Short-term Contrarian profits:
The case of the Jakarta Stock Exchange
THESIS
A. Syarif Munawi
S. 1497995
Master of Science Business Administration
University of Groningen
Abstract
This paper investigates the presence of contrarian profits and the sources of these profits on the Jakarta Stock Exchange (JSX) over the period from 1994 through 2004. The paper examines five size-sorted portfolios that are rebalanced annually. The contrarian profits are estimated using the Lo and MacKinlay (1990) contrarian strategy in which these profits are calculated every week for all five sized portfolios. The sources of contrarian profits are estimated by employing The Jegadeesh and Titman (1995) model that decomposes the contrarian profits into three sources: profits due to common factor reaction, overreaction to firm-specific information, and profits unrelated to the two previous factors. The findings suggest that albeit without significant negative serial correlation of portfolio returns, all weekly average contrarian profits are positive and significant at the 5% level except for the large and largest stocks portfolio. The average profit of the large stocks portfolio is significantly positive at the 10% level, whereas that of the largest stocks portfolio is insignificant. However, under the assumption of time-varying betas, the primary source of the total contrarian profits is not either the lead-lag relation or overreaction to firm-specific information. The total contrarian profits stem predominantly from the profits unrelated to the two previous factors. The results find that the observed relationship between the total risk (standard deviation) and the firm size seems to be negatively related. The observed profits contributions also seem to be negatively related to firm size. Taken together, these results imply that, the contrarian profits is merely stemming from the trade-off between risks and returns. The results also suggest that the contrarian profits can be explained by the size effect.
Preface
The idea of the thesis arose whilst I took the behavioral finance course taught by Prof. F. M. Tempelaar in the second semester of the 2004/2005 MScBA program in Finance at the University of Groningen. The topic of irrational investor, which suggests psychological biases are perceived to influence the behavior of investors in making their investment decisions, fascinates me since it provides some new alternative interesting explanations of how the stock market works. Then overreaction hypothesis is assigned to be the main issue of the thesis since it is one of the interesting consequences of the irrational investor.
My first acknowledgement should be given to my supervisor, dr. P. Smid, whom I would like to express my sincere gratitude for his help and guidance, the fruitful discussions, and above all, for the excellent supervising. He has always been a tremendous help for me ever since the beginning. He has always given me fresh ideas on how to best approach the problems at hands. My grateful thanks also go to Prof. R. Lensink as the co-assessor who has given some valuable comments on the thesis.
There have been a number of people in the past to which I owe their help and supports for improving my skills and knowledge in the research disciplines. My seniors, Adler H. Manurung and Ratih Rahmadewi of Nikko Securities Indonesia with whom I closely worked for many years, had been very helpful to me in providing insights and understandings particularly about the Jakarta Stock Exchange.
My gratitude also goes to my classmates in the 2004/2005 MScBA program in Finance at the University of Groningen. Also for my Indonesian friends, for with their presence and friendships, I am not feeling too far away from home.
I would also like to express my appreciation to the residences of the Nijenborgh Student House. With them, I am growing and learning a lot every day. I feel very lucky to have such friendly atmosphere in the Nijenborgh. I also thank them for helping me in reviewing this thesis, in order to meet the English standard of writing.
Last but not least, the extremely grateful thanks go to my beloved parents, Prof. Ummu Salamah and Prof. Cecep Syarifuddin, my lovely brothers, Abd. Syakur A., Aji A. Wahid, M. Ali Ramdhani, Irfan Nabhani and Hilmi Aulawi, and also to their families, for their best wishes, great love, and care. I am pretty sure that they must be very happy to see what I have accomplished so far.
Finally, after the long and hard works, I am very glad that I can finish this thesis on time. I hope that this research can be placed in a broader window, and be useful for whomever wants to explore the knowledge related to the topic of this study. As for myself, I hope that I can perform better and greater researches in the future.
TABLE OF CONTENTS
Abstract ... 1 Preface ... 2 TABLE OF CONTENTS ... 3 LIST OF TABLES ... 4 CHAPTER I ... 5 INTRODUCTION... 5 CHAPTER II ... 7 LITERATURE REVIEW... 72.1. Empirical studies... 7
2.1.1. Overreaction hypothesis... 7
2.1.2. Negative serial correlation as an indication of the profitable contrarian strategy .. 8
2.1.3. Contrarian profits ... 9
2.1.4. Decomposition of contrarian profits ... 9
2.2. Empirical studies outside USA ... 11
2.3. Summary of empirical literature review ... 11
CHAPTER III... 13
DATA AND METHODOLOGY ... 13
3.1. Data ... 13
3.2. Methodology ... 13
3.2.1. Serial correlation... 13
3.2.2. The contrarian profits... 14
3.2.3. Decomposition of contrarian profits ... 16
3.2.4. Time-varying factor sensitivities ... 17
CHAPTER IV... 19
SAMPLES AND RESULTS ... 19
4.1. Samples ... 19
4.2. Results... 20
4.2.1. Serial correlation... 20
4.2.2. Contrarian profits ... 21
4.2.3. Decomposition of contrarian profits ... 22
4.2.4. Time-variation in factor sensitivities ... 26
CHAPTER V ... 30
CONCLUSION AND RECOMMENDATION ... 30
5.1. Conclusion ... 30
5.2. Recommendation ... 31
LIST OF TABLES
Table 1. Summary of literature review... 12
Table 2. The number of samples used ... 19
Table 3. Descriptive statistics of stock returns ... 20
Table 4. Testing for serial correlation in the stock returns and the contrarian profits... 21
Table 5. Average estimates of stock returns sensitivities to current and lagged market returns and decomposition of contrarian profits over the period from 1994 through 2004 ... 23
Table 6. Decomposition of contrarian profits for each year under the assumption that the betas are constant over time ... 25
Table 7. Decomposition of contrarian profits with time-varying factor sensitivities over the period from 1994 through 2004... 26
CHAPTER I
INTRODUCTION
For many years academicians and practitioners within the finance field have been interested in developing and testing models of stock prices behavior. Several studies have been conducted to find out to what extent the past history of a common stock price can be used to make meaningful predictions about the future price of the stock.
Fama (1965) points out that there are negative serial correlations of stock returns. Jegadeesh (1990) concludes that monthly returns on individual stocks exhibit significant negative first-order serial correlations and significant positive higher-order serial correlations. This fact surprises many economists since the existence of serial correlations of stock returns implies the predictability of stock returns.
Some studies explain that this predictability is due to the stock market overreaction hypothesis. For instance, DeBondt and Thaler (1985) report that some portfolios of prior losers are found to outperform prior winners. They attribute the performance of a contrarian strategy to behavior irrationality of investors. Lehmann (1990) proposes that portfolios of stocks that have positive returns in one week typically have negative returns in the next week and vice versa.
This phenomenon is interesting since any evidence supporting the overreaction hypothesis may indicate the presence of weak-form market inefficiency. However, some studies have emerged that offer contradictory findings about the overreaction hypothesis. For instance, Chan (1988) argues that the risks of winners and losers are not constant over time. Davidson and Dutia (1988) propose that the previous winners are likely to be the winners for the next period. Zarowin (1990) suggests that the phenomenon of return reversals is consistent with the size and January phenomenon, but not with the market overreaction phenomenon.
