Asymmetric risk spillovers between Shanghai and Hong Kong stock markets under China’s capital account liberalization

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Asymmetric risk spillovers between Shanghai and Hong Kong stock markets under China’s capital account liberalization Kun Yanga,b, Yu Weic, Shouwei Lia,b, Jianmin Hea,b, a b c

⁎

School of Economics and Management, Southeast University, Nanjing, China Research Center for Financial Complexity and Risk Management, Southeast University, Nanjing, China School of Finance, Yunnan University of Finance and Economics, Kunming, China

ARTICLE INFO

ABSTRACT

Keywords: Financial liberalization Asymmetric risk spillover CoVaR Variational mode decomposition Realized volatility

In this paper, we investigate the asymmetric risk spillovers between Shanghai and Hong Kong stock markets under the backdrop of China’s capital account liberalization by measuring the Conditional Value-at-Risk (CoVaR) based on adjusted realized volatilities and variational mode decomposition based copula model. The empirical results show that, the asymmetric features of risk spillovers between the two markets are significant and manifest different states before and after the Shanghai-Hong Kong Stock Connect and Shenzhen-Hong Kong Stock Connect schemes. More specifically, first, the downside risk spillovers from Hong Kong to Shanghai are significantly larger than its upside risk spillovers, while the risk spillovers from Shanghai to Hong Kong is on the contrary. Second, the short-run risk spillovers are more drastic than the long-run risk spillovers, except the risk spillovers from Shanghai to Hong Kong after the Shenzhen-Hong Kong Stock Connect scheme. Finally, by comparing the risk spillovers from two directions, the importance of Shanghai stock market gradually rises up with the implementations of Stock Connect schemes.

1. Introduction During the past two decades, Chinese government has launched a series of financial liberalization policies to strengthen the linkages between domestic and international capital markets and achieves good policy performance, such as the Qualified Foreign Institutional Investors (QFII), the Renminbi Qualified Foreign Institutional Investor (RQFII) and multiple exchange rate reforms. In order to further improve the bi-directional opening of capital markets, the Shanghai-Hong Kong Stock Connect and Shenzhen-Hong Kong Stock Connect schemes1 which allow investors to trade shares listed on the other stock markets are carried out on November 11, 2014 and December 5, 2016, respectively. With the implementations of two capital account liberalization schemes, the capital flows and dependence between mainland China and Hong Kong stock markets have massive increases (Huang & Ji, 2017; Wu, Huang, & Ni, 2017; Zhang & Li, 2018). Whereas, the surges of capital flows can also increase the risk spillovers between two stock markets, which results in investment risk and unstable financial environment (Yang, Shi, Wang, & Jing, 2018). Thus, it is meaningful for market

Corresponding author at: School of Economics and Management, Southeast University, Nanjing, China. E-mail address: [email protected] (J. He). 1 Shanghai (Shenzhen)-Hong Kong Stock Connect scheme initiated by the Shanghai (Shenzhen) Stock Exchange and Hong Kong Stock Exchange is an interconnection mechanism between different stock markets, which allows investors in a specific stock market to buy and sell shares listed on another stock market through the local securities companies. More details can be found in Shanghai Stock Exchange website (http://www.sse.com. cn/) and Shenzhen Stock Exchange website (http://www.szse.cn/). ⁎

https://doi.org/10.1016/j.najef.2019.101100 Received 7 May 2019; Received in revised form 2 September 2019; Accepted 21 October 2019 1062-9408/ © 2019 Elsevier Inc. All rights reserved.

Please cite this article as: Kun Yang, et al., North American Journal of Economics and Finance, https://doi.org/10.1016/j.najef.2019.101100

