We set out to empirically identify the presence of the disposition effect in the Chinese stock markets by evaluating the data of the Shanghai Stock Exchange (SSE) covering the period of 2008 to 2010. The main findings of our empirical analysis are that the investors tend to realise the gains and hold onto the losses longer in the SSE. The A shares market, which is dominated by individual investors, shows the same result, while the investors in the B shares market, which is dominated by institutions, tend to buy past winning stocks and sell past losers. Furthermore, the individual investors are likely to ignore the firm size when they select their average holding periods.
There have been substantial events that have happened throughout the history of stock markets all over the globe that cannot be explained by the neoclassical economic theory, such as the Great Depression of 1929, the Internet bubble of the 1990s and the recent global financial crisis dating from August 2007. The recent financial crisis has lead to the collapse of large financial institutions, the bankruptcy of government and publicly owned banks, and it has even contributed to the European sovereign-debt crisis. One distinctive feature in all of these events is that the stock prices present a dramatic shift from their fundamentals, which seems to defy the hypothesis of traditional finance models. Investors are considered as rational individuals or institutions and tend to force the capital market prices equal to the present value of the sum of future dividends in the standard financial theory, implying that the prices are random walking and show the tendency of mean reversion. However, such models ignore the sentiment of investors. Investor behaviours show bounded rationality due to psychological bias when it comes to making investment decisions. Therefore, researchers have been working to offer an alternative model which includes the cognitive process, behavioural finance theory.
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Nowadays, there is no doubt that investors' sentiment, such as overconfidence, conservatism and representativeness, have a significant impact on asset prices and the question now becomes how to measure the effect and to what extent this impact is. Generally speaking, there are two approaches to demonstrate this question. The first one is 'top down' and macroeconomic. This method takes the investor sentiment as an exogenous variable and explains the unusual and abnormal daily patterns in the markets in a very simple and well-understood way. Baker and Wurgler (2007) claim that it is feasible to measure investor sentiment and that waves of sentiment are of importance in affecting the whole share market and the individual companies. In more specific terms, the stocks that are likely to be disproportionately affected by investor sentiment are those from small and instable start-up firms and it is difficult to value or arbitrage them. The second methodology, by contrast, is 'bottom up' and microeconomic, in which scholars aim to provide micro-foundations to 'top down' and show how investors misprice the stocks by overreacting or under-reacting to past market capitalisation and fundamentals. Furthermore, they make models to forecast the future stock volume and price based on the investment behaviours. Shefrin (2005) draws a conclusion that the stock mispricing is related to the short sales limitations.
In this paper, one effect of the investor sentiment, the disposition reaction, is examined. Recent research indicates that investors tend to sell the assets on which they have been enjoying gains on during the past period due to their attitude of risk aversion, while they are likely to hold the assets on which they have been experiencing losses in the past several days owing to a redundancy to admit losses. The particular reasons why investors show totally different reactions when faced with gains and losses will be discussed in detail in the following section. The disposition to sell winners too early and to ride losers too long is defined as the disposition effect by Shefrin and Statman (1985). In this paper, the disposition effect is investigated by analysing the relation between average holding periods of stocks and their past returns. In particular, utilising daily data of Chinese stocks covering the period 2008 to 2010, this study uses the methodology adopted by Visaltanachoti et al.(2007) to construct a two-stage least square regression model containing average holding periods, annual returns, liquidity and volatility of the assets and the firm size. We extend the approach of Visaltanachoti et al. (2007) in a comprehensive way, through updating the data in order to consider the effect of the recent financial crisis and introduction of the impact of firm size on individual investors' behaviour. Three specific issues are discussed in this article: (i) Does the disposition effect exist significantly in the Chinese stock markets? (ii) If we get a positive result in (i), then is there a difference between when individuals and institutions make investment decisions? (iii) Furthermore, what about the shares of big publicly listed firms and those of a small size from individual dominated markets in terms of the disposition effect?
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The findings in this article are expressed as follows. Firstly, there is a strong tendency in the Chinese stock markets to realise gains and hold onto losses, consistent with the study of Feng and Seasholes (2005). Secondly, individuals and institutions tend to make different investment decisions. The individual customers are likely to sell their winning stocks sooner and keep their losing shares longer, while the institutional investors will perform according to the neoclassical theory through selling losses and holding onto winners. Chen, Kim, Nofsinger and Rui (2007) take a further step to integrate the trading experience and investors' behaviour. Finally, the firm size seems to have no impact on the decision of individual investment. This result is different from that of Kumar (2009), who claims that the disposition effect is stronger for stocks with lower market capitalisation.