DeBondt and Thaler claim that the stock market overreaction can lead to long-term contrarian profits by employing a contrarian strategy, i.e., a strategy involving buying stocks that perform poorly in the past (losers) and short selling stocks that perform well (winners) in the past. When stock returns are negatively autocorrelated, such a strategy could earn positive expected profits since current losers are likely to become future winners and current winners are likely to become future losers.
return reversals may still earn positive expected profits. This is due to the effects of cross-serial covariances from which contrarian strategies unintentionally benefit.
Jegadeesh and Titman (1995) criticize the Lo and MacKinlay argument and suggest that the cross-serial covariance may be a misleading measure of the contribution of the lead-lag structure to the profitability of contrarian strategies. Their study shows that the primary source of the contrarian profits is not the lead–lag structure effect but the overreaction to firm-specific information.
So far, however, there has been little discussion about the contrarian strategies in emerging markets. Given some different characteristics of emerging markets such as thin trading, low liquidity and possibly less informed investors, it is interesting to explore this phenomenon in an emerging market, particularly on the Jakarta Stock Exchange (henceforth JSX).
Since Lehmann (1990) and Lo and MacKinlay (1990) find that the contrarian strategies are also profitable for short-term (weekly) horizons, the main issue addressed in this paper is whether weekly contrarian profits are present on the JSX. If they exist, the next question is whether the profits are due to the stock market overreaction.
Here, specifically some research questions are presented to answer the above main issue: Firstly, are there any negative serial correlations of stock returns on the JSX? Secondly, by applying the Lo and MacKinlay contrarian strategy, are there any short-term (weekly) contrarian profits on the JSX? Thirdly, by employing the decomposition model of Jegadeesh and Titman, is the overreaction to firm-specific information a primary source of the total short-term contrarian profits? Fourthly, if there are any time-varying factor sensitivities, is the overreaction to firm-specific information still a primary source of the total short-term contrarian profits?
CHAPTER II
LITERATURE REVIEW
2.1. Empirical studies
2.1.1. Overreaction hypothesis
The most influential paper on the market overreaction hypothesis is probably DeBondt and Thaler (1985), henceforth DT, who find evidence of price reversals in 36-month stock returns. DT investigate whether the investor’s tendency to overreact to unexpected and dramatic new events affects the stock prices. They suggest that if stock prices systematically overshoot, then their reversal should be predictable from past returns data alone. DT propose two hypotheses. First, subsequent price movements in the opposite direction will follow extreme movements in stock prices. Second, the more extreme the initial price movement, the greater will be the subsequent adjustment.
Their paper shows that the losers outperform the market by, on average, 19.6%, thirty-six months after the portfolios are initially formed. On the other hand, the winners earn about 5.0% less than the market. Thus, the difference between the two extreme portfolios equals 24.6%. Since most of the excess returns are realized in January, their findings are consistent with the January effect.
The implication of the overreaction hypothesis is the contrarian strategy. However, since the contrarian strategy is a trading rule based on past prices, which implies a violation of the weakest form of the efficient market hypothesis, this strategy has been criticized by a number of writers. For instance, Chan (1988) offers an alternative interpretation of the evidence on the performance of the contrarian strategy. Chan proposes that the risks of winners and losers are not constant over time. If market value is a good proxy for risk, the losers are safer in the beginning but become riskier than the winners by the end of the formation period. The loser’s betas increase after a period of abnormal loss, and the winner’s betas decrease after a period of abnormal gain. Based on his finding, Chan suggests that if beta is estimated in the previous period (rank period), the estimated beta would be a biased estimate of the beta in the next period (test period). Chan admits that these differences between his and DT’s conclusion are due to the different empirical methods used.
The study of Davidson and Dutia (1988), henceforth DD, also contradicts the overreaction investment strategy, although by using a different method. DD argue that the previous winners are likely to be the winners for the next period. The January effect is insignificant. The study of DD is in agreement with Chan’s statement that the estimation of the abnormal returns of the contrarian strategy is sensitive to the estimation models used.
In a follow-up study, DeBondt and Thaler (1987) provide additional evidence consistent with the overreaction hypothesis. The winner-loser effect cannot be attributed to changes in risk as measured by betas. The winner-loser effect is not primarily a size-effect.
Zarowin (1990) argues that the notion that the winner-loser effect is not primarily a size effect might be a mistake. He argues that the losers tend to be among smaller firms, while the winners tend to be among larger firms. When the losers are smaller than the winners, the losers outperform the winners; when the winners are smaller than the losers, the winners outperform the losers. But when size is controlled for, the losers outperform the winners only in January. There is no differential performance between the losers and the winners with equal size outside of January. He argues that his findings are consistent with the size and January effect, but not with the market overreaction hypothesis.
2.1.2. Negative serial correlation as an indication of the profitable contrarian strategy
The specific consequence of the market overreaction hypothesis is the profitability of a contrarian strategy, namely a strategy that exploits negative serial correlations of stock returns (Lo and MacKinlay, 1990). Concerning this implication, Jegadeesh (1990) examines the serial correlations of monthly individual stock returns on the NYSE. He finds that there are significant negative first-order serial correlations and significant positive twelve-month serial correlations. His findings, which imply the stock prices predictability, support the overreaction hypothesis. Jegadeesh suggests that this predictability of stock prices can be explained either by market inefficiency or by systematic changes in expected stock returns.
2.1.3. Contrarian profits
Lehmann (1990) argues that the time-variation issue could be accounted for by examining asset returns over short time intervals. Systematic short-run changes in fundamental value should be small in amount to be of importance in an efficient market with unpredictable information arrivals.
His paper considers a portfolio strategy involving buying the previous week’s losers and short selling the previous week’s winners. The results show that the portfolios of stocks that have positive returns in one week typically have negative returns in the next week, while those with negative returns in one week typically have positive returns in the next week. The results strongly suggest not only a rejection of the efficient markets hypothesis but confirm the market overreaction hypothesis as well. LM propose a slightly different model to estimate the contrarian profits, even though the basic idea is still the same. Every week the previous week’s winners are shorted and the previous week’s losers are kept long. Portfolios are rebalanced every week.
2.1.4. Decomposition of contrarian profits
LM question the reverse implication that the profitability of contrarian investment strategies is evidence of the market overreaction. They argue that the profitability of contrarian investment strategies is not necessarily a consequence of the stock market overreaction. Even if the individual stock returns have no serial correlation, portfolio strategies that attempt to exploit return reversals may still earn positive expected profits. These profits are due to the effect of lead-lag structures, which is measured by the average of cross-serial covariances of stock returns, from which contrarian strategies unintentionally benefit. LM argue that the lead-lag effect comes up since some stocks react more quickly to information than the others. The illustration of this effect goes as follows: if the increase in a particular stock today implies that another certain stock will probably also increase the day after, then a contrarian strategy will be profitable even if the stock returns are unpredictable using its past returns alone.
