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The impact of oil prices on international financial markets
Dawid Brychcy*
Departament d’Economia i d’Historia Economica
IDEA, Universitat Autonoma de Barcelona
March 2006
Abstract
In this paper using univariate and multivariate GARCH models we investigate the influence
of the oil prices on international financial markets. We test different specification of
the conditional mean equation taking returns on oil prices and volatility of oil prices as the
explanatory variables. The multivariate GARCH model are used to test the transmission of
shocks from oil prices to stock markets. The results show that oil prices have impact on all
the stock markets but this influence takes different forms. We have obtained that only DJIA
and S&P500 react to the changes in in returns on oil prices. This impact is negative and
very low. There are no asymmetric effects of the changes of oil prices on the stock markets
and there are no lagged effects. The returns on American stock markets are influenced by
the volatility of oil prices as well and this effect seems to be more significative than the
impact of returns on oil prices. Analyzing the dynamic of correlation between each stock
market index and oil prices separately, we see that in all the cases but DAX, the estimated
correlation was very small and not statistically significant, so that we may claim that there
is no transmission of shocks from oil prices to stock markets (in the daily data framework).
JEL classification: F3, G1, C5, C12
Keywords: .Oil prices, volatility transmission, GARCH, stock markets
1 Introduction
In this paper we evaluate the influence of the returns on the oil prices on international financial
markets. Using the family of GARCH models (both univariate and multivariate) we assess
spillover effects from the changes in the oil prices to the main stock markets in the world. In our
analysis we include the returns on the DJIA, S&P500, NASDAQ, FTSE100, DAX, NIKKEI225
and the returns on the WTI crude price.
Oil belongs to the most important resources in the economy and plays the crucial role in
setting the economic policies. The relation between oil price changes, economic activity and
employment is an issue that has been studied during long time. In a pioneer work Hamilton
(1983) showed that oil price increases are responsible for almost every post World War II US
recession, except the one in 1960.
The oil prices affect economy through many channels. The initial impact of changes in oil
prices is through the transfer of income from consumers to producers, and on the international
level from oil-importing countries to oil-exporting countries. Higher oil prices increase costs in
almost all industries, particularly in such energy-intensive sectors like transport and are likely
to lead to an increase in inflation, the severity of which will depend on the extent to which
companies pass on higher oil prices of their final product, on the consequences for wages and
on the effectiveness of the anti-inflationary policies. A tightening of macroeconomic policies in
respond to higher oil prices and increasing inflation would have an impact on global financial
markets. The impact of higher oil prices on income, business profits and inflation lowers the
value of financial assets.
Stock prices are the discounted values of expected future cash flows. Oil prices can affect
both the expected cash flows and discount rates for different reasons. Oil prices affect future
cash flows as important input in the production process. The increasing oil prices rise the cost of
production and lower benefits of the companies - this effect depends on whether the company is
a net producer or net consumer of oil. Oil prices can affect the stock prices through the discount
rates as well. The expected discount rate is the sum of the expected inflation rate and expected
real interest rate, both of which may in turn depend on oil prices.
Although a bulk of economic research has studied the relation between oil price changes
and economic activity, there is little research on the relationship between oil price shocks and
financial markets.
In the related literature most of the authors (Jones and Kaul, 1996; Huang et al., 1996;
Sadorsky, 1999) have focused on the linear dependencies between oil prices and oil price changes
and stock returns and present different results. Huang et al. conclude that oil futures returns
do lead only individual oil companies and the petroleum index sector but do not have impact on
S&P500 stock index or other sector indices; Sadorsky shows that oil prices and the volatility of
oil prices both play important roles in affecting real stock returns. Ciner (2001), however, takes
another approach. He examines the dynamic linkage between oil prices and the stock markets.
The author uses the same data set as Huang et al. and the extended data set and relying
on nonlinear Granger causality test (Beak and Broke (1992) and Hiemstra and Jones(1994))
provides evidence that oil shocks indeed affect stock index returns, which is opposite to the
previous works based on the linear dependencies.
In this work, using the daily data for the period 1984 - 2005, we analyze and assess the relation
between oil prices and oil price volatility and main stock index prices. We will consider the prices
of WTI crude and main world stock indices - DJIA, NASDAQ, S&P500, DAX, FTSE100 and
NIKKEI225.
