Adaptive Portfolio Management using Evolutionary Algorithm - Essay Example

? Adaptive Portfolio Management using Evolutionary Algorithm A Dissertation Proposal* Farhad Bahramy 31. July Table of Contents Introduction: 3 2.Motivation: 4 3.Problem Definition: 4 4.Relevant Literature: 6 5.Proposed Approach: 8 I.Market Trends 8 II.Execution rules 9 III.Risk management rules 10 IV.Representation: 10 V.Evolutionary Process: 12 VI.Evaluation of the strategies: 15 VII.Execution of adapting the strategies: 16 VIII.Performance measurement: 17 6.Question to Be Answered 17 7.Expected Contribution 17 8.Work Plan: 18 9.References: 18 1. Introduction: Portfolio management is the process of managing assets i.e. stocks, bonds, etc., such that a large return with a low risk is obtained. Forecasting price movements in financial markets is an important part of constructing portfolios. Most traders believe that the financial markets are not fully efficient and that there exist temporary predictability, which could be exploited for collecting excess returns above the market average [1]. Consequently, many financial institutions have developed decision support systems to help traders and analysts make decisions about portfolio management more quickly and more effectively. Technical indicators use statistics to determine trends in security prices and are often used by financial markets and private traders to assist with portfolio management. A survey of foreign exchange traders in London [2] estimates that up to 90% of traders use some form of technical indicators and trading rules in their daily trading. Technical indicators assume that securities move according to trends and patterns that are continued over a short periods of time until another trend is triggered by the change in the market condition. The success of technical indicators depends on how one interprets the signals. Expert human traders are capable of combining several technical indicators and trading rules to arrive at composite strategies which are used in portfolio selection, execution and risk management. The process of arriving at such strategies requires high experience, expertise and often long and tidies hours of observation of historical and current market data to test and fine-tune different combinations of technical indicators and trading rules. Although there are agreements that financial markets do sometimes show periods where certain trading rules work [3], it is very hard to find evidence that a single trading strategy can function over an extended period of time. This can be due to the fact that financial markets are constantly evolving, and that when a trading rule is found to work it would not take long before it is exploited until it no longer harvests a significant profit. This forces the traders and technical analyst to constantly create new strategies or retune the existing strategies so that they would work under the new market conditions. The goal of my research would be to create a system that emulates human behaviour in combining a set of simple rules and technical indicators to create sophisticated trading strategies. The system then would constantly evolve those strategies or creating new strategies that would adapt to changing market conditions. 2. Motivation: In the past several years, there has been a notable increase in the use of financial modeling and optimization tools such as algorithmic trading and automated portfolio management in financial industries. In addition to the pressure on asset management firms to reduce costs and maintain a more stable and predictable performance in the aftermath of the downturn in the world’s markets in recent years, three other general trends have contributed to this increase. First, there has been an increase of interest in predictive models for asset returns. Predictive models assume that it is possible to make conditional forecasts of future returns—an objective that was previously considered not achievable by classical financial theory. Second, the wide availability of sophisticated and specialized software packages has enabled generating and exploiting these forecasts in portfolio management, often in combination with optimization and simulation techniques. Third, the continuous increase in computer speed and the simultaneous decrease in hardware costs have made the necessary computing power affordable even to small firms. As of 2009, high-frequency trading firms account for 73% of all US equity trading volume [4] The notable interest in use of technology in portfolio management in financial industry in the last two decades has attracted many academics. Varies research has been undertaken and interesting results have been obtained (this is discussed in details in section 4). However, in all the researches undertaken so far there have been no attempts to create a system with complete portfolio management capabilities. A complete portfolio management system should provide portfolio selection, portfolio execution and risk management. In most researches the concentrations were on the portfolio selection while portfolio execution and the risk management were left out or received very little attention. Realising the limitation within this area, I believe that an in-depth research needs to be done in order to understand whether a complete portfolio optimisation is achievable and whether it outperforms the current models available. 