Disposition Effect Among Contrarian and Momentum Investors

Transcription

1 See discussions, stats, and author profiles for this publication at: Disposition Effect Among Contrarian and Momentum Investors ARTICLE in JOURNAL OF BEHAVIORAL FINANCE JULY 2012 Impact Factor: 0.14 DOI: / CITATIONS 4 READS 34 3 AUTHORS, INCLUDING: Elżbieta Kubińska Cracow University of Economics 19 PUBLICATIONS 20 CITATIONS SEE PROFILE Łukasz Markiewicz Kozminski University 16 PUBLICATIONS 29 CITATIONS SEE PROFILE Available from: Łukasz Markiewicz Retrieved on: 11 December 2015

2 THE JOURNAL OF BEHAVIORAL FINANCE, 13: , 2012 Copyright C The Institute of Behavioral Finance ISSN: / online DOI: / Disposition Effect Among Contrarian and Momentum Investors Elżbieta Kubińska Cracow University of Economics Łukasz Markiewicz and Tadeusz Tyszka Kozminski University Downloaded by [ ] at 03:56 10 September 2012 We provide evidence of disposition effect propensity for stock trading simulation participants employing a contrarian versus a momentum strategy. We found that even subjects playing with chips rather than real money remain vulnerable to those effects. Both tendencies were generally evident in our sample, but we also found individual differences. Subjects seemed to be contrarians both on position opening and on position closing. The main hypothesis of this paper states that contrarian investors are more prone to the disposition effect than are momentum traders. The model proposed by Dacey and Zielonka [2008] plays a crucial role in formulating this hypothesis. We consider the disposition effect not only in terms of the value function but also of the probability weighting function. In accordance with our hypothesis, we found that contrarian traders are more prone to the disposition effect. Keywords: Momentum and contrarian strategy, Disposition effect, Valuation function, Probability weighting function INTRODUCTION Shefrin and Statman [1985] describe the disposition effect, which they characterize as a tendency to sell the winning stock but to keep the losing stock. This tendency was later shown both in experimental data (Gneezy [2003], Weber and Camerer [1998]), as well as in the analysis of real trading decisions (Barber, Lee, Liu and Odean [2007], Dhar and Kumar [2001], Grinblatt and Keloharju [2001], Kubińska and Markiewicz [2008], Odean [1998], Shapira and Venezia [2001], Szyszka and Zielonka [2007]). The disposition effect is typically attributed to prospect theory (Kahneman and Tversky [1979], Tversky and Kahneman [1992]) and more specifically to the S-shaped value function. Indeed, when investors experience the growth of their stock prices, they are in a domain of gain. When investors experience the fall of their stock prices, they are in a domain of loss. The S-shaped value function shows that people are risk-averse in the domain of Address correspondence to Łukasz Markiewicz, Kozminski University, Warsaw, Poland. lmarkiewicz@kozminski.edu.pl gain and risk-prone in the domain of loss. Thus, investors are more prone to close the position and sell the stock after observing uptrends than after observing downtrends. Recently, however, various doubts have been raised whether prospect theory can explain the disposition effect (e.g., Barberis and Xiong [2009], Kaustia [2010]). On the other hand, Dacey and Zielonka [2008] proposed a model where they explain the disposition effect not only in terms of the value function but also in terms of the probability weighting function. They claim that the investor does not always yield to the disposition effect by keeping the stock after a downtrend and selling the stock after an uptrend. If, after observing an uptrend, the investor expects further growth, then he does not sell the stock. The investor succumbs to the disposition effect while selling the stocks after observing an uptrend, but the probability of further growth is high and it might be wiser to keep the stock. Similarly, the shareholder does not always yield to the disposition effect after observing a downtrend. This occurs when the investor keeps the stock after observing a downtrend, and the probability of the growth of the stock is small. According to Dacey and Zielonka, the explanation of the disposition effect should take into account both functions described in

3 Downloaded by [ ] at 03:56 10 September 2012 the prospect theory: the value function and the probability weighting function. Recent research shows huge heterogeneity among investors in their disposition effect propensity (Barber et al. [2007], Dhar and Zhu [2006]). Dhar and Zhu, using the same trading database (in ) as Barber and Odean [1999], showed that some of the traders behaved in a way consistent with the disposition effect while others did not. When analyzed on a general level, the data show that the group as a whole can be considered as moderately vulnerable to the disposition effect. However, there was a group of about 20% of investors who behaved contrary to the disposition effect they were willing to sell the losing stock and to keep the gaining stock. Dhar and Zhu do not explain why some investors are prone to the disposition effect while others are not. They do report, however, that investors sophistication level (measured as age and professional status) has a great influence on disposition effect propensity and increases the chances of investors immunity to the disposition effect. This result has been confirmed by Barber et al., who pointed out that individual investors are more vulnerable to the disposition effect than the presumably more sophisticated investment fund managers. There is a series of research studies showing that, on the basis of the same trend observations, some individuals seem to believe in trend continuation while others seem to believe in trend reversal. In these studies, the participants, observing a sequence of random events, were asked to make predictions about the next events. Thus, their strategy of the forecasting of uncertain events was ascertained. These experimental studies (e.g., Tyszka, Zielonka, Dacey and Sawicki [2008]) show that subjects either tend to predict that the next event will be a continuation of the recent trend (momentum strategy), or they tend to predict that the next