Empirical Results and Analysis under Different Market Scenarios

The lag lengths of the TAIEX returns and sentiment indices are determined before the causality test is performed. The numbers of lagged terms in the VAR models are decided parsimoniously by the Akaike information criterion (AIC) and the Schwarz criterion (SC). Table 3 presents the general causality tests. The results show that there is a feedback relationship between returns and sentiment, in both levels and first differences, and including TVIX and ARMS. As for the other two derivatives market sentiment indicators, TPCV and TPCO, these have no leading effect.

The positive and negative market return scenarios indicate whether the market returns are greater than zero or not. The results of these Granger-causality tests are presented in Table 4. The TVIX Granger causes returns when the return is greater than zero. However, the sentiment indicators are Granger-caused by returns while the return is smaller than zero. In short, TVIX could be a leading indicator while the market returns are positive.

The other situations with which we are concerned in this study are whether the sentiment is grouped in the top 20% or the bottom 20%. Most of the results, which are presented in Table 5, show that there is no distinct causal relationship between sentiment and returns although the TVIX and TPCV Granger cause returns while in the bottom 20%. Considering that the critical values of the overreaction scenarios are determined subjectively, the feedback relationship may be mixed.

Finally, there is the causality test between the returns and sentiment indicators in the extreme levels of investor sentiment that are determined by the threshold model.

The threshold tests for each sentiment indicator are presented in Table 6 and the percentages for each regime classified by threshold model are shown in Table 7. The threshold tests show that the higher regime of TVIX and the lower regime of ARMS are not significant. Besides, the other sentiment indicators give rise to significant critical values of the higher and lower regimes that can represent the oversold and overbought situations.

Table 3 General Causality Tests between Returns and Sentiment

Sentiment Hypothesis

H₀₁ H₀₂ H₀₃ H₀₄

TVIX 2.7533 (0.0642)* 3.9627 (0.0193)** 4.3919 (0.0364)** 6.4175 (0.0115)**

TPCV 0.0196 (0.9806) 0.9918 (0.3713) 0.1901 (0.9031) 6.4853 (0.0002)***

TPCO 0.4045 (0.5249) 51.7436 (<0.0001)*** 3.0538 (0.0809)* 30.2449 (<0.0001)***

ARMS 4.8131 (0.0083)*** 19.369 (<0.0001)*** 2.5839 (0.0173)** 9.0376 (<0.0001)***

Notes: The numbers of lagged terms in the VAR models are decided parsimoniously by the Akaike information criterion (AIC) and the Schwarz criterion (SC). H₀₁: Granger-noncausality from sentiment to returns, i.e., sentiment does not cause returns. H₀₂: Granger-noncausality from returns to sentiment, i.e., returns do not cause sentiment. H₀₃: Granger-noncausality from changes in sentiment to returns, i.e., changes in sentiment do not cause returns. H₀₄: Granger-noncausality from returns to changes in sentiment, i.e., returns do not cause changes in sentiment. Values in the table and the parentheses are F test statistics and p-values, respectively. *, **, and *** indicate significance at the 10%, 5% and 1%

levels, respectively.

Table 4 Causality Tests between Returns and Sentiment – Considering the Positive and Negative Market Return Scenarios

Sentiment Hypothesis

H₀₁ H₀₂ H₀₃ H₀₄

Panel A Positive Return

TVIX 33.5609 (<0.0001)*** 0.4766 (0.6212) 3.8761 (0.0495)** 0.0607 (0.8056) TPCV 0.4318 (0.6496) 2.1598 (0.1164) 1.0806 (0.3568) 5.9478 (0.0005)***

TPCO 4.9796 (0.0261)** 15.1619 (0.0001)*** 0.782 (0.377) 7.5925 (0.0061)***

ARMS 13.4788 (<0.0001)*** 9.4277 (0.0001)*** 4.7919 (0.0001)*** 5.8443 (<0.0001)***

Panel B Negative Return

TVIX 23.7999 (<0.0001)*** 4.9421 (0.0075)*** 0.0029 (0.9569) 9.9774 (0.0017)***

TPCV 1.2442 (0.2891) 0.2446 (0.7831) 0.8122 (0.4876) 2.5514 (0.0551)*

TPCO 2.2443 (0.1348) 61.2698 (<0.0001)*** 0.118 (0.7314) 42.7464 (<0.0001)***

ARMS 0.5613 (0.5708) 11.2781 (<0.0001)*** 1.3231 (0.2451) 4.7347 (0.0001)***

Notes: This table presents the causality tests between returns and sentiment considering the positive and negative market return scenarios. The numbers of lagged terms in the VAR models are decided respectively. *, **, and *** indicate significance at the 10%, 5% and 1% levels, respectively.

