Investor overreaction and global financial crisis: A case of Pakistan stock exchange

Abstract Recently, the investor overreaction catches the attention of the academicians and practitioners. The topic comes under the limelight of academicians and policymakers. This study, therefore, addresses investor overreaction and its relationship with the global financial crisis for the period of 2004–15. The study used stratified random sampling technique; equal allocation method of Krejcie and Morgan. By adopting the methodology of Debondt and Thaler, the study finds that there is highly significant overreaction (distinct reversal) in the stock market in the global-financial crisis period, which may attribute to the aggressive behavior of individual investors in the market. Overreaction has also been shown in the line graph shaded area which opposes the efficient market hypothesis and verifies the presence of a weak form of efficiency. Econometric tests are applied for robustness check that confirms weak form of efficiency in the PSX. The study has implications for both the investors and policymakers. This study is quintessential for those investors who have the aptitude to look introspectively and to evaluate their behavioral biases. Further, investors would learn to transmute behaviors and to build portfolios which will help them to stick to their long-term investment strategies and hence achieve their investment goals.


PUBLIC INTEREST STATEMENT
This research is an application of behavioral finance on the real-world problems. It explains that stock markets are exposed to investors' biases that subject to the spill-over effect of other stock markets. The scholars interested in the realm of behavioral finance can use our findings in their research for in-depth insights. Every investor trading in the stock market suffers biases in shortrun, while return to normal position later on shows overreaction, that is, showing more aggressive behavior in the market. If investors face bad news that directly affect the investors' behavior in negative way, it results in irrational decisions. More specifically this paper investigated the impact of global financial crisis on the investors' decisions in the stock market of Pakistan. The study highlighted the issue that investors in the stock market possess less information. Further, they do not make rational decisions in short-run in the market, which consequently leads to investor overreaction.

Introduction
Stock market prediction has always been a matter of debate for market analysts. One of the general questions is that why do securities prices change? No one came with real and precise answer. One aspect is that stock-price predictions and understanding stock market's whereabouts is not possible. In another view, it could be predicted with the help of historical market data and its trend (Bachelier, 1900;Malkiel, 2003). It is common that the fluctuation in the trading of stocks in the market is linked with many other factors; like any natural disasters, political uncertainties, recession across the world, wars, oil prices, economic conditions, globalization, and bad news about the stock market, and so on. The above news has direct and indirect impacts on the market (Otchere & Chan, 2010).
Market analyst studies stock market inefficiencies in which securities mispriced from their fundamental values and those securities become overvalued or undervalued in the stock market. Further, it either causes investor underreaction or overreaction in financial terminologies in the stock market that oppose efficient market hypothesis (hereafter; EMH) and verify the presence of weak form of efficiency. The literature of behavioral finance is categorized in two main areas; the overreaction identification in the EMH that explains by behavioral models like DeBondt and Thaler (1985) and the identification of the investor biases inconsistent with classical economic theories of rational behaviors like that discussed by Barber & Odean (1999); Pompian (2011). The market efficiency is essential in a country because when the market is inefficient in adjustment to the news. Then, the less informed investors tend to overreact and the analysts as well as the savvy investors leave behind the market by receiving overvalued and undervalued securities information. Consequently, they earn abnormal returns in that period (Mehmood et al., 2012). Research in experimental psychology asserts that when an investor violates Bayes' rule that would subsequently tend to overreact to unanticipated news. So, it is essential to know whether this behavior matter at the market level or not. In investor overreaction, stock price tends to depart from their fundamental values; with good news it goes up, while declines with bad news. However, over a period of time prices come back to their old position by exhibiting that prices have overreacted and then corrects itself.
The study of overreaction is well-understood phenomena and explained meticulously (DeBondt & Thaler, 1985;Poterba & Summers, 1988;Howe, 1986;Brown & Harlow, 1988;Fama, 1970;Smith, 2016;Ball, Kothari & Shankeen, 1995). Jegadeesh and Titman (1993) had come with more detailed evidences in favor of momentum effect in short run and contrarian effect in long run. Besides, some other studies investigated investor overreaction in developing markets. For instance, Sohail and Javid (), Bhutta and Shah (2014), and Soomro et al. (2016) conducted study in Karachi Stock Exchange, and Vardar and Okan (2008) investigated in Istanbul Stock Exchange. The results of the above studies were mixed and inconclusive. These studies targeted top 30 and 100 index based on market capitalization, which lacked generalizability. Different methodologies were used that lacked cohesiveness. Similarly, this is the first study of investor overreaction according to the best knowledge of author that aims to cover all sectors till date that addresses this gap in the present literature. The study contributed through constructing portfolios on the basis of weekly ACARs 1 in the long-run. So, it provides better understanding and concrete results of investor overreaction till date in Pakistan Stock Exchange (hereinafter; PSX). The main objective of the study is to check the investor overreaction in the pre-financial, amid and postfinancial crisis' period. Along with it, random walk test is applied as a robustness-check in favor of weak form of efficiency. Overreaction (Crime of small numbers) of the investors is considered inconsistent with EMH. The methodology of DeBondt and Thaler (1985) based on portfolios of ACARs is mostly exploited and considered the most appropriate method of detecting the impact of news on stock prices.
The main findings of the study indicate that there exists highly significant overreaction in the stock market employed t-test: T-SAEV Two-Sample Assuming Equal Variances. The study divulges that there is distinct reversal for the global financial crisis, which exposes a high degree of overreaction in these different periods that may be attributable to the aggressive behavior of individual investor in the market. It could be inferred from the findings that Pakistan is an emerging economy that has partial linkages to the worldwide financial markets. Econometric tests are used as a robustness-check and it confirmed weak form of efficiency in the PSX.
This study is quintessential implications for those investors who have the aptitude to observe introspectively and evaluate their behavioral biases. Several individual investors who elect either to do it themselves or to rely on financial advisor merely for incidental advice. They often find themselves incapable to separate their emotions at the time of investment decisions. This overreaction does not have to be an enduring happening. After studying this research and investigating profoundly into their behaviors, investors can definitely learn to transmute behaviors and to build portfolios that help them stick to their long-term investment strategies. Hence, they achieve their investment goals.
Section one provides background and gap of the study. Section two includes history, basic theme, literature, and hypotheses. Section three has the methodology and statistical techniques. Section four encompasses descriptive statistics, investor overreaction, and random walk tests for robustness check. Conclusion, findings, recommendations and implications, future research and limitations are abridged in section five.

