The Efficient Market Hypothesis has been regarded as a model so far, when the hypothesis was stated by Fama (1970). The theory states the rational behavior was proceed by the rational investors in the securities market and the investors’ decision was built on the expected theory, risk aversion and maximize the utility function. Since 1980s, plenty of empirical studies indicate that the investors’ behavior do not match the traditional theory in the real situation, in addition, most investors whose behavior is not rational at all, for example, investors usually make decisions with overconfidence, overoptimistic and cognitive bias which generate the result is not the optimal decision-making in the true life.
Many anomalies which could not explained by the traditional theory; therefore, the behavior finance theory was developed based on the psychology and attempt to explain these anomalies; Kahneman and Tverskey (1979) state that investors are unable to make decision with adequate and available information rather than like the individual was described in the EMH who will do complete analysis to all situations. They think most people has cognitive bias and makes decision based on the rule of thumb. In fact, investors’ decisions will depend on their psychological factors, the environment or the error news so that the market is not perfect as the efficient market; it implies that there are arbitrage chances in the market. Two investment-related anomalies are momentum and contrarian strategy.
Momentum strategy states that the stock will continue to rise or continue to decline in the short term so that buying the past winner and selling the past loser; contrarian strategy is contrary, which means the price will adjust reverse so that buying the past loser and selling the past winner. The views of the two strategies are the former means the existence of the underreaction, the latter means the existence of the overreaction.
Since Jegadeesh and Titman (1993) state the momentum strategy and the De Bondt and Thaler (1985) state the contrarian strategy, many researchers who began to study the source of the abnormal return in order to examine whether if the profitability exist or not. Such as Chan (1988) states the time-varying risk, Zarowin (1989) points out the seasonal effect, Moskowitz and Grinblatt (1999) address the industrial momentum and Conrad and Kual (1998) propose the time series predictability or cross-sectional variation in the mean returns. By the past researches, we can find that the market anomalies who are often accompanied by the psychological factors of the investors and the accuracy of the interpretation of information which leads the market price to overreaction and underreaction.
In Taiwan, the major investment tool is stock; as the table 1-1 displays that the percentage of the domestic individuals is much higher, there were at least 60% over the past 10 years, in addition, Chen et al (2006) point out that Taiwan stock market is not weak-efficient market. Therefore, there are characteristics of shorter holding period and higher turnover which leads that the fluctuation is larger in Taiwan; however, the De Bondt and Thalet (1985) find out the past loser would have higher return than the past winner when holding them for 3-5 years. Furthermore, Jegadeesh and Titman (1993) state that implement the momentum strategy could 1% excess return. According to these evidence, momentum and contrarian strategy were supported in USA. The features of Taiwan stock market are unlike the USA stock market so that it is worthy to study that whether if the momentum strategy or contrarian strategy is suitable to implement in Taiwan.
Table 1-1: the Proportion of Types of Investors in Taiwan Stock Market
The study collects daily data to examine the stock market whether if the momentum effect exists based on the momentum strategy. It also tests whether if getting the excess return when holding different period based on the prior return, or implementing the contrarian strategy will be better than using momentum strategy.
In the traditional financial theory, the Capital Asset Pricing Model, CAPM and the Efficient Market Hypothesis, EMH are cornerstones which had dominated the modern financial field for decades. In recent years, there are plenty of empirical evidences indicate that lots of anomaly against the traditional financial theory. The study will use momentum strategy to examine whether if gain the significant return in Taiwan stock market.
The profit of the momentum strategy is equal the loss of the contrarian strategy; on the contrast, the loss of the momentum strategy is equal the profit of the contrarian strategy. In other words, investors could get the significant profit by implementing the momentum strategy; they would get loss by exploiting the contrarian strategy or vice versa; therefore, the study including the related review about the contrarian strategy.
