Change in Stock Market Overreaction-Effect over Time:
Evidence from the S&P 500
Groningen, July 2010
Tim Klein Koerkamp
T.M.Klein.Koerkamp@student.rug.nl Student Number: 1553712
Master Thesis: Msc BA Finance
Change in Stock Market Overreaction-Effect over Time:
Evidence from the S&P 500
T.M. Klein Koerkamp Master Thesis
July 2010
ABSTRACT
This paper examines whether the effect has changed over time. The overreaction-effect is analyzed over the period 1973 - 2009, using return data of stocks listed on the S&P 500. This period is divided into two equal periods to determine whether the overreaction-effect has changed over time. After controlling for risk and size, no evidence to support the overreaction-effect is found in the first period. Contrary, after controlling for risk and size, in the second period evidence to support the overreaction-effect is found. The overreaction-effect found in the second period is caused the large firms in the winner and loser portfolios. By comparing the first and second period it is concluded that the differences between the two periods provide evidence that the overreaction-effect has changed over time.
JEL Codes: G11, G14, G17
1. Introduction
In the general area of behavioral finance attention has been paid to the relation between investor’s psychology and investment returns and the consequences for the efficient market hypothesis. One of the topics in the field of behavioral finance that facilitates in research towards investors psychology and the market efficiency hypothesis is overreaction. Overreaction is a well known phenomenon in finance which holds that stock prices systematically overshoot as a consequence of excessive investor optimism or pessimism.
The overreaction hypothesis is first examined by DeBondt and Thaler (1985). They found evidence for systematic price reversal of stocks and called it the overreaction-effect. This effect suggests that stock prices overreact in the initial period and subsequently reverse in the following period. The overreaction theory is a violation of the market efficiency hypothesis. In general, the efficient market theory concerns whether prices at any point in time fully reflect all available information (Fama 1970). The overreaction-effect contradicts with the efficient market theory since it suggests a systematic reversal instead of a random walk of share prices. When share prices show a systematic reversal they become predictable. This predictability of stock returns is one of the most controversial topics in financial research. Although there is consensus about the predictability of returns, there is a widespread disagreement about the underlying reasons for this predictability (Chan 1988; Ball and Kothari 1989; Zarowin 1990; Chopra, Lakonishok and Ritter 1992; Dissanake 1997). Dynamic markets and the inconclusiveness of previous research make the overreaction-effect still an interesting research field. The internet and the increasing importance and improvement of communication tools resulting in fast information stream, change the stock market environment. Due to the changing environment, stock market investments are no longer limited to financial professionals and elite investors. The internet enabled individuals to have easy access to the stock market. Consequently, more individuals started to participate actively in stock markets. In addition, institutional investors channeled more capital of pension funds to the stock markets which caused an exponential increase in the volumes traded on the stock market. Thus, during the last twenty years the stock market environment has changed. Over time the stock market has continuously adapted to new technology, regulation and market circumstances. These continuous changes and developments feed the empirical issue whether the overreaction-effect has changed over time.
determine whether the overreaction-effect has changed. Excluding a three-year formation period, the first period starts in January 1976 and ends in December 1992 and the second period starts in January 1993 and ends in December 2009. The results indicate that the overreaction-effect has changed over time. After controlling for risk and size no support for the overreaction hypothesis is found in the first period. Contrary, the results of the second period support the overreaction hypothesis. The results in this period indicate that the overreaction-effect is caused by the large firms in the portfolios. Evidence that the results in the first period differ from the results in the second period, confirms that the overreaction-effect has changed over time.
This study is a useful contribution to the existing overreaction literature. The focus on the differences in the overreaction-effect between time periods results in a more detailed understanding of the overreaction theory. As a consequence of these new insights, financial professionals and the investing public can make more optimal decisions in their investment strategies by using past returns in creating a contrarian investment strategy. This strategy holds that investors should simultaneously buy (long) past losers and sell (short) past winners, yielding arbitrage profits.
The remainder of this paper is organized as follows. The following section elaborates on the theoretical background of the overreaction hypothesis and presents an extensive overview on the relevant literature. At the end of this section the hypothesis tested in this paper is formulated. The third and fourth sections describe the data and the methodology used to conduct the research. The fifth section reports on the results. Finally, section six presents the conclusions and puts forward limitations and suggestions for further research.
2. Theoretical Overview
This section presents an overview of the relevant theoretical and empirical literature about the overreaction-effect. The overview starts with findings of experimental psychology research to explain the overreaction-effect. This is followed by studies that present evidence supporting the overreaction-effect. The overview continues with studies presenting alternative explanations for the existence of the overreaction-effect. Additionally, confirming results supporting the overreaction-effect are put forward. At the end of this section the literature review is summarized in a table (table 1) and the main hypothesis of this paper is presented.
2.1. Overreaction
overweighting recent information, individuals base their decision not on prior probabilities but on their beliefs. These beliefs are based on how similar or representative the event is compared to their apparent ideas and concepts. In other words, individuals make decisions according to a simple matching rule. This matching rule holds that individuals evaluate the likelihood that B is related to A, by the degree to which A is representative of B.
By linking the matching rule to the stock market DeBondt and Thaler (1985) argued that investors are too optimistic when receiving good news and are too pessimistic by receiving bad news. According to DeBondt and Thaler (1985) the excessive reaction of investors could result in a move of stock prices from their ‘true value’. The overreaction hypothesis is built on this movement of stock prices. The hypothesis asserts that stocks underperforming (outperforming) the market over a period of time will outperform (underperform) the market over a subsequent and similar time period. Consequently, they argued that the efficient market theory does not hold since the movement of stock prices from their ‘true value’ contradicts with the efficient market hypothesis. According to Fama (1970) an efficient market is a market in which security prices reflect all relevant information and prices will instantaneously and unbiased adjust to new information. The overreaction hypothesis, just described above, predicts that individuals react excessively to unexpected news, resulting in a move of stock prices from their true value. In other words, stock prices do not reflect all relevant information. Thus the overreaction hypothesis implies inefficiency in the stock market.
earned at the start of each year, namely in the 1st, 13th and 25th month. DeBondt and Thaler (1985) explained this effect by tax-loss selling around January.
The results obtained by DeBondt and Thaler (1985) on the US market have also been observed in other markets. Alonso and Rubio (1990) examined the overreaction hypothesis in the Spanish market. Twelve months after portfolio formation, losers win 24.5% more than winners. Furthermore, their results show a similar overreaction pattern of stock returns in both earnings per share and the price earnings ratio. Power, Lonie and Lonie (1991) found in the period from 1983 to 1987 evidence supporting the overreaction hypothesis on the UK Market. In this period, the loser portfolio outperformed the market with 86% and winner portfolio underperformed the market with 47%. Zamri and Hussain (2001) studied overreaction and seasonality in the returns of stocks traded on Malaysia's Kuala Lumpur Stock Exchange (KLSE). Their results indicate that stocks in the winner and loser portfolio experience a reversal in the following three years. They also found evidence that a contrarian trading strategy could be profitable.
