1

The Impact of Interest Rate Adjustment Policy on the

volatility of China’s stock market Jiping Yang Shuai Yuan

School of Economics and Management, Beihang University, Beijing 100191, China

Abstract: In this paper, we investigate how the interest rate adjustment affects the volatility of China’s stock market. We use GARCH model based on normal distribution and EGARCH model based on t distribution to analyze the impact of the interest rate adjustment from Nov. 22, 2014 on the volatility of closing and overnight returns of the Shanghai Composite Index in China’s stock market based on two months before and after that day respectively. At the same time, we use GARCH model based on normal and t distribution to analyze NASDAQ Index in the stock market of US for comparison. We find that the reduction of the interest rate increases the volatility of closing and overnight returns of the Shanghai Composite Index. On the contrary, the adjustment of interest rate has no significant impact on the volatility of US stock market. We reach the conclusion that the development level of stock market affect the impact of the adjustment of the interest rate.

Keywords: interest rate adjustment; closing return; overnight return; volatility; GARCH Model; EGARCH Model; excess return

1. Introduction

There is a growing number of studies focusing on the effect of economic news on the

volatility of daily returns in stock markets in recent years. The existing literature highlights

how the news affect the volatility of the market. Gordon (1962), Campbell and Shiller (1988)

decompose that the price of a share in equilibrium is determined by the discounted value of

the expected cash flows accruing to the share. Campbell and Ammer (1993) decompose the

variance of unexpected excess returns implied by the dividend discount model into three

factors: news about future dividends, interest rates and excess returns. Many empirical studies

have been performed by different researchers in order to test the links between the interest

rate adjustment and the volatility of stock market. Glosten, Jagannathan and Runkle (1993)

conclude that the increase of short-term interest rate can cause fluctuations in the stock

market. Bomfim (2003) finds that the impact of monetary policy changes on the volatility of

the stock price is not statistically significant. Kholodilin, Montagnoli, Napolitano and

Siliverstovs (2009) find that an increase in the interest rate will result in a decrease in stock

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market on the day the monetary policy stock is announced. Krieger, Nathan and Vazquez

(2015) examine the responses of US (VIX) and their findings indicate that the US volatility

levels do not respond to ECB meeting announcements.

Furthermore, different reactions of daily and overnight returns towards the interest rate

adjustment have been investigated by many researchers. Chan, Chockalingam and Lai (2000)

reach the conclusion that local price movements affect both the opening and closing returns

of foreign stocks. Nicholas (2006) examines the economic value of overnight information to

users of risk management models. The results show that overnight information has significant

impact on the conditional volatility of daytime traded S&P 500 securities. Ahoniemi and

Lanne (2013) mention that the extant literature on realized volatility has yet to reach a

consensus on how to treat overnight returns, which will reflect information accumulated

during non-trading hours.

Most of the existing researches focus on the impact of policy on volatility of western stock

markets, very few of them made direct researches on the impact of the interest rate

adjustment towards the volatility of both the daily and overnight returns in China’s stock

market or compared the volatility of China’s stock market to that of US and analyzed the

possible reasons for the volatility of the market.

Therefore, different from the existing researches, we uses the daily and overnight returns

of Shanghai Composite Index to analyze the impact of the government announcement

towards the volatility of the market in and out of trading hours. We also investigate the

impact of interest rate adjustment on the US stock market for comparison. We find that the

volatility of US stock market is not significantly impacted by the adjustment of the interest

rate at that time.

The rest of paper is structured as follows. The next section presents the formal model.

Section 3 describes the data and the estimation results. The final section concludes.

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2. The Research Model

2.1. The GARCH Model Let ty denote a financial time series and a simple data generating model by t ty Xβ ε= + ,

where the random error tε is normally distributed conditionally on past information. And let

th denote the conditional variance of tε at time t, and then the ARCH (q) process can be

described as

2 2 2 20 1 1 2 2 1 1t t t t q t qh α α ε α ε α ε α ε− − − −= + + + + + (1)

The GARCH model is extended from the ARCH model, which is generalized to the

situation that the conditional variance of tε can be the function of lagged conditional

variance as well as past realization of the disturbance term. The GARCH (p, q) process takes

the form

t ty Xβ ε= +

21 0

1 1[ | ]

p q

t t t i t i i t ki k

Var h hε α α ε β− − −= =

Ω = = + +∑ ∑ (2)

2.2. The TGARCH Model

The TAGRCH model is mainly based on the GARCH model to describe the impacts of

different kinds of news on the capital market. By adding into the GARCH model dummy

variables, the TGARCH model reflects asymmetric effect of good news and bad news. The

basic form of the TGARCH model is given as

t ty Xβ ε= +

2 21 0 1 1

1 1[ | ]

p q

t t t i t i t t i t ki k

Var h d hε α α ε λε β− − − − −= =

Ω = = + + +∑ ∑ (3)

Where 0td = when 0tε ≥ and 1td = when 0tε < .

