Chapter 2 Literature Review
2.2 Behavioral Finance
Efficient Market Hypothesis (EMH) has dominated financial market more than 3 decades.
Nevertheless, many empirical anomalies, e.g., price earning ratio effect, size effect, intraday effect, overnight effect, weekend effect, January effect and etc., have been discovered that invalidate efficient Market Hypothesis. Arthur [67] indicated ”As the situation is replayed regularly, we look for the patterns, and we use these to construct temporary expectation models or hypothesis to work with. ”
Kahneman and Tversky wanted to build a parsimonious theory to fit a number of violations of classical rationality that they had uncovered in empirical work. Expected utility theory which concerns with “how” uncertainty decision should be made, but Prospect Theory concerns with “how” decisions are actually made. Expected utility theory says that the expected utility is the sum of the probability weighted outcomes measured in terms of utility as formula (5).
∑
PtU(xt ) (5)Prospect Theory thought the weights are not the true probability, and the utilities are
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determined by a value function as formula (6) rather than a utility function :
∑
π(Pt)V(xt -r) (6)Where π is non-linear weighting function, r is the reference point which is value function to be evaluated. For example, people are not looking at the levels of final wealth they can attain but also gain and loss relative to some reference points, which may vary from situation to situation, and display a loss aversion [3].
Prospect Theory is a descriptive theory of choice under uncertainty. There are many patterns about cognitive biases. For instance, there are certainty effect, overconfidence, framing, mental accounting, isolation etc. A behavioral finance research Ritter [38] also found Overconfidence, framing effect, and mental accounting, three common effects affecting investment decisions.
People often predict future uncertain events by taking a short history of data and asking what broader picture history is representative. They often do not pay enough attention to the possibility that the recent history is generated by chance rather than by the “model” they are constructing.
2.3 Evolutionary Algorithms
Evolutionary algorithms simulate the model of natural evolution. The basic idea of evolutionary algorithms is survival of the fittest, the weak was die. Subsequently we overview two well known evolutionary algorithms: genetic algorithms and learning classifier systems.
2.3.1 Genetic Algorithms
Genetic Algorithms are evolutionary search algorithms that simulate the basic principles of natural evolution such as selection, inheritance, mutation, and population dynamics. The basic concepts of GA’s are introduced by Holland [7]. GA’s have been
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successfully applied to various domains, such as electrical devices [37, 55], pattern recognition [70], business [28,78, 79], parameters optimization [26, 74, 75] and performed the best on various evolutionary algorithms [69].
Genetic algorithms are global optimization techniques that avoid many of the shortcomings exhibited by local search techniques on different search spaces [40]. In addition, Grefenstete showed that the standard GA, GAs outperform several classical optimization techniques on task environment. Therefore, a genetic algorithm based parameter optimization approach is proposed in the first stage of this study. The pseudo codes ( see Figure 2-1) is a summary of a general Genetic Algorithm [4].
Figure 2-1. A summary of a general Genetic Algorithm
Genetic algorithms model genetic evolution. The characteristics of individuals are therefore expressed by using genotypes. Financial markets are dynamic environments, and investors invariably to find it’s difficult by judging the state of the investment environment. Under such circumstances, Genetic algorithms can provide suitable solutions to questions.
Genetic algorithms have the following basic operating procedures [13]:
Step 0: initialize population.
Step 1: evaluate（compute fitness）
Step 2: select
1. Let g=0.
2. Initialize the initial generation Cg
3. While not converged
(a) Evaluate the fitness of each individual (b) g=g+1
(c) select parents from Cg-1
(d) recombine selected parents through crossover to form offspring Og
(e) mutate offspring in Og
(f) select the new generation from previous generation Cg-1 and the offspring Og
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Step 3: crossover Step 4: mutate
Step 5: update population
Step 6: return to step 1 while not reaching terminated condition
Economic behavior is a kind of adaptive behavior [73]. While scholars were proposed that human beings adjust themselves to adapt the environmental changes, the use of standard quantitative tools to create models of human economic decision-making has proved difficulty.
It would greatly facilitate the optimization of decision-making quality if economic decision-making could be expressed as a set of simple rules. Chan, et al. [47] proposed a fuzzy rule-base stock selection model with rate of return, current ratio, and yield rate as input factors. This model uses Genetic algorithm to find each company's appraisal grade and employs a multi-period random capital allocation model; empirical results indicate that
investment portfolios constructed by using this method perform well in terms of predicted rate of return, variance, and utility value. Venugopal, et al. [57] proposed a Genetic Algorithm Model for portfolio selection. This model considers both equity and debt securities and vice versa. The computerized dynamic portfolio has outperformed the SENSEX throughout the testing period.
