VSB – TECHNICAL UNIVERSITY OF OSTRAVA FACULTY OF ECONOMICS
DEPARTMENT OF FINANCE
Assessment of Students’ Behavioral in FX Trading
Student: Bc. Bahate Maidiya
Supervisor of the bachelor thesis: Ing. Martina Novotná, Ph.D
Ostrava 2018
Acknowledgement
This diploma thesis was supported within the SGS Project No. 2016/54: Modelling of Behavioral Factors in Financial Markets.
CONTENTS
1 Introduction ... 5
2 Main Principles of Behavioral Finance... 7
2.1 Behavioral Finance and Efficient Market Hypothesis ... 7
2.1.1 Brief Introduction of Behavioral Finance ... 7
2.1.2 Efficient Market Hypothesis ... 8
2.2 Market Anomalies - Herding Effect ... 11
2.2.1 Definition of Herding Effect ... 11
2.2.2 Theoretical Research of Herding Effect ... 13
2.2.3 Recent Empirical Studies of Herding Effect ... 15
3 Description of Methodology ... 19
3.1 Estimation of the Model... 19
3.2 Statistical Verification ... 20
3.2.1 T-test ... 20
3.2.2 F-test ... 22
3.3 Econometric Verification ... 23
3.3.1 Autocorrelation Correlation ... 23
3.3.2 Multicolinearity... 24
3.4 Economic Verification ... 25
3.4.1 Model Specification ... 25
3.4.2 Normality of Residual Component ... 26
4 Assessment of Student Behavioral Factors in FX Trading ... 28
4.1 Data Modification and Description of the Model ... 28
4.1.1 Data Modification ... 28
4.1.2 Description of the Hypothesis ... 31
4.2 The Buying Herding Model ... 32
4.2.1 Statistic Verification ... 32
4.2.2 Econometric verification of the model ... 36
4.2.3 Economic Verification ... 39
4.2.4 The Summary for The Buying Herding. ... 42
4.3 The Selling Herding Model ... 43
4.3.1 Statistic Verification ... 43
4.3.2 The Summary for the Selling Herding ... 44
5 conclusion ... 46
Bibliography ... 48
List of Abbreviations ... 51 Declaration of Utilization of Results from the Diploma Thesis
List of Annexs Annexes
1 INTRODUCTION
Behavioral finance is a relatively new field that seeks to combine behavioral and cognitive psychological theory with conventional economics and finance to provide clarifications of the statement: “Why people make irrational financial decisions”. Generally speaking, in economics and finance the term herding or herd behavior means the process where economic agents are imitating each other actions and/or base on their decisions upon the actions of others.
Therefore, the aim of this thesis is to test if the student trading behavioral is influenced by each other’s trading decisions. The objective traders are the students from Faculty of Economic of VSB-TUO. The students were involved in a course project and they used the demo version of Oanda platform with the virtual exchange currency account start with 100,000 USD. The time period is from the 20th February 2016 to the 20th May 2016. Thus, the historical trading details can give us the information such as the type of trade (buy or sell), unit, buying frequency, and number of active students for each day, and the account balance during each day of the trading period.
This thesis contains five chapters. The first chapter is the general introduction of this thesis.
The second chapter is the background of behavioral finance and herding behavior.
Attention is paid on more specific explanation of the efficient market hypothesis. Some recent research of several countries related to herding effect are introduced. From all this information some supports for the following test can be provided. The third chapter, is introducing the methodology for the tests. Theoretical of the application is represented in this chapter. The fourth chapter presents the main result by using STATA software. We sum up all 65 students trading behavioral into daily data. The trading behavioral in the data include: buying or selling frequency, buying or selling units, the number of active students for buying or selling and the daily open and close balance sum for all students. Then we use statistical tests to see whether the number of active students is influenced by which factor. After that, we use regression analysis to show relationship between the active students and other variables. All data are shown in annexes. From all analyzed outcomes we can make conclusion whether the herding effect exists between students or if there are no relationships among each other’s trading behavioral. The last chapter provides the
conclusion of whole thesis. Based on our results we can provide some suggestions for further study and analysis in the conclusion.
2 MAIN PRINCIPLES OF BEHAVIORAL FINANCE
In this chapter, we explain what are the behavioral finance and the main principles of herding effect. This chapter is divided into two main parts. First parts will be introduction of the behavioral finance and efficient market hypothesis (EMH). The second parts it is about the herding effect.
2.1 Behavioral Finance and Efficient Market Hypothesis
Behavioral finance it is a new science, which is related with our behavioral and financial market. Within the theory of behavioral finance we should understand the main hypothesis of it. This hypothesis is called Efficient Markets Hypothesis (EMH).
2.1.1 Brief Introduction of Behavioral Finance
Behavioral finance is intersecting edge study between finance, psychology, behavioral, Sociology and some other studies. From the studies the economists want to explain the irrational trades and the decision rules. From the behavioral finance point of views, they believe that the stock price it is not only about the fundamental values. It’s also influenced by the investors’ behaviors. We also could understand it as the investor psychology could make big changes for the price in the financial market. It compare the investor is rational or not. And by analyzing the investor behavioral we can get a lot of important result, which can explain the irrational trading. By the result we can find a better way to invest our money to get more return. In this area, the research not only studies the financial and statistical result, but also includes the psychology research.
Economic and finance it is all about people and society. No matter its micro or macro way we will consider it. The society environment gives us a lot of influence to our decisions. In stock market, when someone sell the stock in the lowest price compare with others, his stock will be bought first. Then the price will get higher. So in financial market it’s not only about the company and the price. It’s also about the time and the trading.
When the hypothesis assumed the market is efficient, we can start to create the model and got the perfect result. But the market it’s not always efficient. In this situation when the market have other variables can cause the changes happened in market which is bubbles and crashes, and come from various cognitive biases, human errors and responses. And the investors herding could be explained as the reaction after the extreme cases which is not rational and the result could be really different compare with the fundamental analyses.
This is the reason the studies are really important for the investors’ decision-making and the role player in the financial market.
2.1.2 Efficient Market Hypothesis
Efficient market hypothesis it is all about how the market price changes. From the information the market price would changes fast or slow, efficient or not. This is the entire hypothesis trying to study.
Bachelier is the first finds efficient Markets Hypothesis in 1990. He gets the result from random changes of the Brownian motion and the price changes in stock market. And he realized the efficient of the market information: the pass and the event happened now even the futures will effect on the market price. He assumed the basic principal if the stock price will always follow the fair game model.