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management department, investors and researchers to probe the impacts of Stock Connect schemes on risk spillovers between mainland China and Hong Kong stock markets. The impacts of two Stock Connect schemes on the risk spillovers between mainland China and other stock markets have been discussed to a certain extent (Zhang & Jaffry, 2015; Huo & Ahmed, 2017; Chow, Chui, Cheng, & Wong, 2018; Yang, Wei, He, & Li, 2019). For example, Huo and Ahmed (2017) hold that the risk spillovers from Shanghai to Hong Kong are significantly strengthened after the Shanghai-Hong Kong Stock Connect scheme. Yang et al. (2019) find that two Stock Connect schemes can improve the downside risk spillovers between mainland China and London stock markets in most cases. However, the previous literatures pour more attention into the variations of overall risk contagions and ignore the asymmetric features of risk spillovers. In fact, due to different market fundamentals, investor trading strategies and importance of stock markets, the risk spillovers may vary across bear and bull conditions, under short- and long-run horizons and from different spillover directions (Li & Wei, 2018). Meanwhile, since the risk spillovers under different market conditions, investment horizons and spillover directions may be differently affected by two Stock Connect schemes, the asymmetric features of risk spillovers may vary with the implications of Stock Connect schemes. Therefore, accurately measuring the risk spillovers between mainland China and Hong Kong stock markets from different perspectives and further analyzing their asymmetric features at different stages of Stock Connect schemes, can provide more targeted and comprehensive references to prevent financial risk contagions and deepen China’s financial reform. This paper aims to compare the risk spillovers between Shanghai and Hong Kong markets under different market conditions, investment horizons and spillover directions before and after the two Stock Connect schemes launched in China. First, the adjusted realized volatilities which are calculated by 5-min high-frequency price data are used to standardize stock residuals. Second, the variational mode decomposition (VMD) approach is introduced to decompose the standardized residuals into short- and long-run modes. Next, twenty-two types of static, time-varying, symmetric and asymmetric copula functions are constructed to depict the possible dependence between Shanghai and Hong Kong stock markets. Then, the best fitted copula function is selected to calculate the short- and long-run downside and upside Conditional Value-at-Risk (CoVaR) and delta Conditional Value-at-Risk (ΔCoVaR) of Shanghai and Hong Kong stock markets, and the asymmetric features of risk spillovers at different stages are further tested by bootstrap Kolmogorov-Smirnov approach. Finally, the traditional dynamic conditional correlation MVGARCH (DCC-MVGARCH) model is utilized as a robustness check. Thus, this paper contributes to the literature in the following three facets. First, the asymmetric risk spillovers between Shanghai and Hong Kong stock markets are discussed under the backdrop of two Stock Connect schemes. Though the impacts of Stock Connect schemes on risk spillovers have been discussed to a certain extent, the asymmetric features of risk spillovers under different market conditions, investment horizons and spillover directions before and after two Stock Connect schemes are ignored. Therefore, we use the CoVaR framework proposed by Adrian and Brunnermeier (2016) and modified by Girardi and Ergün (2013) to quantify the risk spillovers from two directions. Furthermore, to accurately depict the asymmetric features of risk spillovers under different market conditions and investment horizons, on the one hand, the copula function which is superior to the bivariate quantile regression and multivariate GARCH approaches in depicting asymmetric tail dependence is utilized to measure the downside and upside CoVaRs (Reboredo and Ugolini, 2018; Ji et al., 2018a). On the other hand, the VMD model proposed by Dragomiretskiy and Zosso (2014) is introduced to measure the CoVaRs under different investment horizons. Compared with the traditional discrete wavelet transform (DWT), maximal overlap discrete wavelet transform (MODWT) and ensemble empirical mode decomposition (EEMD) approaches, the VMD method can adaptively and non-recursively decompose the original series into numerous modes which represent different time scales (Lahmiri, 2016; Li, Chen, Zi, & Pan, 2017), thus can depict the risk spillovers under multi-investment horizons more accurately. On that basis, the bootstrap Kolmogorov-Smirnov test proposed by Abadie (2002) is utilized to discuss the asymmetric features of risk spillovers by comparing the cumulative distributions of corresponding delta CoVaRs. Second, the adjusted realized volatilities are introduced to construct copula functions, which can depict the risk spillovers between stock markets more effectively. The current researches commonly use GARCH- or SV-type models to estimate historical volatility and further apply it to build copula model. However, these low-frequency volatility models which are limited by daily or lower frequency data ignore the intraday transaction information and may cause biased estimates and forecasts (Wen, Gong, & Cai, 2016; Ma, Wei, Chen, & He, 2018). With the widespread availability of high-frequency data, the realized volatility proposed by Andersen and Bollerslev (1998) and Andersen, Bollerslev, Diebold, and Ebens (2001) is gradually used to replace the historical volatility in financial risk management. More specially, since volatility measures are crucial for portfolio research (Shin, 2018), the realized volatility is increasingly introduced to analyze dependence, future hedge and portfolio diversification in recent years (Ning, Xu, & Wirjanto, 2008; Mendes and Accioly, 2012; Avdulaj & Barunik, 2015; Lai, 2018). Whereas, few literatures are found to use the realized volatility to quantify risk spillover. Third, the findings of this paper extend the conclusions of previous literatures which do not focus on the asymmetric features of risk spillovers between Shanghai and Hong Kong markets, and can provide more perspectives for financial risk management. On the one hand, in the existing researches, Zhang and Jaffry (2015) holds that there is no volatility spillover before the Shanghai-Hong Kong Stock Connect scheme, while Huo and Ahmed (2017) achieve a contrary conclusion. This paper provides strong evidence of bidirectional risk and volatility spillovers and further confirms the conclusions of Huo and Ahmed (2017). On the other hand, Huo and Ahmed (2017) and Chow et al. (2018) point out that the Shanghai-Hong Kong Stock Connect scheme enhances the leading power of Shanghai stock market. Similarly, this paper finds that the importance of Shanghai stock market increasingly rises up with the implementations of Stock Connect schemes. More specifically, the short-run risk spillovers from Shanghai to Hong Kong become comparable with that from Hong Kong to Shanghai, and the long-run risk spillovers from Shanghai to Hong Kong become significantly larger than that from Hong Kong to Shanghai. Whereas, we also achieve some different conclusions that Hong Kong stock market dominates Shanghai stock market in the short-run before the Shenzhen Stock Connect scheme. Moreover, the asymmetric 2

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features of risk spillovers under different market conditions and investment horizons are also proved and manifest slightly different states at different stages of Stock Connect schemes, which is not obtained in the previous researches. In terms of bear or bull conditions, the downside risk spillovers from Hong Kong to Shanghai are significantly larger than its upside risk spillovers, while the upside risk spillovers from Shanghai to Hong Kong are more intense than its downside risk spillovers. Regarding to the short- or longrun investment horizons, the short-run risk spillovers are dramatic than the long-run risk spillovers in most cases, except the risk spillovers from Shanghai to Hong Kong after the Shenzhen-Hong Kong Stock Connect scheme. The remainder of this paper is organized as follows: Section 2 introduces the methodology. Section 3 describes the data and descriptive statistics. Section 4 and 5 discuss the empirical results. Section 6 concludes. 2. Methodology 2.1. Constructing marginal distribution using adjusted realized volatility and VMD According to the descriptive statistics for stock returns in section 3, Shanghai stock market shows significant auto-correlation, while Hong Kong stock market is not auto-correlated. Thus, the return series of Shanghai and Hong Kong stock markets can be assumed as Eq. (1) and Eq. (2), respectively.