3. Problem Definition: Many problems in financial markets involve the choice of an optimum solution subject to one or more constraints on the set of feasible choices. Mathematically, an optimization problem can be written as eq. 1 Where is an objective function and are constraints defined, respectively, as and * Both and should be differentiable functions. Portfolio Optimization problems can be defined as followings: Given a set of investments how does one find a portfolio that has the lowest risk (i.e. lowest volatility or lowest variance) and yields an acceptable expected return. Investors want to select their portfolio to minimize risk while simultaneously maximising the return. These two objectives can sometimes oppose each other. For example, consider a portfolio in which all the resources are in a single stock with highest possible return. Although this portfolio has a high amount of expected return, it is also very risky. If the stock drops, the portfolio does not have any other assets that could compensate for this reduction. On the other hand, if a portfolio consists of equal investments in all possible stocks, it cannot take advantage of any stocks that will probably perform better than others. Economists have long studied the ways that investors attempt to balance risk versus return, but it was Harry Markowitz [5], who defined ‘risk’ as the variance in portfolio return. eq. 2 eq. 3 Where set of stocks can be represented as an n ? 1 vector, ? is the (n ? n) covariance matrix for the assets, is the ((n ? 1) vector of returns and is the covariance between stock i and stock j. These are estimated from historical data for stock prices. E?cient portfolios are found by solving the optimization problem eq. 4 Where ‘?’ is a parameter denoting the investor’s risk tolerance. If ‘?’ is large, then will be close to zero, meaning that the investor does not have much risk tolerance Conversely, if ? is small, then 1? will be large, placing more emphasis on return. 4. Relevant Literature: In recent years many papers which describe various applications of nature-inspired algorithms to financial modeling have been published; in this section I will review some of these works. One of the areas of application of financial models is the development of trading rules to indicate when and whether investors should buy or sell various financial instruments. Research in this area has received greater attention over recent years as newer computational algorithms are being developed each day and evolving to accommodate complex trading strategies. In an efficient capital market (arbitrage-free) it would not be possible for traders to make a profit from past data as all relevant information for pricing a security today would be incorporated in today’s price. Therefore, many research papers in this domain during the past 17 years (see [6], [7], [8], in [9] and [10]) correlate the issue of market efficiency with the ability of genetic algorithms to literally “beat the market” (i.e., profit from a perceived arbitrage opportunity). Studies such as these highlight the scope for genetic algorithms to provide trading strategies, based on pattern recognition, and profit from equity market trading. However, the outcome from such strategies has largely been somewhat mixed. Although there is general consensus that financial markets do sometimes exhibit periods where certain trading rules work, it is hard to find clear evidence that a single trading rule can continue to perform effectively and generate returns over an extended period of time. This is probably due to the fact that financial markets are ever-evolving, and in fact given the number of technical analysts that are employed in all the major financial trading institutions, when a trading rule is found to work it would not be long before it is exploited until it no longer yields a significant profit. It is therefore more interesting to see if trading rules can be constructed that are capable of adapting constantly based on the changes and the general direction of the markets. An adaptive trading strategy seems to be more promising than static approaches. Besides genetic algorithms, other natural search techniques have also been applied to solve financial problems. Artificial neural networks have attracted a lot of interest over the past decade. A selection includes: [11] presents an index forecasting approach; [12] applies an ANN to currency exchange rate prediction by anticipating the direction of price change using signal processing methods for series with high noise and small sample sizes; [13] describes a neural evolutionary approach to find correlation based models among financial derivatives; [14] evaluates credit risk and predicting using ANNs; and [15] discusses a neural network for option pricing. Generally when neural networks are used on noisy data sets such as those from stock markets, they have the tendency to over-fit the problem and are often easy to trap into local minima. A daw back of the above approaches is that they all concentrate on portfolio selection and pay very little attention to risk management. Most recently, numerous applications of