The remainder of this paper is organised as follows. Section II reviews the related literature to analyse the theoretical reasons of the disposition effect and compare the empirical results from different countries. Section III describes the data and the Chinese stock markets so that it can be clearly seen how the author makes groups based on the status quo of China. Section IV provides the methodology of the definition of the variables and the link between them. Furthermore, it shows a table of summary statistics and gives an overview of the stock market in China. Section V makes an attempt to answer the three issues alluded to at the end of last paragraph, the disposition effect in Chinese stock markets as a whole, between the individual and institutional investors, and between the publicly listed 'mega-cap' firms and those with a relatively small size. Section VI offers some concluding remarks and recommendations for future research.
2. Literature review
The Prospect Theory by Kahneman and Tverskey (1979) has been a hot issue in recent years and a large number of empirical analyses have been conducted on the basis of it around the whole world due to the increasing number of abnormal price trends and unusual and unexplained events in the financial markets. Together with the Mental Accounting theory by Thaler (1985), they constitute the fundamental theories in behavioural finance and have successfully explained some anomalies in stock markets.
One major and distinctive feature in Prospect Theory is that it replaces the utility function with value function, which presents as an S-curve in the diagram below, with the x axis representing the gains or losses and the y axis demonstrating the value of assets or portfolios. The origin refers to the reference point. It is shown clearly in Diagram 1 that the value function is a concave curve in the area of gains and a convex one when it comes to the losses. The shape of this curve is mainly attributed to the different attitudes when the investors are faced with losses and gains. Generally, the individuals are risk avoiding when they are enjoying gains and risk seeking when they are suffering losses (Kahneman and Tverskey (1979)). Furthermore, the reference point plays an important role in deciding the gains or losses. The total wealth is not considered any more. By contrast, the investors compare their wealth of the status quo with the past level to decide whether they are gaining or losing. However, the standard to choose a reference point is subjective and is affected by a variety of aspects of the investors. At present, there is not a unified methodology to compute the reference point, which offers a large number of possibilities to carry out further research. Odean (1998) calculates the reference point utilising a function of past returns with the same weight. The proxy in the article of Weber and Camerer (1998) is two different accounting principles--the "first in, first out" (FIFO) principle and the "last in, first out" (LIFO) principle.
One prevailing explanation of the disposition effect refers to the prospect theory and, in particular, to the asymmetric risk seeking. Shefrin and Statman (1985) hold the opinion that the investors are reluctant to admit their losses and feel painful for the regret caused by their inability to make correct investment decisions. They, therefore, tend to have their observations of stock returns in detail and postpone realising their losses. Furthermore, it is suggested by Kahenerman and Tversky (1979) that loss aversion will lead to regret aversion directly, which makes the investors believe firmly that the optimal portfolio selection is one decision by which they can minimise their regrets. However, there is still debate on this issue. Thorsten and Vlcek (2011) point out the contradiction that those investors who realise gains faster and hold on to losses longer would not have invested in assets in the first place, while the normal prospect theory is based on the past value of the parameters, which means that the investment has to be made in the first place. Another explanation lies on the rationale that the investors hold the belief that systematic price reversals for stocks exist in the long-term time. De Bondt and Thaler (1985 and 1987), utilising the Centre for Research in Securities Prices (CRSP) monthly return data, found that, consistent with the behavioural hypothesis of investor overreaction, past losers outperform past winners and further evidence is shown in their follow-up paper by comparing with two other alternative hypothesis including the firm size and risk betas. Shefrin (2001) analyses the psychology of investors and concludes that individuals appear to form judgements inconsistent with the standard modern finance theory: the relation between returns and risk is negative, implying that a safer stock is expected to have a higher return. Weber and Camerer (1998) deny mean reversion in an experimental way, although being in favour of the disposition effect.
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Substantial evidence has shown that the disposition effect exists around the whole world. For instance, Grinblatt and Keloharju (2000) analyse the extent to which past returns determine the propensity to buy and sell using the unique data of Finland; Locke and Mann (2005) show that the behaviour of full time traders are consistent with the disposition effect in the stock markets of Chicago; Brown et. al. (2006) analysed a large sample of daily data from the Australia Stock Exchange share market for investors in IPO and index stocks over the period 1995 to 2000 and concluded that investors across different classes all appear to hold onto losses and were eager to realise gains; the same result is also obtained in Asian countries, like the evidence from Hyuk and Yunsung (2009) in the Korean stock index futures market.
