Volatility Index and the Return-Volatility Relation: Intraday Evidence from China

Transcription

1 Volatility Index and the Return-Volatility Relation: Intraday Evidence from China Jupeng Li a, Xingguo Luo b* and Xiaoli Yu c a Shanghai Stock Exchange, Shanghai , China. b School of Economics and Academy of Financial Research, Zhejiang University, Hangzhou , China. c School of Economics, Zhejiang University, Hangzhou , China. * Corresponding author. Abstract In this paper, we investigate the validity of the Shanghai Stock Exchange's revised implied volatility index (ivx) and the return-volatility relation using unique intraday data. In particular, we examine the role of the stock market crashes and how ivx performs in the trading strategies. Our results indicate that ivx is negatively correlated with the underlying when there are fears of large drops and ivx is strongly related to the realized volatility, especially for the jumps. Further, we find the return-volatility relation is more asymmetric in the upper quantiles when a robust quantile regression is employed, and some abnormal positive correlations distinguish the Chinese market from other markets. Besides, higher frequency results indicate that the behavioral theories are better than the fundamental theories in explaining the relation. Keywords: SSE ivx; Intraday Data; Return-Volatility Relation

2 1. Introduction In June 2015, the listing of the SSE 50 ETF options was followed by the establishment of the Chinese implied volatility index (ivix). Later, the revised implied volatility index (ivx) was released in November 2016 and is updated in real time. ivx is a VIX-like measure 1 of the stock market's expectation of volatility implied by SSE 50 ETF options. From December 2015 to January 2018, the monthly turnover of the SSE 50 ETF option has increased from 427,000 to million. The Chinese options market begins to contain rich information, but there is limited research as far as we know. In particular, Zheng et al. (2017) find that the daily ivix (old version of ivx) is positively related to the SSE 50 ETF. It seems that ivix should be referred to as the greed index rather than the fear index for VIX (Whaley, 2000). Meanwhile, there is an ongoing debate about the convincing explanation of the asymmetric return-volatility relation that volatility responds intensively to negative return shocks rather than positive. Taking advantage of high frequency data, Talukdar et al. (2017) document that behavioral explanations are more suitable to explain the puzzling phenomenon. This finding is very different from previous studies based on low frequency (daily, weekly or monthly) data and claimed that the leverage effect and/or the volatility feedback effect is the cause of the asymmetric relation (e.g., Schwert, 1990; Duffee, 1995; Campbell and Hentschel, 1992). 1 The current VIX index value quotes the expected annualized change in the S&P 500 index over the following 30 days, as computed from options-based theory and current options-market data. 1

3 In this paper, we present the first empirical evidence on questions posed by these concerns: Is ivx an effective volatility measure of the stock market and should we refer to ivx as the "fear index" or the "greed index"? Considering the short-term asymmetric return-volatility relation, what is the uniqueness of the Chinese market and which theory can provide the convincing explanation for our higher frequency results? Moreover, if ivx is informative of the stock market, how ivx performs in the trading strategies? At the empirical level, we employ a heterogeneity-consistent quantile regression model (QRM) along with sub-sample OLS regressions. Shefrin (2001, 2008) and others suggest that investors heterogeneous beliefs about the asset payoffs lead to a multimodal and fat-tail stock index return distribution. Therefore, heterogeneity is important for financial studies. Besides, we are interested in the validity of ivx during the 2015 stock market crashes, so a set of sub-sample analyses are utilized. Specially, our contributions may be broken down into the following five areas. First of all, while several studies investigate the predictive ability of the CBOE VIX index in forecasting future realized volatility (Moraux et al., 1999; Siriopoulos and Fassas, 2009), our paper presents new high-frequency evidence for the comovement between ivx and the stock market volatility in a shorter term. Different from the previous studies, we distinguish between continuous (BPV) and discontinuous (Jump) parts of the realized volatility and highlight the impact of the stock crashes by a set of subsample analyses. Second, whether ivx should be referred to as a fear index or a greed index 2

4 is still controversial. We revisit this issue with the intraday ivx index and there are different discoveries from the daily results of Zheng et al. (2017). Although ivx is positively related to the underlying price at certain times, it is negatively related to the price during the market crashes and has a significant negative comovement with the return, especially the negative return of the SSE 50 ETF. More important, ivx can negatively predict the short-term market declines and act as the barometer of the crises. Hence, our empirical results indicate that ivx is more valid as the fear index. Third, we examine the features of the short-term asymmetric volatility phenomenon in the Chinese market for the first time. The detected asymmetry is found to be incremental during China s 2015 stock market crash and the 2016 Circuit-Breaker. More important, the extensive quantile regressions show abnormal positive comovements between ivx and the underlying returns and we believe that the main reasons lie in the unique underlying stocks and investor structure. Fourth, the ongoing debate whether the behavioral theories or the fundamental theories can provide better explanation for the asymmetric return-volatility relation drive us to find new evidence from the Chinese market. Innovatively, we compare samples in different frequencies and show more detail results in this issue. Five, the perform of new-revised ivx in the trading strategies is first examined. We test how ivx performs in the selecting the trading strategies, where two traditional trading strategies including the MACD rules (the Moving Average Convergence Divergence) and the KDJ rules (the Random Index) are mainly 3