After years of study, expect the working, cowls and jones research, there have no more experience showed up about the price in stock market. Within the computer and new technology comes to our life. Kendall had the research about the price and stock price in USA and UK. He realized the price changes in randomly in 1953. But after Roberts explained their have a sequence produced by a random sequence has no difference between USA stock prices. And then Osborne found the stock prices it is similar to the behavior of particles in a fluid. And even after he used physics theory to explain the changes of the stock prices. From the thesis of Coonter we could see the Random Walk Theory test, and from his thesis he tried to assume the stock prices is following the fair game model.
Samuelson and Mandelbrot explained the fair game model and the random walk theory in mathematic way. And they also explained the correlation between them. From
the theory they got three main form and Fama advanced efficient market hypothesis in 1970.
Efficient market hypothesis include three main principles. The first in this hypothesis all the investors, finance manager, corporate and companies are all rational. The will use all research to get profit from the trading. And they are all carefully making decisions between rick and benefits. The second it is about the stock price. In this market the stock price shows as the balance between the demand and the supple. The investors who want to buy its equal to the investors who want to sell. It could also be understand as the overpriced investors as equal as the underpriced investors. In the case that if that is not equal. There will have arbitrage probability. They will invest fast to make arbitrage trades.
It will cause the price get back to the equal level again. The last it’s the stock price it’s the real information about this stock. It is called information efficiency. When the information changed, the stock price will change as well. When there is overpriced or underpriced information comes out. Investors will make trading and when the information is well known by everybody. The stock price will get back to its value.
We could understand the efficient market hypothesis as “no free lunch in the world”.
In this world there is nothing that you can get for free. In a normal market that is efficient, everybody wants to earn money easy. But only walking on the street and checking the road if there is money for us to pick it is not rational. We need to make analysis of the stock which we invested its waste of our money. But obviously this hypothesis is only a hypothesis. In reality not everybody it is rational, and it is not always rational. This hypothesis it is not hundred percent correct. In this world you cannot explain everybody as the same. This hypothesis makes the market as simple as we wish but the people are more complicated than we think.
There also have two different definitions about EMH. The first it’s internally efficient markets. It also called operationally efficient markets. It is mainly mature when the investor trades during the trades how much money they need to pay for the transactions.
And another definition called externally efficient markets. Also called pricing efficient markets. In this studies, explained the stock price can be fast effect by the new comer information or not. This “information” includes the companies, industries and domestic or
foreign published useful information. But also include some not published information, which like the private information.
In this hypothesis there is three assumptions. The first it’s all investors are trying to earn the most profit from the information they could get. The second it’s the market will react really fast and correct when there is new market information. The stock price it’s shown all information. The last its competition of the market cause the stock price change the previous equilibrium to new equilibrium. And the new information cause the changes of the price have independence.
Also in the efficient market hypothesis there are three forms, which are weak form efficiency, semi-strong form efficiency and strong form of efficiency market. Use this hypothesis we could understand how to trade or we can make analysis for the portfolio.
The relationship between the three forms of efficient market and the effectiveness of securities investment analysis can be expressed in the following Table 2.1:
Table 2.1 The relationship between market effectiveness and investment analysis Technical
analysis
Fundamental analysis
Inside information
Portfolio management Not efficient Efficient Efficient Efficient Positive & active Week efficiency Inefficient Efficient Efficient Positive & active Semi-strong
efficiency
Inefficient Inefficient Efficient Positive & active
Strong efficiency Inefficient Inefficient Inefficient Negative conservative Source: MABLIB; Author
http://wiki.mbalib.com/wiki/有效市场假说
When the market it’s no efficient, so it mean the price still cannot react for the history information. So in this case we could use technical analysis and fundamental analysis to predict the price for the futures. And get profit from the good decisions. And in the week efficiency market, the stock prices have already reflected in current prices. The future predictions or the future changes of the stock prices have nothing to do with the
historical prices. These cause the technical analysis become useless. But the fundamental analysis could use as the analysis of the stock that the published information still didn’t reflect fully on the price yet. So we can find some wrong determined stock and make profit from them. If the market is semi-strong efficiency market, the published information will be useless for predict the future price. The prices for tomorrow will depends on the new information that come out tomorrow. We will need some inner information that is not known as everybody. And use the information to make benefit. And when it is strong efficiency market all information it is already been reacted in the price now. Even the inner private information.
2.2 Market Anomalies - Herding Effect
The rational man and the absolute arbitrage it is the basic of the efficient market hypothesis. It is also the base of the nowadays-economic theory. From long time of the testing and analyzing, the psychologist point of view starts to enter the financial area. The behavioral finance studies grown really fast by more and more research of the peoples.
The market anomalies it is about the changes of the stock price that you cannot explain by the efficient market hypothesis. In the market there is happened sometimes when some returns are not predictable and making extreme income from the investment.
Mainly the market anomalies it is included calendar effect, the equity premium puzzle, herding effect, scale effect, over react and so on. Here we are going to introduce herding effect.
2.2.1 Definition of Herding Effect
The effect of the sheep flock it is also called herding effect. It means the public influences the individuals when they are making decisions. Instead of being rational they choose to follow the herd mentality. The sheep flock it is a really massed organization.
Normally the sheep are blind and only following the head of the sheep. Wherever the head of the sheep flock go, whole flock of the sheep will follow. Even though the head of the sheep maybe make the wrong decision which is like getting closer to the wolf or going
even farther from the grass. The flocks of the sheep still follow. However this type of behavioral it’s a figure of speech about the people when they are investing. When the investors only follow the big environment without making their own decisions. It will easily cause the loose or fails. In financial market we think the herding behavioral it’s a special situation which when the investor are limited rational. We can understand it as when the information inequality, investor will easily get influenced by other investors, coping the trading behavioral of others. There is also other situation like over dependent on the public opinion without considering by themselves. Because the herding effect had infectiousness, hence we consider between more individuals herding behavioral it is herding effect.
The very first advance it is from Keynes. He point out that during the day-by-day volatile return from the trading. Obviously between the investors that appeared a kind of group polarization, even though could happen as a ridiculous emotion that could influence the whole market behavioral. After he explained the sheep flock behavioral as beauty contest. The financial investment it is similar with the beauty contest. From the group of beauty we should find the one who are going to win the contest, then the correct guess could get you a big price. But here the main principle is not require you to choose the one you think she is the beautiful. Inversely you need to choose the one you think the most people will choose her and she will be the winner. From this point of view everybody is going to choose the one she is the most people whom chosen. No matter you really admit she is the most beautiful one or not. Thus the herding effect happened.