Jegadeesh and Titman (1995), henceforth JT, criticize the LM contrarian strategy after applying the strategy to fifty size-sorted portfolios. The fifty size-sorted portfolios actually generate small negative returns albeit the significance of positive cross-serial covariances among these portfolio returns. Their findings indicate that the cross-serial covariance may be a misleading measure of the contribution of lead-lag effect to the contrarian profits. Consequently, the cross-serial covariance does not directly relate the overreaction or delayed reaction to the contrarian profits.
JT suggest that the lead-lag structure in stock returns comes up not because of the overreaction or delayed reaction to specific-firm information, but because of differences in the timeliness of stock price reaction to common factors. On average, stock prices do not fully react to common factors contemporaneously. There is also a delayed reaction to common factors. The delayed reaction, which gives rise to the lead-lag structure, will in general affect the cross-serial covariance.
Based on how the stock prices respond to information, JT separately examine the stock price reaction to common factors and firm-specific information and proposed a decomposition model that directly relates the overreaction or delayed reaction to contrarian profits. Their model illustrates that the overreaction or delayed reaction to common factors affects contrarian profits in a different way than the overreaction or delayed reaction to firm-specific information. For instance, the overreaction to firm-specific information always contributes to contrarian profits, whereas the overreaction to common factors can either reduce or increase the profits. Furthermore, if contemporaneous and lagged betas are positively correlated, then the lead-lag structure does not increase contrarian profits but in fact reduce them. JT suggest that since large firms react almost instantaneously to common factors, while small firms react with a delay, the large firms lead the small firms, but the reverse is not true.
Their empirical evidence shows that the stock prices seemingly overreact to firm-specific information. The contrarian profits due to the delayed reaction explain less than one percent of the total contrarian profits.
2.2. Empirical studies outside USA
Baytas and Cakici (1999) evaluate the performance of arbitrage portfolios based on past performance, price, and size in seven industrialized countries (US, Canada, UK, Japan, Germany, France, and Italy). All except the US show that returns to long-term contrarian strategies seem to be generally significant. Forner and Marhuenda (2003) report that long-term contrarian strategies yield positive abnormal returns on the Spanish Stock Exchange. Lee, Chan, Faff and Kalev (2003) find that significant positive short-term contrarian profits exist in Australia.
Among other studies that examine emerging markets are Hameed and Ting (2000) who provide evidence on short-term predictability of stock returns on the Malaysian stock market, Kang and Ni (2002) who find that there are statistically significant abnormal profits for some short-horizon contrarian strategies on the China Stock Exchange, and Galariotis (2004) who suggest that short-run contrarian profits are present on the Athena Stock Exchange.
2.3. Summary of empirical literature review
Several empirical studies show evidence of stock returns predictability based on past information, which contradicts the weakest form of market efficiency. DeBondt and Thaler (1985, 1987) find that prior losers outperform prior winners. It has been demonstrated that there are negative serial correlations of stock returns (see Fama, 1965 and Jegadeesh, 1990). A number of writers support the short-term contrarian strategy (see Lehmann, 1990; Hameed and Ting, 2000; Kang and Ni, 2002 and Galariotis, 2004), and the long-term contrarian strategy (see Jegadeesh, 1990; DeBondt and Thaler, 1985, 1987 and Lee, Chan, Faff and Kalev, 2003).
In their seminal article, Lo and MacKinlay (1990) argue that the profitability of contrarian strategies is not necessarily the result of stock market overreaction. They maintain that the overreaction to firm-specific information is not a primary source of contrarian profits. They introduce a second potential source of contrarian profits that arise when some stocks react more quickly to information than the others. This source of contrarian profits is referred to as a lead–lag structure in stock returns, which is the main source of contrarian profits.
Several attempts have been made to propose some possible alternative explanations of the contrarian profits: firm size effect (see Zarowin, 1990), January effect (See Zarowin, 1990; Jegadeesh, 1990, and DeBondt and Thaler, 1985) and time varying market risk (see Chan, 1988 and Conrad and Kaul, 1989). However, after accounting for the time-variation in factor sensitivities, Jegadeesh and Titman (1995) maintain that the contrarian profits are still significant.
There are also some empirical reports of profitable short-term contrarian strategies in markets outside the US. For example, Baytas and Cakici (1999) in seven industrialized countries (US, Canada, UK, Japan, Germany, France, and Italy), Forner and Marhuenda (2003) in Spain, Lee, Chan, Faff and Kalev (2003) in Australia, Hameed and Ting (2000) in Malaysia, Kang and Ni (2002) in China, and Galariotis (2004) in Greece.
Table 1. Summary of literature review
First-order Negative Serial correlation Contrarian profits/Returns Size effect January effect Time varying
Author/Results Individual Portfolio Reversals effect
US Market
Fama (1965) 3
DeBondt and Thaler (1985,1987) 3*)
3**)
Chan (1988) 2 3*)
Conrad and Kaul (1989) 3
Davidson and Dutia (1989) 2 2 3
Zarowin (1990) 2 3**) 3**)
Lehmann (1990) 3**)
Jegadeesh (1990) 3**) 3*) 3*)
Lo and MacKinlay (1990) 3 2 3**)
Jegadeesh and Titman (1995) 3 2
Outside US Markets
Bali and Cakici (1999) 3 3
Hameed and Ting (2000) 3**) 3
Kang and Ni (2002) 3 *) 3 2
Forner and Marhuenda (2003) 3
Lee, Chan, Faff and Kalev (2003) 3*) 3
Galariotis (2004) 2 3 3 3 2
Note : 3 and 2 indicates yes (confirmed) and no (against and/or insignificant), respectively. *)
: significant at 5% and **) : significant at 1%
CHAPTER III
DATA AND METHODOLOGY
3.1. Data
The paper uses DataStream data on weekly prices and market values for all stocks listed on the JSX in the period of 1994 and 2004. Stocks with at least 260 consecutive listing weeks (five years) are picked to avoid a downward bias of serial covariance estimates that is known to occur in small samples (Galariotis, 2004). Stocks that have no weekly returns in one-year period are also excluded to filter out illiquid stocks. The Jakarta Composite Index (JCI) is used as a proxy for the common factor. The JCI is a value-weighted average of all individual stock indexes (excluding dividend) listed in the JSX. Returns are continuously compounded, defined as the first difference of the logarithmic price levels. Since the JSX does not provide individual stock indices that take the dividends into account, the calculation of the stock returns also do not include the dividends.
3.2. Methodology
3.2.1. Serial correlation
To find out whether there is any possible winning contrarian strategy, the existences of serial correlations of weekly stock returns are investigated. Every year stocks are ranked on the basis of the previous year-end stock market capitalization (number of shares times market price). Stocks are assigned to five size-sorted sub-samples (portfolios) and all stocks portfolio. Each portfolio contains approximately 20% of all stock samples. The processes are repeated each year for 11 years data. The equally weighted portfolio returns are estimated by simply averaging all stock returns in the sample on a weekly basis. The descriptive returns statistics, i.e. the values of mean, standard error, minimum, maximum, skewness and kurtosis are also presented and analyzed.