Literature review
Efficient Market Hypothesis suggests that investors irrationally respond to good and bad news causing stock prices to depart from their intrinsic value. Although over some period of time, stock prices slowly revert to their intrinsic value and it suggests that prices overreact in the early period. As investors ascertain their mistakes, then prices return to their intrinsic value. Particularly, stocks with previously low returns will afterward experience relatively high returns, while stocks that had previously performed better would show weak performance in the future. Interestingly, the application linked with overreactions is the capability to earn abnormal profits via implementing a contrarian strategy. This possibility acts as a serious blow to EMH (Fama, 1970). Likewise, a substantial body of pragmatic literature has provided manifestation for overreaction in the stock markets. The pioneer school of thoughts of DeBondt and Thaler (1985) is consistent with the overreaction hypothesis, in which the authors find that the loser-portfolio outperforms the winner one. It was the first attempt at the behavioral principle of investors in the stock market which is also called the winner-loser effect. Moreover, they affirmed that security prices could be predicted on the basis of historical prices that contradict the weak form of EMH.
Studies revealed that stock returns are positively correlated in the short-run, while negatively correlated in long-run (Jegadesh & Titman, 1993). This suggests that investors act excessively optimistically (Overreact) for prior winners in the short-run. Poterba and Summers (1988) and Fama (1970) also affirmed the results of the study of DeBondt and Thaler (1985).
The overreaction hypothesis has become central in behavioral finance in current years. Brown and Harlow (1988) came with improvement on studying the magnitude, directional effect, and intensity of the investor overreaction in NYSE in the simplest way, which supports the study of DeBondt and Thaler (1985). Moreover, investors overweight short news and attract more than a proportional share of investors' attention in the market. Jegadeesh and Titman (1993) found evidence in favor of shortterm momentum effect as well as long-term contrarian effect. Howe's report (1986) based on the one-week large depreciation in stock price, that explained the winner exhibits negative abnormal returns after the post-period portfolio formation. Bowman and Irvesan (1998) presented evidence in favor of overreaction as short-term reversals, while found contradictory long-term overreaction. Ball et al. (1995) conducted a study in NYSE-AMEX and argued that the DeBondt and Thaler (1985) loser stocks were found having low prices. Their study is further criticized on formation period (December), while the results of the study were found inconsistent with the overreaction of June and July. Ali et al. (2011) investigated overreaction in Bursa Malaysia and found that there was a lower level of overreactions for winner stocks. Ali et al. (2011) investigated the stock overreaction on the shariahcompliant stock in Bursa Malaysia for the period 1988-2009 and argued that there was stronger overreaction before financial crisis in Asia in 1997 and in 2008, which decreased later on. Alrabadi (2012) examined the short-term reaction of shocks on the Amman Stock Exchange and found that there is an under reaction for both positive and negative shocks.
The investor excessive overconfidence and increased optimism in the bullish market "NASDAQ" caused investor overreaction in the Taiwanese stock market, while no effect was found on U.S side (Chang et al., 2011). Yang and Luo (2014) analyzed during rumors clarification, ACAR's were positively significant in the Bull market, while ACAR's were significantly negative in Bear market conditions. In both conditions, investors could not differentiate between true and false rumors. Bhutta and Shah (2014) found that corporate governance had no impact on investor reaction. Additionally, Sohail and Javid () examined investor underreaction and overreaction in financial crisis, targeting KSE. The study showed the winners portfolio exhibited a huge increase in price in the initial four weeks and that shows insignificant overreaction. On the other hand, the losers portfolio having enormous price drops and does not show any significant reaction in the global financial crisis in Pakistan. Irshad and Sarwar (2013) investigated the weak form efficiency of KSE in which fundamental analysis can easily earn abnormal return utilizing different stock valuation techniques. Soomro et al. (2016) conducted a study on five cement firms of PSX, which was based on average abnormal returns and found that all investor overreactions are insignificant, except the eleventh and twelfth months.