Traditional Financial Theory
Efficiency Market Hypothesis (EMH)
EMH states that the share price will fully reflect in all the related information correctly and immediately. According to the hypothesis, no investment strategy can earn excess return, in other words, no one can bet the market by any trading strategy as the market is equilibrium. In the traditional finance, the model was assumed with the agents are rational which means that the agents could renew their concept accurately and make right decision. Shleifer(2000) point out that the EMH was established on three assumption. First, all investors are assumed to be rational and hence they are able to assess the securities. As the investors who obtain new information about the securities they bought, they will correctly and quickly respond to the news by rising up the price as it’s a good news or bringing price down as it’s a bad news. Hence, as the assumption, all asset prices should adjust to the information immediately. Even though most of all investors are not rational, their trading is random and it could balance the price effect. The influence on price will cancel each other out as investors have wrong decision making in the market. Despite most people with homogeneous irrational behavioral, the price would return to be rational by exploiting arbitrage mechanism. For example, buy the underpriced asset on a market and sell the identical or similar asset on the other market which leads the price back to balance. However, some market phenomena corroborate performances which could not be explained by the hypothesis.
Capital Asset Pricing Model (CAPM)
CAPM was developed by Sharpe et al (1960).It illustrate that the relationship between the required return of securities and the systemic risk, as an equilibrium. In addition, the purpose of the model is assist investors to decide the price of the asset. Its assumptions are much tough than EMH, it assumes that all the investors who can get the same information in the same time and only concern the trade-off of risk and return as they chose investment targets. Furthermore, there is no transaction cost, no tax and no limitation on security trading in the perfect market.
Barberis N., & Thaler R. (2002) point out that behavioral finance is a new and a better approach to interpret that not all agents are rational at all. The new method involves two components which are limits to arbitrage and psychology.
Limit to Arbitrage
Shleifer, A. and Vishny, R. (1997) point out that the market is inefficient and the traders are irrational and the interaction between the rational and irrational, the irrational trading will bring enormous and long standing impact on price. If rational traders who want to play the power of arbitrage, they have to be provided with some essential conditions. First, the irrational traders could not be too much, or they will dominate the market. Second, the market must to permit the low cost shorting which only for rational traders, otherwise, irrational traders who make the price deviation by short selling. Finally, the true value of assets should be come to light, or these irrational traders would not adjust their behavior until they realize that their evaluation of the stock price is error. Apparently, these conditions above mentioned are difficult to satisfy, therefore, Shleifer, A. and Vishny, R. (1997) call it ‘Limit to Arbitrage.’
Behavioral financial scholars think that irrational investors’ decision would be affected by their own beliefs and preferences. Some reasons caused the irrationality were summarized as follow. First, investors would make decision by following their beliefs. Sometimes, they are too over optimism to ignore whether the fact is or not. Overconfidence is one of concepts which were explained various phenomena, empirical studies have shown that investors often over-believe the accuracy of their judgement. Sudak and Suslova states that people has insufficient knowledge of the confidence level so that they mistake as predicting. As a result of information insufficiency which leading to the overconfidence and investors do wrong decisions. Consequently, it not only causes investors who take too much money on transaction costs, but also leads the market to overreaction. Moreover, representativeness is one of problems. Shefrin (2000) points out that the individual makes judgement on past stereotypes. It means when investors build a cognitive, they will keep it for a long time and hold a strong suspicion on new evidence. Kahneman and Tversky (1973) state that people tend to classified events on the basis of past experiences, and then assess how much the probability is which will make them over-believe the possibility of history repeat. Some of the time, the representativeness heuristic is a useful method to infer results; however, it sometimes brings serious biases. Such as base rate neglect and sample size neglect bias. Second is individual preference. In the traditional finance, there are more mathematical models were given; the most acceptable rational model is expected utility theory. Despite these models are standardized, it can not to explain phenomena which violate the traditional pricing theory and EMH around 1980s. Since 1980s, behavioral finance has become vital gradually, there are two related theories to the field. One is that most phenomena could not be interpreted by the traditional finance, other one is related to ‘Prospect Theory’ by Kahneman and Tversky (1979). Kahneman and Tversky (1979) address the prospect theory which point out that the traditional utility theory is unable to describe the decision-making under the uncertainty condition. Kahneman and Tversky summarized three effects to explain these anomalies were written as follow:
The effect means people will much emphasize on the certain result instead of uncertain outcome. For instance, there are two questions, and each question has two gambles. The first one: (1) People has 40% opportunity to win $6,000, 59% to earn $4,000, 1% get nothing.(2) People will get $4,000. The second is (1) There has 40% opportunity to win $6,000, 60% get nothing. (2) There has 41% opportunity to win $4,000, 59% get nothing. According to the results show, there is 82% people will choose the (2) in the first question; 83% people will choose the (1) in the second question. In terms of utility theory, the preference of question one is μ ($4000)> 0.40μ ($6,000) +0.59μ ($4,000); the preference of question two is 0.41μ ($4,000) <0.40μ ($6,000). Obviously, it departs from the utility theory.
