Analysis of Behavioural Reactions

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Analysis of Behavioural Reactions inrelation to the Efficient Market Hypothesis

Algorithmic Approach of Technical Swing Trading

Gilbert Sanjaya

366965

Jean-Paul van Brakel

370549

May 25, 2014

Abstract

This research tries to model the movement price of stock prices using a behavioral approachinstead of the conventional and theoretical financial economics approach. By employing a the-oretical framework of behavioral economics, incorporating underreactions as well as overre-actions, this paper deducts that the Efficient Market Hypothesis (EMH) does not accuratelyrepresent the movement of stock prices compared to a more behavioral framework. Specifically,this is tested by developing a model that imitates the technical analysis trading strategy calledSwing-Trading. This is then used to compare it to a linear model based on the EMH. Sub-sequently, the models will be tested on four major indices: S&P500, AEX 25, FTSE 100 andthe NIKKEI 225. These indices will be tested on short and long run samples respectively. Ashypothesized, the model algorithm conveys that the behavioral model indeed presents a more

accurate prediction of the movement of stock prices compared to the model that obeys to theEMH assumptions.

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Contents

1 Introduction 3

2 Theoretical Framework 4

2.1 Efficient Market Hypothesis (EMH) . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 Overconfidence and Overreaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.3 Pessimism and Underreaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.4 Deduction and Hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3 Model 7

4 Methodology 8

5 Results 10

6 Conclusion 13

7 Limitations and Suggestions for Further research 137.1 Model Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137.2 Hypothetical Deduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137.3 Parameter Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147.4 Impact of Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

A Appendix 16

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1 Introduction

In financial markets, it is an open secret that stock prices are subject to uncertainty and anomaly.The Efficient Market Hypothesis (EMH), first developed by Fama (1998), conveys that a stock price

is effi

cient if it reflects all possible information on the market and hence one cannot consistentlyachieve abnormal return in excess of average market return. Indeed, empirical evidences have foundthat the return of a security consistently demonstrates a remonstrance to the view that securities arerationally priced to reflect all publicly available information (Daniel, Hirshleifer, & Subrahmanyam,1998). One possibility is that these anomalies are random deviations to be expected under the EMH(Fama, 1998).

An alternative pathway is to explain this inefficient security pricing and the phenomenon of re-alised abnormal returns, by scrutinizing the validity of a rational risk premium. Conceivably,variation in marginal utility across investors implies that a risk premium should vary but nonethe-less in a similar fashion across rational investors with the similar marginal utility. To explain thepredictable variations in market return, Campbell and Cochrane (1994) developed a model that ex-plains a utility function with an extreme habit of persistence to facilitate different preferences. The

model sustains extreme variations in marginal utilities with which it hypothesizes that marginalutility should correlate strongly with cross-sectional statistics such as returns on the size, book-to-market, and momentum portfolios. However, the findings indicate that such correlation is notpresent. Given this evidence, the explanation of abnormal returns can also be attributed to theimperfect rationality of investors (Daniel, Hirshleifer, & Subrahmanyam, 1998). For instance, in apaper Prospect Theory: an Analysis of Decision Making Risk, Kahneman and Tversky state thatexpectations have a fundamental role in the decision-making process (Wilkinson & Klaes, 2012). Itcan thereon be deduced that deviations in security prices could also be driven by investors irrationalexpectations.

While investors decisions are influenced by various cognitive biases, this paper will focus on twodecision heuristics: overreaction and underreaction. People have a tendency to exaggerate events.This has already been observed in the era of David Ricardo. Being an investor himself, he stated

that he had made all his money by observing that people generally exaggerated the importance ofevents. If there was reason for a small advance in stock value, he bought a large sum of it becauseof his certainty that an unreasonable advance would occur due to this overexaggeration (Brue &Grant, 2007).

Overreaction and underreaction are closely linked to the information available to investors, yetit is caused not by the type of information but rather on the psychological state of the investors.Assume that new information is released, irrespective to what and how the information is released.Further, assume that the information is correct and is publicly available. The EMH model doesnot disprove the existence of overreaction or underreaction in this case. However, EMH strictlyassumes that the price of a security will return to its efficient value after some period of overreactionor underreaction. This paper will check the credibility of this statement: whether investors expec-tations are rational in the sense that stock prices converge back to an equilibrium value. Therefore,

behavioural overreactions and underreactions in this paper are more relevant in the context of psy-chological economics instead of the conventional economic theory of rationality.