2.2. Controlling Results
The results of the US, Spanish, UK and Malaysian market presented in section 2.1 support the existence of the overreaction-effect. However, other studies questioned the results of DeBondt and Thaler (1985) and discuss alternatives to explain the overreaction-effect (Chan 1988; Ball and Kothari 1989; Zarowin 1990; Conrad and Kaul 1993). Chan (1988) argued that the risks of winner and loser stocks are not constant over the time. Consequently, Chan (1988) suggested that the estimation of abnormal returns may be sensitive to the assessment of risks. The foundation of this thought lies in the theory that the leverage of a loser firm increases as the stock price falls, which increases the risk of a stock. This increase of risk increases the equity beta when a series of abnormal returns occurs. By using CAPM, an increasing equity beta results in an increasing expected return of the stock. According to Chan (1988) this could be an explanation of the abnormal returns found by DeBondt and Thaler (1985). Using monthly stock data from December 1926 to December 1985, Chan (1988) tested for this equity beta hypothesis. He created similar portfolios as DeBondt and Thaler (1985) and controlled for the potential leverage effect. The results show a small abnormal return. Chan (1988) concluded that these abnormal returns were too small for having an economically significant effect and therefore do not support the overreaction hypothesis.
expected returns. The results of Ball and Kothari (1989) show that the serial correlation in portfolios’ abnormal returns are significant. However, Ball and Kothari (1989) found that the size of the abnormal returns is very small and therefore they concluded that this result is economically insignificant.
Despite of these results, there are other studies which question whether risk fully explains the overreaction-effect (Chopra et all. 1992; Newton da Costa 1994; Dissanake 1997). Newton da Costa (1994) found evidence that risk, as measured by CAPM-betas using the method by Chan (1988), cannot fully account for the difference between the winner portfolio and the loser portfolio. He tested the overreaction hypothesis on the Brazilian market by using monthly data collected from the Sao Paulo Stock Exchange over the period from January 1970 till December 1989. He controlled for risk, using CAPM-betas, and found statistically significant results that loser portfolios outperformed the market by 17.63% and winner portfolios underperformed the market by -20.25%.
Another alternative to explain the overreaction-effect is put forward by Zarowin (1990). He argued that the size of a firm explains the overreaction hypothesis. According to Zarowin loser portfolios are portfolios with smaller firms and winner portfolios are portfolios with larger firms since firms in the loser portfolio have lost market value and therefore became smaller. Zarowin (1990) combined this size of the firms in the portfolios to a well known phenomenon in finance that small firms outperform large firms (Schwert 1983). Thus, Zarowin (1990) suggested that the overreaction-effect is not determined by over- or underweighting of information by investors or due to differences in risk discrepancies, but due to the size-effect. To control for this potential size-effect Zarowin (1990) reexamined the article of DeBondt and Thaler (1985) and adapted the methodology to control for size. He found that the loser portfolio only outperforms the winner portfolio when the loser portfolio is smaller than the winner portfolio. Vice versa, if the winner portfolio is smaller than the loser portfolio, the winner portfolio outperforms the loser portfolio. Furthermore, when the loser and winner portfolio are of compatible sizes, the loser portfolio only have significant different performance in January. Zarowin (1990) concluded that the market is not characterized by an overreaction-effect as hypothesized by DeBondt and Thaler (1985), but the overreaction-effect is just a manifestation of the size-effect.
These results are consistent with the overreaction hypothesis but in contrast to the findings of Chan (1988), Ball and Kothari (1989) and Zarowin (1990). In addition, they explored the generality of the effects in both January and non-January months. Their results show that the overreaction-effect is disproportionately concentrated in January which was also reported by DeBondt and Thaler (1985). In contrast, Clare and Thomas (1995) indicated that loser portfolios outperform winner portfolios by a statistically significant 1.7% per year on the UK stock market. However, after controlling for firm size they demonstrate that the 1.7% return difference can be explained by the size-effect, which confirms the findings of Zarowin (1990). Furthermore, Clare and Thomas (1995) concluded that their results provide no evidence to support the overreaction hypothesis on the UK market.
In addition to risk and size as an explanation for the overreaction-effect a third alternative explanation is introduced by Conrad and Kaul (1993). In their study they argued that the overreaction hypothesis could be explained by factors as bid-ask errors, non-synchronous trading, or price discreteness. They state, that returns to the contrarian strategy found in overreaction studies are upwardly biased since they are obtained by cumulating single-period returns over long time intervals. Conrad and Kaul (1993) stated that this cumulating process not only cumulates ‘true’ returns but also the upward bias in single-period returns induced by measurement errors. They argued that the upward bias in low-priced firms’ single-period returns is substantially larger than the bias in the returns of high-priced firms. According to Conrad and Kaul (1993) this result is a spurious upward drift of the arbitrage portfolio return unrelated to the overreaction-effect and the remaining ‘true’ returns to loser or winner firms have no relation with the overreaction-effect.
2.3. Confirming Results
In the existing literature four explanations of the overreaction-effect are distinguished. The first explanation holds that the overreaction-effect is a manifestation of fundamental market inefficiency (DeBondt and Thaler 1985; Chopra et al. 1991). The second explanation state that the overreaction-effect is caused by risk mis-measurement (Chan 1988; Ball and Kothari 1989). The third explanation argues that the overreaction-effect is another version of the size-effect (Zarowin 1990). The fourth explanation puts forward that the overreaction-effect is created by bid-ask effects and infrequent trading (Conrad and Kaul 1993).
effects and the infrequent trading as suggested by Conrad and Kaul (1993). Secondly, it reduces the possibility that reversals are primarily a firm-size phenomenon as suggested by Zarowin (1990). The data is controlled for risk to examine the alternative explanation of Chan (1988) and Ball and Kothari (1989). The results of Dissanake (1997) show that on average, the loser portfolio outperformed winners by nearly 100% in the four years after portfolio formation. Furthermore, the overreaction-effect was not eliminated by using a method similar to Chan (1988) to adjust for risk. Additionally, by using the methodology of Ball and Kothari (1989), Dissanake found that on average, the arbitrage portfolio earned a statistically significant 11.74% per year. Dissanake (1997) also controlled for the January-effect and found a strong seasonal pattern on the curve of the loser portfolio, especially around the turn of the year. In sum, even though using two different methods which have been advocated for dealing with time-varying risk, Dissanake (1997) provides evidence largely consistent with the overreaction hypothesis of DeBondt and Thaler (1985). For that reason, he concluded that the overreaction-effect can be explained by fundamental market inefficiency.
are in line with the overreaction hypothesis. Chiao and Hueng (2005) suggested that size and book-to-market ratio are two significant firm characteristics that explain stock returns. They tested this hypothesis by controlling the overreaction-effect on the Japanese stock market for book-to-market ratio and size. Their results show that these two factors cannot fully explain the overreaction-effect. Therefore, Chiao and Hueng (2005) concluded that, after controlling for size and book to market ratio, the overreaction-effect is significant.