5 considered. The results indicate that the KDJ rules performs better than the MACD rules and ivx plays an important role in the selecting the strategies for the 50 ETF. The rest of the paper is structured as follows. Section 2 introduces the data and the methodology, and four hypotheses. Section 3 shows the results of our empirical studies and our conclusions are presented in Section 4. 2.Data, Methodology and Hypotheses 2.1 The SSE ivx Index In this paper, we use the high frequency 1-minute data of the revised implied volatility index (ivx). Our data is provided by SSE with the entire sample period from 9 th Feb 2015 to 14 th Feb Dennis et al. (2006) presents evidence that innovations in index implied volatility, which is calculated as daily VIX change, are good proxies for innovations in expected stock return and the volatility. Their finding drives us to investigate the performance of the innovations of the SSE ivx index. And besides the 1-minute intervals, we utilize more frequencies data to investigate the validity of the ivx index, where the last ivx of the interval is selected as the new-frequency ivx value. 2.2 The Return and Realized Volatility of the SSE 50 ETF We calculate the return of the SSE 50 ETF at the 1-minute, 5-minute and 30-minute intervals. The Δ-period intraday return is defined by: Ret t,i = log(p t+i ) log (P t+(i 1) ) (1) And we employ the 30-minute and 60-minute realized volatility to portray the 4

6 volatility movement of the SSE 50 ETF, which is calculated by the quadratic sum of the index return for the SSE 50 ETT on interval t, M = 1/ : M 2 RV t = Ret t,i i=1 (2) Moreover, following Bollerslev et al. (2016), we further decompose RV into its continuous (BPV) and discontinuous (Jump) variations using the Bi-Power Variation (BPV) measure of Barndorff-Nielsen and Shephard (2004): M 1 BPV t = μ 2 1 Ret t,i Ret t,i+1 (3) i=1 Jump t = max [RV t BPV t, 0] (4) Where RV t is the realized volatility of the index on interval t, BPV t is the continuous part of the realized volatility, μ 1 = 2/π = E( Z ) (Z is a standard normally distributed random variable), Ret t,i is the Δ-period intraday return, and Jump t is the Jump variation of the realized volatility. Table 1 reports the summary statistics for the ivx index, the return and the realized volatility of the SSE 50 ETF. The descriptive statistics at the 1-minute intervals (Panel A) and the 5-minute intervals (Panel B) are included. Summary statistics of the both panels are from 9 th Feb 2015 to 14 th Feb All variables are not standardized in Table 1 but we use the standardized variables in the following regressions. High kurtosis can be seen in the series of ivx changes, realized volatility (especially the Jump parts), which indicates changes in the series are highly leptokurtic. 2.3 Methodology 5

7 For the preliminary analyses, we use the correlation coefficients ρ to measure the contemporaneous correlation between ivx and the SSE 50 ETF (X and Y in the following formula), which is calculated as: ρ = σx, Y σxσy Cov(X, Y) = σxσy (5) where Cov(X, Y) is the covariance of X and Y and σx (σy) is the variances of uni-variables. Further, we study the forecasting power of ivx for the future realized volatility and the return of the SSE 50 ETF with OLS regression models (6) to (10). In particular, we distinguish the continuous and the discontinuous part of the realized volatility and examine the correlation between ivx and the future negative return: RV t = C + β 1 ivx t 1 + β 2 RV t 1 + ε t (6) Jump t = C + β 1 ivx t 1 + β 2 Jump t 1 + ε t (7) BPV t = C + β 1 ivx t 1 + β 2 BPV t 1 + ε t (8) Ret t = C + β 1 ivx t 1 + β 2 Ret t 1 + ε t (9) Ret t 1 = C + β 1 ivx t 1 + β 2 Ret t 1 + ε t (10) where RV t is the realized volatility, BPV t is the continuous part and Jump t is the discontinuous part of the realized volatility. Ret t is the return of the SSE 50 ETF. Ret t 1 denotes negative returns. ivx t is the first-order difference of the ivx index. ivx t 1 denotes the first-order lag and so on. We show results at both 30-minute and 60-minute frequencies for the realized volatility forecasting and show results at 1-minute, 5-minute and 30-minute frequencies for the return forecasting. What s more, we have an insight into the related subsample in this part. While the full sample is 6

8 from 9 th Feb 2015 to 14 th Feb 2018, we examine two subsamples in this part: the 2015 Crash Period from 1 st Jun 2015 to 31 st Aug 2015 and the 2016 Circuit-Breaker Period from 4 th Jan 2016 to 7 th Jan Following Hibbert et al. (2008) and Talukdar et al. (2017), we use the Quantile Regression Model (QRM) to document the asymmetric return-volatility relations. As financial markets are heterogeneous due to the existence of different investor groups, the quantile regressions provide a free estimate of heterogeneity and is more compatible to testing the different behavior of the investors. Given a quantile τ = 0.05, 0.10,,0.50,,0.90,0.95, we define the quantile regression model: ivx t = C + β 1 Ret + t + β 2 Ret t + β 3 Ret + t 1 + β 4 Ret + t 2 + β 5 Ret t 1 + β 6 Ret t 2 +β 7 ivx t 1 + β 8 ivx t 2 + ε t (11) The first-order and the second-order lagged returns are added in the model (11) to compare the effect of the contemporaneous events and the lagged events. And we show results of both 1-minute and 30-minute intervals to see the asymmetric volatility phenomenon at the trading of different frequencies. Besides, the OLS regression is taken for the comparison in this part. 2.4 Hypotheses As options represent the consensus of market participants regarding expected future volatility, we suppose the ivx index, implied by the market prices of options, is forward looking for the future realized volatility of the underlying asset. Therefore, we propose: 7