2.3.2 Learning Classifier Systems
Learning classifier systems is more often apply to forecast in dynamic environments than genetic algorithms (GAs) because of their use of spatial search methods in generate rational solutions adapted in environmental conditions and their abilities to constantly engage in self-aware learning to provide real-time strategic information appropriate to the
environments. In addition, classifier systems evolve accurate, maximally general classifiers that efficiently cover the state-action space of the problem and allow the system’s
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“knowledge” to be readily seen [48] . Financial markets are dynamic environments. Under such circumstances, learning classifier systems can provide the suitable solutions to questions.
Learning classifier system technology has been applied in many areas in recent years. For instance, in robotics and automatic driving systems [49], learning classifier systems have been used to develop learning robots. In the area of physician database knowledge access, Holmes [6] proposed the EpiCS platform with the goal of correctly assessing disease risk.
Figure 2-2. Operation diagram of extended classifier systems (Butz & Wilson, 2002) Extended classifier systems (XCS; see Figure 2-2) have the following basic operating procedures:
Step 0: Initialization of the classifier population.
Step 1: The detector obtains binary environmental state values consisting of (0,1) values from the environment.
Step 2: Information is obtained from the detector and used in comparison with the classifier population. If there are no classifiers meeting appropriate conditions in the classifier population, a rule discovery mechanism is used to establish and screen classifiers meeting conditions to a match set. Classifiers meeting the appropriate conditions must incorporate the information obtained by the detector.
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Step 3: Classifiers in the match set are classified according to their action. The predictive value and fitness value of classifiers with identical actions are weighted, yield a prediction array containing prediction values in various states of action.
Step 4: Select the prediction values in various states in the prediction array that have the greatest predictive value, and replicate them in the action set.
Step 5: The effector is converted according to the action set to another state that can be recognized by the external environment, and performs actions and operations on the external environment.
Step 6: The compensation allocation mechanism updates the parameters of all classifiers in the action set with the actual rewards obtained when the effector acted on the environment; actual rewards are used to update the original prediction values, prediction error values, and fitness value parameters.
Step 7: A GA operation caused the classifier population to evolve is performed once every fixed interval. After evaluating each classifier's accuracy and experience, inappropriate classifiers are discarded.
Following continuous improvement by many researchers, Wilson proposed an extended classifier system (XCS) in 1995 [63]. Wilson's XCS model strives to achieve accuracy in forecasting returns, eliminates message list, adds prediction arrays and action sets in order to improve classifier system effectiveness, and uses niche-genetic algorithms to implement evolution of rules. Beltrametti, et al. [45] used an LCS model to study the foreign exchange market, the empirical results of this research showed that classifier systems can classify external information and generate suitable predictions, while evolving appropriate trading rules in response to environmental changes. Furthermore, other scholars have used classifier systems to analyze the trading of individual stocks by using price indicators as inputs and
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individual stocks sell signals as outputs. For instance, Liao and Chen [76] used price and volume indicators including closing prices, 6-day average prices, and the OBV indicator as input factors, while Schulenburg and Ross [60] used average price and volume as input factors; both obtained experimental results significantly are better than both buy-and-hold and random trading strategies.
Multi-agent extended classifier systems use multiple extended classifier systems operating in coordination to achieve even better results from decision-making assistance.
Homogeneous or heterogeneous extended classifier systems can individually sense the state of the environment, and the integration of the learning results different extended classifier
systems sensing the environment can yield sound recommendations. For instance, a multi-agent extended classifier systems applied to urban traffic congestion providing route recommendations in accordance with news, the weather forecast, and levels of road
congestion [46] yield an excellent result. Furthermore, multi-agent extended classifier systems have been applied to air transportation and financial applications. For example, airlines use a heterogeneous multi-agent extended classifier system to solve aircraft route problems [77], and a multi-agent extended classifier system has been used to perform securities research involving many different types of investment targets [71].