(
)(
)
(
)
∑
∑
+ = − − − − + = − − − = T k t k t p k t p k t p k t p T k t t p t p k R R R R R R 1 2 , , , , 1 , ,ρ
………. (1)where Rp,t is the return on portfolio p in time t,
R
p,tis the average return on portfolio p over period
t, Rp,t−k is the return on portfolio p in time t-k,
R
p,t−1is the average return on portfolio p over
period t-k, T is total number of observations, and
ρ
kis the serial correlation coefficient of lag k.Since the negative serial correlation is an indication of the market overreaction hypothesis, the expectation hypotheses are:
H0: There are no significant serial correlations of portfolio returns at the 5% level;
H1: There are significant negative serial correlations of portfolio returns at the 5% level.
3.2.2. The contrarian profits
In case there is any serial correlation, the question arises as to whether contrarian profits are exploitable. Employing the same portfolio contrarian strategy as Jegadeesh and Titman (1995), Lo and Mackinley (1990) and Galariotis (2004) did, every week the previous week’s winners are shorted and the previous week’s losers are kept long. Portfolios are rebalanced every week. The portfolio weight assigned to stock i for time t is:
(
, 1 1 , 1 − − − − = it t t i R R)
Nω
………..………… (2) where∑
= − − = N i t i t R N R 1 1 , 1 1 ……… (3)N is the number of stocks in the sample, Ri,t−1 and Rt−1 are the stock return i in time t – 1 and the
equally weighted portfolio return in time t – 1, respectively. The
ω
i,tcan be positive or negative. If theω
i,t is negative, the stock will be sold short, and ifω
i,tis positive, the stock will be purchased. By construction, the total investment at any given time is zero since the total weight, , is zero.However, the dollar investments in the long and short sides of the portfolio vary over time depending on the returns realizations in time t - 1. Thus, the sample groups are rearranged every week, and the time t profit of this contrarian strategy, denoted as
∑
=N i1
ω
i,t(
∑
= − − − − = N i t i t t i t R R R N 1 , 1 1 , 1π
)
……….………..…………. (4)where Ri,t is the stock return i in time t. Then
π
is calculated as the average ofπ
t for each samplegroup for the whole period.
According to Lehmann (1990), these are profits because this is a zero net investment strategy, and hence, returns are not defined. However, these are percentages, not absolute amounts. To put it in perspective, the other study (See Lo and Mackinlay, 1990) normalizes the investments in the long and short positions to one dollar. Thus, the contrarian profits are in terms of absolute dollar amounts. The total investment long (or short) in time t is given by
I
twhere:∑
= ≡ N i t i t I 1 , 2 1ω
……….………. (5)However, the latter approach makes no difference since it is merely a translation into an absolute amount without affecting the relative value of these profits. The contrarian profits for the all stocks and each portfolio are presented and analyzed.
By assuming that a nominal amount of Indonesian Rupiah (IDR) is initially invested in the market portfolio via holding the same proportion of each stock that comprises the market index, winner stocks are not required to be sold short any longer in implementing the contrarian strategy. Thus, this paper regards this strategy as holding a market portfolio with the contrarian strategy. Since each stock in the market index is already owned, over-weighting or under-weighting the stocks position relative to the market index is only to be done. Therefore, unlike typical short-selling practices, the paid dividends need not to be surrendered in case the short-sold stocks earn dividends.
The paper also assumes that the loss dividends due to the under-weighted dividend-paying stocks are canceled out by the dividends earned from the over-weighted dividend-paying stocks.
As mentioned in the literature review (see section 2.1.4), portfolio strategies that attempt to exploit return reversals may still earn positive expected profits even if returns on individual stocks temporally have no serial correlation. Therefore, regardless of the type of signal (positive or negative) for the observed serial correlation, by using LM model, this paper proposes that:
H0: There are no significant positive values of the average contrarian profits at the 5% level.
3.2.3. Decomposition of contrarian profits
Following Jegadeesh and Titman (1995) and Galariotis (2004), in order to estimate the sensitivities of weekly individual stock returns to contemporaneous and lagged common factor returns, this paper uses the following time series regression:
t i t m i t m i i it a b R b R e R = + 0, , + 1, ,−1+ , ……….………..………..……… (6)
Where is the intercept, is the return of stock i in time t, is the return of the market
portfolio in time t, is the residual of stock i at time t, and and are the estimated sensitivities of stock i to contemporaneous and lagged common factor returns, respectively. This regression (5) is estimated separately for each stock in each portfolio each year for the full sample over the whole observation period. This provides estimates of for each stock in each
portfolio each year for the full sample. Then
i
a
Ri,t Rm,t t i e, b0,i b1,i 1 0,
,
b
b
a
i 0b and
b
1 are calculated as the average of and foreach portfolio for the whole period and for each year.
0
b
b
1The results are presented to investigate whether the stock returns fully react contemporaneously and/or with a delay to the common factor. If the value of
b
1 is significantly positive, then the stock returns react with a delay to the common factor.By assuming that the stock returns are generated by the process described by equation (6), thus, the decomposition of expected contrarian profits is given below:
( )
2ˆ
2 m aE
π
=
−
σ
−
Ω
−
δ
σ
………..………..………. (7) where(
2 1 21
∑
=−
=
N i i aa
a
N
σ
)
………...………. (8)(
∑
= − ≡ Ω N i t i t e e N 1 1 , , 1 , cov 1)
……….. (9)(
)(
{
∑
= − − = N i i i b b b b E N 1 1 , 1 0 , 0 1 ˆδ
)}
………..………… (10)The equation (7) decomposes expected contrarian profits into three factors. The first factor, −Ω, is the negative of the average serial covariance of the idiosyncratic components of returns that provides an estimate of the profits due to stock price reaction to firm-specific information. The sign of Ω is determined by stock price reaction to firm-specific information. For instance, the will be negative if stock prices tend to overreact to firm-specific information and then correct the overreaction in the
following period, thus contributes positively to the contrarian profits. The second factor, , is the part of contrarian profits attributable to differences in the timeliness of stock price reaction to common factors. When the cross-sectional average covariance of contemporaneous and lagged betas is negative
δ
ˆ
( )
δ
ˆ<0 , common factor reactions could contribute positively to contrarian profits, while if it is positive( )
δ
ˆ>0 the opposite holds. The(
−
δ
ˆ
σ
m2)
provides an estimate of the profits due to common factor reaction. The last factor, , is the cross-sectional variance of intercepts that provides an estimate of the profits unrelated to the two previous factors.2
a
σ
−
Eventually, the value of three factors (
−
δ
ˆ
σ
m2,Ω and ) are presented and compared to one another to seek in-depth how each factor contributes to the total contrarian profits.2
a
σ
−
Lo and MacKinlay (1990) argue that the profitability of contrarian investment strategies need not be the result of stock market overreaction. However, if the overreaction hypothesis works, then the contribution of overreaction to firm-specific information should be a main source, and hence, higher than the other factors (Jegadeesh and Titman, 1995). This leads to the following hypotheses:
H0: The contribution of the overreaction to firm-specific information is not different from either the
contribution of lead-lag structure effect or the profits unrelated to those factors at the 5% level.
H1: The contribution of the overreaction to firm-specific information is significantly higher than
either the contribution of lead-lag structure effect or the profits unrelated to those factors at the 5% level.