Individual has preference for risk seeking in the face of loss; on the other hand, the individual preference for risk aversion. The effect out of accord with expected utility theory, which can be seen that individual puts emphasis on a reference point relative to the wealth change instead of the expected utility of final wealth.
The effect confer investors have different decisions because of the statement of scenarios. For instance, the player will get $70 in advance, and then choose one decision of two options in the gamble. Gamble one: (1) 30% keep all; 70% loss all. (2) Keep $30.Most people will choose the option 2 in the gamble one. Gamble two: (1) 30% keep all; 70% loss all. (2) Loss $40.However, most people will choose the option 1 in the gamble two, despite the result of gamble two is the same as gamble one.
Underreaction and Momentum Trading Strategy
Underreaction means the asset prices are unable to reacting reasonable prices immediately and currently when there is new information; the price will appear the stronger always the winner and the weaker always the loser, in other words, the prices will continue upward or downward in the prior trend. Therefore, manipulating the strategy which is buying the prior better stock and selling the prior the worse stock, it will get the excess return. We use the following examples to explain:
Jagadeesh and Titman (1993) examine the listed stocks in the New York Security Exchange (NYSE) and American Stock Exchange (AMEX) from 1965 to 1989. In the experiment, Jagadeesh and Titman select four different periods (3, 6,9,12 months) as ranking period and holding period, it forms 16 portfolio periods. Based on the ranking of the average return during the ranking period, the top decile as be a winner portfolio and the bottom decile as be a loser portfolio. The result shows that it has abnormal return (12.01%) as the ranking period and holding period are 6 months when buying the winner portfolio. Additional evidence shows that the reason for the abnormal return is that the delayed reactions due to firm-specific information, rather than systematic risk. Moreover, the result also indicates that the return would be higher as the small size or the large Beta sample.
Chan, Jegadwwsh and Lakonisok (1996) test that whether if the predictable of the future return over the past performance because of the underreaction to information, in particular to the past earning announcement. They use the sample collected from NYSEã€AMEX and Nasdaq during 1977 to 1993, exploit the return of over the past six monthsã€ standardize unpredicted return ã€ the abnormal return around the declaration of earnings and the average portfolio of the next 6 months predicted return. In terms of the four criterions to build a portfolio and the result indicate that the stock market has the compensation of the return continued.
Rouwenhorst (1998) examine the stocks of the 12 European Nations with the same methodology of Jegadeesh and Titman (1993), the evidence shows that it could profit as usual when using momentum strategy in European. The result is similar to Jegadeesh and Titman made in USA, and it has much significant level. In addition, Chui, Titman and Wei (2001) verify that Japan is the only one where without obviously significant momentum effect in the stock market.
Even thought Barberies et al. (1998) and Hong and Stein (1999) have different explanations for investors’ behavioural modes, they agree that the effect of momentum Strategy is majority from information asymmetries which caused underreaction and overreaction In addition, Jegadeesh and Titman (2001) asses extra 9 years to test the major profit is due to overreaction, which support the issue of behavioural modes.
Schiereck et al. (1999) asses the stocks listed on Frankfurt Stock Exchange in order to examine the performance of the short term and long term in German stock market. The experiment evidence shows that the result is similar, although the stock structure, society, culture and economy environment is distinguish with USA. The result indicate that there has abnormal return either short run ( one month) or long run (three years to five years) when exploiting the contrarian strategy; in the mid-term ( three months to twelve months), implementing momentum strategy which could have significant abnormal return. Lee and Swaminathan (2000) point out the “momentum life cycle.” The cycle, in addition considering the price momentum based on the prior return, it also takes the former turnover rate into consideration. In the winner portfolio, high turnover rate is the standard of terminal momentum and the low turnover is the standard of former momentum; in the contrary, in the loser portfolio, either the winner with high turnover or the loser with low turnover, it will reverse in the future.