Hypotheses
H1: There is an overreaction in the global financial crisis period.
H2: There is no overreaction in the pre and post-global financial crisis period.
H3: Portfolio of loser ACARs does perform better than that of the winners in crisis period.

Research approach of Portfolios and data description
According to paradigm diversity, the positivist paradigm is used to test the overreaction hypothesis. Through this quantitative approach, daily closing stock prices (2500 observations/closing prices for each firm) of 70 firms were collected and then converted into 500 weekly returns. Data were collected from 70 firms through equal allocation method of stratified random sampling technique (Krejcie & Morgan, 1970), which includes two firms from each sector (total of 35 sectors) of PSX. The study was conducted for the period of 2004-2015. The core concern of the study is to investigate investor's overreaction using the methodology of DeBondt and Thaler (1985). Consequently, three econometric unit root tests were used for the robustness check of the study.

Methodology of the study
The ACARs winner and loser portfolios are constructed in descending order, where winner ACARs are first 25 (out of 70 firms) outperformed stocks and the loser ACARs are the last 25 stocks that showed worst performance. The results of ACAR portfolios that comprises 21 weeks which were checked with a gap of 22 weeks from 500 entire sample. Portfolios are constructed which include formation period (1st week), then next t-24, t-48, t-72, t-96, t-120, t-144, . . . .t-480, tracked from 2004 till 2015. At last, three econometric unit root tests (ADF, PP, and KPPS) are applied on 2500 stock prices for robustness check of the study. The portfolios of the study are based on ACARs which is the methodology of DeBondt and Thaler (1985). In the first step, historical returns are calculated for the selected stocks.
R t is the Actual returns, P 1 is today's price and P 0 is the beginning price. In the second phase, the Expected Returns are calculated where ER i is the Expected Returns which is considered equal to the market index (PSX) return.
R m,t is the market returns in which Pakistan Stock Exchange 100 index is taken. Then, abnormal returns are calculated by way of.
AR i,t is the abnormal returns of security "i" over the period " t". R i,t is the actual/historical returns, and ER i,t is equal to market return (PSX). Furthermore, the Cumulative Abnormal Returns are calculated as.
CAR i,t is the Cumulative Abnormal Returns of stock "i" over the period 't'.
Hence, Average Cumulative Abnormal Returns (ACARs) are constructed by applying t-Test: Two-Sample Assuming Equal Variances, the first 25 best stocks that became "Winners" and the last 25 stocks that performed worst are said to be "losers". Then, the 25 shares that performed best are combined to form a winner portfolio.
The same portfolio combination is done for making a portfolio of loser stocks.
Then, the overreaction and under-reaction can be calculated as follows: ACARs loser À ACARs winner >0 overreaction ð Þ ACARs loser À ACARs winner <0 underreaction ð Þ If the results of these portfolios are greater than zero, then it will be an overreaction in the market and vice versa.