Table 5 Causality Tests between Returns and Sentiment – Sentiments Grouped at the Top, Median and Bottom Levels

Sentiment Hypothesis

H₀₁ H₀₂ H₀₃ H₀₄

Panel A Top 20% of the sentiment

TVIX 3.8314 (0.0233)** 8.6299 (0.0003)*** 0.0076 (0.9308) 56.8343 (<0.0001)***

TPCV 1.943 (0.1461) 0.8829 (0.4152) 1.4031 (0.2432) 1.9424 (0.1242) TPCO 0.4743 (0.4918) 2.7216 (0.1006) 0.0001 (0.9938) 0.2948 (0.5877) ARMS 1.4385 (0.2398) 3.3526 (0.037)** 1.1535 (0.3333) 2.6497 (0.0173)**

Panel B Median of the sentiment

TVIX 2.686 (0.069)* 8.3332 (0.0003)*** 0.0053 (0.9417) 4.2173 (0.0405)**

TPCV 1.4351 (0.2389) 1.0379 (0.3548) 1.5621 (0.1975) 1.7258 (0.1605) TPCO 28.2164 (<0.0001)*** 25.3552 (<0.0001)*** 0.701 (0.4028) 27.3828 (<0.0001)***

ARMS 13.3482 (<0.0001)*** 3.2147 (0.0409)** 7.4548 (<0.0001)*** 0.6305 (0.7059) Panel C Bottom 20% of the sentiment

TVIX 0.3011 (0.7404) 3.3127 (0.0385)** 3.6214 (0.0585)* 0.7986 (0.3726) TPCV 10.5245 (<0.0001)*** 1.7001 (0.1854) 4.4979 (0.0045)*** 1.8991 (0.1312) TPCO 20.0555 (<0.0001)*** 16.3919 (0.0001)*** 0.7241 (0.3959) 0.7776 (0.379) ARMS 0.3037 (0.7384) 1.7525 (0.1761) 2.1734 (0.0474)** 5.4883 (<0.0001)***

Notes: This table presents causality tests between returns and sentiment considering the sentiments grouped at the top, median and bottom levels. The numbers of lagged terms in the VAR models are decided parsimoniously by the Akaike information criterion (AIC) and the Schwarz criterion (SC). H01: Granger-noncausality from sentiment to returns, i.e., sentiment does not cause returns. H₀₂: Granger-noncausality from returns to sentiment, i.e., returns do not cause sentiment. H₀₃: Granger-noncausality from changes in sentiment to returns, i.e., changes in sentiment do not cause returns. H04: Granger-noncausality from returns to changes in sentiment, i.e., returns do not cause changes in sentiment. Values in the table and the parentheses are F test statistics and p-values, respectively. *, **, and *** indicate significance at the 10%, 5% and 1% levels, respectively.

Table 6 Threshold Test

Notes: This table presents the threshold tests. The upper regime is the regime above the average level of the sentiment indicators. The lower regime is the regime below the average level of the sentiment indicators. *, **, and *** indicate significance at the 10%, 5% and 1% levels, respectively.

Table 7 Percentage of Each Regime Classified by Threshold Model

Higher Regime Typical Regime Lower Regime

TVIX 39%

TPCV 14% 42% 44%

TPCO 14% 57% 29%

ARMS 10%

ΔTVIX 15% 74% 10%

ΔTPCV 13% 68% 19%

ΔTPCO 24% 50% 26%

ΔARMS 15% 46% 39%

Notes: This table presents the percentages of different regimes classified by the threshold model. The higher regime is the regime above the higher threshold which is above the average level of the sentiment indicators. The lower regime is the regime below the lower threshold which is below the average level of the sentiment indicators. The typical regime is the regime between the higher and lower thresholds of the sentiment indicators. The blank of the higher regime and typical regime of TVIX indicates that the threshold test is not significant in the upper regime of the TVIX level. The blank of the lower regime and typical regime of ARMS indicates that the threshold test is not significant in the lower regime of the ARMS level.

The results of the causality relationship in the oversold and overbought situations are shown in Table 8. We can find that the market sentiment indicator, ARMS, leads returns while in the upper regime. Both the equity market and derivatives market sentiment indicators, ARMS and TPCV, Granger cause returns in the median regime.

In the lower regime, only the sentiment indicators in the derivatives market, TVIX and TPCV, Granger cause returns. From these findings, we can conclude that the equity or derivatives markets sentiment indicators perform differently in terms of the lead-lag relationship between returns while the sentiments are in the higher, median or lower regimes. Our study suggests that investors can adjust their portfolios by analyzing the sentiment indicators for different scenarios.

Table 8 Causality Tests between Returns and Sentiment - Application of the Multivariate Threshold Model

Sentiment Hypothesis

H₀₁ H₀₂ H₀₃ H₀₄

Panel A Upper regime (above the higher threshold)

TVIX

TPCV 0.7388 (0.4796) 1.1357 (0.3243) 0.5386 (0.6567) 0.7615 (0.5178) TPCO 0.0732 (0.7871) 0.5083 (0.4771) 0.0589 (0.8084) 0.0922 (0.7616) ARMS 3.4356 (0.0364)** 0.8965 (0.4115) 1.5796 (0.1574) 3.0123 (0.0085)***

Panel B Typical regime (between the two thresholds)

TVIX

TPCV 5.7821 (0.0033)*** 0.1239 (0.8835) 2.3032 (0.0759)* 3.1818 (0.0235)**

TPCO 29.5417 (<0.0001)*** 39.5976 (<0.0001)*** 1.4719 (0.2256) 16.3007 (0.0001)***

ARMS

Panel C Lower regime (below the lower threshold)

TVIX 4.4883 (0.0118)** 5.8011 (0.0033)*** 3.8007 (0.0541)* 0.5805 (0.4479) TPCV 7.0184 (0.001)*** 1.3517 (0.2599) 4.4569 (0.0048)*** 1.6189 (0.1865) TPCO 10.7606 (0.0012)*** 18.2885 (<0.0001)*** 0.8613 (0.3542) 0.4873 (0.4858)

ARMS typical regime of TVIX and ARMS, and the lower regime of ARMS indicate that the threshold test is not significant in that scenario. Therefore, the causality tests are not examined in these scenarios. *, **, and *** indicate significance at the 10%, 5% and 1% levels, respectively.