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The aim of the research is to develop a behavioral algorithm that models stock prices under theinfluence of overreactions and underreactions. By modeling such behaviour, this paper aims toshed a light on uncertainty in financial markets by exhibiting a more realistic view of the generalbehavior of investors. The algorithmic model will be divided into two parts: a linear model and a

behavioral one. Additionally, the algorithm has been programmed so that it can detect structuralbreaks whenever it encounters anomalous values that deviate from the models predictions with acertain threshold. Intuitively, the model with less parameter break implies a better estimator inexplaining the movement of stock prices. By systematically inspecting the performance of eachmodel, this research will try to answer the following research question and its subquestion:

Research Question

To what extent can the behavioral model explain the movements of stock indices, assuming the

movements occur in the cyclic pattern of the sine wave function.

Do security prices behave in accordance with the EMH or in a repetitive, behaviorial

pattern of overreactions and onderreactions?

2 Theoretical Framework

2.1 Efficient Market Hypothesis (EMH)

Efficient Market Hypothesis (EMH) is a theory that states that in efficient financial market, se-curity prices fully reflect available information in a rapid and unbiased fashion and thus provideunbiased estimates of the underlying value (Basu, 1977). The focus of EMH lies on the informationsharing between the investor and thus the classification of the EMH is based on how informationare perceived and spread among investors.

EMH is generally accepted as a paramount theory in explaining the movement in security prices.However, the 1990s period saw a decline of believe in the EMH. Jensen (1978) has presented one

of the earliest findings that contradict the deduction of the EMH, in which he has found severalanomalous evidences of securities that deviate from the EMH deduction. DeBondt and Thaler(1995) found that stock market overreaction has been more persistent than what EMH predicts.Their findings are against EMH and urges researchers and investors to be more lenient towards abehavioral finance approach that focusses on irrationality of individuals and the imperfection of thefinancial markets.

The centrifugal criticism towards EMH is mainly attributed to its conventional rational theory,which assumes homo economicus; a fully rational human being. Herbert A. Simon (1955), propo-nent of bounded rationality theory, states that individual rationality is limited by the informationthey posses, the cognitive limitation in their minds, and the finite amount of time to make a decision.This induces the investors to use heuristics, or simple processes that replace complex optimizationin many decisions making processes. This is done rather than rigid-rational optimization (Simon,

1955). Kanheman, Tversky, and Thaler (1986) propose that the imperfection in capital marketare caused by the combination of cognitive biases and various predictable errors in decision mak-ing. This is due to bounded rationality. Abnormal returns can thus be realized by exploiting theirrationality of the investors, for example through overconfidence and pessimism.

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2.2 Overconfidence and Overreaction

Perhaps the most robust finding in the psychology of judgment is that people are overconfident -(De Bondt & Thaler, 1995)

As DeBondt and Thaler (1995) suggest, overconfidence has been one of the most common cognitivebiases that has been found in many contexts. For instance, physicians often make false-confidentdiagnoses, psychologist tends to overgeneralize findings, and security analysts make overconfident

judgments. Experts are no exception; being an expert does not mean that rationality is enhanced.Rather, Griffin and Tversky (1992) suggest that expert tend to be more overconfident than an in-experienced individual. Additionally, Einhorn (1980) found that overconfidence is more prominentin tasks that involve judgment, (e.g., stock trading), than for mechanical tasks (e.g., engineer de-signing) and more severe for tasks that require delayed feedback (e.g., forecasting financial returns),than tasks that provide immediate and conclusive feedback.

Daniel, Hirshleifer, and Subrahmanyam (1998) coined the fundamental aspect of overconfidence,biased self-attribution, that is, the confidence of investor grows when public information is in linewith his/her information, but does not fall commensurately when public information contradictshis/her information. This fact has been psychologically tested1, as further research concludes thatpeople tend to credit themselves for past success and blame external factors for failure (Daniel,Hirshleifer, & Subrahmanyam, 1998).