The results show that oil prices have impact on all the stock markets but this influence takes
different form. We have obtained that only DJIA and S&P500 directly react to the changes in
returns on oil prices. This impact is negative and very low. There are no asymmetric effects
of the changes of oil prices on the stock markets and already one day lag does not have any
influence more. The returns on American stock markets are influenced by the volatility of oil
prices as well and this effect seems to be more significative.
Using multivariate GARCH models we can analyze the transmission of shocks between markets.
Analyzing the dynamic of correlation between each stock market index and oil prices
separately, using CC-MVGARCH model, we see that in all the cases but DAX, the estimated
correlation was very small and not statistically significant, so that we may claim that there is no transmission of shocks from oil prices to stock markets (in the daily data framework).
The paper is organized as follows. Section 2 discusses the specification of the models we will
use in this paper. Section 3 presents the data and stock markets we consider in the analysis and
delivers results on the preliminary checkings of the data. In Section 4 we discuss the results of
the estimated models and in the Section 5 we conclude and sketch further research possibilities.
2 Model specification
In this section we present the univariate and multivariate models that we want to estimate in
the empirical part.
In the univariate analysis we will first estimate the model for the returns of oil prices.
Following we will propose the GARCH models for each of the stock markets taking the returns
on oil prices as the explanatory variable in the mean equation. This specification will show us if
there is any impact of the returns on oil prices on returns of each of the stock markets (conditional
mean). We will also analyze the lagged returns of oil prices as the explanatory variables to
investigate if the changes of oil prices in the past influence the stock markets contemporaneously.
Another specification we will test takes the estimated conditional volatility of returns on oil
prices as the explanatory variable in the mean equation of the returns on stock markets, here
we can analyze if the returns of the stock markets depend on the volatility of oil prices. Further
analyzing the way the oil prices influence stock market we will construct the dummy variable
that will account for the sign of the returns on oil prices to see if there is asymmetry in the
relationship between returns on stock markets and returns on oil prices.
While in the first part we want to investigate the impact of oil price on the returns on stock
markets with the multivariate GARCH model we want to check if there is the transmission
of shocks between stock markets and oil prices. We may try to answer the questions about
the relationship between volatilities and correlations between stock markets and oil prices, if
the shocks in one of the market lead the volatilities in other markets or if this relationship is
symmetric or asymmetric one.
2.1 Univariate analysis
For the univariate analysis we want to consider GARCH models. The GARCH models have been
developed to account for empirical regularities in financial data, such that volatility clustering,
fat tails or leverage effects.
For the conditional variance ht we consider the linear GARCH model in which the positive
and negative shocks have the same impact on conditional volatility. To account for the possible
asymmetry in the impact of shocks with different sign we will consider the Exponential GARCH
model (EGARCH) of Nelson (1991) and GJR - GARCH model of Glosten, Jagannathan and
Runkle (1993).
To check the presence of GARCH effects in the conditional volatility equation we use the
ARCH-LM test proposed by Engle (1982) and to detect the leverage effects in conditional volatility (asymmetry) we consider the Sign Bias, Negative and Positive Size Bias tests proposed by Engle and Ng (1993). All the tests are discussed in the appendix.
In the next step we want to consider the multivariate models that will allow us to study the
relations between the volatilities and correlations of the stock markets and oil prices.
2.2 Multivariate analysis
Following the success of the ARCH and GARCH models in describing the time-varying variances of economic data in the univariate case the extension to the multivariate case has been developed immediately. Bauwens et. al (2003) discuss the most important developments in multivariate ARCH-type modelling. Several applications of multivariate GARCH models (MVGARCH, hereafter) can be found in the financial literature: Bollerslev (1990), Karolyi (1995), Tse and Tsui (2000), among others.
The extension from a univariate GARCH model to the N - variate model requires allowing
the conditional variance-covariance matrix of the N dimensional zero mean random variables
εt (errors from the model that we obtain by estimating the mean equation) to depend on the
elements of the information set. Let {zt} be a sequence of (N x 1) i.i.d vector such that
zt ∼ F (0, IN )
with F continuous density function. Let {εt} be a sequence (N x 1) random vectors defined
as
εt = H1/2t zt
where
Et−1(εt) = 0
Et−1(εtε0t) = Ht
where Ht is a matrix (N x N) positive definite. The parametrization of Ht as a multivariate
GARCH, which means as a function of the information set Φt−1, allows each element of Ht to
depend on q lagged of the squares and cross-products of εt, as well as p lagged values of the
elements of Ht.