2.4 Hypothesis
From the first study of DeBondt and Thaler (1985) till the results of Chiao and Hueng (2005), 20 years of research on the overreaction-effect is discussed. During these two decades, stock markets have changed. In their long history, stock markets are continuously adapted to new technology, regulation, new investors and new believes or in broad sense, to their entire environment. For example, new technology instruments have been implemented to improve stock exchanges. On the NYSE, millions of dollars have been spent to install sophisticated electronic equipment for cost-efficient execution of trades and for upgrading trading capacity. This started already in 1844, with the invention of the telegraph. The telegraph improved the stock exchange by broadening the market participation by facilitating communication with brokers and investors outside New York City. Another example of technological improvement is the implementation of the central quote system in 1929. This system provides instantaneous bid-ask prices by phone, which stimulated the NYSE to meet the volume growth. More recently, in 2008 the exchange launched NYSE real-time stock prices which enabled internet and media organizations to buy real-time, last-trade market data from the NYSE and provide it broadly and free of charge to the public.
The change in the extent of the overreaction-effect is discussable. DeBondt and Thaler (1985) argued that the overreaction-effect can not exist when the market is fully efficient. This feed the thought that, the more efficient a stock market is the smaller the overreaction-effect is. Whether stock markets have become more efficient is debatable. According to Freund and Pagano (2002), recent modernization of stock markets leads to lower execution costs, which attracts more investors and increases trading volume and liquidity. Therefore they state that automatic exchanges could lead to greater market efficiency. Evans (2006) examined whether the trading system modernization has a significant impact on the efficiency of a future market. He concluded that electronic trading systems can make future markets more efficient. Ates and Wang (2004) conducted research on the difference of price discovery process between floor trading and electronic trading on the S&P 500 and Nasdaq 100 index futures markets. They found empirical evidence that screen trading makes a greater contribution to price discovery by investors relative to open-outcry trading. This suggests that investors nowadays are faster aware of the true value of a stock. The findings of Freund and Pagano (2002), Evans (2006) and Ates and Wang (2004) suggest that stock markets have become more efficient due to new information technology. Due to this improved efficiency, stock prices are faster available and more transparent suggesting that stock prices reflect more optimal the ‘true-value’ of the stock. Thus, since the market have become more efficient, the overreaction-effect should have become smaller.
value. Thus, on the one hand it is arguable that the overreaction-effect could have increased due to more individuals entered the stock market. On the other hand it is arguable that the overreaction-effect has become smaller due to improved technology making the stock market more efficient. Therefore the following hypothesis is tested in this paper:
:
0
H The overreaction-effect has not changed over time
:
1
H The overreaction-effect has changed over time
In sum, DeBondt and Thaler (1985) started empirical studies on the overreaction-effect. Their study is followed by an extensive list of articles which extended the insight on the overreaction-effect. Most studies support the overreaction-effect as found by DeBondt and Thaler (1985). However, there are studies that criticize the methodology used by DeBondt and Thaler (1985) and argue that other variables such as risk (Chan 1988; Ball and Kothari 1989) or size (Zarowin 1990) should be taken into account when considering the overreaction-effect. An overview of these studies is presented in table 1.
Table 1: Literature Overview
Author Data Market Number of
Stocks
Portfolio Duration
Main Findings ORH
DeBondt and Thaler (1985)
1926 – 1982 Monthly
US (NYSE) 35 3 Years Overreaction-effect of 24.6% over a three-year time period. Overreaction-effect is asymmetrical.
Positive abnormal returns in January.
Yes
Chan (1988) 1929 – 1985 Monthly
US (NYSE) 35 3 Years Controlled the overreaction-effect for risk by using leverage effect.
Economically insignificant abnormal return found.
No
Ball and Kothari (1989)
1930 – 1981 Monthly
US (NYSE) Quintiles 5 Years Negative serial correlation in relative returns and relative risks.
Found an overreaction-effect of 15.65%; After controlling for risk, the overreaction-effect reduced to 2.0%.
No
Zarowin (1990) 1926 – 1978 Monthly
US (NYSE) Quintiles 3 Years Size-effect explains overreaction-effect instead of risk or January-effect.
No
Alonso and Rubio (1990)
1965 – 1984 Monthly
Spanish Market
5 3 Years 1 Year after portfolio formation, loser portfolio outperform winner portfolios with 24.5%.
Overreaction-effect found in E/Shares and P/E ratios.
Yes
Power (1991) 1973 – 1987 Monthly
GBR (London SE)
30 5 Years Loser portfolio outperformed the market with 86% and the winner portfolio underperformed the market with 47%.
Yes Chopra, Lakonishok, and Ritter (1992) 1926 – 1986 Monthly
US (NYSE) Quintiles 5 Years Significant overreaction-effect after adjusting for size and beta.
Smaller firm losers outperform winners up to 10% per year during the subsequent five years.
Overreaction-effect is concentrated in January
Yes
Conrad and Kaul (1993)
1926 – 1988 Monthly
US (NYSE) 35 3 Years Low priced stocks have a larger upward bias due to the bid-ask bias.
Overreaction-effect explained by factors as bid-ask errors, non-synchronous trading, or price discreteness.
No
Table 1: Continued:
Author Data Market Number of
Stocks
Portfolio Duration
Main findings ORH
Newton da Costa (1994) 1970 – 1989 Monthly Brazil (Sau Paulo SE)
Quintiles 1 Year Risk cannot explain the difference in return between the winner portfolio and the loser portfolio.
Loser (winner) outperformed (underperformed) the market by 17.63% (-20.25%).
Yes
Clare and Thomas (1995) 1955 – 1990 Monthly GBR (London SE) Quintiles 1, 2 and 3 Years
Loser portfolios outperform winner portfolios by a significant 1.7% per year.
Return difference can be explained by the small firm effect.
No Dissanake (1997) 1955 – 1975 Monthly GBR (FT 500 Index Deciles 3 to 5 Years
Support for the overreaction-effect found after controlling for risk, size and bid-ask spread.
Seasonal pattern on losers curve; January effect.
Yes Zamri and Hussain (2001) 1986 – 1995 Monthly MYS (Kuala Lumpur SE)
Deciles 3 Years Stocks in the winner (loser) portfolio experience a reversal in the following three years.
Month of the year effect found.
Yes
Benou and Richie (2003) 1990 – 1999 Monthly US (S&P 100) Trigger Value 1, 2 and 3 Years
Overreaction-effect found for large firms.
Overreaction-effect differs between three industries. Technology industry experienced the largest reversal.
Yes
Wang, Burton and Power (2004)
1994 – 2000 Weekly
CHN
(Shanghai SE)
25 20 weeks Winners underperformed the market, by 0.55%, while the loser outperformed the market by 0.52%.
Yes
Chiao and Hueng (2005)
1975 – 1999 Monthly
JPN (Tokyo SE)
Quintiles 5 Years Book-to-market ratio and size cannot fully explain the overreaction-effect.
