The month of the year effect explained by prospect theory on Polish Stock Exchange

Transcription

1 The month of the year effect explained by prospect theory on Polish Stock Exchange Renata Dudzińska-Baryła and Ewa Michalska 1 Abstract The month of the year anomaly is one of the most important calendar anomalies that have been observed in many stock exchanges in all over the world. Our work is devoted to examine this effect on the Polish Stock Exchange. In the first part of our research we analyse the statistical significance of mean rates of return of WIG index (based on quotation between ). Next we employ the econometric model with dummy variable. We discovered the April and December effects. Those effects we try to explain by the disposition effect. The disposition effect is the way the investors act and can be modelled by the rules of prospect theory. Key words Month of the year effect, seasonality on stock exchange, prospect theory, disposition effect. 1. Calendar effects on Stock Exchanges The seasonal anomalies on the capital market are the subject of many researches. Calendar effects are the stock price anomalies that are attributed to calendar: month of the year effect, week of the month effect or day of the week effect. The existence of seasonal effects were documented for the first time by Rozeff and Kinney [10], who have showed that mean rates of return of shares quoted on the New York Stock Exchange in years are statistically higher in January than the mean rates of return in other month. The seasonality on the stock exchanges were studied on many markets. Usually the January effect is observed [6, 7], but on the Kuwait Stock Exchange, Al-Saad and Moosa [1] have found that higher rates of return are in July rather than in other months. The most famous explanation of the January effect is that investors sell losing stocks in December because of tax reasons (tax loss selling hypothesis). The other explanation is that institutional investors are selling bad papers to avoid presenting them in annual report. After the publication of the report they reconstruct the portfolio and buy similar stocks which are undervaluated causing increase in prices especially of small firms. The other observed effect is the holiday effect, where the rates of return in the days before stock market holidays are usually higher than in other trading days. Ariel [3] has explored the rate of return of index in taking into account the holiday, e.g. New Year, Independence Day, Thanksgiving Holiday or Christmas. He proved that the rate of return in the day before holiday was higher than in other days. Whereas two days before holiday and one day after holiday rates of return were similar to the mean rate of return. One of the possible explanation is that people are in the pleasurable, optimistic mood and they feel inclined to buy stocks and, as a consequence, this leads to systemically high rate of returns. 1 dr Renata Dudzińska-Baryła, University of Economics in Katowice, 1 Maja 50, Katowice, Poland, renata.dudzinska@ae.katowice.pl; dr Ewa Michalska, University of Economics in Katowice, 1 Maja 50, Katowice, Poland, ewa.michalska@ae.katowice.pl.

2 The researchers also have examined the day of the week effect. Keim and Stambaugh [9] have analysed the rates of return of the Standard and Poor s index in years Their research confirmed the appearance of the Monday effect, that is the Monday rates of return were negative and statistically significant. Their analysis suggested also that rates of return in the last workday (Saturday in or Friday in ) were higher than the mean rate of return. There are many explanations for the Monday effect but none of these are satisfactory enough. One of them, grounded in the behavioural finance, is the fact that people tend to announce good news immediately, and with bad news they wait until Friday. The announcement of bad news in Friday leads to negative rate of return on the following trading session. The phenomena of seasonal anomalies are examined in different ways. The simplest way is the mean analysis. Researchers calculates mean rates of return for selected periods (e.g. month of the year or day of the week, etc) and check if they are significantly positive or negative or higher (or lower) than the mean rate of return. The other way of research seasonality effects is to make use of various econometric models like e.g. GARCH or the model with dummy variable. In our research we will use the analysis of means and the model with dummy variable. Furthermore, the explanation will be sought based on the behavioral approach, particularly the prospect theory. 2. Prospect theory and disposition effect Prospect theory have been proposed by Kahneman and Tversky in 1979 [8] and extended in 1992 [12] as a cumulative prospect theory. The main idea of prospect theory is that people valuate gains or losses relative to the reference point instead of the final wealth. On the basis of their research, Kahneman and Tversky stated that decision makers do not perceive gains and losses in the same manner. They hypothesized that the value function for changes of wealth is concave above the reference point and often convex below this point. It is consistent with diminishing marginal value of gains and losses (with the increase of their absolute magnitude). The concavity of the value function for gains means that decision makers are risk averse and they choose certain decision and do not take risky action which gives the same expected gain. Whereas considering losses decision makers are risk-prone (convexity of the value function) and they choose to take risky loss than certain loss of the same expected value. The other very important feature of the value function is the difference of the slope of the curve for gains and for losses. The value function is steeper for losses than for gains. This means that decision makers feel the loss more than the gain of the same absolute value. The research of Kahneman and Tversky has also revealed that people overweight events with low probability and underweight ones with middle or high probability. The consequence of the fact that people are risk-averse when faced gains is that they sell winning stocks too early in order to realize gains. On the other hand, people are risk-seeking when faced losses and they hold losing stocks too long in order to avoid realizing losses. This phenomenon is known as disposition effect and was explored by Shefrin and Statman for the first time [11]. Dacey and Zielonka have explained the concepts of too early and too long based on the prospect theory approach [5].