Data empirical analysis and discussions
The above table 1 shows the result of descriptive statistics of the portfolios of ACARs for the whole sample and separately for the loser and winner portfolios. The mean returns, maximum (minimum) returns, the standard deviation (0.4321) is high for the loser ACARs than the standard deviation (0.3116) of the winner ACARs that revealed high risk in loser ACARs. The winner ACARs are positively skewed, while the loser ACARs is negatively skewed. Both winner and loser ACARs kurtosis show more flatness in the distribution and is platykurtic. The observations in the last row show 21 weeks out of 500 with a gap of 22 in each.
H2: There is no overreaction in the pre-crisis period in the stock market.
The investor reaction results based on ACARs on weekly basis are given in the Table 2 which is picked from the whole sample. In the pre-financial crisis period (2004-06), 120 weeks were selected to check the results of the said hypothesis. The results exhibited highly significant overreaction in the week 20 (0.221), week 90 (0.276), and week 100 (0.374). Conclusively, in the normal periods, that is, when there is no good or bad news, then investors don't exhibit overreaction and the winners stay winners and the loser stay losers.
H1: There is an overreaction in the global financial crisis period in the stock market.
The overreaction hypothesis is checked during the global financial crisis period (2007-09) in table 3. The results disclosed that the investors seemed to follow the phenomena of overreaction. The EMH asserts that financial markets are efficient, which do not hold in the case of Pakistan, as it is an emerging economy. This hypothesis is valid in the period of financial crisis, as the investors show excessive optimism to risk-taking in the form of overreaction. The difference in the ACARs of winner and loser portfolios is positive (showed overreaction) in almost all the periods which show that the investors in a developing country such as Pakistan exhibits overreaction to the global financial crisis. H2: There is no overreaction in the post-global financial crisis period in the stock market.
The above hypothesis is also checked in the post-financial crisis period (2010-12) in table 4, the results showed that the investors did not show any significant overreaction except in few periods. Conclusively, the investors' overreaction was only limited to almost two years, since the start of the financial crisis period. Later on, the impact of the bad news diminished in the stock market.
H1: There is an overreaction in the global financial crisis period in the stock market. ACARs loser ACARs winner >0

Table 3. Investor overreaction on weekly basis in the global financial crisis period (2007-09)
Week The overreaction hypothesis is also checked for the whole period of the study (i.e. 2004-15) and the results are presented in Table 5. The results indicated that the investors appeared to follow the phenomena of overreaction in the crisis period . The results of the study assert that the  Pakistani stock market is a weak-form efficient market in which investors get influenced by the outside news. This hypothesis is valid for the whole period of 10 years to confirm the overreaction effect except in the pre-crisis period in which the investors exhibit excessive aversion to risk-taking In the Figure 1, the Y-axis displays the ACARs, while the X-axis shows the time period (weeks) before the financial crisis period . The blue line shows the movement of winner portfolios, while the red line shows the movement of loser portfolios of ACARs. In the pre-financial crisis period, the portfolio of losers ACARs does not perform better than that of the winner portfolios. The loser portfolios ACARs are lower in almost all of the weeks in pre-crisis period.