event will be a reversal of the recent trend (contrarian strategy). On the other hand, researchers of the investment decisions on financial markets define investment strategies momentum versus contrarian on the base of investors purchase and sale decisions. Momentum strategy is defined as a tendency for purchasing a stock recently rising in price and/or a tendency for selling a stock recently falling in price. Contrarian strategy is defined as a tendency to take the opposite perspective and invest against market trends. These definitions of momentum and contrarian strategies are not precise and generate different operationalization of the concept of recently rising or falling of the stock price. Our operationalization will be presented later. Regardless of the exact operationalization of the momentum versus contrarian investment strategies, we assume that there is a correspondence between the forecasting and investment strategies. Namely, we assume that both the prediction and investment decisions are based on a subject s belief in the occurrence of the next event, that is, in the continuation or reversal of the trend. DISPOSITION EFFECT 215 As far as experimental and polling-based studies are concerned, De Bondt s findings [1991] suggest that financial professionals expect trend reversing while laymen consistently bet on trend continuation (De Bondt [1993]). Similar results were found later by Tyszka et al. [2008], who confirmed that unsophisticated forecasters usually predict trend continuation. However, these results are inconsistent with other findings: Morrin et al. [2002] experimentally examined the forecasting strategy of professional stock market analysts and found that they use mostly momentum strategy. Using a similar experimental approach, the nonprofessional subjects researched by Andreassen [1987, 1988] generally followed a contrarian strategy. On the other side, analysis based on real investment decisions made in the actual stock exchange environment suggest completely opposite results. Contradicting the above-mentioned studies, when analyzing real market data the nonprofessional investors appeared to follow a contrarian strategy (Dhar and Kumar [2001], Goetzmann and Massa [2002], Grinblatt and Keloharju [2000, 2001], Jackson [2003], Kubińska and Markiewicz [2008]). Also, Odean [1998] investigated the disposition effect and found indirect evidence for the contrarian tendency of nonprofessional individual investors. In a nonexperimental study, Grinblatt, Titman and Wermers [1995] found that professional managers most often used a momentum strategy. However, the aforementioned studies of real investment analyses investigated only one side of the market at a time (professional or nonprofessional), and only a few studies investigated both professional and nonprofessional investors at the same time. As a major example, Choe, Kho and Stulz [1999] found that individual investors in Korea revealed a short-term contrarian strategy while foreign investors (considered to be more sophisticated) were more likely to use a momentum strategy. Likewise, Grinblatt and Keloharju [2000] analyzed the records from Finland of foreign investors and domestic traders collected at the same time and within the same trading environment. However, they investigated only buy transactions (excluding sell transactions). They found that foreign institutional investors (considered as more sophisticated, since institutional investors tend to be more rational than individual traders) generally followed a momentum strategy while domestic households tended to follow a contrarian strategy (see also Grinblatt and Keloharju [2001]). One could raise the question if the momentum or contrarian disposition really exists, that is, whether the phenomenon is persistent enough to be called a disposition. Dhar and Kumar [2001] demonstrated that 98% of the U.S. investors studied subsequently followed one of the chosen strategies (momentum or contrarian) during the investigated time period of 6 years. Likewise, Goetzmann and Massa [2002] found that investors consistently employed a particular strategy over the 2-year period investigated. Similarly, Grinblatt and Keloharju [2000] showed that investors have a consistent

4 Downloaded by [ ] at 03:56 10 September E. KUBIŃSKA ET AL. attitude toward trends and follow a chosen strategy (momentum or contrarian), regardless of the investigated time horizon (week, month, or year). They conclude that the consistency across these horizons could indicate that momentum or contrarian behavior represents a fundamental attitude towards past returns as a determinant of buys and sells (p. 58). Finally, Tyszka et al. [2008] found individual differences in general beliefs about the continuation or reversal of trends in various (natural and social) processes. Some tended to believe in the trend s continuation, while others tended to predict the trend s reversal. Moreover, these general beliefs about the trend continuation or its reversal affected their forecasting strategy. In the present research, we raise the question of whether investors vulnerability to the disposition effect is related to their forecasting strategy, that is, a propensity to use the contrarian rather than the momentum strategy. Following Dacey and Zielonka [2008], we assume that the disposition effect is a consequence of two factors: (1) the value function and (2) the probability weighting function. There is no ground for the claim that the followers of contrarian versus momentum strategies differ in terms of the value function. In line with the value function, both contrarian and momentum traders will tend to sell the winning stock (due to risk aversion in the domain of gain) and will tend to keep the losing stock (due to risk proneness in the domain of loss). However, by their very definitions, contrarian and momentum traders should differ concerning their assessments of the probability of the stock price changes. When investors hold a growing stock and are momentum traders, they predict a trend continuation, that is, expect further growth of the stock price. When investors are contrarian traders, they predict a trend reversal, that is, expect the stock price to fall. Thus, while the first type of investor