rt = w + a 0 rt

1

(1)

+ et ,

(2)

rt = E (rt ) + et ,

where rt is the return at time t , w is the constant term of regression equation, a0 indicates the impacts of historical returns on current returns, E (rt ) states the mean of returns and et is the stock residuals. Furthermore, the standardized residuals are calculated as z t = et RVt , in which et is the stock residuals and RVt states the adjusted realized volatility which contains the intraday transaction information and overnight information. Using the method proposed by Hansen and Lunde (2006), the adjusted realized volatility RVt can be computed as:

e2 i=1 i

RVt =

i=1

RVi

RVt ,

(3) 1 r2 j = 1 (t 1) + j· ,

where ei denotes the residual series obtained from Eq. (1) or Eq. (2), and RVt = is the realized volatility proposed by Andersen and Bollerslev (1998) and Andersen et al. (2001). In order to analyze the risk spillovers under different investment horizons, the VMD method is used to decompose standardized residuals z t into ten modes which indicate different investment cycles respectively, according to the suggestions of Mensi, Hammoudeh, Shahzad, and Shahbaz (2017). The VMD approach can adaptively decompose time series f into discrete k numbers of modes uk (t ) , and each mode needs to be mostly compact around a center frequency to minimize the sum of estimated bandwidths. The constrained variational model can be expressed as:

min =

{uk},{ k }

j t

(t ) +

t k

2

uk (t ) e

j kt

s. t.

uk = f ,

(4)

k

2

where t indicates the partial derivative, (t ) is the Dirac distribution, represents the convolution, {uk} states the set of modes decomposed from the original signal f and { k } is the set of center frequencies. Introducing the Lagrange multiplier and the quadratic penalty factor , the constrained variational problem is transformed into an unconstrained variational problem. Thus, the augmented Lagrange function can be written as:

L ({uk}, {

k },

)=

t k

(t ) +

j t

2

uk (t )

+

f

2

uk

2 2

+

,f

uk .

(5)

Then, the decomposed mode, center frequency and Lagrange multiplier are updated in the Fourier domain as Eq. (6) to Eq. (8) until meet the convergence condition k ukn + 1 ukn 22 ukn 22 .

f ukn + 1 = n+1 k

=

ui + i k

1+2 (

n+ 1

}

k)

2

|uk ( )|2 d

0

n

+

.

(6)

.

|uk ( )|2 d

0

{

2

(7)

ukn + 1 ,

f

(8)

k

where is the time step. On the basis of decomposed modes obtained from VMD method, the extreme value theory (EVT) is used to separately describe the 3

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Table 1 Binary copula functions. This table presents the main features of eleven types of binary copula functions. L , U , LU and UL indicate the lower- and upper-tail dependence, respectively. (·) and T (·) refer to the bivariate standard normal distribution function with correlation and the bivariate Student’s t distribution function with degree-of-freedom and correlation , respectively. 1 (·) and t 1 (·) denote the standard normal distribution function and the Student’s t distribution function with degree-of-freedom , respectively. P.D. and N.D. state positive and negative dependence, respectively. Lower-Lower, Upper-Upper, Lower-Upper and Upper-Lower indicate that the corresponding copula function can depict lower, upper, lower–upper and upper-lower tail dependence between two markets, respectively. Type

Formula

Gaussian

CN (u, v; ) =

Student’s t

Parameter 1 (u),

(

1

CST (u, v; , ) = T (t

Gumbel

CG (u, v; ) = exp( CRG (u, v; ) = u + CR1G (u, v ; ) = v CR2G (u, v; ) = u

Rotated Gumbel Half-Rotated1 Gumbel Half-Rotated2 Gumbel Clayton

( 1, 1)

P.D. and N.D.

( 1, 1)

P.D. and N.D.

None

1

(1,

)

P.D.

Upper-Upper

(1, (1, (1, (0,

) ) ) )

P.D. N.D. N.D. P.D.

Lower-Lower Lower-Upper Upper-Lower Lower-Lower

(0, (0, (0, (0,

) ) ) )

(1,

)

(v )) 1

(( log u) + ( log v ) ) ) v 1 + CG (1 u, 1 v; ) CG (1 u, v; ) CG (u, 1 v; )

CJC (u, v; , ) = 1

{1

Tail dependence

1 (v ))

(u), t

CC (u, v; ) = (u + v 1) 1 CRC (u, v; ) = u + v 1 + CC (1 u, 1 v; ) CR1C (u, v; ) = v CC (1 u, v; ) CR2C (u, v; ) = u CC (u, 1 v ; ) CSJC (u, v; , ) = 0.5(CJC (u, v ; , ) + CJC (1 u, 1

Rotated Clayton Half-Rotated1 Clayton Half-Rotated2 Clayton Symmetrized JoeClayton

Dependence

{[1

(1

u) ]

+ [1

v; , ) + u + v

(1

v) ]

1}

1

1)

}1

P.D. N.D. N.D. P.D.

