAD chromosome (which inclues both the SMAC an MAD genes): Table - An example of a Chromosome SMAC MAD Chromosome FEATURES OF THE GA The Genetic Algorithm use for the optimization uses a stanar optimization proceure. The selection of iniviuals for crossover is chosen base on a roulette wheel selection (but only the best half of the population enters the selection process), an the probability of being chosen is equal to the ratio: iniviual fitness function / Sum of fitness of all iniviuals. Each iniviual can be chosen any number of times for crossover (the only exception is that an iniviual cannot be chosen to crossover with himself). The crossover is a one-point crossover, each breaing generates the two possible istinct chilren an inclues them in the population. In the chromosome of only one inicator (SMAC or MAD) the chilren are create by swapping the long an shortest MA ay. In the SMAC & MAD chromosome the chilren are create by swapping the 2 genes that represent each Inicator (the first chilren takes the SMAC genes from parent A, an MAD genes from parent B, an the secon chilren the other way aroun). The fitness function use is the average return of the iniviual for the 4 Stocks Inexes chosen, uring the years of the train (993 to 2003). Figure 5 - Histogram of returns of the MAD Chromosome, from 2004 to RESULTS The optimization proceure escribe above was run fifty times for each approach namely, MAD, SMAC an SMAC & MAD, aitionally 50 ranom strategies were evaluate (The ranom strategy consists in each ay eciing a ranom trae: long, shortsell or o nothing, each with one thir chance of occur.). In each run the best iniviual obtaine was evaluate for the test perio (2004 to 2009) for the yearly return of the average of the 4 Inexes. The histogram for the returns of the 50 runs for each chromosome is presente in Figure 5 an Figure 6 (values are in % of occurrences in the 50 runs). In Figure 7 although the percentage go only to 50% for better perception of the other values, the Buy & Hol as 00% on the 2.5 column, an the ranom strategy has 88% on the less than 2.5 column. As we can see in this figures, all the chromosomes beat the Buy an Hol an the ranom strategy, this confirms the valiity of the Technical Inicators use. Figure 6 - Histogram of returns of the SMAC Chromosome, from 2004 to 2009 Figure 7 - Histogram of returns of the Buy & Hol, Ranom SMAC& MAD, an SMAC & MAD, from 2004 to 2009

6 Aitionally we can see that the optimize chromosomes have better results that the ranom chromosome that as an almost uniforms istribution along all the return values. In the other han the SMAC has a curve similar to the Gaussian curve exhibiting pronounce tails. The MAD accumulates aroun two values: 7.5% an 9.5%. An finally the SMAC & MAD Compost Chromosome is very similar with a Gaussian curve, which proves that this strategy has the most soli results. The etaile statistics can be seen in Table 2. Table 2 - Statistics of the returns in the test perio for the ifferent strategies. Best: Average: Meian: Worst: Buy & Ranom SMAC SMAC MAD Hol Strategy & MAD 2.6% 0.% 0.5% 8.58% 0.2% 2.6% 8.5% 8.7% -.0% 9.0% 2.6% 8.9% 8.0% -.% 9.2% 2.6% 6.3% 6.8% -7.33% 7.3% In this table is possible to see that the Buy & Hol an the Ranom Strategy have the lowest Worst, Meian, Average an Best Values. An that the SMAC & MAD have Average, Meian, an Worst value beating all the other strategies (an the Best value is not far away from the first). This means that using the optimize SMAC & MAD, not only the expecte profit is better, but the possibility of a ba return happen uring the test perio has a low probability of occur, an even if it occurs the return will not be too low (the worst return of the SMAC & MAD in 50 runs in the test perio is 7.3%). Results incluing the use of RSI an MACD were not inclue since they performe worse than using only the SMAC & MAD. The reason is that RSI an MACD are short term inicators, an in this strategy we are looking for a meium-long term time perio. This teaches a precious lesson that is not by incluing many inicators that a better strategy can be prouce. In reality using only two inicators performe better than using the four inicators. The reason can be explaine by over fitting in the training perio that oes not translate to goo results in the testing perio. 