Though there is the belief in the presence of irrational trading from investors, such as riding losses and selling winners, different conclusions are seemed to be reached when further detailed examinations are carried out. For example, Grinblatt and Keloharju (2000) suggest that after some factors, like trading style, are controlled for, Finnish retail investors turn out to be reluctant to sell winners, which is inconsistent with the result of Odean (1998). They also distinguish the behaviour from professional traders and individual investors and claim that the foreign institutional investors tend to outperform the domestic retail customers by reducing the disposition effect (Grinblatt and Keloharju (2001)). Generally speaking, the inexperienced, less knowledgeable and frequently trading individual investors show a stronger tendency to hold onto assets which have lost values in the past and sell assets which have gained, while the proficient, professional and relatively sensible institutional traders make investment decisions based on the past realised returns and are more likely to engage in herding. Odean et al. (2007) found that individual investors exhibit the bias--sell investments that are held for a profit at a faster rate than investments held for a loss, with a large sample from the Taiwan Stock Exchange (TSE), covering all trading and identity of all investors, around one billion and four million respectively over a five year period from 1995 to 1999. On the contrary, institutions, such as mutual funds, exhibit an opposing trading pattern. They are more likely to be momentum investors and buy past winning stocks and sell past losers. What's more, the so-called herding behaviour can be observed among the institutional investors. They tend to move together and find it apt to follow their counterparts. Odean et al. (2007) study the sample from the TSE and conclude that the investment behaviour of foreigners and mutual funds seem to be inconsistent with the disposition effect. Wermers (1999) gives strong evidence of the herding behaviour of trading in growth-oriented funds and trades of small stocks by analysing data from 1975 through 1994.
3. Description of data and Chinese Stock Markets
Before proceeding, it is useful to describe the Chinese Stock Markets. The China Stock Exchange is very different from all other developed and developing countries, especially in government supervision and distribution of investors. At present, there are two stock markets: the Shanghai Stock Exchange (SHSE) and the Shenzhen Stock Exchange (SZSE), established in 1990 and 1991 respectively. The initial purpose to set up the stock market was to serve the economic reform in the 1990s in China, which partly explains the constitution of Chinese investment traders. Two sections were divided rigorously in both two markets from the beginning, while the two markets don't show big differences, except the place and number of publicly listed firms, which gives us the possibility to analyse the Chinese stock markets by investigating data from one stock market. One section issues the so-called A shares and the other section issues the B shares. The A shares are owned domestically and denominated in the Chinese currency (RMB), while the B shares are possessed by foreign investors and denominated in US or Hong Kong dollars. Though it is allowed for local investors to trade in B shares since the beginning of 2001, the high cost of the transaction fee and strict supervision make it difficult to transform the domestic currency to US or Hong Kong dollars, leaving local residents reluctant or unable to invest in B shares. The A shares have been much more frequently and actively traded than B shares. For example, the market capitalisation of A shares were around 10543 billion RMB, accounting for about 99.7% of total market capitalisation during the first seven months in 2012  , which emphasises the underlying impact of the A shares section.
Generally speaking, the A shares market is absolutely dominated by individual investors, while an extremely large number of traders in the B shares market are institutions, which provides a good opportunity to distinguish the behaviour between individual customers and institutional traders and the potential to investigate the contrarian and momentum strategies. Furthermore, around 97% individuals invested less than 500 thousand RMB on the stock market according to a survey of the year 2009  . It indicates that the analysis of A-share market represent an average level of individual behaviour. One basic reason for the individual investor dominance phenomena refers to the initial background of establishing the stock markets indicated as above. As a product of the experiments of economic reform, the uncertainty and inadequate experience confine the presence of institutional investors. Another important factor is due to the limited types of financial instruments, such as the mechanism of short selling, implying that the experts from institutions cannot utilise the financial markets efficiently to make profits. The immediate consequence is a promotion of irrational investing behaviour, owing to the large proportion of individual customers. The typical investors in the A shares market show a lack of professional knowledge and know little about the financial instruments or the operation of the whole stock market. They behave more like speculators rather than arbitrageurs, bidding the prices of assets up in a short time and driving them down quickly. They tend to make investment decisions based on past performances of shares and their own sentiment instead of trying to seek correct and useful information on particular firms, which is inconsistent with the developed countries. The whole financial market is more likely to be affected by the performance of an individual dominating A share market due to the specific characteristics.
As indicated in section I, efforts are made to compare the behaviour of individual investors and institutional traders in this paper. There have been 951publicly listed firms until August of 2012, with 941 A shares issued and 54 B shares issued. We do not analyse the data of all of the companies, we only selected some typical daily data covering the period 2008 to 2010. In particular, 20 B shares were selected from the whole pool covering all industries and 20 A shares were chosen from the SSE 180 Index. SSE 180 is a benchmark index reflecting the Shanghai market and serves as a performance benchmark for investment and a basis for financial innovation by restructuring and renaming the SSE 30 Index in a scientific and objective method. Since the adjustment list for the SSE 180 Corporate Governance Index is reported every half year, the A shares chosen should be included in the SSE 180 during the six periods over the three years 2008 to 2010 and contain all of the five sectors-industrial, commercial, real estate, public utilities and conglomerates section.