2.3 Pessimism and Underreaction

The existence of pessimism and underreaction can be associated with the behavioral economic con-cept of loss aversion, that is, that losses loom larger than gains (Kahneman & Tversky, ProspectTheory: An Analysis of Decision under Risk, 1979). For example, most people would not bet moneyon a symmetrical bet. In financial markets, it is common for firms to pre-book revenues that it hasnot yet received and delay or spread recording costs over several time periods (Wilkinson & Klaes,2012). Furthermore, Burgstahler and Dichev (1997) find that firms are more likely to announcesmall reported gains than small reported losses. Indeed, firms try to boost investors confidencesince they are well aware that investors subconsciously underweigh the probability of success assuggested by loss aversion.

As previously suggested by Griffin and Tversky (1992), underreaction is less common among experts,but inexperienced individuals are more prone to it. Nevertheless, these empirical and theoreticalfinding implicates that, in financial markets, irrationality is a common bias and every agent issubjected to cognitive limitation of overconfidence or pessimism.

2.4 Deduction and Hypothesis

Extracting the fundamental component of abovementioned theories, this paper attempts to test theconventional EMH model against a behavioural model. For instance, consider new information of apossible merger between two firms is expected to increase stock price. The stock price function assuggested by EMH would be constant around its efficient value (Figure 1a). EMH model can also

1Daniel, Hirshleifer, and Subharmanyam (1998) have referred these findings to several psychological literatures.See: Fischhoff(1982), Langer and Roth (1975), Miller and Ross (1975), Taylor and Brown (1988).

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incorporate overreaction or underreaction of investors. However, EMH assumes that overreactiononly occurs temporarily as observed from Figure 1b.

shock

(a) A shock without overreaction according to EMH

shock

(b) A shock with overreaction according to EMH

Figure 1: Visualisation of how shocks are incorporated in stock prices according to the EMH

This paper attempts to reject the rigid assumption of EMH that stock prices stay around its

effi

cient value. The centrifugal deduction is that overreaction and underreaction does not occuronly around the period of time just after new information is released, as suggested by the EMH,but rather systematically incorporated in stock price over time and at any moment in time. Theunique characteristic of each investor, whether it is overconfident, pessimistic, or even close tobeing rational, will be aggregated and reflected in the stock price in a repetitive pattern. Thosecharacteristics would then create a remonstrance against the theory of the existence of an efficientvalue of a stock price. This deduction would be the basis of this papers hypothesis:

Hypothesis 1: Stock prices always deviate around a moving mean because of structural

underreaction and overreaction of investors

Opposed to the EMH, the behavioural pattern of stock movements suggests that investors neverreach an equilibrium: stocks exhibit repetitive states of subsequently optimism, euphoria, slowingdown, reversal, disappointment and pessimism. This implicates that a shock either systematicallychanges the moving mean of this cyclic pattern or enlarges the states of the patterns temporarilyor permanently.

shock

Figure 2: A shock according to Behavioral Reactions

Hence, after (and before) any effect of new information kicks in, the investors perception is neverconstant or efficient. Rather, it keeps deviating around its efficient value due to infinite loop of

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overreaction and underreaction over time. The implication of the proposition above is visualised inFigure 2. This Figure exhivits a pattern that may occur upon a shock in the stock price, accordingto the behavioral framework.

3 Model

So far, the abovementioned theoretical framework presents a deduction that reject the assumptionof perfect markets and provides evidence for a behavioral approach towards the movement of stockprices. To test the deduction, two models that take the structure of the behavioral framework, byutilizing technical analysis, as well as the assumptions of the Efficient Market Hypothesis (EMH)will be developed. The specific (quantifiable) assumptions of the EMH that will be targeted boildown to the assumptions that holds under the Weak-Form EMH as developed by Fama (1970):

Excess returns cannot be earned in the long run by using investment strategies based onhistorical share prices or other historical data.

Technical analysis techniques will not be able to consistently produce excess returns.

Share prices exhibit no serial dependencies, meaning that there are no patterns to assetprices that make it possible to outperform the overall market systematically.

Henceforth, the model that obeys the assumption of EMH will utilize linear-representation func-tion, as it closely resembles the theoretical deduction of EMH. In the subsequent result it can beobserved that the graphical representation of linear model also mimics that of EMH. Intuitively,this is logical since linear function models the shock similar to the rigid-straight line shape of EMHmodel.