Yes
3. Data
To conduct this study, data consisting of all monthly capital adjusted values of all stocks listed on the S&P 500 in December 2009 are used. To conduct reliable research on the change of the overreaction-effect it is important that the length of the data period is as large as possible. Since Thomas Reuters DataStream provides data from 1973 till now, the time period used in this study starts in January 1973 and ends in December 2009. There are two reasons for focusing on data from S&P 500. Firstly, it simply provides enough stocks to format reliable portfolios. Secondly, most overreaction studies use data of several American stock exchanges (DeBondt and Thaler 1985; Zarowin 1990; Conrad and Kaul 1995; Benou and Richie 2003). Therefore, using data from the S&P 500 enables this study to compare it more easily with previous work on the overreaction-effect. Capital adjusted close values are used to correct stocks for capital changes like stock splits and dividends. By doing so, the stock prices across all companies are more consistent over time.
Since data is used from all stocks listed on the S&P 500 in December 2009, the number of stocks in the data varies over the time period. This follows from the fact that not all shares listed on the S&P 500 in December 2009 were listed on the S&P 500 in January 1973. In this period, new firms were introduced to the market and other firms were delisted. For example, information technology companies such as Microsoft and Apple are listed on the S&P 500 in December 2009. These stocks are introduced on the S&P 500 respectively in April 1984 and January 1981. For that reason these firms were not listed on the S&P 500 in 1973. The introduction of stocks in the period from 1973 till 2009, leads to a database consisting of 233 companies in 1973 increasing to a database consisting of 499 companies in December 2009. Because of this variable number of companies in every month, the monthly market return is calculated by the equally weighted average of the return of all stocks available in a month. The rate of Three-month US-Treasury Bills is used as risk free rate and the size of a firm is determined by the market value of the firm at the end of the portfolio formation period.
each formation and test period over all the data from 1973 till 2009 and the two sub-periods 1976 till 1992 and 1993 and 2009.
Table 2: Descriptive Statistics
Loser/ Winner Nr. of Obs. Mean (CAR)
Median STD Min. Max. Jarque-Bera All Data L 32 -0.685*** -0.696 0.216 -1.269 -0.063 19.980 1973 - 2006 Formation period W 32 0.737*** 0.776 0.232 -0.010 1.165 41.762 L 32 0.021 -0.024 0.156 -0.325 0.331 0.806 1976 - 2009 Test Period W 32 0.008*** 0.026 0.190 -0.609 0.368 9.513 Period 1 L 16 -0.618*** -0.695 0.229 -0.827 -0.063 11.130 1973 - 1990 Formation period W 16 0.663** 0.727 0.288 -0.010 1.052 6.165 L 16 0.003 -0.008 0.141 -0.325 0.219 0.443 1976 - 1992 Test Period W 16 0.077 0.072 0.174 -0.244 0.368 0.352 Period 2 L 16 -0.752** -0.703 0.185 -1.269 -0.550 7.989 1991 - 2006 Formation period W 16 0.812** 0.802 0.127 0.651 1.165 7.134 L 16 0.038 -0.045 0.173 -0.168 0.331 1.930 1993 - 2009 Test Period W 16 -0.060*** -0.010 -0.184 -0.609 0.156 13.216
* Significant at 10% level, ** significant at 5% level *** significant at 1% level
4. Methodology
This section provides an overview of the methodology used to test the hypothesis as formulated at the end of section two. The methodology is made up out of three parts. Firstly, the methodology to test an overreaction is briefly presented. The second and third part consists of the methodology to control the overreaction-effect for the variables risk and size. Furthermore, each part elaborates how the change of the overreaction-effect is examined.
4.1. Determination of the Overreaction-Effect
The first step is to determine whether there is an overreaction on the S&P 500. DeBondt and Thaler (1985) start their research by calculating the abnormal return of every stock in every month. These stock returns are calculated using the natural logarithm of the start value of the next month divided by the start value of the current month. From the month return of each stock the equally-weighted average monthly rate of return of all stocks in that month is subtracted, resulting in the monthly abnormal returns of each stock. In formula this holds:
Where Ui,t is the market-adjusted abnormal return of stock i at month t, Ri,t is the return of
stock i at month t, Rm,t is the equally-weighted average monthly market rate of return m at month t,
pi,t is the price of stock i in month t and Nt is the number of stocks listed on the S&P 500 in
month t.
Cumulative return of stocks over each formation period is calculated with the use of the market-adjusted abnormal return Ui,t. Formation periods are three-year periods starting at the first
month of a year. The three year length of the formation period is used to be consistent with other studies (DeBondt and Thaler 1985; Chan 1988; Zarowin 1990). The first formation period starts in January 1973 and ends in December 1976, the next formation period starts in January 1974 and ends in December 1977, so forth till the last period from January 2004 till December 2006. In this way 32 formation periods of cumulative abnormal returns are calculated. Since this study uses only 36 year of data, overlapping periods are used because the consequence of using non-overlapping periods is a large reduction in the sample size. In formula the cumulative abnormal return of stock i at the end of formation period n is:
∑
= = 35 0 , , t n i n i AR CAR (2)Where CUi,n is the cumulative abnormal return of stock i in formation period n. Then the
CUi,n are ranked from low to high and portfolios are formed. Firms in the top quintiles are
assigned to the winner portfolio and stocks in the bottom quintiles are assigned to the loser portfolio. Quintiles are used to ensure that the portfolios are well diversified (Clare and Thomas 1995). For both winner and loser portfolios in each 32 overlapping three year formation periods the cumulative abnormal return (CAR) of all securities in the portfolio over the next three years are calculated. This is the test period. Thus, the first formation period has a length from January 1973 till December 1976 and has a test period from January 1977 till December 1979. The second formation period has a length from January 1974 till December 1977 and has a test period from January 1978 till December 1980 up to the last formation period (32nd) from January 2004 till December 2006 and a test period from January 2007 till December 2009.
Using the CAR's from all 32 test periods, average CAR's (ACAR) are calculated for both winner and loser portfolios and for each month between t = 1 and t = 36. They are denoted
ACARL,n,t and ACARW,n,t with L is the loser portfolio, W is the winner portfolio, n is the number of
the average return of the winner portfolio and using a t-test to check whether there is a significant difference in investment performance (equation 3).
(ACAR
L,n,t – ACAR W,n,t) > 0. (3)
When the return on the arbitrage portfolio (ACARL,n,t – ACARW,n,t) is significantly
different from zero, the overreaction hypothesis is accepted. To examine whether the overreaction-effect has changed over time, the data from 1973 till 2009 is divided into two periods. The analysis for the overreaction-effect is also conducted over these two periods. This means that ACARL,n,t and ACARW,n,t are calculated over the whole data period as well as over the
two sub-periods. By dividing the data into two periods it can be tested whether the return of the arbitrage portfolio differs between the two periods. This is examined with a t-test as presented in equation 4. Where 1 stands for the first period and 2 stands for the second period.
