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3. Data and Methodology
3.1 Data Description
We obtain complete trading data for all market traders in the market of TAIEX futures, which is traded on the TAIFEX (Taiwan Future Exchange) for 1,241 trading days from January 2004 to December 2008. The TAIEX futures are future contracts on Taiwan Stock Exchange Index, which is a capitalization weighted index comprised of all common stocks on Taiwan Stock Exchange (TSE). TAIFEX is an order-driven electronic futures market in which there are no market makers, thus futures prices are determined by limit orders of market traders.
On the TAIFEX, the trading hours are 8:45 a.m. to 1:45 p.m., from Monday through Friday excluding public holidays. The contract sizes are the TAIEX value X 200 New Taiwan Dollars. The daily price limit is +/- 7% of the settlement price on the previous day. Delivery months include the spot month, the next calendar month, and the next three quarterly months. The last trading day is the third Wednesday of the delivery month for each contract. All contracts are exercised on expiration date automatically and are settled with cash. We select only nearby contracts in our analysis because of liquidity.
The dataset presents the detail information of transactions. It contains the date of transactions, its direction (sell or buy), transaction price, trading quantity, the identity of account and trader types. According to TAIFEX, traders are classified into four types: foreign institutional traders, domestic institutional traders, futures proprietary firms, and individual traders. Because of the identifiable information, we are able to determine the trading activities of different trader types.
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3.2 Research Methodology and Hypotheses
Originally, hedonic editing hypothesis suggests that investors better off combining losses mentally to maximize the value. However, according to
quasi-hedonic editing hypothesis and loss-avoidance hypothesis, investors may fail to integrate losses because they become more loss averse after experiencing a previous loss and this inclination is stronger within big losses scenarios.
In this paper, we focus on pure losses case. We know that the size of prior losses is an essential cause for subsequent trading activities. Therefore, we consider that bigger loss makes investors insensitive toward an additional loss so that they are less risk averse and trade more. On the other hand, smaller loss sensitizes investors to the next loss, which is the reason why they are more risk averse and trade less. To
examine the limit of hedonic editing, we test whether the subsequent trading activities is affected by prior loss results.
First, we grab the trading data of two serial losses from dataset. We regard two serial losses as a reference day. Secondly, we follow Yu-Jane Liu, Chih-Ling Tsai, Ming-Chun Wang and Ning Zhu (2010) to compute the average of trade size and the number of trades respectively on the following 5 days. Trade size is the total quantity of transacted contracts and the number of trades is the trading frequency in the same day, which can be considered as proxy variables for trading activities.
Following, we divide our data by the size of losses. There are two methods we define loss size. One is absolute return, by which we regard less than -10% in return as big loss, falling in -3% to -10% as medium loss, and greater than -3% as small loss.
The other is return distribution, by which we consider the return on each trading account to be normal distribution and independent, because we think everyone has different mental editing rules. We define loss size by return distribution in each
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trading account. We view the top thirty percent of loss degree as big loss, the
intermediate forty percent as medium loss, and the bottom thirty percent as small loss.
Table 1 summarizes the definition of loss sizes.
Lastly, we comply with the big-, medium-, and small- loss rules to form three sample groups. They have the same size of subsequent loss, while the prior loss size is greatest in group 1 and smallest in group 3. The two serial losses are independent and there are 30 data at least in each sample group. Table 2 presents the characteristics for each group. Investors in group 1 are supposed to be more risk seeking and trade more afterward because they are numbed by greater prior losses. However, smaller prior losses result in sensitizing investors in group 3 so that they become more risk averse and trade less. Investors in group 2 have middle risk attitude toward subsequent trading activities.
We test the difference of trade size and the number of trades on the following 5 days between three groups. The significant level is 5%. After that, we further examine whether the result is influenced by trader types. Based on the literature we mentioned above, we derive two hypotheses in this paper.
Hypothesis 1: Trade size in group 1 is greater than group 2 and trade size in group 2 is greater than group 3 on the following 5 days of the reference day.
Hypothesis 2: Number of trades in group 1 is greater than group 2 and number of trades in group 2 is greater than group 3 on the following 5 days of the reference day.
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國立 政 治 大 學
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N a tio na
l C h engchi U ni ve rs it y
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The definition of loss sizes by absolute return and return distribution. By absolute return, big loss is defined when the loss is more than 10% while small loss is smaller than 10%. Medium loss is between big loss and small loss. By return distribution, we consider the return on each day as a normal distribution. The loss which lies on the top of 30% is called big loss and which on the bottom of 30% is small loss. Medium loss is intermediate.
absolute return return distribution
Big loss < -10% Top 30% of loss degree
Medium loss Between -3% and -10% Intermediate 40% of loss degree
Small loss > -3% Bottom 30% of loss degree
Table 2
The characteristics of three sample groups. In this table, we follow the definition of loss size to form three sample groups. All these three groups are assumed to have the equivalent size of subsequent loss. However, the prior loss of group 1 is the biggest, next is group 2, and group 3 has the smallest prior loss.
Prior loss Subsequent loss
Group 1 Big Small
Group 2 Medium Small
Group 3 Small Small
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We present our empirical results in this chapter. By the methodology we described above, we apply two proxy variables of trading activities respectively in our
hypothesis 1 and 2. We compare the trading activities between the three groups to figure out if prior loss degree has impact on subsequent trading behaviors. Then, we test whether trader type is an essential factor of subsequent trading behaviors. Finally, we do some robustness checks by dividing our sample into two periods to confirm our empirical results is objective.
As above, we follow two methods to define loss sizes. Section 4.1 shows statistic results for all investors, section 4.2 for different trader types, and in section 4.3, we provide results for robustness checks.
4.1 All Investors by Trade Size and Number of Trades
From the statistic summary in Table 3, we can grab some information for all investors. As we mentioned above, there are two methods which we use to define big-, medium-, and small- loss. The two methods are absolute return and return distribution.
Thus, we provide the results by two methods separately. Panel A is for absolute return method and panel B for return distribution method. Both of them show the average trade size and number of trades on the following 5 days for each group. In sum, we can obviously see the average of trade size and trading frequency decrease from group 1 through group 3. They are the biggest in group 1, followed by group 2, and the smallest in group 3.
Then, we analyze the trading data and compare the difference of trading activities for three groups by T-test with significant level of 5%. We examine the mean difference between group 1-2 and group 2-3 respectively. Almost all P-value are