Munich Personal RePEc Archive
Will Stock Rise on Valentine’s Day?
Chong, Terence Tai Leung and Hou, Siqi
The Chinese University of Hong Kong
14 February 2020
Online at https://mpra.ub.uni-muenchen.de/99058/
MPRA Paper No. 99058, posted 18 Mar 2020 09:32 UTC
W ill S to ck Ris e o n Vale n tin e ’s D ay?
Terence Tai Leung Chong 1 Siqi H ou
Departm ent of Econom ics, The Chinese University of H ong Kong
8 / 3/ 20 20
Abs tra ct
This study is a pioneer in academic literature to investigate the relationship between Valentine’s Day and stock market returns of major economies around the world. The findings indicate that stock returns are higher on the days when Valentine’s Day is approaching than on other days for most cases, showing
“the Valentine Effect” in the stock market. Specific control variables for Valentine’s Day are also introduced to eliminate the potential influence of other effects. Unlike other holiday effects in previous literature, the Valentine’s Day Effect cannot be explained by many conventional theories, such as tax-loss selling and the inventory adjustment hypothesis.
Ke yw o rd s : Valentine Effect;Tax-loss Selling H ypothesis; Inventory Adjustm ent H ypothesis.
2
1 Introduction
The belief that Valentine’s Day is associated with em otion fluctuation has prevailed anecdotally and em pirically in the literature of psychology and business m arketing. Valentine’s Day was nam ed after a Christian m artyr and dates back to the 5th century. It is celebrated on February 14 each year and is recognized as a significant cultural and com m ercial celebration of love and rom ance. It is also foun d that this occasion is associated with extrem e em otions, and com m ercialism contributes to people’s strong feelings and experiences, thus generating love or hate, which m ight be exhibited in stock m arkets (Morse and Neuberg 20 0 4; Close and Zinkhan 20 0 6).
To date, there has been considerable quantities of em pirical research identifying different kinds of calendar effects in stock m arkets. A well-known calendar anom aly is the holiday effect, which concerns abnorm al returns on the day preceding a holiday. Such anom alies appear to be in conflict with the weak- form efficient m arket hypothesis (EMH ), in which historical prices or return sequences cannot be used as the basis of m arginally profitable trading rules (Fama 1970 ). As such, the existence of the holiday effect has significant theoretical im plications. In addition, if the holiday effect exists, investors may m ake profits by constructing specialized trading strategies based on this effect.
This study is inspired by a psychological hypothesis. In this paper, the Valentine Effect is assum ed to be a subset of the larger category of calendar and seasonal effects that depict abnorm al stock returns and volatility during the week, m onth, or year.
However, this assum ption has been deem ed to be at odds with previous research on other calendar anom alies, including the holiday closings (public holiday effect ) (Ariel 1990 ), seasonal affective disorder (week 44 effect ) (Levy and Yagil 20 12), and window dressing (month of the year effect ) (Rozeff an d Kinney J r 1976; Lakonishok and Sm idt 198 8 ). Since Valentine’s Day is not recognized as a public holiday in any country, and stock m arkets are not closed. Conventional explanations for holiday effects, such as tax-loss selling and the inventory adjustm ent hypothesis, are hence not applicable to this special occasion. The psychological aspects of investors’ behavior tend to offer the m ost prom ising explanation for this effect, which is against the m ain assum ption of rational behavior in traditional econom ics. Substantial research evidence suggests that there is a relationship between psychological aspects and behavioral decisions in individual econom ies. For example, Gardner (198 5) found that m oods play a significant role in retail consum er behavior. For stock m arkets, em pirical evidence on the Moon effect show how investors’ m oods and the extent of their aggressiveness differ during the m oon phase and influence their stock m arket perform ance (Brahm ana et al.
20 14). In behavioral finance, som e docum ented evidence also discussed the relationship between m oods and investment decisions (See inter alia, Coval and Shumway 20 0 5; Ben-David and H irshleifer 20 12). Valentine’s Day, the day when love is in the air, is likely to have a significant im pact on the sentim ent of investors, suggesting that investors’ behavior m ight be affected such that capital is
4
invested in or withdrawn from a certain stock, which could generate a noteworthy im pact on the whole equity m arket.
To investigate the relation between Valentine’s Day and stock returns, this study first exam ines the largest stock m arket in the world, the US stock m arket, by using the Dow J ones Industrial Average. In this paper, an econom etric m odel com bining an autoregressive m oving average (ARMA) m odel and a generalized autoregressive conditional heteroscedasticity (GARCH) m odel is estim ated to test the abnorm al pattern of the Valentine Effect. Dum m y variables for Valentine’s Day are introduced to the m odel, and different control variables are added in sequence in order to avoid other calendar-related anom alies. The findings indicate that the US stock returns are significantly higher when Valentine’s Day is approaching (three days before Valentine’s Day and on Valentine’s Day). To control for other anom alies, the regression is run with different dum m y variables, such as those corresponding to the Monday effect, the Full-m oon effect, and the holiday effect. The Valentine Effect persists after controlling for these calendar effects. For robustness tests, this study replaces the Dow J ones Industrial Average with another im portant US stock m arket index, Standard & Poor’s 50 0 Index. The estim ated coefficient of the Valentine Effect still rem ains statistically significant.
To further confirm whether this Valentine Effect is a global phenom enon, the sam e analysis is perform ed on other global stock m arkets, which include m ajor stock indices in the world (the UK, Germany, France, J apan, H ong Kong, and China). A sim ilar Valentine Effect is found in the UK, France, an d China. It
is noteworthy that China exhibits the m ost profound effect (0 .72), which is followed by France (0 .18 ) and the UK (0 .14). Given the unexpected perform ance of Chin a’s stock m arket returns, additional exam inations are adm inistered by introducing specific dum m y variables and separating the Valentine dum m y variable. The estim ated Valentine Effect still shows sim ilar movement after elim inating different potential effects.
This paper exam ines whether Valentine’s Day, which is a stim ulus of investor behavior, has an effect on stock m arkets and how it influences m arket returns.
This study distinguishes itself from previous literature in three ways. Firstly, un- like prior research on extensive holiday effects, this study focuses specifically on a single celebration, Valentine’s Day, which is not a public holiday in any country. Secondly, while m any other studies which gen erally use the classic econom etric m odel, such as the ordinary least squares (OLS) m ethod (Geweke and Porter-H udak 198 3), this study, however, applies the ARMA-GARCH m odel (Bollerslev 198 6), using different sam ples from 1 J anuary 1990 to 1 March 20 19. Such a m odel can deal with autocorrelation and tim e-varying variance in the sam ple data, which appears to be a better tool in this research.