Week (Dates) ACAR (W) ACAR (L) Losers-Winners p-Value
The Figure 2 shows the winner and loser portfolios' performance in the global financial crisis period . It is shown that the losers' portfolio performed better in the whole period than the winner portfolio in the crisis period, which shows overreaction in the global financial crisis period. The figure further indicates that losers become winners and the winners become losers in the crisis period, which ratifies the investor's contrarian strategies in Pakistan's stock market. The Figure 3 exhibits ACARs performance on Y-axis, whereas the periods (weeks) on X-axis. As presented in the graph, the loser portfolio of ACARs is lower in performance at point 04, 05, 06, 08, 09, 11, and 12 than that of the winner's portfolio. The line graph indicates that losers stay losers and the winners remain winners in the post-crisis period which confirms momentum strategies of investors trading. Moreover, in few circumstances, the loser portfolios' performance becomes equal to that of the winners' portfolios. The results confirmed that investors who trade in Pakistan's stock market do emphasize the news as well as on the external economic situations. So, they act according to the news at the time of trading in security market.
In the Figure 4, the highest performance of loser portfolios on weekly basis in the period of financial crisis is at point "9" while the worst performance of winners at point "9" on the X-axis is recorded as well. The magnitude recorded for the Pakistan stock market is less than that of the given studies in the existing literature and puts forward that the overreaction is low to some extent in this emerging stock market. Moreover, the investors' overreaction exists for a long-run (almost three years) in the global financial crisis period.
As the overreaction hypothesis predicts that the winner portfolios performed poorly in the financial crisis period, while loser portfolios performed well, as the shaded area exhibits the investor behavior in the financial crisis period in a more transparent way. The results indicated that selling the winners and buying the losers trading strategy earned excess ACARs. Overall, the study concludes that the loser portfolios earned positive ACARs in the stock market which suggests that implementing contrarian strategies by buying losers' shares and selling winners' shares is likely to be a profitable strategy in the crisis period. Table 6 shows the result of the Econometric ADF unit root test which is applied on the 2500 daily average stock prices to check random walk in 70 firms listed in PSX. The result revealed that the daily stock prices of the 70seventy firms are non-stationary at a level in which the value of the "tau" statistic is less than the critical values at 1% and 5% levels but exhibit stationarity at the first difference where the 'tau' statistic value is greater than the critical values.

The above table confirms the stock prices of 70 firms (listed in PSX) that follow random walk
The Table 7 exhibits the result of the Phillips-Perron unit root test which is applied on the 2500 daily average stock prices to check the random walk in the 70 firms listed PSX. The result indicated that the average stock prices are non-stationary at level but become stationary at first difference.

The above table confirms the stock prices of 70 firms (listed in PSX) that follow random walk
The above Table 8 shows KPSS test statistic that isare used after ADF and PP test to provide scrupulous and factual results. Henceforth, the results of these three different time series unit root tests exhibit that the Pakistan stock market follows random walk and proves that PSX is a weak form of an efficient market. The result of the study is consistent with the finding of the existing studies (see, for instance, Karan & Kapusuzoglu, 2010;& Mehmood et al., 2012).

Conclusion
The results revealed that stock returns demonstrate patterns and show consistency with investors' overreaction in Pakistan's stock market, particularly in the case of the global financial crisis period . The portfolios of loser ACARs outperformed of the winner ACARs. The loser portfolios showed more positive returns than that of the winner portfolios during the financial crisis period. The outcomes are consistent with the results of existing literature (see, Wang et al., 2004;Ahmad & Tjan, 2004;Wiggenhorn & Madura, 2005;Sohail & Javid, ;and Soomro et al., 2016).
The study contributed to the existing literature in examining the investor's overreaction based on pre-crisis, within crisis, and post-crisis periods in an emerging market. Generally, the results of the study illustrate strong evidence in support of the presence of overreaction in Pakistan's stock market. The study is carried out in the weak form of the efficient market because in weak form the investors do not receive adequate and accurate information about security prices and market tradings in which fundamental analysis can easily earn abnormal returns through utilizing different stock valuation techniques. As a result, the investors do not retort rationally to the news and investors follow what other experts and proficient class of investors trade in the stock market, which resultantly causes overreaction.
Findings of the study showed that there is a distinct reversal for pre-crisis, amid crisis, and postcrisis periods. It further exposes low degree of any reaction in these different periods that may be attributable to the restrictive behavior of individual investors in the market. It could be inferred from the findings of the study that Pakistan as an emerging economy and has partial linkages to worldwide financial markets, as there is less financial innovation and liberalization. Thus being an emerging market, Pakistan stocks are not prevented from direct impact of financial crisis that   spillover worldwide. Conclusively, Pakistan is not well insulated against the contagion impact in the international financial market.

Future recommendations
Future studies may focus on different sectors of the economy to find out investors' responses whether they show overreaction or under-reaction. Secondly, research is needed to take other different micro-and macro-variables in the stock market that affect investor trading. Thirdly, a similar study may be carried out in different economies to compare the intensity, direction, and magnitude of the investor reaction. Fourthly, other countries' spillover impact can be checked in this stock marketw.r.t to the U.S. Lastly, there is a need to investigate the impact of different