What's more, we also aim to investigate the data for both big size firms and small ones from the A shares market and examine whether the market capitalisation and trading value of firms affect the investment behaviour of individual investors when they are faced with gains or losses from stocks. Similarly, we select shares from some typical indices. 15 shares of big firms are chosen from the SSE Mega-cap Index and 15 shares of small firms from the SSE Small-cap Index, covering the three year period ending in 2010. The SSE Mega-cap Index was launched in April, 2009 and consists of 20 of the largest and most liquid stocks traded on the Shanghai Stock Exchange, which aims to comprehensively reflect the price fluctuation and performance of the mega cap enterprises listed on the SSE. By observing the adjustment list announced every six months, we can find that there is not a significant difference in the constitution of the SSE Mega-cap Index containing firms, which makes it feasible to analyse data of 2008, during which year, the SSE Mega-cap Index had not been launched. On the contrary, the SSE Small-cap Index aims to reflect the performance of Small-cap stocks by ranking the market capitalisation and trading value. Its adjustment report is also released twice a year and the 15 shares selected need to be included in the index during the three years. For the analysis of the whole Shanghai Stock Exchange, different size of firms and both types of investors-individual and institutional all need to be taken into account. Seventy shares are selected on the basis of this standard  . All the data we need is from Datastream and the website of the Shanghai Stock Exchange.
4. Methodology and Summary Statistics
There is not a unified and unique methodology to measure the disposition effect. Lakonishok and Smidt (1986) created a relationship between past price changes and current volume and concluded that there are both tax and non-tax related incentives. They claim that the non-tax incentives induce investors to realise gains and to avoid realising losses, thus creating a positive cross-sectional correlation between trading volume in a given month and price changes in past months. Ferris et al. (1988) and Bremer and Kato (1996) agree with this conclusion. Odean (1998) investigated trading records for 10,000 accounts at a large discount brokerage house and measured the disposition effect by calculating proportion of gains realised (PGR) and proportions of losses realised (PLR). The result of this article shows that there is a strong tendency for individual investors to hold losing investments too long and sell winning investments too soon. Feng and Seasholes (2005) defy the methodology of Odean by claiming that the PGR-PLR might become zero of one when one only sells the winning or losing stocks and utilises the Hazard model to prove the presence of the disposition effect. Weber and Camerer (1998) conducted a laboratory experiment of the disposition effect and found that the subjects are around 50 percent more likely to sell the winners rather than the losses, which confirmed the results obtained with field data. Shapira and Venezia (2001) hold the perspective that the holding period of investments is an efficient way to examine the disposition effect-the average holding period for winning investments should be less than that for the losing stocks if the disposition effect exists.
In this study, tax related incentives are ignored, owing to the uncertain and instable tax policy in the Chinese stock markets. The laboratory method is also abandoned, since the subjects are not readily available. We, therefore, used a regression method to assess the disposition effect. This allowed us to control for investor characteristics and market condition. In particular, we tested the disposition effect by analysing the relationship between the average holding period and annual return of a particular stock in five groups of panel data-shares in the SHSE, A shares in the SHSE, B shares in the SHSE, shares of Mega-cap firms in the SHSE and shares of Small-cap firms in the SHSE. By utilising the methodology of Visaltanachoti et al. (2007), we considered the illiquidity, firm size and volatility of returns of one share as the determining factors of its average holding period. In particular, in line with Aktins and Dyl (1997), the average holding period of firm for year is the ratio of the numbers of common shares outstanding in the firm to the value of all trades for the stock on a particular day .
Where is the average holding period on equity for year , is the number of common shares outstanding for stock on day of year , is the respective daily trading value of stock for year and is the total number of trading days of stock in year , which may vary due to some unexpected reasons of a particular stock and need to exclude the number of holidays and weekends.
There are a large number of measures for the liquidity of equities. Due to a lack of micro-foundation data in the Chinese stock markets, we adopted a crude and readily available method to calculate the illiquidity of equities in the Shanghai Stock Market. Following the study of Amihud's (2002), we found that the illiquidity of one stock can be computed by dividing the absolute return of stock by the total trading volume on a particular day. Therefore, for each year , the illiquidity for each firm's stock is measured as follows:
Where measures the illiquidity of stock for year , is the absolute return of the stock on day for year , is the respective daily trading value of stock for year and is the total number of trading days of stock in year .