Thirdly, this study introduces control variables to elim inate the potential inference of other calendar effects, such as the Monday effect (J affe et al. 198 9) and the Full-moon effect (Yuan et al. 20 0 6).
The rem aining research is organized as follows. Section 2 provides a review of the literature. The data and the econom etric m odel used in this study are introduced in Section 3 and Section 4 respectively. Results are shown in Section 5. Finally, Section 6 concludes the paper.
6
2 Lite ra tu re Re vie w
Num erous studies have been conducted to explore the abnorm al patterns in stock returns, which appear to challenge the weak form efficient m arket hypothesis. Early literature put forward the definition of the “holiday effect”, which refers to irregular positive stock returns reported on days preceding exchange holidays (Fields 1934). The results of that investigation, which m easures the extent of the preholiday-covering m ovem ent, afford a reasonable basis for generalization about short selling for the period before 1931.
According to daily stock returns on the Dow J ones Industrial Average (DJ IA) from 18 97 to 1965, the average returns for the US stock m arket on pre-holidays were approxim ately 23 tim es higher than those on other trading days (Lakonishok and Sm idt 198 8 ).2 Ariel (1990 ) found large positive returns accruing to stocks on pre-holiday trading days in the US stock m arket and further exam ined the hourly returns and the closing bids to confirm the tim e point. The study covers eight holidays, nam ely New Year’s Day, President’s Day, Good Friday, Mem orial Day, Fourth of J uly, Labor Day, Thanksgiving and Christm as.
The holiday effect has been shown to be robust across international m arkets.
Kim and Park (1994) exam ined the pre-holiday effect in several m arkets, finding evidence of this effect in the stock m arkets of the US, the UK and J apan.
Their work indicates that the holiday effect is not driven by institutional arrangem ents, since the effect rem ains persistent across countries.
2Lakon ishok an d Sm idt classify days as preholiday, postholiday, or regular (neither) without regard to the day of the week. The em pirical result shows that the average preholiday rate of return is 0 .220 percent for the whole sam ple, com pared with the regular daily rate of return of 0 .0 0 94 percen t per day.
Institutional factors such as trading m ethods, clearing m echanism s and bid-ask spreads cannot explain the existence of such an effect because these factors vary across countries. Som e perspectives from the behavior of the Israeli (Lauterbach and Ungar 1992) suggest the existence of significantly higher post-holiday returns but only slightly higher pre-holiday returns in the Tel Aviv Stock Exchange.
Chong et al. (20 0 5) argued that pre-holiday effects have declined in the m ajor international m arkets of the US, the UK, and H on g Kong, and it is only statistically significant for the US until the late 1990 s.
In addition to the holiday effect, there is substantial evidence showing daily, weekly, and m onthly return patterns in academ ic literature. Em pirical studies have docum ented the existence of different stock returns processes on different week- days, and the Monday effect is the m ost frequently m entioned one am ong these studies. Using the Standard and Poor’s Com posite Stock Index, Cross (1973) found that the m ean returns on Mondays are lower than those on other weekdays in the US m arkets. Sm irlock and Starks (198 6) exam ined the day-of-the-week effect and intraday effects using hourly data of stock returns for the Dow J ones Industrial Average. In their study, the sam ple period is divided into several subperiods, and the return from the Friday close to the Monday open was positive from 1963 to 1968 , while it turned to be negative over the period from 1968 to 1974; and for the post-1974 period, the non-trading weekend effect characterized by abnorm al returns from the Friday close to the Monday open disappeared. It indicates that the intraday effect may not be stable.
As for weekly frequen cy, Levy an d Yagil (20 12) exam ined the weekly rates of return from the stock indices of 20 countries, including Am erica, Europe, Asia, Africa, and Australia. The result shows that Week 44 was positive in 19
8
out of the 20 countries in the sam ple; and am ong which 18 of them are statistically significant at least at the 10 % level.3 In contrast to Week 44, Week 43 was negative at the 10 % significance level in 19 out of 20 countries.
Com paring different m onthly rates of return on the New York Stock Exchange from 190 4 to 1974, the study reports that the J anuary stock returns have a significantly higher perform ance relative to other m onths of the year (Rozeff and Kinney J r 1976). The May-to-October effect is classified into m onthly anom alies. It indicates that stock returns are significantly lower during the May-October period than during the rest of the year and shows that m ost investors sell in May in 36 of the 37 countries in their sam ple, especially in European countries (Boum an and J acobsen 20 0 2; J acobsen and Marquering 20 0 8 ). There is also another turn-of-the-m onth effect, the October effect.
Cadsby (198 9) finds that average returns in October are significantly lower than those in other m onths for an equally weighted index of the New York Stock Exchange from 1963 to 198 5. However, recent studies have foun d that the effect disappears gradually. For exam ple, Szakm ary and Kiefer (20 0 4) exam ined the S&P 50 0 Index and their results suggest that there are no abnorm al movements for these m onthly effects.
A range of explanations have been proposed for these calendar anom alies. The day-of-the-week effect is attributed to tim e zones in Condoyanni (198 7) ’s paper, which exam ines the US stock m arket and six other national capital m arkets, nam ely Sydney, Toronto, London, Tokyo, Paris, and Singapore. They concluded that tim e zones set boundaries to the speed of reaction, at least as reflected in changes in general stock indices. The “week 44 effect” m entioned above is
3H ere, the 44th week specifically refers to the period from October 29 to Novem ber 4.
traced to investors’ m oods, in particular, the seasonal affective disorder (SAD), a condition where shorter hours of daylight have a negative im pact on investors’
sentim ent, which in duces further variation in their investment decisions (Kam stra et al. 20 0 3). Tax-loss selling (Branch 1977) and institutional investor window dressing (Lakonishok and Sm idt 1988 ) are two m ain explanations of the J anuary effect.
However, the existence of the holiday effect is still hardly explained. For instance, one of the rational explanations, the inventory adjustm ent hypothesis, cannot be backed up in advanced em erging m arkets because they lack institutional ownership (Pettengill 198 9), an d it is not applicable to non-public holidays, like the Valentine’s Day in this study. Therefore, som e studies argue that such holiday effects can be due to m ood behavior. Specifically, Fabozzi et al.
(1994) indicated that the effect of cheered investor m ood around holidays has a positive im pact on future m arket returns in light of higher trading volum es around exchange-open holidays. The exten sive literature proposes m ultiple explanations for various calendar effects in stock m arkets;
a single specific holiday, especially celebrations that are not public holidays in any countries.