evolutionary computation have been published: [16] describes a dynamic asset allocation system in which a model was optimized using evolutionary computation to determine optimal portfolio weights given trade recommendations; a genetic programming approach for combining trading rules in autonomous agents so that the rules complement each other is given in [17]; [18] presents a linear genetic programming system for trading that uses intraday data; grammatical evolution for evolving human readable trading rules is extensively discussed in [19]; an application of genetic programming for discovering trading rules that are applicable in the short term is given in [20]; finally,[21] uses a double-stage genetic optimization algorithm for portfolio selection. In the first stage, a genetic algorithm is used to identify good quality assets in terms of asset ranking. In the second stage, investment allocation in the selected good quality assets is optimized using a genetic algorithm based on Markowitz’s theory. The most relevant work I propose to adopt in relation to my proposed research is [22] where an evolutionary algorithm is used to create an adaptive system that learns to form rules from a very small set of technical indicators that can adapt to dynamic market conditions. Even though the performance of the system is not up to the expectation, it shows great potential in having the capability of adapting to different condition in the market. The average performance of this approach can be due to several reasons. First, the portfolio execution uses a very naive method of simply going long on best rank stocks and going short the worst ranked stocks, holding them until the stocks are not among the best/worst ranked stocks anymore. Second, the algorithm contains no risk management module and all the resources are utilized among the ranked stocks. A better approach would be to have some sort of risk management mechanism that distributes the available resources among the stocks according to their individual volatility (risk). Thirdly, very few indicators are used in this approach. Therefore, trying to define composite rules from this very limited selection of indicators seems highly unlikely. Finally, the evaluation of the algorithm’s performance is not very accurate and fair. This approach compares the performance of the system with the performance of some naive methods such as Buy and Hold which is not a very practical approach in today’s financial markets. This weak evaluation is quite common among most of the other approaches discussed above. 5. Proposed Approach: The proposed approach is to create two distinct strategy types. First, by using an evolutionary algorithm on historical stock market data and fuzzy representation, a set of portfolio selections & execution strategies will be evolved from pool of predetermined technical indicators. Each strategy would contain conditions in which stocks should be selected for trading and how the trades should be executed. Once the stock selection & execution strategies are devised, an evolutionary algorithm, with the objective of minimising risks and maximising the returns, and a fuzzy representation would be used on a trading dataset. These selection & execution strategies shall constitute a comprehensive risk management strategy that is devised from a pool of predetermined risk management rules. To confine the search space for the evolutionary algorithms, a set of common and recurring trends in the market (e.g. bullish and bearish) will be identified and integrated into the system. Each selection & execution strategy will be assigned to its corresponding trends depending on best performance. Once strategies for both stock selection-execution and risk management are evolved, they would be used to trade stocks in various simulations. To adapt to new conditions in the markets after each trading period the evolutionary process for the strategies will be repeated. I. Market Trends A market trend is a “putative tendency” of a financial market to move in a particular direction over time [23]. These trends are classified as ‘secular’ for long time frames, ‘primary’ for medium time frames, and’ secondary’ lasting short times.[24] Traders identify market trends using technical analysis by determining when prices reach support and resistance levels within a given timeframe. In the proposed study, technical indicators will be used to identify the most common and important trends in the markets. For instance, the Commodity Channel Index (CCI) is originally designed to identify cyclical patterns in commodities [25], but it is widely used to identify bullish and bearish trends in the markets based on the following criteria: If increasein(CCI) > 100 { Trend = BULLISH; } If decreasein(CCI) < 100 { Trend = BEARISH; } The system shall constantly update the trend in the market during the training and trading periods. Each portfolio selection strategy will be assigned to one or more portfolio selection-execution groups depending on relative performance. The market trends in this research would be used to reduce the search space. Therefore, when trying to select a strategy, the corresponding market trend would be identified first and then the corresponding strategies that are known to perform well under that