The herding behavioral has three main characteristics. The first is the first one who made their decision that will cause important influence to other investors. The second is the herding actions will effect investors make wrong decisions. The last is when the investors realized their mistake, they will try to make new decisions which is opposite from the previous one. This can make a new round of the herding effect that is opposite trades.
From the characteristics we could found out that there are always two conditions to follow:
other investors actions could be seen or observed. Otherwise there will be no herding. Then the decisions are not made at the same time, there should have the early sheep and the followers.
2.2.2 Theoretical Research of Herding Effect
Herding behavioral it is a really complicated phenomenon. The reason cause herding behavioral happened is from the herding instinctive and limited rational factors and so on. But from the research and the papers we could found that there are mainly two type of herding behavioral. One is called irrational herding behavioral. And another one is rational herding behavioral. The first one it is the blond mimic of other investors’ actions without own thoughts. But the rational herding it is means when the information is not equality and with the unconfident or other emotions causes the herding happens. In this situation the herding could be the best choice. The researchers are more studies the rational herding behavioral. Also from the studies of herding effect, the researchers found out that there could be pseudo herding. From this result we can get another theory it is about pseudo herding.
So basically we can divide the herding effect as herding and pseudo herding. From the herding behavioral we also can divide it into three types: base on the information inequality, based on the fame and base on the salary structures.
Base on the information inequality
The first one who advances the model for the information inequality is Banerjee in 1992. He thinks when the market information is inequality and the investors are rational.
Then they are going to follow the forgoer’s choice and make their decision. Hence the herding happens. Base on this model, Bikhehandani, Welch and Hirshleifer advance the BHW model in 1992. In this model they assume that value of the assets are unknown.
Investors have not only the published information about the assets but also have the related information about the value of assets more or less all and that is private. Because all investors only can get to know other investors actions. But no other investors’ private information. So if the investors are making their decision with the orders and the cost of the investment will not change by time. The forgoer’s decision will make efficient influence to the followers. And this will cause the herding happen.
Base on the fame
This is theory advanced by Scharfstein and Stein. Graham developed the theory and found out the fame model base on the herding behavioral. In the history of herding effect studies, Keynes already point out that the irregular victory compare with the regular failures, the second one will be better for protect your fame in 1936. From this result we can assume two fund managers, one with better ability and another are not. Assume when they are facing the same finance decisions, from the personal point of view the better ability fund manager would get high quality information. Vice versa another fund manager with lower ability will get lower quality of information. In this situation will cause the equal result: the better fund manager will make decision through his information, and the others will ignore his own information and he will mimic the better ability fund manager’s behavioral. This herding happens it is because of the fame effect. This type of herding which from fame mainly is used for analyzing the fund manager and the stock analyzer and so on. In this case if the fund manager are not confident with their own information then the rational action is they should herd. And when most of the professional traders are considering as this way, herding effect happens.
Base on the salary structures
The very first advanced of this theory is Brenan and Roll in 1993. After their paper advanced, Maug and Naik developed and complete this model after. The funds holders are under the risk of ethical risk and adverse selection. Their best strategy would be better if they sign a contract that related with the payment percentage. It means the payment for the fund manager will be influenced by the index from the funds and so on. But this will make the fund manager over consider the index but making the right decision. This will cause the inefficient of the portfolio. From this situation the fund manager will get really stressed if their result ranked in the lower position. The smart fund manager would drop the information he has and also no using the unique investment strategy incase their performance will not have good result. This will cause the herding happens. And in this situation even though the investment was failed still it is easier to accept by the investors compare with the other decisions.
Froot, Scharfstein and Stein advanced the herding that based on the behavioral principle similarity. From the other way you could say that this is belongs to the herding effect. If we consider it more specific, the pseudo herding means when the investors facing the same problem in the similar situation, they will make the similar decision without herding. It is only coincidence. Not the herding. Compare with the individual investors, the financial institutions are more taking in account about the market information. And the way in which they are going to analyze it is with the similar model or software. In all this as background the decision could be similar even is not about following. So from the outlook we maybe could consider this situation as herding behavioral.
2.2.3 Recent Empirical Studies of Herding Effect
Recent years the herding effect attracts a lot of economists to study about it. Mainly there are two thoughts: first is the study of the theoretical model. And another is to test and prove of the herding is exists. From the previous pages you already know the theory and the model in nowadays. With the following, will be the empirical study result of the herding effect.
The empirical study of the herding effect it is mainly divided into two parts. The one is to study the co-movement that is based on dynamic correlation. The study through the market investment behavioral consistence to decide if there are herding exist. And the other one is to study the dispersion level of the stock return when there are big changes in the financial market.
Base on the co-movement
Lakonishok, Shleifer and Vishny (LSV) proposed a new method for measuring herd behavior. They define herd behavior as the average tendency of fund managers to buy and sell certain stocks, and then created LSV index for constructed as evaluation index.
Research shows that in their sample, fund managers do not have obvious herd behavior.
But trading with the small-company stocks, herd behavior is more likely to occur. Their explanation is that there is less public information about small companies' stocks, so managers are more concerned with the actions of other managers. The LSV method can only measure the herd behavior approximately, but still this method has been widely used.
Since then, Lobao and Kamesaka used this method to test the stock market in Portugal and Japan, there was a significant herding effect.
Corsetti and so on studied the transmission mechanism of financial crisis, and believed that some markets had contagion effect, and some markets have herding effect and they were interdependent. Contagion effect means the phenomenon that there is a significant increase in the co-variance trend in the stock market when a country is affected by a big event. The herding effect refers to the phenomenon that the stock market has maintained a high correlation. They think some recent studies highlighting that “there is no contagion effects, only the herding effect”. It is because the variance of the stock market in the specific country is caused by unrealistic assumptions. They built a standard factor model of stock returns, to reconsider the financial market contagion effect of recent empirical studies on the correlation analysis of bivariate. As an empirical study on the international impact of the Hong Kong stock market crisis in December 1997, the results show that contagion effects have been found in at least five countries.
