University of Groningen Msc Finance
Master Thesis
“What goes up must come down?”
∗A study on whether the Dutch stock market is subject to long and short term price reversals
Author: Ewout Schoemakers Address: Lage der A, 37a
9718 BM Groningen Mail: e.j.schoemakers@gmail.com Phone: +31626856351
Student number: s2232936
Place and date: Groningen, June 21, 2013 Supervisor: Drs. S. Bumann
2nd supervisor: Dr. M.M. Kramer
Contents Tables ... 3 Figures ... 3 Abstract ... 4 1. Introduction ... 4 2. Literature review ... 6
2.1. State of the art... 6
2.2. Overreaction ... 7
2.3. Underreaction ... 8
2.4. Theoretical explanations for price reversals ... 8
3. Methodology ... 10
3.1. Long term reversals ... 10
3.2. Short term reversals ... 11
4. Data ... 13
4.1. Data on long term reversals ... 13
4.2. Data on short term reversals ... 14
4.2.1. Bid-ask spread. ... 15
5. Results ... 16
5.1. Long term price reversal ... 16
5.1.1. Monthly contribution to the reversal. ... 19
5.2. Short term price reversal ... 20
5.2.1. Data set with all stocks ... 20
5.2.2. Data set filtered from penny stocks ... 21
5.2.3. Data set with high dividend paying stocks ... 23
5.2.4. Data set with medium dividend paying stocks ... 25
Tables
Table 1. Overview of papers on price reversals and momentum. 9
Table 2. Descriptive statistics of the MSCI Netherlands index. 14 Table 3. Number of stocks in the data set in each starting period. 14
Table 4. Bid-ask spread per data set. 16
Table 5. Difference in ACAR between winner and loser portfolio. 18 Table 6. Results OLS regression, entire data set and data set filtered from penny stocks. 22 Table 7. Results OLS regression, high and medium dividend stocks. 24
Figures
Figure 1. Graphical presentation of methodology on long term reversals. 10 Figure 2. Graphical presentation of methodology on short term reversals. 12
Figure 3. Graphical presentation of the CARs. 16
“What goes up must come down?”
A study on whether the Dutch stock market is subject to long and short term price reversals
EWOUT SCHOEMAKERS∗ Abstract
The objective of this paper is to test whether the Dutch stock market is subject to long and short term price reversals. The results on long term reversals do not present unambiguous evidence for the reversal hypothesis. On the short term, this analysis finds evidence for losers reversing into winners in multiple timeframes, although the winners seem to reverse on an intra-week period only. The results show that the reversals are lower for high dividend paying stocks although the difference is not significant. After subtracting the bid-ask spread from the returns there is no significant alpha left.
Keywords: Efficient market, Price reversal and Overreaction. JEL codes: G02, G10 and G14.
1. Introduction
A subject in the finance literature that attracted much attention, are anomalies in the market. This paper focusses on the anomaly/phenomenon price reversal. Price reversals are best explained as follows, the winners (losers) of today will be the losers (winners) of tomorrow. Price reversals do not just occur on a daily basis but on a weekly and monthly basis as well. Price reversals even occur on an intraday basis. An example of a medium term price reversal is the case of British Petroleum (BP). In 2010 there was an explosion on one of their oil platforms the “Deepwater Horizon” in the Gulf of Mexico. The oil spill led to a price drop From 641 to 305 in two months. After the announcement by the experts, on the estimated costs, the price reversed up to 407 the following month. This is an example that can be explained by the fact that the market overreacted to the event. Not all price reversals can be explained this easily, although De Bondt and Thaler (1985) claim that overreaction of the market is an important factor of price reversals. The phenomenon price reversal is explained in different ways, although in the end most explanations conclude that the market is not able to analyse all available information efficiently, leading to the price reversal.
Due to internet, communication technology and mass communication tools information is now more quickly and cheaply available for more people than before. What the effect of this technology is on price reversals, whether this technology increases or decreases price reversals, is not clear. Also due to technology more individuals have started participating in the stock market. Pension funds have started
participating in the stock markets more intensely because of the high returns1. For these reasons it is still important and interesting for a wide public to get a better understanding of the market as it could assist the investing public and professionals in their decisions.
After the financial crisis stocks have been subject to large price movements. The phenomenon of price reversals is an interesting factor for portfolio strategies in this setting but also in a more stable market it can still be interesting to base a portfolio strategy on price reversals. Previous research by Scherer et al. (2010) find the strategy of buying last week losers and selling last week winners creates significant alpha. The results of Scherer et al. (2010) show that buying losers creates a higher alpha than selling the winners. For this strategy you must know on what time span a reversal actually occurs. More recent research by Yulong et al. (2005) find evidence of overreaction for the winners and losers on the Nasdaq although they do not find significant evidence for overreaction on the NYSE for either winners or losers. This indicates that even markets within the same country are different in their behaviour. This piece of research attributes to the big stream on research that is performed on this phenomenon, where most research focused on markets outside of the Dutch market this analysis contributes by investigating the behaviour of stock returns in the Dutch market.
The following hypotheses are formulated,
H1 High abnormal returns in the Dutch stock market are followed by returns in the opposite direction in the long run.
H2 Extreme returns on the Dutch stock market are followed by returns in the opposite direction in the short run.
H3 Stocks that pay high dividends reverse less compared to stocks paying low dividends.
As previous research on markets outside the Netherlands show, reversals occur on different timespans. Therefore this research analyses the Dutch stock market on price reversals on the long and short term. For an investor that is long term orientated and is not actively buying and selling stocks the long term reversals are interesting to take into account for deciding which stocks to purchase. For the more active investors the short term price reversals could be interesting. Step one studies the long term price reversals. This is done with a similar approach used by De Bondt and Thaler (1985). In step two the short term reversals are studied. Step three focuses at the short term reversals based on a selection of the amount of dividend paid. It is of use to know what kind of stocks are more likely to reverse and which are not, before actively buying and selling stocks based on the expected price reversals. So you would need to differentiate the stocks based on some characteristic. Following common sense one could expect that companies that promise to pay a certain amount of dividend on their stock and often hold provisions for it are less likely to be subject to big price reversals. Also, according to some
1
theories, e.g. Allen et al. (2000), institutional investors prefer high dividend paying stocks due to tax advantages, though according to others, institutional investors are overconfident and because of this overconfidence stocks that are popular with institutional investors are expected to reverse more.
Using the literature of interest available, Section 2 explains price reversals, momentum and possible explanations for price reversals. Section 3 describes the methodology used to test the hypotheses. Thereafter a detailed overview of the data is presented in section 4. Section 5 displays the results followed by a thorough robustness analysis on short term reversals. In Section 6 and 7 the conclusion is presented and a discussion of this paper is given.
2. Literature review
This section explains important findings and developments that concern the phenomenon “price reversal”. After presenting the state of the art on price reversals, various explanations for overreaction are addressed. The contradicting phenomenon momentum is also touched on. The last part of this section will give possible theoretical explanations for the occurrence of price reversals.
2.1. State of the art
A lot of research on different markets and market levels has been performed, beginning with the research of De Bondt and Thaler (1985, 1987) with evidence for long term price reversals (2-5 years). What is interesting is that the price reversal for the loser portfolio was stronger than that of the winner portfolio. Also, the results suggest that the reversal effect is explained by the large abnormal returns in January (January effect). Later research by Brown and Van Harlow (1988) and Bremer and Sweeney (1991) find evidence for short term reversals. Bremer and Sweeney (1991) find that negative ten day returns are followed by positive returns in the following two days.
The most famous explanation of price reversals is overreaction of the market to new information. The most important research that finds evidence against the this explanation is presented by Zarowin (1990), Conrad and Gautam (1993) and Fama and French (1996).
Zarowin (1990) repeats the research of De Bondt and Thaler (1985) although he looks at the effect of extreme earnings announcements. He finds that poor earners outperform good earners in subsequent years however poor performers are significantly smaller in size. The findings suggest that instead of investor overreaction to earnings, the smaller firms reverse, the company size is responsible for overreaction.
market portfolio, (ii) difference between return on a portfolio of small stocks to the return on a portfolio of large stocks and (iii) difference between return on low book to market and high book to market stocks. This would mean that the phenomenon price reversal can be explained by these three factors. The three factor model is not able to explain the contradicting momentum phenomenon. For an investor, price reversals can be an interesting phenomenon to take into consideration in his investment strategy. Scherer et al. (2010) tests whether it is possible to create alpha when you sell past week winners and buy past week losers taking transaction costs into account, using non-overlapping trading times. The study finds that alpha is created although the selling of winners is not adding significant profit. The research of Atkins and Dyle (1990) presents evidence for short run overreaction for sharp price declines within a day. They also note that this result is in line with market efficiency when the transaction costs are taken into account, meaning that traders cannot profit from the overreaction. Lehmann (1990) finds that weekly positive stock returns are followed by negative returns in the following week and that negative weekly stock returns are followed by positive returns. Lehmann (1990) suggest that arbitrage profits from trading on these patterns is profitable even after adjusting for transaction costs and the bid-ask spread.
2.2. Overreaction
De Bondt and Thaler (1985) argue that price reversals are caused by overreaction of the market. This would imply a violation of market efficiency. Investors unable to correctly value news, resulting in overreacting to good and bad news. In case of semi strong efficient markets it is expected that the overreaction on a specific event is corrected by the market after one or two days, although De Bondt and Thaler (1985) measure overreaction over a period of 36 months. After 36 months of overreaction they find significant evidence for price reversals. An explanation for this is that firms cannot always stay on top of their competitors and changing markets result in new winners. Barberis et al. (1998) explain the overreaction as is shown in Equation 1
, , … , | , , … , , (1) where z is denoted as the news the investor hears in period t, G stands for good news and B stands for bad news. Here you see that there is constantly more reaction to bad news than there is to good news leading to a fundamentally undervalued stock, when investors realise this, the stock reverses back to the fundamental value. This can go the other way around as well.
2.3. Underreaction
Contradicting with price reversal is the phenomenon momentum. Momentum means that winners (losers) will be winners (losers). Empirical evidence for momentum in equities is found by Jegadeesh and Titman (1993, 2001), Chan et al. (1996) and Rouwenhorst (1998). The two phenomenon are contradicting but according to Scherer et al. (2010) they should not rule each other out. This is possible because price reversals are found for short term periods (1-2 weeks) and on long term periods (3-5 years). Momentum is on the other hand found for portfolios based on the returns of the past 1-12 months, and the portfolios with winners (losers) are held for another 1-12 months.
The phenomenon momentum can be explained by to underreaction to new information or conservatism. The underreaction leads to positive autocorrelation in the returns. Evidence for this autocorrelation between returns is found by Bernard and Thomas (1990). The next periods have to correct for this autocorrelation. Underreaction is explained by Barberis et al. (1998) in the following Equation
| | , (2)
The news z can be either Good (G) or bad (B) for next period t. Equation 2 shows how momentum can be explained by consistently underreacting to bad news. This would lead to a slowly adapting stock price, resulting in momentum, a loser will be a loser until prices fully incorporated the bad news.
2.4. Theoretical explanations for price reversals
There are several explanations for why price reversals occur and how it is possible that these reversals occur. Barberis et al. (1998) explain overreaction and underreaction in the market by a model that is based on psychological evidence. Underreaction is explained by conservatism, slowly changing beliefs in the face of new evidence. Overreaction is explained by representativeness heuristic, meaning that investors evaluate information based on their previous experience.
Daniel et al. (2001) explain price reversals by the overconfidence of investors and biased self-attribution. They find that investor psychology could play an important role in under and overreaction by the market. They say that experts tend to be overconfident compared to inexperienced investors. Therefore, the experts tend to put too much weight on good news and less weight on bad news. After a few years when it turns out that this confidence had no fundamental basis, the price reverses. This explanation would suggest market inefficiency because it takes multiple years for investors to realise that the price is overrated (bubble forming). Another theory that is rather similar to the overconfidence theory is the overoptimistic hypothesis that explains reversals for winners and momentum for losers due to the fact that investors overreact to good news and underreact to bad news.
within a week. Why this is seen in markets is not clear but it is said that the positive sentiment around the dividend payment stirs up the stock price to its previous level, hence benefitting the stock holder again. A more simple explanation is the bid-ask bounce. When stocks are not frequently traded and the price of the stock is small the bid-ask spread can cause a reversal effect. When markets are more volatile spread widens as well.
How prices can deviate from their efficient price is explained by De long et al. (1990a) and Shleifer and Vishny (1997). According to De long et al. (1990a) and Shleifer and Vishny (1997) arbitrage is not always able to work because of the unpredictability of the investor sentiment. This unpredictability of the investor sentiment leads to risk for the arbitrageurs. In case investor sentiment becomes stronger, e.g. to noise traders, prices move further away from their efficient price. This can result in losses in the short run and scare investors that are unble to correctly price the assets. Other reasons why arbitrage does not always do what it is supposed to do, can be due to transaction costs and idiosyncratic risk. Shleifer and Vishny (1997) and Pontiff (2006) classify idiosyncratic risk as main arbitrage holding cost. Mclean (2010) tests whether idiosyncratic risk can help explain price reversals and momentum. Mclean (2010) finds that there is a positive correlation between α and idiosyncratic risk in the reversal portfolio which suggests that idiosyncratic risk could be limiting arbitrage. So even in efficient markets price reversals can occur.
Authors Countries Period Analysis level Findings
Grant et al. (2005) US ( S&P 500) 1987-2002 Futures contract Intraday reversal Kudryavtsev (2013) US ( Dow Jones) 2002-2011 Stocks Daily reversal Wang and Yu (2004) US 1983-2000 Futures markets One week reversal
Lehmann (1990) US 1962-1986 Stocks One week reversal
Scherer et al. (2010) Global 2001-2009 Global markets One week reversal Bremer and Sweeney (1991) US (Fortune 500) 1962-1986 Stocks Two week estimation, two
day reversal
Jegadeesh and Titman (1993) US 1965-1989 Stocks Six months formation, six to twelve month momentum Rouwenhorst (1998) Europe 1978-1995 Stocks Six months formation, six to
twelve month momentum De Bondt and Thaler (1985) US 1930-1977 Stocks Three to five year reversal
3. Methodology 3.1. Long term reversals
The analysis of long term reversals draws heavily on De Bondt and Thaler (1985). To find the winners and the losers, the abnormal returns need to be calculated. De Bondt and Thaler (1985) used three types of return residuals and they find that it does not make a difference which returns are used. Therefore this research uses the market adjusted return approach. With this approach the abnormal returns are obtained by subtracting the market return from the stock returns, in this case the market return is the return from the MSCI Netherlands return index. The abnormal return (AR) is calculated as follows
, (3)
where is the monthly return of stock i and is the monthly return of the MSCI Netherlands index. De Bondt and Thaler (1985) used the average return of all the stocks in the sample for the market return. This research uses the MSCI Netherlands for the market return because it is known for being a good indicator of the market and is available from 1963. The data set consists of 122 stocks. All stocks that had no missing values are used. As time passes the sample becomes larger.
The analysis proceeds in five steps. The first two steps are shown on a timeline(see Figure 1).
.
CU ACAR
1973,1976…
0 Formation period 0-36 months 36 Holding period 36-72 months 72
Figure 1. Graphical presentation of methodology on long term reversals. The time frame for one of the 12
repeated steps with a formation period of 36 months and a holding period of 36 months.
Step 1) For each stock, the abnormal return is calculated. To determine the winners and losers the cumulative abnormal return (CU) over a period of 36 months is calculated. In case the cumulative abnormal return is positive (negative), it is a winner (loser). This is done starting in December 1973, December 1976, etc. This step is repeated until 2008 (12 time frames). The starting point is December 1973 because enough reliable data was available from this moment.
Step 2) In each time frame the ten stocks with the highest CU are winners and the ten stocks with the lowest CU are the losers. The 12 portfolios that are formed over time are different in size since the sample grows over time. In the first three-year period the sample only consists of 30 stocks, in the last period the sample consists of over a 100 stocks. In order to make the portfolio’s more substantial there are also portfolios formed that consists of 15 winners and losers. The number of winners and losers are equal in each time frame. The abnormal returns of the winner and loser portfolios are calculated for
month 37 until month 72. This way each month has its own cumulative abnormal return (CAR). Using the CARs from all the individual months of the 12 timeframes the average cumulative abnormal return for winners and losers is calculated, denoted by ACARw,t and ACARl,t, respectively. According to the overreaction hypothesis for t>0, ACARw,t < 0 and for ACARl,t > 0, (ACARl,t – ACARw,t ) > 0.
Step3) To test whether the results are significant we first need the variance of the CARs. This is given by
∑ ,!," ,
!# $ ∑ %,!,!!# %, /2( 1, (4) Because the samples are of equal size N, the variance of the difference of sample means equals 2 /( and the t-statistic (t) is
* +, ,/,2 /( , (5) The relevant t statistic for each individual post formation months can be found. However, this is no independent evidence because the abnormal returns can be driven by returns from specific months. Step 4) In order for the separate months to represent independent evidence and in order to judge whether, for a month t, the average residual return makes a contribution to either ACAR, it is tested whether it is significantly different from zero. The sample standard deviation of the winner portfolio is equal to
- .∑ /01,2,3 /01,34 " "
!# , (6)
Where is the average abnormal return.
SinceSt /√( represents the sample estimate of the standard error of ARw,t, the t-statistic (t) equals * 6,/73
√", (7)
With Equation 7 it is tested whether one individual month, for example January, is responsible for the reversal effect.
3.2. Short term reversals
Short term price reversals are investigated based on buying last weeks losers and selling last weeks winners. To make a clear distinction between winners and loser reversals there is one portfolio short in winners and one portfolio long in losers. This makes the results easier to interpret.
The approach that is used is based on the research by Jegadeesh and Titman (1993) who use this approach for finding momentum using monthly data. See Figure 2 for graphical presentation of the research approach for obtaining the return of one day. The research on short term reversals can be explained in 4 steps.
Step 1) Based on the formation period of five days, returns of the stocks are ranked. The stocks with the highest returns are the winners and the stocks with the lowest returns are the losers.
Step 3) The daily returns of the portfolios are the individual daily stock returns multipliet by 1/n, where n is the number of stocks in the portfolio. For the winner portfolios it is multiplied by -1/n. Step 4) To increase the power of the analysis, the portfolios have overlapping holding periods. In case the holding period is five days, the daily return is based on the average of the returns of the five portfolios held on to on that day.
01/01/2009 Formation Period 02/01/2009 Formation Period 03/01/2009 Formation Period 04/01/2009 Formation Period 05/01/2009 Formation Period 06/01/2009 Holding Period 07/01/2009 Holding Period 08/01/2009 Holding Period 09/01/2009 Holding Period 10/01/2009 Holding Period 11/01/2009 12/01/2009 13/01/2009 14/01/2009
Figure 2. Graphical presentation of methodology on short term reversals. The daily returns are calculated with a
formation period of 5 days and a holding period of 5 days.
The daily returns are regressed with the return of the market, to find Jenssen’s alpha, which can be interpreted as the intercept of the portfolio. The portfolio return is the dependent variable and is regressed against the market return. The regression is as follows
8 9 $ : 8, (8)
Ri is the daily return after buying/selling the losers/winners, Rf is the risk free rate and Rm is the daily return of the MSCI. The : of the portfolio can be interpreted as the sensitivity for changes in the market of the portfolio. In case of a positive significant alpha the portfolio is able to produce higher returns than the market. In this analysis a significant positive alpha indicates that there is a reversal effect. Equation 8 is strongly based on the Sharp- Lintner Capital Asset Pricing Model (CAPM). The CAPM is based on the assumption that the market portfolio is mean-variance efficient. The market is the only variable in the model which implies that differences in expected returns of assets are entirely explained by differences in market beta. There are no additional variables with explanatory power for determining expected returns.
The assumption that is made in the CAPM is questionable. Fama and French (1996) find two additional variables that determine/explain returns. The returns are, besides the market, explained by
the size and value effect. To see whether the alpha is really indicating outperformance of the market due to the reversal effect the returns are regressed against the Fama and French three factor model. The three factor model of Fama and French explains the returns with two additional variables. The small minus big (SMB) factor and the high minus low (HML) factor.
The regression is as follows
8 : 8 $ ;7∙ = $ ;>∙ ?=@ $ 9, (9) Beta accounts for the part explained by the market, ;7 explains what part of the returns is due to size effect and ;> explains what part of the return is due to value effect.
According to Bremer and Sweeney (1991) negative returns, after a ten day formation period, are followed by positive returns in the following two days. Therefore the formation period is ten days and the investment period is two days. For robustness checks different formation periods are tested and different investment periods are used. For the robustness regarding the results of Bremer and Sweeney, a holding period of two and one day is used after a formation period of ten days. To test the one week reversal, a formation period of five days is used and for robustness, a holding period of one, two and five. In case the Dutch stock market is subject to intra week reversals a formation period of three days with a holding period of one day is tested as well. Finally, for robustness, the portfolios – with all formation and holding periods – are based on a percentage of two, five and ten of the winners and losers.
As discussed in the literature review, it is interesting to see whether price reversals are different for stocks that pay high dividends or low dividends. To test this, the data set is split up into two data sets, one data set with returns from stocks that pay high dividends, dividend > 4%, and one data set with returns from stocks that pay medium dividends, 0% < dividend < 4%. The data set with stocks that pay no dividends is not substantial enough and mainly consists out of penny stocks. For this reason the no dividend group is left out. To see whether the alpha is significantly larger for the medium dividend paying stocks the returns of the high dividend portfolios are subtracted from the returns of the medium dividend portfolios. What is left of the returns is regressed against the Fama and French three factor model, in case there is still significant alpha this indicates that the reversals of the medium dividend paying stocks is significantly larger.
4. Data
4.1. Data on long term reversals
means that the dividends are reinvested. This way the return is independent of dividend payments because cash outflows in the form of dividends do not lead to lower returns.
The monthly return is calculated as shown below
A A /A , (10)
Where RI is the monthly total return index of stock i. The RI is obtained from Datastream. For the market return the RI of the MSCI Netherlands index is used. Table 2 shows the descriptive statistics of the MSCI Netherlands returns. The average 0.009 monthly return is a really high mean for a period of 40 years. MSCI Netherlands (1973-2013) Mean 1.010 Standard Error 0.002 Median 1.013 Standard Deviation 0.053 Sample Variance 0.003 Kurtosis 2.364 Skewness -0.478 Largest 1.225 Smallest 0.777
Table 2. Descriptive statistics of the MSCI Netherlands index.
Table 3 shows the number of stocks available over the testing period. In 1973 only 30 stocks were available and it grows to 107 stocks in 2009.
Year 1 9 7 3 1 9 7 6 1 9 7 9 1 9 8 2 1 9 8 5 1 9 8 8 1 9 9 1 1 9 9 4 1 9 9 7 2 0 0 0 2 0 0 3 2 0 0 6 2 0 0 9 No. Stocks 30 32 33 33 37 53 58 63 72 94 96 101 107
Table 3. Number of stocks in the data set in each starting period.
4.2. Data on short term reversals
For the short term reversals, daily stock data over the period 2009 until 2013 is used. This period is not influenced by the financial crisis starting in 2008. The decision to not include the start of the financial crisis is because of the fact that it is a rare kind of event and could therefore decrease power of the results. Instead of the monthly return index (long term) the daily return index is used from the LNLALSHR stocks. The returns are calculated with the same approach that is used to calculate the monthly returns. See Equation 10.
set is filtered from the stocks that have an average price below three euro over the period 2009 till 2013 (Bradley et al., (2006)).
The third data set consist of all the stocks from the second data set that have a dividend yield higher than 4%. The fourth data set consists of all the stocks from the second data set that have a dividend yield between zero and 4%. To decide the dividend yield of a stock, the dividends on the LNLALSHR stocks are obtained in Datastream using the dividend yield code (DY). The dividend yield expresses the dividend per share as a percentage of the share price. The DY from Datastream is based on an anticipated annual dividend and excludes special or once-off dividends. The DY per share is gross dividend yield, taxes are not subtracted.
To perform the regression the daily market return and the risk free rate is required. For the market return the RI of the MSCI Netherlands index is used. This is obtained from Datastream using the MSNETHL code. For the risk free rate the overnight Euribor rates are used. Compared with the Fama and French risk free rate, the European risk free rates are higher, although it is questioned whether the overnight Euribor is still risk free since the credit crisis of 2008. The risk free rates could be biased upwards. This is not expected to significantly influence the results, seeing that the rate is not higher than 0.006% during the period 2009 till 2013. The American daily risk free rate that is used by Fama and French themselves is zero for the period 2009 till 2013
As explained in the section on methodology there are two variables added to the regression. The small minus big (SMB) factor is obtained by subtracting the large cap from the small cap (size effect). The large and small cap are found using the Datastream codes MSLNETL and MSSNETE which stands for MSCI Netherlands large cap and MSCI Netherlands small cap. The high minus low (HML) factor is obtained by the RI of MSCI Netherlands growth index subtracted from the RI of MSCI Netherlands value index. The Datastream codes for the two variables are MSVNETL and MSGNETL.
4.2.1. Bid-ask spread.
The bid-ask spread can lead to price reversals, especially for the penny stocks, the bid-ask spread can result in price changes of 30%. Taking this into account, it is clear that there is no alpha left in case this is regressed. To see whether the bid-ask spread is accountable for the price reversal, the bid-ask spread is deducted from the returns. The spreads are calculated following the approach of Korajczyk and Sadka (2004)
BCDE I.K/7FGH/7F GH (11)
the ask and is divided by the average bid-ask of that day. The average spread, of all the stocks over the entire period, are given in Table 4.
Bid-ask spread no penny stocks 0.0187074
Bid-ask spread high dividend stocks 0.0099948
Bid-ask spread medium dividend stocks 0.0119077
Table 4.Bid-ask spread per data set.
The average bid-ask is subtracted from the returns and the returns that are adjusted for the bid-ask spread are regressed following Equation 9.
5. Results
In this section, firstly the results on long term price reversals are presented, and secondly, the results on short term price reversals are presented.
5.1. Long term price reversal
The results of the test explained in the methodology are found in Figure 3. The results are inconsistent with the reversal hypothesis. Over the last four decades loser portfolios have not outperformed the market. Figure 3 shows that there is no reason to accept the hypothesis for long term reversals for loser portfolios in the Dutch stock market.
Figure 3. Graphical presentation of the CARs. Cumulative average abnormal return of 12 three-year test
periods between January 1973 and December 2008. Winner portfolio and loser portfolio. Length of formation: Three years. Winner and loser portfolios consist of ten stocks.
The winner portfolio reverses into a loser after 15 months this is expected based on previous research by De Bondt and Thaler (1985).
The winners have underperformed the market by 10.85%. The total difference in cumulative average return between the extreme portfolios, ( ACARL,36 – ACARW,36) is equal to -12.80% ( t-statistic:-2.984) This means that the loser portfolio underperforms compared to the winner portfolio with 12.80% even though the winners are already underperforming the market by 10.85%. The loser portfolio does not reverse into a winner after the formation period. The winners reverse into losers although the old losers still perform worse and are still underperforming compared to the winners. The fact that the losers still strongly underperform to the market would rather indicate that there is evidence found for long term momentum for losers. The results for the losers are even more striking taking into account that the data is not adjusted against the survivorship bias, stocks that are in the data set are only stocks that survived until now.
Figure 4. Graphical presentation of the CARs. Cumulative average abnormal return of 12 three-year test
periods between January 1973 and December 2008. Winner portfolio and loser portfolio. Length of formation: Three years. Winner and loser portfolios consist of 15 stocks.
Figure 4 shows that the 15 biggest losers are not underperforming the market. The winners, although still perform better than the losers and outperform the market as well. The losers underperform the winners with 9.06% after 36 months although they do outperform the market. The 15 losers show a reversal into winners alalthough the effect seems to only last for 17 months and is mainly the result of the first six months, after 17 months they perform similar to the market and after 26 months the losers seem to become losers again. The 15 winners are winners for another 30 months and seem to reverse after 30 months. The results strongly differ between the two samples of ten stocks and 15 stocks. For the sample of 15 winners and losers the losers reverse and for the sample of ten winners and losers the winners revers. Can these five extra stocks per timeframe influence the results? To see what the
difference is when the top five are left out, there is one sample that consists of stocks with ranked winners and losers number six till 15. The results show that the losers are outperforming the winners over 36 months with 8.09% and a t-statistic of 3.316. It seems that the five biggest losers are resulting in the sample to lose over the post formation months and that the five biggest winners are responsible for the high returns of the winners. This suggests that the bigger the winner the bigger the reversal, and the bigger the loser the smaller the reversal. This is not in line with the findings of De Bondt and Thaler (1987) and Chopra et al. (1992) that support that the bigger the loser the stronger the reversal.
De Bondt and Thaler (1985) find evidence for long term reversals of loser portfolios using the same estimation period of three years. The difference in their method is that they use the average return of the stocks that are in the sample and in this research the MSCI Netherlands is used. The average monthly return of the MSCI is 0.9%, this is 10.8% on a yearly basis which is a high average for 36 years. This could mean that both lines shift slightly up, although it does not change the conclusions that the portfolios do not always reverse. The results of the test with three, two and one year formation periods and different number of stocks are presented in Table 5. See appendix A for graphical representation of the results from Table 5.
Length of the formation
period
CAR at the end of the
formation period Difference in CAR ( t-Statistics) Average
No. of
stocks Portfolio Winner Portfolio Loser Months after portfolio formation
1 12 24 36 3 year periods 10 2.042 -0.609 (-0.737) -0.031 -0.050 (-1.164) -0.120 (-2.805) -0.128 (-2.984) 3 year periods 15 1.842 -0.538 0.000 (-0.009) 0.014 (-0.543) -0.069 (-2.650) -0.091 (-3.489) 3year periods* 10 1.532 -0.460 0.002 (0.090) 0.085 (3.480) 0.058 (2.362) 0.081 (3.316) 3 year periods 26 1.614 -0.429 0.001 (0.031) 0.011 (0.358) -0.059 (-2.003) -0.062 (-2.091) 2 year periods 10 1.842 -0.527 0.013 (-0.788) 0.005 (-0.297) -0.036 (-2.235) -0.062 (-3.831) 2year period 15 1.662 -0.457 0.008 (0.654) 0.029 (2.345) 0.016 (1.292) -0.015 (-1.168) 1 year periods 10 1.522 -0.392 0.015 (-0.554) -0.078 (-2.856) -0.123 (-4.478) -0.143 (-5.22) 1 year periods 15 1.411 -0.335 0.014 (-0.719) -0.059 (-3.014) -0.082 (-4.223) -0.086 (-4.402)
Table 5. Difference in ACAR between winner and loser portfolio. Differences in Cumulative Average Abnormal
Returns between the winner and loser Portfolios at the end of the formation period. Up to three years after the formation period.
The results present significant evidence that losers will be losers compared to the winners although what the results not show is that the losers actually do manage to outperform the market in most cases, because the losers reverse into stocks that manage to generate positive abnormal returns. There are two big exceptions in the results. Firstly, only in case the three year formation period portfolios consist out of the ten biggest losers they generate negative abnormal returns in the post formation period. Secondly, the winners manage to keep outperforming the market in all cases except in case the three year formation period portfolios consist out of the ten biggest winners the winners reverse into losers. The results on long term reversals do not present unambiguous evidence for the reversal hypothesis. The winner and loser portfolio reverses or does not reverses depending on the rank of the stocks in the portfolio. High ranked losers do not reverse and high ranked winners do reverse.
5.1.1. Monthly contribution to the reversal.
To see whether the reversal effect for the winner portfolio is indeed due to a reversal and is not driven by sensitivity for seasonality Table 8 in appendix B shows whether the average monthly abnormal return is significantly different from zero.
Around January the returns always make a big swing upwards and the loser portfolios clearly manage to outperform the market. Table 8 shows that high significant returns are made in month 13, 25 and 37. This indicates that the month February drives the returns of the loser portfolios. This is similar to the results of De Bondt and Thaler (1985) where the returns of the loser portfolio are driven by high returns during January. Where the loser portfolios of De Bondt and Thaler (1985) have returns that are quite similar to the market and are driven by the January returns, the loser portfolios of this research underperform to the market most of the year. In the months 12, 24 and 36 the returns for the loser portfolio are negative. This would mean that the negative returns of January are followed by positive returns in February. The figures in appendix A show that not only February is responsible for the high returns of the loser portfolios, it seems that first three months are responsible for high returns.
5.2. Short term price reversal
This sub-section first presents the results on the entire data set. Secondly, it presents the results when the data set is filtered from outliers (penny stocks). Thirdly, it presents the results when the data set is divided into stocks that pay high and medium dividends. Finally, the two data sets with high and medium dividend stocks are adjusted for the bid-ask spread.
5.2.1. Data set with all stocks
The left side of Table 6 presents the results from the Fama and French (1996) three factor model after performing OLS regression. The returns (dependent variable) of the portfolios are based on different formation and holding periods. The returns of the portfolios are based on a different percentage of the winners (losers).
The results of the short term price reversals present evidence of significant short term reversals. The daily alpha is up to 1.9% for the top 2% losers with formation period of three days and are held on to for one subsequent day. The alpha is positive for all the loser portfolios, which supports the reversal hypothesis. The alpha of the winner portfolio is only significant for the portfolios with a formation period of three days and a holding period of one day. When increasing the percentage of winners in the portfolio the alpha declines. This indicates that the stronger winners reverse more. The SMB factor that accounts for the size effect is highly significant in case the portfolios are formed with 5% or 10 % of the winners / losers. In case the portfolios are formed based on 2% of the winners the SMB factor becomes less significant. This suggests that the reversals mainly arise from smaller firms. The HML factor is only significant in the winner and loser portfolios when the portfolios are based on 5% or 10% of the winners.
5.2.2. Data set filtered from penny stocks
The results – penny stocks are filtered out – are presented on the right site of Table 6. Table 6 gives the results for the Fama and French coefficients after performing the OLS regression. The portfolio returns are less extreme, the sum of the portfolio returns of the filtered data set is smaller than the sum of the previous portfolios. The coefficients of the regression have become higher and more significant, also the adjusted R2 has become higher. The results show higher coefficients for the market factor indicating that the market explains more of the returns. The beta of the short portfolios is negative and the beta of the long portfolios is positive. When the alphas on the left side of Table 6 are compared to the alphas on the right side of Table 6, the alphas on the right side are smaller. Where the left side gives a daily alpha of 1.2 % for the 2% winner portfolio with formation period of ten days and holding period of two days, the right side gives a daily alpha of 0.2%. Now the data is filtered from penny stocks the reversals have become much smaller. The portfolios that consist of more stocks have a lower alpha, this shows that the reversals are stronger for the highly ranked winners and losers. The beta of the loser portfolios is higher compared to the beta of the winner portfolios, this is expected in a bull market. Therefore the returns of the winner portfolios are less easy explained by the market and are lower.
The beta coefficients are all below one, why the beta is this low cannot be explained. It could be that the daily returns consist of noise and in case the returns are converted into weekly returns the beta coefficients become higher.
Days % Winner portfolios Loser portfolios Winner portfolios (no penny stocks) Loser portfolios (no penny stocks) FP HP W/L Alpha Beta SMB HML Alpha Beta SMB HML Alpha Beta SMB HML Alpha Beta SMB HML 10 2 2 -0.001 -0.452** -0.573** -0.049 0.012** 0.548** 0.515* 0.186 0.000 -0.581** -0.512** -0.112* 0.002** 0.650** 0.417** 0.194** 10 1 2 -0.001 -0.427** -0.469* -0.168 0.011** 0.417* 0.467 0.301 0.000 -0.560** -0.447** -0.167** 0.002** 0.669** 0.435** 0.155** 5 2 2 0.001 -0.418* -0.524* -0.154 0.015** 0.534* 0.575* 0.240 0.001 0.588** -0.469** -0.151* 0.004** 0.652** 0.416** 0.207** 5 1 2 0.000 -0.435** -0.531* -0.247 0.016** 0.379 0.480 0.317 0.001 -0.559** -0.430** -0.205** 0.003** 0.730** 0.520** 0.123* 5 5 2 0.002 -0.604** -0.513* 0.088 0.016** 0.332 0.380 0.476 0.001 -0.601** -0.529** -0.107 0.003** 0.649** 0.291* 0.257** 3 1 2 0.004** -0.481** -0.599* -0.255 0.019** 0.368 0.303 0.319 0.002* -0.522** -0.468** -0.200** 0.005** 0.744** 0.513** 0.164* 10 2 5 0.000 -0.582** -0.528** -0.054 0.005** 0.611** 0.432** 0.154* 0.000 -0.674** -0.493** -0.093** 0.002** 0.766** 0.459** 0.133** 10 1 5 0.000 -0.565** -0.495** -0.097 0.005** 0.589** 0.446** 0.177 0.000 -0.664** -0.465** -0.110** 0.001** 0.750** 0.455** 0.130** 5 2 5 0.001 -0.564** -0.527** -0.084 0.007** 0.612** 0.420** 0.183* 0.000 -0.668** -0.475** -0.109** 0.002** 0.777** 0.455** 0.136** 5 1 5 0.001 -0.559** -0.491** -0.124* 0.008** 0.614** 0.453** 0.172* 0.001* -0.669** -0.459** -0.118** 0.002** 0.753** 0.477** 0.153** 5 5 5 0.001 -0.596** -0.435** -0.014 0.007** 0.614** 0.411** 0.256** 0.001 -0.674** -0.486** -0.083* 0.002** 0.794** 0.401** 0.153** 3 1 5 0.002** -0.569** -0.513** -0.119 0.009** 0.602** 0.413** 0.186* 0.001** -0.649** -0.478** -0.110** 0.003** 0.763** 0.482** 0.166** 10 2 10 0.000 -0.640** -0.485** -0.056 0.003** 0.703** 0.468** 0.106* 0.000 -0.703** -0.475** -0.068** 0.001** 0.806** 0.493** 0.077** 10 1 10 0.000 -0.627** -0.455** -0.080** 0.003** 0.672** 0.486** 0.120 0.000 -0.699** -0.455** -0.074** 0.001** 0.799** 0.497** 0.085** 5 2 10 0.001 -0.630** -0.480** -0.066 0.004** 0.719** 0.434** 0.126** 0.000 -0.702** -0.456** -0.064** 0.002** 0.814** 0.490** 0.084** 5 1 10 0.000 -0.622** -0.445** -0.091** 0.004** 0.686** 0.481** 0.126** 0.000 -0.694** -0.453** -0.074** 0.001** 0.818** 0.532** 0.087** 5 5 10 0.001* -0.619** -0.415** -0.049 0.004** 0.717** 0.467** 0.150** 0.000 -0.695** -0.461** -0.073** 0.001** 0.850** 0.503** 0.083** 3 1 10 0.001** -0.630** -0.458** -0.094* 0.005** 0.680** 0.452** 0.134** 0.001** -0.691** -0.468** -0.070** 0.002** 0.827** 0.536** 0.089** * significant with p<5% ** significant with p<1%
Table 6. Results OLS regression, entire data set and data set filtered from penny stocks. Results of the coefficients from the Fama and French three factor model after
Now the penny stocks are is filtered from the data set the HML factor is able to explain the returns for most timeframes. The winner reversals are actually for most timeframes completely explained by the market, SMB and HML factor. There is only a significant alpha left with a formation period of three days and an holding period of one day. The analysis shows that size and value effect explain a large part of the reversal effect. The loser portfolios are largely explained by the Fama and French three factor model as well, although in all timeframes significant alpha is found meaning that the prices are clearly reversing in different timeframes.
The results for the losers and winners are in line with the findings of weekly reversals by Lehmann (1990), although for the winners the results are not strong and seem to more exist on an intra-week timeframe. Where Bremer and Sweeney (1991) only find significant evidence for loser portfolios with formation period of ten days and holding period of two days this analysis finds evidence for reversals in multiple time frames. Or is there an important factor left out of the regression that manages to explain the returns? This analysis can only explain the alpha saying that there are price reversals in the market.
Now there is evidence for the price reversals on the short run the data set can be split to test the price reversals on a new characteristic, dividends.
5.2.3. Data set with high dividend paying stocks
Days % Winner portfolios (high dividend) Loser portfolios (high dividend) Winner portfolios (medium dividend) Loser portfolios (medium dividend) FP HP W/L Alpha Beta SMB HML Alpha Beta SMB HML Alpha Beta SMB HML Alpha Beta SMB HML 10 2 5 0.000 -0.646** -0.416** -0.171** 0.001* 0.738** 0.249** 0.253** 0.000 -0.774** -0.453** -0.070* 0.001** 0.900** 0.564** 0.054 10 1 5 0.000 -0.660** -0.378** -0.171** 0.001** 0.743** 0.284** 0.265** 0.000 -0.768** -0.433** -0.074* 0.001** 0.876** 0.539** 0.056 5 2 5 0.001 -0.651** -0.410** -0.182** 0.001** 0.706** 0.192** 0.302** 0.000 -0.758** -0.407** -0.085* 0.002** 0.933** 0.564** 0.046 5 1 5 0.001 -0.657** -0.408** -0.174** 0.001** 0.717** 0.236** 0.313** 0.000 -0.771** -0.407** -0.069 0.002** 0.881** 0.535** 0.077* 5 5 5 0.001 -0.655** -0.421** -0.138** 0.001 0.772** 0.162* 0.297** 0.000 -0.751** -0.379** -0.089 0.002** 0.942** 0.580** 0.114* 3 1 5 0.001** -0.649** -0.424** -0.142** 0.002** 0.724** 0.228** 0.350** 0.001 -0.783** -0.440** -0.064 0.002** 0.886** 0.531** 0.065 10 2 10 0.000 -0.641** -0.381** -0.138** 0.001* 0.748** 0.354** 0.172** 0.000 -0.785** -0.450** -0.045 0.001** 0.927** 0.575** 0.022 10 1 10 0.000 -0.642** -0.403** -0.124** 0.001* 0.728** 0.378** 0.167** 0.000 -0.800** -0.462** -0.037 0.001** 0.911** 0.552** 0.04 5 2 10 0.000 -0.651** -0.401** -0.122** 0.001** 0.758** 0.346** 0.176** 0.000 -0.783** -0.406** -0.04 0.001** 0.947** 0.573** 0.028 5 1 10 0.000 -0.641** -0.409** -0.121** 0.001** 0.744** 0.372** 0.169** 0.000 -0.804** -0.347** -0.028 0.001** 0.930** 0.573** 0.039 5 5 10 0.000 -0.643** -0.422** -0.127** 0.001* 0.782** 0.326** 0.173** 0.000 -0.764** -0.402** -0.072* 0.001** 0.971** 0.628** 0.066 3 1 10 0.001* -0.631** -0.426** -0.109** 0.001** 0.741** 0.378** 0.190** 0.000 -0.807** -0.467** -0.018 0.002** 0.924** 0.564** 0.041 * significant with p<5% ** significant with p<1%
5.2.4. Data set with medium dividend paying stocks
The right side of Table 7 presents the results after performing the OLS regression on the returns of medium dividend paying stocks as dependent variable and the Fama and French factors as explanatory variables. The beta coefficients of the loser portfolios from the medium paying dividend stocks are higher than the beta coefficients of the previous tables. For the winner portfolios the returns are explained by the Fama and French three factor model resulting in no significant alpha.
Again most of the returns can be explained by the SMB factor. The HML factor is not explaining any returns of the winner portfolios.
For the loser portfolios, alpha is significant, though compared with the high dividend paying stocks, the alphas are higher for medium paying dividend stocks. The alpha is decreasing as the dividends are higher. This is in line with the null hypothesis. Where higher dividend are expected to lead to more stable prices. The difference is not significant, see appendix C for the results of the regression where the high dividend portfolio returns are subtracted from the returns of the medium dividend portfolios
5.2.5. Bid-ask spread
In case the transaction costs – bid-ask spreads – are subtracted from the returns there is no significant alpha left for either the high or for the medium dividend samples. The alphas become negative, see appendix D. This is similar to most research that finds that it is not possible to profit from the short term reversal effect and that a big part of the reversal is explained by the bid-ask spread and the Fama and French factors. The Dutch stock market is clearly subject to short term reversals. Especially the loser portfolios reverse. The bid-ask spread is not the reason for the reversal. Because if that were the case the winner portfolios – that have the same spread – should have the same alpha. Apart from demonstrating short term reversals, the analysis suggests that the reversals are occurring because arbitrage is not able to do its work, due to transaction costs. The results are similar to the results of Atkins and Dyl (1990) who also find reversals and find that it is not possible to profit from the price reversal after transaction costs. The results are contradicting with the findings of Lehmann (1990) who finds evidence that it is profitable, even though Lehmann (1990) in addition to the bid-ask spread also subtracts transaction costs from the returns.
6. Conclusion
The results on long term reversals do not present unambiguous evidence for the reversal hypothesis. The winner and loser portfolios reverse or do not reverse depending on the rank of their stocks. High ranked losers do not reverse while high ranked winners do. The results are different to the results of De Bondt and Thaler (1985) and Chopra et al. (1992). Although most of the excessive returns of the loser portfolios are made during the first quarter of the year which is similar to the findings of De Bondt and Thaler (1985) where most of the excessive returns are made in January.
After completing this study, this study has to conclude that further research is needed on long term price reversals in the Dutch stock market, as well as on the relationship between the rank of the winner/loser and the reversal.
The results on short term price reversals present significant evidence for short term price reversals in multiple timeframes. The loser portfolios are subject to larger reversals than the winner portfolios for all data sets. The result that losers reverse more than winners is similar to the findings of Lehmann (1990), Atkins and Dyl (1990) and Scherer et al. (2010). Most winner portfolios are completely explained by the Fama and French three factor model. The winners only reverse on a intraweek basis, three day formation period and one day holding period. The losers reverse in all timeframes and the reversal is strongest on an intraweek basis, three day formation period and one day holding period.
The data set, filtered from penny stocks, is subject to smaller reversals. This can be explained by the fact that the stocks, in the portfolios based on the data set with all stocks, are mainly penny stocks that make big price swings when being traded, due to relatively high transaction costs and big bid-ask spreads. In case the data set is split into high and medium dividend paying stocks the losers still reverse in multiple timeframes and reverse more than the winners. The loser portfolios of medium paying dividend stocks have higher alphas than the portfolios of high dividend paying stocks, although the difference is not significant.
7. Discussion/Future work
The regression on short term reversal uses overlapping periods to give the test more power. Because the amount of data on the Dutch stock market is limited, it might be suitable to use overlapping periods for the research on long term reversals as well. Using overlapping periods makes it possible to test the five year formation period as well and include more stocks in the portfolios. Because overlapping periods gives the opportunity to start in a later timeframe where more stocks are available. Now the different methods have led to an inconsistency in the paper. Also, in this paper the decision is made to research both long term and short term reversals. Looking back on the research there is enough to test by just focussing on one time horizon. The research on long term reversals is not done thoroughly enough to be able to draw conclusions.
For the bid-ask spread, the average bid-ask spread over a period of years, for all stocks in the data set is used. It would be interesting to see what the actual bit-ask spread of the stock was in the relevant time periods. This would make the results more robust than they are now using the average bid-ask spread.
The betas from the regression on short term reversals seem to be low, all beta’s are lower than one. The reason for this is not immediately clear. It could be that there is a lot of noise in the daily returns, or that the market is not suitable for explaining the returns of the portfolios.
The period 2009 to 2013 is a bull market, over the entire period stock returns are around 40%. For future research it would interesting to test the short term reversal phenomenon in a bear market as well. This research focuses on the short term reversals and the relationship between the amount of dividend. It is interesting to do further research on reversals and other factors.
In the introduction it is stated that the markets have changes over the years due to technology and more market participants, it would be interesting to see how the short term reversals are changing over the years. Is there a trend?
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Appendix A 0.9 1 1.1 1.2 1.3 0 6 12 18 24 30 36 Winner Loser A C A R Months Figure 5. Average cumulative abnormal returns. Formation period three years. As much stock as possible. Average number of stocks: 26.
0.8 0.9 1 1.1 1.2 1.3 0 6 12 18 24 30 36 Winner Loser
Figure 6. Average cumulative abnormal returns. Formation period three years. Ranked winners and lossers number 10-15.
A C A R Months 0.9 0.95 1 1.05 1.1 1.15 0 6 12 18 24 30 36 Winner Loser A C A R Months
Figure 7. Average cumulative abnormal returns. Formation period two years. Average number of stocks: 10
0.8 0.9 1 1.1 1.2 1.3 0 6 12 18 24 30 36 Winner Loser A C A R Months Figure 9. Average cumulative abnormal returns. Formation period one year. Average number of stocks: 10
Appendix B
Table 8. Test for seasonality. For seasonality effects in the returns, the individual monthly average abnormal returns are tested on whether they significantly differ from
zero. Length of the formation period (No. of stocks)
Individual monthly AR for the winners (t-Statistic) Individual monthly AR for the losers (t-Statistic) Months after portfolio formation Months after portfolio formation
Appendix C
Days % Return medium dividend minus return high dividend (loser portfolios)
FP HP W/L Alpha Beta SMB HML 10 2 5 0.000 0.854** 0.648** 0.013 10 1 5 0.000 0.132** 0.255** -0.209** 5 2 5 0.000 0.227** 0.372** -0.256** 5 1 5 0.000 0.164** 0.299** -0.236** 5 5 5 0.001 0.170* 0.418** -0.183** 3 1 5 0.000 0.162** 0.303** -0.285** 10 2 10 0.000 0.180** 0.220** -0.150** 10 1 10 0.000 0.182** 0.174** -0.126** 5 2 10 0.000 0.188** 0227** -0.148** 5 1 10 0.000 0.186** 0.202** -0.130** 5 5 10 0.000 0.189** 0.302** -0.107* 3 1 10 0.000 0.183** 0.186** -0.149** * significant with p<5% ** significant with p<1%
Table 9. Results OLS regression to test for higher alpha. OLS regression to test whether the beta is higher for
Appendix D
Table 10. Results of the coefficients from the Fama and French three factor model after bid-ask spread is subtracted from the returns. The returns (dependent variable) have
different formation and holding periods. The portfolios are based on a different percentage of the winners (losers). The data set is filtered from penny stocks. On the left side are the results of the portfolios that consists of stocks that pay dividend > 4% and on the right site the results of the portfolios the consists of stocks that pay 0 < DY < 4%