2.3. The EGARCH Model Let tR denote a financial time series and a simple data generating model be

01

m

t i t i ti

R Rλ λ ε−=

= + +∑ , where the random error tε is normally distributed conditionally on

past information. And let th denote the conditional variance of tε at time t, the basic form

of the EGARCH model could be represented as

4

01

m

t i t i ti

R Rλ λ ε−=

= + +∑ (4)

01 1

ln( ) ( / / ) ln( )p q

t i t i t i i t i t i j t ji j

h h h hα α ε ϕ ε θ− − − − −= =

= + + +∑ ∑ (5)

where, ( 0,1,2, ,m)i iλ = , ( 0,1,2, , )i i pα = , ( 1,2, , )i i pϕ = , ( 1,2, , )j j qθ = are

estimated coefficients.

In order to investigate the effect of the interest rate reduction on the volatility of daily and

overnight return series of Shanghai Composite Index in China stock market, dummy variable

td is introduced in the establishment of all models, where 0td = before the interest rate

adjustment and 1td = after that date.

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3. Empirical Analysis

3.1. Data and Preliminary Statistics

On Nov. 21, 2014, the benchmark interest rate of RMB loan was down-regulated by the

People’s Bank of China by 0.40%. In order to rule out the influence of downward interest rate

adjustments on the volatility of China’s stock market, we choose Shanghai Composite Index

from Sept. 10, 2014 to Jan. 30, 2015 as research data, namely, two months before and after the

RMB interest cut on Nov. 21, 2014. Similarly, we choose NASDAQ Index from May. 8, 1995

to Aug. 30, 1995 as research data to investigate the stock market of US.

Let otp and c

tp denote the opening and closing index of the t th trading day

respectively, we have

1(ln( ) ln( ))*100−= −n o ct t tr p p , 1(ln( ) ln( ))*100−= −c c

t t tr p p (6)

Here tr and ntr represent the closing and overnight return respectively. The return series

are multiplied by 100 times in order that the series could be better fitted and more easily

measured.

The two time periods we selected are from Sept. 10, 2014 to Nov. 21, 2014, and from Nov.

24, 2014 to Jan. 30, 2015, respectively. The adjustment of the interest rate happened on Nov.

22, 2014. Similarly, we select both closing and overnight returns of NASDAQ Index from

May. 8, 1995 to Aug. 30, 1995. The adjustment of the interest rate happened on Jul. 5, 1995.

The graph of the closing and overnight returns series of Shanghai Composite Index and

NASDAQ Index are presented in Fig. 1, Fig. 2, Fig. 3 and Fig. 4, where the red line denotes

the date of the interest rate adjustment. It is obvious that the volatility of closing and

overnight returns of Shanghai Composite Index increases after the interest rate adjustment.

On the contrary, the volatility of NASDAQ Index is not significantly affected after the

interest rate adjustment.

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Figure 1. The closing return series of Shanghai

Composite Index Figure 2. The overnight return series of

Shanghai Composite Index

Figure 3. The closing return series of NASDAQ

Index Figure 4. The overnight return series of

NASDAQ Index

3.2. Descriptive statistics and ARCH Effect of Return Series

Table 1 presents estimation results on the descriptive statistics of the closing and overnight

returns of Shanghai Composite Index and NASDAQ Index. Take the closing return of

Shanghai Composite Index as an example. The first-order autocorrelation coefficient of

closing return of Shanghai Composite Index is -0.02, and serial correlation tests show that the

Ljung-Box (10)Q statistic is significantly less than the critical value at the 5% significance

level. Therefore, we accept the null hypothesis of independence.

At the same time, the serial correlation test in closing return of NASDAQ Index show that

Ljung-Box (10)Q statistic is significantly greater than the critical value at the 5%

significance level. Therefore, the closing returns of NASDAQ Index can be predicted from

the previous returns.

Table 1. Descriptive Statistics of Return Series of Shanghai Composite Index

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Table 1 also shows that the return series of both Shanghai Composite Index and NASDAQ

Index are stationary with 5% significance level. Therefore, we carry out ARCH-LM test on

the return series and find that the ARCH effect is obvious.

