HERD BEHAVIOR IN THE ERA OF QUANTITATIVE EASING:
EVIDENCE FROM THE ISTANBUL STOCK EXCHANGE
Master Thesis in Int’l Finance Author: Yener Kus
Student Number: 10845240
Supervisor: Asst. Prof. Rafael Matta Amsterdam, August 2016
2
ACKNOWLEDGEMENTS
I would like to express my gratitude to my supervisor Asst. Prof. Rafael Almeida da Matta for all guidance and helpful comments in the research process. Last but the most important appreciation to my inspiring family, Mr. Habip Kus, Mrs. Aynur Kus, Mr. Taner Kaan Kus, Mrs. Neslihan Kus, Ms. Sedef Kus and Ms. Bade Kus. You all have been the source of my life, my strength and my light into the darkness.
3
ABSTRACT
In this study, the Istanbul Stock Exchange (BIST) in Turkey is analyzed for herd behavior with a market-wide approach. The models, which are developed by Christie and Huang (1995) and Chang, Cheng, and Khorana (2000), are employed to detect herd behavior for the daily data obtained from 2009 to 2015. Being an emerging market, investigating the Turkish stock market during this time period is especially interesting since the time interval in our study covers the expansionary policy of the FED. We expected that such an expansionary policy might affect Istanbul Stock Exchange in terms of herding.
Christie and Huang (1995) uses cross-sectional standard deviation (CSSD) as a measurement of dispersion. As a result of CSSD analysis, no evidence of herding is found in BIST. Further, we performed our analysis by employing cross-sectional absolute deviation (CSAD) which is used as a measurement of dispersion by Chang, Cheng, and Khorana (2000). Again, no evidence of herding is found in BIST after CSAD analysis.
As Chang, Cheng, and Khorana (2000) states that the linear and increasing function between market return and dispersion will be impaired when market participants start to herd during excessive market movements. As a result, the relationship will be non-linearly increasing or decreasing in case the presence of herd behavior. This time, we performed our analysis for CSAD not only for all days but also for up and down market days as sub-periods. Our empirical results concluded that BIST is a herd free market for all days, up market and down market days.
4 TABLE OF CONTENTS Acknowledgments……….………..…. 2 Abstract………..………….. 3 1. Introduction………. 5 2. Theoretical Background...………..……….. 8
2.1 Efficient Market Hypothesis vs Behavioral Finance……….………….. 8
2.2 Herd Behavior in Financial Markets……….………. 9
3. Previous Empirical Research…..……… 12
4. Quantitative Easing……….. 15
5. Methodology………...……… 16
5.1 Christie and Huang Model………. 17
5.2 Chang Cheng and Khorana Models………... 18
6. Data and Descriptive Statistics ………... 21
7. Empirical Results.……….……... 26
8. Conclusion………... 29
9. References………... 31
10. Appendix……….. 33
5
1. INTRODUCTION
Herd behavior is possible to be illustrated with the following example: After reviewing all available travel blogs, a couple decides to enjoy their honeymoon in one of the top rated peaceful silent place. Upon arrival at the travel agency to buy flight tickets and arrange accommodation, they discover surprisingly, that no couple is interested in that place, while another cheerfully crowded place is trendy among the honeymoon couples, and finding a room is barely possible. This circumstance will possibly make the couple question their prior choice. Travel agent asks that inevitable question: where do you want to go? Should they go for their first decision or believe in majority’s choice of place for the honeymoon?
The same dilemma as the couple experience at the travel agency also exists among investors in a stock market. When other investors’ choice is in a certain way, how confident is an investor if his independent decision differs from the market? The decision of a rational investor is based on available information and it would not be impaired by psychological drivers such as the common decision of other investors. The tendency for investors to imitate the behavior of others in stock markets is called herding. Nofsinger and Sias (1999) defined herding as a group of the market participants act in the same way within a certain time period. Also, Banerjee (1992) defined herd behavior as market participants who imitate the others, even though their private information recommends acting in another way.
The Efficient Market Hypothesis is defined as the market in which investment decision of firms and similarly investment decision of all other investors among the securities of these firms are based on the fully available information. Accordingly, prices of these securities fully reflect all available information. Such a market which is constituted by prices based on all available information is called efficient (Fama, 1970). Based on the Efficient Market Hypothesis, market participants tend to buy stocks which are undervalued or sell the ones which are overvalued. In contrast, the participants who mimic the others act against to the Efficient Market Hypothesis and buy or sell the stocks that others are buying or selling. In other words, market participants start to act like ancient people who didn’t grasp the condition of the environment and stick to each other to feel secure (Caparrelli et al., 2004). Also, Wylie (2005) defined herding as it starts
6
when market participants do not move according to their available information, but they take the others’ preference into consideration as an investment decision, and eventually trading way of the group members becomes in parallel (Wylie, 2005).
In Turkey, Christie and Huang (1995) and Chang, Cheng and Khorana (2000) methods were used in many studies to test herd behavior. Altay (2008) examined the presence of herd behavior in BIST from 1997 to 2008. He used daily returns of all stocks between January 1997 and February 2008. He found the evidence of herd behavior in BIST by the implementation of the methodology which is based on Christie and Huang (1995) regression model. Also, by using Chang, Cheng, and Khorana (2000) regression models, he concluded herd behavior towards the market is a general trend for the whole market, but he could not find the evidence of herding in the sub-periods of December 2003-April 2004 and May-October 2006. Similarly, Coban (2009) examined the herd behavior in BIST for the same period (from 1997 to 2008). He used both models to test herd behavior. In contrast to Altay (2008), he found no evidence of herd behavior as a result of two different regression models. Ozdogan (2009) examined herd behavior from 2006 to 2008 for the banking sector. She employed Christie and Huang (1995) method to measure herd behavior by using daily returns of the 11 publicly traded bank stocks between December 2006 and December 2008. She found no evidence of herding for the mentioned period. Can (2014) analyzed herd behavior of BIST from 1997 to 2013. She employed two different models by using daily and monthly returns of all stocks from 1997 to 2013. Based on Christie and Huang (1995) method she found no evidence of herd behavior in BIST for daily and monthly intervals. Based on Chang, Cheng, and Khorana (2000), again she found no evidence of herd behavior except monthly down market. Dogukanli and Ergun (2015) examined the existence of herd behavior for 15 industries from 2000 to 2012 by using Christie and Huang (1995) method. They used daily and weekly stock returns of 15 industries in BIST between January 2000 and September 2012. They found no evidence of herding. It is obvious to say that conclusions are possible to differ according to the chosen time interval, sub-groups or sub-periods.