0 ) (
)
(ACAR1,L,n,t −ACAR1,W,n,t − ACAR2,L,n,t −ACAR2,W,n,t > (4)
4.2. Control for Risk
The second step is to control the overreaction-effect for differences in risk (Chan 1988) and seasonality (DeBondt and Thaler 1985) by estimating the difference between beta of the loser and winner portfolio (Equation 5). The difference in return between the loser and winner portfolio is regressed against the market return (RM,t) minus the risk free rate (RF,t). If α1 is significant then
there is an abnormal return, controlled for risk. Additionally, equation 5 controls for anomalies in seasonality. Because most seasonal anomalies are found in January a dummy variable D1 is
introduced. This dummy has a value of 1 in the month January and a value of 0 otherwise. If α2 is
significant, then anomalies in seasonality are found. The analysis to control for risk is conducted over the period from 1973 till 2009 and over the two sub-periods. To observe changes in the overreaction-effect over time, the results of the first and second period are compared.
t t F t M t W L t W L R R D R − , =
α
1 +β
− , ( , − , )+α
2 1+ε
(5)test periods, overlapping data is used to determine the overreaction-effect. To be consistent with the results of section 4.1 and to deal with dependence in abnormal returns in the overlapping data, the Newey-West procedure is employed when equation 5 is estimated. This way the standard errors of equation 5 are corrected for both autocorrelation and heteroscedasticity. However, when controlling for risk, the period from 1973 till 2009 as well as the two sub-periods consists of 32 or 16 years times 12 months of observations. This provides sufficient data to estimate equation 5 also on non-overlapping periods. The analysis using non-overlapping data is conducted to amplify the results of the estimates over the overlapping data.
4.3 Control for Size-Effect
The third step is to control for the size effect. This is done by using the methodology of Zarowin (1990). First, the size of each firm is determined by using the market value of each firm at the start of each test period. Then, all firms are ranked from 1 to 5 based on their size. This means that the smallest 20% of the firms are indicated with a 1 and the largest 20% of the firms are indicated with a 5. In addition, each firm is indexed by i,j where the i refers to prior period return performance and j refers to size. In this way 25 groups are formed, where for example 1,1 refers to the smallest losers, 1,2 refers to the next smallest losers, 5,1 are the smallest winners and 5,5 are the largest winners. Finally, to control for size discrepancies the Jensen’s performance test is conducted on 5 groups of losers (L) and winners (W) that are matched by size. An overview of these groups is presented in table 3.
Table 3: Overview of Groups to Control for Size Matched Portfolio’s
Group Index i,j Descriptive
A 1,1 vs. 5,1 Smallest losers vs. Smallest Winners
B 1,2 vs. 5,2
C 1,3 vs. 5,3
D 1,4 vs. 5,4
E 1,5 vs. 5,5 Largest Losers vs. Largest Winners
i = the return of a portfolio and j is the size of a portfolio where 1 represents the smallest 20% in return (i) of size (j) and 5 represents the largest 20% in return (i) of size (j).
non-overlapping periods as well as non-overlapping periods. Again the two sub-periods are used to determine whether the overreaction-effect has changed over time.
5. Results
This section presents the results of the methodology described above. The first part puts forward the results of the overreaction analysis. The second and third part present the results of the overreaction-effect after the control for differences in risk and size. The last part of this section takes together the results of the first, second and third part to examine whether the overreaction-effect has changed over time.
5.1 Overreaction
Figure 1 shows that the average cumulative average return lines of the winner and loser portfolio highly fluctuate. This implies that both winner and loser portfolio outperform and underperform relative to the market in several months. The winner portfolio shows an underperformance relative to the market, 18 out of 36 months and the loser portfolio shows 13 out of 36 months an underperformance relative to the market.
Whether the differences between the average cumulative abnormal return between the winner and loser portfolio in the three periods are significant is determined by a t-test assuming unequal variances. The results of this t-test are reported in table 4. All positive (negative) differences indicate that the abnormal return of the loser portfolio is larger (smaller) than the abnormal return of the winner portfolio. Over the 32-year test period no statistically significant differences are found. Over the first 16-year test period, from 1976 till 1992, statistical differences are found in every month in which the t-test is conducted. The strongest difference is observed in month 12 with a negative difference between the loser and winner portfolio of -8.3%, significant on a 1% level. In the 13th and 24th month significant differences are found in abnormal return on a 5% level; in the 1th, 25th and 36th month the differences are significant on a 10% level. The results in the first 16-year test period however, do not support the overreaction hypothesis since the abnormal return of the winner portfolio is larger than the abnormal return of the loser portfolio. This result is in contrast to the overreaction hypothesis which predicts that the loser portfolio outperforms the winner portfolio. In the second 16-year test period, from 1993 till 2009, statistical differences are found only in the 24th and 36th month of the test period. These differences are positive and significant on a 10% level. This result supports the overreaction hypothesis since the loser portfolio outperforms the winner portfolio in this period. Furthermore, a t-test is used to examine whether the difference in return on the arbitrage portfolio differs between the two sub-periods. With exception of the first months, in all months significant difference in return on the arbitrage portfolio are found. This result indicates that the return on the arbitrage portfolio has changed and therefore that the overreaction-effect has changed over time.
Table 4: Differences in Average Cumulative Average Abnormal Returns Between the Winner and Loser Portfolio at the end of the Formation
Period, and 1, 12, 13, 24, 25 and 36 Months into the Test Period
Difference in ACAR (t-Statistics) ACAR at the end of
the Formation
Period Month After Portfolio Formation
Date, Length of the Formation Period and Number of Overlapping Replications Winner Portfolio Loser Portfolio 1 12 13 24 25 36
32 three year periods1 0.737 -0.685 0.008 -0.024 -0.022 0.000 -0.007 0.012
1976-2007 (-1,040) (0,929) (0,860) (-0,002) (0,185) (-0,287)
16 three year periods1 0.663 -0.618 0,016 -0,083 -0,072 -0,083 -0,079 -0,073
1976-1992 (-1.397)* (2.554)*** (2.143)** (1.689)** (1.630)* (1.313)*
16 three year periods1 0.812 -0.752 0.000 0.035 0.027 0.083 0.065 0.098
1993-2009 (0.046) (-0.883) (-0.700) (-1.574)* (-1.203) (-1.554)*
Difference 1th and 0.148 -0.134 0.016 -0.118 -0.099 -0.167 -0.144 -0.172
2th period2 (0.832) (0.044)** (0.076)* (-1.789)** (-1.536)* (0.057)*
* Significant at 10% level, ** significant at 5% level *** significant at 1% level, T-Statistic assuming unequal variances.
In sum, over the period 1973 till 2009 no significant results are found to support the overreaction hypothesis. By dividing this period into two sub-periods of 16 years, significant results in both periods are obtained. The results of the first 16-year period are in contrast to the overreaction hypothesis. In the first period the winner portfolio outperforms the loser portfolio. The results of the second 16-year period are in contrast to the first 16-year period and support the overreaction hypothesis. The loser portfolio consequently outperforms the winner portfolio in the second period. Furthermore, the return on the arbitrage portfolio differs between the two sub-periods. This result indicates that the overreaction-effect has changed over time.