3.3. Comparison of GARCH models with different error distribution

In order to select the appropriate GARCH models, we compare different GARCH models

with normal and t distribution respectively. Let 2( )t tr r− denotes the actual volatility 2tσ of

return series and the conditional variance 2ˆ tσ derived from the models represents the

estimate of volatility.

We use six different indexes to quantify the difference between values of the estimator and

the true values of the parameters. These indexes are the Mean Squared Error (MSE1, MSE2),

Shanghai Composite Index NASDAQ Index

Closing Return Overnight Return Closing Return Overnight Return

Mean 0.335466 -0.080829 0.219857 0.113758

Median 0.291746 -0.006270 0.411043 0.099200

Maximum 4.635794 1.725462 1.879730 1.281054

Minimum -8.017542 -5.690286 -3.674051 -0.523422

Standard deviation 1.754276 0.747514 0.874603 0.234380

Skewness -1.138861 -4.368672 -1.253334 1.413916

Kurtosis 8.441628 34.59475 6.675161 9.889446

JB 139.1973* 4298.277* 65.96731* 184.8703*

1ρ -0.020 -0.033 0.250* -0.081

2ρ -0.118 -0.057 -0.002 -0.009

Diagnostic tests on the residuals

Unit Root Test -9.7875* -9.9526* -8.5208* -9.4724*

L-Box (10)Q 8.3705 10.254 10.782 6.9072

L-Box 2 (10)Q 8.9406 0.4448 12.506 1.1082

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the Mean Absolute Error (MAE1, MAE2), Quasi-Likelihood loss function error (QLIKE) and

squared log error loss function ( 2R LN) respectively, defined as follows.

21

1

1 ˆ( )σ σ=

= −∑n

t tt

MSEn

, 2 2 22

1

1 ˆ( )σ σ=

= −∑n

t tt

MSEn

11

1σ̂ σ

=

= −∑n

t tt

MAEn

, 2 22

1

1σ̂ σ

=

= −∑n

t tt

MAEn

2 2 2

1

1 ˆ ˆ(ln( ) )σ σ σ −

=

= +∑n

t t tt

QLIKEn ,

2 2 2 2

1

1 ˆ[ln( )]σ σ −

=

= ∑n

t tt

R LNn (7)

Table 2 presents the values of all indexes. The selection of our models is determined by the

value of indexes. The models that have the smallest indexes among MSE1, MSE2, MAE1,

MAE2, QLIKE and 2R LN are the adequate models that we will select in our paper.

Table 2. Prediction ability of GARCH Models with normal and t distribution Model 1MSE 2MSE 1MAE 2MAE QLIKE 2R LN

Shanghai Composite Index

GARCH-N(1,1)

tr 1.3116 54.4129 0.7763 2.8534 1.5033 7.1187

ntr 0.6033 10.1553 0.6184 0.9659 0.6841 13.4897

GARCH-T(1,1)

tr 1.3707 55.5107 0.7906 2.9122 1.5253 7.2800

ntr 0.6325 10.3310 0.6241 0.9669 0.9605 13.9796

TARCH-N(1,1) tr 1.5238 57.6649 0.8290 3.1386 1.5229 7.5356

ntr 0.8418 10.5940 0.7848 1.2821 0.5349 16.0668

TARCH-T(1,1)

tr 1.5391 57.7517 0.8388 3.1713 1.5243 7.6313

ntr 0.6898 10.3877 0.6718 1.0540 0.7243 14.6401

EGARCH-N(1,1)

tr 1.6251 63.5617 0.9150 3.3397 1.6638 8.1852

ntr 0.3264 9.9579 0.2778 0.5376 -0.3409 5.8150

EGARCH-T(1,1)

tr 1.5966 63.8100 0.9043 3.3264 1.6065 8.1257

ntr 0.3172 9.5126 0.3040 0.5720 -0.5893 6.2672

NASDAQ Index

GARCH-N(1,1)

tr 0.2817 2.6577 0.4142 0.7039 0.4367 4.9346

ntr 0.0304 0.0247 0.1334 0.0605 -2.1478 10.5759

GARCH-T(1,1) tr 0.2237 2.1811 0.3748 0.6269 0.3169 4.5817

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ntr 0.0360 0.0239 0.1466 0.0664 -1.8960 13.3670