9 Hypothesis 1 ivx is an effective volatility measure of the stock market. If Hypothesis 1 holds, we expect to see a strong correlation between ivx and both the contemporaneous and future realized volatility of the SSE 50 ETF. The SSE 50 Index consists of 50 constituent stocks with large market size, high liquidity and strong representation. Thus, if ivx can represent and predict the realized volatility of the SSE 50 ETF, to some extent, we believe that ivx may be an important barometer for the volatility of the stock market in China. While the CBOE VIX index is often referred to as the investors fear gauge (e.g., Whaley, 2000), for the SSE ivx, whether it is the fear index or the greed index is still under discussion. Zheng et al. (2017) find that daily ivix (old version of the SSE volatility index) is positively related to the SSE 50 ETF and the investor sentiment. And they suppose the ivix in China should be referred to as the greed index rather than the fear index. In this paper, we revisit this issue with the intraday ivx index and propose: Hypothesis 2 ivx is the greed index. Based on high frequency data, if Hypothesis 2 holds, we should observe similar results as Zheng et al. (2017). In particular, we highlight the correlation between ivx and the negative returns of the SSE 50 ETF and employ a series of the subsample analyses in the crashes, which may show more details in this issue. The correlation between stock market returns and volatility has been the subject of a number of studies in the finance literature. Referring to the studies of Badshah 8

10 (2013) and Talukdar et al. (2017), we suppose that the asymmetry of return-volatility may be related to investor heterogeneity. For that pessimistic investors tend to overestimate the risk and underestimate the return, they response to the positive and negative returns more asymmetrically. Thus, the extreme tails of the ivx changes distribution where pessimistic investors gather may show stronger asymmetry. Based on these conjectures, we propose: Hypothesis 3 The asymmetric relation between return and ivx changes is asymmetric, especially in the upper quantiles of the ivx changes distribution. If Hypothesis 3 holds, the negative return shocks tend to imply higher future volatility than do positive return shocks of the same magnitude, which is widely researched as the asymmetric volatility phenomenon. What s more, if the asymmetry relationship is more significant in the upper quantiles of the ivx changes distribution than the lower quantiles, then OLS regression may result in the deviation. Traditionally, two competing hypotheses, the leverage hypothesis and the volatility feedback hypothesis 2, have been widely used to explain the asymmetric volatility phenomenon based on low frequency data (daily, weekly or monthly) Meanwhile, there are some new research taking advantage of high frequency data and supposing the behavioral explanations, such as the affect and representativeness heuristics, is more suitable to explain the asymmetric return-volatility relation in the 2 Specifically, the leverage hypothesis suggests that a negative return should make the firm more levered, hence riskier and therefore lead to higher volatility (e.g., Christie, 1982; Schwert, 1990; Duffee, 1995); The volatility feedback hypothesis states that the negative change in expected return tends to be intensified whereas the positive change in the expected return tends to be dampened (e.g., French, Schwert, and Stambaugh, 1987; Campbell and Hentschel, 1992). 9

11 short term (e.g., Hibbert et al., 2008; Talukdar. et al., 2017; Bekiros et al.,2017). The converse findings drive us to compare samples in different frequencies and test Hypothesis 4: Hypothesis 4 In higher frequency results, behavioral theories are better than the fundamental theories in explaining the asymmetric return-volatility relation. As the traditional theory emphasizes the impact of lag events, while behavioral theory highlights the impact of contemporaneous events, if hypothesis 4 holds, contemporaneous returns (both positive and negative) should be the most important factors in our regressions. 3. Empirical Results 3.1 ivx and the Stock Market Volatility In this section we explore the degree of market co-movement between ivx and the stock market volatility. Intuitively, we find that ivx and realized volatility of the SSE 50 ETF show a strong comovement in the Panel A of Figure 1. And during the stock market crashes, as reported in the Panel B and C of Figure 2, the correlation is more prominent. Moreover, based on the following empirical results, we believe that ivx is an effective volatility measure of the stock market and accept Hypothesis 1. The contemporaneous correlation between ivx and the realized volatility are reported in Table 2. Both 30-minute (Panel A) and 60-minute (Panel B) frequencies show strong correlations and we find the lower-frequency sample performs better. Taking 60-minute results as an example, the correlation coefficient between ivx and 10

12 the realized volatility is up to This comovement may mainly come from the correlation between ivx and the discontinuous part of the volatility (the jump rather than the BPV) for that the correlation coefficient is with jump versus with BPV. Through the subsample analyses, we find that the correlation is more significant during the 2015 stock market crash, which increases to This finding shows that ivx will have better risk prediction ability during the crashes. For the forecasting regressions, Table 3 shows that after controlling for the lagged realized volatility, the lagged ivx index has positive predictive power for the future volatility. While the regression coefficients are larger at 60-minute frequency, the t value is more significant at 30-minute intervals than the lower frequency. Consistent with the contemporaneous results, during the 2015 stock market crash, the lagged ivx performs better than lagged realized volatility with larger regression coefficients and the more significant t-values, indicating that ivx shows stronger forecasting power in the market crashes. What important, we also find ivx has an incremental forecasting power for the jump rather than BPV. For the jump, we find ivx is positively significant with coefficient of (30-minute) and (60-minute), while decreases to (30-minute) and (60-minute) for the BPV. This unique finding indicates that ivx is more related to the future discontinuous variations. 3.2 The Fear Index or the Greed Index? Referring to the previous literature, Zheng et al. (2017) find that daily ivix (old version of the SSE volatility index) is positively related to the SSE 50 ETF and the 11