Boyer et al. though empirical research believe the global stock market crisis is transmitted through the holdings of international investors in 2006. And now in the emerging markets, there is a more serious co-movement in the period of big fluctuations.
In this case the herd behavior is obvious. It therefore concluded that the chain reaction of the financial crisis could be explained by the transmission of the crisis caused by the herd effect, rather than the fundamental change.
Chiang et al. believed that the early contagion effect of the Asian financial crisis was obvious, and the herding effect in the late stage of the crisis became dominant. They used the data sequence from 9 Asian countries' stock return from 1990 to 2003 to establish a dynamic conditional correlation model. By analyzing the correlation coefficient sequence, they divided the Asian financial crisis into two stages: In the first stage, there is a phenomenon of after-crisis correlation enhancement (contagion effect). The second stage shows the phenomenon of continuous high correlation (herding effect). The statistical analysis of correlation coefficients also found during the crisis, the variance has changed, the conclusion plays an important role.
Based on dispersion degree
Another study of empirical testing of the sheep effect in financial markets when there's a big fluctuation in the stock market and we get the dispersion level of stock returns.
Christie and Huang proposed to test the "herd behavior" in the market with CSSD (cross section standard deviation). That is, when there is a big fluctuation in the market, from the trend of the standard deviation of the stock returns to determine whether the stock market has the herd effect or not. They looked at USA stock market yields. It was not obvious that the herd behavior was an evident during the stock market volatility. The CSSD is just a conservative estimate of herd behavior. The results underestimating the extent of herd behavior. Chang et al. improved the CSSD method. This paper proposes a method to measure the consistency of investors' decisions with CSAD. When they studied the stock markets in the United States, Japan, South Korea, Hong Kong and Taiwan. The stock market in South Korea and Taiwan has a significant herd behavior. Only appeared some of the herd behavior in the Japanese market. The U.S. and Hong Kong markets do not have herd behavior. And they also use two empirical comparisons to prove that CSAS is wilder used than CSSD. But neither do CSSD nor CSAD can’t distinguish between herd behavior and pseudo-herd behavior. Based on this, Nofsinger and Hwang respectively put forward their own innovative testing methods. And it had a good result.
Zhouand Lai also studied the stock market in Hong Kong. He believes that investors who have herding behavior are mainly based on fundamental analysis rather than technical analysis in 2009. And found that herd behavior is more likely to occur in small company stocks and in recessions. And investors are more prone to herd when they sell stocks than when they buy stocks. And they proved by research when investors with "information" are instructed by the wrong signals, fashion leaders play an important role in herd behavior.
The study subjects were moved to China, and Demirer and Kutan studied whether there was herd behavior in Chinese stock market. They used the individual enterprise data and departmental data. And separately studies the Shanghai stock exchange and Shenzhen stock exchange data. Respectively analyzes the abnormal rising and falling of the market index return with dispersion degree. Demirer and Kutan believe that there is no herd behavior in Chinese stock market, and Chinese market investors are independent and
rational investors. At the same time, the model data shows that, in the period of great changes in the total market index, the return on equity is more dispersed. The results support rational capital pricing model and efficient market hypothesis. However, Tan et al.
Said in a research report about Chinese stock market. In the rise and fall of the stock market, there is a herd behavior in Chinese A-share and B-share markets. And in the raising stock market with high volume and high volatility the herd behavior in A-shares is particularly significant.
Chiang et al. pointed out that the empirical research of most scholars is limited to a single or a few national markets. There are two drawbacks to this: First of all from the point of view of econometrics. When important explanatory variables were been forgotten. The least squares estimator has probability of biased. The model will give the wrong information. The second is the results from data from selected countries shown only the local behavior. So the results do not fully reflect the wider global phenomenon. Chiang and others looked at herding behavior in global markets. They analyze the daily data from 18 countries since 1988 to 2009. It found out that there is no herd behavior in Latin American markets. But there are herd behaviors in developed and Asian markets. And the herd behavior is also present the asymmetrical in the rise and fall of the stock market. Asian markets have the same result. Research shows that the financial crisis will cause herding in the crisis country. The contagion effect spreads the crisis to neighbor countries. During the financial crisis, herd behavior has been seen in both the USA and Latin American markets. As a result, different conclusions have been drawn from the studies listed above.
In general, more herd behavior happens in emerging markets not developed markets.
3 DESCRIPTION OF METHODOLOGY
In this thesis, the relationship between students trading activity will be analyzed. By using the econometric statistical methods we can find which factor could be most related to the number of active students. This chapter can be divided into three parts which are estimation of the model, statistical verification and econometric verification. In this chapter, after a brief introduction about the estimation of the model we will explain the methodology that will be used to analyze herding effect existence in this thesis.
3.1 Estimation of the Model
In this part mainly described the theory of estimation of the econometric model.
Linear regression model
Linear regression model is a linear approach for modelling the relationship between dependent variable Y and other independent variables X1 X2 to Xn. The econometric model starts from this model:
𝑌𝑡 = 𝛽1+ 𝛽2𝑋2𝑡+ 𝛽3𝑋3𝑡 + ⋯ + 𝛽𝑘𝑋𝑘𝑡 + 𝜇𝑡, 𝑡 = 1, … , 𝑛 (3.1) where 𝑌𝑡 is the dependent variable, 𝛽1 is the constant, 𝛽2 , 𝛽3 ….and 𝛽𝑘 is the coefficient for each 𝑋𝑘𝑡. 𝜇𝑡 is the error term. Where 𝑌𝑡 is the dependent variable what we analyze and we analyze the changes after the independent variable change. If 𝛽i >0 means the variables X and Y are directly related, or positively correlated. If 𝛽i =0 means the variables X and Y are independent. If 𝛽i <0 means the variables X and Y are inversely correlated or negatively correlated.
The estimation regression we use is the ordinary least squares (OLS) unweight linear regression analysis. In statistics, ordinary least squares or linear least squares is a method for estimating the unknown parameters in a linear regression model. OLS chooses the parameters of a linear function of a set of explanatory variables by minimizing the sum of the squares of the differences between the observed dependent variable (values of the variable being predicted) in the given data-set and those predicted by the linear function.