All

Upper-Upper Upper-Lower Lower-Upper Lower-Lower, UpperUpper

lower- and upper-tail distributions. More specifically, the marginal distributions between lower- and upper-tail thresholds are estimated by the Gaussian kernel estimation method, and the tail distributions are modelled using the peaks-over-threshold approach. Therefore, the tail estimation can be calculated as:

1

F (z ) =

Nu n

1

(1

1

(z Nu e n

z u

u) ,

),

0,

= 0,

(9)

where z indicates the decomposed mode; u , and are the tail threshold, scale parameter and tail parameter, respectively; n and Nu state the sample size and observations over tail threshold, respectively. 2.2. Measuring risk spillover based on copula approach Using the marginal distributions obtained from section 2.1, copula models can be constructed to depict the dependence and risk spillovers under different investment horizons. Copula function is a joint distribution function which couples the marginal distributions and can be defined as: (10)

FXY (x , y ) = C (FX (x ), FY (y )),

where FX (x ) and FY (y ) are the marginal distributions and C (·) states the copula distribution function. This paper chooses eleven types of static copula models to depict the possible dependence between Shanghai and Hong Kong stock markets. Table 1 summarizes the main features of these copula functions. Moreover, their corresponding time-varying parameter copulas are also introduced to describe the dynamic evolution of dependence. The evolution processes of parameters can be found in Liu et al. (2017) and Li and Wei (2018). Then, we measure the downside and upside risk spillovers based on the dependence between two stock markets. Value-at-Risk (VaR) quantifies the maximum probable loss within a specific confidence level and time. On that basis, the A-B CoVaR is proposed by Adrian and Brunnermeier (2016) to reflect the VaR of one market conditional on the different states of another market. Furthermore, Girardi and Ergün (2013) modify it as G-E CoVaR which allows us to consider more serious loss and promote its monotonicity regarding to the dependence parameter. The downside CoVaR2 can be expressed as:

Pr(rt j

CoVaR j , t rti

VaR i , t ) = ,

(11)

VaR , t , in which VaR conditional on where CoVaR , t states the VaR of market j at the confidence level 1 of market i at the confidence level 1 . Similarly, the upside CoVaR can be written as: j

Pr(rt j where CoVaR 2

rti

CoVaR j , t rti j

,t

VaR1i

,t)

i

= ,

is the β-quantile of market j conditional on

i

,t

indicates the VaR (12)

rti

VaR1i

,t ,

in which

VaR1i

Note that the CoVaR mentioned in this paper denotes the G-E CoVaR, unless otherwise stated. 4

,t

states the VaR of market i at the

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Table 2 Descriptive statistics for returns and adjusted realized volatilities. J-B denotes the Jarque-Bera statistics for normality. Q(10) is the Ljung-Box Q statistics with 10 lags. ARCH(10) refers to the Engle’s Lagrange multiplier test for heteroskedasticity with 10 lags. ADF is the Augmented DickeyFuller test. ***, ** and * indicate significance at 1%, 5% and 10% levels, respectively. Statistic

Market

Mean

SH HSI SH HSI

r RV

0.000 0.000 0.000 0.000

confidence level 1 respectively, as:

Std.

Kurtosis

0.015 0.011 0.000 0.000

Skewness

***

J-B

***

10.033 6.423*** 54.846*** 108.317***

−1.044 −0.192*** 6.356*** 8.868***

2998.348 660.857*** 158744.343*** 635420.515***

t

59.563 10.527 3432.845*** 812.098***

***

26.358 5.866*** 58.826*** 10.460***

ADF –33.673*** −34.729*** −3.997*** −13.368***

(13)

t

F r j (z j, t )

ARCH(10) ***

. Then, combining the copula functions mentioned above, the CoVaRs in Eqs. (11) and (12) can be expressed,

C F r j (z j, t ), F rti (z i , t ) = · F rti (z i , t ),

1

Q(10) ***

F rti (z1i

,t)

+ C F r j (z j, t ), F rti (z1i t

,t )

= ·F rti (z1i

, t ),

(14)

where z is the decomposed mode and F (·) denotes the distribution function of stock returns. Hence, giving the confidence levels of market i and j, asset distributions and copula parameters, we can solve the values of z j, t from Eqs. (13) and (14), respectively. Afterwards, the downside and upside CoVaRs can be easily calculated as:

CoVaR j , t (VaR i , t ) = at + RVt z j, t ,

(15)

where at is the conditional mean and RVt denotes the adjusted realized volatility. Moreover, the risk spillover CoVaR j ,it is given by

the difference between Value-at-Risk VaR j , t conditional on extreme return VaR i , t and the Value-at-Risk VaR j , t conditional on normal state VaR i0.5, t . It can be expressed as:

CoVaR j ,it = CoVaR j , t (VaR i , t )

CoVaR j , t (VaR i0.5, t).