To incorporate behavioral analysis, this paper will consider the notion of the set of strategies alsoreferred to as technical analysis. Taylor (1992) defines technical analysis as the method of providingforecasts or trading advice on the basis of largely visual inspection of past prices, without regard

to any underlying economic or fundamental analysis. In order to implement a counterargumentagainst the EMH, a strategy out of the set of technical analysis strategies will be taken and appliedin such a way that it contradicts and/or provides counterevidence for the claims made by the EMHregarding technical analysis.

Specifically, a form of technical strategy called Swing-trading will be used. A scientific report byPan (2004) conveys that perspective of Swing-trading is the pervasive existence of multilevel swingsand abrupt momentum moves in the market prices, business fundamentals, mass psychology, andnews flow. The dualism of swing versus momentum may resemble the wave-particle dualism inquantum mechanics, however with much higher nonlinearity and sophistication of human tradersas building elements of the markets (Pan, 2004). This view forms the Swingtum Market Hypothe-sis, which is arguably better in explaining the reality in financial market than EMH. Additionally,one of the motivations of employing Swing-trading strategy is that the notion that is the main

assumption of the Swing-trading strategy is exactly as what this paper hypothesized: that stockprice always deviates around its efficient value.

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In order to model this dependency, a use of rigorous patterns that takes into account this self-repeating pattern, the sine function, will be utilized. The sine function is chosen as an element ofthe behavioral model since it resembles not only the overreaction and underreactions present in themain structure of the behavioral framework but it also coheres to the widely popular framework

which is known as the Elliott wave principle (Elliott, 1994).

The Elliott Wave Theory is generally acknowledged as a well-performing pattern for basic technicalanalysis strategies. It is based on a certain cyclic laws in human behavior psychology and focuseson the different stages of over- and underreactions, which can be seen in the final visualization ofthe framework that Elliott developed:

Figure 3: The basic structure of the Elliott Wave Pattern

These two underlying aspects of behavioral cycles propose the main argument for the approach.Using the sine function as the repeating pattern in the model is therefore inline with the generallyacknowledged frameworks, both for stock trading and cyclic analysis of time-series. Using the sinefunction also forces our model to incorporate dependency of future prices on historical data, as thesine function features cycles by definition. Explicitly modeling this autocorrelation is therefore, ifsuccessful, an argument for the existence of stable Swing-trading strategies. This could potentiallygenerate constant above-market returns, contradicting the EMH assumption as described before.

4 Methodology

In order to keep inline with the definition of the EMH, keeping in mind that shocks and/or changesin market structure are allowed. This means that we must develop not just a model but an algorithmwhich self-adjusts when necessary. This poses a challenge as selection criteria must be applied inorder to model these structural breaks. We have chosen to limit the freedom of our model to twodifferent parameters:

k = deviations

p = intra

model period size

Herein, deviations is the number of k standard deviations from the previous model. These kdeviations serve as the threshold for auto-adjusting. In other words: if future observations surpass

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this threshold (a breakpoint), the algoritm will adjust itself by constructing a new model from thisbreakpoint on forwards.

The intramodel period sizeis the total number of periods on which seperate models are con-

structed with the total sample size. This means that if a breakpoint occurs in a intra

model period sizeblock, the model will adjust itself accordingly.

The main strategy of our algorithm is the following:

i = 0

p = 5 0 (or chosen differently)

1. Apply model withold coefficients from period ito period i+p

2. Regress newmodel from period ito period i +p

3. Check whether observations from periodito periodi+padhere to the old model: observations

that deviate more thank times the standard deviation of the old model are considered breaks(which are in period b).

(a) If no breaks: apply old model from ito i+p

(b) If breaks: apply old model from i to i+b, apply new model from breakpoint (period b)to period i +p

4. i= i+p and return to step 1 until all observations are covered

We will allow independent values ofpbetween the two models with the only restriction being thatplinear pnonlinear. However, we do takek fixed as k = 2. This means that breaks are only recordedwhen observations deviate more than 2 standard deviations from the old model. The choice ofkcould also be varied to track results.

This algorithm will be used with two different models.

The first one is the linear one (which rejects the possibility of Swing Trading) and over- andunderreactions and is in line with the EMH:

yi = 0+ 1 xi

Where xi is period number i and yi is the stock (or index) price in period i.

The second model is the behavioural model, which is in line with Swing Trading and the WaveTheory:

yi= 0+ 1xi+ 2sin(3 xi+ 4)

Estimation methods are Ordinary Least Squares for the linear model and for the sine model thetrust-region-reflective algorithm which is a commonly used algorithm for Nonlinear Least-Squaresoptimisation.

