4. Data and Methodology
4.5 Arbitrage Risk
Where Ask price and bid price are the closing ask and bid prices on day t, respectively, and the time subscript t indicates that the dealer sets these prices after observing all the independent variables through day t.
4.4 Liquidity Effect
To compute a measure of liquidity effect, we use volume turnover (trading volume divided by shares outstanding) instead of trading volume, so that unusually high volume in a few large stocks does not disproportionately affect the market volume. The turnover ratio is calculated as given below. The denominator is the reference period turnover standardized by market turnover during the reference period, while the numerator is the event period turnover standardized by market turnover during the event period. In the following equation, Tit is the turnover for firm i at time t, the subscript m refers to the market. For the purpose of measuring turnover, the definition of “market” is restricted to CSI 300 stocks. The post-change turnover ratio is the 60-day average trading turnover (with a minimum of 30 days) beginning 61 trading days after the effective date. Thus, trading after the effective date must last for at least 90 days:
We proxy for arbitrage risk using residual standard deviation. We construct a variable that measures arbitrage risk in the spirit of Wurgler and Zhuravskaya (2002), which propose that high-arbitrage-risk stocks have steeper demand curves than low-arbitrage-risk stocks, and, therefore, a positive sign of the ArbRisk coefficient. Arbitrage risk is measured as the variance of the residuals of the Fama- French and the momentum factor model,
𝑅𝑖𝑡− 𝑅𝑓𝑡 = α + 𝛽1𝑖(𝑅𝑚𝑡− 𝑅𝑓𝑡) + 𝛽2𝑖𝑆𝑀𝐵 + 𝛽3𝑖𝐻𝑀𝐿 + 𝛽4𝑖𝑈𝑀𝐷 (5)
(6)
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Where 𝑅𝑚𝑡is the return on the CSI 300 index, 𝑅𝑓𝑡 is the one-month Treasury bill rates, 𝑆𝑀𝐵 is the small-minus-big return, 𝐻𝑀𝐿 is the high-minus-low return, and; 𝑈𝑀𝐷 is the Carhart momentum factor. The parameters are estimated over a (-252, 252) trading day window. In Wurgler and Zhuravskaya (2002), two arbitrage-risk measures, A1 and A2, are suggested: A1 is the variance of the residuals of the excess return market model regression estimated over a (-365, -20) day window. A2 is the residual variance of the excess returns on industry- (three digit SIC), size-, and book-to-market-matched close substitute stocks.
We only examine A1 in our analysis, since A1 and A2 have a correlation of 0.98 (Wurgler and Zhuravskaya, 2002) and lack of data.
5 Effect of Composition Change
To measure the composition change, we compute the AR using the window period 88 day before and after the announcement date and 252 days before and after the announcement date. Table 2 reports the abnormal returns of inclusion to CSI 300 index. As shows in panel A, the MAR on the announcement date is positive in both window periods (-88, 88) and (-252,252), but not significant in (-252,252) due to the lack of data. Panel B show the MCAR of inclusion stocks nine days before and after the announcement date. The results of after period are positive and significant which indicate the CSI 300 inclusion stocks experience an increase after the change. Moreover, there is a significant increase before the effective date and between the announcement date and effective date in (-88, 88) window period.
Table 3 reports the abnormal returns of exclusion from CSI 300 index. As shown in panel A, the MAR on the announcement date is negative in both window periods (-88, 88) and (-252,252), but not significant in (-88, 88). Panel B show the MCAR of inclusion stocks nine days before and after the announcement date. The results of after period are negative and significant which indicate the CSI 300 exclusion stocks experience a decrease after the
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Table 2 Abnormal return of inclusion
𝑀𝐴𝑅 = 1
𝑁∑ 𝐴𝑅𝑖
𝑁
𝑖=0
The AR for the firm is the abnormal return measured by the OLS method of the window period. The CAR is the cumulative abnormal return of the window period.
Abnormal return
∗, ∗∗, and ∗∗∗ denote significance at the 10%, 5%, or 1% level, respectively.
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Table 3 Abnormal return of exclusion
𝑀𝐴𝑅 = 1
𝑁∑ 𝐴𝑅𝑖
𝑁
𝑖=0
The AR for the firm is the abnormal return measured by the OLS method of the window period. The CAR is the cumulative abnormal return of the window period
Abnormal return
∗, ∗∗, and ∗∗∗ denote significance at the 10%, 5%, or 1% level, respectively.
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change. Moreover, there is a decrease before the effective date which is not significant and the return between the announcement date and effective date are negative and significant in the window period of (-88, 88) but not the (-252, 252).
Figure 2 and 3 shown the cumulative abnormal return in (-88, 88) and (-252, 252) window period using OLS estimation in the period. In figure 2, AR of inclusion stocks increases after the announcement date and reverse after the 61st day and AR of exclusion stocks decreases initially and reverse after 13rd day after the announcement period. It is worth to note that the average CAR of exclusion stocks raises more than that of inclusion stocks in 67th day after the announcement date. The reason of this abnormal finding may because of the immature behavior of the investor of CSI 300 Index, 83% of market value of China stock market held by individual investors. We also find an unordinary result in window period (-252, 252), as shown in figure 3, inclusion stocks price drop and exclusion stocks price rise sharply in 252 days after the composition change announcement date.
Figure 2 the cumulative abnormal return in (1, 88) window period
-4.00%
-3.00%
-2.00%
-1.00%
0.00%
1.00%
2.00%
3.00%
4.00%
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88
InclusionAR ExclusionAR
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Figure 3 the cumulative abnormal return in (1, 253) window period using regression
Figure 4 the cumulative abnormal return in (1, 253) window period using 𝑅𝑖𝑡− 𝑅𝑚𝑡
-15 -10 -5 0 5 10 15 20
1 10 19 28 37 46 55 64 73 82 91 100 109 118 127 136 145 154 163 172 181 190 199 208 217 226 235 244 253
Inclution AR ExclusionAR
-4 -2 0 2 4 6 8 10 12 14
1 10 19 28 37 46 55 64 73 82 91 100 109 118 127 136 145 154 163 172 181 190 199 208 217 226 235 244
Exclusion CAR Inclusion CAR
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We also compute the changes of four variable and compare the results before and after the composition change using statistical test. The significance of the mean (median) is tested with a standard t-test (sign test), while the significance of the proportions is tested using the binomial distribution.