is motivated to keep the stock, the second is motivated to sell. On the other hand, when investors possess a falling stock and are momentum traders, they expect the continuing fall of the stock price. When investors are contrarian traders, they expect the stock price to rise. Thus, the first is motivated to sell the stock while the second is motivated to keep the stock. Let us now summarize the motivational propensities of momentum and contrarian traders when they possess a stock increasing in value versus a falling stock. When a stock is growing, the momentum trader experiences conflicting motivation: being in the domain of gain, the investor is motivated to sell the stock. At the same time, forecasting trend continuation, the investor is motivated not to sell. By contrast, the contrarian trader receives two consistent hints to sell the stock: being in the domain of gain, the investor is motivated to sell the stock, and the same tendency is strengthened by the expectation that the stock price will fall. Thus, we can conclude that after observing an uptrend, momentum traders are less motivated to sell the stock than are contrarian traders. On the other hand, when the momentum trader holds falling stock, being in the domain of loss, the investor is motivated to keep the stock. However at the same time, the investor expects a further fall of the stock price and is motivated to sell the stock. Again, a momentum investor experiences conflicting motivation. By contrast, the contrarian investor holding a falling stock receives two consistent hints to keep the stock: being in the domain of loss, the trader is motivated to keep the stock, and the same tendency is strengthened by the expectation of stock price growth. Thus, we can conclude that after observing a downtrend, momentum traders are less motivated to keep a stock than are contrarian traders. On the basis of the above reasoning, we formulate the hypothesis: Contrarian investors are more prone to the disposition effect than are momentum traders. Data Set METHOD This study examines the records of investment decisions of participants in an internet investment simulation organized by business press publisher Parkiet. The registration time for the game was November 13 30, 2006, and the end of the game was January 19, The simulation lasted business days, during which time the Warsaw Stock Exchange (WSE) was operating. The participants were motivated by valuable prizes (e.g., tuition paid for CFA and MBA courses) and by social incentives, since a list of the top 100 performers was published in PARKIET s business newspaper and the complete ranking of all participants was updated daily and available on the organizer s website. Each participant was given virtual capital of 100,000 PLN (approx. $41,000) and was allowed to invest the entrusted capital only in Polish blue chip stocks, that is, the 20 biggest companies on the WSE, listed in WIG20 index. Transactions (both buy and sell) were commissioned, with a proportional fee of 0.5% value of the particular transaction. The fee was similar to that actually borne by real investors at this time in Poland, varying in the range of %, depending on the order channel (usually 0.5% for internet order placement). The game participants were also allowed to use short-selling mechanisms, that is, selling of borrowed stocks that a partaker does not actually possess at the time, having a chance to make a profit on the stock when the price decreased. Shortselling orders were commissioned with additional payment accounting for 0.02% of the daily value of the raised loan. The simulation participants did not interact with each other but only with the Polish stock market. At no point did they buy and sell stock from each other. Altogether, 5,957 subjects declared investment simulation participation; however, only 3,897 of them made any transactions during the game. Out of 3,897, we decided to exclude 27 subjects (less than 0.6%) due to inchoate records. Only

5 DISPOSITION EFFECT 217 TABLE 1 Descriptive Statistics of Participants N = 3,870 Mean Std. Dev. (PLR), each defined as: PGR = Realized Gain Realized Gain + Paper Gain (1) Downloaded by [ ] at 03:56 10 September 2012 Investor personal characteristics Age Gender dummy Investor activity Total turnover (PLN) 577, ,200 Turnover not generated by day trading 528, ,982 (PLN) Conducted transaction Investors performance Total paid commissions (PLN) 2,936 3,008 Final portfolio value after commissions 97,945 13,535 (PLN) Final portfolio value before commissions (PLN) 100,882 13,845 Gender dummy is set to one (zero) if the trader is female (male). the remaining 3,870 were considered to be the participants (N = 3,870). Our subjects were Polish students, so they were fresh investors with little or no previous experience on the stock market, so generalization beyond this group of investors poses some difficulties. The great majority of our participants were men (81%), with an average age of 22.8 years for the total sample. Basic descriptive statistics 1 are presented in Table 1. The characteristic of being young men has been linked (Kumar [2009]) to higher risk-taking propensity. In addition, in a tournament it is worth taking large risks in order to make it to the top 100 or to win the scholarship. Thus our participants were likely to be less risk-averse than the general population of investors. However, the subjects demonstrated their heterogeneity in our results, so we believe there are the bases for generalization of our results. Methodology for Investigating the Disposition Effect Our methodology to investigate the existence of the disposition effect among investors is similar to the one used by Odean [1998]. Therefore, we checked the portfolio composition during each day that a sell transaction had taken place and the portfolio contained at least two stocks. We determined if stocks were gaining (G) or losing (L) investment value by comparing their average purchase prices with their closing prices on that day. 2 Next we checked if the stock was sold that day. If so, we called it a realized gain (RG) or a realized loss (RL). If the stock was in the portfolio but not traded that day, we called it a paper gain (PG) or a paper loss (PL). Next we computed