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Now we will use both models and the proposed algorithm to test the hypothesis on four majorindices (Figure 4). We use Adjusted CloseEnd-Of-Day data from Yahoo Finance for this purpose.The indices will be tested for different intervals (different values for p) to see whether the sine wavealgorithm outperforms the linear algorithm both for long term and short term investing.

Index Available data period Long term sample Short term sample

S&P 500 1990/01 - 2014/05 1990/01 - 2014/05 2012/01 - 2014/05AEX 1992/10 - 2014/05 1995/07 - 2014/05 2012/01 - 2014/05FTSE 100 1994/01 - 2014/05 1994/01 - 2014/05 2012/01 - 2014/05Nikkei 225 1992/01 - 2014/05 1992/01 - 2014/05 2012/01 - 2014/05

Figure 4: Data samples per index

Relative performance is tracked with the following three measures:The Root-Mean-Square Error (RMSE) measure of fit. This performance measure is applicableas the sine model only performs better than the linear model if the data does indeed feature

seasonality or cyclic behaviour of some sort. Therefore the RMSE measure is a great tool to trackrelative performance between the models for each index. An added advantage is that the RMSErepresents the sample standard deviation of the residuals, revealing information about the volatilityof the model when it does not perform well. This is important as volatility is the main measure ofaccuracy in financial models (Christoffersen & Diebold, 2006).

RMSE =

vuut 1n

nXt=1

(byt yt)2Likewise, we will employ the Mean Absolute Error (MAE) and Mean Percentage Squared Error(MSPE) as each of these criteria may provide useful and additional information.

MAE =

1

n

n

Xi=1

|byt yt| MPSE = 1nn

Xi=1byt ytyt

2

5 Results

In the table below is an overview of the acquired results of the employed measures of fit as describedin the Section Methodology:Judging from the results in Figure 5, it is easy to see that the nonlinear model consistently out-performs the linear model on the Long Term sample. Likewise, judging from Figure 6, the samepattern appears for the Short Term sample. All measures of fit point in the same direction: it isclear that stock prices should not be modelled in a linear fashion. The sine wave model clearlyprevails in both time frames.

The statistics also reveal that the nonlinear model relatively performs better compared to thelinear model on the Short Term sample than it does on the Long Term sample. This could becaused by the fact that the Long Term sample also features times of recession or other large shocksthat the Small Term sample does not have. It could also be the case that the behavioral pattern

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LINEAR model NONLINEAR (sine) modelIndex p RMSE MAE MPSE p RMSE MAE MPSES&P 500 900 130.19 89.84 0.01613 2000 84.93 66.46 0.01024AEX 25 900 85.12 69.19 0.06314 3500 65.43 53.80 0.04474

FTSE 100 1000 603.57 455.64 0.01598 4000 508.26 383.60 0.01267NIKKEI 225 1000 1940.32 1621.10 0.02310 2000 1603.67 1287.02 0.01932

Figure 5: Results of the Measures of Fit for the Long Term sample

LINEAR model NONLINEAR (sine) modelIndex p RMSE MAE MPSE p RMSE MAE MPSES&P 500 150 34.56 29.54 0.00053 150 22.81 17.07 0.00021AEX 25 80 8.64 7.18 0.00064 80 5.48 4.38 0.00024FTSE 100 100 131.54 107.32 0.00045 100 98.56 76.93 0.00025NIKKEI 225 100 572.30 447.20 0.00224 100 543.68 407.20 0.00194

Figure 6: Results of the Measures of Fit for the Short Term sample

is more apparant in the Short Term. This argument would be backed up by the fact that SwingTrading strategies are often used on the Primary and Intermediate classifications of the ElliottWave Theory (Elliott, 1994).

However, the results of both models should not be judged solely by their respective measuresof fit. A visual comparison of the models is also crucial in analysing how well the shapes of themodels fit to the shapes of the stock indices. A visual overview of the models estimating one ofthe indices (AEX) is given on page 12. An overview of the other indices (S&P 500, FTSE 100,NIKKEI 225) can be found in the Appendix on page 17. From these visualisation it is possible todeduce the same result: the behavioral model clearly follows the movements of the stock indices in

a more natural and accurate way. The sine wave estimations of two seperate breaks also seem toapproximately connect at break points. This could mean that the sine model could potentially bea great tool for approximating future movements of the stock indices. Also the fact that the sinewave model requires less breaks support this inference. This would still need to be investigated infurther research.