3.2.4. Time-varying factor sensitivities
Following Jegadeesh and Titman (1995), in order to account for the time-variation in factor sensitivities, the paper employs the following regression:
(
mt m)
t t tα
α
R Rγθ
μ
π
= + − − 2 + −1 + 1 , 1 0 ………... (11) Where∑
==
Nt t t i t te
N
1 2 ,1
θ
tπ
is the contrarian profit in time t, Rm is the average of common factor returns over the period ofportfolio formation (one-year period), and are the residuals estimated from equation (6). The estimates of contrarian profits due to the delayed reaction to the common factor and to the
overreaction to firm-specific information are given by
α
1σ
M2 and ⎟ ⎠ ⎞ ⎜ ⎝ ⎛∑
= − T t t T 1 1 1θ
γ
, respectively. Thisdecomposition does not require that b0,iand b1,i be constant over time.
To answer the question as to what extent each factor contributes to the total contrarian profits, similar to section 3.2.3., the ratios of each factor are presented and compared to one another relative to the average contrarian profits
( )
π
.Lastly, even if there is time variation in betas (Conrad and Kaul, 1988 and Chan, 1988), the contribution of the overreaction to firm-specific information should be still the primary factor of the total contrarian profits. Then, the hypotheses are:
H0: The contribution of the overreaction to firm-specific information is not different from either the
contribution of lead-lag structure effect or the profits unrelated to those factors at the 5% level.
H1: The contribution of the overreaction to firm-specific information is significantly higher than
CHAPTER IV
SAMPLES AND RESULTS
4.1. Samples
The paper uses weekly prices and market values for all stocks listed in the JSX over the period from 1994 through 2004. Stocks with at least 260 consecutive weeks (five years) are picked to avoid downward bias of the serial covariance estimates that is known to occur in small samples (Galariotis, 2004). Stocks that have no weekly returns in one-year period are also excluded to filter out illiquid stocks.
Table 2. The number of samples used
Stocks portfolio 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 Average
Smallest 27 33 37 40 44 45 47 50 48 49 49 43 Small 26 33 37 39 43 45 46 49 48 49 48 42 Medium 27 33 37 39 44 45 46 50 48 48 48 42 Large 26 33 37 41 43 45 46 49 48 49 48 42 Largest 27 33 37 38 44 45 47 50 49 49 49 43 All stocks 133 165 185 197 218 225 232 248 241 244 242 212
Stocks are assigned to five size-sorted sub-samples (portfolio). Each portfolio contains around 20% of all stock samples. The processes are repeated each year for 11 years data. The numbers of samples used in the paper are presented in table 2. The total number of samples for the whole observation period is 2,330.
could double and even more. The observed relationship between the total risk (standard deviation) and the mean returns seems to be positive.
Table 3. Descriptive statistics of stock returns
All Stocks Smallest Stocks Small Stocks Medium Stocks Large Stocks Largest Stocks Mean -0.001178 0.001464 -0.001227 -0.001162 -0.002778 -0.002261 Std. Dev. 0.108445 0.122157 0.116689 0.109373 0.100467 0.090544 Minimum -2.699240 -1.596511 -1.380741 -1.576881 -1.653045 -2.699240 Maximum 2.232761 1.718746 1.108368 2.232761 1.129384 0.852996 Skewness 0.099919 0.431363 -0.0132021 0.648924 -0.102798 -1.246381 Kurtosis 21.363137 19.05449 17.27616 27.99987 22.66431 45.66700
The distributions of weekly returns of the smallest and medium stocks portfolio are skewed to the right (positive skewness), while the distributions of small, large and largest stocks portfolios are skewed to the left (negative skewness). For the all stocks portfolio, the distribution is skewed to the right. The kurtosis coefficients for the all stocks sample and the five size-sorted portfolios, which are much higher than three, indicate that the tails are much thicker or higher than the tail of the normal distribution.
4.2. Results
4.2.1. Serial correlation
Interestingly, eight-week serial correlations are significantly negative at the five percent level for all five size-sorted portfolios except for the largest stock portfolio. It possibly suggest that the contrarian strategies are more appropriate using an eight-week lag in the JSX. However, this possibility is left unanswered in this study since the objective of the paper is to investigate the short-term (weekly) contrarian profits.
4.2.2. Contrarian profits
Despite the fact that there are no significant negative first-order serial correlations of weekly portfolio returns in JSX, since LM state that even if the returns on individual stocks have no serial correlation, portfolio strategies that attempt to exploit return reversals may still earn positive expected contrarian profits, the next research question is whether there are any weekly contrarian profits.
The results for the contrarian strategies over the period from 1994 through 2001 are presented in Table 4 Panel B. In estimating the profits, portfolios are rebalanced every week. On average, there are 42 firms in each sub-sample each week. It can be seen from the table that all weekly average contrarian profits are significantly positive at the 5% level except for the large and largest stocks portfolio. The average profit of the large stocks portfolio is significantly positive at the 10% level, whereas that of the largest stocks portfolio is insignificant. These findings are consistent with LM that even though there are no significant negative first-order serial correlations, there are contrarian profits, which are due to the effects of cross-serial covariances (cross effect).
Table 4. Testing for serial correlation in the stock returns and the contrarian profits
All Stocks Smallest
Stocks Small Stocks Medium Stocks Large Stocks Largest Stocks
Panel A. Serial correlation
Order 1 0.214 (0.00) 0.307 (0.00) 0.153 (0.00) 0.242 (0.00) 0.158 (0.00) 0.026 (0.54) 2 0.213 (0.00) 0.186 (0.00) 0.152 (0.00) 0.19 (0.00) 0.216 (0.00) 0.149 (0.00) 3 0.162 (0.00) 0.176 (0.00) 0.072 (0.00) 0.149 (0.00) 0.147 (0.00) 0.109 (0.00) 4 0.138 (0.00) 0.215 (0.00) 0.132 (0.00) 0.091 (0.00) 0.128 (0.00) 0.029 (0.00) 8 -0.004 (0.00) -0.102 (0.00) -0.022 (0.00) -0.034 (0.00) -0.009 (0.00) 0.005 (0.00)
Panel B. Contrarian profits
πx 103 0.579 [0.00] 0.189 [0.00] 0.175 [0.00] 0.131 [0.00] 0.053 [0.075] 0.031 [0.21]
% of all stocks profit 100% 32.71% 30.18% 22.60% 9.20% 5.32%
Notes:
Panel A. The numbers in parentheses are the probabilities for the Ljung-Box statistics for testing the null hypothesis of no serial correlation.
The winners and the losers for all samples are relative to the same benchmark, i.e. the equal weighted portfolio returns that consist of all stocks in the sample. Thus, the performance or the contribution of each portfolio to the total contrarian profits can be directly compared to one another. For instance, the average profit of the smallest stocks portfolio (πx 103) is 0.189, which is approximately six times larger than that of the largest stocks portfolio (0.131). More than 85% of the total contrarian profits come from the smallest, small and medium stocks portfolio. The profits grow steadily from the largest stocks portfolio (0.031%) to the smallest stocks portfolio (0.189%). The observed contrarian profits seem to be negatively related to firm size. Thus it suggests that the contrarian profits can be explained by the size effect.