the number of realized gains (RG), realized losses (RL), paper gains (PG), and paper losses (PL) for every participant in the game and for the whole sample. Thereafter, the following ratios were calculated: the Proportion of Gain Realized (PGR) and Proportion of Loss Realized PLR = Realized Loss Realized Loss + Paper Loss The measure of the disposition effect (DE) is defined as the difference between an investor s PGR and PLR: (2) Disposition effect (DE) = PGR PLR (3) This index takes more positive values when there is a stronger tendency for realizing gains than losses, and more negative values when there is a stronger tendency for realizing losses than gains. The index takes a value of 0 in the case where no tendency is revealed. Therefore, a more positive DE index shows a higher propensity toward the disposition effect. Since the DE index can be affected by portfolio size 3 as well as by trading frequency (Odean [1998]), we followed Dhar and Zhu [2006] and adopted three other measures of the disposition effect. We used the ratio defined as a proportion of PGR PLR proposed by Odean [1998], which is not as dependent as the DE index on the transitions frequency. We implemented another measure that was previously suggested by Weber and Camerer [1998]: WB = RG PG RL + PL where RG and RL are defined like before. This variable remains unbounded with respect to the investor s trading frequency and portfolio size. Finally, we also used the ratio proposed by Dhar and Zhu [2006], who created another index (DZ) that avoids the above-mentioned scaling bias: DZ = RG RL PG (5) PL where PG, PL, RG, RL are defined as in Odean s approach. We also adopted Shefrin and Statman s [1985] method called first-in, first-out to investigate the disposition effect; that is, we measured the time between the first position opening and the closing (or partial closing) separately for gaining and losing positions. Methodology for Investigating the Trend Following Propensity To investigate the forecasting strategy employed by investors, we had to compare investors decisions to buy or sell the stock to the traded stock s price history. 4 We assumed that investors who usually buy gaining stocks and sell losing stocks follow momentum strategy, and vice versa: investors who usually buy losing stocks and sell gaining stocks follow contrarian strategy. Thus, for each investor we investigated the total number of aforementioned transactions for each traded stock and for each period of its price history. (4)

6 Downloaded by [ ] at 03:56 10 September E. KUBIŃSKA ET AL. FIGURE 1 The frequency of all 940 unit of measurement (47 days x 20 stock). We think that the participants were focused on short-term trends because of the short duration of the game. Following the experiment of Tyszka et al. [2008], we decided to investigate the trend by checking whether the price of the stock went up or down from one day to the next. For each day, we assigned the number that represented the length of the present price trend, that is, the number of days in which the price of the asset goes in the same direction. We start counting the trend s length from the day of trend reversal. For example, if the price of the stock on consecutive days are 35, 36.2, 37, 37.3, 38, 37.5, 36.2, 35.1, and the first observation is the moment of trend reversal (i.e., the price at the previous day is higher than 35), then those days are coded as 1, +4, 3. The frequency of the particular trend duration for all 20 stocks traded during the simulation is shown as FIGURE 1. Next, we checked the quantity and the total volume of buy and sell transactions for every number representing the length of the trend. Then we summed the results for all positive (2...10) and negative ( ) values of measurement units, excluding 5 1 and 1. There could be a bias in our results, namely the respondents could have traded more during periods when the price went up, because during the period of the game, there were more days with prices increases than decreases, as can be seen in Figure 1. The days with a rising price tendency are more frequent than the days with a falling price tendency (55:45). Therefore, we decided to weight our results by the distribution of days in which the particular price trend occurred. It is important to distinguish between weighted and unweighted results in the remaining presentation. Additionally, to characterize individual investor s propensity for contrarian strategy dependence, we introduced two ratios: 1. Buying propensity during downtrends (B D ): B D No. of buy transactions during downtrends = Total No. of buy transactions (6) 2. Selling propensity during uptrends (S U ): S U = No. of sell transactions during uptrends Total No. of sell transactions (7) We have defined contrarian strategy as a tendency for purchasing a stock recently falling in price and/or a tendency for selling a stock recently growing in price. Therefore, an investor who follows a contrarian strategy should gain high values of ratios B D, S U. Both aforementioned indexes (B D, S U ) take values between 0 and 1, where 0 means a momentum strategy propensity and 1 means a contrarian strategy propensity. We have calculated indexes (B D, S U ) on the basis of unweighted data, since it is used to investigate individual differences among investors, who act in the same investing reality and are exposed to the same price changes, rather than investigating the characterizing general tendency of the total sample. The decision to analyze a prognostic strategy separately for position opening and closing stays in line with the literature review. Odean [1999] points out the need for such a separation, since both types of decision: to buy and to sell are qualitatively different from each other. One can say that the selling decision is easier, since selecting a stock for an owned portfolio (3 or 4 stocks, in most cases) is easier than selecting stocks from a much wider market portfolio (a couple of hundred stocks). While buying, investors care mostly about future stock price movements, but while selling, the investors take into consideration both past and possible future price movements as well as connected tax issues. Therefore, the buy decision seems to be influenced more by anchors (past or expected prices), while sell decisions involve both a reference point (as a consequence of possessing), as well as the above-mentioned anchors. One can conclude that, for measuring trend dependence, the buy situation is more pure, since it is free of the influence of other tendencies (connected with possessing), which provide noise in the data analysis. The employed methodology assumes some simplification, since even a trader with a short investing perspective is influenced not only by between-days trends but also by intraday trends. However, this influence is not investigated by our methodology. Furthermore, we also believe there is no sense to research long-term trends in the present data set, since there is a small chance that, in such a short game period (lasting a maximum of 47 days), traders counted on long-term trend reversals (often lasting one year or longer). While investing money in the short term, the investors simply had to focus on short-term price movements. There are studies suggesting that short-term trends have more influence on investors than long ones (Tyszka et al. [2008]). Similarly Grinblatt and Keloharju reported that stocks with large positive returns in the recent past (...) are more likely to be sold [2001, p. 590]. RESULTS Investors Reveal the Disposition Effect Tendency Since we investigated the disposition effect, which concerns investors tendency for delaying the sale of losing stock, in

7 DISPOSITION EFFECT 219 Downloaded by [ ] at 03:56 10 September 2012 TABLE 2 The Percentage of First Position Closed While in Domain and Loss Domain First long position Remaining open Closed SUM Lose Gain SUM the initial stage of analysis we focused on the proportion of gaining and losing, remaining open and closed positions. Given that the period of the simulation is limited (maximum of 47 days), we investigated the first opened long position that potentially could have lasted the longest. The analysis of investors tendency for closing the first position for gaining and losing stocks suggests that investors have a strong inclination toward not realizing paper losses, as presented in TABLE 2. The majority of respondents who did not close their first long position until the end of the game actually kept a losing position (701 out of 1,065, or 65%). On the other hand, among those who closed their first long position, 59% (1,490 out of 2,509) closed a gaining position and only 41% closed a losing one. It appears that investors are reluctant to close a losing position. The Pearson chi-square test confirms a statistically significant association between the position s closing and its profitability (χ2 (1) = , p <.0001). This supports the obtained substantial odds ratio (Edwards [1963]), indicating that the odds of a profitable position closing were 3 times higher than for an unprofitable position. Following the Shefrin and Statman [1985] first-in, firstout method, the time between the first position opening and the closing (or partial closing) was also measured separately for gaining and losing positions. Our respondents did not reveal a tendency for the disposition effect on the basis of positions closed only by themselves. On average, they closed losing stocks after 7.25 days, while closing gaining stocks after 8.26 days (TABLE 3). However, analyzing only closed investments excludes over 30% of first transactions that were not closed until the Base: Those who closed their first position themselves Losing position when closing Gaining position when closing TABLE 3 The Average Length of First Long Position Number of cases Mean number of days between opening and closing the position t (2457) = 2.882; p < Base: All participants Losing position when closing Gaining position when closing TABLE 4 The Average Length of First Long Position WITH FORCED CLOSING on the Last Simulation Day Number of cases Mean number of days between opening and closing the position t (3153) = ; p < end of the game. As shown in Table 2, the huge majority of unclosed investments were losing ones. Therefore, during the last day of the simulation, we decided to close all unclosed positions (whether gaining or losing). This is in accordance with the simulation rules, since participants could not manage their portfolios after the last day of the simulation. The result of the analysis with the inclusion of this procedure is presented in TABLE 4. The average duration of losing positions was days and days for gaining positions. The difference between those two values is statistically significant (t [3153] = ; p <.0001) and shows that simulation game participants as a whole act in accordance with the disposition effect. For a final analysis, we used Odean s [1998] methodology to calculate PGR and PLR by summing up all realized/paper losses/gains across the sample, and we obtained PGR =.453 and PLR =.368 to produce DE = The positive sign of this ratio confirms the tendency of investors as a whole toward the disposition effect. Odean [1998] calculated DE to show a general disposition effect propensity in an investigated sample, regardless of the individual heterogeneity in disposition effect propensity among particular investors. However, we believe that it is more interesting to go beyond the general level and investigate the individual propensity for the disposition effect. The mean individual PGR, PLR and other individual disposition effect indicators are presented in TABLE 5. However, even when calculated on the individual level, the mean PGR remains statistically significantly higher than the mean PLR (t [2539] = 7.607; p <.0001). This outcome stays in line with the positive value of the other employed ratios 7 (TABLE 5) and confirms that investors have a strong tendency toward the disposition effect. Investors Reveal a Contrarian Tendency We investigated the hypothesis that investors reveal a contrarian tendency in two situations, the first one at position opening and the second at position closing. In the case of position opening (stock buying), contrarian traders will be more active during stock losing periods than during stock gaining periods. In the case of position closing (stock selling),

8 Downloaded by [ ] at 03:56 10 September E. KUBIŃSKA ET AL. TABLE 5 Disposition Effect Measures Calculated on Individual Level Disposition effect measures Mean index values Whole Sample, All, N = 3,870 Base of the ratio, N = Lost portion of the sample PGR ,748 29% PLR ,616 32% DE ,540 34% WB ,824 27% PGR by PLR ,072 46% DZ ,727 55% for DE index indicates that the coefficient estimate is statistically significantly different from zero at the level p <.01. contrarian traders will be more active during stock gaining periods than during stock losing periods. The average number of buy and sell transactions for individual participants in the cases of gaining and losing periods is presented as Figure 2. The results presented on Panel A suggest that the respondents as a whole: (1) buy stocks more frequently when prices go up than when prices go down, which would suggest a momentum buy strategy. (2) sell stocks more frequently when prices go up than when prices go down, which would suggest a contrarian sell strategy. We previously mentioned the problem of the frequency of transaction occurrence during the given trend; that is, respondents can buy more often during an uptrend. This is not the result of their investment strategy; rather, there are more days with price increases than decreases during the investigated period. To avoid this bias, we decided to weight data by the actual distribution of days in which the particular price trend occurred. The weighted results are presented on Figure 2 (Panel B) and suggest that the respondents as a whole: (1) buy stocks more frequently when prices go down than when prices go up, (2) sell stocks more frequently when prices go up than when prices go down, and both actions suggest that the investigated group of investors has a consistent tendency for contrarian actions. Next we switch our analysis from an aggregate approach to an individual one. Thus ratios of buying propensity during downtrends (B D ) and selling propensity during uptrends (S U ) have been calculated on the basis of unweighted data. Those indexes describe each individual s tendency to follow a contrarian or momentum strategy. Investors propensities toward a contrarian strategy (B D and S U ) do not correlate highly among buy and sell situations (contrarian index for position opening versus position closing: r[3177] =.096; p <.0001). Contrarians are More Prone to the Disposition Effect than are Momentum Traders To test the main hypothesis of this paper, we examined the variation in disposition effect propensity across investors with different trading styles and demographics. Therefore we conducted four separate regression analyses, with four disposition effect propensity indicators, each used as the dependent variable: (1) DE, (2) PGR/PLR, (3) WB and (4) DZ. The selected dependent variables correlated moderately with each other: r from.468 to.762 (p <.0001). FIGURE 2 Average number of buy and sell transactions in the case of decreasing and increasing trend.

9 Downloaded by [ ] at 03:56 10 September 2012 In each regression model, we used the same set of independent variables, which were chosen on the basis of previous research. Following other studies (Dhar and Kumar [2001], Kumar and Lim [2008]), we controlled the two demographic variables of gender and age. We also controlled the degree of investor s sophistication, following previous studies (Barber et al. [2007], Dhar and Zhu [2006], Feng and Seasholes [2005]), with a proxy of being a business college student and included a short-sell dummy variable. 8 Finally, we also controlled diversification propensity. Goetzmann and Kumar [2008] suggested that disposition effect propensity can be related to diversification skills, and it is possible that investors prone to the disposition effect (and avoiding selling losers) often end with a relatively well diversified portfolio of losers. Therefore, three separate measures have been employed: normalized portfolio variance (NV), sum of squared portfolio weights (SSPW) and average number of stocks in the portfolio (Avg. No.), as proposed by previous research. The NV is a normalized portfolio variance, which is the portfolio value variance divided by the average variance of the stocks in the portfolio (Goetzmann and Kumar [2008]). This ratio reflects the skill of minimizing the average correlation among stocks in the portfolio (with smallest values indicating highest diversification skills). The SSPW concerns different aspect of diversification (Blume and Friend [1975]) by comparing the weight of each asset in an investor s portfolio to its weight in the market portfolio (in this study, the ideal portfolio built by blue chips of the WIG20 index). The values of the index stay between 0 and 1, with 0 indicating a portfolio that would be a perfect copy of the ideal portfolio. Finally a naïve diversification measure has been used (Hedesström [2006], Hedesström, Svedsäter and Gärling [2006, 2009]) with Avg. No. reflecting the average number of stocks creating the traders portfolio. Furthermore, the total number of transactions was also controlled in the regression equation (as advised by Dhar and Kumar [2001]). To check the relationship proposed by our hypothesis, two indexes were included: buying propensity during downtrends (B D ) and selling propensity during uptrends (S U ). The values of ratios B D and S U are close to 1 for the investor who follows a contrarian strategy. Although each dependent variable covers a different aspect of the disposition effect, the results of four separate regressions presented in Table 6 (Panel A) remain consistent across all employed disposition effect ratios. Nonprofessionals revealed a higher propensity toward the disposition effect, as did individuals with smaller average numbers of stocks in the portfolio and with higher numbers of conducted transactions (which is the result opposite to that demonstrated by Kumar and Lim [2008]). However, both indexes, buying propensity during downtrends (B D ) and selling propensity during uptrends (S U ) appeared to be the most important coefficients in all regression analyses. They have the highest capability to account for variation in disposition effect propensity. The model built on both DISPOSITION EFFECT 221 demographic and contrarian tendency variables accounts for 22% of DE variability themselves (Panel A), while the much smaller model built only on indexes B D and S U accounts for 20% of DE variability (Panel B). The results presented in Panel B of Table 6 imply that the selling propensity during uptrends (S U ) appeared to have 2 to 3 times more explanatory value than the buying propensity during downtrends (B D ). As mentioned before, the value 0 of indexes B D and S U means a momentum strategy propensity and 1 means a contrarian strategy propensity. Indexes B D, S U can be problematic with the interpretation of their intermediate results. (Investors might be showing a mixture of momentum and contrarian trends, or possibly do not care about trends.) Therefore, as a robustness test, we decided to repeat the regression analyses replacing two indexes S U and B D with four dummy variables, marking the membership to one of four segments: M B, C B, M S or C S. A respondent was marked as a momentum trader (M B, M S ) if his score on index B D or S U stayed in the lowest 20% of participants. A respondent was marked as a contrarian trader (C B, C S ) if his score on index B D or S U stayed in the highest 20% of participants. The results of these additional analyses are presented in Table 7 and are important, since they confirm the conclusions drawn before. The contrarian label increases the size of disposition effect, while the momentum label decreases it. Again contrarian and momentum tendency measured on position closing have stronger effects than contrarian and momentum tendency measured on position opening. DISCUSSION In accordance with our hypothesis, we found that contrarian traders are more prone to the disposition effect than are momentum traders. The contrarian tendency measured by buying propensity during downtrends (B D ) and selling propensity during uptrends (S U ) have the highest capability to account for variation in disposition effect propensity. Our hypothesis was based on the assumption that investors decisions are determined by both the value and the probability of the prospect. Thus, apart of the shape of the value function, we also consider investors beliefs in trend continuation or trend reversal during the downtrend or the uptrend. One might even say that finding contrarian traders to be more prone to the disposition effect is obvious, since cashing on winners and holding losers, which is the essence of the disposition effect, is also consistent with contrarian behavior with respect to sell transactions. However, it is worth emphasizing that both contrarian ratios (while position opening and position closing) are slightly correlated with each other and both contribute statistically significantly to accounting for disposition effect propensity. The contrarians tendency while position opening (B D ) remains a highly statistically significant indicator in all presented regression models, and this correlation cannot be explained by measuring the same phenomenon.

10 222 E. KUBIŃSKA ET AL. TABLE 6 Regression Analysis - Dependent Variable Ratios of Disposition Effect Propensity (1) (2) (3) (4) DE = PGR-PLR WB = RG PL RG+PL LN ( PGR PLR + 1) RG DZ = RL PG PL Beta t-test Beta t-test Beta t-test Beta t-test Downloaded by [ ] at 03:56 10 September 2012 Panel A (Constant) Demographic Gender ± Age Investors sophistication Short sell ± Business College ± Portfolio No. of transactions NV SSPW Avg. No Prognostic strategy B D S U N 2,519 2,790 2,059 1,718 R % 22.1% 27.0% 16.6% F D sig Panel B (Constant) B D 0, S U 0, N 2,540 2,824 2,072 1,727 R % 21.5% 22.3% 15.6% F ( ) indicate that the value is statistically significant at the level p <.05 (p <.001). ± denotes dummy variable. Gender dummy is set to one (zero) if the trader is female (male). Thus, an investor s strategy while position opening predicts the investor s propensity toward the disposition effect that is observed while position closing, and those two actions are distant in time. There is a fundamental question regarding who are momentum investors and who are contrarian investors. Tyszka et al. [2008], p. 107) claim that: people differ in their perceptions of the world with respect to continuation or reversal of trend in various processes. Some people tend to believe that series of events are positively correlated, and the occurrence of a given event means for them that a streak will continue. Other people seem to believe that series of events are negatively correlated, and the occurrence of a given event means for them that a streak will reverse. Following the Dhar and Kumar [2001] remark that investors exhibit systematic differences in trading behavior that often get lost in average level analyses, we decided to check trendbased trading tendency and disposition effect on the individual level. Our results support the claim that investors exhibit systematic differences in (a) in disposition effect propensity and (b) in employing contrarian versus momentum strategy. Thus, this paper contributes to the small but growing number of empirical studies analyzing investors decisions on the individual level (Dhar and Zhu [2006], Kumar and Lim [2008]). Our primary explanation of the relationship between the disposition effect and contrarian forecasting strategy is based on the assumption that the two components, the value and the probability of the prospect, determine investors decisions. However, one can also try to explain this relationship in terms of investors shift of their reference points. First, one has to notice that behavior of contrarian investors is in compliance with prospect theory, while the behavior of momentum investors is not. Contrarian traders exhibit risk-seeking behavior in the domain of losing stocks during the downtrend and are risk-averse in the domain of gaining stocks during the uptrend. On the other hand, the momentum investors exhibit risk-seeking behavior in the domain of gaining stocks during