To explain this method the formula shows as follow:
𝜇𝑖 = 𝑌𝑖 − (𝛽1+ 𝛽2∙ 𝑋2+ 𝛽3∙ 𝑋3+∙∙∙ +𝛽𝑖∙ 𝑋𝑖) (3.2) where 𝜇𝑖 is means the difference between the actual Y value and the Y value obtained from the regression model. For obtain estimates of the 𝛽 coefficients have to sum up the error term 𝜇𝑖 and get the result as small as possible. From the theoretical and practical reasons, the method of OLS does not minimize the sum of the error term. Hence the minimization of the error term as follow:
∑ 𝜇𝑖2= ∑(𝑌𝑖− 𝛽1− 𝛽2∙ 𝑋2− 𝛽3∙ 𝑋3−∙∙∙ −𝛽𝑖∙ 𝑋𝑖)2 (3.3)
where ∑ 𝜇𝑖2 is the sum of the squared error term.
According to the previous formula (3.3), we know the sample value of Y and the X, but we do not know the values of the β coefficients. Therefore, to minimize the error sum of squares (ESS) we have to find those values of β coefficients that will make ESS as small as possible. Obviously, ESS is now a function of β coefficients.
3.2 Statistical Verification
In this part, the relationship between the number of activity student and other variables will be analyzed with statistical methods. This chapter can be divided into two parts which are t-test and F-test.
Generally we need to create a model which is Formula (3.1).
3.2.1 T-test
This statistic verification it is the test for the coefficient 𝛽𝑖 , here in this thesis we have two 𝛽𝑖 so we need to do this test twice for the test. And at the same time we do not test the 𝛽1 the constant.
We assume the normal distribution of residual component at the level of significance α → 𝜇𝑡 ≈ (0, 𝜎2) and the principle is to compare the critical value and the calculated value. The first we should make hypothesis.
Hypothesis:
H0: 𝛽𝑖 = 0 (𝛽𝑖− 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑖𝑠 𝑛𝑜𝑡 𝑠𝑡𝑎𝑡𝑖𝑠𝑡𝑖𝑐𝑎𝑙𝑙𝑦 𝑠𝑖𝑔𝑛𝑖𝑓𝑖𝑐𝑎𝑛𝑡) H1: 𝛽𝑖 ≠ 0 (𝛽𝑖 − 𝑐𝑜𝑒𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑖𝑠 𝑠𝑡𝑎𝑡𝑖𝑠𝑡𝑖𝑐𝑎𝑙𝑙𝑦 𝑠𝑖𝑔𝑛𝑖𝑓𝑖𝑐𝑎𝑛𝑡) For the 𝑡𝑐𝑎𝑙 we need the formula be as below:
𝑡𝑐𝑎𝑙𝛽̂ 𝛽𝑖 − 𝑖
𝜎𝛽̂𝑖 ~𝑡𝛼(𝑛 − 𝑘) (3.4) where the 𝛽̂𝑖 is the estimated parameter i. 𝛽𝑖 is our hypothesis about parameter i. σ𝛽̂𝑖 is standard deviation of parameter 𝛽i. n is number of observations. k is number of estimated coefficients (including intercept). α is significant level (here is 5%)
Decision rules:
If |𝑇𝑐𝑎𝑚𝑝𝑢𝑡𝑒𝑑 |> 𝑇𝛼 (𝑛−𝑘), reject H0 at the level of significance level α and accept H1. It means we can assume that 𝛽𝑖.
If |𝑇𝑐𝑎𝑚𝑝𝑢𝑡𝑒𝑑|< 𝑇𝛼 (𝑛−𝑘), reject H1, and accept H0. So we cannot assume this parameter is statistically significant.
Calculate 𝑇𝛼 (𝑛−𝑘) by excel and the comment are “TINV”.
where α is the level of significance. n is number of observation, and k is number of 𝛽𝑖. As the result if:
𝛽𝑖 is statistically significant and good for the economic theory, from this we could get 𝛽𝑖 should stay in model.
𝛽𝑖 is statistically significant but is not good for the economic theory further we should think about not using 𝛽𝑖.
𝛽𝑖 is not significant but should be in the model based on the economic theory thus we should think about using of 𝛽𝑖
𝛽𝑖 is not statistically significant and is not good for the economic theory then 𝛽𝑖 should leave model.
If the P-value is less than the significance level our testing, we should reject the null hypothesis (H0) that this parameter is equal to zero.
If the P-value is higher than the significance level our testing, we should accept the null hypothesis (H0) that this parameter is equal to zero.
3.2.2 F-test
For test need to use F-test to test the whole model. We assume normal distribution of residual component − 𝑢𝑡≈ 𝑁(0, 𝜎2) at the level of significance α. The principle of this test is to compare the critical value and the calculated value.
Hypothesis:
H0: 𝛽2 = 𝛽3 = 0 (𝛽𝑖, Where i >1 are not statistically efficient → whole model is not statistically efficient)
H1: 𝛽2 ≠ 0 ∨ 𝛽3 ≠ 0 (at least one 𝛽𝑖is not equal 0)
Hence for the calculation need 𝐹𝑐𝑎𝑙 and 𝐹𝑐𝑟𝑖𝑡, here is the formula:
𝐹𝑐𝑎𝑙 =
𝐸𝑆𝑆 𝑘−1𝑅𝑆𝑆 𝑛−𝑘
∼ 𝐹𝛼(𝑘 − 1; 𝑛 − 𝑘) (3.5) where ESS is explained sum of squares, RSS is residual sum of squares, n is number of observation, k is number of 𝛽𝑖
For 𝐹𝑐𝑟𝑖𝑡we can use excel formula comment as “FINV”.
Decision rule:
If 𝐹𝑐𝑎𝑙 > 𝐹𝛼 (k − 1; n − k) reject H0 at the level of significance α (5%), accept H1. It means the whole model is good.
If 𝐹𝑐𝑎𝑙 < 𝐹𝛼 (k − 1; n − k) reject H1, and accept H0. It means the model is statistically significant.
If the P-value is less than the significance level our testing, we should reject the null hypothesis (H0) that all slope coefficients are equal to zero.
If the P-value is higher than the significance level our testing, we should accept the null hypothesis (H0) that all slope coefficients are not equal to zero.
3.3 Econometric Verification
From the econometric verification is going to test the statistical significant of whole model and parameters. We mainly focus on the analysis of the theory of autocorrelation and multicollinearity.