3 3. Research on month of the year effect on Polish Stock Exchange 3.1 Data, empirical analysis and results To analyse the month of the year effect the quotations of the WIG index (the main index on the Polish Stock Exchange) from January 2000 to December 2009 were collected. For every quotation the rates of return in relation to the mean quotation of the previous month were calculated. For such a set of data we investigate if the mean of rates of return in particular month is significantly different from the mean of the other months (marked as m 0 ). We test the hypothesises of the following form: H : m = m 0 0 H1 : m < m0 or m > m0 The alternative hypothesis is formulated in dependence on the value of the mean from sample, that is lower or higher than m 0. If the mean for analysed month is significantly lower or higher than m 0 (adequately) than we observe the anomaly. But we are interested especially in the case where the mean for considered month is significantly higher than m 0. Such a situation is called the effect of that month. For calculations we use PASW Statistics. Our results are presented in table 1. Only for two months the means of rates of return are significantly higher than the mean of the other months (at the 1% significance level). There are: April and December. Month N Mean Standard deviation Tested value (m 0 ) t-value Degrees of freedom Significance (two-sided) January 194 0, , , , ,24999 February 202-0, , , , ,07382 March 216-0, , , , ,00004 April 197 0, , , , ,00000 May 203 0, , , , ,99073 June 207 0, , , , ,16929 July 221 0, , , , ,26503 August 214 0, , , , ,40530 September 213 0, , , , ,19360 October 223-0, , , , ,00031 November 201 0, , , , ,82748 December 197 0, , , , ,00000 Table 1: Descriptive statistics and significance level for mean rates of return In the next step, as a confirmation of the anomaly for April and December, we estimated the regression model with dummy variable: Rt = α 0 + α i Di + εt (1) where: R t rate of return of WIG index for day t, D i dummy variable equalled 1 for month i (i = April, December) and 0 otherwise, α 0, α i parameters of the model, ε t stochastic disturbance term.

4 If α i parameter is significantly different from zero it means that the effect of i th month exists. The value of α i represents the difference between the mean rate of return in i th month and the mean rate of return in other months. Table 2 shows estimates of the regression model (1) with dummy variable for April. Both parameters are significant at the 1% significance level. The analogous results for the December are presented in table 3. In this case parameters are also significant at the 1% significance level. Summarizing, on the Polish Stock Exchange we can observe both the April and the December effects (as shown in tables 2 and 3). α 0 0, , ,888 0,00010 α April 0, , ,673 0,00000 Table 2: Testing significance of April anomaly α 0 0, , ,562 0,00001 α December 0, , ,191 0,00143 Table 3: Testing significance of December anomaly We also estimated the analogous regression model with the dummy variable for January, but the parameter for dummy variable appears insignificant. JANUARY Parameter estimates Standard Error t-value Significance α 0 0, , ,082 0,00000 α January 0, , ,333 0,18265 Table 4: Testing significance of January anomaly In the following part we will try to verify that the observed anomalies are connected with the disposition effect. The hypothesis is that the higher rates of return in April (December) are the consequence of the bearish March (November). It can be justified based on behavioural approach. Investors are risk-seeking and tend to hold losers during March (November). The selling pressure is reduced. When shares become undervaluated in April (December) demand increases, which in turn causes the increase in prices. When March (November) is bullish the higher rates of return in April (December) are not so noticeable. The following research is carried out separately for April and December. In order to test whether the April or December anomaly is the revision of bearish or bullish market performance in the preceding month (March or November), we partitioned the data into two sub-samples accordingly. Similarly to [4], we define March (or November) as bearish if the mean rate of return is lower than the mean rate of return of preceding ten months. Calculating the means we exclude obviously March (November) and also April (December) as a month of anomaly. On the other hand, March (or November) we define bullish if the mean rate of return is higher than the mean rate of return of preceding ten months. Calculations needed for definition of sub-samples are shown in table 5 (for April anomaly) and table 6 (for December anomaly).