(16)

In order to discuss the significance of risk spillovers, the bootstrap Kolmogorov-Smirnov approach proposed by Abadie (2002) is used to compare the cumulative distributions of CoVaR j , t (VaR i , t ) and CoVaR j , t (VaR i0.5, t ) . The null hypothesis is no significant risk spillover from market i to j and the test statistic can be defined as:

KSmn =

mn m+n

1 2

sup Fm (x ) x

Gn (x ) ,

(17)

where Fm (x ) and Gn (x ) are the cumulative distributions of two samples, respectively. Furthermore, we can also analyze the asymmetric features of risk spillovers from the perspectives of market condition, investment horizon and spillover direction by comparing the cumulative distributions of corresponding delta CoVaRs. 3. Data and descriptive statistics For the empirical analysis, we choose the Shanghai Stock Exchange Composite Index (SH) and Hang Sheng Index (HSI) as the proxies of mainland China and Hong Kong stock markets, respectively. The data used in this paper is daily closing price and daily realized volatilities calculated by 5-min high-frequency trading data from January 1, 2013 to August 31, 2018. The data sample can be collected from the Wind database and Oxford-Man Institute's “realized library”. After removing the unmatched data, the logarithmic returns and adjusted realized volatilities can be calculated as Eq. (18) and Eq. (3), respectively.

rt = ln(Pt )

(18)

ln(Pt 1), i = 1, 2, ...,n,

where Pt is the daily closing price. Then, the descriptive statistics for stock returns and adjusted realized volatilities are shown in Table 2. Table 2 presents that all the stock returns and adjusted realized volatilities are fat-tailed and skewed distributed. The Jarque-Bera tests show that all the returns and adjusted realized volatilities reject the null hypothesis of normal distribution at the 1% significance level. The Ljung-Box Q statistics reveal that the major returns and adjusted realized volatilities are auto-correlated except the Hong Kong stock return series. The Lagrange multiplier tests provide strong evidence of volatility clustering for all series. The Augmented Dickey-Fuller tests suggest that the stock returns and adjusted realized volatilities are stationary, implying that they can be further used in econometric analysis. 5

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Table 3 Test results for standardized residuals. Q(10) is the Ljung-Box Q statistics with 10 lags. ARCH(10) refers to the Engle’s Lagrange multiplier test for heteroskedasticity with 10 lags. BDS denotes the BDS test for independently identically distribution. The p-values are reported in square brackets. Market

Q(10)

ARCH(10)

BDS

SH

12.596 [0.247] 4.648 [0.913]

1.522 [0.126] 1.773 [0.061]

−1.838 [0.066] −1.847 [0.065]

HSI

4. Empirical results 4.1. Marginal distribution results In this section, we use the adjusted realized volatilities and VMD approach to construct marginal distributions. Considering the Shanghai stock returns show significant auto-correlation, we assume that it refers to an autoregressive process with 1 lag. While the Hong Kong stock returns are assumed to follow a simple mean reversion. Then, the adjusted realized volatilities are introduced to normalize the stock residuals. Three tests for standardized residuals are carried out and their results are summarized in Table 3. From Table 3, the Ljung-Box Q statistics and Lagrange multiplier tests reveal that the auto-correlation and volatility clustering features are not significant. The BDS tests show that the conditional returns are independently identically distribution (i.i.d.) at the 1% significance level. Thus, the filtering method based on adjusted realized volatility is effective. Since the standardized residuals which have filtered out the impacts of stylized facts can actually reflect the variation features (Mensi et al., 2017), we further use the VMD approach to decompose the standardized residuals into ten modes and indicate these decomposed series as VMD1 to VMD10, in which the VMD10 and VMD1 are selected to represent the short- and long-run standardized residuals respectively. Fig. 1 presents the raw, short-run and long-run return series. From Fig. 1, the short-run return series manifest more drastic fluctuations and significant volatility clustering compared to the long-run series. Next, the extreme value theory is used to separately depict the lower- and upper-tail distributions. We choose ± 10% tail observations as extreme values according to the suggestions of DuMouchel (1983). Table 4 reports the GPD estimation and one-sample Kolmogorov-Smirnov test results. The Kolmogorov-Smirnov tests show that we cannot reject the null hypothesis of correct specification of marginal distribution model at the 1% significant level, indicating that all the marginal distributions meet the requirements of copula functions and can be further used in copula modelling. 4.2. Dependence and risk spillovers In this part, we utilize the short- and long-run marginal distributions to depict the dependence and risk spillovers under multi-

Fig. 1. Variational mode decompositions for the SH and HIS returns. Fig. 1 shows the raw, short-run and long-run returns of two stock markets, in which the short- and long-run returns are calculated by the VMD10 and VMD1 respectively. 6

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Table 4 GPD estimation and KS test results. uL , L and L are the lower-tail threshold, scale parameter and tail parameter, respectively. uU , U and U are the upper-tail threshold, scale parameter and tail parameter, respectively. KS denotes the p-values of one-sample Kolmogorov-Smirnov tests for uniform distribution. Market