13 investor sentiment. Thus, they suppose the ivix in China should be referred to as the greed index rather than the fear index. In this section, our study utilizes intraday data of the new-revised ivx index and find different evidences. Although ivx is positively related to the price of the SSE 50 ETF in the full sample, it is negatively related to the price in the market crashes and has a strong negative co-movement with the return, especially the negative return of the SSE 50 ETF. More important, ivx can negatively predict the short-term market declines and act as the barometer of the crises and we believe that being the effective barometer for the market crashes is the core features of the fear index. Thus, we believe ivx is valid ae the fear index and reject Hypothesis 2. Intuitively, Figure 2 shows the time series of ivx and the SSE 50 ETF in the full sample and during the stock market crashes. For the full-sample time series of ivx and the price of the SSE 50 ETF (Panel A), it is intuitively that there are no obvious negative correlations between ivx and underlying price. And ivx seems to be positively related to the positive return and negatively correlated with the negative return in Panel B. Besides, the 1-minute time series of ivx and the underlying price are plotted during the 2015 stock crash (Panel C) and the 2016 Circuit-Breaker period (Panel D). As expected, the negative correlation between ivx and index price is much stronger during the market falls than in the full sample. Consistent with the intuitive observations in Figure 1. Table 4 presents the contemporaneous correlations between ivx and the price (Panel A), the ivx changes and the return (Panel B), and the ivx changes and the negative return of the SSE 50 12

14 ETF (Panel C). We find that the correlations decrease as the frequency increases. Taking 30-minute results as an example, in Panel A, ivx and underlying price are significantly positively correlated in the full sample with a coefficient of 0.142, which is in line with Zheng et al. (2017). Differently, we find the correlations between ivx and underlying price became significantly negative during the crashes and the coefficients change to (for the 2015 Crash) and (for the 2016 Circuit-Breaker). Further in Panel B, the ivx changes is negatively related to the returns. The coefficient is in full sample and changes to and in the two stock market crashes respectively. In particular, the negative returns of the SSE 50 ETF have incremental negative correlations with ivx tested by Panel C. The coefficient is more significant as in full sample and even more notable in the crash subsamples. Moreover, we investigate the forecasting power of the ivx changes for the returns of the SSE 50 ETF in Table 5. ivx changes has a weak correlation with the future return but can negatively predict the negative returns at 1% significant level in the short term. This finding further proves ivx is more sensitive to the negative returns and act as an effective barometer of the market crashes. Different from previous studies which show stable negative correlations between VIX and its underlying (e.g., Badshah, 2013; Talukdar et al., 2017), ivx is positively related to the underlying price in our full sample. We believe the main reasons lie in investor structure and underlying stocks. The SSE 50 index consists of large-cap stocks and is supported by the Chinese government. Facing high volatilities, the retail 13

15 investors who dominate the Chinese market tend to show over-optimism and myopic loss aversion. The speculative behaviors of the retail investors would raise the price and contribute to the unique positive comovement between implied volatility and the underlying price. 3.3 Short-term Evidence in Chinese Market In this part, we find robust evidence that negative return shocks tend to imply higher future volatility than do positive return shocks of the same magnitude and the detected asymmetry is more significant in the upper quantiles of the ivx changes distribution than the lower quantiles. Thus, we can t reject Hypothesis 3. For the results of the OLS regressions of the 1-minute intervals reported by Table 6, we find that the impact of both the contemporaneous and the lagged negative return on ivx changes is stronger than that of the positive return, resulting in asymmetry. For example, the regression results include (Ret + t ) versus (Ret t ) in the full sample and ( Ret + t ) versus ( Ret t ) at the 2015 crash. The return-volatility relation is more asymmetric in the crashes as the positive returns tend to be insignificant and the results remain robust in the forecasting OLS regressions. For the results of the quantile regressions in Table 6, we find that the upper quantiles of the ivx changes are more asymmetric in the return-volatility relation. For example, at the upper most quantile, that is τ = 0.95 in our analysis, the coefficient of positive return is and the coefficient of negative return is In contrast, at the lowest quantile, that is τ = 0.05, the coefficient of positive return is and the coefficient of negative return is

16 More important, we find that the OSL regressions in upper and lower quantiles is biased compared with the quantile regression. In Figure 3, we show the asymmetric ivx responses to the positive and negative returns of the SSE 50 ETF and the results are robust at three different data intervals including 1-minute, 5-minute and 30-minute. Specifically, at the upper quantiles, OLS significantly underestimates (overestimates) the effect of negative (positive) return changes on the ivx change. And this is the opposite of the case of the lower quantiles. In particular, the positive returns are found to be positively correlated with ivx changes at the upper quantile. While at the lower quintile, negative returns and the volatility changes are also positively correlated. These findings are consistent with the abnormal positive relation between ivx and the underlying price, and we believe the reasons also relate to the large-cap underlying stocks and the unique investor structure in the Chinese stock market where retail investors dominate. When market declines, investors of the SSE 50 ETF may not show too much panic as the Chinese government provides support for its stability. Moreover, the retail investors tend to show myopic loss aversion and are not subject to strict risk management requirements as the institutional investors. So, they are unwilling to reduce their position massively and volatility changes slowly in a downward trend, which is in line with the results at the lower quantiles. And in the rising market, some retail investors want to realize the profits, while others want to buy on the upswing. These different decisions lead the volatility to increase and ivx changes sharply, which may result in the positive return-volatility relation at the upper quantiles of our results. 15

