Post on 15-Apr-2017
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
2
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.
3
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.
5
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.
6
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
7
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
8
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
9
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
10
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.
12
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.
13
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.
14
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.