Lower-tail

Upper-tail

µL Short-run Long-run

SH HSI SH HSI

−0.3170 −0.3172 −0.2735 −0.3025

L

L

−0.1921 −0.2251 −0.3820 −0.3722

0.1579 0.1395 0.1536 0.1686

µU 0.3172 0.3176 0.2909 0.3016

KS U

−0.1611 −0.1234 −0.7730 −0.1841

U

0.1473 0.1185 0.2175 0.1418

0.939 0.883 0.375 0.754

investment horizons. The fitting results of twenty-two types of copulas are summarized in Table 5. From Table 5, first, The AIC values of time-varying copulas are smaller than that of corresponding static copulas, revealing that the time-varying copulas are superior to their corresponding static copulas in depicting the dependence between Shanghai and Hong Kong stock markets, and thus the relations among Shanghai and Hong Kong markets are dynamic. Second, the time-varying Student’s t copula achieves the smallest AIC values than the other time-varying copula functions, implying that there is relatively significant symmetric tail dependence between Shanghai and Hong Kong stock markets. Third, the static and dynamic Half-Rotated copulas which can only depict negative dependence (Ji et al., 2018b, 2019) obtain significantly larger AIC values than all the other copula functions which can characterize positive dependence. It indicates that the obviously positive relations exist between Shanghai and Hong Kong stock markets. Based on the time-varying Student’s t copula model, the short- and long-run delta CoVaRs of Shanghai and Hong Kong markets at 5% and 95% quantile levels are calculated. Considering the risk spillovers between Shanghai and Hong Kong markets may vary with the implementations of Shanghai-Hong Kong Stock Connect and Shenzhen-Hong Kong Stock Connect schemes, we focus on the possibly different states of risk spillovers before and after two Stock Connect schemes, by dividing the whole sample into three periods according to the launches of these schemes (i.e., November 11, 2014 and December 5, 2016). First, we separately calculate the means of delta CoVaRs in three periods and analyze the significance of risk spillovers using the bootstrap Kolmogorov-Smirnov test. The summary statistics for delta CoVaR at different stages are summarized in Table 6. Table 6 demonstrates that the risk spillovers between Shanghai and Hong Kong stock markets are both significant and manifest some asymmetrical states. Then, to intuitively demonstrate the variations of risk spillovers in three periods, the short- and long-run downside and upside delta CoVaRs of Shanghai and Hong Kong markets are shown in Fig. 2. From Fig. 2, first, the short-run risk spillovers are more drastic than the long-run risk spillovers in most cases. The main reason is that short-run markets are largely affected by speculative factors and emergency events, which often trigger dramatic volatility and Table 5 Fitting results of different bivariate copula functions. The AIC values of copula functions are listed in this table. The smaller the AIC value, the better the fitting results of the corresponding copula function. Bold denotes the smallest AIC value in a specific investment horizon. Copula Panel A: Static copula Gaussian Student’s t Gumbel Rotated Gumbel Half-Rotated1 Gumbel Half-Rotated2 Gumbel Clayton Rotated Clayton Half-Rotated1 Clayton Half-Rotated2 Clayton Symmetrized Joe-Clayton Panel B: Time-varying parameter copula Time-varying Gaussian Time-varying Student’s t Time-varying Gumbel Time-varying Rotated Gumbel Time-varying Half-Rotated1 Gumbel Time-varying Half-Rotated2 Gumbel Time-varying Clayton Time-varying Rotated Clayton Time-varying Half-Rotated1 Clayton Time-varying Half-Rotated2 Clayton Time-varying Symmetrized Joe-Clayton

7

Short-run

Long-run

−266.417 −273.891 −242.760 −245.870 155.940 155.681 −205.451 −204.314 0.079 0.080 −267.157

−274.478 −321.528 −269.468 −293.922 159.344 135.919 −255.049 −207.754 0.062 0.090 −321.959

−421.571 −701.046 −448.352 −454.379 −27.354 −27.532 −387.372 −382.062 −21.573 −21.286 −456.613

−465.750 −937.732 −414.500 −653.814 −15.658 −14.314 −526.032 −618.045 −13.616 −11.250 −699.260

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Table 6 Summary statistics for delta CoVaR in three periods. The means of delta CoVaRs in three periods are reported in this table. D and U denote the downside and upside, respectively. *** and * indicate that the null hypothesis of no significant risk spillovers is rejected at 1% and 10% levels, respectively. HSI → SH

SH → HSI

Short-run

Period 1

ΔCoVaR(D) −0.00136***

ΔCoVaR(U) 0.00135***

ΔCoVaR(D) −0.00106***

ΔCoVaR(U) 0.00110***

Long-run

Period Period Period Period Period

−0.00229*** −0.00095*** −0.00076*** −0.00109*** −0.00072***

0.00228*** 0.00094*** 0.00056*** 0.00079* 0.00055***

−0.00112*** −0.00086*** −0.00078*** −0.00078*** −0.00093***

0.00116*** 0.00089*** 0.00101*** 0.00103*** 0.00115***

2 3 1 2 3

Fig. 2. Short- and long-run downside and upside delta CoVaRs of Shanghai and Hong Kong stock markets. D and U denote the downside and upside, respectively.