Hsu (1999) use the different time period to examine the Taiwan stock and he finds there is a significant positive monthly average return by implementing the contrarian strategy in the long investment period( 3 years); there is a negative monthly average return by using the same strategy in the short investment period( 1 month). In the middle investment period (3 months to 12 months), there is a positive monthly return by exploiting the momentum strategy. In addition, the opportunity for positive return is higher as the market in the long period by using momentum strategy; in the short period, the opportunity for positive return is higher by using contrarian strategy. The result is similar with the American and Germany stock market.
Chen (2000) finds that Taiwan stock market exist the industry momentum strategy which is an appropriate investment strategy for short, middle and long term and the performance is better than the momentum strategy on individual stock. The result also proves that Taiwan stock market is in accordance with the momentum life cycle theory.
Hsieh (1994) analyse the performance of the momentum strategy from 1975 to 1993 in Taiwan stock market. The result shows that the momentum strategy has significant correlation with season effect but without the size effect.
Overreaction and Contrarian Trading Strategy
Overreaction means the individual has emphasis on recent relevant news too much which leads the stock price would excess the reasonable price and the price will be adjusted later which is the phenomenon of price reversal, such as the overshoot price will go down and the overselling price will go up. If the stock market has the phenomenon of overreaction, the investors will earn the excess return by buying the prior overselling stock and selling the prior overshooting stock. The phenomenon negates the efficient market hypothesis and hence it causes a wide range of studies. We use the following examples to explain:
According to the source of CRSP, De Bondt and Thaler (1985, 1987) point out that the overreaction has exist in the market and the weak efficient market hypothesis disconfirms. They state two essential assumption of overreaction:
The stock price will move with the opposite direction
The greater of the change in former stock price, the adjustment is also larger in the later.
De Bondt and Thaler collected the data of New York Security Exchange (NYSE) from 01/1926 to 12/1982, selecting the top 35 companies as a winner portfolio and the final 35 companies as a loser portfolio with the ranking based on return. The empirical result shows that the loser portfolio over the past 3-5 years has better performance than the winner portfolio when hold them 3-5 years; in other words, overreaction has truly exist in the stock market; hence, they state the contrarian strategy: buying the loser portfolio and selling the winner portfolio, it will earn excess profit.
Zarowin (1989) states that the source of profit neither from the investors’ overreaction or risk change, it is related to the scale of a company. As usual, the scale of companies in the loser portfolio is smaller than the winner portfolio; even thought the return of small size winner portfolio is larger than the large-scale loser portfolio.
Fama and French (1996) find that the three-factor model could not only explain the abnormal return relative to the book value/ market value, size and price/ earnings, but also the contrarian strategy.
Conrad and Kaul (1998) find the contrarian strategy has significant return in the short term (1 month) and long term (3 years to 5years), but has not exist in the middle term ( 3~12month). Chou, Wei and Chung (2007) examine the Japan stock market with the contrarian strategy, the result shows that there has existed significant profit which main source is cross autocorrelation, not overreaction.
Lu (1994) studies the profit source of contrarian strategy in Taiwan stock market. He finds the contrarian strategy will loss more as the stocks continuous either move-up or down which imply the return of stock possesses strong positive autocorrelation. The profit of cross-section autocorrelation would be less than the loss of the positive autocorrelation if the portfolio built by the lead-lag relationship.
Lin (1992) examine whether if the Taiwan stock market has overreaction, she collect the monthly return of stocks listed on Taiwan stock market from 1981 to 1991. The evidence shows that there is no overreaction in short run; in long term, there is overreaction. Moreover, the overreaction of the loser portfolio is greater than the winner portfolio, the asymmetry indicate investors are easy to over-pessimistic for the bad news caused they sold a large number of shares and hence the selling is spring up; on the contrast, investors who are wait and see as face the good news which leads to the overreaction of loser portfolio is greater than the winner portfolio.
Yang (1998) considers the contrarian strategy is universal in foreign countries which not take various factors into account; therefore, he examine the monthly return during 20 years in Taiwan stock market, the study not only including systematic risk factor but also the season effect and the size effect. The empirical evidence indicates that the contrarian strategy is not suitable for application in Taiwan.