We estimated the disposition effect in the Chinese stock market in a regression model as follows:
Where is the average time that investors hold a specific stock for the year , is the respective return of stock for year , implies the illiquidity of stock at that year, is the market capitalisation of stock , which signals the size of the firm and computed by the share price timing the number of common shares outstanding, is the volatility of the firm's daily stock returns during year , which can be observed by calculating the variance of its respective daily return and is a dummy variable for A shares, which is used to indicate the absence or presence of A shares in the regression model and takes the numerical value one when there are A shares and value zero when they are absent. We carried out a natural logarithmic transformation for all the variables except the indicator variable and the annual return of stocks, since taking a log of the distribution is a useful way to reduce or eliminate the severe skewness or the heteroscedasticity between variables and still keeps the relationship in the regression function unchanged.
It is worth noting that we could not just use the single ordinary least squares (OLS) in this regression analysis. Recalling the standard OLS, it is assumed that errors in the explanatory variables are uncorrelated with the explained variables. When this is not the case, linear regression using OLS no longer provides the optimal estimated results for the model. In terms of predicting the value of holding periods, the average length of time that traders hold stocks and the respective illiquidity of a particular stock are quite likely to be determined simultaneously after taking their co-determiner-the volatility of the stocks into account. If we still take the illiquidity of equities as an exogenous independent variable, the estimated results will be spurious by showing the character of bias and inconsistency. Therefore, we needed to adopt the two-stage least squares regression. In the first stage, instrumental variables, which are uncorrelated with error terms, were introduced to compute values of the problematic predictors. Then, in the second stage, the computed values obtained above were employed to estimate a linear regression model of the dependent variables. We will get the optimal results from the two-stage regression model, since the computed values are based on variables that are uncorrelated with the errors. In this linear regression function, it is an appropriate procedure to use the illiquidity of one stock for the past year as an instrumental variable. On one hand, the illiquidity for the previous year is in essence highly correlated with the endogenous dependent variable-the illiquidity for this year, conditional on all the other variables. On the other hand, no theoretical rationale or evidence found from the existed literature show that the lagged illiquidity is jointly determined with this year's holding periods  , which indicates that the previous year's illiquidity of stocks is uncorrelated with the error term in the explanatory equation and will not suffer from the same problem as the illiquidity of this year.
Therefore, the first stage estimated model is expressed as follows:
Where is the lagged value of the illiquidity of the stocks for firm over the previous year , and is the respective estimated value for this year. Similarly, we include two control variables in the equation: market capitalisation of stock during this year (), which represents the size of firms and the volatility of stock daily returns over the year (). We then use the new illiquidity for this year estimated in equation 4 to replace the original illiquidity for this year in equation 3 in order to get the optimal estimates.
By defining every variable, we can compute the average length of time that investors tend to hold the stocks for, the average illiquidity of stocks, the market capitalisation of the firms in terms of millions Yuan and the percent variance of the daily common stock return for each year from 2008 to 2010 through the original data. They were then reorganised in Table 1 so that we can get an overview of the Chinese stock markets and compare the different characteristics in different panels. The AVERAGE, MEDIAN and STDEV in the table represent the value of mean, median and standard deviation respectively for the four variables.
In general, the trend of the parameters for A shares seems to be consistent with that for the whole Shanghai Stock Market, which may be a consequence of the large proportion of market capitalisation for A shares among the total stocks. In particular, in terms of the holding periods, there is a big difference between 2008 and 2009, which is likely to suggest the effect of the financial crisis during 2008 driving share prices down sharply. The relatively longer time for investors to hold stocks implies that they are reluctant to sell stocks and tend to hold onto them when they are faced with the loss from shares. The B shares, by contrary, seem not to follow the same pattern as A shares or the whole stock market, with its holding period going up year by year and showing no signal of obvious change. As indicated above, the B shares section in the SSE is dominated by foreign and institutional investors, which provides the potential to explain this through the constitution of investors in different panel data. The distribution of illiquidity for all the five groups of data over the three years is quite unstable and highly skewed. It is shown in the table that the value of standard deviation for illiquidity is relatively large and there is an obvious difference between the average and median of illiquidity. Similarly, compared with the value for the year 2009, the illiquidity for the previous year is higher, which is likely to be a result of the credit crisis as well. The market capitalisation shows a trend of going up over the three years for all the data, which suggests the changing path of the average annual share price owing to a similar level of the number of shares outstanding each year. The average market capitalisation of the publicly listed companies in the Shanghai Stock Exchange was 143,876 million Yuan in 2009, an increase of about 6,000 million Yuan compared with the value for the previous year 2008 (8,534 million Yuan). The respective median market capitalisation increased from 6,208 million Yuan to 120,973 million Yuan during the two year period of 2008 to 2009. A dramatic increase is also shown in the average market capitalisation for the listed firms in the A shares section, B shares section and mega-cap and small-cap enterprises over the two years, though some of them are not as obvious as that of the whole stock market. The volatility of listed firms in the B shares section seems to be slightly less than that of those from the A shares section over the period of 2008 to 2010. At the same time, the equities of small-cap firms seem to be more volatile than those of the mega-cap firms.