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Figure 7: AEX Long Term Models

500 1000 1500 2000 2500 3000 3500 4000 45000

100

200

300

400

500

600

700

800

Trading day in sample (days)

AEX

IndexPrice(EUR)

AEX

Model+k*st.dev.

!k*st.dev.

500 1000 1500 2000 2500 3000 3500 4000 45000

100

200

300

400

500

600

700

800


AEXIndexPrice(EUR)

AEX

Model

+k*st.dev.!k*st.dev.

Figure 8: AEX Short Term Models

50 100 150 200 250 300 350 400 450 500 550260

280

300

320

340

360

380

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420


AEX

IndexPrice(EUR

)

AEX

Model


50 100 150 200 250 300 350 400 450 500 550280

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IndexPrice

(EUR)

AEX

Model

+k*st.dev.

!k*st.dev.

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6 Conclusion

Based on the result above, the abovementioned research question and subquestion can then beanswered. Indeed, less parameter breaks are needed for the sine model compared to the linear

one. This means that the sine model performs better in a sense that it requires fewer adjustments.Conceivably, the sine model can estimate the movements of the indices more accurately comparedto the linear model as all measures of fit point in this direction. Judging from the resulting graphs,also visually the sine wave seems to predict future patterns and movements of the indices betterthan the linear model. This fact is justified both in short run and long run analysis, enhancing thevalidity of the findings.

The implication is that the theoretical deduction in the beginning of this paper is then justified:overreaction or underreaction does not occur only in one period of time. Rather, it structurallyincorporates itself in security prices over time, causing fluctuations and deviations that cannot beexplained solely by the EMH. This merely reflects the fact that each investor has different marginalvaluations and behavioral patterns, where one might me overconfident and one might be pessimistic.However, the combined optimism and pessimism in respectively the bullish or bearish side of the

market leads to combined, predictable, patterns that fluctuates over time. This theory, proposed byElliott (1994), can therefore also be found empirically. Another important conclusion that can bedrawn is that the release of new information might not be the main catalyst in which overreaction orunderreaction occurs. Rather, those cognitive biases have been persistently incorporated along withthe movement of stock prices due to the irrationality of investors. Arguably then, the model thatis based on the technical-swing trading strategy gives a more accurate estimation in determiningthe movements of stock prices. This opposes the rigid-rationality analysis of conventional financialeconomic theory, stated by the EMH.

7 Limitations and Suggestions for Further research

There are several limitations to the finding of abovementioned technical swing analysis and several

suggestions for future research has been presented as follows.

7.1 Model Limitations

The main limitation of using the sine wave as the prominent pattern in regressing on market datais that the sine function is rather smooth. Stock prices, on the other hand, can exhibit very quickincreases and declines. An example of this problem is visualised in the following graph:Clearly, the steep declines and rises cannot be modelled very accurately by the sine wave. Therefore,an alternative pattern that is able to capture these fast movements would improve the model.

7.2 Hypothetical Deduction

The theoretical deduction of this paper is mainly based on intuitive assumptions of irrationality,

that is, it assumes a market with many agents that behave diff

erently and unique behavioral patternof each agent is the main cause of fluctuations. Thus, the finding might not be generalizable toevery sector of financial market, especially to the market that consist of relatively few stakeholders

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300 350 400 450

330

340

350

360

370

380

390

Figure 9: Example of sine wave not fitting the AEX data well

or low number of shares outstanding. Further research is advisable to test the validity of behavioralmodel in such market to test its validity towards a market with less behavioral pattern.

7.3 Parameter Estimation

The parameters that are chosen for the models (pandk) are chosen based on empirical findings. Ananalytical approximation for these parameters might lead to better performance. Further researchon deriving better parameters (with, for example, maximum likelihood estimation) is necessaryin order to verify the developed sine algorithm as a reliable alternative to existing techniques formodeling behavioral patterns in the financial markets.