2.4 Technical Analysis
Technical analysis is a method of stock price trend analysis that uses statistics or other quantitative methods to convert data consisting chiefly of historical prices and trading volume to charts or indicators with different implications and forecast future stock price trend according to cyclic tendencies to achieve excess returns. Technical analysis is using the
“buy-sell” holder historical information to figure out long-short term reflection under the stock market and psychology [16]. After converting historical price and volume data to various indicators, technical analysis can forecast the direction of stock price fluctuations and
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trading times. Although many market factors can disturb price trends, technical analysis can still improve the quality of investor decisions. Blume, et al. [44] incorporated trading volume to examine the relationship between price and volume. Their results verified that the signal transmitted by trading volume can reveal price fluctuation information, which implies that the use of trading volume as an auxiliary signal can significantly increase performance. Technical analysis is not a way to accurate the stock price, but it really helps the success probability [5].
Such as CRISMA system [61] used Cumulative Volume, Relative Strength Index, Moving Average to do “ buy and sell decision” With transaction cost or not, CRISMA outperformed the Buy & Hold strategy. Gencay and Stengos adopted Price and Volume Moving Averages, investigated Dow Jones index, explored that Volume can improve predicting ability [56].
Mark used 9K, 9KD, 18ADX, 18MACD, and S&P500 etc. as neural network input factors, this model also predict well [52]. Our study reference those above mentioned input factors, using moving average (MA), stochastic indicators (KD), moving average convergence divergence (MACD), relative strength index (RSI) and Williams %R (WMS %R) as this research model input factors.
Kendall and Su [72] used particle swarm optimization to find the best proportion of risk assets. This method, which was based on the mean-variance model and used the Sharpe ratio as its fitness function; although the performance was slightly different, the Kendall and Su method dramatically shortened solution time. Huang and et al.[42] proposed an optimal portfolio capital allocation model, input factor including RSI, BIAS, Psychological Line, Volume Ratio, which employed recurrent neural network to generate decision information and the result discovered about 90% related with the rules extracted by Full-RE algorithm.
2.5 Summary
This study attempts to use evolutionary algorithms to perform research and constructs portfolio insurance decision support models prevent investors from over- or under-reaction,
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and reduce common investment mistakes and achieving investment goals. In first stage, we construct decision support model using GAs with stock market raw data as input factors, and using extended classifier systems in second stage with technical indicators as input factors to improve performance of decision support models. Both decision support models are based on TIPP which protects principal and locks in profits is more conservative strategy than other strategies.
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Chapter 3
Design of Decision Support Models
This chapter discusses the approach taken by this research. First, it’s an overview of the research framework and the following two sections explain the design of decision support models based on genetic algorithms and extended classifier systems respectively.
3.1 Research Framework
Figure 3-1. Research architecture
Conventional economics and financial management research models assume that investors are rational, and consistently take maximization of their own gain as their foremost consideration. Nevertheless, scholars of behavioral finance have recently discovered that people frequently make erroneous decisions due to the isolation effect, framing effect, and so on. In view of the fact that bounded rationality [34] factors often cause people to have decision-making biases, this study has therefore sought to construct a dynamic portfolio insurance decision support model as shown in Figure 3-1. This model is proposed to prevent people from making poor decisions due to the influence of their cognitive biases.
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Most principal protected investment employs the five basic operating steps [2] as shown in Figure 3-2.
Figure 3-2. Principal Protected Investment Cycle
Selection of a principal protection strategy is the first step. The second step is to determine the reset interval and the third step is to fix the insured percentage. The fourth step is to allocate the assets which apart from selection financial commodities constituting risky and non-risky assets. The final step is constantly monitoring the state of investment portfolio and adjusting the proportion of risky and non-risky assets.
We notice that the above steps as principal protected investment cycle. When the investment period comes to term or adjustment is invalid, we restart a new cycle again.
The portfolio insurance adjustment example is shown in Figure 3-3. It reveals that when the current value of assets in an investment portfolio exceeds the upper assets adjustment limit, profit taking will be performed and the assets in the investment portfolio will be adjusted. When the current value of assets in an investment portfolio exceeds the lower assets adjustment limit, assets will be sold at a
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loss and the asset allocation in the investment portfolio adjusted. A series of appropriately-timed asset adjustments thus serves to achieve the goal of TIPP strategy.
Figure 3-3. Example of portfolio insurance adjustment
When a TIPP strategy is used, it is necessary to set insurance percentage reflecting investors' Tolerance levels in order to achieve the portfolio insurance goal.
The parameter Multiplier (M) is the risky asset trading leverage multiple setting.