Starting from the end of 2008, US Federal Reserve (FED) launched Quantitative Easing (QE) program. Ross (2015) explains the effect of QE as stock markets tend to boost in case of easing policy or downturn in a case of tightening policy by FED. Bhattarai et al. (2015) found that
7
financial indicators of emerging market economies have been significantly affected by expansionary QE program by FED in terms of appreciation of exchange rates, a decrease in long-term bond yields, and an increase in both stock markets and capital inflows. Wang (2008) concluded that emerging markets tend to herd more than developed markets. Also, Hwang and Salmon (2004), stated that herding is generally discussed in large price movements of stock markets, such as crisis or booming. Being an emerging market, investigating the Turkish stock market during 2009 to 2015 is especially interesting since the time interval in our study covers the expansionary policy of the FED. We estimate that such an expansionary policy might affect Istanbul Stock Exchange (hereinafter BIST) in terms of herding.
This study aims to analyze whether herd behavior, measured with a market-wide approach, is present in BIST between the period of 2009 and 2015 by using daily returns of all stocks in BIST and BIST All-Shares Index as an indicator of market return. This study will be an additional research in the field of herding behavior analysis of BIST that specifically covers the QE period.
H0: There is no herd behavior in BIST in the era of QE
H1: There is herd behavior in BIST in the era of QE
In this study, the hypothesis will be tested using Christie and Huang (1995) and Chang, Cheng and Khorana (2000) methods and the regression analyses will be employed in order to reach to the results.
8
2. THEORETICAL BACKGROUND
In this section efficient market hypothesis and behavioral finance will be discussed, and respectively literature review regarding herd behavior in financial markets will be presented.
2.1 EFFICIENT MARKET HYPOTHESIS VERSUS BEHAVIORAL FINANCE
There are two contrast views of investment behavior in financial markets, namely traditional Efficient Market Hypothesis (EMH) and behavioral finance.
EMH is defined as the market in which investment decision of firms and similarly investment decision of all other investors among the securities of these firms are based on the fully available information. Accordingly, prices of these securities fully reflect all available information. Such a market which is constituted by prices based on all available information is called efficient. In his paper, three different forms of EMH were discussed. First, weak form, in which prices reflect all historical prices. Second, semi-strong form, in which the matter is whether other publicly available information is reflected in the prices. Third, strong form, in which the matter is whether private information is reflected in the prices (Fama, 1970). Malkiel (2003) extended the definition of EMH as “prices fully reflect all known information, and even uninformed investors buying a diversified portfolio at the tableau of prices given by the market will obtain a rate of return as generous as that achieved by the experts.” He also stated that “efficient financial markets do not allow investors to earn above-average returns without accepting above-average risks”. He illustrated efficiency in the financial markets with the following tale between a finance professor and a student. They come across a $100 bill lying on the ground. The student stops and tries to pick up the bill. However, professor interrupts and says: “Don’t bother-if it were really a $100 bill, it wouldn’t be there.” He also extended that “True value will win out in the end. Before the fact, there is no way in which investors can reliably exploit any anomalies or patterns that might exist.” (Malkiel, 2003).
In contrast to EMH, Shiller (2003) raised another discussion on Behavioral Finance which is a mixture of psychology, sociology, and finance. Shiller (2003) criticized EMH in terms of underestimating psychological effect. For instance, EMH might lead to remarkably wrong assumptions of cases such as extensive stock market bubbles. We need to avoid EMH
9
presumptions foreseeing that prices always fully reflect all available information. At this point, behavioral finance explains the underlying reason for stock market boom which is followed by crash after 2000 (Shiller, 2003).
Ritter (2003) points out that there are two main parts supporting behavioral finance: subjective behaviorism and limits to arbitrage. Subjectively refers to the way that people think. There are lots of previous research proving that people make systematic errors in how they think. They feel reckless and their choice might be biased. Behavioral finance takes subjective behaviorism out of its scope. Limits to arbitrage are used in order to estimate in which cases arbitrage forces will be sufficient. Aiming to differentiate intentional choices from erroneous thoughts, there are models developed in behavioral finance for irrational investors. Because people are bad Bayesians, erroneous choices appear. EMH is a main supporting part to Modern Finance. Based on EMH, correct prices will be reflected as a result of a clash between market participants searching for exceptional returns. While EMH presumes rationality of markets, it does not presume that all market participants are prudent. While EMH presumes that markets make impartial predictions, it does not presume that markets can predict the future. As a contradiction to EMH assumptions, behavioral finance discusses that markets are inefficiently informed in some cases (Ritter, 2003). Barberis and Thaler (2002) explains limits to arbitrage as a contradictory view to EMH. Limits to arbitrage might lead to significant mispricing.
2.2 HERD BEHAVIOR IN FINANCIAL MARKETS
There are a number of different studies within the field of herd behavior in financial markets in the area of Behavioral Finance.
In the early 1990s, herd behavior was introduced. Banerjee (1992) defined herd behavior as market participants who imitate the others even though their private information recommends acting in another way. Chiang and Zheng (2010) discuss that if investors start to herd around the market consensus, stock prices can be impaired by market participants’ behavior regardless of economic essentials. Consequently, stocks do not reflect correct prices. There are two different routes for empirical research of herd behavior. The first route for analyzing herding behavior targets on the characteristic of moving together based on dynamic interaction. The second route
10
targets on the cross-sectional correlation dispersion in stock returns within the day of enormous market price movement.
The presence of herding is against to EMH. EMH indicates that informed market participants foresee possible prices, accordingly, they predict future price according to model such as the CAPM. So that, market participants can estimate the equilibrium price and analyze it according to the existent price. If the current price is not consistent with the expected return, the current price will adapt to expected return by vacuuming all the available information. Based on the Efficient Market Hypothesis, market participants tend to buy stocks which are undervalued or sell the ones which are overvalued. In contrast, the participants who mimic the others act against to the Efficient Market Hypothesis and buy or sell the stocks that others are buying or selling. In other words, market participants start to act like ancient people who didn’t grasp the condition of the environment and stick to each other to feel secure (Caparrelli et al., 2004).
In their paper, Hwang and Salmon (2004) discuss that notwithstanding their own private information or expectations, when market participants agree to mimic the opinion or the direction of others, herd behavior appears. In financial markets, herding is a crucial behavior factor and it occurs especially when excessive market movement is in place (Hwang and Salmon, 2004).