4. RETURN ON INVESTMENT In the next table we can see the yearly average return in the test perio of the three best chromosomes foun in the training perio, with the respective number of traes, contrary to the return (which is annualize), the number of traes isplaye is the average number of traes for the four Inexes, uring all the testing perio (6 years). In this table we can see that the MAD & SMAC strategy have the best, the secon an fourth best results. This means that this is the most optimal an robust strategy, because it s the one who maintains the best results from the training perio to the testing perio. Table 3 -Yearly average return an Total Number of Traes of the various strategies teste from 2004 to 2009 R SharpeRatio = σ R f Average Return Total Nº Traes Buy & Hol 2.55% SMAC (227, 20) 8.34% 8 SMAC (225, 20) 8.27% 9 SMAC (222, 20) 7.73% 0 MAD (0, ) 8.5% 6 MAD (2, 0) 8.0% 5 MAD (2, ) 7.52% 4 MAD(86, 45) & SMAC(202, 93) 9.37% 0 MAD (08, 20) & SMAC(206, 95) 8.38% 2 MAD(2, ) & SMAC(242, 28) 8.27% 4.2 SHARPE RATIO The Sharpe Ratio is a measure that was create by Nobel Prize William Sharpe, to measure the rewar-to-variability ratio of a traing strategy [9]. This measure allow to compare two strategies with ifferent returns, an see if the aitional return of one strategy is ue to applying a more risky strategy, or to a smarter investment strategy. The Sharpe Ratio formula is (5): Where R is the average return of the strategy, R f is the risk free rate (normally the rate of the US treasuries security). An σ is the stanar eviation of the strategy. The risk free rate must be on a treasury security with the same time-frame that the investment strategy, since we are consiering 6 years, the more suitable security is the 5 year Treasury Note. A secure investment woul be buying a 5 year Treasury Note on 2004 an with a 3.36% yiel. Table 4 - Sharpe Ratio of the various strategies (5) Average Sharpe Ratio Buy & Hol SMAC (227, 20) SMAC (225, 20) 0.53 SMAC (222, 20) MAD (0, ) MAD (2, 0) MAD (2, ) 0.34 MAD(86, 45) & SMAC(202, 93) MAD (08, 20) & SMAC(206, 95) MAD(2, ) & SMAC(242, 28) 0.458

7 Figure 8 Evolution of the return of the Buy an Hol, an the MAD (08, 20) & SMAC(206, 95) strategy, on S&P500 from 2004 to In Table 4 we can see that the MAD & SMAC strategy has worse Sharpe Ratio results that the SMAC strategy (the SMAC has the best an secon best result, while the MAD & SMAC has the thir an fourth an fifth best Sharpe Ratio. The values of the MAD & SMAC are more stable with small ifferences between the best an the worst. This means that the returns showe in Table 3 are ue to the MAD & SMAC strategy being a bit more riskier (with more variance in the yearly returns) than the SMAC strategy. This means that the eciing factor on the choice of these two strategies is the investor profile risk. The investor can choose between a strategy with better returns but more volatility (the SMAC & MAD ) an the SMAC with more regular but less attractive results. In Figure 8 we can see the evolution of the return of the strategy with the best results in the training perio, uring the test perio, compare with the evolution of the Buy an Hol. In this graphic we can see that in Bull Markets the Buy an Hol strategy has better returns that other strategies, but the situation changes completely when the Bear Bear appears, an the MAD & SMAC, not only oes not loses capital, but also has a great recovery of capital. Finally in the en of the Bear Market, the MAD & SMAC oes not recognize right away the change an looses some capital an then stays out of the market for a while, until it etects the current uppertren an enters long again. In Figure 9 we can see the traing signals generate for the same strategy uring the testing perio. The arrows means opening positions (up arrow represent long buys, an own arrows shortsells.) an the crosses means the close of the open positions. In the beginning of the perio we can see the strategy tries to follow the short upwar trens of the market an avoiing the ownwar trens. When the market exibits clear trens, like the en of the Bull Market in 2006 an 2007 the strategy clear ientifies an follow the trens, an when the trens are changing (en of 2007 an mile of 2009) it first sells the active position, an enter the contrary position uppon more confirmation of the effective tren change. Then when the markets starts up again in 2009 first it exists the short position, stays out of the market until it is sure that there is a new uptren an then enters long again. The propose strategy is best suite for meium an long term investment since it only takes a ecision after the confirmation of a tren is clear, it has the great avantage of avoiing long perios of owntrens. The classical stategy of Buy an Hol that is only goo in markets that o not exibite bear markets like the 80s an 90s in the S&P500 oes not perform well in markets characterize by long bear markets. Figure 9 - Long an Short signals for the MAD (08, 20) & SMAC(206, 95) strategy for the S&P 500 from 2004 to 2009.