In our model we will estimate two multivariate GARCH models - the Constant Correlation
Multivariate GARCH model (CC-MVGARCH, hereafter) proposed by Bollerslev (1990) and
Dynamic Conditional Correlation Multivariate GARCH model (DCC-MVGARCH) proposed by
Engle (2002). In the first model the conditional correlations are constant while in the second
one they evolve with the time.
2.2.1 CC-MVGARCH model
Bollerslev (1990) introduced the Constant Correlation MVGARCH model (CC-MVGARCH),
where univariate GARCH models are estimated for each series and then the correlation matrix is
estimated using the standard closed formMLE correlation estimator using transformed residuals.
The assumption of constant correlation makes estimating a large model feasible and ensures that the estimator is positive definite, simply by requiring each univariate conditional variance to be
non-zero and the correlation matrix to be full rank.
In this model the matrix of variances-covariances Ht is proposed to be
{Ht}ii = hit
{Ht}ij = hijt = ρijphitphjt i 6= j
We can partition the matrix Ht as
Ht = DtRDt
where Dt is the (N x N) diagonal matrix with the conditional standard deviations along the
diagonal, {Dt}ii = √hiit and R denote the matrix of conditional correlations with (i, j)th element
being ρij and ρii = 1. So it follows that the (i, j)th element of Ht is given as
hijt = ρijphiithjjt
It follows that Ht will be positive definite for all t if and only if each element of the N
conditional variances are will defined and R is positive definite.
Due to its computational simplicity, the CC-MVGARCH model is used in the empirical
research. However, while the constant-correlation assumption provides a convenient model for
estimation, some studies find that the assumption is not supported by some financial data. Tse
(2000) found that the stock returns across different national exhibit time-varying correlations.
Thus, there is a need to extend the MVGARCH models to incorporate time-varying correlations
and yet retain the requirement about the positive -definiteness during the estimation.
Tse (2000) proposes a testing procedure of a null hypothesis of constant conditional correlation
against an ARCH in correlation alternative, Engle and Sheppard (2001) propose a test of
null of constant correlation against the alternative of dynamic conditional correlation, that only
requires consistent estimate of the constant conditional correlation, and can be implemented
using a vector autoregression.
The assumption that the conditional correlation are constant may seem unrealistic in many
empirical applications. Engle (2002) and Tse and Tsui (2002) propose a generalization of the
CC-MVGARCH model by making the conditional correlation matrix time dependent.
2.2.2 DCC-MVGARCH model
Engle (2002) proposes a dynamic conditional correlation model (DCC-MVGARCH) in which
returns can be either mean zero or the residuals from a filtered time series with the time varying
variance covariance matrix
Ht = DtRtDt
where Dt is the (N x N) diagonal matrix of the time-varying standard deviations from
univariate GARCH model.
The specification of the univariate GARCH model is not limited to the standard GARCH(p, q),
but can include any GARCH process with normally distributed errors that satisfies stationarity
and non-negativity constraints.
In this model Rt is defined as
Rt = diag(q−1/211,t , ..., q−1/2NN,t)Qtdiag(q−1/211,t , ..., q−1/2NN,t)
where the (N x N) positive definite matrix Qt = (qij,t) is given by
Qt = (1 −MXm=1αm −N Xn=1βn)Q +MXm=1αmzt−mz0 t−m +N Xn=1βnQt−n
where Q is the unconditional covariance matrix of the standardized residuals resulting from
the first stage estimation, and α and β are nonnegative scalar parameters satisfying PM
m=1 αm+PNn=1 βn < 1.