According to Bikhchandani and Sharma (2001), the decision of investors might be erroneous at all for all of them when they are affected by the others and accordingly start to herd around a decision. The undisputable intent of market participants to mimic the attitude of other participants leads to herding. This case differs from “spurious herding” in which market participants face similar trouble and information leading to an alike decision. “Spurious herding” counts as an efficient result while “intentional herding” does not count as an efficient result. Differentiation of these two behavior characteristics is difficult due to the fact that many elements affect investment decision (Bikhchandani and Sharma, 2001).
Some authors suggest that there are different types of herd behavior in financial markets. Devenow and Welch (1996) point out to non-rational and rational views. Non-rational herd behavior focuses on psychology and believes that investors behave like lemmings, follows each
11
other instinctively and beyond the rational outcomes. The rational herd behavior focuses on externalities, most favorable opinion construction which is altered by information obstacles or motivation matters. Rational herd behavior can be discussed with the different type of reasons. Bikhchandani and Sharma (2001) presented the important ones as “imperfect information”, “concern for reputation” and “compensation structures”.
The first form of rational herding is “imperfect information”. Assume that investors receive an equivalent level of investment decisions under the unclear circumstance and have private information for the correct decision making. Under this circumstance, this private information of an investor may arise as a result of an investigation. Although all information is publicly available, the quality of information flow is uncertain. In the market, seeing each other investor’s move is possible however, it is not the same for observing private information or signal that each investor receives. If market participants have some thoughts about correct investment move, then conclusions about an investor’s private information can be concluded from the actions chosen. In this case, it is possible that herd behavior appears (Bikhchandani and Sharma, 2001).
The second form of rational herding is “concern for reputation”. According to the skills of managers, it is possible for one manager to mimic investment decision of the other managers. Suppose that there are two managers who faced with a similar investment opportunity. These two managers might be high or low skilled whereas one of them is high skilled and the other one is low skilled. When one of the managers is of high skilled and the other is not, it is possible for herd behavior. The low skilled manager might mimic the investment decision of the high-skilled manager although her own information tells her otherwise (Bikhchandani and Sharma, 2001).
The third and final form of rational herding is “compensation structures”. If a manager’s compensation depends on how her performance is in comparison with the others, then the decision of the manager might be impaired by the others. In this case, herding is possible to appear (Bikhchandani and Sharma, 2001).
According to Hwang and Salmon (2004); apart from being rational or irrational incentives for herding, it is obviously crucial to differentiate analytically whether movements are common or correlated. While one of the movement ways causes market inefficiency, or in other words,
12
herding. The other one is a way of efficient market movement which is based on all available information. Hwang and Salmon (2004) introduced with a new statistical method which is very similar to Christie and Huang’s (1995) method. Their method differs in terms of using the information held in the cross-sectional movements of the market. Differently from herding by investors, their method grabs market-wide herding when the expectation of the market converge on specific stocks or stock classes. Also, their method is comparably straightforward because they use observed returns.
Henker et al. (2006) examined the herding by constructing subgroups, such as particular industry sectors. Simply, their method differs from classical herding definitions in terms of measuring herding of a subgroup of investors rather than using methods only for individuals.
In this paper, empirical research is performed similarly to Hwang and Salmon’s market-wide approach.
3. PREVIOUS EMPIRICAL RESEARCH
Christie and Huang (1995) introduced a method to measure herd behavior which is still used today. Aiming to analyze herd behavior, they used dispersion, or in other words cross-sectional standard deviation (CSSD) of stock returns. Christie and Huang (1995) explained as “When individual returns herd around the market consensus, dispersions are predicted to be relatively low. In contrast, rational asset pricing models predict an increase in dispersion because individual returns are repelled away from the market return when stocks differ in their sensitivity to market movements. The results for both daily and monthly returns are inconsistent with the presence of herding during periods of large price movements”.
Their study led to another wide-spread method to measure herd behavior. Chang et al. (2000) used cross-sectional absolute standard deviation (CSAD) of returns in their model to detect herd behavior. Their assumption in the model based on that CAPM estimates dispersions as a linear function of the market return as well as predicting that the dispersions are an increasing function of the market return. They employed the model in the stock markets of U.S., Hong Kong, South
13
Korea, Japan and Taiwan. They found U.S. and Hong Kong as a herd free markets and Japan as a partial evidence of herding. For emerging markets, South Korea and Taiwan, they found significant evidence of herding.
Followings are some worldwide samples of empirical research and results.
Caparrelli et al. (2004) examined Italian Stock Exchange from 1988 to 2001 for herd behavior analysis. They used both Christie and Huang model and Chang, Cheng and Khorana models. Based on Christie and Huang model they found a significant level of herding especially during excessive market movements. However, when they repeated the analysis for subgroups of small-cap stocks and large-small-cap stocks, they concluded different results for each group. For large-small-cap stocks, herding was higher than small-cap stocks. Also, they found that herding is more significant when the market is in a downward trend.
Tessaromatis and Thomas (2009) analyzed herd behavior in the Athens Stock Exchange from 1985 to 2004. They argue that “Rational asset pricing suggests that given the exposure of stock prices to systematic factors, large market price increases or decreases will be associated with a larger dispersion of individual stock returns around the market aggregate. In contrast, if herding occurs, stock prices will be tightly clustered around the market aggregate”. They used Christie and Huang model and Chang, Cheng and Khorana models in their analysis. While they found little evidence herding for the entire time period, they found some different results when they repeated the analysis for sub-periods. Between 1998 and 2004, and for both up and down market trend, they found significant level of herding. When they split the entire period into yearly sub-periods, they found a significant level of herding in some yearly sub-periods whereas no herding in others. Moreover, they concluded no significant difference between large-cap and small-cap stocks in terms of herd behavior characteristic.
Chiang and Zeng (2010) examined herding behavior for 18 countries from 1988 to 2009. They found significant herd behavior in advanced stock markets (except the U.S.) and in Asian markets. They found evidence that herding behavior of non-US markets is explained by the stock return dispersions in the US. Except the US and Latin American markets, they found significant herding
14
both for up and down markets. On the other hand, herding in Asian markets is more significant in up-market days than in down-market days.
Ohlson (2010) examined Stockholm Stock Exchange in Sweden for measuring herd behavior from 1998 to 2009 by using market-wide approach. He used Christie and Huang model and Chang, Cheng, and Khorana models in his analysis. He found significant herd behavior in the bullish market by measuring daily basis over the entire time period. He divided the entire period into the yearly sub-periods and concluded herd behavior in bullish markets of 2005 and 2007. Also, he repeated the analysis according to stock sizes and concluded with significant herding in large-cap stocks.
