Robustness check

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expected returns than low BE/ME stocks. It shows a kind of unconditional explanatory power.

Overall, the above patterns suggest that when sentiment is high, stocks are probably more attractive to optimists and unattractive to arbitrage. Small-cap stocks, young stocks, high-volatility stocks, unprofitable stocks and distressed stocks are likely to experience lower subsequent returns.

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In order to test the robustness of the impact of investor sentiment on stock returns, I use monthly returns of Shanghai and Shenzhen 300 Index (which is HS300) instead of monthly returns of A-share composite market as the measurement of market return. The HS300 data comes from CSMAR database.

Table 4-19 ADF test result

t-Statistic Prob.*

Augmented Dickey-Fuller test statistic -10.87 0.0000

Test critical values: 1% level -3.48

5% level -2.88

10% level -2.58

*MacKinnon (1996) one-sided p-values.

As is shown in Table 4-19, the absolute value of ADF test statistic is 10.8695, higher than the ones of critical value, which means HS300 is a stable sequence.

Thus it is reasonable to structure the vector auto regression model like (4.5) and (4.6):

𝐻𝑆300 = - 0.000368𝐼𝑆𝐼_𝑡−1 + 0.110514𝐻𝑆300_𝑡−1+ 0.0282 (4.5) 𝐼𝑆𝐼= 0.703414𝐼𝑆𝐼_𝑡−1 + 56.401204𝑆𝑚𝑎𝑙𝑙𝑆𝐴𝑅_𝑡−1 + 15.999 (4.6)

The fitness of model (4.5) is 0.018, while the fitness of model (4.6) is 0.595.

The latter one is more reasonable, which means there is a lag effect on the impact of stock market returns on investor sentiment. The effects of stock market return and investor sentiment on sluggish investor sentiment are positive and the effect from stock market return is higher.

Table 4-20 shows the result of Granger causality test between ISI and HS300.

If p-value of the test is below 0.05, it means the null hypothesis can be rejected and X can Granger cause Y. It can be seen from the table that HS300 can Granger cause ISI but ISI cannot Granger cause HS300. As a result, there exists unidirectional causality between HS300 and ISI. HS300 is the Granger cause of

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ISI. At a significant level of 10%, the change in stock market return can cause the change in investor sentiment index, however, the change in investor sentiment cannot cause the change in stock return.

Table 4-20 Granger Causality Test

H0 Chi-sq df Prob.

HS300 does not Granger cause ISI 16.1621 1 0.0001

ISI does not Granger cause HS300 1.2625 1 0.2612

To further test the interrelation and whole influence between ISI and HS300, I’m going to do the impulse response function. Figure 4-21 and Figure 4-22 show the impact of the unit standard deviation of ISI and HS300 causes on ISI and HS300. The left side of Figure 4-21 reflects the impact ISI gives on itself. After a positive impact in the current period, ISI itself shows the largest positive impulse in the first period and gradually declines. It declined to 0 around the tenth period.

The right side of Figure 4-21 reflects the impact HS300 gives on ISI. After a positive impact in the current period, ISI didn’t show an immediate fluctuation in the first period. There’s an increasing positive impulse between the first and second period, which declines gradually after the third period and converges to 0 after the tenth period. It means the impact of HS300 would cause positive fluctuation on ISI in short term, and the single impulse response tend to converge to zero in the long term. There is also one-period lag in the effect, which is the same result with above model. It means the effect of investor sentiment on stock return is a one-period lag effect.

Figure 4-21

0 4 8 12

1 2 3 4 5 6 7 8 9 10

Response of ISI to ISI

0 4 8 12

1 2 3 4 5 6 7 8 9 10

Response of ISI to HS300 Response to Cholesky One S.D. (d.f. adjusted) Innovations ?2 S.E.

43 Figure 4-22

.00 .02 .04 .06

1 2 3 4 5 6 7 8 9 10

Response of HS300 to ISI

.00 .02 .04 .06

1 2 3 4 5 6 7 8 9 10

Response of HS300 to HS300 Response to Cholesky One S.D. (d.f. adjusted) Innovations ?2 S.E.

The left side of Figure 4-22 reflects the impact ISI gives on HS300. After a positive impact in the current period, HS300 shows the largest positive impulse immediately in the first period and gradually declines between the first and third period. There’s even a slight negative impact in the third period and then declines, converging to 0 in the tenth period. It means the impact of ISI would cause positive fluctuation on HS300 in short term, and the single impulse response tend to converge to zero in the long term. The right side of Figure 4-22 reflects the impact HS300 gives on itself. After a positive impact in the current period, HS300 shows an immediate fluctuation in the first period and declines quickly to zero around the third period. It means the stock market return is mostly affected by its own reasons.

Table 4-23 and Table 4-24 show the result of variance decomposition of ISI and HS300. As is shown in Table 4-23, the contribution rate of HS300 to ISI is 0 in the first period and gradually increases. At around the tenth period, ISI can explain 90.895% of its variance variation, and HS300 can explain 9.105% of its variance variation. It means in the long run, change of ISI is mainly affected by itself.

Table 4-23 Variance Decomposition of ISI

Period S.E. ISI HS300

1 12.125 100.000 0.000

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2 16.154 94.296 5.704

3 17.847 92.231 7.769

4 18.568 91.449 8.551

5 18.881 91.131 8.869

6 19.019 90.996 9.004

7 19.080 90.937 9.063

8 19.106 90.911 9.089

9 19.118 90.899 9.100

10 19.124 90.895 9.105

As is shown in Table 4-24, the contribution rate of ISI to HS300 is 11.975% in the first period and gradually increases. At around the tenth period, ISI can explain 12.391% of its variance variation, and HS300 can explain 87.609% of its variance variation. It means in the long run, the change of HS300 is mainly affected by itself.

In summary, the influence of investor sentiment on stock market returns is consistent with the above analysis results and robust. The effect of investor sentiment on stock return is a lag effect. The change in stock market return can cause change in investor sentiment. Stock market return is the Granger cause of investor sentiment.

Table 4-24 Variance Decomposition of HS300

Period S.E. ISI HS300

1 0.072909 11.975 88.025

2 0.073319 11.894 88.106

3 0.073422 12.134 87.866

4 0.073491 12.274 87.726

5 0.073526 12.339 87.661

6 0.073541 12.368 87.632

7 0.073548 12.381 87.619

8 0.073551 12.387 87.613

9 0.073552 12.389 87.611

10 0.073553 12.391 87.609

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In document The Influence of Investor Sentiment on Chinese Stock Market Returns (pagina 44-49)