To sum up, overreaction and underreaction both mean that events cause the securities prices fluctuate dramatically. For overreaction, it means that the price excess the rational price and then generate the phenomenon of reversion; the underreaction means that prices under the normal price and then generate the phenomenon of the same amendments. Furthermore, we can make summarise from the empirical studies discussed above, the superior stock will keep on a rise and the poor stock will continue to decline in the short time; nevertheless, it will reverse in the long time. In most countries, the empirical studies have different result because the difference in the methodology and the sample collection. In the study, we will use stocks in the Taiwan 50 Index to test whether if the existence of the overreaction and underreaction.
The data used in the paper is Taiwan 50 Index which is trading on the Taiwan Stock Exchange. All the data selected from Yahoo Finance. TSEC issued the Taiwan 50 Index which co-produced with FTSE on 29/10/2002. The index includes the top-50 companies listed in the stock market, which represents the performance of blue-chip stocks; in the meanwhile, the index is the first tradable index in Taiwan stock market. TSEC opens from 09:00 a.m. until 13:35 p.m. on each trading day; the spot price of Taiwan 50 Index will be calculated by the latest price of the constituent stocks per 15 seconds. The constituent stocks of Taiwan 50 Index are based on the listed stocks in TSEC, which have to pass three check standards such as (1) market value (2) free float (3) liquidity. According to the three standards, the top 50 companies would be adjusted; therefore, the collection date of the sample was on 16th Jun 2010, moreover, some of the constituent stocks which listed on the TSEC are not long; therefore, this paper collects the daily stock price of top 50 companies from 02/01/2006 to 31/12/2009; all prices are adjusted for dividends, right issues and stock splits. According the Industry Classification Benchmark (ICB) which was built by FTSE Group and DJ Indexes, the index is including 8 industries; they are oil and gas production (500), materials (1000), industry (2000), consumer goods (3000), consumer services (3000), telecommunication (6000), finance (8000) and technology (9000).
The Momentum Strategy
No Time Lag between the Ranking Period and Holding Period
In this study, we selected stocks based on their average return over the past 3, 6,9,12 months and hold these stocks at the same period lag over the next 3, 6,9,12 months. Totally, there are 16 strategies. The strategy used in the study nearly same methodology which pointed out by Jedadeesh and Titman (1993). The portfolio construction of momentum strategy as follow: the strategy called as ranking period/holding period strategy (or J months/K months strategy) which means that calculate the average return of the 50 stocks over the past J months, and then ranking stocks in ascending order based on the past return. According to the ranking, all stocks divided into five portfolios with equal weight. The performance of the top portfolio is the worst, it called the loser portfolio; the bottom portfolio is the best, it called the winner portfolio. Portfolio A1 stands for the stocks with the lowest performance in the portfolio; portfolio A5 stands for the stocks with the highest performance. Stocks have equivalent weight in each portfolio, then, implement the momentum strategy buys the winner portfolio and holds it for K months, sells the loser portfolio in each month t. In addition, in order to strengthen the power of the detection, we adopt the overlapping period method to select samples and test them. In this study, the entire period is separated into five sub-time periods; each sub-time period was form a portfolio based on the return of over the past J months, and observes the return change in the holding period K which is following the ranking period J. For instance, if the J=6, K=6, the portfolio foundation day is from 01/07/2006 until 01/07/2009 (data period: 02/01/2006 to 31/12/2009), and the portfolio will be choose once repeat for the next month.