Table 1 Summary Statistics
HOLDING PERIODS (DAYS)
SHANGHAI STOCK EXCHANGE
SHANGHAI STOCK EXCHANGE
MARKET CAPITALIZATION (*10^6 YUAN)
SHANGHAI STOCK EXCHANGE
VOLATILITY (% PER YEAR)
SHANGHAI STOCK EXCHANGE
5. Empirical evidence and discussion
5.1 The disposition effect in the Shanghai Stock Exchange
To evaluate the tendency for investors to hold onto losing assets and realise winning assets in the Shanghai Stock Market, we need to estimate the coefficients of Equation 3. The result is shown in Panel A of Table 2 according to a two-stage least squares regression over the period of 2008 to 2010. If we assume a 5% significant level and use a * to denote a significant coefficient, we can clearly see the relationship between the variables by observing their respective coefficients.
The regression coefficients on the annual return of stocks were negative and significant, which implies the presence of the disposition effect in the whole stock market of Shanghai. For example, the value in the year 2008 shows that every unit increase in the annual return of stocks will bring a 1.611 unit decrease in the average holding periods. When the asset return is negatively related with its respective holding period, the investors posses the stocks that have gained during the period for a shorter horizon of time and vice versa. This result is consistent with the existed empirical evidence from a large number of countries as indicated in Section II. The coefficients on the illiquidity of stocks were positive during the three years and significant in the year 2008 and 2010. The values are less than one, ranging from 0.241 to 0.892. It is intuitive and comprehensible to explain the positive relationship between the stock illiquidity and its average length of time for traders to hold. The liquidity of stocks is confined by the transaction cost to a large extent, as a higher cost, especially the bid-ask spread, which is quite likely to restrict investors from trading and induce a lack of liquidity for stocks. It has been widely accepted that the higher the transaction cost, the shorter the time investors tend to hold on to the assets for (Atkins and Dyl, 1997). The regression coefficients on the variable market capitalisation were also positive and significant in each year from 2008 to 2010. The market capitalisation is defined as the share price multiplied by the number of shares in issue, providing a total value for the firm's shares outstanding and can be employed as a proxy for the size of the publicly traded firm. The most significant impact happens in the year 2008, during which time the average holding periods increase 1.875 units with each unit increase in the market capitalisation. The following year, 2009, shows a least significant effect of firm size on the holding periods, which may be a result of the economy recovery. The positive correlation between the market capitalisation and the length of period during which the assets are held suggests that shares from a larger firm are likely to be possessed by the investors for a longer time than those from a relatively smaller company. What's more, the regression coefficients on the volatility were significant in every year and were expressed as a negative value in the year 2009 and 2010, -1.739 and -1.095 respectively. The year 2008 is an exception, showing a positive value of 0.237. Typically, it is assumed that the investors are eager to realise their gains and therefore have a shorter time horizon to hold onto the stocks, when the daily returns on assets are more volatile, which provides an explanation for the negative number of the coefficients on the asset volatility. The exception occurs in the year 2008 when the financial crisis spread all over the world, which may have caused an unusual change in the sentiment of the investors. On the other hand, it may be a consequence of the lack of a large sample. We only investigated the data from around 70 firms of the Shanghai Stock Market in which there are over 900 publicly listed enterprises. The adjusted ranges from a minimum value of 0.21 to a maximum value of 0.59.
The regression results reported here support the presence of the disposition effect in the Shanghai Stock Market in China. The investors tend to sell the assets whose returns are increasing during the past period at a faster rate than the assets whose returns are decreasing.
5.2 The Comparison of the Disposition Effect between A-shares and B-shares
As it has been proved above, the investors in the Chinese Shanghai Stock Market show a strong tendency to hold onto losing stocks and realise gaining equities. Furthermore, we want to analyse the behaviour between individual and institutional investors by comparing the results of the A shares section (absolutely dominated by individual customers) and the B shares section (absolutely dominated by the institutions) in the Shanghai Stock Market. The same two-stage least squares regression model is applied here. The results are reported in Panel B and Panel C of Table 2, which represents the individuals and institutions respectively.