5 Year Mean for Mean for May (preceding March year)-february Type Range of data , ,02003 bearish May 2000-April , ,00477 bearish May 2001-April , ,00874 bullish May 2002-April , ,05060 bearish May 2003-April , ,01087 bearish May 2004-April , ,03872 bearish May 2005-April , ,02576 bearish May 2006-April , ,01762 bearish May 2007-April , ,07031 bullish May 2008-April 2009 Table 5: Definition of bearish or bullish March and ranges of data (for April anomaly) Year Mean for Mean for November January-October Type Range of data , ,02907 bullish January-December , ,00286 bullish January-December , ,03709 bearish January-December , ,02204 bearish January-December , ,02330 bullish January-December , ,03020 bullish January-December , ,01985 bearish January-December , ,06008 bearish January-December , ,03819 bearish January-December 2009 Table 6: Definition of bearish or bullish November and ranges of data (for December anomaly) Exploring the dependency between April anomaly and disposition effect, we estimated the regression model (1) with dummy variable for April. If the April anomaly is caused by the disposition effect then the parameter α April should be significant for the sub-sample with bearish March. Whereas, for the sub-sample with bullish March the parameter should be insignificant. In our case in both sub-samples parameters as significant (table 7 and 8), which means that regardless of bearish or bullish March the April anomaly appears. Thus, this anomaly is not caused by disposition effect. α 0 0, , ,151 0,00000 α April 0, , ,824 0,00014 Table 7: Testing significance of April anomaly for the sub-sample with bearish March α 0-0, , ,878 0,00000 α April 0, , ,623 0,00000 Table 8: Testing significance of April anomaly for the sub-sample with bullish March The results for December anomaly are amazing. In both sub-samples (for bearish and bullish November) the parameters for dummy variables representing December appeared insignificant (table 9 and 10). It means that for these sub-samples we cannot observe the dependency that mean rates of return in December are higher than in other months. So, why

6 these results are different from the previous results? The case is in the different sets of data. In the beginning (table 1 and 3) the rates of return were taken from February 2000 to December 2009, but in the last test the data were from January 2001 to December 2009 (partitioned into two sub-samples). Probably high mean rate of return in December 2000 (0,04628), which was twice higher than mean rate of return for all Decembers in , cause the observed earlier December anomaly. α 0 0, , ,202 0,00140 α December 0, , ,929 0,35305 Table 9: Testing significance of December anomaly for the sub-sample with bearish November α 0 0, , ,296 0,00000 α December 0, , ,415 0,01590 Table 10: Testing significance of December anomaly for the sub-sample with bullish November Let us define in another way the bearish and bullish market before the month of anomaly. Similarly to Chien and Chen [4] we assume that a market is defined as bullish in March (November) if both rates of return in February and March (October and November) were positive. In the same way a market is defined as bearish in March (November) if both rates of return in February and March (October and November) were negative. The years with months with mixed (one positive and one negative) rates of return are omitted. Tables 11 and 12 contain the calculations, definition of type of market and data for sub-samples. Year Mean for February Mean for March Type Range of data , ,10502 bearish May 2000-April , ,01161 bearish May 2001-April , ,00240 bearish May 2002-April , ,03018 bullish May 2003-April , ,00275 bullish May 2004-April , ,01555 bullish May 2005-April , ,00518 omitted , ,04570 bearish May 2007-April , ,03087 omitted Table 11: Definition of bearish or bullish March (based on two months) and ranges of data (for April anomaly)