Lindhe (2012) performed his analysis to measure herd behavior characteristics in four Nordic countries (Denmark, Finland, Norway, and Sweden) by using the data between 2001 and 2012. He found significant evidence of herding in Finland both up-and-down markets while he could not find any herding in Denmark, Norway, and Sweden. Considering sub-periods, he found significant herding in Finland in down market of 2001 and the up-market of 2004. Moreover, he found significant evidence of herding across national borders. He concluded that both Finland and Sweden herd around the US market while all Nordic countries herd around the European market.
Also in Turkey, Christie and Huang (1995) and Chang, Cheng, and Khorana (2000) methods were widely used in many studies.
Altay (2008) examined the presence of herd behavior in BIST from 1997 to 2008 by using Christie and Huang model and Chang, Cheng, and Khorana models. He found significant evidence of herd behavior in BIST by using both models. When he divided the time period into sub-periods, he could not find herding between December 2013-April 2014 and May 2006-October 2006. Similarly, Coban (2009) examined the herd behavior in BIST for the same period. In contrast to Altay (2008), he found no evidence of herd behavior. He employed both Christie and Huang model and Chang, Cheng, and Khorana models. As a result, he could not find any evidence of herding.
15
Ozdogan (2009) examined herd behavior from 2006 to 2008 for the banking sector. She employed Christie and Huang (1995) method to measure herd behavior by using daily returns of the 11 publicly traded bank stocks between December 2006 and December 2008. She found no evidence of herding for the mentioned period.
Can (2014) analyzed herd behavior in BIST from 1997 to 2013. She employed two different models by using daily and monthly returns of all stocks from 1997 to 2013. Based on Christie and Huang (1995) method she found no evidence of herd behavior in BIST for daily and monthly intervals. Based on Chang, Cheng, and Khorana (2000), again she found no evidence of herd behavior except monthly down market.
Dogukanli and Ergun (2015) examined the existence of herd behavior for 15 industries from 2000 to 2012 by using Christie and Huang (1995) method. They used daily and weekly stock returns of 15 industries in BIST between January 2000 and September 2012. They found no evidence of herding.
It is obvious to say that conclusions are possible to differ according to the chosen time interval, sub-groups or sub-periods.
4. QUANTITATIVE EASING
Policy interest rates of central banks were sharply cut in the months before and even after the Lehman crisis in the US in August 2008 by the FED. This policy has been implemented in an effort to support demand in the face of weakening output and employment. The FED and other central banks have applied unconventional monetary policies in the form of quantitative easing because interest rates were already fairly low. They started to large-scale purchases of financial assets (LSAPs), such as long-dated government bonds and mortgage-backed securities (Lim et al., 2014).
QE is such an unconventional monetary policy that aims to purchase securities from the market in return for increasing the money emission in the economy. QE is such an instrument which used in extraordinary economic conditions, such as economic and financial crises. QE program has been applied by the FED more than once. Starting from the early stages of 2008 financial crisis,
16
the FED applied first QE program (QE1) to meet liquidity requirement of the markets between November 2008 and March 2010. Within this period, the FED purchased mortgage backed securities and treasury bills amounting to USD 2.1 trillion from the markets. After the presence of European debt crisis, the FED relaunched second QE program (QE2). They purchased USD 600 billion of treasury securities between November 2010 and June 2011. Because the US economy could not succeed the desired level, the FED launched another round of QE program (QE3) in September 2012 and as an open-ended program, they bought USD 85 billion of securities each month (Bouraoui, 2015).
Starting from the end of 2008, US Federal Reserve (FED) launched Quantitative Easing (QE) program. Ross (2015) explains the effect of QE on the stock markets as stock markets tend to boost in case of easing policy or downturn in a case of tightening policy by FED. Lim et al. (2014) point out that QE has a significant impact on capital inflows, especially in emerging markets. Bhattarai et al. (2015) found that financial indicators of emerging market economies have been significantly affected by expansionary QE program by FED in terms of appreciation of exchange rates, a decrease in long-term bond yields, and an increase in both stock markets and capital inflows. Wang (2008) concluded that emerging markets tend to herd more than developed markets. Also, Hwang and Salmon (2004), stated that herding is generally discussed in large price movements of stock markets, such as crisis or booming. Being an emerging market, investigating the Turkish stock market during 2009 to 2015 is especially interesting since the time interval in our study covers the expansionary policy of the FED. We expect that such an expansionary policy might affect Istanbul Stock Exchange in terms of herding.
5. METHODOLOGY
This study measures herd behavior in the stock exchange of Istanbul in Turkey from January 2009 until December 2015. The timeframe is selected in particular to measure whether any behavioral change of investors in BIST in the era of QE in comparison with the previous studies.
17
The daily data of closing prices of all stocks and BIST index during the time interval were obtained from Bloomberg terminal. To calculate the dispersions, daily returns of the stocks and market indicators were calculated.
There are two alternative ways of calculating returns. One of them is log returns. However, in this study the following formula will be used to calculate returns:
, , 1
, 1 ,t it it / i ti P P P
R
Ri,t is the return rate of stock i on day t, Pi,t is the closing price of stock i on day t and Pi,t-1 is the closing price of stock i on the previous day (t-1).
5.1 CHRISTIE AND HUANG (CH) MODEL
In 1995, Christie and Huang introduced a new model to analyze dispersion of stock returns. They focused on how herd behavior may reflect itself in stock returns. Under the conventional description of herd behavior, an instinctive measure of the effect of herd behavior on a market is a dispersion which is described as the cross-sectional standard deviation (CSSD) of returns. Dispersions may be explained as it measures how far away the individual returns to the mean. They are distributed around zero in case returns move in parallel with the market return. They start to differentiate from zero in case individual returns begin to vary from the market return. Empirical research proves that dispersions increase significantly in the event of excessive market movements.
The cross-sectional standard deviation, CSSD, is measured with:
1 1 2 , ,
N R R CSSD N i t m t i t (1), where Ri,t denotes observed stock return of each stock at time t, Rm,t denotes the return of BIST-All Index at time t, and N is the number of stocks in the portfolio at time t.
To test herding during excessive market movements, Christie and Huang (1995) developed following regression model with dummy variables:
18 t U t U L t D t D D CSSD (2)
, where DL or DU denotes market with a “1” if the market return on day t falls under extreme 1% and 5% lower or upper tails of the market return distributions, and “0” otherwise. The α coefficient denotes the mean dispersion of the sample excluding the regions corresponding to the two dummy variables. Rational asset pricing models predict significantly positive coefficients for andD U, and negative estimates of and D Uwould be consistent with the presence of herd behavior (Christie and Huang, 1995).