3.3.1 Autocorrelation Correlation
Autocorrelation of residual part we can understand as serial dependence time series residues and residues time delayed series. The main idea shown in below:
𝜇𝑡= 𝜌1𝜇𝑡−1 + 𝜌2𝜇𝑡−2+ ⋯ + 𝜌𝑘𝜇𝑘−1+ 𝜖𝑡 (3.6)
The causes:
- Inertia time series
- Inappropriate specification of mathematical form of model
- Inclusion of error from responsible variables into the random conponent - Average data and so on
Consequences:
Estimation of 𝛽𝑖 are not good, if there is autocorrelation, we should put it away. We get two method to estimate the autocorrelation: graphical tests and DW tests. Here we oly use the DW test because it is better to see the result.
Generally the model will be like (3.1) and the hypothesis will be : H0: ρ = 0 (no autocorrelation of 1st order)
H1: ρ ≠ 0 (autocorrelation of 1st order)
d-statistics: d≈ 2 ∗ (1 − 𝜌̂) the formula will be as below (3.5).
𝑑
𝑐𝑎𝑙=
∑𝑛𝑡=1∑𝜇̂−𝜇𝑡𝜇̂̂𝑡−1𝑡2
𝑛𝑡=1 (3.7) where the 𝑑𝐿 is the lower confidential interval, the 𝑑𝑈 – upper confidential interval.
After we finished the calsulation we can get the result for the first order:
d-statistics: ρ ∈ [−1,1]
if ρ = −1 negetive dependence → d = 4 if ρ = 0 no dependence
if ρ = 1positive dependence →d = 0 decision is to compare the 𝑑𝑐𝑎𝑙 and the 𝑑𝐿 .
3.3.2 Multicolinearity
Multicolinearity is the existence of a linear relationship between the observations of the explanatory variables. Failure to comply with Gauss-Markov requirements for least squares estimation: Matrix X does not have full rank and matrix 𝑋𝑇X has determinant close to zero (the statistical estimation error). The error in this model has specification.
The perfect co-linearity would be det (𝑋𝑇𝑋)−1= 0.
The multicolinearity: det (𝑋𝑇𝑋)−1 = 0 Causes:
The same trend of economic time series;
Non-experimental nature of data in cross-sectional analysis Improper delay of explanatory variables,
Inadequate use of artificial variables
→ Multicollinearity is the problem of the sample.
The consequences is to estimations of parameters have large variance and covariance which can cause incorrect testing of the hypothesis. Also to find the influence of individual explanatory variables cannot be separated.
The used techniques are correlation matrix, multiple correlation coefficient and correlation rate. The factors change variability, tolerance level, the characteristics of the correlation matrix, shares variability. We are looking for the presence of dependency between explanatory variables, strength of dependency between explanatory variables and form of dependency between explanatory variables.
Correlation matrix:
𝑟𝑋𝑖,𝑋𝑗 for 𝑋𝑖 ≠ 𝑌𝑗 , where i, j = 2, 3,…,k,
General rule are |𝑟𝑋𝑖, 𝑋𝑗| < 0.8 (does not apply to the main diagonal)
So for the result here will be used with STATA comment as “vif”. It means variance inflation factor. If the result smaller than 0.8 we assume the model does not have multicollinearity.
3.4 Economic Verification
After the econometric test, in this part we have economic verification for the model.
the economic verification include model specification and test for residual normalization.
3.4.1 Model Specification
Model specification is made if all important variables are in the model and linear dependence is the good one for the model. In this part we should focus on predicted values and residuals. We arr looking at the development of standardized residuals. The development has to be in confidential interval 95% with [-1.96;1.96].
There is two methods to test the model. we use the Ramsay RESET Test which works with understandized predicted values.
This prediction we use STATA software. After we have predicted variables. create the hypothesis for our model correctly specifies test.
Hypothesis:
H0: regression model is correctly specified.
H1: regress model is not correctly specified
We need to calculate 𝐹𝑐𝑎𝑙 and 𝐹𝑐𝑟𝑖𝑡 with the formula as follow:
𝐹𝑐𝑎𝑙 =
𝑅𝑛𝑒𝑤2 −𝑅𝑜𝑙𝑑2 𝑑𝑓1 1−𝑅𝑛𝑒𝑤2
𝑑𝑓2
~ 𝐹(𝑑𝑓1, 𝑑𝑓2). (3.8)
where 𝑑𝑓1is number of new variables, 𝑑𝑓2 is n-k (k is number of coefficient in new model plus constant and n is number of observations.
We can get
𝐹
𝑐𝑟𝑖𝑡 from excel buy FINV (𝑑𝑓
1, 𝑑𝑓
2).
Decision rule:
𝐹
𝑐𝑎𝑙>
𝐹𝑐𝑟𝑖𝑡 , we disapprove H0 at significance level of α𝐹
𝑐𝑎𝑙<
𝐹𝑐𝑟𝑖𝑡 , we accept H0 at significance level of α and our model is correctly specified.3.4.2 Normality of residual component
The main concern about normality is that the confidence intervals and tests reported by your statistical software mean what they are supposed to. The consequences is invalid tests for regression parameters and confidence intervals are unreliable.
We need to use the residual so here we need to predict. The comments in STATA written as “regress Y, X1, X2, X3” after we get the result we comment for prediction of the residual.
Here in this thesis we use the graphical tests for our model. The histogram graph, the P-P plot and the Q-Q plot. From the graph result we can get the normality of the residual component really obvious.
If the result of the histogram graph at the 0 point are the highest, it means the residuals are normal.
If the result of the P-P plot and Q-Q plot the result of the start and the end are more closer to the estimation line, it means the residuals are normal.
4 ASSESSMENT OF STUDENT BEHAVIORAL FACTORS IN FX TRADING
In this chapter we start to test our sample data. We try to prove there are some herding effect happen between students as well. Moreover we are going to find out that which variable have correlation with the herding behavioral and the relationship between the variables.
4.1 Data Modification and Description of the Model
In this thesis, the original data are panel data. We will do some preparation of data for the calculation. Hence the first step with be the data preparation. Then we can start our hypothesis and describe the model.
4.1.1 Data Modification
The objective students are from economic faculty in VSB-TUO academic year 2015/2016. The trading period is 20th February 2016 to 20th May 2016. It is 96 days and 65 students. Hence here is a sample of the data in below Table 4.1.