risk contagions. Second, the risk spillovers from two directions are quite different. In the short-run horizon, the risk spillovers from Hong Kong to Shanghai are slightly greater than that from Shanghai to Hong Kong in period 1. Then, with the implementation of Shanghai-Hong Kong Stock Connect scheme, the risk spillovers from Hong Kong to Shanghai steeply increase. However, Shanghai stock market show greater risk spillovers than Hong Kong market in the end of period 2, and the risk spillovers from two directions turn comparable in period 3. Two possible reasons are that the Shanghai stock market is hugely shocked by the international hot money after the Shanghai-Hong Kong Stock Connect scheme, and the Southbound flows of funds vastly increase in 2016 (Burdekin & Siklos, 2018). In the long-run horizon, the overall risk spillovers from Shanghai to Hong Kong are larger than that from Hong Kong to Shanghai, indicating that the Shanghai stock market has become more crucial in recent years owing to the rapidly developing economy and gradually improving financial liberalization of mainland China. 4.3. Asymmetric features of risk spillover effects In this part, we further test the asymmetric features of risk spillovers under different market conditions, investment horizons and spillover directions by using the bootstrap Kolmogorov-Smirnov method. The results are summarized in Tables 7–9, respectively. First, regarding to bear and bull conditions, all the p-values in Table 7 are smaller than 0.1, indicating that the downside risk spillovers from Hong Kong to Shanghai are significantly larger than its upside risk spillovers. Thus, compared with positive information, bad news from Hong Kong stock market has greater impacts on Shanghai market owing to the imperfect risk prevention measures and numerous irrational investors in mainland China stock market. While the risk spillovers from Shanghai to Hong Kong is on the contrary. The possible reason is that the major investors in Hong Kong stock market are optimistic about the business conditions of mainland China for a long time and regard the two Stock Connect schemes as greatly good news. Second, concerning short- and long-run investment horizons, Table 8 demonstrates that the short-run stock markets show relatively greater risk spillovers except the risk spillovers from Shanghai to Hong Kong in period 3. The reasons behand the facts that, on 8

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Table 7 The bootstrap Kolmogorov-Smirnov tests of equal downside and upside delta CoVaRs. The p-values are reported in square brackets. D and U denote the downside and upside, respectively. H0: CoVaRSH HSI (D) = CoVaRSH HSI (U) H1:

Period 1 Period 2 Period 3

CoVaRSH HSI (D)

>

H0: CoVaRHSI SH (D) = CoVaRHSI SH (U)

CoVaRSH HSI (U)

H1: CoVaRHSI

SH (D)

<

CoVaRHSI

SH (U)

Short-run

Long-run

Short-run

Long-run

0.8604 [0.0000] 0.7650 [0.0000] 0.7398 [0.0000]

0.6957 [0.0000] 0.5031 [0.0000] 0.8458 [0.0000]

0.8604 [0.0000] 0.7629 [0.0000] 0.7398 [0.0000]

0.6957 [0.0000] 0.5052 [0.0000] 0.8458 [0.0000]

Table 8 The bootstrap Kolmogorov-Smirnov tests of equal short- and long-run delta CoVaRs. The p-values are reported in square brackets. S and L denote the short- and long-run, respectively. H0: CoVaRSH HSI (S) = CoVaRSH H1: CoVaRSH

Period 1 Period 2 Period 3

HSI (S)

>

HSI (L)

H0: CoVaRHSI SH (S) = CoVaRHSI

CoVaRSH HSI (L)

H1: CoVaRHSI

SH (S)

SH (L)

CoVaRHSI SH (L)

Downside

Upside

Downside

Upside

0.3387 [0.0000] 0.2289 [0.0000] 0.1928 [0.0000]

0.5126 [0.0000] 0.3217 [0.0000] 0.3325 [0.0000]

0.1327 [0.0009] 0.1464 [0.0000] 0.0867 [0.0881]

0.0938 [0.0427] 0.1464 [0.0000] 0.1590 [0.0000]

Table 9 The bootstrap Kolmogorov-Smirnov tests of equal delta CoVaRs of Shanghai and Hong Kong stock markets. The p-values are reported in square brackets. S and L denote the short- and long-run, respectively.

Period 1 Period 2 Period 3

H0: CoVaRSH HSI (S) = CoVaRHSI SH (S)

H0: CoVaRSH HSI (L) = CoVaRHSI SH (L)

H1: CoVaRSH

H1: CoVaRSH

HSI (S)

>

CoVaRHSI SH (S)

HSI (L)

<

CoVaRHSI SH (L)

Downside

Upside

Downside

Upside

0.2265 [0.0000] 0.3773 [0.0000] 0.0699 [0.2630]

0.1762 [0.0000] 0.3546 [0.0000] 0.0458 [0.7772]

0.0503 [0.6370] 0.1629 [0.0000] 0.1928 [0.0000]

0.4394 [0.0000] 0.1258 [0.0009] 0.4458 [0.0000]

the one hand, short-run markets are heavily influenced by speculative factors and emergency events which result in drastic volatility and risk spillovers. On the other hand, since the A-share price is often higher than the share price of the same company listed in Hong Kong stock market (i.e., A-H share premium), the number of long-run investors from mainland China to Hong Kong gradually increases with the implementations of Stock Connect schemes. Third, in terms of risk spillover directions, Table 9 manifests that there are significantly larger short-run risk spillovers from Hong Kong to Shanghai in period 1 and period 2, while the short-run risk spillovers from two directions are comparable in period 3. Moreover, the long-run risk spillovers from Shanghai to Hong Kong are larger than that from Hong Kong to Shanghai, except the downside risk spillovers in period 1. All these test results indicate that, in the first place, the importance of Shanghai stock market is gradually increasing with the implementations of two Stock Connect schemes. More specifically, Hong Kong stock market is no longer the leading market in the short-run after the Shenzhen Stock Connect scheme, and Shanghai stock market begins to dominate Hong Kong stock market in the long-run after the Shanghai-Hong Kong Stock Connect scheme, whether in bull or bear conditions. In the second place, as a developed stock market, Hong Kong stock market plays the leading role in the short-run before two Stock Connect schemes, and still dominates Shanghai stock market after the Shanghai-Hong Kong Stock Connect scheme because of the influences of international hot money. Finally, due to the rapidly developing economy and gradually improving financial liberalization of mainland China, Shanghai stock market also manifests leading power under the bull condition and the long-run horizon before two Stock Connect schemes.