Furtherm ore, m ost of the studies generally use the OLS m ethod, which is widely used to estim ate the param eters of a linear regression m odel but requires strict assum ptions about data characteristics, such as hom oscedasticity and no autocorrelation. In reality, particularly for financial returns, there are som e stylized facts (Cont 20 0 1) that the OLS m odel is not able to capture, specifically leptokurtosis and volatility clustering. As such, running an OLS regression may give a spurious result. In view of this, we adopt a GARCH
10
type m odel to exam ine the Valentine Effect in stock m arkets, as GARCH m odels are able to m odel stock returns displaying volatility clustering.
Given the extensive docum entation of the correlation between holiday effects and investor behaviors, the hypothesis in this study is that investors m ay value financial assets higher during Valentine’s Day than other trading days.
This paper is the first to link Valentine’s Day alone to stock returns. Gilbert and Karahalios (20 10 ) derived a quantitative m easure of aggregate anxiety and worry from weblogs in the US, which is nam ed as the Anxiety Index. They found that the Anxiety Index has a blip coinciding with Valentine’s Day. Som e m ore recent studies have quantified sentim ents by using data from different social m edia platform s, like Facebook and Twitter, and exam ined the relation between such sentim ent indices and the stock m arket perform ance (Siganos et al. 20 17). Most of them give a rather sketchy depiction of Valentine’s Day. All in all, their studies are concurrent with and independent of this study. The findings of this paper may provide a m ore detailed discussion about the Valentine Effect, and their findings com plem ent this study in term s of persuasive explanations.
3 D a ta
This research uses eight stock m arket indices to exam ine the stock return s and volatility behaviors around the tim e of Valentine’s Day. The daily stock prices of these stock m arket in dices, denom inated in local currencies, are obtained from Yahoo Finance using Python. These indices are the Dow J ones Industrial Average (US), FTSE 10 0 Index (UK), DAX Perform ance Index (Germ any), CAC 40 In dex (France), Nikkei 225 Index (J apan), H ang Seng Index (H ong Kong), and Shanghai Com posite Index (China). For robustness purposes, another im portant index, S&P 50 0 Index, is em ployed to investigate the US stock m arket. The current study ten ds to exam ine returns rather than prices, and the prices used in this study are adjusted closing prices, which are often used when exam ining historical returns.4 The stock m arket returns in this study are calculated as the n atural logarithm of the adjusted closing price relative to successive closing price.5 This paper covers a m ore recent sam ple period, which is from 1 J anuary 1990 to 1 March 20 19. During this period, the stock return experienced 30 Valentine’s Days, providing stronger em pirical evidence.
To ensure that the data is usable, this paper first em ploys the augm ented Dickey-Fuller (ADF) tests with intercept and with intercept and trend (Dickey and Fuller 1979) for these eight stock return series. The augm ented Dickey-Fuller statistic tests the stationarity of the tim e series, which is a negative num ber. More
4As Investopedia defin ed, adjusted closin g price am ends a stock’s closin g price to accurately reflect that stock’s value after accoun tin g for an y corporate action s. See m ore details about adjusted closin g price in https : / / w w w .in vestopedia.com / term s/ a/ adjustedclosingprice.asp
5 −
12
specifically, the m ore negative it is, the m ore likely the null hypothesis will be rejected. The results are reported in Table 1, including the t-statistics and p- values. From the table, it is found that the null hypothesis of a unit root is rejected at the 1% significance level for all cases. In other words, all the data used in this study are stationary.
Table 1: Unit Root Test
ADF T-stat (with intercept) ADF T-stat (with intercept and trend)
US -64.516 -64.5126
(0 .0 0 0 1)*** (0 .0 0 0 0 )***
UK -63.6356 -63.6354
(0 .0 0 0 1)*** (0 .0 0 0 0 )***
Germ any -62.5978 -62.5937
(0 .0 0 0 1)*** (0 .0 0 0 0 )***
France -62.730 9 -62.728
(0 .0 0 0 1)*** (0 .0 0 0 0 )***
J apan -62.78 0 9 -62.8 18 5
(0 .0 0 0 1)*** (0 .0 0 0 0 )***
H ong Kong -60 .240 9 -60 .250 6
(0 .0 0 0 1)*** (0 .0 0 0 0 )***
China -55.8228 -55.8 561
(0 .0 0 0 1)*** (0 .0 0 0 0 )***
S&P 50 0 -64.5683 -64.5649
(0 .0 0 0 1)*** (0 .0 0 0 0 )***
Robust standard errors in parentheses:
*** represents p<0 .0 1, ** represents p<0 .0 5, * represen ts p<0 .1
Table 2 sum m arizes the descriptive statistics for the daily returns for these stock m arket indexes. It covers the m ean, standard deviation, skewness, and kurtosis for each of the return series. Moreover, J arque-Bera statistics and the ARCH -LM test statistics are also provided. As can be seen in Table 2, except for J apan, all m arkets had positive m ean returns during the period. Am ong these indexes, China had the highest m ean returns (0 .0 4%), followed by the US (0 .0 30 %), whereas J apan had the lowest m ean returns (−0 .0 0 8 %) during this sam ple period.
Of these return series, the standard deviation is found to be the highest in Chin a (2.28 38 %), and the lowest one is the US (1.0 58 8 %). Apart from China, the skewness of all daily returns is negative, indicating that there is a greater possibility for a decrease than increase in these stock m arkets. The kurtosis for all return series is m ore than three, which suggests fat-tailed distributions. The J arque-Bera test (Dickey and Fuller 1979) is a goodness-of-fit test determ ining whether the sam ple tim e series have skewness and kurtosis m atching that of a norm al distribution.6 The reported results in Table 2 are sm aller than the 1%
level of significance for all return series, in other words, they all reject the null hypothesis of norm al distribution. This result is consistent with the Q-Q (quantile-quantile) plots in Figure 3 (see Appendix).