17 3.4 Behavior Theories or the Fundamental Theories? Resorting to Table 6 again, we find that the contemporaneous explanatory variables are more important than the lagged variables. Thus, Hypothesis 4 is accepted. Taking Table 6 as an example, the t-values of Ret t, Ret t 1, and Ret t 2 in the upper most quantiles are , , , respectively. And in the lower most quantiles, the t-values of Ret + t, Ret + + t 1, and Ret t 2 are , , , respectively. As the lag order increases, the effect of the variable decreases. Compared with the Table 6 based on the 1-minute sample, we find that the results are different in Table 7 with the lower frequency 30-minute sample. In Table 6, ten in eleven quantities have more significant contemporaneous variables compared with the lagged variables. While in the Table 7, the ratio dropped to five in eleven quantities. Therefore, we believe that in higher frequency trading, it is more appropriate to apply behavior theory. 3.5 The Trading Strategies To examine the role of the volatility index in the strategic trading, we use ivx to select the trading strategies for the 50 ETF. We mainly consider traditional strategies: the MACD rules (the Moving Average Convergence Divergence), and the KDJ rules (the Random Index). The MACD rules is one of the simplest and popular indicators developed by Appel (1979). Using two moving averages, the indicator calculates trend-following characteristics by subtracting the longer moving average from the shorter moving average. The KDJ rules consider of the random amplitude in the 16

18 course of the fluctuation of stock price. And there are three lines standing for random indicators in the stock, namely K line, D line and the J line (Schulmeister, 2008). The test period is from January 4, 2016 to February 14, 2018 and the net value at the beginning is set at 1 yuan. The MACD indicator parameter is (12, 26, 9) and the KDJ indicator parameter is (9, 3, 3). Based on the ivx index, we filter the trading strategies in four cases. Firstly, according to the MACD rules, when DIF>0 3, the underlying price shows unilateral trend or large fluctuations, the volatility index will rise and the MACD rules are appropriate in this case. Secondly, when the underlying price is consolidated and DIF<0, the volatility index shows a downward trend and the KDJ rules are appropriate. Thirdly, if the volatility index is higher than 45, it shows that the panic spreads in the market and the market are overbought or oversold. It is suitable to adopt the KDJ rules in this case. Finally, When the volatility index is below 20, the underlying price is consolidated and the KDJ rules are appropriate. Specifically, when we choose the MACD rules, we can buy at DIF>0 and sell at DIF<0. And when we choose the KDJ rules, we can buy when the J value is above 80 and drops for the first time and sell when the J value is below 20 and rises for the first time. Table 8 shows the performance of the strategies and we find that the KDJ rules is significantly better than the MACD rules, which gain higher final net values, higher Sharpe ratio and the lower maximum withdrawal. For that ivx is in a downward 3 This MACD indicator indicates the big band trend and DIF means the amount of a small band of fluctuation. If the market shows an upward trend, the deviation in the line speed is gradually expanded. While the MACD is still moving along the trend, it results in the cross situation of DIF and MACD, namely buy signal. And the contrary can be the sell signal. 17

19 trend and stay below 0.2, the KDJ rules is selected, which is confirmed to be the optimal decision. Thus, we believe that ivx plays an important role in the selection strategy. 4. Conclusions In this paper, we investigate the validity of the Shanghai Stock Exchange's revised implied volatility index (ivx) and the return-volatility relation using unique intraday data. We test four hypotheses and have following primary findings. We believe that ivx is an effective volatility measure of the stock market. On the one hand, ivx has a strong contemporaneous correlation with realized volatility, which mainly comes from the comovement between the ivx and the discontinuous part of the volatility. On the other hand, we find that ivx has a positive forecasting power for the future volatility and provides a more effective forecast than the lagged realized volatility in the crashes. While Zheng et al. (2017) suppose that daily ivix (old version of the SSE volatility index) should be referred to as the greed index rather than the fear index. We revisit this issue with the intraday new-revised ivx index and draw different conclusions. Although ivx is positively related to the price of the SSE 50 ETF in the full sample, it is negatively related to the price in the market crashes and has a significant negative comovement with the return, especially the negative return of the SSE 50 ETF. More important, ivx can negatively predict the short-term market declines and act as the barometer of the crises. Thus, our empirical results indicate that the SSE ivx is more in line with the fear index. 18

20 Further, our study documents the asymmetric relation between return and ivx changes and examines the uniqueness of the Chinese market. We find in the crashes, such as the 2015 stock market crash and the 2016 Circuit-Breaker in China, the detected asymmetry is more prominent. Consistently, upper quantiles of the ivx changes are found to be more asymmetric in the return-volatility relation. And we observe that the behavioral theory rather than the traditional hypotheses is most appropriate in explaining the short-term asymmetric volatility phenomenon, especially in sample of higher frequency. Some abnormal positive relations distinguish the Chinese market and the US market. ivx has a positive comovement with the underlying price in the full sample. In particular, the positive returns are positively correlated with ivx changes at the upper quantile. And at the lower quintile, negative returns and the volatility changes are also positively correlated. And we believe that the main reasons may lie in different underlying stocks and the investor structure. What s more, we examine how ivx performs in the selecting the trading strategies and two traditional trading strategies including the MACD rules (the Moving Average Convergence Divergence) and the KDJ rules (the Random Index) are mainly considered. The results indicate that the KDJ rules performs better than the MACD rules and ivx plays an important role in the selecting the strategies for the 50 ETF. 19