5.2 Control for Risk
As explained in section two, the overreaction-effect could be explained by differences in risk between the winner and loser portfolio. To test whether risk influences the overreaction-effect a regression analysis is conducted (section 4.2, equation 5). Just as in section 5.1, the regression analysis is conducted on the whole sample and on two sub-periods. In addition, the analyses are also conducted on the periods using overlapping and non-overlapping data. The results are presented in table 5. A significant alpha indicates that the return on the arbitrage portfolio can not be explained by the difference in risk between the loser and winner portfolio. Furthermore, a positive (negative) and significant beta means that the loser portfolio is characterized with higher (lower) systematic risk than winner portfolio’s. The dummy variable (D) controls for anomalies in January.
Table 5: Risk Control Test of the Overreaction Hypothesis
Overlapping Non-Overlapping 1976-2009 1976-1992 1993-2009 1976-2009 1976-1992 1993-2009 Alpha (α) 0.001 -0.001 0.003 0.002 -0.004 0.007 (0.928) (-0.468) (1.685)* (0.692) (-1.565) (1.921)* Beta (β) -0.206 -0.171 -0.247 -0.250 -0.179 -0.327 (-5.120)*** (-3.246)*** (-4.540)*** (-6.038)*** (-3.778)*** (-4.989)*** Month (D) 0.002 0.015 -0.011 0.000 0.029 -0.034 (0.481) (2.220)** (-1.616)* -0.001 (3.639)*** (-2.708)*** n 1152 576 576 408 204 204 R-squared 0.061 0.058 0.082 0.083 0.104 0.144
* Significant at 10% level, ** significant at 5% level *** significant at 1% level.
t t f t M t W L t W L R R D R − , =α1+β − ,( , − ,)+α2 1+ε
α = Jensen’s Performance Index. β = Difference in CAPM Beta between loser and winner portfolio. D = Month dummy with a value of 1 in January and 0 other.
winner and loser portfolio. The negative sign indicates that the beta of the winner portfolio is larger than the beta of the loser portfolio. The significant higher beta of the winner portfolio is according to CAPM associated with higher return. However, table 4 indicates that the results of both winner and loser portfolio do not differ significantly. In other words, investors receive the same return buying the winner portfolio or the loser portfolio but face higher risk when buying the winner portfolio than investors buying the loser portfolio. Thus, the overreaction-effect is not found in the return of the stocks but in the risk profile of both portfolios. This risk profile does support the overreaction-effect since investors who buy the winner portfolio are not compensated for the risk they take.
A significant beta on a 1% level is found in the period 1976 till 1992 using a non-overlapping and non-overlapping period. The beta is in both non-non-overlapping and non-overlapping period negative. This indicates that the winner portfolio is riskier than the loser portfolio. Table 4 shows that the cumulative average abnormal return of the winner portfolio is significantly higher than then the loser portfolio. According to the results in table 5, this difference can be fully explained by the higher risk of the winner portfolio since alpha does not significantly differ from zero in both overlapping and non-overlapping data. This result is partly in line with the result of Chan (1988). According to Chan, the loser portfolio outperforms the winner portfolio. Risk can fully explain this difference between the winner en loser portfolio. The results obtained in the period from 1976 till 1992 demonstrate that the winner portfolio outperforms the loser portfolio. Nevertheless, the difference between the loser and winner portfolio is fully explained by differences in risk, which is in line with the findings of Chan (1988).
In the period 1993 till 2009, a significant positive alpha and a significant negative beta are found in both the non-overlapping and overlapping data. The negative beta indicates that the winner portfolio is associated with higher risk than the loser portfolio. This is remarkable since the winner portfolio in this period performed worse (-6.0%) than the loser portfolio (+3.8%). The significant alpha indicates that differences in risk do not fully explain the outperformance of the loser portfolio relative to the winner portfolio. This result is in line with Newton da Costa (1994) who also found that risk cannot fully explain the overreaction-effect. However, the result contradicts with the findings of Chan (1988) and Ball and Kothari (1989). They stated that risk fully explains the difference in performance between the two portfolios.
found in both the overlapping and non-overlapping data. This result implies that the difference in return in January is larger than in the other months. In the period from 1993 till 2009 a negative coefficient is found in January. This indicates that the difference in return between the two portfolios is smaller in January than in the other months.
In sum, in all analyses, negative differences in risk are found between the winner and loser portfolio. The difference in risk is noteworthy, since no differences in returns are found over the whole period from 1976 till 2009. Therefore the difference in risk indicates that an investor who buys the loser portfolio can get the same return with a lower risk as an investor who buys the winner portfolio with a higher risk. The riskier winner portfolio in the period from 1976 till 1992 is expected since the winner portfolio outperforms the loser portfolio in this period. The difference in risk fully explains the difference in return between the winner and loser portfolio in this period. In the period from 1993 till 2009 the higher risk of the winner portfolio is remarkable since the loser portfolio is outperforming the winner portfolio. It follows that the difference in risk cannot fully explain the difference in return between the two portfolio’s supporting the overreaction hypothesis in this period.
5.3. Control for Size
Zarowin (1990) argued that the overreaction-effect is just another manifestation of the size effect. He stated that the market value of firms in the loser portfolio have decreased in the formation period due to their relatively negative results. Vice versa, the market value of firms in the winner portfolio should have increased in the formation period due to the their relatively positive results. Therefore Zarowin (1990) argued that the average market value of the loser portfolio should be smaller than the average market value of the winner portfolios.
To examine whether size explains the overreaction-effect each portfolio is independently ranked for size and return. This ensures that firms in the smallest quintile are really small and vice versa, that the firms in the largest quintile are really large with respect to all firms in the sample. First, all winner and loser firms in a portfolio are used to calculate the average size of the winner and loser portfolios in each year. Secondly, the Jensen’s performance test is conducted on size-matched portfolios to control for size discrepancies.
other words, losers have in 18 out of 32 years a higher average size-rank than winner portfolios. The 18 times that loser firms are larger than winner firms are equally distributed among the first 16 and second 16 years. This result contradicts with the founding of Zarowin (1990). He found that losers have a higher size-rank only 4 out of 17 years.