Table 2: Descriptive Statistics
Observations Mean (%) Std.Dev.(%) Skewness Kurtosis J arque-Bera ARCH -LM test
US 7333 0 .0 30 3 1.0 593 -0 .18 58 8 .1541 20 325.720 5 1967.8 452
(0 .0 0 0 0 )**** (0 .0 0 0 0 )***
UK 7355 0 .0 145 1.0 92 -0 .1241 6.0 670 11280 .9639 1928 .5476
(0 .0 0 0 0 )*** (0 .0 0 0 0 )***
Germ an y 7369 0 .0 252 1.40 44 -0 .1223 4.6939 6771.7521 1418 .8 8 0 5 (0 .0 0 0 0 )*** (0 .0 0 0 0 )***
Fran ce 7334 0 .0 143 1.3660 -0 .0 694 4.68 70 670 7.2935 1334.3136 (0 .0 0 0 0 )*** (0 .0 0 0 0 )***
J apan 7166 -0 .0 0 81 1.510 2 -0 .1477 5.4132 8 760 .5557 130 8 .1543 (0 .0 0 0 0 )*** (0 .0 0 0 0 )***
H on g Kon g 7197 0 .0 322 1.568 9 -0 .0 235 9.6119 27662.410 5 1557.5931 (0 .0 0 0 0 )*** (0 .0 0 0 0 )***
Chin a 6939 0 .0 490 2.28 38 5.318 0 156.0 54 70 63462.3726 41.6445 (0 .0 0 0 0 )*** (0 .0 0 0 0 )***
S&P50 0 7341 0 .0 30 2 1.0 58 8 -0 .18 58 8 .1663 20 40 9.0 30 3 1970 .6156 (0 .0 0 0 0 )*** (0 .0 0 0 0 )***
Robust stan dard errors in paren theses: *** represen ts p<0 .0 1, ** represents p<0 .0 5, * represents p<0 .1
6 The Jarque–Bera test statistic (JB) is defined as: , where n is the number of observations; S is the sample skewness; C is the sample kurtosis; and k is the number of regressors.
14
Therefore, the data used in this study cannot be approxim ated well by a norm al distribution, which violates the requirem ent of the OLS m odel in classical linear regression m odels. Additionally, the last colum n in Table 2 depicts the result of the ARCH -LM test, which is a standard test to detect autoregressive conditional heteroscedasticity (Engle 198 2). These statistics indicate that all of these daily return series reject the null hypothesis of no heteroscedasticity.
Alternatively speaking, the variance of the daily returns in these stock m arkets is not constant but varies across tim e. As m entioned before, financial tim e series always exhibit volatility clustering, which can be seen in Figure 1 in the Appendix. The outcom es of these tables and figures sheds light upon a suitable econom etric m odel for this study in the next step.
4 Me th o d o lo gy
As discussed before, m ost previous literature used the OLS regression, which is a statistical m ethod that estim ates the relationship between independent variables and a dependent variable, to study the daily stock returns aroun d holiday periods. The OLS m odel can be form ulated as below:
(1)
, where Rtis the daily return at tim e t; c is an intercept term ; and represents a dum m y variable which is equal to one for som e specific calendar days, such as Monday or a whole m onth, and zero otherwise. In the equation, is the error term . After com puting the regression, if the coefficient β of the dum m y variable is significantly positive, it suggests that the stock returns on calendar
days included in the study is significantly higher or lower than those on other trading days, which can directly confirm the existence of calendar anom alies in the stock m arket. In particular, the significant β coefficient for the holiday dum m y will confirm a holiday effect for the stock return series.
Nevertheless, the OLS m ethod m ight not be applicable to exam ining the abnorm al movement in stock m arkets due to its em pirically strict but invalid assum ptions, for exam ple, the error term s of the sam ple data m ust be norm ally distributed and hom oscedastic. Thus, the results of studies em ploying the OLS regression m odel in preceding literature may be m isleading.
As presented in Table 1 and Table 2, the return series in this study fail to follow a norm al distribution and have the problem s of autocorrelation and tim e-varying variance, which do not satisfy the assum ptions of the OLS m ethod. Besides, volatility clustering shown in Figure 1 indicates that these stock return series contradict a sim ple random walk m odel, violating another OLS assum ption of random sam pling. In light of these findings, an alternative m odel which does not require distributional assum ptions for residuals is explored to exam ine seasonal anom alies.
Properties of these financial tim e series have led to the use of the GARCH m odel. This study augm ents the GARCH m odel by integrating an ARMA m odel to exam ine seven selected international stock m arket indexes (US, UK, Germany, France, J apan, H ong Kong, and China). The ARMA(p,q)-GARCH(m,n) m odel can overcom e the m ain weakness of the OLS m ethod in exam ining the stock returns.
The superiority of this m odel is twofold. First, the ARMA(p,q) part can handle the autocorrelation problem in the data; Secondly, the GARCH(m,n) portion can help to capture the heteroskedastic characteristic of the data.
16
t
t t
t t
(2) , where 2|Ωt−i N (0, σ2); here, Ωt−i represents the inform ation set at tim e t − i:
(3)
In Equation (2), represents the daily return at tim e t, which depends on its past values , the error term , its past shocks . It should be noted that the error term here is no longer a white noise process but a GARCH process. In the GARCH com ponent, σ2 (conditional variance) is one period ahead of the forecast variance based on this historical data. is a constant term ; (the ARCH
term ) is news about volatility from the previous period m easured as a lag of squared residuals from the m ean equation, while the estim ated coefficients, and , capture the presence of heteroscedasticity in the data. In this study, after different p, q, m , and n are selected for this m odel, it is found that the AIC values obtain ed by ARMA(1,1)-GARCH (1,1) are relatively sm all. 7 Therefore, the m odel, selected for this research, is the ARMA(1,1)-GARCH (1,1) m odel as shown below :
(4) , where s2|Ωt−1∼ N (0, σ2); here, Ωt−1 represents the inform ation set at tim e t−1:
(5)
7The selection process can be foun d in Appen dices.
To exam ine the Valentine’s Day effect in the stock m arket, Equation (4) is augm ented with two additional dum m y variables, representing the days right before Valentine’s Day and the days after this special day:
(6) , where the dum m y variable will be equal to one if the observation falls within three trading days prior to Valentine’s Day and on Valentine’s Day, an d zero otherwise. is another dum m y variable that will take a value of one for three trading days after Valentine’s Day and zero otherwise. The significance of the coefficients for these two dum m y variables will indicate the existence of a is- or post-Valentine effect on stock returns. Specifically, the is-Valentine effect denotes abnormal stock market return performance three trading days before and on Valentine’s Day, while the post Valentine effect refer to the unusual behavior three trading days after Valentine’s Day in stock m arkets.
Furtherm ore, in case other anom alies interfere with the results of this m odel, we need to introduce control variables to elim inate the variance error. But there are num erous calendar effects, and it is not feasible to address all effects that have an im pact on the Valentine Effect. For this reason, the focus is on the anom alies which are, arguably, the m ost possible ones that can affect daily stock returns, as revealed in the literature of financial econom ics. The m ost significant calendar effect on a daily basis is the Monday effect, as considerable research has confirm ed its negative return throughout over 10 0 years of trading activity (Pettengill 20 0 3). Therefore, the dum m y variable Mt is introduced, which will take a value of 1 if day t is a Monday, and zero otherwise. The significance of the
18
coefficient for the dum m y variable Mt suggests the presence of Mon day effect in stock returns.
(7)
Since Valentine’s Day is on February 14, the calendar day in question m ight coincide with the full m oon period in the lun ar calendar, which suggests that the Full Moon Effect is a potential factor interfering with the results of this study.
Therefore, this paper introduces a Full-Moon dum m y (Ft) as a control variable.
When Ft = 1, day t is around the full m oon period of a m onth, and Ft = 0 for the rem aining days in that m onth: 8
(8 ) Sim ilarly, the significance of the estim ated coefficient of Ft indicates the influence of full m oon periods on stock returns.
5 Re s u lts
5 .1 Th e Va le n t in e Effe ct in t h e U S s t o ck m a r k e t
The first result in this paper is to give a portrayal of the Valentine Effect in the US stock m arket, and the selected ticker is the Dow J ones Industrial Average (DJ IA)9, which is one of the oldest stock indices in the world, as well as the m ost
8 A full m oon period can be defined as span n in g from N days before the full m oon day to the full m oon day an d N days after the full m oon day (N = 3 or 7) (Yuan et al. 20 0 6). In this paper, a full m oon period is defined as the period between the 13th an d the 15th days in a lun ar calen dar.
9 The Dow J on es Industrial Average (DJ IA) is a m arket in dex com posed of 30 large com pan ies, an d its tim ely com putation for its con stituent com panies m akes it an extrem ely useful in dicator for represen tin g short-term m arket m ovem en ts (Rudd 1979). Thus, the DJ IA is an apt proxy particularly for this study.
cited and widely recognized one. Table 3 presents the estim ation result of the ARMA(1,1)-GARCH (1,1) m odel in the US stock m arket. The estim ates show that except for the dum m y variables, all coefficients in the m ean and variance m odels are statistically significant, and the values of the estim ated param eters µ, α and β, satisfy the requirem ent of GARCH stability. Panel A depicts the estim ates of the m ean equation, which uses an ARMA process to m odel the daily m arket returns with the is- an d post- Valentine’s Day dum m y variables. Panel B displays the estim ates of the conditional variance equation. In addition, the AIC values show the goodness of fit of the m odels.
Estim ates in panel A reveal the results after exam ining the Valentine Effect with the is- and post- Valentine’s Day dum m y variables. The estim ated coefficients of the is-Valentine dum m y (λisV) are statistically significant at the 1%
level. More specifically, the positive value (0 .1914) of the estim ated coefficient (λisV) suggests that stock returns are 19.14% higher when Valentine’s Day is approaching, com pared to the returns on other trading days. All estim ates in Panel B are statistically significant, m eaning that the GARCH part of the m odel fits the data well.
20
Then, two control variables, the Monday dum m y and the Full-Moon dummy, are introduced to Model 2 and Model 3 respectively. Although control variables are included, the estim ated coefficient of the is-Valentine dum m y variable (λisV) is still positive and statistically significant. Note that the values of the estim ated coefficient (λisV) are 0 .1418 and 0 .1925 respectively in Model 2 and Model 3, which seem to be affected by the newly introduced control variables. On the contrary, it is found that post-Valentine’ Day effect is not significant for all m odels from Table 3. The estim ated value of the post-Valentine dum m y variable is about 0 .0 9, while the p-values indicate that the estim ates are statistically insignificant, all of which are over the 10 % significance level. As for control variables, the Monday dum m y is found to be positive and significant at the 5%
level, and the estim ated coefficient rem ains about 0 .0 51, while the Full Moon effect is found to be weak in the US stock m arket. Despite this, the significant is- Valentine effect is still consistent with the result of the first m odel without adding any control variables. The result in Panel A suggests that there exists a significant Valentine Effect in the US stock m arket for these three m odels, which is consistent with the hypothesis that stock returns are affected by this rom antic day.
On the other hand, in Panel B, the estim ated coefficients of both lagged squared residuals and lagged conditional variance in the Variance Equation are statistically significant at the 1% level, which suggests that using the ARMA(1,1)- GARCH (1,1) m odel to describe the volatility of the Rtseries is appropriate.
Furtherm ore, the sum of the ARCH and GARCH (α1 + β1) coefficients of the US stock m arket index is close to a un it root, which indicates that shocks to volatility have a persistent effect on the conditional variance.
Table 3: The Valentine Effect in the US Stock Market
(1) (2) (3)
Model 1 Model 2 Model 3
Panel A: Mean equation
c 0 .0 567*** 0 .0 469*** 0 .0 512***
(0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )***
ϕ(AR(1)) 0 .9584*** 0 .9582*** 0 .9581***
(0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )***
θ(MA(1)) -0 .9714*** -0 .9712*** -0 .9711***
(0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )***
λisV 0 .1914***
(0 .0 0 12)***
0 .1418 **
(0 .0 18 2)**
0 .1925***
(0 .0 0 12)***
λpostV 0 .0 854 0 .0 947 0 .0 943
(0 .4147) (0 .3662) (0 .3623)
γM 0 .0 512**
(0 .0 356)**
0 .0 513**
(0 .0 352)**
ρF -0 .0 413
(0 .148 5)
Panel B: Variance equation
µ 0 .0 160 *** 0 .0 159*** 0 .0 160 ***
(0 .0 0 28)*** (0 .0 0 22)*** (0 .0 0 18)***
α 0 .0 942*** 0 .0 942*** 0 .0 948***
(0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )***
β 0 .890 8*** 0 .890 9*** 0 .890 3***
(0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )***
Goodness of fit statistics
AIC 2.58 59 2.58 29 2.58 29
Robust standard errors in parentheses
*** p<0 .0 1, ** p<0 .0 5, * p<0 .1
22
For a robustness check, this paper also exam ines the Valentine Effect by using another im portant index in the US stock m arket, the S&P 50 0 Index, which is an Am erican stock m arket index based on the m arket capitalizations of 50 0 large com panies having com m on stock listed on the NYSE, NASDAQ, or the Cboe BZX Exchange. The sam ple period rem ains the sam e as in Table 3, and Table 4 presents the results.
Table 4: Robustness Tests for the US Stock Market (S&P 50 0 )
(1) (2) (3)
Model 1 Model 2 Model 3
Panel A: Mean equation
C 0 .0 555*** 0 .0 50 3*** 0 .0 538***
(0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )***
ϕ(AR(1)) 0 .90 11 0 .90 13*** 0 .8998***
(0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )***
θ(MA(1)) -0 .9250 -0 .9251*** -0 .9237***
(0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )***
λisV 0 .1773***
(0 .0 0 54)***
0 .1760 ***
(0 .0 0 55)***
0 .178 2***
(0 .0 0 48)***
λpostV 0 .0 325 0 .0 369 0 .0 356
( 0 .7949) (0 .768 3) (0 .7744)
γM 0 .0 273 0 .0 272
(0 .260 7) (0 .2626)
ρF -0 .0 340
(0 .2262)
Panel B: Variance equation
µ 0 .0 149*** 0 .0 149*** 0 .0 149***
(0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )***
Α 0 .0 917*** 0 .0 918*** 0 .0 922***
(0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )***
Β 0 .8 951*** 0 .8951*** 0 .8946***
(0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )***
Goodness of fit statistics
AIC 2.6247 2.6248 2.6249
Robust standard errors in parentheses
*** p<0 .0 1, ** p<0 .0 5, * p<0 .1
The estim ated coefficient for (λisV) is about 0 .17 and is significant at the 1%
level for all m odels. It is consistent with the results shown by the Dow J ones Industrial Average Index. This suggests that the Valentine Effect is still robust after changing the assessm ent in dex and controlling for other anom alies.
24
To conclude, all results in this section suggest that the is-Valentine effect (three trading days before and on February 14) is present in the US stock m arket, but no traces of the post-Valentine effect have been found. Based on the findings in Table 3 and Table 4, one may argue that abnorm al perform ance on days near Valentine’s Day m ight be universal in other stock m arkets. To confirm the existence of Valentine Effect, this paper further investigates the daily stock returns of m ajor global stock m arket indices.
5 .2 In t e r n a t io n a l Ev id e n ce o f Va le n t in e Effe ct
In the case that Valentine Effect in the US stock m arket is an isolated case, the paper exam ines the Valentine Effect in global stock m arkets, including the European and Asian econom ies. Note that for the stock m arkets of the UK, France, Germany, J apan, H ong Kong, and China, this study takes FTSE 10 0 , DAX, CAC 40 , Nikkei 225, H ang Seng Index, and Shanghai Com posite Index as the proxies, respectively.
Our findings from the other six stock m arkets are m ixed. Table 5 is the result of the fitted m odel without the control variables, revealing that the Valentine Effect is present in only three stock m arkets, which are those of the UK, France, and China. The is-Valentine dum m y variable (λisV ) is positive and significan t at the 5% level for the stock m arkets of the UK and France, and at the 1% level for the Chinese stock m arket. In contrast, the estim ated coefficient for λisV in the m ean equation is statistically insignificant for Germany, J apan, and H ong Kong, indicating that stock returns in these three stock m arkets are not
affected by Valentine’s Day. Additionally, it is interesting to note that, out of these stock m arkets, the m ost profound effect is exhibited in the Chinese m arket. The is- Valentine dum m y variable (λisV) of 0 .7261 indicates that stock returns in China are 72.61% higher on the period three days before the Valentine’s Day and in cluding that day, than returns on other trading days. The US has the second highest is-Valentine increm ental returns (19.42%), followed by a country known for its rom ance, France (18 .8 6%), and then the UK (14.0 3%). The findings are consistent with the expectation that stock returns in global stock m arkets are affected by Valentine Effect at different levels.
In the following parts, Table 6 and Table 7 separately present the em pirical results after adding the Monday dum m y and the Full-Moon dum m y variables;
the estim ated coefficient (λisV) in Panel A rem ains statistically significant in the stock m arkets of the UK, France, and China, which is consistent with the estim ated results of the m odel without control variables. To be m ore specific, the is-Valentine effect is stronger when the Monday dum m y and the Full-Moon dum m y are included with a lower significance level. The estim ated coefficient of the Monday dum m y is found to be significant in France and J apan and both of them are negative, at -0 .0 578 and -0 .0 78 8 respectively. It suggests that in France and J apan, stock returns exhibit a downward movement on Mondays. From Table 7, the Full Moon effect is less significant, with only France and J apan having a significant coefficient of Ft at the 10 % significance level. On the other hand, it is found that for m ost cases in this study, the estim ated coefficients for the dum m y
λpostV are all statistically insignificant, except for the UK and China. The UK
stock m arket has a positive post-Valentine dum m y variable (0 .20 28) at the 10 % significance level, while China shows a significant and negative post-Valentine
26
dum m y variable (-0 .648 3) at the 1% level. This im plies that stock returns in these two m arkets tend to perform abnorm ally on days after Valentine’s Day.
Table 5: The Valentine’s Day Effect in Global Stock Markets
US UK Germ any France J apan H ong Kong China
Panel A: Mean equation
C 0 .0 567*** 0 .0 342*** 0 .0 629*** 0 .0 440 *** 0 .0 369 0 .0 644*** 0 .0 276*
(0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 1)*** (0 .38 46) (0 .0 0 0 0 )*** (0 .0 637)*
ϕ(AR(1)) 0 .958 4*** 0 .9520 *** 0 .8 8 57*** 0 .8 556*** 0 .9320 *** -0 .2268 0 .7659***
(0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .70 67) (0 .0 0 0 0 )***
θ(MA(1)) -0 .9714*** -0 .9655*** -0 .8 98 1*** -0 .8 78 0 *** -0 .940 7*** 0 .2820 -0 .780 6***
(0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .6355) (0 .0 0 0 0 )***
λisV 0 .1942*** 0 .140 3** 0 .1434 0 .18 8 6** 0 .2256 0 .1247 0 .7261***
(0 .0 0 12)** (0 .0 20 1)** (0 .128 0 ) (0 .0 172)** (0 .1572) (0 .3513) (0 .0 0 12)***
λpostV 0 .0 854 0 .20 47** 0 .1169 0 .1436 0 .20 17 0 .2213 -0 .6485***
(0 .4147) (0 .0 125)** (0 .2374) (0 .2170 ) (0 .1733) (0 .150 8 ) (0 .0 0 27)***
Panel B: Variance equation
µ 0 .0 160 *** 0 .0 150 *** 0 .0 28 2*** 0 .0 277*** 0 .0 539*** 0 .0 292*** 0 .0 538***
(0 .0 0 28)*** (0 .0 0 0 3)*** (0 .0 0 20 )*** (0 .0 0 0 5)*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )***
Α 0 .0 942*** 0 .0 913*** 0 .0 8 28 *** 0 .0 90 3*** 0 .1120 *** 0 .0 768*** 0 .1482***
(0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )***
Β 0 .8 90 8 *** 0 .8 954*** 0 .90 15*** 0 .8 954*** 0 .8 669*** 0 .910 3*** 0 .850 7***
(0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )***
Goodness of fit statistics
AIC 2.58 33 2.6739 3.20 0 0 3.190 7 3.4365 3.38 29 3.8 58 3
27
Goodness of fit statistics
AIC 2.5829 2.6740 3.20 0 2 3.190 5 3.4365 3.3831 3.8585
Table 6: The Valentine Effect in Global Stock Market after Controlling for the Monday Effect
US UK Germ any France J apan H ong Kong China
Panel A: Mean equation
C 0 .0 469*** 0 .0 392*** 0 .0 574*** 0 .0 554*** 0 .0 519*** 0 .0 70 0 *** 0 .0 250
(0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 2)*** (0 .0 0 0 0 )*** (0 .130 2) ϕ(AR(1)) 0 .958 2*** 0 .9518 *** 0 .8 8 62*** 0 .8 557*** 0 .9316*** -0 .2526 0 .7664***
(0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .5941) (0 .0 0 0 0 )***
θ(MA(1)) -0 .9712*** -0 .9653*** -0 .8 98 5*** -0 .8 78 2*** -0 .940 4*** 0 .30 74 -0 .7811***
(0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .510 3) (0 .0 0 0 0 )***
λisV 0 .1914*** 0 .1418 ** 0 .1419 0 .1911** 0 .2238 0 .1252 0 .7293***
(0 .0 0 12)*** (0 .0 18 6)** (0 .1317) (0 .0 164)** (0 .160 7) (0 .3496) (0 .0 0 12)***
λpostV 0 .0 947 0 .20 36** 0 .118 9 0 .1396 0 .198 6 0 .2221 -0 .6477***
(0 .3662) (0 .0 136)** (0 .2292) (0 .2333) (0 .18 15) (0 .1495) (0 .0 0 29)***
γM 0 .0 512** -0 .0 270 0 .0 274 -0 .0 578 * -0 .0 78 8 ** -0 .0 282 0 .0 134
(0 .0 356)** (0 .2616) (0 .4171) (0 .0 68 2)* (0 .0 276)** (0 .40 45) (0 .720 6)
Panel B: Variance equation
µ 0 .0 159*** 0 .0 151*** 0 .0 28 2*** 0 .0 278 *** 0 .0 536*** 0 .0 292*** 0 .0 539***
(0 .0 0 22)*** (0 .0 0 0 2)*** (0 .0 0 11)*** (0 .0 0 0 6)*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )***
Α 0 .0 942*** 0 .0 914*** 0 .0 8 28 *** 0 .0 90 6*** 0 .1121*** 0 .0 768*** 0 .1484***
(0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )***
Β 0 .8 90 9*** 0 .8 953*** 0 .90 15*** 0 .8 950 *** 0 .8 669*** 0 .910 2*** 0 .850 5***
(0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )***
28
Goodness of fit statistics
AIC 2.5829 2.6742 3.20 0 4 3.190 6 3.4359 3.3834 3.8588
Table 7: The Valentine Effect in Global Stock Market after Controlling for the Monday Effect and the Full-Moon Effect
US UK Germ any France J apan H ong Kong China
Panel A: Mean equation
C 0 .0 512*** 0 .0 412*** 0 .0 599*** 0 .0 595*** 0 .0 60 5*** 0 .0 710 *** 0 .0 251
(0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 2)*** (0 .0 0 0 0 )*** (0 .1490 ) ϕ(AR(1)) 0 .958 1*** 0 .9518 *** 0 .8 8 59*** 0 .8 547*** 0 .9325*** -0 .2536 0 .7663***
(0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .5926) (0 .0 0 0 0 )***
θ(MA(1)) -0 .9711*** -0 .9653*** -0 .8 98 2*** -0 .8772*** -0 .9411*** 0 .30 83 -0 .78 11***
(0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .50 91) (0 .0 0 0 0 )***
λisV 0 .1925*** 0 .1418 ** 0 .1417 0 .190 6** 0 .2222 0 .1250 0 .7290 ***
(0 .0 0 12)*** (0 .0 18 2)** (0 .1331) (0 .0 169)** (0 .1642) (0 .350 1) (0 .0 0 13)***
λpostV 0 .0 943 0 .20 28 ** 0 .118 8 0 .138 8 0 .1942 0 .2221 -0 .648 3***
(0 .3623) (0 .0 141)** (0 .2297) (0 .2375) (0 .1917) (0 .1493) ( 0 .0 0 31)***
γM 0 .0 513** -0 .0 268 0 .0 277 -0 .0 576* -0 .0 78 7** -0 .0 282 0 .0 134
(0 .0 352)** (0 .2645) (0 .4137) (0 .0 694)* (0 .0 279)** (0 .40 48 ) (0 .7213)
ρF -0 .0 413 -0 .0 20 2 -0 .0 237 -0 .0 40 2* -0 .0 8 16* -0 .0 0 92 -0 .0 0 0 8
(0 .148 5) (0 .5339) (0 .5755) (0 .3323)* (0 .0 750 )* (0 .8 40 2) (0 .98 64)
Panel B: Variance equation
µ 0 .0 160 *** 0 .0 151*** 0 .0 28 3*** 0 .0 279*** 0 .0 537*** 0 .0 292*** 0 .0 539***
(0 .0 0 18 )*** (0 .0 0 0 2)*** (0 .0 0 11)*** (0 .0 0 0 6)*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )***
Α 0 .0 948 *** 0 .0 914*** 0 .0 8 29*** 0 .0 90 7*** 0 .1119*** 0 .0 769*** 0 .148 4***
(0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )***
Β 0 .8 90 3*** 0 .8 953*** 0 .90 13*** 0 .8 948 *** 0 .8 669*** 0 .910 2*** 0 .8 50 5***
(0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )***
29
30
5 .3 Th e Pr e s e n ce o f Va le n t in e Effe ct in Ch i n a
Furtherm ore, it is noteworthy that the estim ated coefficient for the post- Valentine’s Day effect is significantly negative for China’s stock m arket. The findings are consistent with the expectation that great differences between the period prior to and after Valentine’s Day are associated with investor m ood, which suggests that it is possible for investors to be in a positive m ood before Valentine’s Day, leading to changes in trading patterns, which in turn lead to changes in returns. Nevertheless, what can not be ignored is that, in China’s stock m arket, Valentine’s Day is usually close to the Spring Festival and even falls within the period of public holidays. Thus, this seem s to challenge the previous hypothesis that the abn orm al perform ance of stock returns is solely caused by Valentine’s Day. Accordingly, this study further delves into China’s Valentine’s Day. Firstly, this study scrutinizes the Lunar and the Gregorian calendars of 1990 -20 19 and finds that nearly half of all Valentine’s Days fell into the Spring Festival period, during which China’s stock m arket is closed.10 This suggests that the significant Valentine Effect present in Table 6 m ight som etim es be confused with the Spring Festival effect. In light of this, we introduce two Spring Festival dum m y variables (Yuan and Gupta 20 14), which are ξpreN, taking a value of one for observations which are at least three trading days before the Spring Festival public holidays and zero otherwise, and ξpostN, which assigns a value of one to observations which are three trading days after the Spring Festival public holidays and zero otherwise.11 The m ean equation of the m odel for
10Specific details for the Valen tin e’s Day in the Lun ar calen dar can be foun d in Appen dices.
11According to the regulation s of the State Coun cil, the Sprin g Festival public holidays start from the Lun ar New Year’s Eve to the 6th day of the first m on th in Lun ar calendar.
China’s stock m arket is augm ented as follows:
32
(9) Table 8 presents the results after controlling for the Sprin g Festival effect, and the estim ated coefficients of the is-Valentine and post-Valentine dum m y variables are still significant at the 1% level. Although the value of the estim ated coefficient of λisVhas decreased substantially from 0 .729 in Model 3 to 0 .0 0 65 in Model 4, it is still statistically significant at the 1% level. A sim ilar change occurs in the estim ated coefficient of λpostV, with the size reducing from 0 .648 3 to - 0 .0 0 56 at the 1% significance level. Such a result further indicates that the Valentine Effect still exists, though the effect is considerably weakened by the Spring Festival effect. For the Spring Festival dummy, the estim ated coefficient is found to be positive (0 .0 0 59) and significant at the 1% level, suggesting that stock returns experience larger movements on days after the Spring Festival public holidays than on other trading days.
To better understand how Valentine’s Day specifically affects China’s stock m arket, this study sets separate dum m y variables for pre-Valentine’s Day and post-Valentine’s Day periods.12 Since the Monday effect and the Full Moon effect do not exert influence on China’s stock m arket, as evidenced in Table 8 , these two dum m y variables are om itted in this process.
12The specific dum m y variables are defined as follows. λisV represen ts the Valentine’s Day.
λpreV1, λpreV2 an d λpreV3 are the three days before the Valentine’s Day, whereas λpostV1, λpostV2
an d λpostV3 den ote their coun terparts for the post-Valen tin e’s Day period.
Table 8 : Adding Spring Festival Dum m y Variables to the Estim ation
(1) (2) (3) (4)
Model 1 Model 2 Model 3 Model 4
Panel A: Mean equation
c 0 .0 276* 0 .0 250 0 .0 251 0 .0 0 0 2
(0 .0 637)* (0 .130 2) (0 .1490 ) (0 .2221) ϕ(AR(1)) 0 .7659*** 0 .7664*** 0 .7663*** 0 .758 8 ***
(0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )***
θ(MA(1)) -0 .780 6*** -0 .7811*** -0 .78 11**** -0 .7751***
(0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )***
λisV 0 .7261***
(0 .0 0 12)***
0 .7293***
(0 .0 0 12)***
0 .7290 ***
(0 .0 0 13)***
0 .0 0 65***
(0 .0 0 0 0 )***
λpostV -0 .6485*** -0 .6477*** -0 .6483*** -0 .0 0 56***
(0 .0 0 27)*** (0 .0 0 29)*** (0 .0 0 31)*** (0 .0 0 45)***
γM 0 .0 134 0 .0 134 0 .0 0 0 2
(0 .720 6) (0 .7213) (0 .58 67)
ρF -0 .0 0 0 8 0 .0 0 0 0
(0 .98 64) (0 .9135)
ξpreN -0 .0 0 0 5
(0 .770 7)
ξpostN 0 .0 0 59***
(0 .0 0 0 0 )***
Panel B: Variance equation
µ 0 .0 538*** 0 .0 539*** 0 .0 539*** 0 .0 0 0 0
(0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .1396)
α 0 .1482*** 0 .1484*** 0 .1484*** 0 .1469***
(0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )***
β 0 .850 7*** 0 .850 5*** 0 .850 5*** 0 .8 520 ***
(0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )*** (0 .0 0 0 0 )***
Goodness of fit statistics
AIC 2.6247 2.6248 2.6249 -5.3521
Robust standard errors in parentheses
*** p<0 .0 1, ** p<0 .0 5, * p<0 .1
From Table 9, it can be seen that the estim ated coefficient of the Valentine’s Day dum m y (λisV ) rem ains statistically significant, which is about 0 .8 425, indicating that this is n ot a negligible effect. The sim ilar statistically significant results are also found for the coefficients of λpreV 2 and λpostV 3.
34
Specifically, the estim ated value of λpreV2 is 0 .68 at the 10 % significance level, which is considerably im pactful as well. The coefficient of λpostV3 is significant and negative, with a value of -1.20 . The signs of the coefficients for the pre- and the post- Valentine’s Day periods are still positive and negative respectively, which is consistent with the results in Table 6. Based on these findings, we can further confirm the existence of the Valentine Effect and locate the abnorm al perform ances in China’s stock m arket two days before and three days after Valentine’s Day.
Table 9: Specific Dum m ies for Valentine Effect in China’s Stock m arket
Estim ate Std. Error t value Pr(> |t|)
Panel A: Mean equation
C 0 .0 262 0 .0 149 1.7615 0 .0 78 1
ϕ(AR(1)) 0 .7619 0 .120 0 6.3497 0 .0 0 0 0 θ(MA(1)) -0 .7770 0 .1155 -6.7236 0 .0 0 0 0
λisV 0 .8 425 0 .40 89 2.0 60 1 0 .0 393
λpreV 1 0 .1954 0 .368 9 0 .5296 0 .5963
λpreV 2 0 .68 22 0 .3624 1.8 8 26 0 .0 597
λpreV 3 0 .5595 0 .3762 1.48 71 0 .1369
λpostV 1 -0 .2636 0 .40 60 -0 .6494 0 .5160
λpostV 2 -0 .240 0 0 .328 5 -0 .730 4 0 .4651
λpostV 3 -1.20 33 0 .2883 -4.1728 0 .0 0 0 0
ξpreN -0 .0 239 0 .18 28 -0 .1312 0 .8 955
ξpostN 0 .4635 0 .2134 2.1720 0 .0 298
Panel B: Variance equation
µ 0 .0 516 0 .0 0 90 5.70 31 0 .0 0 0 0
Α 0 .1474 0 .0 0 79 18 .4414 0 .0 0 0 0
Β 0 .8 515 0 .0 0 92 92.1363 0 .0 0 0 0
Goodness of fit statistics AIC BIC SIC H QIC 3.8 58 0 3.8 728 3.8 58 0 3.8 631
Overall, this section reports the m ajor findings of this paper. It aim s to exam ine the existence of Valentine Effect in stock m arkets. Daily stock data was