Table. 4.1 The original details data of student No.37 Student no. Type Currency Pair Units Time
(UTC)
Price Balance
37 Buy
Market
EUR/USD 10 2016/3/10 1.09696 100000 37 Sell Market USD/CAD 500 2016/3/14 1.32114 100000 37 Sell Market USD/CAD 500 2016/3/14 1.32987 100000
37 Buy
Market
GBP/USD 5000 2016/3/22 1.42101 99991.7
37 Buy
Market
USD/CHF 10000 2016/3/31 0.95879 99993.1 Source: Oanda; Objective Student No.37
https://www.oanda.com/
From this Table 4.1 we found this is the trading details with the time period, the student No.20 are doing trades. The students’ activity are shown in each rows. The type means it is a buying or selling activity. The unit means how many piece of currency they trade. Using the time and the balance we get the information of the open and close balance of each students of each days. Then we use the type and units to get other important items:
the buying or selling frequency, the buying or selling units and the number of active students for buying or selling. Hence first we need to prepare the daily balance for each student. We need to find each student’s each day’s last activities to find their close balance.
And the close balance for today represent the open balance for tomorrow. The sample is shown in Table 4.2.
Table 4.2 The sample of daily balance of the student No. 37
Date Open balance Close balance Profit
2016/2/22 100000 99435.86 -564.14
2016/2/23 99435.86 99435.86 0
2016/2/24 99435.86 99435.86 0
2016/2/25 99435.86 99435.86 0
2016/2/26 99435.86 99435.86 0
2016/2/27 99435.86 99435.86 0
2016/2/28 99435.86 99435.86 0
2016/3/4 99435.86 99439.39 3.53
Source: Author
From this Table 4.2 we can see there are open balance, close balance and profit of each student of each day. Then we sum each day’s open and close balance of all 65 students. The sample of the balance we get it is shown as below.
Table 4.3 The sample of sum of daily balance Date Sum of the open
balance
Sum of the close
balance Profit
2016/2/22 6500000 6506132.1 6132.1
2016/2/23 6506132.1 6509883.29 3751.19
2016/2/24 6509883.29 6397616.14 -112267
2016/2/25 6397616.14 6405020.54 7404.4
2016/2/26 6405020.54 6429531.37 24510.8
2016/2/27 6429531.37 6429461.1 -70.27
2016/2/28 6429461.1 6429524.26 63.16
Source: Author
From this Table 4.3 we can get the daily open balance and the close balance for all 65 students. Here the sample is the start week of the trading. After we have the open balance and close balance. We need to find activates of all students. We use the type and units to get other important items: the buying or selling frequency, the buying or selling units and the number of active students for buying or selling. From the original data we prepared the new table which the sample is shown as below.
Table 4.4 The sample of the data for calculation Date Buying
frequency
Buying unit
Buying activities
students
Selling
frequency Selling unit
Selling activities
student
2016/2/22 178 24400200 12 136 17358800 20
2016/2/23 99 24933900 18 71 17602230 13
2016/2/24 87 11982980 18 70 15761150 15
2016/2/25 93 37516032 20 96 3943000 13
2016/2/26 78 19815910 17 67 20367189 12
2016/2/27 0 0 0 0 0 0
2016/2/28 3 510100 2 5 516600 4
Source: Author
We can found that from this Table 4.4 we have the most important item which we can use for our hypothesis. This is only the first week of the trading. And this will give us a lot of idea about the test and how to make our model.
4.1.2 Description of the Hypothesis
From the psychology point of view, the herding could be divided into two situation:
buying herding and selling herding. And in our case, the students are not only trading with their interest. But also they are doing the trade for the bonus of the class and the result.
This trading game is been taking account as the obligatory work. That’s why if there are more student doing the trade no matter is buying or selling. This activities could influence each other to check their account and make some movement. Especially we are the classmates or the schoolmates. The students are more in a closed group with each other.
So in this case the trading activities are not only about what they buy or sell. It is more about did they buy or sell. So the activity student will be the main subject we are going to have a look.
We want to know what the most important variable is for the students who are willing to make trades. That’s reason we assume the dependent variable as the number of activity students today. We want to test what could influence students to make trade. From the trading activities we get the variables. The variable which we could use for our hypothesis will be shown as below Table 4.5.
Table 4.5 The items for the hypothesis model
BUYING HHERDING symbol SELLING HERDING symbol
Number of buying activity student N𝑡 Number of selling activity student SN𝑡
Open balance O𝑡 Open balance O𝑡
Buying frequency from yesterday BF𝑡−1 Buying frequency from yesterday BF𝑡−1 Buying unit from yesterday BU𝑡−1 Buying unit from yesterday BU𝑡−1 Selling frequency from yesterday SF𝑡−1 Selling frequency from yesterday SF𝑡−1 Selling unit from yesterday SU𝑡−1 Selling unit from yesterday SU𝑡−1 Source: Author
From this Table 4.5 we could understand that we want to analyze the relationship between the number of activity students today (N𝑡) and the other items which is shown above. From the logical and psychological point of view we think the open balance of today it is the important item for the students who want to buy or sell their currency. So here we assume the open balance of today (O𝑡) are the first independent variable. From the Table 4.5 we can going to test if there are relationship between the number of activity students
today (N𝑡) and the other variables. Then we create model for the most correlated variables.
From the model, we can test if there are herding effect happen between students or not.
4.2 The Buying Herding Model
First, we need to see the pair correlation of the sample variables and choose the high correlated variable and create the model. After all the test we can get the summery.
4.2.1 Statistic Verification
Model Estimation
From Table 4.5 we could see that number of activity students today (N𝑡) is the dependent variable. And within the first variable it is taking in our account as the open balance of today (O𝑡). Then we make the pair test for the other variables to find out that which one is the second variable for this model. We make a simple linear model for this herding effect for buying students. The formula will be shown as below:
𝑁𝑡 = 𝛽1+ 𝛽2∙ 𝑂𝑡+ 𝛽3∙ 𝑋𝑡+ 𝜀𝑡 (4.1) where the dependent variable N𝑡 is the number of activity students today. The other independent variables are O𝑡 is the open balance of today, the 𝑋𝑡 is the other independent variable we choose. The 𝛽1 is the constant term, 𝛽2 is the transaction factor, the 𝛽3 is the preference factor (𝛽3 > 0). Because of the herding effect logic, in this model when 𝑋𝑡 increase the N𝑡 have to increase as well. Only could be positive relevant between this two variables. and the 𝜀𝑡 is the residual. All coefficient 𝛽1, 𝛽2 𝑎𝑛𝑑 𝛽3 needed to be found by following calculation.