11 DISPOSITION EFFECT 223 TABLE 7 Regression Analysis. Dependent Variable Ratios of Disposition Effect Propensity. (The Sample Contains Only Those Participants Who Conducted Minimum 5 Transitions Buy and Sell) (1) (2) (3) (4) (DE) = PGR-PLR WB = RG PL RG+PL LN ( PGR PLR + 1) RG DZ = RL PG PL Beta t-test Beta t-test Beta t-test Beta t-test Downloaded by [ ] at 03:56 10 September 2012 (Constant) Demographic Gender ± Age Investors sophistication Short sell ± Business College ± Portfolio No. of transactions NV SSPW Avg. No Prognostic strategy M B ± C B ± M S ± C S ± N 1,925 2,025 1,678 1,470 R % 22.3% 21.5% 15.6% F ( ) indicates that the value is statistically significant at the level p <.05 (p <.001). ± denotes a dummy variable. Gender dummy is set to one (zero) if the trader is female (male). the uptrend and a risk-averse attitude in the domain of losing stocks during the downtrend. Explaining the disposition effect by means of prospect theory, we take as a reference point the most natural value the purchase price. Investors using prognostic trend strategy are looking for the trend reversal points, when one trend ends and the next one starts, as those values can differ from the purchase price. Momentum investors believe in the continuance of existing trends in the market, and we suppose that they take some predicted value of the price, assuming the continuation of the present trend. Let us consider a momentum investor who holds a stock that has an uptrend. This investor takes some higher value as a reference point, hoping this to be the sell price, which is higher then the purchase price. By taking this reference point, this investor is in the domain of loss and in this case she/he is risk seeking. The trader does not close the position and thus does not yield to the disposition effect. If this investor holds a stock that is in a downtrend, then she/he takes as a reference point some smaller value than the current price and the purchase price. With respect to this point, his position is considered to be a gaining one, so the trader exhibits risk-averse behavior of selling the stock and, again, does not yield to the disposition effect. The action of selling a losing stock, considering the purchase price as the reference point, is simply accepting a smaller loss. The momentum investor is also behaving according to prospect theory, but with a reference point different from the purchase price. However, this explanation definitely needs further empirical investigation. We found that even subjects playing with chips (and not with real money) remain vulnerable to the same effects (disposition effect and following contrarian vs. momentum strategy) as investors in the real market. This is an interesting finding in the light of methodological debate on the impact of monetary rewards on the behavior of experimental subjects. Generally, among psychologists (cf. Dawes [1988]) there is a belief that monetary rewards are not very important and not necessary for laboratory experiments. On the other hand, experimental economists argue that monetary incentives do matter. Smith and Walker [1993] reviewed studies in experimental economics, comparing the effect of monetary rewards, and found that increased rewards shift the central tendency of the data toward the prediction of the rational models (p. 245). Assuming the generality of Smith and Walker s conclusion, one could pursue the following rule: if when conducting research without monetary rewards or with low monetary rewards we obtain a result that is not compatible with a rational model, then it is necessary to check whether increased rewards shift the results toward a rational solution. On the other hand, if when conducting research with monetary rewards

12 Downloaded by [ ] at 03:56 10 September E. KUBIŃSKA ET AL. we obtain a result that is not compatible with a rational model, then it is likely that this result would also be obtained in research without monetary rewards. This may be an important methodological guide. This seems to justify using hypothetical choices in situations where we already know that, even under high monetary rewards, individuals exhibit irrational tendencies. In our case, the finding that subjects playing with chips 9 remain vulnerable to the same effects as in the real market namely, the disposition effect and following contrarian versus momentum strategy seems to justify testing the relationship between the disposition effect and the forecasting strategy (contrarian versus momentum) based on data where investors were not using real money. ACKNOWLEDGMENTS We are grateful to Prof. Frederic Widlak, Prof. Elke Weber and Prof. Gur Huberman for their help and comments. We also appreciate all the advice and critiques from our colleagues at the Centre for Economic Psychology and Decision Sciences, Kozminski University, Warsaw, Poland. Lukasz Markiewicz gratefully acknowledges research support from the Fulbright research grant. Lukasz Markiewicz and Elzbieta Kubinska were also supported by a KBN grant (3083/B/H03/2010/38) The authors also thank Polish business publisher PARKIET Co. for making the trading records available for this research. NOTES 1. Markiewicz and Weber s [forthcoming] paper presents the sample characteristic and investment simulation procedures in more details. 2. In this way we differ from Odean, who compared the purchase price to both the high and low price of the stock for that day. A paper gain was recorded if the purchase price was lower than both high and low price of that day, and a paper loss if the purchase price was higher than both high and low price of that day. 3. For example, the investors with the same proportion of realized gains to losses might have different DE indices, depending on the total number of stocks held in the portfolio. Both PLR and PGR tend to be smaller for investors with larger portfolios and who traded more frequently. 4. We obtained stock price history from the portal Money.pl for the time period of the investment simulation. 5. We are convinced that price reversal lasting only 1 day could not be considered as a real trends, but rather some fluctuation. 6. PGR by PLR = 1.230; WB = 0.325; DZ = It is worth of notice that we get different bases in case each of these indexes. Since all these indexes are based on division, the cases have been sent to missing values each time when denominator accounted to zero. Therefore, in the case of DE ratio, we excluded the observation in which either PLR or PGR are undefined, due to the fact the investor didn t have a loser or winner in the portfolio. 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