5.2 CHANG CHENG AND KHORANA (CCK) MODELS
In 2000, Chang, Cheng, and Khorana modified the model of Christie and Huang (1995) in terms of using dummy variable test with the cross-sectional absolute deviation (CSAD) as a measure of dispersion instead of using CSSD. They discussed that rational asset pricing models estimate that relationship between stock return and dispersions are linear as well as dispersions are an increasing function of market return. When market participants start to herd during excessive market movements, the linear and increasing function between market return and dispersion will be impaired. As a result, the relationship will be non-linearly increasing or decreasing.
N i t m t i t R R N CSAD 1 , , | | 1 (3), where Ri,t denotes the observed return of stock i at time t, Rm,t denotes market return or BIST all-shares Index return at time t, and N is the number of stocks in the portfolio.
Alternatively, the CSAD is tested with the same regression formula as the CSSD model:
t U t U L t D t D D CSAD (4)
, where DL or DU denotes the market with a “1” if the market return on day t falls under extreme 1% and 5% lower or upper tails of the distribution of market returns, and “0” otherwise. The
19
If market participants are more likely to herd during periods of large movements, there would be a less proportional increase (or even decrease) in the CSAD measure.
To test the relation following regression equation is used:
t t m t m t R R CSAD 1 . 2 2. (5)
, where Rm,t stand for market return. A significantly negative coefficient implies evidence of 2
herd behavior.
The relationships between CSAD and market return might be asymmetric and herd behavior can be tested for both bull and bear markets separately.
t UP t m UP UP t m UP UP t R R CSAD 1 , 2 ( . )2 Rm,t > 0 (5a) t DOWN t m DOWN DOWN t m DOWN DOWN t R R CSAD 1 , 2 ( . )2 Rm,t < 0 (5b)
, where Rm,t denotes the market return, UP t m R , ( DOWN t m
R . ) is the absolute value of market return of all available securities on day t when the market is up and (down). The reason of absolute value usage in equations (5), (5a), and (5b) is simplifying the comparison of the coefficients. In case of excessive market movements, investors herd around indicators such as the market return and CSAD starts to non-linear relation against market return. This non-linear relation indicates to herd behavior which would be explained by a negative and statistically significant coefficient 2
(Chang, Cheng, and Khorana, 2000).
Followings summarize each step that we will use in our analysis:
1- We will obtain daily market prices of each stock and BIST All Shares Index covering our time period.
2- We will obtain daily return rates for stocks and index by using daily prices.
3- We will employ formula (1) and formula (3) to obtain CSSD and CSAD as a measurement of dispersion.
20
4- We will determine 1% and 5% upper or lower tails of market return distributions in order to obtain dummy variables. Then, we will regress dummy variables against CSSD (formula 2) and interpret the results.
5- Similar to CSSD method, this time, we will regress dummy variables against CSAD (formula 4) and interpret the results.
6- To research non-linearity which is explained in Chang, Cheng, and Khorana (2000) model, we will repeat one regression model for 3 different market conditions. These are all market days (formula 5), up-market days (formula 5a), and down-market days (formula 5b). Then, we will interpret each result in terms of herd behavior characteristic.
Based on our regression models, followings will be used to interpret our results.
t U t U L t D t D D CSSD and t U t U L t D t D D CSAD
Figure 1: Estimation of Beta Coefficients for Dummy Variable Models A further step to analyze CSAD in terms of non-linearity:
t t m t m t R R
CSAD 1 . 2 2. , with respect to all market days
t UP t m UP UP t m UP UP t R R
CSAD 1 , 2 ( . )2 , with respect to up market days t DOWN t m DOWN DOWN t m DOWN DOWN t R R
CSAD 1 , 2 ( . )2 , with respect to down market days
Significantly negative β coefficients estimate herd
behavior
Significantly positive β coefficients estimate rational market
21
Figure 2: Estimation of Non-Linearity Test
6. DATA AND DESCRIPTIVE STATISTICS
At the beginning of our time period, there was the total of 283 stocks in BIST. After listed and delisted stocks, our time period ended with the total of 422 stocks. Within the time period, the maximum number of stocks reached to 424. Table 1 shows the descriptive statistics for cross-sectional standard deviation (CSSD), cross-cross-sectional absolute deviation (CSAD) and BIST-All Index return on the daily basis. Our sample contains 1761 daily observations. The period is from 02.01.2009 to 31.12.2015. We obtained daily prices of each stock and BIST All Shares Index in the time period by using Bloomberg terminal. We converted those daily prices into daily returns in order to obtain CSSD and CSAD dispersions. BIST All Shares Index return is used as a market return (Rm). # Stocks CSSD CSAD Rm # observation days 1761 1761 1761 Maximum 424 0.294 0.0507 0.0712 Minimum 283 0.0126 0.0084 -0.1046 Mean 355 0.0277 0.0172 0.0007 Median 354 0.0268 0.0164 0.0012 Standard Deviation 0.0091 0.0039 0.0149
Table 1: Descriptive Statistics covering all shares during 2009 to 2015
Significantly negative γ2 coefficient estimates herd behavior
Positive γ2coefficient estimates linear relation between dispersion
22
The maximum market return (0.0712) is observed on 10.05.2010 and the minimum (-0.1046) is observed on 03.06.2013. The maximum CSSD (0.294) is observed on 18.01.2010 and the minimum CSSD (0.0126) is observed on 08.09.2010. Maximum CSAD (0.0507) is observed on 08.06.2015 and the minimum CSAD (0.0084) is observed on 08.09.2010. When the standard deviations of CSSD and CSAD compared, CSSD’s standard deviation is higher than CSAD’s. It may be argued that data set of CSAD is more concentrated around the mean.
For determination of lower and upper tails of market returns which will be used to determine dummy variables boundaries, we used SPSS data analyzer and concluded the following boundaries:
Figure 3: Boundaries for Dummy Variable Construction
Dummy variables are constructed according to above-mentioned boundaries. Based on 1% upper and lower tails, for market returns which are upper than 0.0456 and lower than -0.0484, dummy variables concluded “1”, otherwise “0”. Based on 5% upper and lower tails, for market returns which are upper than 0.0303 and lower than -0.0305, dummy variables concluded “1”, otherwise “0”.
The following figure presents historical developments of BIST-All Shares and S&P 500 index during the time period 2009-2015.
23
Figure 4: Historical Stock Market Development in Turkey and the U.S. in the era of QE
Although fluctuations in BIST are more than S&P 500, in general, stock exchange markets in Turkey and the U.S. are in an increasing trend in the era Quantitative Easing. This general increasing trend confirms our assumption which has been already discussed in Quantitative Easing section of this study. Ross (2015) explains the effect of QE as stock markets tend to boost in case of easing policy or downturn in a case of tightening policy by FED.