The regression results in the A shares section in the SSE are similar to that in the whole SSE with some exceptions. For example, the regression coefficient on the illiquidity of stocks showed a negative value of -0.438 in the year 2008 and was not
Table 2 Disposition Effect on the SSE, A-shares and B-shares
Panel A: Shanghai Stock Exchange
Panel B: A shares
Panel C: B shares
significant in the year 2010. The remaining regression coefficients provide robust evidence for the hypothesis we have obtained in the analysis of the Shanghai Stock Market. For instance, the firm size had a positive effect on the average holding periods. The volatility of stock returns negatively affected the holding periods and the absolute value of coefficients showed a decreasing trend from 1.318 to 0.572, indicating a smaller part of changes in average holding periods which can be explained by the changes in the variance of stock returns. The figures ranged from 0.29 to 0.42. This result shows that the individual investors possess the psychological biases-- reluctant to admit their inability in investing by holding onto the losing assets and eager to realise their gains in the stock market. Most of the individual traders in China have little professional knowledge in the economic realm and possess insufficient trading experience, which forces them to follow their own judgement (usually irrational), even the rumours in the stock market, rather than searching the fundamental information of particular firms. When they are faced with the losses from shares in the market, they are likely to show a tendency of regret reversion and the only way for them to retain pride is to insist on holding the assets until they are re-gaining. There are a large number of other heuristic biases in the behaviour of the individual investors in the Chinese stock market, such as the anchoring effect, overtrading and so on, which is an interesting topic to conduct further research on.
On the contrary, it can be clearly seen from Panel C of Table 2 that investors in the B shares section in the SSE (dominated by institutions) show a different performance when it comes to the return of assets. The regression coefficients on the asset returns were still negative values during the three year period of 2008 to 2010 (-1.002, -1.387 and -0.651 respectively). However, they were not significant at a 5% level in the year 2008 and 2009. The regression coefficients on the explanatory variable illiquidity of stocks were only significant in the year 2008, with the values less than one. Since we have carried out a two-stage least squares regression by introducing the instrumental variable--the lagged illiquidity of stocks in order to eliminate the skewness, this insignificant result will not have been caused by the incorrect character of the error term. A further study of a large sample (such as the B-shares in the whole of the Chinese stock markets) over a longer period (like ten years or more) would need to be conducted to test the unsatisfactory consequence. The regression coefficients on the market capitalisation and the volatility seem to follow the same pattern with that of the stocks in the A shares section and in the SSE. The absolute value of coefficients on the volatility in the B-share section are about 50 percent less than that in the A-share section, which indicates that the volatility had a less impact on the average holding periods in the B-share market. The figures ranged from 0.24 to 0.56. This ambiguous result indicates that the institutional investors may not show a strong tendency to realise gains and stick on losses in the Chinese stock market. They tend to make investment decisions based on the past prices and sell the losing stocks as soon as possible to make profits. Odean (2007) found that the mutual funds are not only the momentum investors, selling the losing assets and keeping the winning shares but also engaged in herding.
In conclusion, the individual investors in the Chinese stock market exhibit a tendency to realise gains and hold on to losses while the institutions make adverse investment decisions. This result is in line with the existing study of other countries (Grinblatt and Keloharju 2001, and Odean 2007). Furthermore, if the individuals tend to make contrarian investment decisions and the institutions are likely to be momentum investors, will they make profits by choosing an opposite pattern or can only one of them make the optimal portfolio selection? This question can be further discussed in other studies.
5.3 The Comparison of Disposition Effect between the Mega-cap and Small-cap Firms
Firstly, we got the evidence that the disposition effect existed in the Chinese Shanghai stock market over the three year period of 2008 to 2010. Then, it is shown that only the individual investors exhibit a tendency to hold onto the losses and realise their gains, while the institutions tend to make absolutely opposite investment decisions. Furthermore, we want to analyse whether the size of firms have an effect when we estimate the relationship between asset returns and the average time of holding stocks for individual investors.
We investigated the daily data of fifteen firms included in the mega-cap index and fifteen firms contained in the small-cap index in the SSE during the three years from 2008 to 2010. The regression model is as follows after controlling the size of the firm:
where is the average length of time that the traders hold a specific share for the year , is the respective return of share for year , is an indicator of
the illiquidity of share at that year and is the volatility of the firm's daily stock returns during year , which can be obtained by computing the variance of its respective daily return. A natural logarithmic distribution was carried out for all the variables except the annual return of stocks, in order to reduce or eliminate the severe skewness or the heteroscedasticity between variables.