ranking period (J=6) holding period (K=6)
01/2006 06/2006 07/2006(foundation day) 12/2006
ranking period (J=6) holding period (K=6)
02/2006 07/2006 08/2006(foundation day) 01/2007
ranking period (J=6) holding period (K=6)
01/2009 06/2009 07/2009(foundation day) 12/2009
Figure 3-1: portfolio formation
One Month Lag between the Ranking Period and Holding Period
The first approach we mentioned above, the portfolio was constructed after the ranking period immediately; however, the information is unable to obtain immediately, Jegadeesh (1990) and Lehmann (1990) state that the trading strategy of the instant portfolio would be affected by the bid-ask bounce, the price pressure and non-synchronous trading. Consequently, constructing a portfolio skip one month after the ranking period which refer to the method by Jegadeesh and Lehmann (1990); in other words, there is an interval of one month between the ranking period and holding period. For example, J=6 K=3
ranking period (J=6) holding period (K=3)
01/2006 06/2006 08/2006 (foundation day) 10/2006
ranking period (J=6) holding period (K=3)
02/2006 07/2006 09/2006 (foundation day) 10/2006
ranking period (J=6) holding period (K=3)
01/2009 06/2006 08/2006 (foundation day) 10/2006
Figure 3-2: Portfolio formation
Portfolio Construction with No Time Lag
Calculate the average return of all the stock prices over the past period, from t-q to t-1, the length of the period is p
Ri (t-q, t-1) =/n,
: the return of stock i at the time j
n : the length of the period
Ri (t-q, t-1): the average return of the stock i over the past period
And rank the return as asecending order and divided into five portfolios by equally weight. According to this ranking, construct a portfolio at the beginning day of the holding period; therefore, the day we called it foundation day. If implement momentum strategy, buying the winner portfolio and selling the loser portfolio. If implement strategy, selling the winner portfolio and buying the loser portfolio which formed a zero-cost portfolio.
Portfolio Construction with One Month Lag
The Ne is stand for the number of stocks in each portfolio, rij is stand for the return of the stock i in the time j. The length of the holding period is p, the average return of the portfolio from t to t+p-1 is as following:
ARp (t, t+p-1) =
ARp (t, t+p-1): the average return of the portfolio from t to t+p-1
The average return of portfolio by skipping one month:
ARp (t+1, t+p) =
The average return of immediate investment portfolio and the skip one month portfolio by implementing momentum strategy as follow:
No time lag: ARc= ARw (t, t+p-1)- ARl (t, t+p-1),
Skip one month: ARc= ARw (t+1, t+p)- ARl (t+1, t+p)
ARw is average return for the winner portfolio
ARl is average return for the loser portfolio
The average abnormal returns (AAR) on momentum portfolio (Pi) are calculated as follow:
Rm= Monthly average return on market (value-weighted index and
The Result of No Time Lag
Table 4-1 demonstrates the monthly average return for the five momentum portfolios from 2006 to 2009. The average return difference between P5 (top-winners) and P1 (top-losers) is -0.054% during the four years. The P1 (top-losers) outperformed the P5 (the winners) over the past 4 years; however, it present that the five portfolio did not beat the market either use equal-weight index or value-weight index. The difference between the winners (P4&P5) and the equal-weight value/ value-weight of index is approximate -1.15%/ -0.8%. As the figure 4-1 illustrates, the trend was form a V shape, the performance of the top-loser is the best and hence here it support the contrarian strategy not momentum.
As the table 4-2 displays, when implementing the strategy as the individuals hold the top-loser (P1) for 3-month ranking period (K3) based on the prior return over the past either 3-month (J3)or 6-month(J6), they would get the return which is 2.76% or 2.71% among these strategies . It also reports that regardless of the length of the average return of the period is which investors based on, when the holding period are 3 or 6 months, the average returns for the five portfolios would be positive; however, when investors hold one of five portfolio for 9-month or 12-month ranking period, the average returns would be negative, except generated the strategy on J9, K9 for P2 and P4. For the top-loser (P1), the average returns decrease progressively as the ranking period became longer as the holding period is 3 months. Further, the trend of the top-winner (P5) is similar with the top-loser (P1). As the result, the mean of monthly average return are 2.99%, 0.189%, 0.155%, 0.279% and 0.258% , from the top-loser (P1) to the top-winner (P5), respectively.
The average returns difference between the top-winner and the top-loser from -0.399% to -0.269% .The momentum strategy is buying the top-winner (P5) and selling the top-loser (P1). Hence, as the result, when the return is negative which means the top-loser is outperform the top-winner during the experiment period. In contrast, as the return is positive this represents that investors can earn profits by exploiting the momentum strategy. Three of sixteen strategies have positive return which are as J=9, K=6(0.003%), J=9, K=9(4.805) and J=12, K=12(0.161). The highest return is implement the momentum strategy for J=K=9 (4.805%). As the finding report in table 4-3, the performances were underperform which presents that regardless of the length you rank and hold for , the top-winner was underperform the top-loser. As a resu