7 Year Mean for October Mean for November Type Range of data , ,10690 bullish January-December , ,06338 bullish January-December , ,03918 omitted , ,00699 bullish January-December , ,02862 omitted , ,05241 bullish January-December , ,08819 omitted , ,10943 bearish January-December , ,02278 bullish January-December 2009 Table 12: Definition of bearish or bullish November (based on two months) and ranges of data (for December anomaly) Having new ranges of data we again estimated the model with dummy variable (1). If the April (December) anomaly is caused by disposition effect then the parameter α April should be significant for the sub-sample with bearish March (November). Whereas, for the sub-sample with bullish March (November) the parameter should be insignificant. At 1% significance level the April anomaly is caused by the disposition effect (tables 13 and 14). The analogous results are obtained for December anomaly (tables 15 and 16). α 0-0, , ,698 0,00000 α April 0, , ,818 0,00014 Table 13: Testing significance of April anomaly for the sub-sample with bearish March (based on two months) α 0 0, , ,288 0,00000 α April 0, , ,633 0,52689 Table 14: Testing significance of April anomaly for the sub-sample with bullish March (based on two months) α 0-0, , ,466 0,00000 α December 0, , ,745 0,00022 Table 15: Testing significance of December anomaly for the sub-sample with bearish November (based on two months) α 0 0, , ,939 0,00000 α December 0, , ,674 0,50033 Table 16: Testing significance of December anomaly for the sub-sample with bullish November (based on two months) Apparently on the Polish Stock Exchange one previous bearish month is not enough. High mean rate of return (month with anomaly) is observed after two months with negative mean rates of return.

8 4. Conclusions There are many empirical studies which prove that month of the year effect is observed not only in USA, and in other developed markets, but also in the emerging markets (Malaysia, Hong Kong, Turkey, Ghana, Pakistan). Our results showed that on the Polish Stock Exchange there is no January effect. Instead of that we observed the April effect and the December effect. Next we verified that the April effect can be explained by the disposition effect on condition that the bearish market is observed during two preceding months (February and March). The analogous explanation we obtained for the December effect on the same condition. The Polish Stock Exchange is not exceptional. Alagidede and Panagiotidis [2] also found the April effect on the Ghana Stock Exchange. Reference [1] AL-SAAD K., MOOSA I.: Seasonality in stock returns: evidence from an emerging market, Applied Financial Economics, 2005 (Vol. 15), pp [2] ALAGIDEDE P., PANAGIOTIDIS T.: Calendar anomalies in the Ghana stock exchange, working paper , Discussion Paper Series, Loughboorough University, Department of Economics, [3] ARIEL R.A.: High stock returns before holidays: existence and evidence on possible causes, The Journal of Finance, 1990 (Vol. 45, No. 5), pp [4] CHIEN C.C., CHEN T.C.: Can the January anomaly in Taiwan s stock market be explained by the prospect theory, Quantitative Finance, 2008 (Vol. 8, No. 4), pp [5] DACEY R., ZIELONKA P.: A detailed prospect theory explanation of the disposition effect, The Journal of Behavioral Finance, 2008 (Vol. 9), pp [6] FAMA E.: Efficient Capital Markets II, Journal of Finance, 1991 (Vol. 46, No. 5), pp [7] GULTEKIN M.N., GULTEKIN N.B.: Stock market seasonality: international evidence, Journal of Financial Economics, 1983 (Vol. 12), pp [8] KAHNEMAN, D., TVERSKY, A.: Prospect theory: an analysis of decision under risk, Econometrica, 1979 (Vol. 47), pp [9] KEIM D.B., STAMBAUGH R.F.: A further investigation of the weekend effect in stock returns, The Journal of Finance, 1984 (Vol. 39, No. 3), pp [10] ROZEFF M.S., KINNEY W.R.: Capital Market Seasonality: the Case of Stock Returns, Journal of Financial Economics, 1976 (No. 3), pp [11] SHEFRIN H., STATMAN M.: The disposition to sell winners too early and ride losers too long: theory and evidence, Journal of Finance, 1985 (Vol. 40), pp [12] TVERSKY, A., KAHNEMAN, D.: Advances in prospect theory: cumulative representation of uncertainty, Journal of Risk and Uncertainty, 1992 (Vol. 5), pp

9 Summary The month of the year anomaly is one of the most important calendar anomalies that have been observed in many stock exchanges in all over the world. Our work is devoted to examine this effect on the Polish Stock Exchange. In the first part of our research we analyse the statistical significance of mean rates of return of WIG index (based on quotation between ). Next we employ the econometric model with dummy variable. We discovered the April and December effects. Those effects we try to explain by the disposition effect. The disposition effect is the way the investors act and can be modelled by the rules of prospect theory.