Similarly, we employed the two-stage least squares regression by introducing the illiquidity of the previous year as an instrumental variable. There was no theoretical foundation or evidence found from field data based literature that the previous year's illiquidity is jointly determined with this year's holding periods. What's more, the lagged illiquidity is highly correlated with this year's illiquidity. These two characteristics of the illiquidity of the previous year allowed us to use it as the instrumental variable in the regression method. The first stage regression equation is expressed as follows:
where all the parameters have the same economic implications as listed above.
The regression result is reported in Table 3 with two groups of data during the three years ending in 2010. We also needed to estimate the coefficients of each variable to evaluate the disposition effect. We also constructed a 95% confidence interval to reflect the reliability and employed a * to denote the significance of a parameter.
It is shown in Table 3 that both regression coefficients on the returns of the stocks of firms in the mega-cap index and in the small-cap index were negative and significant over the three years from 2008 to 2010, with the exception of an insignificant prediction for the shares of firms contained in the mega-cap index in the year 2010. These results suggested that when individuals make investment decisions, they tend to treat the big and small firms as the same in terms of the average length of time to hold the shares--the preference to sell the assets whose returns have increased in the value during the past period and keep the stocks whose returns have decreased in the value exists both in the shares of big and small firms. In particular, the absolute values of coefficients on returns possessed a maximum value in 2008, for both mega-cap firms panel and small-cap firms panel (3.154 and 4.412 respectively). It indicates that individuals are especially sensitive to stock returns during the financial crisis. The effect of other variables remains unchanged. The regression coefficients on the illiquidity of stocks were positive and significant (with the exception of the year 2010), which can be considered as a proxy of the correlation between the transaction cost and the average holding period. The negative and significant values on the coefficients of volatility showed as an indicator of the negative relationship between the variance of daily returns of assets and its respective holding period. The figures ranged from 0.21 to 0.49 for the mega-cap firms' regressions and from 0.12 to 0.57 for the small-cap firms.
Therefore, the size of the firms seems to have no underlying impact on the decision process when individual investors determine to realise or hold onto the winning stocks.
Table 3 Disposition Effect on the Mega-cap and Small-cap Firms
Panel A: Mega-cap Firms
Panel B: Small-cap Firms
One of the most striking patterns in the financial markets is the tendency of investors to sell the assets whose returns have been going up in value over the past period too soon and hold onto the assets whose returns have been decreasing in value during the previous trading days for too long, which is defined as the disposition effect (Shefrin and Statman, 1985). There are a large number of explanations for the disposition effect. The prevailing reasons refer to the prospect theory (Kahneman and Tversky, 1979), the mental accounting theory (Thaler, 1985) and the regress aversion theory (Shefrin and Statman, 1985). However, none of them is a perfect explanation and research has been conducted which contradicts them. A variety of studies have been carried out to provide robust evidence of the presence of the disposition effect in different countries--developed and developing, European and Asian as indicated in the literature review. The implications of the disposition effect on the financial markets have included a lot of areas, such as trading volume and asset pricing.
In this article, we try to analyse the disposition effect in the Chinese stock markets by investigating data of the Shanghai Stock Exchange (SSE) over five groups--the firms in the Shanghai Stock Market, in the A shares section of the SSE, in the B shares section of the SSE, in the mega-cap index and in the small-cap index during a three year period of 2008 to 2010. We use a two-stage ordinary least squares regression model after considering the fact that the average holding period and the illiquidity of assets may be determined simultaneously, rather than with the ordinary least squares methodology. By investigating the relationship between the average length of time for investors to hold stocks and the asset returns, the results obtained are expressed as follows: Firstly, there is a strong tendency for the investors in the Chinese stock markets to realise their gains and hold onto their losses. Secondly, the A shares section and the B shares section show different performance in terms of the holding period reacted to the asset returns. This may be the effect of the dominance of individual investors in the A shares and institutional traders in the B shares. In particular, the individuals tend to make contrarian investment strategies by selling the winning stocks too soon and keeping the losing shares too long while the institutions are likely to be momentum investors and engage in herding behaviour. Due to the absolutely large proportion of individual investors, the whole stock market exhibits the same pattern as the A shares section. Thirdly, the individual investors show the disposition effect on both large and small firms. What's more, robust evidence is also given that there is a positive correlation between the average holding period and the illiquidity of stocks. The holding periods tend to be longer with a larger size firm. Finally, it is concluded that the volatility of asset returns are negatively related with the average holding period.
Further study can be conducted using a larger sample over a longer period, since the sample space is not large enough to obtain a totally satisfactory result due to the limited ability of the author. In addition, a further step may be taken by considering the reason, implication or probability of profits with different investment strategies between the individual and institutional investors.