Changes in M can have a tremendous influence on the performance of an investment portfolio. It may impossible to protect the principal when M is too large, and market participation will be very low when M is too small [2], which will preclude maximization of returns. Because of this, dynamic adjustment of M which respect to the environment is the only way to achieve the goals of principal protection and maximum returns. Tolerance (T) provides a basis for adjustment exposure to total assets. Trading must be performed to adjust the proportion of risky assets whenever this threshold is exceeded. For instance, if T=5%, trading will be performed when the change in the net value of risky assets exceeds 5%. If, at the time, M=4, no action will be taken when risky assets are in the 3.8-4.2 range. The investment portfolio will be
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adjusted again if it exceeds this range. Major factors that affect portfolio insurance performance include trading cost [66]; when trading costs are taken into consideration, the frequency of trades is seen to influence returns on the invested assets. As a consequence, if the T is too small, too many unnecessary trades may be performed during periods of consolidation, and the performance of the portfolio insurance will suffer. Because of this, it is necessary to dynamically select appropriate T values in view of overall market trends in order to avoid needless trading costs.
Framing effect is considered a very important psychological bias in the study of behavioral finance. Framing bias notes the tendency of decision maker is respond to various situations differently based on the context in which a choice is presented (framed) [9]. The framing effect refers to when, under circumstances of limited knowledge, investors' reactions to information are invariably reactions directly to the received information, the reality behind which they are unable to scrutinize [53].
Financial investment requires the making of decisions in an uncertain situation. Hence, framing influences decisions. In today's complex financial investment environment, a principal protection investment strategy decision-making assistance model is needed to prevent investors from over- or under-reaction, and help investors to avoid risk and achieve stable return.
3.2 GA-based TIPP Models
Genetic Algorithms (GAs) model genetic evolution. It was first introduced by John Holland [7]. The original GAs are bit string representation, proportional selection and crossover as the primary method to produce new individuals. Up to now, several changes have been developed to the original GAs, which are different representation schemes, selection, crossover, mutation and elitism operators.
In this study, each chromosome consists of gene Multiplier and Tolerance. The
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relative parameters setting in GA is listed as following.
Multiplier：a real number between 0 and 5 Tolerance：a real number between 0 and 10 Population size : 200
Crossover rate : 0.5 Mutation rate : 0.001
Fitness value : Return on Invest(ROI) Termination condition :
(1) difference between offspring and parent < 0.000001 or (2) 1000 generation
Training period : 1 year
This research model of TIPP a new portfolio insurance model is based on Continuous Genetic Algorithm (CGA). The objective of proposed model is going to find out an adequate Multiplier, Tolerance for trade and rebalance operating.
In this study, we first generate individuals of two times population size, and then select the better 50% of individuals to form the initial population. According to crossover rate, remain the previous generation (1-Pc)*P individuals to the next generation continuously evaluated. The rest individuals are randomly selected from parent individuals, and then mating offspring. The mating process [11] is randomly select nth gene to crossover. For example, consider the two parents to be
Parent1 = [Pm1 Pm2 …… PdNpar] Parent2 = [Pd1 Pd2 …… PmNpar]
where the m and d subscripts discriminate between the mom and the dad parent.
Pm1 represents first gene in mom chromosome, and so forth.
Two new genes are generated by following operations.
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Pnew1 = Pmn-β（Pmn-Pdn） (7)
Pnew2 = Pdn+β（Pmn-Pdn） (8)
which
P represents gene m stands for mom d stands for dad
n represents nth gene
β is a random value between 0 and 1
and then combine to form new children chromosomes : offspring1 = [Pm1 Pm2 …Pnew1…Pd]
offspring2 = [Pd1 Pd2 …Pnew1…Pm]
The next step is mutation operation. Mutation mechanism is avoided evolution converge procedure from the local optimized solution. In this research, we generate a random value, if it is less than mutation rate, mutation operation will be performed.
We choose randomly a chromosome and then replace it’s one gene among others by a new value.
There are two GA-based models in our research, one is GA optimized TIPP model (GA-TIPP model), another one is GA dynamic optimized TIPP model (GA-DTIPP model). The difference between GA-TIPP and GA-DTIPP models is GA-DTIPP must to find out a new suitable Multiplier and Tolerance after rebalance operation.
There are two GA-based models in our research, one is GA optimized TIPP model (GA-TIPP model), another one is GA dynamic optimized TIPP model (GA-DTIPP model). The difference between GA-TIPP and GA-DTIPP models is GA-DTIPP must to find out a new suitable Multiplier and Tolerance after rebalance operation.