21 References Appel, G., The moving average convergence-divergence trading method: advanced version. Scientific Investment Systems. Badshah, I. U., Quantile regression analysis of the asymmetric return-volatility relation. Journal of Futures Markets 33(3), Barndorff-Nielsen, O.E., Shephard, N., Power and bipower variation with stochastic volatility and jumps, Journal of Financial Econometrics 2(1), Bekiros S, Jlassi M, Naoui K, et al., The asymmetric relationship between returns and implied volatility: Evidence from global stock markets. Journal of Financial Stability 30, Bollerslev T, Patton A J, Quaedvlieg R., Exploiting the errors: A simple approach for improved volatility forecasting, Journal of Econometrics 192(1), Campbell J Y, Hentschel L., No news is good news: An asymmetric model of changing volatility in stock returns. Journal of financial Economics 31(3), Christie A A., The stochastic behavior of common stock variances: Value, leverage and interest rate effects. Journal of financial Economics 10(4), Dennis P, Mayhew S, Stivers C., 2006 Stock returns, implied volatility innovations, and the asymmetric volatility phenomenon. Journal of Financial and Quantitative Analysis 41(2), Duffee G R., Stock returns and volatility a firm-level analysis. Journal of 20

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24 Figure 1 Time Series of ivx, Price and Return of the SSE 50 ETF Notes: Panel A of this figure plots the 1-minute time series of ivx and the price of the SSE 50 ETF and Panel B is for 1-minute ivx and the return. The sample period of Panel A and B is from 9 th Feb 2015 to 14 th Feb Panel C shows the 1-minute time series of ivx and the price during the 2015 stock crash, which is from 1 st Jun 2015 to 31 st Aug And Panel D shows the same series as Panel C but during the 2016 Circuit-Breaker period, which is from 4 th Jan 2016 to 7 th Jan The data series are not standardized. 23

25 Figure 2 Time Series of ivx and the Realized volatility of the SSE 50 ETF Notes: Panel A of this figure plots the 30-minute time series of ivx and the realized volatility of the SSE 50 ETF and Panel B is for 30-minute jump and continuous components of the realized volatility. The sample period of Panel A and B is from 9 th Feb 2015 to 14 th Feb Panel C shows the 30-minute time series of ivx and the realized volatility during the 2015 stock crash, which is from 1 st Jun 2015 to 31 st Aug And Panel D shows the same series as Panel C but during the 2016 Circuit-Breaker period, which is from 4 th Jan 2016 to 7 th Jan The data series are not standardized. 24

26 Figure 3 Asymmetry in Return-Volatility Relations: Quantile Plots Notes: Figure 3 shows the asymmetric ivx responses to contemporaneous positive and negative returns of the SSE 50 ETF. Panel A, C and E are for the positive returns while Panel B, D and F are for the neagtive returns. We show the results at three different data intervals including 1-minute, 5-minute and 30-minute. 25

27 Table 1 Preliminary Data Analysis Panel A. Descriptive Statistics at the 1-minute Intervals Mean Std. Skewness Kurtosis Min Max Dev. ivx t Price t Ret t Panel B. Descriptive Statistics at the 30-minute Intervals Mean Std. Skewness Kurtosis Min Max Dev. ivx t Price t Ret t RV t BPV t Jump t Notes: Summary statistics of the both panels are from 9 th Feb 2015 to 14 th Feb All variables are not standardized. ivx t is the first order difference of the ivx index. Price t and Ret t are the price and the return of the SSE 50 ETF. RV t is the realized volatility of the SSE 50 ETF, which are decomposed into the jump (Jump t ) part and continuous (BPV t ) part. 26

28 Table 2 ivx and the Contemporaneous Realized Volatility Panel A. Correlation Coefficients at 30-minute frequency RV t Jump t BPV t Full Sample 0.417*** 0.369*** 0.157*** The 2015 Crash Period 0.426*** 0.366*** 0.157*** Panel B. Correlation Coefficients at 60-minute frequency RV t Jump t BPV t full sample 0.470*** 0.427*** 0.224*** The 2015 Crash Period 0.494*** 0.433*** 0.242*** Notes: Table 2 presents correlation coefficients between ivx and the realized volatility at both 30-minute (Panel A) and 60-minute (Panel B) frequencies. RV t is the realized volatility of the SSE 50 ETF, which are decomposed into the jump (Jump t ) and continuous (BPV t ) parts. The full sample is from 9 th Feb 2015 to 14 th Feb 2018 and the 2015 Crash Period is from 1 st Jun 2015 to 31 st Aug ***, ** and * denote statistical significance at the 1% level, 5% and 10% level respectively. 27

29 Table 3 ivx and the Future Realized Volatility RV t ivx t 1 RV t 1 Constant t R 2 full sample 30-min 0.242***(20.27) 0.411***(34.34) 0.001(0.08) min 0.256***(15.33) 0.436***(26.13) (-0.00) The 2015 Crash Period 30-min 1.212***(6.78) 0.289***(6.77) ***(-4.08) min 1.378***(5.44) 0.269***(4.35) ***(-3.31) Jump t ivx t 1 Jump t 1 Constant t R 2 full sample 30-min 0.245***(19.88) 0.328***(26.59) 0.000(0.00) min 0.267***(15.51) 0.358***(20.81) (-0.08) The 2015 Crash Period 30-min 1.182***(6.35) 0.227***(5.23) ***(-3.74) min 1.383***(5.31) 0.211***(3.41) ***(-3.17) BPV t ivx t 1 BPV t 1 Constant t R 2 full sample 30-min 0.153***(11.69) (-0.82) (-0.03) min 0.199***(10.75) 0.061***(3.27) 0.001(0.03) The 2015 Crash Period 30-min 0.662***(3.37) (-1.23) **(-2.06) min 0.859***(3.11) (-0.02) *(-1.86) Notes: Table 3 presents the results of the forecasting regressions: RV t = C + β 1 ivx t 1 + β 2 RV t 1 + ε t, Jump t = C + β 1 ivx t 1 + β 2 Jump t 1 + ε t and BPV t = C + β 1 ivx t 1 + β 2 BPV t 1 + ε t. RV t is the realized volatility of the SSE 50 ETF where RV t 1 denotes its first-order lag. Jump t is the discontinuous variations and BPV t is the continuous variations. We show results at both 30-minute and 60-minute frequencies and have an insight into the related subsample. The full sample is from 9 th Feb 2015 to 14 th Feb 2018 and the 2015 Crash Period is from 1 st Jun 2015 to 31 st Aug ***, ** and * denote statistical significance at the 1% level, 5% and 10% level respectively. 28