8 5. CONCLUSIONS This ocument presente the use of Genetic Algorithms to optimize the parameters of various Technical Inicators an with them create various traing strategies. The results obtain showe that this strategies beat significantly the Buy an Hol (the MAD & SMAC strategy ha an average of 9.0% against the 2.6% of the Buy an Hol), once more proving the valiity of Technical Analysis. Finally the optimize MAD & SMAC strategy is compare with the ranom strategy, with excellent results: the optimize has an average of return of 9.0% against the -.0% of the ranom strategy. The use of the MAD & SMAC has also shown better results than the use of any of the inicators iniviually. 6. BIBLIOGRAPHY [] Boas-Sagi, D. J., Fernánez, P., Hialgo, J. I., Soltero, F. J., an Risco-Martín, J. L. Multiobjective optimization of technical market inicators. In Proceeings of the GECCO '09 Annual Conference Companion on Genetic an Evolutionary Computation Conference, Montreal, Canaa, 2009, [2] Brock, William & Lakonishok, Josef & LeBaron, Blake, 992. Simple Technical Traing Rules an the Stochastic Properties of Stock Returns. Journal of Finance, American Finance Association, vol. 47(5), pp [3] Canegrati, E., A Non-Ranom Walk own Canary Wharf, in MPRA Paper. 2008, University Library of Munich. [4] Chan, E. P., Quantitative Traing, John Wiley an Sons, New Jersey, [5] Ellis, Craig A. & Parbery, Simon A., Is smarter better? A comparison of aaptive, an simple moving average traing strategies. Research in International Business an Finance, Elsevier, vol. 9(3), 2005, [6] Fama, Eugene F., 998. Market efficiency, long-term returns, an behavioral finance. Journal of Financial Economics, Elsevier, vol. 49(3), pp [7] Fernánez-Blanco, P., et al., Technical market inicators optimization using evolutionary algorithms. in Proceeings of the 2008 GECCO conference companion on Genetic an evolutionary computation Atlanta, USA, [8] Gorgulho, A., Neves, R. an Horta N., et al., Using GAs to Balance Technical Inicators on StockPicking for Financial Portfolio Composition. in Proceeings of the 2009 GECCO conference companion on Genetic an evolutionary computation Montreal, Canaa, [9] Hassan, G. an Clack C., "Robustness of Multiple Objective GP Stock-Picking in Unstable Financial Markets," in Genetic an Evolutionary Computation Conference, Montreal, Canaa, 2009, [0] Jegaeesh, N., an Titman, S. Returns to buying winners an selling losers: Implica-tions for stock market efficiency, Journal of Finance 48, 993, [] Kaufman, P. J., New Traing Systems An Methos, John Wiley & Sons Inc., San Francisco, CA [2] Kimoto, T. an Asakawa, K., Stock Market Preiction System with Moular Neural Networks, IJCNN International Joint Conference on Neural Networks, vol., 990, -6. [3] Kirkpatrick, C. D. an Dahlquist R. D., Technical Analysis, FT press [4] Leigh, W., Moani N. an Hightower, R., A computational implementation of stock charting: abrupt volume increase as signal for movement in New York Stock Exchange Composite Inex, Decision Support Systems, Volume 37, Issue 4, September 2004, pp [5] Leigh, W., Frohlich, C. J., Hornik, S., Purvis, R. L. an Roberts, T. L., Traing With a Stock Chart Heuristic, IEEE Transactions on systems, man, an cybernetics Part A: Systems an Humans, vol. 38, no., january 2008 [6] Leigh, W. an Purvis, R., Implementation an valiation of an opportunistic stock market timing heuristic: One-ay share volume spike as buy signal, Expert Systems with Applications, Volume 35, Issue 4, November 2008, [7] Michalewicz, 994. Genetic Algorithms + Data Structures = Evolution Programs. Springer-Verlag, 2n eition, 994 [8] Rey, D. M. an Schmi, M. M., "Feasible momentum strategies: Evience from the Swiss stock market," Financial Markets Portfolio Management, vol. 2, 2007, [9] Sharpe, W. F, The Sharpe Ratio. Journal of Portfolio Management 2 () 994, [20] Wagman, L, "Stock Portfolio Evaluation: An Application of Genetic-Programming-Base Technical Analysis," Genetic Algorithms an Genetic Programming at Stanfor, 2003, [2] Yan, W. an Clack, C., Evolving Robust GP Solutions for Hege Fun Stock Selection in Emerging Markets, in Proceeings of the 2007 GECCO conference companion on Genetic an evolutionary computation. 2007, Lonon, UK,