Figure 5: Histogram and Descriptive Statistics of BIST Daily Market Return
0 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000
BIST All Shares
0 500 1000 1500 2000 2500 3000 3500 4000 4500
S&P 500
Rm Mean 0.0007 Median 0.0012 Standard Deviation 0.0149 Kurtosis 3.2212 Skewness -0.3546 Minimum -0.1046 Maximum 0.0712 Observations 176124
Histogram of market return is normally distributed with positive mean and median values, and it has slightly negative skewness. Kurtosis value is very close to 3 which is considered to be a reasonable kurtosis for normal distribution. We observed the total of 1761 daily returns. 950 of them is for up-market days and 811 of them is for down-market days.
Figure 6: Histogram and Descriptive Statistics of Daily CSSD
As illustrated in Figure 6, daily statistics of CSSD is positively skewed and it has excess kurtosis. Positively skewed variables’ mean is larger than its medians. As it is seen from the above figure, the mean is larger than its median.
CSSD Mean 0.027726 Median 0.026802 Standard Deviation 0.009097 Kurtosis 475.7651 Skewness 17.79059 Minimum 0.012593 Maximum 0.294009 Observations 1761
25
Figure 7: Histogram and Descriptive Statistics of Daily CSAD
As illustrated in Figure 7, skewness and kurtosis values of CSAD is relatively lower than CSSD. Similar to CSSD, it has positive skewness, mean and median values. Because it has positive skewness, its mean value is higher than its median value. Furthermore, the skewness for both CSSD and CSAD is positive and they have excess kurtosis. Hence, we can reject the null hypothesis of normally distributed stock return dispersions.
Figure 8: Daily Relationship of CSSD and CSAD with respect to Daily Market Return
CSAD Mean 0.017181 Median 0.016432 Standard Deviation 0.003936 Kurtosis 8.388988 Skewness 2.053317 Minimum 0.008395 Maximum 0.050723 Observations 1761
26
Figure 8 shows that CSSD has more linearity while CSAD is more parabolic. It may be discussed that the CSSD is not a decreasing function of the market return which is expected when herd behavior exists. Hence, it is possible that herd behavior is not present in BIST. The relationship between CSAD and Rm is more parabolic with respect to the relationship between CSSD and Rm. It is evident that Chang, Cheng, and Khorana (2000) supported the idea of being non-linearly increasing or decreasing relationship between dispersion and market return in case of herd behavior. As the graph indicates, there is a possibility of herd behavior according to CSAD and Rm relationship. However, it is not possible to estimate by only analyzing the graphs, we need to interpret the empirical results which will be presented in the following chapter.
7. EMPIRICAL RESULTS
Dummy variables regression test was performed by using CSSD as a dispersion measurement. Table 2 shows the regression results for CSSD. Left column of the table (1) shows the results for 1% criterion, and right column (2) shows the results for 5% criterion. For the data set, there is no heteroscedasticity found. Dependent variable: CSSD (1) (2) 1% criterion 5% criterion 0.028*** 0.027*** (127.904) (124.786) L t D 0.015*** 0.007*** (4.545) (5.208) U t D 0.012*** 0.007*** (3.643) (5.032) N 1761 1761 Adj. R2 0.018 0.027
Table 2: Christie and Huang’s Dummy Model covering stocks during 2009 to 2015 Note: *, **, and *** indicate significance at 10%, 5%, and 1%, respectively. Robust t-statistics are reported in parentheses.
27
As exhibited in Table 2, for the daily data, constant () and coefficients for dummy variables ( D
,U) are positive and statistically significant at 99% confidence level both in the extreme 1% and 5% lower or upper tails of the market return distributions. According to Christie and Huang (1995), rational asset pricing models predict significantly positive coefficients for andD U, and negative estimates of and D Uwould be consistent with the presence of herd behavior. Thus, it indicates evidence of a herd free market, since the and D U are positive and t-values are significant. The evidence is consistent with rational asset pricing models. The parameter represents the average dispersion under normal market phases when dummy variables are not applicable. Adjusted R-square values are used to explain how well are the independent variables predict the dependent variable. Adjusted R square of 5% criterion is higher because more observations fall than the 1% criterion.
After this method, CSAD was used as a dispersion measurement and dummy model of Chang, Cheng, and Khorana (2000) was used for testing herd behavior. Table 3 shows the result. Left column of the table (1) shows the results for 1% criterion, and right column (2) shows the results for 5% criterion. For the data set, there is no heteroscedasticity found.
Dependent variable: CSAD
(1) (2) 1% criterion 5% criterion 0.017*** 0.017*** (193.176) (199.211) L t D 0.016*** 0.008*** (11.872) (15.096) U t D 0.014*** 0.010*** (10.394) (18.301) N 1761 1761 Adj. R2 0.123 0.237
Table 3: Chang, Cheng and Khorana’s Dummy Model covering stocks during 2009 to 2015 Note: *, **, and *** indicate significance at 10%, 5%, and 1%, respectively. Robust t-statistics are reported in parentheses.
28
As exhibited in Table 3, constant () and coefficients for dummy variables ( ,D U) are statistically significant at 99% confidence level both in the extreme 1% and 5% lower or upper tails of the market return distributions. According to Chang, Cheng and Khorana (2000), presence
of herd behavior is determined by statistically significant negative values for D or U. Due to the fact that, both and D Uare positive and statistically significant, evidence of a herd free market is indicated. Adjusted R-square values are relatively higher than the CH’s dummy model because CSAD distribution is less affected by outliers. The model with 1% criterion explains the 12.3% of the changes in the dependent variable, and the model with 5% criterion explains 23.7% of the changes in the dependent variable.
Since dispersion and market return may have a non-linear relationship, CCK’s model was applied. In addition to all market conditions, up market and down market conditions as sub-periods are analyzed separately. Table 4 shows the regression results for all days, up-market days, and down-market days respectively. There is no heteroscedasticity found in the data set.
Dependent variable: CSAD
(1) All Days (2) Up Market Days (3) Down Market Days
t t m t m t R R CSAD 1 . 2 2. t UP t m UP UP t m UP UP t R R CSAD 2 . 2 , 1 ( ) t DOWN t m DOWN DOWN t m DOWN DOWN t R R CSAD 2 . 2 , 1 ( ) 0.014*** 0.014*** 0.015*** (113.327) (78.429) (79.457) 1 0.242*** 0.231*** 0.225*** (16.830) (9.857) (11.595) 2 0.344 1.237** 0.258 (1.190) (2.273) (0.733) N 1761 950 811 Adj. R2 0.434 0.456 0.417
Table 4: Chang, Cheng and Khorana’s Linearity Model covering stocks during 2009 to 2015 Note: *, **, and *** indicate significance at 10%, 5%, and 1%, respectively. Robust t-statistics are reported in parentheses.
