The reverse volatility asymmetry in Chinese financial market

Abstract

We investigate the intraday return–volatility correlation in Chinese financial market with high-frequency transaction data of individual stocks. In contrast to the widely accepted theory of volatility asymmetry (i.e. negative returns induce higher price volatilities than positive ones), we show that the price volatilities in Chinese market react more intensively to positive returns than their reaction to negative returns. This reverse volatility asymmetry is mainly due to the higher trading volume associated with positive returns, that is, in Chinese market the investors’ rushing for a price rising stock makes the positive returns arouse higher volatility than their negative counterparts. So in an average sense, a positive return–volatility correlation is observed for most of the individual stocks in our sample. Besides, price jumps play an important role in the significance of this positive correlation. For most of the individual stocks in our sample, the positive correlation is insignificant until jumps are totally eliminated in both return and volatility. For multiple stocks analysed together, the jumps of individual stocks are mostly diversified, and therefore a significant positive return–volatility correlation shows up irrespective of the existence of jumps. Moreover, our results are robust in different market conditions, no matter in depression or flourish.

Keywords:

• leverage effect
• reverse volatility asymmetry
• local variance measures
• jumps

JEL Classification:

• G10
• G11
• G14

Notes

¹ See Cox and Ross (1976) for an example.

² See Bekaert and Wu (2000) for a review of some influential articles in this field.

³ See Bollerslev et al. (2008) (US stock markets), Qiu et al. (2006) (German stock markets) and Bekaert and Wu (2000) (Japanese stock markets) and so on.

⁴ These descriptions about Chinese investors are consistent with the warrant bubble example of Xiong and Yu (2011), which shows the existence of some naive investors in Chinese market. They do not clearly understand the trading rule but trade actively in the market.

⁵ The definitions and related literatures of these two effects will be introduced in Section 2.

⁶ See Andersen et al. (2001a, b) and Corsi (2009) to know better about the long memory property of volatility.

⁷ See Andersen and Dobrev (2007), Huang and Tauchen (2005) and Corsi and Reno (2012) for more details about the contribution of jumps to daily volatility.

⁸ To know better about the distribution characteristic of jumps, see Ané and Métais (2010) for details.

⁹ Cai and Zheng (2004) find that institutional investors as a group own more than half of US publicly traded equities and make more than 50% of all trades in the US stock market.

¹⁰ See, for example, Nelson (1991), Bekaert and Wu (2000), Bollerslev and Tauchen (2006).

¹¹ See Bekaert and Wu (2000), Bollerslev and Tauchen (2006) for further details of this different causalities.

¹² For a review of researches with daily data, see Bekaert and Wu (2000).

¹³ As suggested in Corsi et al. (2010), the choice of the bandwidth parameter L is not crucial.

¹⁴ See Barndorff-Nielsen and Shephard (2002, 2004, 2005, 2007) and Barndorff-Nielsen et al. (2006) for more introduction about Bipower variation.

¹⁵ This estimator of local variance is just a simple application of the results in estimating the diffusion coefficient when the diffusion process is continuous and has no jump. See Florens-Zmirou (1993), Jiang and Knight (1997) and Stanton (1997) for more details on this estimator.

¹⁶ are the return–volatility correlations on day t. So when calculating the linear correlations, we restrict the calculation within a trading day. This excludes the overnight effect and finally, average correlations of all the sample days are computed.

¹⁷ Note that the return series corresponding to the no-jump estimator of local variance (NJLV) is the no-jump return series in this context and all the following analysis of return–volatility correlation (including the regression equations).

¹⁸ The instructions for Figs 2 and 3 are similar and therefore omitted in the following pages.

¹⁹ Since the sample is 5 min returns and in Chinese market, the trading time in one day is only 4 hours, so every trading day we have 48 observations. We treat all the trading day as a cross-section sample and ignore the time effect longer than 1 day. In other words, we only concentrate on the return–volatility correlation in average intraday level.

²⁰ We only select five lagged terms and preceding terms, because in our empirical process we find that the coefficients can preserve their significance within five terms averagely. To save place we do not add terms further than five terms.

²¹ The high-frequency sample length insures the large degree of freedom of the t-distribution (approximately normal), which suggest that in 5% significant level, a regressor is significant when the absolute value of its t-statistic is greater than 1.96.

²² Note that unlike the correlation figures, here the negative returns do not take their absolute value. All the terms have their original signs in the regression.

²³ For further specification of these denotations, see the instruction below Table 3.

²⁴ See, for example, Schwert (1989) and Gallant et al. (1992). Karpoff (1987) provides a detailed review of the empirical research on this positive relationship.

²⁵ Note that volume difference is defined as the difference between positive returns and negative returns in each 5 min interval. And the daily, weekly and monthly difference are the difference between 1 day, 5 days and 22 days sum of all 5-min volume of positive and negative returns.

²⁶ Actually, different from the always falling price in 2008, in 2009, many individual stocks had received a time of reverse from depression, but however, the reverse time is short and the price dropped again after this short reverse, so it is reasonable to treat the market in 2008–2009 as a sample of bear market.