EGARCH-N(1,1)

tr 0.2487 1.6726 0.3978 0.6289 3.5294 5.1786

ntr 0.0479 0.0268 0.1840 0.0863 -1.8948 13.4000

EGARCH-T(1,1)

tr 0.2788 2.1947 0.4180 0.6823 4.0204 5.2629

ntr 0.0451 0.0265 0.1762 0.0817 -1.9254 13.0433

TARCH-N(1,1)

tr 0.3172 3.0765 0.4104 0.7051 0.6175 4.6629

ntr 0.0364 0.0268 0.1481 0.0719 -2.1099 10.2406

TARCH-T(1,1)

tr 0.3159 3.0679 0.4098 0.7037 0.6062 4.6646

ntr 0.0417 0.0279 0.1640 0.0803 -2.0507 11.2581

3.4. Empirical Analysis of Shanghai Composite Index and NASDAQ Index

Table 3 presents the estimation results of both closing and overnight returns. According to

the previous analysis, the models we selected are also presented in the Table 3.

Table 3. Regression Results of GARCH Models with different error distribution

Shanghai Composite Index NASDAQ Index

Coefficient tr ntr tr n

tr

GARCH-N(1,1) EGARCH-T(1,1) GARCH-T(1,1) GARCH-N(1,1)

1c 0.378422* -0.029528 0.224197* 0.111072*

0.0001 0.2368 0.0204 0.0000

2c 0.085556* -0.035042 0.240898 0.001416* 0.0000 0.7425 0.1175 0.0012

3c -0.170286* -0.616180* 0.532284 -0.034135*

0.0000 0.0066 0.0687 0.0257

4c 1.069258* 0.199815* 0.252019 1.038839*

0.0000 0.0281 0.1956 0.0000

5c 0.536097* 0.813598* -0.491061 -0.002636

0.0000 0.0000 0.3596 0.0762

6c 0.352717* 0.596518

0.0000 0.2496

Diagnostic tests on the standardized residuals

Unit Root Test -9.395003* -9.752188* -6.019651* -9.401479*

Skewness 0.182991 -0.134524 -0.547959 0.691323

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Kurtosis 3.224829 7.084919 2.863439 4.922010

JB 0.738141 67.03581* 4.014799 18.68611* (10)Q 7.6273 6.2339 11.793 9.7361

2 (10)Q 9.7252 6.4148 6.0963 3.3310

Table 3 shows that the statistic of Unit Root Test of all models are greater than the critical

value at the 5% significance level, which means that the residuals of these models are white

noisy processes. And therefore, the models we use are adequate.

The estimations of different models are as follows.

1) GARCH-N(1,1) model

Estimation results for closing returns of Shanghai Composite Index are presented as

follows.

The mean equation is 0.378422

(0.0001)ε= +t tr

(8)

The conditional variance equation is 2

1 10.085556-0.170286 1.069258 0.536097 (0.0000) (0.0000) (0.0000) (0.0000)

ε − −= + +t t t th h d (9)

As it turns out, the coefficient of the dummy variance is 5c , which is greater than the

critical value at the 5% significance level. Therefore, the adjustment of the interest rate has

impacted the volatility of Shanghai Composite Index. The coefficient is 0.536097, indicating

that the volatility of closing returns of Shanghai Composite Index increases after the

adjustment of the interest rate.

2) GARCH-T(1,1) model

Estimation results for overnight returns of Shanghai Composite Index are presented as follows.

The mean equation is

11

-0.029528 (0.2368)

ε= +nt tr (10)

The conditional variance equation is

1 11

1 1

| |ln( ) -0.035042-0.616180 0.199815 0.813598ln 0.352717

(0.7425) (0.0066) (0.0281) (0.0000) (0.0000)

ε ε− −−

− −

= + + +t tt t t

t t

h h dh h (11)

Since the coefficient of the dummy variance is greater than the critical value at the 5%

significance level, the adjustment of the interest rate has also impacted the volatility of

Shanghai Composite Index. The coefficient is 0.352717, indicating that the volatility of

overnight returns of Shanghai Composite Index increases after the adjustment of the interest

rate.

3) GARCH-N(1,1) model

Estimation results for closing returns of NASDAQ Index are presented as follows.

The mean equation is

10.224197 0.240898 (0.0204) (0.1175 )

ε−= + +t t tr r (12)

The conditional variance equation is 2

1 10.532284 0.252019 -0.491061 0.596518 (0.0687) (0.1956) (0.3596) (0.2496)

ε − −= + +t t t th h d (13)

On the other hand, when we turn to the closing returns of the stock market of US, it is

obviously that the coefficient of the dummy variance is less than the critical value at the 5%

significance level. Therefore, the adjustment of the interest is silent on the volatility of

NASDAQ Index.