7.4 Impact of Information

Finally, the analysis above does not scrutinize the possible impact of new information on the behav-ioral model. Intuitively, the amplitude of the sine-wave should be higher after the introduction ofnew information since the overreaction and underreaction effect become more eminent. A specificand rigorous research on the impact of information to the behavioral model is also suggested.

Moreover, defendant of EMH argues that financial market will eliminate behavioral deviationsfrom standard model. There are three main reasons for this argument (Wilkinson & Klaes, 2012):

1. Aggregation individual deviations will tend to cancel each other out in the market

2. Experience and Expertise skilled expertise are less likely to suffer from the same biases asnormal people2

3. Competition agents who are biased or irrational will be driven out of market

Additionally, Basu (1977) has found that several empirical evidences on the relation between com-mon stock and price-earnings ratio that EMH deduction is not always incorrect. In general, it isfair to conclude that the evidence is mixed; some of them are in favor of behavioral model, just as

this paper concludes, and others are for EMH.2This deduction contradicts the finding of Griffin and Tversky (1992), which states that experts are tend to be

overconfident. Additionally, one study by Haigh and List (2005) found that experts showed even more bias thannon-experts.

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Concluding, it is important to consider the fundamental deduction for both behavioral model andEMH. Each of the propositions has its own strengths and weaknesses, and phenomena in financialmarket are better explained by looking from both perspectives. Understanding behavioral deduc-

tion is diffi

cult without having grasped the fundamental of EMH. All in all, both deductions arecomplementary to acquire a better understanding of the complex uncertainty-hierarchy of financialmarket.

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[11] Fischhoff, B. (1982). For those condemned to study the past: Heuristics and biases in hindsight.Cambridge: Cambridge University Press.

[12] Griffin, D., & Tversky, A. (1992). The Weighing of Evidence and the Determinants of Confi-dence. Cognitive Psycology (24), 411-435.

[13] Haigh, M., & List, J. (2005). Do professional traders exhibit myopic loss-aversion? An experi-mental analysis. Journal of Finance , 60 (1), 523-534.

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[14] Jensen, M. C. (1978). Some anomalous evidence regarding market efficiency. Journal of Finan-cial Economics , 6 (2-3).

[15] Kahneman , D., & Tversky, A. (1979). Prospect Theory: An Analysis of Decision under Risk.Econometrica , 2 (47), 263-291.

[16] Kahneman, D., Tversky, A., & Thaler , R. (1986). Rational Choice and the Framing of Deci-sions. The Journal of Business 2nd ser. 59.4 25178 (2), 251-78.

[17] Langer, E. J., & Roth, J. (1975). Heads I win tails its chance: The illusion of control as afunction of the sequence of outcomes in a purely chance task. Journal of Personality and SocialPsychology (32), 951-955.

[18] Miller, D. T., & Ross, M. (1975). Self-serving bias in attribution of causality: Fact or fiction?Psychological Bulletin (82), 213-225.

[19] Pan, H. (2004). A Swingtum Theory of Intelligent Finance for Swing Trading and MomentumTrading . Center for Informatics and Applied OptimizationSchool of Information Technologyand Mathematical Sciences University of Ballarat, Mt Helen, VIC 3353, Australia, Center for

Informatics and Applied Optimization. Melbourne: Intelligent Finance Cluster.

[20] Simon, H. A. (1955). A behavioural model of rational choice. Quarterly Journal of Economics(69), 99-118.

[21] Taylor, M. P. (1992). The use of technical analysis in the foreign exchange market. Journal ofInternational Money and Finance , 11 (3), 304314.

[22] Taylor, S. E., & Brown, J. D. (1988). Illusion and well-being: A social psychological perspectiveon mental health,. Psychological Bulletin (103), 193-210.

[23] Wilkinson, N., & Klaes, M. (2012). An Introduction to Behavioral Economics. New York:Palgrave Macmillan.