group will be selected. II. Execution rules Most traders (refer to trading strategies and associated software platforms) use ‘enter’ and ‘exit’ strategies upon identifying a potential trade. The most commonly used strategy in this context is the ‘stop and limit’ approach. Once a trade has been identified it will be bought/sold with a determined amount of tolerance for loss (stop) or gain (limit). Technical traders can also be used to determine the position to enter and exit a trade. For instance, the middle band of a Bollinger Bands indicator is used for entering a trade and the lower and upper bounds are used to exit the trade. In this research all the execution rules will be complete and do not require fine-tuning. Each portfolio selection strategy will have an execution rule that is known to deliver best performance. III. Risk management rules Apart from selection execution strategies for portfolio management, traders also use various risk management rules to reduce their exposure to risks. Rules such as ‘not to trade beyond a certain percentage of the portfolio budget at a time’ or ‘reduce position sizes after a drawdown of X%’ are some of the most common criteria. Most of the risk management rules need to be fine-tuned and improvised. The evolutionary algorithmic approach shall be used for this purpose. IV. Representation: Fuzzy logic uses a form of multi-valued logic; it deals with reasoning that is approximate rather than fixed or exact. Fuzzy systems have been widely used in expert systems, machinery and robotics. Because of their ability to model vague and imprecise information, fuzzy systems have been used with technical indicators in many previous studies. Fuzzy strategy representation enables intuitive natural language interpretation of technical indicator signals and provides a search space of possible strategies that correspond to the set of trading strategies that a human trader could construct. For example a human trader can create the following strategy for selecting stocks: If Moving Average Convergence/Divergence (MACD) of stock(x) < -0.5 { Buy(stock(x)); } The same rule can be represented in fuzzy logic as follows: If MACD is low { rating = 1; } Each fuzzy strategy consists of a set of “IF - THEN” conditions, whereby the “IF” part specifies the technical indicators’ conditions and their properties. The “THEN” part specifies a rating with 10 discrete levels given a stock with these properties. A discrete level rating of ‘1’ indicates a ‘very strong buy’ and a ‘0’ rating means a ‘very strong sell’. The technical indicator inputs are termed linguistic variables in the fuzzy logic component. Each linguistic variable will be assigned a value in the range - extremely low to extremely high. At least one linguistic variable must be defined to construct the associated rules. For the proposed study, over 20 popular technical indicators that are widely used in the market shall be chosen to construct strategies for portfolio selection. Each strategy may use more than one indicator by using operators such as ‘AND’ or ‘OR’. For example: IF (MACD is low) AND (Moving Average is extremely high) THEN { Rating = 0.9; } To avoid creating a very complex strategy that may ‘over-fit’ the training data, a strategy shall contain at least one and no more than 10 technical indicators. To confine the search space, the pool of portfolio selection-execution strategies will not contain more than 30 strategies at any given instant. The value of each linguistic variable is described by one of seven possible fuzzy membership sets. These are defined by describing the relative magnitude of a particular observation as: extremely low very low low medium high very high extremely high Each of these variables is initialized using observations from the historical data and updated whenever new information is observed. For instance, if the Moving average signal for the last 20 day was 70 then the number is divided into 7 sets of equal size, each corresponding to a single value ranging from extremely low (= 10) to extremely high ( = 70). Internally, each portfolio selection-execution strategy is represented using a matrix. With reference to figure 4, columns 1 through to 6 represent the strategy inputs, each corresponding to a linguistic variable and containing a Boolean value indicating whether or not the linguistic variable is active, and a number from 1 to 7 representing a value for the variable (1 corresponds to extremely low and 7 to extremely high). Column 7 corresponds to all the trends that this particular strategy can perform. Columns 8 and 9 represent the execution strategies, each corresponding to an execution rule and containing a Boolean value indicating whether the execution rule is active or not. Finally, column 10 indicates the rule output rating and contains a single floating point value from the set {0.1, 0.2. . . 1.0}. The internal representation for each portfolio selection-execution strategy pool is simply a 30?22+n matrix, where n is the number of execution rules. 