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Table 10 Volatility spillover effects between Shanghai and Hong Kong stock markets based on DCC-MVGARCH. The parameter estimates about volatility spillovers are reported in this table. *** and * indicate significance at 1% and 10% levels, respectively. aSH ,HSI

bSH , HSI ***

Period 1 Period 2 Period 3

***

−0.1899 −0.1805*** 0.0773***

−0.0754 0.0464*** −0.1112***

aHSI ,SH

bHSI , SH

−0.0451 0.0732*** 0.0075

−0.0620*** −0.0260* −0.1419***

Fig. 3. Dynamic conditional correlations between Shanghai and Hong Kong stock markets.

5. Robustness examination In this part, we introduce the commonly used dynamic conditional correlation MVGARCH (DCC-MVGARCH) proposed by Engle (2002) to test the volatility spillovers in three periods, and discuss the impacts of Stock Connect schemes on the dependence between Shanghai and Hong Kong markets, so as to evaluate the robustness of conclusions above. The binary DCC-MVGARCH can be defined as:

rt = at + µt , µt | t 1 ~BN (0, Ht ), Ht = Dt Rt Dt ,

(19)

where rt = (r1, t , r2, t ) is the vector of stock returns; at = (a1, t , a2, t ) denotes the vector of conditional means; µt = (µ1, t , µ 2, t ) represents the vector of residuals and refers to the binary normal distribution with mean 0 and dynamic conditional covariance matrix Ht ; t 1 states 1 2 1 2 1 2 1 2 the information set at time t 1; Dt = diag(h11, t , h 22, t ) denotes the diagonal matrix, in which h11, t and h 22, t are the conditional standard deviations of market 1 and market 2 respectively; Rt = diag(q11,1t 2 , q22,1t 2) Qt diag(q11,1t 2, q22,1t 2 ) is the dynamic correlation

1 2 1 2 matrix, in which q11, t and q22, t state the square root of diagonal elements of Qt and Qt can be modelled as:

Qt = (1

1

2) Q

+

1 t 1 t 1

+

(20)

2 Qt 1,

where 1, 2 0 and 1 + 2 < 1; Q denotes the unconditional correlation matrix of standardized residuals t . To analyze the volatility spillovers between two stock markets, the conditional variances h11, t and h22, t are estimated based on the method of Ling and McAleer (2003). We have:

h11, t = c1,0 + a11 µ1,2t

+ a12 µ 2,2 t

h22, t = c2,0 +

+ a22 µ2,2 t

1 a21 µ1,2 t 1

1

+ b11 h11, t

1

+ b12 h22, t 1,

1

+ b21 h11, t

1

+ b22 h22, t 1,

(21)

where a11 and b11 indicate the impacts of historical residual squared and conditional variance of market 1 on their own current conditional variance, respectively; a12 and b12 denote the effects of historical residual squared and conditional variance of market 2 on the current conditional variance of market 1. If a12 or b12 is significantly different from 0, there is significant volatility spillovers from market 2 to market 1. The DCC-GARCH is separately constructed in three periods and the parameter estimates about volatility spillovers are summarized in Table 10. Table 10 manifests that the bi-directional risk spillovers between Shanghai and Hong Kong exist in three periods, which is consistent with the conclusions of Huo and Ahmed (2017) and the empirical results noted above. Moreover, the dynamic correlation coefficients between Shanghai and Hong Kong markets based on DCC-MVGARCH method are shown in Fig. 3. From Fig. 3, the correlation coefficients slightly increase after the Shanghai-Hong Kong Stock Connect scheme while sharply decrease in 2016. 10

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Meanwhile, it rises up after the implication of Shenzhen-Hong Kong Stock Connect scheme for a period of time. The evolution process of correlation coefficients is similar with the variations of risk spillovers discussed above, which confirms the robustness of conclusions of this paper. 6. Conclusions In this paper, we investigate the asymmetric risk spillovers between Shanghai and Hong Kong stock markets under the backdrop of China’s capital account liberalization by measuring the CoVaR based on adjusted realized volatilities and VMD based copula method. The empirical results show that, the asymmetric features of risk spillovers between the two markets are significant and manifest different states before and after the two Stock Connect schemes. More specifically, First, the downside risk spillovers from Hong Kong to Shanghai are significantly larger than its upside risk spillovers, while the risk spillovers from Shanghai to Hong Kong is on the contrary. Second, the short-run risk spillovers are more drastic than the long-run risk spillovers, except the risk spillovers from Shanghai to Hong Kong after the Shenzhen-Hong Kong Stock Connect scheme. Finally, by comparing the risk spillovers from two directions, the importance of Shanghai stock market is gradually increasing with the implementations of Stock Connect schemes. These results have crucial implications regarding to prevent market risk and deepen China’s financial reform. On the one hand, investors and market management department of mainland China should pour more attention to the short-run risk spillovers resulting from the emergencies, speculation and other factors and the downside risk spillovers from Hong Kong stock market. While the investors and market management department of Hong Kong need to focus on the long-run and upside risk spillovers from mainland China stock market. 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