According to Chang, Cheng, and Khorana (2000), the non-linearity, also evidence of herd behavior, would be captured by a negative and statistically significant coefficient. In our 2
29
regressions, of all days, bull and bear days are found positive which an evidence of a herd free 2
market is. Besides, is not statistically significant except for bull days at 10% level. Since it is 2
not negative, regression implies evidence of herd free market for bull days as well. The model explains 43.4% of the dependent variable for all days, 45.6% for bull days and 41.7% for bear days as shown in the adjusted R-square values.
8. CONCLUSION
In this study, the investment behavior through market participants in BIST is examined, with regard to the presence of herd behavior. Our time period from 2009 to 2015 is chosen in particular to cover Quantitative Easing by the FED. Wang (2008) concluded that emerging markets tend to herd more than developed markets. Also, Hwang and Salmon (2004), stated that herding is generally discussed in large price movements of stock markets, such as crisis or booming. Being an emerging market, investigating the Turkish stock market during 2009 to 2015 is especially interesting since the time interval in our study covers the expansionary policy of the FED. We expected that such an expansionary policy might affect Istanbul Stock Exchange in terms of herding.
Our analysis is based on market-wide approach. Herd behavior arises when market participants follow the performance of market instead of their own preferences based on available information. Models, which are developed by Christie and Huang (1995) and Chang, Cheng, and Khorana (2000), are used to detect herd behavior in the market. These models use dispersions to analyze herding. Christie and Huang (1995) uses cross-sectional standard deviation (CSSD) as a measurement of dispersion. Christie and Huang (1995) discusses that dispersions increase significantly in the event of excessive market movements. For the construction of the dummy variables which will be effective in excessive market movements, we calculated the percentiles of market returns. As a result of CSSD analysis, no evidence of herding is found in BIST. Further, we tested cross-sectional absolute deviation (CSAD) with those dummy variables regression analysis. Again, no evidence of herding is found in BIST for CSAD analysis.
30
As Chang, Cheng, and Khorana (2000) states that the linear and increasing function between market return and dispersion will be impaired when market participants start to herd during excessive market movements. As a result, the relationship will be non-linearly increasing or decreasing in a case of herd behavior. We tested CSAD dispersion in terms of non-linearity not only for all time conditions but also for up and down market days as sub-periods. Our empirical results concluded that BIST is herd free market for all days, up market and down market days. This means that dispersions linearly increase with regard to market returns. Although our prior expectation was to find herd behavior in the era of Quantitative Easing, our empirical research concluded that the QE has not affected BIST in terms of herd behavior. Although Wang (2008) concluded that emerging markets tend to herd more than developed markets, BIST as an emerging market has acted against this statement and concluded as a herd free market.
When compared to previous research in BIST, our results are consistent with the results of Coban (2009) who researched BIST for the time period 1997 to 2008. He found no evidence of herd behavior by using daily data set. Also, results of Can (2014) are in parallel to our results. She found no evidence of herd behavior in BIST by using daily data set from 1997 to 2013. However, our results are inconsistent with the results of Altay (2008) who found evidence of herd behavior in BIST from 1997 to 2008 by using daily data set. When the results are compared within emerging markets, our results are inconsistent with the results of Chang, Cheng, and Khorana (2000) who found significant evidence of herd behavior for 2 emerging countries, which are South Korea and Taiwan.
This study has contributed in providing additional research on herd analysis in Istanbul Stock Exchange (BIST). There has been no previous study that focuses on such a specific time period of Quantitative Easing. However, further studies are needed in order to gain deeper insight. It would be interesting to research herd behavior for other sub-groups such as different sectors, large and small cap stocks. Analyzing for sub-periods such as yearly and monthly breakdown would be interesting to examine whether this yields different results within the QE period. Also, applying Chiang and Zheng (2010) approach which uses the U.S. market as the herd leading index.
31
9. REFERENCES
Altay, E., 2008, Herding in Capital Markets: Analysis of Herding Towards the Market in ISE, BRSA Banking and Financial Markets, Vol. 2 Issue 1, 27-58.
Banerjee, A. V., 1992, A Simple Model of Herd Behavior, The Quarterly Journal of Economics, Vol. 107 No. 3, 797-817.
Barberis, N., and Thaler, R., 2002, A Survey of Behavioral Finance, NBER Working Paper Series, Working Paper No. 9222.
Bhattarai, S., Chatterjee, A., and Park, W.Y., 2015, Effects of US Quantitative Easing on Emerging Market Economies, Federal Reserve Bank of Dallas Globalization and Monetary Policy Institute, Working Paper No. 255.
Bikhchandani, S., and Sharma, S., 2001, Herd Behavior in Financial Markets, IMF Staff Papers, Vol. 47 No. 3, 279-310.
Bouraoui, T., 2015, The Effect of Reducing Quantitative Easing on Emerging Markets, Applied Economics, Vol. 47 Issue 15, 1562-1573.
Can, Z., 2014, Empirical Analysis of Herd Behavior in Borsa Istanbul, Unpublished Master Dissertation, Izmir: Dokuz Eylul University Graduate School of Social Sciences.
Caparrelli, F., D’Arcangelis, A. M., and Cassuto, A.,2004, Herding in the Italian Stock Market: A Case of Behavioral Finance, Journal of Behavioral Finance, Vol. 5 Issue 4, 222-230. Chang, E. C., Cheng, J. W., and Khorana, A. (2000). An Examination of Herd Behavior in Equity
Markets: An International Perspective, Journal of Banking & Finance, Vol. 24, 1651-1679.
Chiang, T. C., and Zheng, D., 2010, An Empirical Analysis of Herd behavior in Global Stock Markets, Journal of Banking & Finance, Vol. 34, 1911-1921.
Christie, W.G., and Huang R. D., 1995, Following the Pied Piper: Do Individual Returns Herd Around the Market?, Financial Analysts Journal, Vol. 51 No. 4, 31-37.
Coban, A. T., 2009, Testing Herd Behavior in ISE, Unpublished Master Dissertation, Cukurova University Graduate School of Social Sciences.
Devenow, A., and Welch, I.,1996, Rational Herding in Financial Economics, European Economic Review, Vol. 40, 603-615.
Dogukanli, H., and Ergun, B., 2015, Herding in Stock Markets: A Research in BIST, The Journal of International Social Research, Vol. 8 Issue 40, 690-699.