4.2.3. Decomposition of contrarian profits
Even though the previous results do not support that there are negative serial correlations, but since there are significant contrarian profits (using the LM contrarian strategy) on the JSX, the paper considers that it is still relevant to examine the overreaction hypothesis since some studies suggests that the contrarian profits are related to the overreaction hypothesis (for instance, JT, 1995). The phenomenon that there are contrarian profits albeit no evidence of negative serial correlations of return portfolios can also be found in the study of the Athena Stock Exchange by Galariotis (2004). To investigate how the overreaction hypothesis contributes to the total contrarian profits, the paper considers the model of Jegadeesh and Titman, as stated in the literature review (see section 3.2.3). This model decomposes the contrarian profits into three factors. The first factor, , provides an estimate of the contrarian profits due to stock price reaction to firm-specific information. The second factor, Ω −
(
ˆ
2)
mσ
δ
−
, provides an estimate of the contrarian profits due to common factor reaction. The last factor, , is the cross-sectional variance of intercepts that provides an estimate of the contrarian profits unrelated to the two previous factors.2
a
σ
−
Since there are significant positive contrarian profits, the research question of the paper is to seek whether the contribution of the overreaction to firm-specific information is the primary source of the total contrarian profits. To investigate the contribution of the various factors to the contrarian profits, the sensitivities of weekly individual stock returns to contemporaneous and lagged common factor returns are estimated using equation (6).
that larger firms react more instantaneously to common factor realizations than smaller firms, consistent with JT.
The table also shows that the stock returns in the JXS do not fully react contemporaneously to the common factor. There is also a delayed reaction to the common factor. For instance, for all stocks, the slope coefficient on the lagged common factor, given by
b
1, is 0.246. In contrast to the findings of JT, however, the observed slope coefficients are seemingly unrelated to firm size. The large stocks portfolio has the highest coefficient (0.383), while the medium stocks has the lowest coefficient (0.281). In other words, the delayed reaction to the common factor is not related to firm size.Table 5. Average estimates of stock returns sensitivities to current and lagged market returns and decomposition of contrarian profits over the period from 1994 through 2004
Stocks portfolio b0
b
1δ
ˆ
2ˆ
mσ
δ
−
x 103 -Ω x 103 −σ
a2 x 10 3 Smallest 0.414 0.290 -0.117 0.165 (14.51%) 1.182 (104.15%) -0.212 (-18.66%) Small 0.489 0.334 -0.446 0.628 (35.29%) 1.388 (77.98%) -0.236 (-13.26%) Medium 0.661 0.281 -0.396 0.558 (36.34%) 1.181 (76.96%) -0.204 (-13.30%) Large 0.840 0.383 -0.113 0.160 (19.41%) 0.867 (105.40%) -0.204 (-24.81%) Largest 1.028 0.305 -0.278 0.391 (38.67%) 0.751 (74.22%) -0.130 (-12.89%) All Stocks 0.808 0.246 -0.223 0.314 (26.06%) 1.087 (90.31%) -0.197 (-16.37%)This table presents the average estimates of the sensitivities of stock returns to current and lagged market returns based on the following time series regression: Rit =ai+b0,iRm,t +b1,iRm,t−1+ei,t
where Ri,t is the return of stock i in time t, Rm,t is the return of the market portfolio in time t, and b0,i and b1,i are the
estimated sensitivities of stock i to contemporaneous and lagged common factor returns, respectively, and:
(
)(
)
{
}
∑
= − − = N i i i b b b b E N 1 1 , 1 0 , 0 1 ˆ δ .This table also presents estimates of various sources of contrarian profits. The −Ω, and , are the estimates of the contrarian profits due to the overreaction to firm specific information, the lead-lag structure and the cross-sectional dispersion of expected returns, respectively. These estimates are presented for the all stocks and five size-sorted sub-samples over the period from 1994-2004 on the JSX. Numbers in parentheses are ratios of the contributions of each factor relative to the total contrarian profits.
2 ˆ m σ δ − 2 a σ −
To examine whether the delayed reaction to the common factor can potentially contribute to the contrarian profits, the cross sectional covariances of contemporaneous and lagged betas, defined as are examined. Since the values of for all stocks and all five size-sorted portfolios are negative, the lead-lag effect may give a positive contribution to the contrarian profits. It simply means that, on average, high betas are followed by low betas and vice versa. The estimation of the contribution of contrarian profit due to lead-lag effect to the total contrarian profits is given by x 10
contrarian profits. Thus, it indicates that the contribution of the contrarian profits due to lead-lag effect is not the primary source of the total contrarian profits, consistent with JT.
However, these findings are unable to demonstrate the relation between the contribution and firm size. Table 5 shows that the small stocks portfolio has the highest contrarian profits due to the lead-lag effect (0.63) while the smallest stocks portfolio has the second lowest profits (0.165). The contrarian profits due to lead-lag effect appear to be unrelated to firm size, opposed to the findings of JT.
The fifth column in the table 5, −Ω x 103, isthe negative of the average autocovariance of the error factor that provides an estimate of the contrarian profits due to the overreaction to firm-specific information. The value of is negative if stock prices tend to overreact to firm-specific information and reverse in the following week, and then positively contributes to the contrarian profits. In this case, stock prices seem to overreact to firm-specific information. The negative of the average autocovariance of the error term is quite large. For instance, the value of
Ω
Ω
− x 103 is 1.087, which is 90.31% of the total contrarian profits, for the all stocks. In all cases the contributions of the overreaction to firm-specific firm to the total contrarian profits for the full sub-sample are larger than 74%.
The contrarian profits due to overreaction to firm-specific information move decreasingly from the small stock portfolio (1.388) to the largest stocks portfolio (0.751) for the full sub-sample. These findings support the idea of JT that the contributions of the overreaction to firm-specific information are, in general, seemingly negatively related to firm size for the full sub-sample.
To statistically test the significance of mean differences among three factors, the estimation of each contribution is recalculated for all five size-sorted portfolios each year for 11 years data (see table 6). The resulting ANOVA F-statistics (50.17) shows that, on a yearly basis, the magnitude of average contrarian profits due to the overreaction to firm-specific information for all stocks is significantly higher than both the profits due to lead-lag effect and the profits unrelated to the two previous factors at the 5% level. These results indicate that the contribution of the overreaction to firm-specific information is the primary source of the total contrarian profits, consistent with JT.
These results suggest that despite the fact that the stock prices underreact to the common factor, the lead-lag effect contributes little to the total contrarian profits. Most of the contrarian profits are attributable to the overreaction to firm-specific information. The effect of the last factor, i.e. the cross-sectional variance of returns, , is the smallest one (-16.37%) for the full sample, consistent with LM and JT.