1 2 3 4 5 6 7 8 9 10 Bool Int Bool Int Bool Int Bool Int Bool Int Bool Int Bool Bool Trends Float Bool Int Bool Int Bool Int Bool Int Bool Int Bool Int Bool Bool Trends Float Bool Int Bool Int Bool Int Bool Int Bool Int Bool Int Bool Bool Trends Float Bool Int Bool Int Bool Int Bool Int Bool Int Bool Int Bool Bool Trends Float Figure:4 Internal representation for portfolio selection & execution strategy with the pool size = 5, technical indicators = 9 and execution rules = 2. Bool indicates a Boolean value: Bool ? {T,F}; Int an integer :Int ? {1, 2, 3, 4, 5, 6, 7}; and Float a float number: Float ? {0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0}. The internal presentation for the proposed risk management strategies will be similar to the above representation. A vector of 1 by 20 will be used implying that there will be 20 risk management rules along with a single management strategy consisting these rules and evolving when required to produce the best results. V. Evolutionary Process: The fuzzy portfolio selection-execution strategies undergo an evolutionary process. An initial population of strategies (genotypes) is selected along with corresponding technical trading strategies that are acceptable in the markets. Once these portfolio selection-execution strategies are identified, they will be applied on a common dataset and all the trades will be recorded. Thereafter, a multi-objective evolutionary process using the recorded trades will be applied to streamline the portfolio management strategy. The dataset for the evolving portfolio selection-execution strategies will be chosen based on whether it represents all the different market trends implemented in this system. Stocks from a wide range of markets will be chosen to help the evolutionary process in developing strategies that can perform well over a wide range of stocks. Flow chart for the evolutionary process of portfolio selection-execution strategies: The evolutionary process for the portfolio risk management strategy is similar with three major differences. First, market trends are not used. Second, the evaluation process is different. Finally at the end of N generation only the best solution is selected. VI. Evaluation of the strategies: Evaluation of Portfolio selection-execution strategies: Each strategy has infinite capital but can buy/sell only one share at a time for every stock. 1. At time t the condition of each stock in the dataset is tested and the trend at the time t will be allocated to a corresponding strategy(s) that exists in the population. Each stock can hold only one share for one stock but can have more than one stock allocated to it. 2. Keep count of the market trend for every strategy that is selected. 3. The allocated stocks are traded in simulation using their correspondent strategies. 4. At time t+1 the condition of each stock in the dataset is tested and will be allocated to its corresponding strategy(s), if it exists in the population. The trading interval (t to t+1) is still subject to further research and can be of any duration ranging from 1 second to 1 minute. 5. The process is repeated until the end of the dataset. 6. The trends assigned for each strategy is counted and if the strategy performs with gain more than X times under particular trend(s), then those trends will be added to the strategy matrix. 7. The performance of each stock is evaluated on the amount of capital gained/lost. 8. The final fitness value of each strategy is determined by considering the performance of the strategy during trading along with two other criteria: I. A penalty for every trade resulting in a loss to guide the evolutionary search away from rule bases that produce undesirable return distributions within the training period (even if the return over the whole period is good). II. A penalty for a strategy with many rules to keep the strategies simpler and prevent over-fitting solutions to training data. Once the selection & execution strategies are evolved they will be used on the same data set. But this time, an initial capital will be assigned to the portfolio and spread among the strategies evenly. All the trades and the overall capital gain/loss will be recorded. 1. An individual strategy is selected from the population and a restriction is applied on the whole trading dataset. 2. The performance of the strategy is evaluated on the amount of capital gained/lost in comparison with the capital gained/lost prior to the application of the strategy. 3. The final fitness value of each strategy is determined by considering the performance of the strategy on trading dataset and two other criteria: I. A penalty for every trade resulting in a loss to guide the evolutionary search away from rule bases that produce undesirable return distributions within the training period (even if the return over the whole period is good). II. A penalty for strategy with many rules to keep the strategies simpler and prevent over-fitting solutions to training data. VII. Execution of adapting the strategies: Once the portfolio selection-execution and risk management strategies are identified, some initial capital will be assigned to the portfolio and simulation trading will be performed as follows: 1. At time t the trend in each stock is identified. 2. At time t the condition of each stock in the list of stocks is identified. 3. A search is performed on the strategies that are identified to perform well under this trend and a strategy matching the stock’s condition is chosen. If there is more than one matching strategy for the sell signal, the strategy with the lowest rating value will be selected. On the other hand, for a buy signal, the strategy with the highest rating value will be selected. 4. If no risk management restriction applies, the chosen stock will execute the trade according to its executing strategy. 5. The process will repeat at t+1 …… t+n (perhaps the end of the trading day). For the adaptation of the strategies, a sliding window to train the strategies will be used. The sliding window uses a historical time window for evaluation of current strategies. The time interval between the windows can be set at the end of each trading day or shorter periods (Subject to further research). VIII. Performance measurement: The performance of the system will be tested against the performance of a human trader. A family friend who is a successful Stock Trader has agreed to assist me in this assessment. Equal capital will be given to both the human trader and the system and they would compete over a period of time using a set of chosen stocks. Likewise, similar conditions will be set for the system to compete with other portfolio management/algorithmic trading systems within the school. 6. Question to Be Answered 1. Are evolutionary algorithms capable identifying an optimum solution from a large domain by restricting the search space to factors like market trends? 2. Can an automated portfolio management approach outperform human traders? 3. Can indicators of portfolio management evolve with changes in the market? 4. Can the evolving strategies respond to sudden changes in the market or do they require more data samples to determine any change in normal execution? 7. Expected Contribution This paper contributes to the existing computing and finance literature in several ways. From a financial perspective, the design and use of learning rules to build and manage a portfolio of assets, that are chosen based on fuzzy logic trading strategies is not well documented or pursued comprehensively. The proposed study will be one of the first attempts to use this methodology to create a complete portfolio management system that performs both portfolio selection-execution and risk management. From the perspective of computer sciences, this research shall determine whether it is possible to use evolutionary algorithms to find an optimum solution from amongst a large domain by restricting the search space to market trends. The proposed study will also compare the performance of such rule-based trading systems against the performance of human traders and identify all other factors other than the discussed strategies that may be required to develop an efficient and reliable trading platform. 8. Work Plan: 2011 Term 1 – Attend Lectures , background research for Master project 2012 Term 2 – Attend Lectures, Mater Project (Subject to discussions with my supervisor) 2012 Summer – Complete Master project thesis 2012 Term 1 – Write a paper about my findings during the master project, research about most popular technical indicators and risk management rules in the market, research on the markets trends, attend complementary lectures 2013 Term2 – Implementation of the first part of the system which is the implementation of the evolving strategies to select and execute stocks, attend complementary lectures 2013 Summer – Write papers about the implemented the second part of the system, which is evolving risk management strategy. 2013 Term 1 – Industrial placement/research 2014 Term 2 – industrial placement/research, write paper about research carried out in the industry. 2014 Summer – Complete any unfinished part of the implementation of the system. Carry on experiment and evaluation of the system compared to human portfolio management and other algorithmic trading methods 2014 Term 1 – compete in the Microsoft Banking Science Algorithmic Trading Competition, write paper on PhD dissertation write up 2015 Term 2 - PhD dissertation write up 2015 Summer – Finish PhD dissertation, defend and graduate 9. References: [1] van den Bergh, W. M.; van den Berg, J., 2002. Mining for pockets of predictability in financial markets. In Meij, J.,editor, Dealing with the Data Flood, pages 763–770. Stichting Toekomstbeeld der Techniek, Den Haag. [2] M. Taylor and H. Allen. The use of technical analysis in foreign exchange markets. J. Int. Money Finance,11:304–314, 1992. [3] W. Brock, Lakonishok, J., and B. LeBaron. Simple technical trading rules and the stochastic properties of stock returns. Journal of Finance, 47:1731–1764, 1992. [4] Rob Iati, The Real Story of Trading Software Espionage, AdvancedTrading.com, July 10, 2009 [5] Markowitz, H. M. 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Springer-Verlag New York, Inc., Secaucus, NJ, USA, 2006. [20]Jean-Yves Potvin, Patrick Soriano, and Maxime Valle. Generating trading rules on the stock markets with genetic programming. Comput. Oper. Res., 31(7):1033–1047, 2004. [23] Start Market Course, George Fontanills, Tommy Gentile, John Wiley and Sons Inc. 2001,p91http://books.google.com/books?id=gtrLvlojNzIC&pg=PA91&dq=stock+market+trends#v=onepage&q=stock%20market%20trends&f=false] [24] Edwards, R.; McGee, J.; Bessetti, W. H. C. (2007). Technical Analysis of Stock Trends. CRC Press. ISBN 9780849337727. Read More