30 Table 4 ivx changes and Contemporaneous Price (Return) ivx and the Price of SSE 50 ETF 30-minute 5-minute 1-minute full sample 0.142*** 0.140*** 0.139*** The 2015 Crash Period *** *** *** The 2016 Circuit-Breaker Period *** *** *** ivx changes and the Return of SSE 50 ETF 30-minute 5-minute 1-minute full sample *** *** *** The 2015 Crash Period *** *** ** The 2016 Circuit-Breaker Period *** *** *** ivx changes and the Negative Return of SSE 50 ETF 30-minute 5-minute 1-minute full sample *** *** *** The 2015 Crash Period *** *** ** The 2016 Circuit-Breaker Period *** *** *** Notes: Table 4 presents correlation coefficients between ivx, the index price (Panel A) and the return (Panel B) of the SSE 50 ETF at 1-minute, 5-minute and 30-minute frequencies. The full sample is from 9 th Feb 2015 to 14 th Feb The 2015 Crash Period is from 1 st Jun 2015 to 31 st Aug 2015 and the 2016 Circuit-Breaker Period is from 4 st Jan 2016 to 7 st Jan ***, ** and * denote statistical significance at the 1% level, 5% and 10% level respectively. 29

31 Table 5 ivx Changes and the Future Return Ret t ivx t 1 Ret t 1 Constant t R 2 full sample 1-min (-1.47) 0.051***(21.56) 0.000(0.07) min *(-1.78) 0.006(1.10) 0.000(0.03) min 0.000(0.01) 0.088***(6.68) (-0.02) The 2015 Crash Period 1-min **(-2.10) 0.070***(8.69) (-1.19) min (-1.04) (-0.07) (-1.32) min 0.203**(2.15) 0.107**(2.39) 0.502***(5.37) Ret t ivx t 1 Ret t 1 Constant t R 2 full sample 1-min ***(-7.45) 0.175***(74.94) 0.000(0.09) min ***(-7.14) 0.139***(26.15) 0.001(0.10) min 0.018(1.14) 0.219***(16.57) (-0.07) The 2015 Crash Period 1-min ***(-4.27) 0.153***(19.18) ***(-32.21) min ***(-2.70) 0.074***(4.08) ***(-16.44) min 0.191*(1.77) 0.223***(4.66) ***(-6.00) Notes: Table 5 presents the results of the forecasting regressions:ret t = C + β 1 ivx t 1 + β 2 Ret t 1 + ε t and Ret t 1 = C + β 1 ivx t 1 + β 2 Ret t 1 + ε t, where Ret t is the return and is negative returns of the SSE 50 ETF. ivx t is the first-order difference of the ivx Ret t 1 index. ivx t 1 denotes the first-order lag and so on. The full sample is from 9 th Feb 2015 to 14 th Feb 2018 and the 2015 Crash Period is from 1 st Jun 2015 to 31 st Aug ***, ** and * denote statistical significance at the 1% level, 5% and 10% level respectively. 30