4) GARCH-N(1,1) model

Estimation results for overnight returns of NASDAQ Index are presented as follows.

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The mean equation is 0.111072

(0.0000) t tr ε= +

(14)

The conditional variance equation is 2

1 10.001416 0.031415 1.038839 0.002636 (0.0012) (0.0257) (0.0000) (0.0762)t t t th h dε − −= − + − (15)

It could be deducted from the estimation results above that since the coefficient of the

dummy variance is less than the critical value at the 5% significance level, the adjustment of

the interest is also silent on the distribution of overnight returns and the volatility of NASDAQ

Index.

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4. Conclusions

There is a question how the volatility of stock market responses to the adjustment of

interest rate. Bernanke and Kuttner (2005) investigate this question by asking whether

monetary policy affects stock values through its effects on real interest rates, expected future

dividends, or expected future stock returns. He finds that the impact of monetary policy

surprises on stock prices seems to come either through expected future excess returns or

future dividends.

The paper’s results are consistent with their findings. Because the China’s stock market is

still underdeveloped, there is an access to get excess return and the adjustment of interest rate

increases the volatility of stock market on both closing and overnight return significantly. On

the other hand, the stock market of US is well-developed and there is less opportunity of

getting excess return. As a result, the impact of interest rate adjustment on the US stock

market is limited. The conclusion shows that the development level of stock market can

determine the impact of monetary policy. In order to make the policy more efficient, the

policymakers should consider the development level of stock market. In China, the interest

rate adjustment is currently affecting the volatility of stock market.

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Acknowledgment

We thank the financial support for this research by National Natural Science Foundation of

China (Grant No. 71271011).

Reference Ahoniemi, K., Lanne, M., 2013. Overnight stock returns and realized volatility. International Journal of

Forecasting, 29, 592-604.

Bernanke, B. S., Kuttner, K. N., 2005. What explains the stock market’s reaction to federal reserve policy?.

Journal of Finance, 60(3), 1221-1257.

Bollerslev, T., 1986. Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics

31, 307-327.

Bomfim, A.N., 2003. Pre-announcement effects, news effects, and volatility: monetary policy and the stock

market. Journal of Banking & Finance, 27(1), 133-151.

Campbell, J.Y., Ammer, J., 1993. What moves the stock and bond markets? A variance decomposition for

long- term asset returns. Journal of Finance, 48(1), 3-37.

Campbell, J.Y., Shiller, R.F., 1988. The dividend-price ratio and expectations of future dividends and

discount factors. Review of Financial Studies, 1(3), 195-228.

Chan, K., Chockalingam, M., Lai, K.W.L., 2000. Overnight information and intraday trading behavior:

evidence from NYSE cross-listed stocks and their local market information. Journal of Multinational

Financial Management, 10(3-4), 495-509.

Engle, R.F., 1982. Autoregressive conditional heteroskedasticity with estimates of the variance of United

Kingdom inflation. Econometrica 50, 987-1008.

Glosten, L.R., Jagannathan, R., Runkle, D.E., 1993. On the relation between the expected value and the

volatility of the nominal excess return on stocks. Journal of Finance, 48(5), 1779-1801.

Gordon, M.J., 1962. The investment, financing and valuation of the corporation. Irwin, R.D., Homewood,

ILL (IL49), 241-245.

Kholodilin, K., Montagnoli, A., Napolitano, O., Siliverstovs, B., 2009, Assessing the impact of the ECB’s

monetary policy on the stock markets: A sectoral view. Economics Letters, 105, 211-213.

Krieger, K., Nathan, M., Vazquez, J., 2015. Comparing US and European market volatility responses to

interest rate policy announcements. International Review of Financial Analysis,

Mandelbrot, B., 1963. The variation of certain speculative prices. Journal of Business 36, 394-419.

Nelson, D.B., 1991. Conditional heteroskedasticity in asset returns: a new approach. Econometrica, 59(2),

347-370.

Nicholas, T., 2006. A note on the importance of overnight information in risk management models. Journal

of Banking & Finance, 31(1), 161-180.

15

Taylor, N., 2007. A note on the importance of overnight information in risk management models. Journal

of Banking & Finance 31, 161-180.

Tsiakas, I., 2008. Overnight information and stochastic volatility: a study of European and US stock

exchanges. Journal of Banking & Finance 32, 251-268.