Table 6: Size Difference between Loser and Winner Portfolio Size Rank Loser Port. ML Size Rank Winner Port. MW 1973 1,915 3,867 3,319 6,031 1974 2,872 5,584 2,383 5,085 * 1975 3,511 6,323 1,936 4,676 * 1976 3,375 6,245 2,021 4,842 * 1977 3,500 6,455 2,208 5,319 * 1978 3,000 6,246 2,854 6,202 * 1979 3,510 6,814 2,204 5,560 * 1980 3,429 7,064 2,980 6,590 * 1981 3,020 6,859 2,333 6,306 * 1982 2,745 6,489 2,510 6,485 1983 2,577 6,635 2,327 6,644 ** 1984 2,296 6,537 2,704 7,094 1985 2,545 6,746 2,852 7,104 1986 2,196 6,491 2,839 7,194 1987 2,233 6,658 2,783 7,226 1988 2,344 6,601 2,918 7,405 1989 2,556 7,153 3,048 7,866 1990 3,047 7,635 2,750 7,505 * 1991 2,955 8,074 3,242 7,585 ** 1992 3,087 7,927 2,507 7,534 * 1993 2,577 7,775 2,634 7,859 1994 2,427 7,775 3,040 8,455 1995 2,303 7,910 3,105 8,786 1996 2,049 7,683 3,927 9,811 1997 2,422 7,853 3,446 9,490 1998 2,422 7,853 3,446 9,490 1999 2,977 8,821 2,767 8,697 * 2000 2,841 8,560 2,523 8,313 * 2001 3,133 9,227 2,689 8,741 * 2002 3,130 9,430 2,739 8,933 * 2003 2,989 9,393 2,763 9,117 * 2004 3,043 9,538 2,915 9,293 *
The Jensen’s performance test is conducted over the whole period from 1973 till 2009 and over the two sub-periods using both overlapping and non-overlapping data. In each period the portfolios of five groups of winner and loser that match by size are examined. The results of the Jensen’s performance test are reported in table 7. A significant alpha indicates that the difference in return between size-matched portfolios is not explained by the size effect. The negative differences in risk between the winner and loser portfolio as presented in table 5 are also found when examining size-matched portfolios. For each period and each group the sign of beta is significantly negative. Furthermore the results are controlled for anomalies in January. These results are presented in table A in Appendix A.
The results in the test period from 1976 till 2009, both in the overlapping and non-overlapping data, show a significant alpha in the two groups (D and E) with the largest firms. This result indicates that there is a difference in return between large firm loser and winner portfolio. This result contradicts to the findings of Zarowin (1990). He argued that the size-effect fully explains the overreaction-effect and found no significant alphas. Other studies demonstrate an overreaction-effect in small firm portfolio (Chopra et all. 1992; Conrad and Kaul 1995). Benou and Richie (2003) however, found an overreaction-effect among large firms which confirms these results.
When the data is analyzed over the two sub-periods, different results are obtained. In the overlapping and non-overlapping period from 1976 till 1993 no significant results are found. This is not surprising since the results of section 5.2 showed that no evidence of the overreaction-effect is found after controlling the period for differences in risk. The significant alpha’s found in group D and E of the whole data period are also founded in the sub-periods from 1993 till 2009. This indicates that the overreaction-effect which is not explained by risk is mainly caused by the difference in return between large winner and large loser firms.
Table 7: Size Control Test of the Overreaction Hypothesis
Jensen's Alpha Estimates (t-statistics)
Overlapping A B C D E 1976 - 2009 0.002 0.000 0.001 0.005 0.004 (n =1152) (0.793) (-0.073) (0.556) (2.511)** (2.037)** R-squared 0.011 0.043 0.049 0.063 0.042 1976 – 1992 0.003 -0.001 -0.002 0.001 0.003 (n =576) (0.914) (-0.543) (-0.958) (0.445) (1.118) R-squared 0.018 0.054 0.044 0.038 0.035 1993 – 2009 0.000 0.001 0.004 0.008 0.005 (n =576) (0.168) (0.336) (1.788)* (2.948)*** (1.773)* R-squared 0.005 0.049 0.081 0.108 0.057 Non Overlapping A B C D E 1976 – 2009 -0.001 0.001 0.002 0.007 0.010 (n =408) (-0.334) (0.457) (0.817) (2.227)** (3.382)*** R-squared 0.005 0.010 0.064 0.096 0.072 1976 – 1992 -0.004 -0.002 -0.002 -0.001 0.001 (n=204) (-0.941) (-0.735) (-0.769) (-0.389) (0.322) R-squared 0.023 0.082 0.064 0.124 0.091 1993 – 2009 0.002 0.005 0.006 0.015 0.010 (n=204) (0.537) (1.000) (1.462) (3.082)*** (2.328)** R-squared 0.003 0.089 0.123 0.136 0.088
* Significant at 10% level, ** significant at 5% level, *** significant at 1% level. The 5 size matched groups are: A: 11 vs. 51, B: 12 vs. 52, C: 13 vs. 53, D: 14 vs. 54, and E: 15 vs. 55. A: are the smallest losers and winners, B: are the next smallest losers and winners, etc., E: are the largest losers and winners.
In sum, over the whole period, significant differences in return are found for the size-matched portfolios consisting of the largest firms. In the first period from 1973 till 1992 no differences in return are found. The differences in return as found in the second period are a result of the differences in return between the two size-matched portfolios consisting of largest firms. This difference in the second period probably explains the difference in return between large firms over the whole period since in the first period no significant results are found.
5.4 Change in Overreaction
analyses in section 5.1 show that in the first period the winner portfolio outperforms the loser portfolio with a statistically significant difference of 7.3% and contrary, in the second period the loser portfolio outperforms the winner portfolio with a statistically significant difference of 6%. Furthermore, significant results are found examining differences in return on the arbitrage portfolio of the first and second period. These outcomes of the overreaction analyses indicate that the overreaction-effect has changed over time. By just averaging ACAR over the whole period, no evidence for the overreaction-effect is found. But by dividing the data into two periods, evidence supporting the overreaction hypothesis is found in the second period. This result can imply that previous work could suffer from misinterpretations of ACAR’s.
Table 8: Overview of the Results
1976-2009 1976-1992 1993-2009
Overreaction No difference in return
between winner and loser portfolio**
Winner portfolio outperforms the loser portfolio with 7.3% after three years**
Loser portfolio outperforms the winner portfolio with 6% after three years*
Control for Risk The winner portfolio is riskier
than the loser portfolio by earning the same return as the loser portfolio*
Differences in risk fully explain the difference in return between the winner and loser portfolio**
After control for risk the loser portfolio is still outperforming the winner portfolio*
Control for Size Differences in return are
found for the size-matched portfolios of large firms*
No differences in return are found after control for risk and size**
The difference in return is a result form the difference in return of the size-matched portfolios of large firms* * = support for the overreaction hypothesis; ** = No support for the overreaction hypothesis
The outcomes of the overreaction analyses are controlled for risk and size (Chan 1988; Zarowin 1990). Firstly, after controlling for risk, no differences in return are found in the first period between the winner and loser portfolio. Contrary, in the second period differences in return between the winner and loser portfolio are found even after controlling for risk. These results also provide evidence that the overreaction-effect has changed. Secondly, after the control for size, in the first period no overreaction-effect is found. Contrary in the second period there is an overreaction-effect. This result amplifies the evidence that the overreaction-effect has changed over time. The observed change is an increase in the difference in return between the winner and loser portfolio. The change in the overreaction-effect is caused by large firms in the portfolios of the second period.
where not active in the first period stocks were not underpriced of over priced and the winner portfolio stayed the winner portfolio and the loser portfolio stayed the loser portfolio. Another explanation is put forward by Benou and Richie (2003). They stated that large firms are more likely to overreact. Since a strong decline of the stock price of a large firm signals the management the need to take action. In other words, large firms have the assets and the potential to react to strong stock price decreases. In contrast, when faced with difficult circumstances, small firms are more likely to sag under competitive pressure or are acquired. Table 8 shows that the average size of both, loser and winner portfolio have increased since January 1973. Therefore, it is arguable large firms in the loser portfolio have more assets and more potential to react to their stock price decline in the second period compared to the first period. This could explain the change in the overreaction-effect.