32 Table 6 Quantile Regressions for the Asymmetric Return-Volatility Relations (1-Minute Data) τ Ret t Ret t Ret t 1 Ret t 2 Ret t 1 Ret t 2 ivx t 1 ivx t 2 Constant t R OLS OLS-Crash OLS-Breaker *** (-56.00) *** (-65.53) *** (-60.48) *** (-55.71) *** (-46.90) 0.003*** (7.50) 0.038*** (62.65) 0.047*** (68.84) 0.060*** (69.89) 0.078*** (70.02) 0.123*** (61.33) 0.005*** (3.74) (1.63) *** (-10.56) 0.101*** (52.53) 0.068*** (62.99) 0.052*** (59.61) 0.039*** (56.79) 0.030*** (49.72) *** (-4.64) *** (-61.56) *** (-68.02) *** (-70.88) *** (-75.71) *** (-65.27) *** (-17.93) *** (-4.55) *** (-3.54) *** (-44.41) *** (-53.30) *** (-51.04) *** (-49.99) *** (-45.99) *** (-13.00) 0.014*** (22.24) 0.021*** (29.91) 0.027*** (31.72) 0.040*** (35.47) 0.063*** (31.33) *** (-12.59) *** (-4.37) (-1.21) OLS F *** OLS F -Crash OLS F -Breaker (-10.00) *** (-3.67) *** (-3.37) *** (-37.49) *** (-47.03) *** (-45.04) *** (-45.20) *** (-42.27) *** (-12.68) 0.011*** (18.09) 0.015*** (21.82) 0.021*** (24.47) 0.028*** (25.59) 0.045*** (22.42) *** (-7.73) ** (-2.25) 0.040* (1.71) *** (-5.33) * (-1.66) (-0.71) 0.069*** (35.76) 0.044*** (40.48) 0.032*** (36.66) 0.025*** (35.92) 0.019*** (30.86) *** (-5.15) *** (-41.25) *** (-47.01) *** (-49.23) *** (-49.93) *** (-41.57) * (-1.93) 0.009* (1.86) *** (-4.57) *** (-5.37) (1.06) *** (-5.45) *** (29.87) 0.038*** (35.11) 0.027*** (30.99) 0.020*** (29.03) 0.015*** (24.17) *** (-5.39) *** (-36.90) *** (-39.36) *** (-42.52) *** (-39.63) *** (-34.25) *** (-9.69) *** (-3.19) *** (-4.16) *** (-12.67) *** (-3.91) * (-1.79) *** (-36.58) *** (-53.67) *** (-61.15) *** (-73.62) *** (-82.13) *** (-97.95) *** (-62.19) *** (-53.72) *** (-40.74) *** (-28.87) *** (-17.97) *** (-77.25) *** (-25.58) (-1.55) *** (-76.70) *** (-25.38) ** (-2.24) *** (-12.23) *** (-15.79) *** (-16.65) *** (-18.40) *** (-15.54) *** (-12.64) *** (-4.92) *** (-3.38) ** (-2.54) (-0.45) (0.46) *** (-20.95) *** (-9.89) (0.10) *** (-20.57) *** (-9.74) *** ( ) *** ( ) *** ( ) *** ( ) *** ( ) *** (-15.80) 0.096*** (173.66) 0.125*** (199.99) 0.164*** (209.53) 0.220*** (215.97) 0.331*** (180.77) (-0.27) (0.11) (0.72) (-0.27) Notes: Table 6 presents the results of the quantile regressions using 1-minute interval data: ivx t = C + β 1 Ret + t + β 2 Ret t + β 3 Ret + t 1 + β 4 Ret + t 2 + β 5 Ret t 1 + β 6 Ret t 2 +β 7 ivx t 1 + β 8 ivx t 2 + ε t, where Ret t + is the return of the SSE 50 ETF and Ret t (Ret t ) denotes positive (negative) returns. ivx t is the first-order difference of the ivx index. We show the lower, the median and the upper quantiles of the regressions. And the OLS regression is taken for the comparison. The sample period is from 9th Feb 2015 to 14 th Feb The 2015 Crash Period is from 1st Jun 2015 to 31st Aug 2015 and the 2016 Circuit-Breaker Period is from 4st Jan 2016 to 7st Jan ***, ** and * denote statistical significance at the 1% level, 5% and 10% level respectively (0.06) (1.08) (0.77)

33 Table 7 Quantile Regressions for the Asymmetric Return-Volatility Relations (30-Minute Data) τ Ret t Ret t Ret t 1 Ret t 2 Ret t 1 Ret t 2 ivx t 1 ivx t 2 Constant t R OLS *** (-13.14) *** (-13.43) *** (-17.37) *** (-17.62) *** (-15.43) *** (-4.09) 0.043*** (8.97) 0.057*** (8.46) 0.101*** (13.15) 0.161*** (16.36) 0.250*** (10.68) (0.99) 0.088*** (8.01) 0.068*** (8.45) 0.045*** (8.30) 0.029*** (6.83) 0.014*** (3.40) *** (-12.52) *** (-24.49) *** (-21.73) *** (-24.40) *** (-23.43) *** (-15.53) *** (-13.09) *** (-8.76) *** (-7.74) *** (-9.13) *** (-10.47) *** (-9.31) ** (-2.48) 0.018*** (3.64) 0.023*** (3.32) 0.035*** (4.56) 0.041*** (4.07) 0.076*** (3.20) *** (-2.58) *** (-4.45) *** (-6.27) *** (-5.96) *** (-5.56) *** (-5.18) ** (-2.19) (0.23) (0.89) 0.016** (2.03) 0.035*** (3.60) 0.100*** (4.32) (-1.54) 0.087*** (7.46) 0.065*** (7.59) 0.043*** (7.55) 0.030*** (6.75) 0.025*** (6.04) * (-1.66) *** (-7.90) *** (-7.49) *** (-9.57) *** (-10.82) *** (-6.55) *** (-6.49) 0.090*** (7.85) 0.074*** (8.75) 0.046*** (8.20) 0.038*** (8.70) 0.036*** (8.64) 0.015*** (4.78) * (-1.68) (-1.24) *** (-3.23) *** (-3.99) ** (-2.51) (-1.08) ** (-2.52) * (-1.83) * (-1.91) (-1.40) (-0.18) 0.011*** (2.84) 0.015** (2.51) 0.017** (2.04) 0.023** (2.34) 0.029** (2.34) (1.49) *** (-31.22) (-1.58) (-1.21) (-1.57) * (-1.76) (-1.39) (-0.22) (-0.23) (-0.04) (0.11) (0.22) (0.24) *** (-12.19) Notes: Table 7 presents the asymmetric return-volatility relations investigated by the quantile *** (-40.73) *** (-39.95) *** (-45.58) *** (-47.29) *** (-40.79) *** (-8.96) 0.107*** (24.29) 0.150*** (24.09) 0.225*** (31.72) 0.319*** (35.12) 0.524*** (24.36) (-0.06) regressions using high frequency 30-minute interval data: ivx t = C + β 1 Ret + t + β 2 Ret t + β 3 Ret + t 1 + β 4 Ret + t 2 + β 5 Ret t 1 + β 6 Ret t 2 +β 7 ivx t 1 + β 8 ivx t 2 + ε t, where Ret t is + the return of the SSE 50 ETF and Ret t (Ret t ) denotes positive (negative) returns. ivx t is the first-order difference of the ivx index. We show the lower, the median and the upper quantiles of the regressions. And the OLS regression is taken for the comparison. The sample period is from 9 th Feb 2015 to 14 th Feb ***, ** and * denote statistical significance at the 1% level, 5% and 10% level respectively