Fama, E.F., 1970, Efficient Capital Markets: A Review of Theory and Empirical Work, The Journal of Finance, Vol. 25 No. 2, 383-417.
32
Henker, J., Henker, T., and Mitsios, A., 2006, Do Investors Herd Intraday in Australian Equities, International Journal of Managerial Finance, Vol. 2 Issue 3, 196-219.
Hwang, S., and Salmon, M., 2004, Market Stress and Herding, Journal of Empirical Finance, Vol. 11, 585-616.
Lim, J.J., Mohapatra S., and Stocker M., 2014, Tinker, Taper, QE, Bye? The Effect of Quantitative Easing on Financial Flows to Developing Countries, Policy Research Working Paper, Working Paper No. 6820.
Lindhe, E., 2012, Herd Behavior in Stock Markets: A Nordic Study, Unpublished Master Dissertation, Lunds Universitet: Ekonomihogskolan.
Malkiel, B. G., 2003, The Efficient Market Hypothesis and Its Critics, Journal of Economic Perspectives, Vol. 17, 59-82.
Nofsinger, J. R., and Sias R. W., 1999, Herding and Feedback Trading by Institutional and Individual Investors, Journal of Finance, No. 6, 2263-2295.
Ohlson, P., 2010, Herd Behavior on the Swedish Stock Exchange, Unpublished Master Dissertation, Jonkoping University International Business School.
Ozdogan, S., 2009, Investor Behavior in a Stock Market: The Case of Bank Stocks in the Istanbul Stock Exchange, Unpublished Master Dissertation, Istanbul Bilgi University Faculty of Economics and Administrative Sciences.
Ritter, J. R., 2003, Behavioral Finance, Pacific-Basin Finance Journal, Vol. 11, 429-437.
Ross, S., 2015, How does quantitative easing in the U.S. affect the stock market?: Investopedia, retrieved from
“http://www.investopedia.com/ask/answers/021015/how-does-quantitative-easing-us-affect-stock-market.asp”.
Shiller, R. J., 2003, From Efficient Markets Theory to Behavioral Finance, Journal of Economic Perspectives, Vol. 17 No. 1, 83-104.
Tessaromatis, N., and Thomas, V., 2009, Herding Behavior in the Athens Stock Exchange, Investment Management and Financial Innovations, Vol. 6, Issue 3, 156-164.
Wang, D., 2008, Herb Behavior Towards the Market Index: Evidence From 21 Financial Markets, University of Navarra IESE Business School, Working Paper No. 776.
Wylie, S., 2005, Fund Manager Herding: A Test of the Accuracy of Empirical Results Using U.K. Data, The Journal of Business, Vol. 78 No. 1, 381-403.
33
10. APPENDIX
10.1 SPSS OUTCOMES
Figure 9: Heteroscedasticity Analysis of CSSD
34
Figure 11: Heteroscedasticity Analysis of CSAD
35
ANOVAa
Model Sum of Squares df Mean Square F Sig.
1 Regression .003 2 .001 16.889 .000b
Residual .143 1758 .000
Total .146 1760
a. Dependent Variable: CSSD
b. Predictors: (Constant), DU_0.99, DL_0.01
Table 5: The Statistics Used to Test Hypotheses about the CSSD Population Means at 99% Confidence Level
Coefficientsa Model Unstandardized Coefficients t Sig. B Std. Error 1 (Constant) .028 .000 127.904 .000 DL_0.01 .015 .003 4.545 .000 DU_0.99 .012 .003 3.643 .000 a. Dependent Variable: CSSD
Table 6: Constant and Coefficient Estimation for CSSD Model at 99% Confidence Level
ANOVAa
Model Sum of Squares df Mean Square F Sig.
1 Regression .004 2 .002 25.565 .000b
Residual .142 1758 .000
Total .146 1760
a. Dependent Variable: CSSD
b. Predictors: (Constant), DU_0.95, DL_0.05
Table 7: The Statistics Used to Test Hypotheses about the CSSD Population Means at 95% Confidence Level
Coefficientsa Model Unstandardized Coefficients t Sig. B Std. Error 1 (Constant) .027 .000 124.786 .000 DL_0.05 .007 .001 5.208 .000 DU_0.95 .007 .001 5.032 .000 a. Dependent Variable: CSSD
36
ANOVAa
Model Sum of Squares df Mean Square F Sig.
1 Regression .003 2 .002 123.925 .000b
Residual .024 1758 .000
Total .027 1760
a. Dependent Variable: CSAD
b. Predictors: (Constant), DU_0.99, DL_0.01
Table 9: The Statistics Used to Test Hypotheses about the CSAD Population Means at 99% Confidence Level
Coefficientsa Model Unstandardized Coefficients t Sig. B Std. Error 1 (Constant) .017 .000 193.176 .000 DL_0.01 .016 .001 11.872 .000 DU_0.99 .014 .001 10.394 .000
a. Dependent Variable: CSAD
Table 10: Constant and Coefficient Estimation for CSAD Model at 99% Confidence Level
ANOVAa
Model Sum of Squares df Mean Square F Sig.
1 Regression .006 2 .003 274.500 .000b
Residual .021 1758 .000
Total .027 1760
a. Dependent Variable: CSAD
b. Predictors: (Constant), DU_0.95, DL_0.05
Table 11: The Statistics Used to Test Hypotheses about the CSAD Population Means at 95% Confidence Level
Coefficientsa Model Unstandardized Coefficients t Sig. B Std. Error 1 (Constant) .017 .000 199.211 .000 DL_0.05 .008 .001 15.096 .000 DU_0.95 .010 .001 18.301 .000
a. Dependent Variable: CSAD
37 Coefficientsa Model Unstandardized Coefficients t Sig. B Std. Error 1 (Constant) .014 .000 113.327 .000 ABS_Rm .242 .014 16.830 .000 Rm_Sqr .344 .289 1.190 .234
a. Dependent Variable: CSAD
Table 13: Constant and Coefficient Estimation for CSAD Non-Linearity Model with regard to All Market Days
Coefficientsa Model Unstandardized Coefficients t Sig. B Std. Error 1 (Constant) .014 .000 78.429 .000 ABS_Rm .231 .023 9.857 .000 Rm_Sqr 1.237 .544 2.273 .023
a. Dependent Variable: CSAD
Table 14: Constant and Coefficient Estimation for CSAD Non-Linearity Model with regard to Up Market Days
Coefficientsa Model Unstandardized Coefficients t Sig. B Std. Error 1 (Constant) .015 .000 79.457 .000 ABS_Rm .225 .019 11.595 .000 Rm_Sqr .258 .352 .733 .464
a. Dependent Variable: CSAD