6. Conclusion
This section presents the main conclusions of this study. Furthermore, it discusses limitations concerning the data and variables used. Finally, suggestions for further research are put forward.
6.1 Conclusions
This study analyzed the change of the overreaction-effect over the period 1973 till 2009. The period is divided into two periods to examine whether the overreaction-effect has changed over time. Excluding a three-year formation period, the first period starts in 1976 and ends in 1992; the second period starts in 1993 and ends in 2009. The results are corrected for risk and size of firms. In this study no evidence is found for the overreaction hypothesis in the period from 1976 till 1992: The winner portfolio outperforms the loser portfolio with a significant 7.3%. In contrast, in the period from 1993 till 2009, the results provide evidence supporting the overreaction hypothesis: The loser portfolio outperforms the winner portfolio with a significant difference of 9.8%. These results demonstrate that the overreaction-effect has changed over time. Therefore, the hypothesis (H0 ) - the overreaction-effect has not changed over time - can be
rejected.
loser firms in the first period and therefore managers have more assets and more potential to react to the stock price decrease of their firm.
6.2 Limitations
The use of S&P 500 data over the period from 1973 till 2009 has resulted in some limitations for the analysis. Obviously, during this period stock markets and stock market environments have changed dramatically. New technologies, the internet, new regulations, bull markets, bear markets and so on, all contributed to these changes. Not all changes could be included in this analyses due to data limitations on the one hand and because not all effects are quantifiable on the other hand.
Firstly, the data consist of stocks that are listed on the S&P 500 on the first of January 2010 which resulted in a dataset with 233 stocks in 1973 and 499 stocks in 2009. Consequently, stocks which are delisted are not taken into account by conducting the analysis. The delisted stocks could influence the overreaction-effect and especially the formation of loser portfolios. However, 233 companies is a sufficient number to conduct a valid analysis on the portfolios. Moreover, since the market return is calculated by the average of return of stocks available in a particular month, the abnormal returns of the portfolios are adapted for the delisted firms.
A second limitation of the data used is the relatively short time period used from 1973 till 2009. Most studies about overreaction use a more extensive database (DeBondt and Thaler 1985; Chan 1988; Zarowin 1990; Conrad and Kaul 1993; Clare and Thomas 1995). Due to the short time period, the analysis is only conducted on two sub-periods. When the 32 years were divided into more periods, the ACAR’s would be calculated over too less observations which would influence the results of section 5.1. Using a larger dataset and more time periods could make the conclusions over the observed direction of the change in the overreaction-effect more reliable. This study found evidence that the overreaction-effect has become larger: in the first period no evidence to support the overreaction-effect is found, in the second period evidence to support the overreaction-effect is found. However, in the period before 1973 the overreaction-effect could be larger or smaller. Thus, in order to have a better understanding of the change in the overreaction-effect over time more periods should be included and analyzed, which implies a need for a larger database.
stronger on positive news (Cooper et all. 2001). Thus, investors show a more dramatical reaction to news depending on the economic circumstances. Therefore economic circumstances can influence the overreaction-effect which could bias the results of this study.
6.3 Suggestions for further research
Considering the limitations, this study still makes an important contribution to the existing literature since it is the first study which analyzes whether the overreaction-effect has changed over time. A well known understanding of the change in the overreaction-effect and understanding of the underlying reasons for this change can help investors to determine an optimal investment strategy. Therefore interesting suggestions to improve this research are put forward.
A follow up study could consider the consequences of data limitations on the outcomes of this study. Therefore, it is recommended to use data in which delisted firms are taken into account. Such data reflect more realistic the circumstances investors are facing since it consist of the firms that: went bankrupt, merged, are acquired or delisted. Furthermore, a follow up study could use a longer time horizon to investigate the change in overreaction-effects and use more periods to examine the change in overreaction-effects. Using more periods can provide a more detailed understanding of the change in overreaction-effects. Additionally, a follow up study could consider economic circumstances as control variable to explain the overreaction-effect.
8. Appendix A
Table A reports the results of differences in risk and anomalies in seasonality when analyzing size-matched portfolios. The results indicate that there are differences in risk for all size-matched portfolios with the exception of the smallest firms and those anomalies in seasonality are mostly found in the two sub-periods.
Table A: Size Control Test of the Overreaction Hypothesis: Results for Beta and Anomalies in January
Coefficient (T-Statistics) Non-Overlapping A B C D E 1976-2009 Beta (β) -0.111 -0.226 -0.231 -0.287 -0.231 (n=408) (-2.290)** (-4.355)*** (-4.465)*** (-4.226)*** (-5.168)*** Month (D) 0.012 0.001 0.011 -0.005 -0.002 (1.944)* (-0.955) (1.810)* (-0.621)* (-0.278) R-squared 0.011 0.043 0.049 0.063 0.042 1973-1992 Beta (β) -0.157 -0.204 -0.149 -0.202 -0.204 (n=204) (-2,054)** (-4.080)*** (-2.313)** (-2.483)** (-3.441)*** Month (D) 0.016 0.016 0.028 0.013 0.010 (1.680)* (2.085)** (3.287)*** (1.147) (0.934) R-squared 0.018 0.054 0.044 0.038 0.035 1993-2009 Beta (β) -0.068 -0.258 -0.322 -0.383 -0.266 (n=204) (-1.057) (-2.960)*** (-4.676)*** (-3.675)*** (-4.231)*** Month (D) 0.009 -0.015 -0.008 -0.025 -0.015 (1.108) (-1.536) (-0.955) (-2.712)*** (-1.650)* R-squared 0.005 0.049 0.081 0.108 0.057 Overlapping A B C D E 1976-2009 Beta (β) -0.091 -0.276 -0.270 -0.380 -0.290 (n=1148) (-1.524) (-5.096)*** (-5.246)*** (-6.455)*** (-5.370)*** Month (D) 0.015 -0.001 0.005 -0.009 -0.013 (1.412) (-0.139) (0.538) (-0.810) (-1.350)* R-squared 0.010 0.061 0.064 0.096 0.072 1973-1992 Beta (β) -0.139 -0.214 -0.134 -0.344 -0.288 (n=574) (-1.541) (-3.529)*** (-2.212)** (-4.858)*** (-3.672)*** Month (D) 0.026 0.029 0.034 0.033 0.000 (1.690)* (2.721)*** (3.219)*** (2.732)*** (-0.004) R-squared 0.023 0.082 0.064 0.124 0.064 1993-2009 Beta (β) -0.053 -0.345 -0.400 -0.428 -0.302 (n=574) (-0.667) (0.000)*** (-5.019)*** (-4.772)*** (-4.008)* Month (D) 0.005 -0.033 -0.027 -0.051 -0.026 (0.351) (0.048)** (-1.761)* (-3.021)*** (-1.853)* R-squared 0.003 0.089 0.123 0.136 0.088
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