A Appendix

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Figure 10: S&P 500 Long Term Models

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Figure 11: S&P 500 Short Term Models

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Figure 12: FTSE 100 Long Term Models

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Figure 14: NIKKEI 225 Long Term Models

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Figure 15: NIKKEI 225 Short Term Models

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Algorithm in Code

% SPECS ****************% final data

S = AEX;

nonlinear = true; % set to false for linear model

deviation = 2;

stepsize = 100;

tryMoreGuesses = true;

% SPECS ****************

dataN = S; breaks = [1]; counter = 1; breakflag = 0;

meanREG = []; lowerREG = []; upperREG = [];

options = optimset('MaxFunEvals',50000,'MaxIter', 10000);

% LINEAR

if (nonlinear)

funsin = @(p,xdata) p(1)*xdata+p(2);

pguess = [80,0.001];

end

% NONLINEAR

if (nonlinear)

funsin = @(p,xdata) p(1)*sin( p(2)*xdata+p(3) ) + p(4) + p(5)*xdata;

end

% post guesses / starting points here:

pguess = [400 0.13 70 9000 2]; pguess2 = [400 0.15 70 9000 2];

pguess3 = [900 0.13 70 15000 2];

% do FIRST regression

data = dataN( breaks(length(breaks)):stepsize,1);

ydata = [data([1:length(data)], 1)];

xdata = breaks(length(breaks)):1:stepsize;

xdata = xdata';

[p,resnorm,,,output] = lsqcurvefit(funsin,pguess,xdata,ydata,[],[],options);stdevOutput = sqrt(resnorm)/sqrt(length(data)1);

if (tryMoreGuesses)

[p2,resnorm2,, ,output2] = lsqcurvefit(funsin,pguess2,xdata,ydata,[],[],options);

stdevOutput2 = sqrt(resnorm2)/sqrt(length(data)1);



if (stdevOutput2 < stdevOutput)

if (stdevOutput3 < stdevOutput2)

p = p3;

stdevOutput = stdevOutput3;

else

p = p2;

stdevOutput = stdevOutput2;end

else


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p = p3;


else

p = p ;

stdevOutput = stdevOutput;

endend

end

Oldp = p;

OldSTDEV = stdevOutput;

lastPos = 1;

for i=stepsize:stepsize:length(dataN)

% do regression from last break to new observation

data = dataN( breaks(length(breaks)):i,1);

ydata = [data([1:length(data)], 1)];

xdata = breaks(length(breaks)):1:i;

xdata = xdata';

[p,resnorm,,,output] = lsqcurvefit(funsin,pguess,xdata,ydata,[],[],options);

stdevOutput = sqrt(resnorm)/sqrt(length(data)1);

if (tryMoreGuesses)






if (stdevOutput3 < stdevOutput2)

p = p3;


else

p = p2;


end

else


p = p3;


else

p = p ;

stdevOutput = stdevOutput;

end

end

end

xdata = lastPos:1:i1;

xdata = xdata';

OldMean = funsin(Oldp,xdata);

OldUpperB = funsin(Oldp,xdata)+deviation*OldSTDEV;

OldLowerB = funsin(Oldp,xdata)deviation*OldSTDEV;

cN = 1;

lastBreak = 0;

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breakflag = 0;

% go over observations again

for j=lastPos:1:i1

if (dataN(j,1) > OldUpperB(cN) | | dataN(j,1) < OldLowerB(cN)) && breakflag == 0

breakflag = 1;breaks = [breaks j];

lastBreak = j;

counter = counter + 1;

end

c N = c N + 1 ;

end

test = xdata;

if (breakflag == 1)

bdata = lastPos:1:lastBreak1;

bdata = bdata';

xdata = lastBreak:1:i1;

xdata = xdata';

end

if (breakflag == 1)

meanREG = [meanREG; funsin(Oldp,bdata)];

upperREG = [upperREG; funsin(Oldp,bdata)+deviation*OldSTDEV];

lowerREG = [lowerREG; funsin(Oldp,bdata)deviation*OldSTDEV];

meanREG = [meanREG; funsin(p,xdata)];

upperREG = [upperREG; funsin(p,xdata)+deviation*stdevOutput];

lowerREG = [lowerREG; funsin(p,xdata)deviation*stdevOutput];

Oldp = p;

OldSTDEV = stdevOutput;

else

meanREG = [meanREG; OldMean];

upperREG = [upperREG; OldUpperB];

lowerREG = [lowerREG; OldLowerB];

end

lastPos = i;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% in real code, the full algorithm is repeated here for the leftover

% which is

% length(dataN) i

% this leftover algorithm is initialised when:

% length(dataN) i > stepsize

%

% this algorithm is removed because otherwise the code would span 7+ pages

%

% For the full code, please consult J.P.G. van Brakel or G. Sanjaya

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

end

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Documents

Analysis of Behavioural Reactions