We test the pair correlation of the variables to see which independent variable could be most fit in. For the correlation we will use the STATA as the software and the Table 4.6 will be shown as also from STATA calculation.
Table. 4.6 The correlation test for the variables
Source: Authors’ calculation
From this Table 4.6 we can found that the most correlated items with the number of buying activity students (𝑁𝑡) from the five other independent variables are open balance from yesterday (𝑂𝑡) 0.5205 and the buying frequency from yesterday (𝐵𝐹𝑡−1) 0.5833. This two variables have the highest correlation compare with others. We test the statistical significance in next calculation. From here we can understand the trading of the students for buying could be influenced by today your balance and the trading frequency from yesterday your classmates did. This really make sense from the psychology point of view.
Now the formula will be changed with the third variable been founded. The new formula will be as below:
𝑁𝑡 = 𝛽1+ 𝛽2∙ 𝑂𝑡+ 𝛽3∙ 𝐵𝐹𝑡−1+ 𝜀𝑡 (4.2) where the 𝐵𝐹𝑡−1 is the buying frequency from the day before. Because the high correlation with the (𝑁𝑡) . Because the data are from all students trades of the day. Hence we cannot use the same days buying frequency. The number of buying activity students create the
0.0000 0.0049 0.0000 0.0000 0.0000
SUt1 0.4223 0.2976 0.7174 0.5313 0.7529 1.0000
0.0000 0.0000 0.0000 0.0001
SFt1 0.5139 0.4882 0.9201 0.3917 1.0000
0.0146 0.1012 0.0000
But1 0.2596 0.1759 0.4413 1.0000
0.0000 0.0000
BFt1 0.5833 0.5819 1.0000
0.0000
Ot 0.5205 1.0000
Nt 1.0000
Nt Ot BFt1 But1 SFt1 SUt1
buying frequency of that day. So there we use the day before buying frequency to see that if the students will be influenced by the behavior of other students from yesterday.
To make the verification of our formula, we make the regression of the data. The result are shown as follows:
Table 4.7 Regression test for Nt, Ot and BFt−1
Source: Authors’ calculation
From the Table 4.7 we can found out that the R-squared is 0.3898. If the result is closer to 1, it means a perfect fit. If the result it is closer to 0 means there are no relationship between the variables. But here the number it is not so big but still it means there are some related relationships between them. Still it is the biggest compare with other variables.
From the P > |𝑡| result we could accept this assumption because the numbers are all lower than the significant level which we are always consider as 5%. That is good. The coefficient of constant is -70.76973. The coefficient of 𝑂𝑡 is 0.0000127 with the units as USD. The coefficient of 𝐵𝐹𝑡−1 is 0.0932694 with the units as times. For the formula. We can finally have all the coefficients. After the regression test we can have our formula even more clear as follow:
𝑁𝑡 = −70.76973 + 0.0000127 ∙ 𝑂𝑡+ 0.0932694 ∙ 𝐵𝐹𝑡−1+ 𝜀𝑡 (4.3)
.
_cons -70.76973 28.97746 -2.44 0.017 -128.3847 -13.15478 BFt1 .0932694 .0229218 4.07 0.000 .0476947 .1388442 Ot .0000127 4.82e-06 2.63 0.010 3.08e-06 .0000222 Nt Coef. Std. Err. t P>|t| [95% Conf. Interval]
Total 6874.5 87 79.0172414 Root MSE = 7.0252 Adj R-squared = 0.3754 Residual 4195.07457 85 49.3538185 R-squared = 0.3898 Model 2679.42543 2 1339.71272 Prob > F = 0.0000 F(2, 85) = 27.15 Source SS df MS Number of obs = 88
After we got this formula we should test the model if the model is working for our hypothesis. Also we need to do t-test and F-test for our model to test the whole model it is significant.
T-test
Here we are going to test if the coefficient is statistically significant or not. And from the hypothesis we can of the T-test we can see as follow:
For 𝛽2 : Hypothesis:
H0: 𝛽2 = 0 H1: 𝛽2 ≠ 0
From the formula (3.4) calculate the Tcal is equal to 2.634855, for the T(crit) we use excel comment “TINV” to get the result. The T(crit) is equal to -1.66298. The result its means the T(cal) = 2.634855 is bigger than T(crit) = |−1.66298| so we reject H0 at the level of significance 5%, it means, we can assume that 𝛽2 is statistically significant.
For 𝛽3 : Hypothesis:
H0: 𝛽3 = 0 H1: 𝛽3 ≠ 0
From the formula (3.4) calculate the T(cal) is equal to 4.069026. The T(crit) we used excel “TINV” and get the result is as -1.66298. It is means the T(cal) = 4.069026 is bigger than T(crit) = |−1.66298| so we reject H0 at the level of significance 5%, it means, we can assume that 𝛽3 is statistically significant.
F-test
F-test is going to test the whole model. In the level of significant 5% we need to compare the critical value and the calculated value. In this calculation we make new hypothesis for our test. The hypothesis as below:
Hypothesis:
H0: 𝛽2 = 𝛽3 = 0 H1: 𝛽2 ≠ 0 ∨ 𝛽3 ≠ 0
We calculate the F value one by one through the formula (3.5) and we get the result as F(cal)= 27.15, and use excel comment “FINV“ we can get the F(crit)= 3.103839. so from the result we could decide that the F(cal) is bigger than F(crit). Here we can reject H0 at the level 5% of significance alfa, it means the whole model is good.
4.2.2 Econometric verification of the model
From here we check the underlying assumptions autocorrelation and multicollinearity.
Autocorrelation
Autocorrelation of residual parts is serial dependent time series residues and residues time delayed series. The main cause of autocorrelation are inertia time series, inappropriate specification of mathematical form of model, inclusion of error from responsible variables into the random component and so on. If there is autocorrelation, we should eliminate it.
Firstly should test autocorrelation with Durbin-Watson test. We make a hypothesis:
H0: ρ =0 (no autocorrelation of 1st order) H1: ρ ≠ 0 (autocorrelation of 1st order)
We should also know where is 𝑑𝑐𝑎𝑙 and where is 𝑑𝐿(lower confidential interval) and 𝑑𝑈(upper confidential interval). By using the command “dwstat“ in STATA we can get
Durbin-Watson d-statistic( 3, 88) = 1.481074
Because our sample size is 88, the number of variables is 3 and the significance level is 5%, according to the website for the DW-test we can find the information as following Table 4.8:
