Seasonalities in China's Stock Markets
Cultural or Structural?
  • 1 0000000404811396https://isni.org/isni/0000000404811396International Monetary Fund

Contributor Notes

Author(s) E-Mail Address: acjason@umich.bus.edu and long@imf.org

In this paper, we examine returns in the Chinese A and B stock markets for evidence of calendar anomalies. We find that both cultural and structural (segmentation) factors play an important role in influencing the pricing of both A- and B-shares in China. There is some evidence of a February turn-of-the-year effect, partly owing to the timing of the Chinese Lunar New Year (CNY); and the holiday effect around the CNY period is stronger and more persistent compared with the other public holidays. The segmentation between the two markets is apparent in the day-of-the-week effect, where B stock markets tend to post significant negative returns on Tuesdays, corresponding with overnight developments in the United States, while significant negative returns are observed on Mondays in the A stock markets. Investment strategies based on some of these calendar anomalies, and allowing for transaction costs, suggest that the A stock markets tend to offer more economically significant returns.

Abstract

In this paper, we examine returns in the Chinese A and B stock markets for evidence of calendar anomalies. We find that both cultural and structural (segmentation) factors play an important role in influencing the pricing of both A- and B-shares in China. There is some evidence of a February turn-of-the-year effect, partly owing to the timing of the Chinese Lunar New Year (CNY); and the holiday effect around the CNY period is stronger and more persistent compared with the other public holidays. The segmentation between the two markets is apparent in the day-of-the-week effect, where B stock markets tend to post significant negative returns on Tuesdays, corresponding with overnight developments in the United States, while significant negative returns are observed on Mondays in the A stock markets. Investment strategies based on some of these calendar anomalies, and allowing for transaction costs, suggest that the A stock markets tend to offer more economically significant returns.

I. Introduction

Seasonalities or calendar anomalies are well documented and are perhaps the best-known examples of inefficiencies in financial markets. Evidence of such seasonalities is readily available for the well-established stock markets in the developed economies, as well as in some emerging market countries.2 The stock market in the People’s Republic of China (hereinafter referred to as “China”), in turn, poses an interesting study in that the market is relatively new, is less developed and has experienced rapid changes in its short history. Moreover, the Chinese stock market has obvious differences from the conventional markets in North America and Europe. It has many unique institutional features, notably the existence of the domestically traded local currency A stock market, which until the end of 2002 was accessible only to local investors; and the hard-currency B stock market, which until early 2001 was accessible only to foreign investors.3 The uniqueness of this market thus allows us to potentially gain some insights into whether institutional and cultural factors play a significant role in determining pricing behavior in stock markets.4

Over the past decade, the China stock market has been transformed from a fledgling emerging market to become the biggest stock market, by capitalization, in Asia outside Japan. China has also been, and is expected to remain, one the world’s fastest-growing economies. During this period, the domestic A stock market has experienced phenomenal growth, structural changes, and rapid development, as evidenced by its increased size, depth, and liquidity (see Table 1). The two major stock exchanges of Shanghai and Shenzhen have recorded sharp increases in A-share index levels (see Figure 1a), as well as a reduction in A-share volatility as the market has developed. In contrast, the performance of the B-shares has been mediocre (see Figure 1b), with its initially low volatility increasing sharply during the 2001 period. That said, both turnover and volume have also improved in the B stock market, as shown in Table 1.

Figure 1.
Figure 1.

Shanghai and Shenzhen Stock Market Indices from Start of Market to December 2002

Citation: IMF Working Papers 2006, 004; 10.5089/9781451862645.001.A001

Source: CSMAR
Table 1.

Summary Performance Statistics for China Stock Markets, from Start of Market to December 2002

article image
Source: CSMARNotes:1. Market value is measured as the market capitalization of the tradable portion of shares.2. Average return and standard deviation of return are computed using the comprehensive indices of the respective markets.

Despite the increasing importance of the China stock market, there is a general paucity of literature on seasonalities relating to this market, in particular, of the turn-of-the-year and the holiday effects. Chen, Kwok, and Rui (2001a) examine share returns of both the Shanghai and Shenzhen A- and B-shares over the January 1995 to December 1997 period and finds differences in returns for the days-of-the-week but only for the later half of their sample. Previously, Mookerjee, and Kim (1999) had considered seasonalities in both the Shenzhen and Shanghai markets within a broader context of an analysis of the serial-dependent structure of returns. For the period from the start of trading for each market until December 1993, they find that the Shenzhen market had significant weekend and holiday effects but the Shanghai market did not. No significant January or early January effect was detected for either market.

Studies by Heaney, Powell, and Shi (1999) and Xu (2000) use calendar anomalies in their examination of China’s stock markets, although these studies neither directly examine nor test for calendar anomalies. Heaney, Powell, and Shi (1999) use tests of seasonalities to show the existence of share price linkages between the A- and B-shares. They conclude that the A stock market is the dominant market for price formation in the B stock market, although the relationship is weaker than expected. Xu (2000) includes the day-of-the-week effect in modeling the time-series properties of returns and conditional variance for the Shanghai Composite and B-share indices. He finds that the day-of-the-week effect is not useful in explaining the conditional daily returns; however, it is significant in explaining the conditional volatility, with the highest volatility tending to occur on Mondays.

In this paper, we examine returns in both the China A and B stock markets for evidence of calendar anomalies, including the holiday and turn-of-the-year effects, which have been largely unexplored in this market. In addition to testing for the existence of the anomalies per se, the split between A-shares, which are held solely by domestic investors, and B-shares, which are held by foreign investors, allows us to determine the impact any potential “cultural differences” may have on any particular seasonality. Additionally, the A-shares participants are supposedly less informed, given their access to fewer information resources than are available to the international institutions that invest in the B stock market (Kim and Shin, 2000). On this basis, we also attempt to determine whether any existing “inefficiencies” observed in stock markets are partly driven by less informed individual investors.

We further include in our study other likely variables that may affect the price-setting and market-making process. For instance, volatility of returns may be used to capture the uncertainty inherent in pricing, while volume and turnover data could be used to determine the liquidity or depth in the market. To date, questions about seasonalities in volatility and volume remain largely unanswered, either within the context of the China or other markets.5 These additional variables may be useful in understanding market behavior (Xu, 2001) as well as interpreting any differences in returns and assessing trading and portfolio implications (Berument and Kiymaz, 2001).

Our findings suggest that both cultural and structural factors play important roles in influencing the pricing of stocks within the China market. We find some evidence of a February—as opposed to a January—turn-of-the-year effect, partly because the Chinese Lunar New Year (hereinafter referred to as CNY) normally occurs in late January or February. There is also a strong CNY holiday effect. Strong evidence also exists for a “half-year effect” and a day-of the-week effect in these markets. The internationally traded B stock markets tend to post negative returns on Tuesdays, corresponding to the negative returns on Mondays in the United States. In contrast, the day-of-the-week effect is manifest over the Friday-to-Monday nontrading period in the “closed” A stock markets. The holiday effect around the culturally based Chinese New Year period also appears stronger compared with the other public holidays, especially for the A-shares. Investment strategies based on these calendar anomalies confirm that the A stock markets tend to be more profitable and offer economically significant returns, even after accounting for transaction costs. Our empirical tests use about 12 years of daily index data from the start of the Shanghai and Shenzhen Stock Exchanges up to December 2002.

The paper is structured as follows. In Section II, we review the literature on seasonalities in stock markets. Section III outlines the distinct institutional features of the Chinese market and the differences between A- and B-shares that are relevant for our study. The data and research method are described in Section IV, followed by a discussion of our findings in Section V. We extend our study to include a more detailed analysis of the holiday effect in Section VI. In Section VII, we use our findings to derive and test possible investment strategies around the identified seasonalities. Section VIII concludes.

II. Literature on Seasonalities

Seasonalities or calendar anomalies are the observance of significantly different share market returns at distinct cusps in time such as on select days of the week, periods of the month or of the year. Most of the calendar anomalies are not new phenomena; indeed, they are well documented, especially for the mature stock markets. We discuss each of these briefly in turn.

A. January (Turn-of-the-Year) Effect

In the January or turn-of-the-year effect, stock returns are found to decline in December of each year, with increases in the following January. This effect was originally documented in studies by Branch (1977), Dyl (1977), Keim (1983), Reinganum (1983), and Roll (1983). The January effect is intriguing in that it has not been traded away, despite the fact that it has been well-known, public information for nearly two decades (Haugen and Jorion, 1996). Two prime reasons have been offered for the January effect: (i) tax-loss selling; and (ii) a small-firm premium that is concentrated in January. In other words, the effect is attributed to small stocks rebounding following the year-end and tax-related selling, where individual stocks performing poorly at year-end are likely to be sold to lock in capital tax losses, to be offset against other income. However, while the January effect is observed in many foreign countries, some countries such as the United Kingdom, New Zealand and Hong Kong (Agrawal and Tandon, 1994) and Australia (Brown, Keim, Kleidon and Marsh, 1983) have months other than December as the tax year-end. Hence, it has been argued the tax-loss selling explanation cannot be the sole determinant of the January effect. However, the January effect is mainly located in small stocks in particular and there appears to be an interaction between small-firm premium and the January effect.6

Some studies have argued that some of the other calendar anomalies play an important role in the manifestation of the January effect. The interaction of calendar effects could potentially obscure the observation of seasonalities in stock price returns, thus the importance of isolating these effects. For example, half of the small-firm premium in January returns occur in the first few days of January (Keim, 1983), while the day-of-the-week effect has been observed to occur primarily or entirely during the month of January (Rogalski, 1984b). Furthermore, it has been argued that the January effect may have more recently moved into November and December. This has been attributed to the requirement that mutual funds report their holdings at the end of October, and from investors buying in anticipation of gains in January.7 It has led to the notion that the January effect may have moderated or relocated to the other months of the year in recent periods. Nevertheless, January has historically been the best month for stocks across all markets. A few countries have returns in January that are greater than the average return for the whole year (Agrawal and Tandon, 1994); in general, this tends to be large and positive in most countries (Gultekin and Gultekin, 1983).

B. Half-Month (Turn-of-the-Month) Effect

Daily stock returns have been found to be higher in the first-half relative to the last-half of the trading month. Using U.S. stock market indices over the period 1963 to 1981, Ariel (1987) conducts the seminal study on this effect. Agrawal and Tandon (1994) subsequently confirm the effect in other international markets. More recently, studies such as Hensel and Ziemba (1996) have refined this test to show that stocks consistently have higher returns on the last day and first four days of the month. The authors note that from 1928 through 1993, returns at the turn of the month were significantly above average; and “the total return from the S&P 500 over this sixty-five-year period was received mostly during the turn of the month” (p. 21). One explanation provided by the authors is that the effect is due to the bulk of cash flows occurring at the end of the month (salaries, interest payments, etc.). The study suggests that investors, especially those making regular purchases, may benefit by investing prior to the turn of the month.

C. Day-of-the-Week (Weekend) Effect

The day-of-the-week effect is the unequal daily mean return observed for financial securities. Monday has been shown to be the “worst” performing day, as the returns on Monday for U.S. stocks tend to be below the norm for the other days of the week. Fields (1931) is credited with the first study documenting this “weekend effect”, at a time when stocks were traded on Saturdays.8 Several early studies such as Cross (1973), French (1980), Gibbons and Hess (1981), and Keim and Stambaugh (1984) have shown that U.S. returns on Monday are worse than other days of the week. Furthermore, Cross (1973), Keim and Stambaugh (1984) and Lakonishok and Smidt (1988) have found higher stock index returns occurring on Fridays. Harris (1986) examines intraday trading for stocks on the New York Stock Exchange and find that the day-of-the-week effect tends to occur in the first 45 minutes of trading as prices fall on Monday; on all other days prices rise during the first 45 minutes. The day-of the-week anomaly has not been traded out of the market and has perpetuated into recent periods, with Chang, Pinegar and Ravichandran (1998) confirming the persistence of this effect for the United States stock market into the 1990s.

The day-of-the-week anomaly is not restricted to the United States market—Jaffe and Westerfield (1985) discover a similar but not identical effect in Australia, Canada, Japan and the United Kingdom. One difference is that the lowest mean returns are not evident on a Monday but a Tuesday for Australia and Japan. The conventional explanation for this is that it represents a flow-through of the Monday effect from the United States to these markets. The authors find that the United States market is particularly important in its influence on the Japanese market, and the influence is strongest on Mondays. Other studies have confirmed the widespread nature of the day-of-the-week effect for international markets, namely, Chang, Pinegar and Ravichandran (1993), Agrawal and Tandon (1994) and Dubois and Louvet (1996). Generally, lower returns tend to occur on Tuesday and higher returns on Friday in the European markets.9 More relevant for our purpose, studies on the Asia-Pacific region confirm the trend of lower Tuesday and higher Friday returns.10 Several arguments have been put forward to explain the day-of-the-week effect, namely: (i) the existence of a settlement effect;11 (ii) information release; (iii) measurement error; (iv) trading behavior of institutional/individual investors; (v) interaction with other calendar anomalies; and (vi) simply a reflection of the moods of participants in the market. However, it has been argued that while the day-of-the-week difference is substantial, it is often virtually impossible to take advantage of this because of trading costs (Chen, Kwok and Rui, 2001; Jacobs and Levy, 1988).

D. Holiday Effect

The holiday effect causes higher-than-normal returns to be observed around holidays, mainly in the pre-holiday period. Lakonishok and Smidt (1988) find that roughly half of the gain in the Dow Jones Industrial Average occurs during the 10 pre-holiday trading days in each year. Using equal- and value-weighted portfolios for the United States stock market, Ariel (1990) shows that over one-third of the positive returns each year are made in the eight trading days prior to a market-closed holiday. This clearly suggests that the frequency of pre-holiday positive return days are significantly higher than the frequency of positive return days for all the other trading days over the period. Cadsby and Ratner (1992) show evidence of significant pre-holiday effects for a number of stock markets, with the European markets being the exception.12

Two possible explanations for the holiday effect are presented by Fabozzi, Ma and Briley (1994). The first is that the effect may be part of the other seasonalities that have already been documented. This is pertinent in situations where holidays occur primarily on specific days of the week or in specific periods such as the beginning or end of the month. This means that a vital part of ascertaining whether there is truly a holiday anomaly is to eliminate the possibility that the holiday is capturing other calendar effects. The second explanation is that the higher pre-holiday returns are a result of a positive holiday sentiment. This occurs when people look forward to the holiday period, are optimistic and focused on non-work activities, and hence are reluctant to trade or close out positions on stock that they hold.13 Interestingly, existing U.S. evidence shows that it is only on public holidays, when the exchange is closed, that significant pre-holiday abnormal returns occur.

Chan, Khanthavit and Thomas (1996) consider the holiday effect within a cultural context for the stock exchanges of Malaysia, Singapore, India and Thailand. They find a stronger holiday effect around cultural holidays, compared to state holidays with no cultural origin. Notably, the Kuala Lumpur, Singapore and Bombay stock exchanges all show significant, positive abnormal returns around cultural holidays. Cadsby and Ratner (1992) and Yen and Shyy (1993) find that cultural holidays, such as the CNY, are related to economically significant abnormal returns in Hong Kong, Japan, Malaysia, Singapore, Korea and Taiwan Province of China. Their findings point to the existence of a “cultural effect” within the holiday effect, at least in Asian stock markets.

III. Institutional Aspects of Chinese Stock Market

A number of unique institutional aspects are apparent in the Chinese stock market. These unique factors make the analysis of seasonalities within this market a valuable and useful exercise. Several studies have described the unique characteristics of the Chinese markets in some detail, notably, Ma (1996), Chui and Kwok (1998), Mookerjee and Yu (1999), Xu (2000), Chen, Kwok and Rui (2001) and Chen, Lee and Rui (2001). The two main institutional aspects pertinent to our study are: (i) the closed nature of the Chinese A stock markets; and (ii) the segmentation of the stock market into A- and B-shares.

The Chinese stock market had previously operated under tight capital controls, with restrictions on foreign investment in the domestic A stock market. This has recently started to change, with China’s accession to the World Trade Organization in December 2000; the opening of the B stock market to domestic investors with hard currency holdings from February 2001; and the implementation of the Qualified Foreign Institutional Investors (QFII) scheme in December 2002, which enables foreign investors to invest in the A stock markets. However, the market has remained largely insulated and free from foreign influence.14 Importantly, some 70 percent of shares are still held by the government, state-owned enterprises (SOEs) and Chinese institutions, and are non-tradable, so the effective free-float of the shares is low. This has restricted the number of shares available to China’s domestic investors and has resulted in artificially strong demand for shares in domestic companies. The strong demand has been further fuelled by the strong increase in economic wealth (GDP), together with the high savings rate of the population and limited viable alternative investment opportunities.15 Thus, we are able to assess seasonalities within the context of a “segmented” market, with trading restrictions. This is important, given that one explanation offered in previous research documenting a Tuesday day-of-the-week effect in Asia-Pacific markets has attributed this effect to a spillover from the United States. The insular nature of China’s A stock market means that price movements may not necessarily be influenced by short-term U.S. stock market performance.16

The second institutional aspect of relevance is the difference between the class A- and B-shares. Up until February 2001, individual Chinese residents could only hold domestic currency A-shares, with hard-currency B-shares restricted to foreign investors, who tend to be institutional investors. Several other features of the segmentation between the two markets follow: First, the settlement time for A-shares is within one day of the transaction (t+1) whereas B-shares require three days (t+3) for settlement. As a result, the B-share returns on Friday should be higher to compensate for the additional delay in receiving shares purchased on Friday. Correspondingly, there is no reason to expect the returns to be lower on the Monday for B-shares under a settlement explanation (Chen, Kwok and Rui, 2001). Second, B-share foreign investors tend to have access to more timely information sources on these companies though established media and the research of private sector analysts. Third, the B stock markets are much smaller, less liquid and have become increasingly more volatile in recent years. It could thus be argued that the segmentation between the A and B stock markets has accentuated the differences in performance between the two markets. The possible result is the observation of different seasonal effects between the two different classes of shares with investors of different sophistication and culture.

IV. Data and Research Method

In this study, three different variables are used to analyze seasonalities, namely, the share price return, volatility and market liquidity. The daily data are sourced from the China Stock Market and Accounting Research (CSMAR) database.17 We include the data from the start of each market to December 2002, as follows:

  • Shanghai Stock Exchange A-shares over the period December 19, 1990 to December 2002;18

  • Shenzhen Stock Exchange A-shares over the period April 3, 1991 to December 2002;19

  • Shanghai Stock Exchange B-shares over the period February 21, 1992 to December 2002;

  • Shenzhen Stock Exchange B-shares over the period March 3, 1992 to December 2002.

The indices are all published by the respective stock exchanges and are value-weighted, which means that there is no bias towards small stocks that could magnify any potential seasonal effects. The slightly different period span for each dataset is not an issue, as we test each market individually, with no cross-linkage. Rather, our main concern is to maximize the number of observations for the relatively “young” stock market.

A. Share Price Returns

The (close-to-close) return at time t, RC,t, is measured in continuous form as the relative difference in the various index value between time t and t-1:

RC,t=ln(IC,t/IC,t1),(1)

where IC,t is the closing index value at time t.

The different calendar effects are identified as follows: We calculate the open-to-close, close-to-close and equally-weighted (as opposed to value-weighted index returns) for all effects. For the January (turn-of-the-year) effect, we compare the January average return with the average of the non-January months. For the half-month effect, we use a similar approach to Ariel (1987), namely to define a “trading” month as the period from the last day of the previous calendar month (inclusive) until the last day of the current calendar month (exclusive). The first-half of the month is then represented by the first 9 days of the trading month, and correspondingly, the last-half would be the last 9 trading days. We use 9 trading days to prevent any overlap for those months that have fewer than 20 trading days. The average number of trading days in the month is 20.7 for both Shanghai and Shenzhen. For the months that have more than 18 trading days, the odd remaining middle days are not included in the classification of the first- or last-half-month. The open-to-close returns are specifically relevant for the day-of-the-week effect, to identify the overnight/weekend effect, relative to the actual returns during the market open period (see below).

To capture the holiday effect, the three days prior to and after each holiday are identified. The three-day pre-holiday period is then compared to (i) the three-day post-holiday period; and (ii) all other daily observations (excluding the three-day post holiday period). In terms of identifying the “holiday” period, the actual date of the observance is not included as part of either the pre- or post-holiday period. Some other points are worth mentioning concerning holidays. For the CNY from 1994, the National Day from 1999 and Labor Day from 2000 onwards, the official holiday periods differ from the “unofficial” holiday periods, during which the stock exchanges were also closed.20 The extended nature of the holiday period may induce higher pre-holiday returns. Another interesting item is that up until the year 2000 only the Shenzhen B stock share market was closed for Easter and Christmas, in order to suit overseas participants. In the same vein the Shenzhen B stock market did not trade on the Mid-Autumn Festival, the Dragon Boat Festival and the Clear Brightness Festival days up to and including the year 2000; many of the overseas investors in this market were based in Hong Kong Special Administrative Region, bordering the Shenzhen Special Economic Zone, where these are official holidays. This practice was discontinued in 2001, and the Shenzhen B stock market now observes only official national holidays in China. Thus, we confine our main analysis of the holiday effect only to national holidays and observances, as shown in Table 2.

Table 2.

List of Public Holidays and Non-Holiday Observances in China, 1991–2002

article image
Note: P.L.A> denotes the People’s Liberation Army.

The Chinese Lunar New Year (CNY) is also considered an auspicious cultural festival. The stock exchanges have usually been closed for a whole week or longer for the CNY from 1994, the National Day from 1999 and Labor Day from 2000.

Dates for the Chinese cultural festivals are obtained from the lunar calendar and then converted using the converter at http://www.mandarintools.com/calconv.html. The Tuen Ng Festival is held on the fifth day of the fifth lunar month. The Mid-Autumn Festival falls on the fifteenth day of the eighth month. The official observance of the Mid-Autumn Festival falls on the following day since the festival starts in the evening.

The Clear Brightness Festival, which is not considered an auspicious festival, is held on the third minor term in early April. It falls on April 4 in a leap year, otherwise on April 5. The Hungry Ghost Festival falls on the seventh month of the Lunar New Year.

B. Volatility and Liquidity

Different measures of volatility and liquidity are used to ensure that the results are robust to different estimators of volatility and liquidity. Some authors (Parkinson, 1980; and Garman and Klass, 1980) have criticized the efficiency of the conventional estimator if we assume the financial series is a continuous random walk. Accordingly, to estimate volatility, we initially use the mean squared (i) deviations of return, (ii) deviations of high-low index values; and (iii) the deviations of high-low relative to open-close or close-to-close index values, as the case may be. However, given that the measures are largely consistent, we only report the results of the conventional measure of standard deviation. The mean squared deviations of (closing) returns are calculated as follows:

σD2=1(n1)t=1n(RC,tR¯C,t)2,(2)

where R¯C,t=1nt=1n(RC,t) and RC/t is as defined in equation (1) above. Similarly, we also use different measures of liquidity: (i) the daily volume, that is, the number of shares traded at time t, Volt and (ii) the dollar amount of turnover at time t, Valt. However, these measures often contain time-related dependence, so it is natural to assume that a time-varying increase in volume and turnover would occur for these markets as they mature. On this basis, we explore and allow for the potential time trend effects in the daily returns, as well as in the volume and volatility.

A number of salient reasons exist as to why we examine volatility and volume in addition to returns: First, some evidence already exists to suggest that volatility differs across the weekdays (Xu, 2000); Farbozzi, Ma and Briley (1994) consider volume effects in relation to holidays. Second, there is some interaction between volume, variance and returns (Chen, Kwok and Rui, 2001). Finally, the approach adds insight in that it helps to explain trading behavior. The differences in returns for the calendar effects may have a trading explanation as evidenced by volatility and volume. Volatility reflects the uncertainty of the value (Agrawal and Tandon, 1994) and volume reflects the extent of disagreement among traders about the value, as well as indicating liquidity. For the longer time period seasonalities, the close-to-close returns are the returns of prime concern.

An examination of the daily return series, as well as the smoothed return series using the 90-day moving average for both A and B markets (Figure 2), reveals some dependence on past observations, but not markedly so. No constant overall trend is apparent. However the volume and dollar value of turnover (Figure 3) show a more discernable time series trend. The trend is partly related to the movement over time itself, as reflected in the third-order polynomial trend line. It is more accurately represented by a 90-day moving average that captures the medium-term dependence in relation to past and future values. The 90-day moving average further captures the cyclical movement in a more comprehensive way as is evident for both the A- and B-shares, and for volume and turnover alike.

Figure 2.
Figure 2.

Shanghai and Shenzhen Stock Markets: Daily Returns from Start of Market to December 2002

(In percent)

Citation: IMF Working Papers 2006, 004; 10.5089/9781451862645.001.A001

Source: CSMAR
Figure 3.
Figure 3.

Shanghai and Shenzhen Stock Markets: Daily Volume and Turnover from Start of Market to December 2002

Citation: IMF Working Papers 2006, 004; 10.5089/9781451862645.001.A001

Source: CSMAR

Given the above observations, we use a standardized abnormal volume and value of turnover. The abnormal volume/turnover is measured using the daily volume/turnover value relative to the 90-day moving average centered on the day of interest and standardized by the standard deviation of volume/turnover over the same 90-day period. The standardized abnormal volume (AVolt) at time t is then represented as follows:

AVolt=(VoltMAVol¯t)σVolt,(3)

where MAVol¯t=1nt=45,t045Volt and σVolt2=1(n1)t=45,t045(VoltMAVol¯t)2. The standardized abnormal dollar value of share turnover (AValt) is calculated in exactly the same manner except the dollar turnover is used in place of the share volume. Effectively, this compares the volume/turnover for any given day relative to the immediate surrounding period as indicative of normalized volume/turnover, and scaled by the standard deviation. This approach prevents any bias that may occur when extreme values are coincidently concentrated in certain periods of time simply because of high or low levels of market activity (as evident in Figure 3), and accordingly manifesting in differences across the various calendar periods examined. It also prevents a small number of extreme absolute values from dominating the analysis. It further allows for increases in normal volume and the dispersion changes in volume that occur over time, as has happened in the Chinese markets (Figure 3).

C. Other Measurement Issues

Rogalski (1984a) and Connolly (1989) raise a number of measurement/econometric concerns in relation to studies of calendar anomalies, which is incorporated into our research method:

(i) The use of large sample sizes and non-normality of index returns can distort the interpretation of traditional test statistics, as the significance level of these tests (e.g., t- and F-statistics) is frequently overstated. As a result, we use non-parametric statistics to test for mean-rank (mean) differences, since these tests do not rely on the assumption of normality.

(ii) Outliers may unduly influence and/or bias the measures of average return, and lead to erroneous conclusions. In order to isolate any such effect, we carry out additional tests on median differences as well as the mean differences. Since the median represents the most likely observation in the distribution, it is less likely to be influenced by extreme observations compared to the mean (arithmetic average).

(iii) Since a substantial portion of the returns for the day-of-the-week effect, especially Monday, appears to be related to the overnight or weekend non-trading period (Rogalski, 1984a), we rework the data using the opening index value to calculate the return, in order to test for this possibility. The open-to-close return at time t is correspondingly calculated as:

RO,t=ln(IC,t/IO,t).(4)

(iv) The anomalies may be inter-linked. For instance, Rogalski (1984b) notes that the day-of-the week effect may be related to the January effect. Equivalently, the day-of-the-week effect may be related to the half-month effect. Similarly, the holiday effect may well be subsumed within the day-of-the-week effect, and/or the other two effects mentioned previously. In order to control for these interactions, we use a similar but not identical method to Fabozzi, Ma and Briley (1994) to de-seasonalize or remove the “other” mean seasonal effects. We remove the January effect and the half-month effect to evaluate any “remaining” day-of-the-week effect; and the January, half-month and the day-of-the-week effects are removed to evaluate any remaining holiday effect. Since it is also possible that the January effect and/or half-month effect are driven by each other or by the day-of-the-week effect, these other effects are also estimated and removed. Given that we have also documented a fluctuation in returns across years (see Table 2), these differences are further controlled for. The following regression is to test for the January residual effect:

RC,t=α+i=111λiYeari+n=14γnDoWn+εJan,t;(5)

the next regression identifies the half-month residual effect:

RC,t=α+i=111λiYeari+k=111γkMnthk+n=14γnDoWn+εHM,t;(6)

the corresponding day-of-the-week residual effect is as follows: 21

RC,t=α+i=111λiYeari+k=111γkMnthk+εDoW,t;(7)

the holiday residual effect is determined in a similar manner as the turn-of-the month effect:

RC,t=α+i=111λiYeari+k=111γkMnthk+n=14γnDoWn+εHol,t,(8)

where Yeari (i = 1,…, 11) is the year dummy which takes the value “1” for year i (1992–2002) and “0” otherwise; Mnthk (k = 1,…, 11) is the month dummy which takes the value “1” for month k and “0” otherwise; and DoWn (n = 1,…, 4) is the dummy which takes the value “1” for day n and “0” otherwise. For the B-share returns, there are only 10 dummy variables rather than 11 as the Shanghai B-shares only begin trading on February 21, 1992 and the Shenzhen B-shares on the March 3, 1992. Testing for the January, turn-of-the-month, day-of-the-week and holiday effects are carried out using εJan,t, εHM,t, εDoW,t and εHol,t, respectively. Once again, we apply non-parametric tests to identify any remaining and appropriate seasonality in the residuals. In other words, the above regressions are equivalent to simply removing the “other” mean effects of the individual days, months, turn-of-the-month periods, and then testing the residuals.

V. Results

Visually, the January effect does not appear evident for both B stock markets, as well as the Shenzhen A stock market (Figure 4). Rather, returns tend to be sharply higher in February, compared to January, suggesting the possibility of a “February effect instead (see discussion in Section V.A). From Figure 4, we see that the mean daily returns for both the B stock markets, as well as the A stock markets, are generally higher in the first-half of the year, from February to June. This suggests the existence of a half-year effect. In the meantime, mean returns for the Shanghai A-shares have been largely positive throughout the 12 months of the calendar year, interspersed with small positive or negative returns.

Figure 4.
Figure 4.

China Stock Markets: Mean Daily Close-to-Close Returns by Month, January 1993 to December 2002

(In percent)

Citation: IMF Working Papers 2006, 004; 10.5089/9781451862645.001.A001

Based on the preceding discussion, we test for the existence of (i) the January or February effect; (ii) the half-year effect; (iii) the half-month effect; (iv) the day-of the week effect; and (v) the holiday effect, in this section. In the first sub-section, we first consider the different seasonalities from the raw returns, as described in equations (1) to (4), which do not take into account the possibility of, nor allow for, any interaction between the effects. The results are presented in Table 3 in five panels—one for each seasonal effect. This is followed in the second sub-section, by an analysis of residual returns obtained from equations (5) to (8), in Table 4. The third sub-section examines the holiday effect in greater detail. Unless specifically stated, we only consider a result “significant” when it is at the 5 percent level, or less.

Table 3.

Unadjusted (Raw) Returns from Start of Market to December 2002

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Notes:Mean Returns: Kruskal-Wallis non-parametric test for equality of means between groups. Direction of Kruskal-Wallis tests (+/-) are based on mean-rank differences between groups.Median Returns: Median non-parametric test for equality of medians between groups. Direction of Median tests (+/-) are based on median differences between groups.Significance levels (in parentheses) for tests of equality of returns are based on one-tailed tests.Standard Deviation: Levene test based on ANOVA for equality of variances between groups. Direction of Levene tests (+/-) are based on differences in standard deviation between groups.Liquidity: Kruskal-Wallis non-parametric test for equality of means between groups.Significance levels for tests for standard deviation and liquidity are two-tailed as for most instances there is no directional expectation.For the January or February (turn-of-the-year) effects, the January average is compared with the average of the non-January months.For the half-year effect, the first-half of the year is defined as February to June, and the secfond-half is defined as July to November. The other two months are not included in the definition of either.For the half-month effect, the first-half of the month is represented by the first 9 days of the trading month, and the second-half by the last 9 trading days. For the months that have more than 18 trading days, the odd remaining middle days are excluded from the first- and second-half definitions.For the holiday effect, three days prior to and after each holiday are identified. The three-day pre-holiday period is then compared to (i) the three-day post-holiday period; and (ii) all other daily observations (excluding the three-day post holiday period). The actual date of the observance is not included as part of either the pre- or post-holiday period.
Table 4.

Adjusted (Residual) Returns, from Start of Market to December 2002

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Notes:Mean Returns: Kruskal-Wallis non-parametric test for equality of means between groups. Direction of Kruskal-Wallis tests (+/-) are based on mean-rank differences between groups.Median Returns: Median non-parametric test for equality of medians between groups. Direction of Median tests (+/-) are based on median differences between groups.Significance levels (in parentheses) for tests of equality of returns are based on one-tailed tests.Standard Deviation: Levene test based on ANOVA for equality of variances between groups. Direction of Levene tests (+/-) are based on differences in standard deviation between groups.Liquidity: Kruskal-Wallis non-parametric test for equality of means between groups.Significance levels for tests for standard deviation and liquidity are two-tailed as for most instances there is no directional expectation.For the January or February (turn-of-the-year) effects, the January average is compared with the average of the non-January months.For the half-year effect, the first-half of the year is defined as February to June, and the secfond-half is defined as July to November. The other two months are not included in the definition of either.For the half-month effect, the first-half of the month is represented by the first 9 days of the trading month, and the second-half by the last 9 trading days. For the months that have more than 18 trading days, the other remaining middle days are excluded from the first- and second-half definitions.For the holiday effect, three days prior to and after each holiday are identified. The three-day pre-holiday period is then compared to (i) the three-day post-holiday period; and (ii) all other daily observations (excluding the three-day post holiday period). The actual date of the observance is not included as part of either the pre- or post-holiday period.