2
a
σ
Table 6. Decomposition of contrarian profits for each year under the assumption that the betas are constant over time
Stocks Portfolio 2 ˆ m σ δ − x 103 -Ω x 103 −
σ
a2 x 103 Stocks Portfolio 2 ˆ m σ δ − x 103 -Ω x 103 −σ
a2 x 103 1994 2000 Smallest 0.299 1.489 -0.097 Smallest 0.535 0.746 -0.198 Small 1.595 1.058 -0.078 Small 0.090 1.576 -0.101 Medium 1.491 0.606 -0.060 Medium -0.253 1.807 -0.106 Large 0.518 0.203 -0.059 Large -0.131 0.698 -0.127 Largest 0.576 0.183 -0.049 Largest 0.182 1.102 -0.082 1995 2001 Smallest 0.570 1.166 -0.064 Smallest -0.172 0.152 -0.127 Small 0.129 0.555 -0.101 Small 0.194 1.092 -0.070 Medium 0.430 0.019 -0.092 Medium -0.116 2.113 -0.089 Large -0.038 0.292 -0.083 Large -0.326 0.348 -0.092 Largest 0.087 0.292 -0.060 Largest -0.056 0.294 -0.127 1996 2002 Smallest 0.002 0.175 -0.104 Smallest -0.253 1.685 -0.115 Small 0.002 0.162 -0.198 Small 1.313 1.332 -0.145 Medium 0.004 0.374 -0.125 Medium 1.219 1.246 -0.089 Large 0.001 0.416 -0.082 Large -0.027 0.639 -0.099 Largest 0.000 0.118 -0.047 Largest 0.174 0.782 -0.113 1997 2003 Smallest 0.006 0.083 -0.179 Smallest 0.138 2.840 -0.194 Small 0.002 0.541 -0.138 Small 0.646 2.031 -0.267 Medium 0.004 0.002 -0.057 Medium 0.514 1.352 -0.358 Large 0.010 0.024 -0.155 Large 0.538 0.211 -0.214 Largest 0.006 0.636 -0.094 Largest 0.272 0.476 -0.136 1998 2004 Smallest 1.089 2.460 -0.172 Smallest 0.094 1.327 -0.109 Small 1.396 2.548 -0.213 Small -0.210 1.582 -0.116 Medium 0.841 2.150 -0.172 Medium -0.247 0.933 -0.108 Large 1.689 2.778 -0.237 Large -0.226 0.441 -0.065 Largest 2.603 2.677 -0.197 Largest -0.236 0.503 -0.045 1999 Smallest -0.824 0.662 -0.174 Average 0.296 1.028 -0.129 Small -0.091 2.101 -0.238Medium 0.696 1.449 -0.189 ANOVA F-statistics : (50.17) [0.00]
Large -0.585 3.148 -0.184
Largest 0.120 0.845 -0.102
Note:
This table presents estimates of various sources of contrarian profits. The −Ω, and , are the estimates of the contrarian profits due to the overreaction to firm specific information, the lead-lag structure and the cross-sectional dispersion of expected returns, respectively. These estimates are presented for five size-sorted sub-samples each year over the period from 1994 through 2004 on the JSX. The ANOVA F statistics and the p-value of the null hypothesis that there are no differences among three factors are presented in a parenthesis and a bracket, respectively.
In summary, the results of Table 5 and 6 indicate that equity returns in the JSX do not fully react contemporaneously to the common factor, but react with a delay (underreaction). Moreover, the contribution of the overreaction to firm-specific information is the primary source of the total contrarian profits and much larger than the contribution of the delayed reaction to the common factor or the effect of the cross-sectional variance of expected returns, which is relatively small.
4.2.4. Time-variation in factor sensitivities
Since several studies suggest that there is variation through time in short-term expected returns (Conrad and Kaul, 1988) and the risks of winner and loser stocks are not constant over time (Chan, 1988), the paper employs equation (11) (see section 3.2.4), which accounts for the time-variation in factor sensitivities. The parameters obtained from equation 11 are used in order to investigate the contribution of three factors to the total contrarian profits with the assumption that betas should not be constant. The results for the full sample and sub-sample are presented in Table 7.
Table 7. Decomposition of contrarian profits with time-varying factor sensitivities over the period from 1994 through 2004
Stocks portfolio 3 0×10 α 3 1×10 α 3 10 × γ 2 3 1σm×10 α 3 1 1 10 1 × ⎟ ⎠ ⎞ ⎜ ⎝ ⎛
∑
= − T t t T θ γ Smallest 0.28 (5.61) -33.04 (-2.44) -3.26 (-1.24) -0.0465 -0.0440 Small 0.30 (6.17) -49.89 (-3.71) -4.90 (-1.70) -0.0702 -0.0598 Medium 0.17 (3.22) -47.92 (-3.24) 2.32 (0.70) -0.0674 0.0247 Large 0.09 (2.31) 17.93 (1.56) -6.87 (-2.54) 0.0252 0.0002 Largest 0.10 (3.36) -0.30 (-0.03) -10.60 (-4.25) -0.0004 0.0000 All Stocks 0.87 (5.83) 37.50 (0.95) -33.42 (-2.98) 0.053 [0.091] 0.001 [0.001] Notes:This table presents a decomposition of the contrarian profits based on equation:
(
mt m)
t t t α α R R γθ μ π = + − − + −1+ 2 1 , 1 0∑
= = Nt t t i t t e N 1 2 , 1 θwhere
π
is the contrarian profit, Rm is the average common factor return, and e are the residuals estimated from equation(6). The estimates of contrarian profits due to the delayed reaction to the common factor and to overreaction are given by and 2 1σM α ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ∑ = − T t t T 1 1 1 θ
γ , respectively. The t- statistics appear in parentheses. Numbers in the square brackets are ratios of
Table 8. Decomposition of contrarian profits for each year under the assumption of time-varying betas Stocks Portfolio 3 10 × γ 2 3 1σm×10 α πt×103−(1)−(2) Stocks Portfolio 3 10 × γ 2 3 1σm×10 α πt×103−(1)−(2) (1) (2) (1) (2) 1994 2000 Smallest -0.049 -0.243 0.307 Smallest -0.085 0.000 0.095 Small -0.022 -0.193 0.224 Small 0.273 -0.161 -0.095 Medium 0.016 -0.046 0.038 Medium 0.174 -0.242 0.083 Large -0.007 -0.043 0.050 Large 0.012 0.105 -0.113 Largest 0.010 -0.075 0.065 Largest -0.006 -0.467 0.482 1995 2001 Smallest -0.026 0.006 0.032 Smallest 0.029 -0.028 0.007 Small -0.005 0.029 -0.019 Small 0.028 -0.009 -0.007 Medium 0.016 -0.012 -0.003 Medium -0.026 -0.147 0.194 Large -0.006 -0.008 0.015 Large 0.015 -0.015 0.002 Largest 0.026 0.004 -0.029 Largest -0.004 0.050 -0.043 1996 2002 Smallest 0.067 -0.044 -0.019 Smallest -0.015 0.077 -0.043 Small 0.032 -0.009 -0.022 Small -0.002 -0.069 0.086 Medium -0.007 0.049 -0.037 Medium -0.093 0.015 0.092 Large 0.021 0.460 -0.473 Large 0.126 0.009 -0.128 Largest 0.026 0.157 -0.181 Largest 0.012 0.019 -0.024 1997 2003 Smallest 0.151 0.041 -0.189 Smallest -0.032 0.310 -0.245 Small 0.091 -0.012 -0.068 Small -0.123 0.245 -0.098 Medium -0.026 0.127 -0.100 Medium -0.003 0.073 -0.057 Large -0.044 -0.101 0.146 Large 0.008 -0.106 0.101 Largest -0.110 -0.377 0.495 Largest -0.024 -0.003 0.032 1998 2004 Smallest -0.033 0.003 -0.001 Smallest -0.068 0.048 0.034 Small -0.136 0.003 0.102 Small -0.017 0.021 0.012 Medium -0.135 -0.001 0.104 Medium -0.012 0.058 -0.038 Large 0.112 0.001 -0.143 Large -0.001 -0.044 0.049 Largest 0.057 0.002 -0.089 Largest -0.028 -0.063 0.094 1999 Smallest -0.131 -0.061 0.212 Average -0.006 -0.011 0.024 Small -0.319 0.005 0.337
Medium -0.137 -0.083 0.241 ANOVA F-statistics : (1.10) [0.33]
Large 0.036 -0.068 0.060
Largest 0.037 0.181 -0.211
Notes:
This table presents a decomposition of contrarian profits based on equation (6). The estimates of contrarian profits due to the delayed reaction to the common factor, due the overreaction to firms-specific information and the profits that unrelated to the two previous factors are given by 2 ,
1σM α ⎟ ⎠ ⎞ ⎜ ⎝ ⎛
∑
= − T t t T 1 1 1 θ γ , and ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − −∑
T= − t t M T 1 1 2 1 1 θ γ σ α π , respectively. TheTable 7 shows that the estimates of the constant,
α
0, are statistically significant at the 5% level for allsamples. The estimates of first slope coefficients, given by
α
1, are statistically significant at the 5% level except for the largest and large stocks portfolio. For the all stocks portfolio, the value ofα
1 is positive but insignificant at the 5% level. On the other hand, the second slope coefficients, given byγ
, are significantly negative at the 5% level for the all stock, largest and large stocks portfolio. The estimate of contrarian profit due to the delayed reaction to the common factor for the all stocks portfolio, given byα
1σ
M2 x 103
is 0.053. Given the average weekly contrarian profit for the all stocks in table 3 Panel B (0.58), this component only contributes approximately 9%.
The estimate of contrarian profit due to the overreaction to firm-specific information, given by
⎟ ⎠ ⎞ ⎜ ⎝ ⎛
∑
= − T t t T 1 1 1 θγ x 103 is 0.1% for the all stocks portfolio. Given the average weekly contrarian profit for the all stocks in table 3 Panel B (0.58), this component only contributes approximately 0.1%.
To statistically test the significance of differences among three factors, the estimation of each contribution is recalculated for all five size-sorted portfolios each year for 11 years data (see table 8). The resulting ANOVA F-statistics (1.10) shows that, on a yearly basis, the magnitude of average contrarian profits due to the overreaction to firm-specific information for all stocks is not significantly different from either the profits due to lead-lag effect or the profits unrelated to the these factors at the 5% level. These results indicate that neither the contribution of the overreaction to firm-specific information nor that of the lead-lag effect is the primary source of the total contrarian profits.
These findings are very interesting since these results have not been described previously. Once the time-variations in factor sensitivities are accounted for, the contribution of the lead-lag structure and the overreaction to firm-specific information become smaller. Under the more realistic assumption of time varying betas, the importance of the firm-specific component and the common factor reaction contribution is actually smaller.
Table 7 shows that for the full sample (all stocks portfolio) the biggest contribution to the total contrarian profits stems from the factor that is unrelated to either the lead-lag relation or the overreaction to firm-specific information. The biggest contributor, , is the cross-sectional variance of intercepts from equation (6) that provides an estimate of the profits unrelated to the other factors. The intercept is the return that unconditional to the common factor and error terms. Thus, since the variance of intercept (or unconditional return) could represent the volatility (or the risk) of the stock returns, it suggest that the contrarian profits can be explained by the relationship between the risks and returns. The higher risks, the higher returns will be.
2 a
σ
There are two alternative possible explanations for these results. First, the table 2 shows that the observed relationship between the total risk (standard deviation) and the firm size seems to be negatively related. Second, the observed profits contributions also seem to be negatively related to firm size. Thus, if the market value is a good proxy of the risk, it suggests that the contrarian profits can be explained by the size effect.
CHAPTER V
CONCLUSION AND RECOMMENDATION
5.1. Conclusion
The purpose of the paper is to seek whether the weekly contrarian profits are present on the JSX and to investigate the contributions of the various factors to the contrarian profits. Returning to the hypotheses/research questions posed at the beginning of this study, it is now possible to state some sub conclusions as follows:
Firstly, in all cases the null hypotheses of no first-order serial correlation are rejected at the 5% level except for the largest stocks portfolio. The results show positive serial correlations. Thus, these findings do not support the expected hypotheses that there are negative serial correlations.
Secondly, all weekly average contrarian profits are significantly positive at the 5% level except for the largest and large stocks portfolio. The average profit of the large stocks portfolio is significantly positive at the 10% level, whereas that of the largest stocks portfolio is insignificant.
Thirdly, the equity returns in the JSX do not fully react contemporaneously to the common factor, but react with a delay. Moreover, under the assumption that the betas are constant over time, the contribution of the overreaction to firm-specific information is the primary source of the total contrarian profits and much larger than both the contribution of the delayed reaction to the common factor and the profits that unrelated to these factors.
Fourthly, under the more realistic assumption of time varying betas, the importance of the firm-specific component and the common factor reaction contribution is actually smaller. The profits obtained from the LM contrarian strategy cannot be explained by either the lead-lag structure effect or the overreaction to firm-specific information. The primary source of the total contrarian profits comes from the factor that is unrelated to either the lead-lag relation or overreaction to firm-specific information, which is the variance of the returns.
All in all, the issue of the overreaction hypothesis is not relevant any longer, especially on the Jakarta Stock Exchange, since under the more realistic assumption of time variation, the profits due to the overreaction to firm-specific information is not a primary source.
However, a number of important limitations need to be considered in this paper. Firstly, even though the paper excludes the stocks that have no weekly returns in a one-year period, this method may ineffectively filter out all illiquid stocks in the samples. The inclusion of some illiquid stocks in the samples may bias the estimations of the serial correlations and the contrarian profits.
Secondly, the contrarian profits of the Lo and Mackinlay strategy do not take the transaction cost into account. Since the strategy, on average, generates approximately 212 round-trip transactions per week, the resulting transaction costs may cancel out the contrarian profits.
Thirdly, this paper uses the same benchmark, i.e. the equal weighted portfolio returns that consist of all stocks in the samples, in determining the stocks position (overweight or underweight). The employment of another benchmark may lead to different results.
5.2. Recommendation
Finally, this research raises many questions to be considered for further investigation. Firstly, as mentioned in section 4.2.1., the contrarian strategies are probably more appropriate using an eight-week lag in the JSX since eight-eight-week serial correlations are significantly negative at the five percent level for the all stocks and five size-sorted portfolios except for the large stock portfolio. It is suggested that the contrarian profits with an eight-week lag are investigated in the future study. Secondly, since the most severe problem in an emerging market is the illiquidity, a future empirical study could possibly consider using only stocks belonging to the LQ45 to filter out illiquid stocks that may bias the estimation of correlation coefficients and contrarian profits. LQ45 is a value-weighted index that comprises the largest and most heavily traded stocks on the JSX.
Thirdly, how the transaction cost affect the potential contrarian profits still remains unanswerable in this case. Further study regarding the role of transaction cost is strongly recommended.
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