The DCC model allows for two stage estimation, where in the first stage univariate GARCH
models are estimated for each of the series, and in the second stage, the standardized residuals,
are used to estimate the parameters of the dynamic correlation specification. The conditional
mean parameters may be consistently estimated in the first stage, prior to the estimation of the
conditional variance parameters, for example for a VARMA model, but not for GARCH-in-mean
models. Bera and Higgins (1993) claim that having block diagonality between the parameters of
the conditional mean and conditional variance (not in the case of the GARCH-in-mean model)
estimation and testing for the mean and variance parameters can be done separately. Estimating
all the parameters simultaneously would increase the efficiency, but is computationally more
difficult and additional parameters need to be estimated. For this reason one usually takes
either a very simple models for conditional mean or considers yt − bμt as the data for fitting the
MVGARCH models.
Before presenting the empirical results we would like shortly discuss the diagnostic checking
for the multivariate GARCH models. Compared to the huge body of diagnostic checks for the
univariate models, only few tests are specific to multivariate case. One natural way is to analyze
the univariate models but contemporaneous correlation of disturbances makes statistics from
individual equations to be not independent, so that the need for joint testing arises.
The starting point are the findings of Li and Mak (1994) who define a general class of squared
residual autocorrelations and produce some useful diagnostic tools. Ling and Li (1997) further
develop this work and derive the asymptotic distribution of the portmanteau statistic in the
multivariate case. The Ling-Li statistic is based on the serial correlation coefficients on the
transformed vector of residuals. They point out that the asymptotic covariances of the standard
residual autocorrelations and the squared residual autocorrelations are all very complicated and
employ the sum of squared residual autocorrelations to develop new portmanteau statistics.
Duchesne and Lalancette (2003) argue that if the inappropriate level of lags of autocorrelations
is selected, the resulting tests statistic may be quite inefficient and suggest more powerful version
of the test based on the spectral density of the transformation of the residuals.
Another approach concerns residual-based diagnostics. These tests involve running regression
of the cross-products of the standardized residuals on some explanatory variables and testing
for the statistical significance of the regression coefficients. The contribution of Tse (2002) is to
establish the asymptotic distribution of the OLS estimator in this context.
3 Data
In this paper we want to investigate the relationship between the main stock market indexes
and the price of the oil crude. All the data we will use come from the Bloomberg and are closing
prices. The prices of the oil crude are in dollars.
We have cleaned the data by removing all the days when at least on one of the stock markets
being considered there was no trade, in such a way we have removed from the sample all the
public holidays or days when the stock markets were closed (e.g. the days after 11/09/2001).
Preparing the data in such a way we have seven time series, each of them of 4949 observation.
The starting day for the sample is 01/01/1984, the day when the FTSE 100 were computed for
the first time and the last observation has the date of 30/06/2005.
For the analysis we consider the DJIA, S&P500 and NASDAQ to represent the most important
stock market indices in United States and most relevant stock market indices for the
world economy, than FTSE100 and DAX30 from UK and Germany as the main European stock
market indices and finally we include in the analysis NIKKEI225 as the main index on the Tokyo
Stock Exchange. The appendix shows the plots of the stock market indexes versus the prices of
oil crude.
Using the historical exchange rate (obtained from Bloomberg) we have converted the values
of the stock market indices from local currency into dollar terms. We consider continuously
compounded returns on the stock market indices and oil prices.
For the crude oil prices we use one of the two mostly watched spot prices - the price of the
West Texas Intermediate (WTI) Cushing Crude Oil.
3.1 Preliminary analysis
In this section we present the results of the analysis of the data. As mentioned before we consider
continuously compounded returns.
We have checked the stationarity of the series of returns using unit root tests (Augmented
Dickey Fuller test). For each of the series of returns we reject the hypothesis about the unit root
test at the level of 5%. So following we will analyze the stationary series of returns[1].
Table 1 displays summary statistics of the data.
Concerning the univariate statistics we observe that the returns on oil prices were characterized
by the highest standard deviation, so the volatility of oil prices were the biggest one among
all the series of returns we consider. The value of the skewness in all the cases is negative which
shows that the returns are left-skewed and the kurtosis in the case of the returns is much higher
than in the case of the series of levels which indicates fat tails in the distribution. Those are the
common stylized facts observed in the series of returns on stock markets.
For each of the series of returns we have performed the Jarque Bera test for the null hypothesis
about the normality of the series. In all the cases we have obtained the p-value of 0.000 which
at 5% level of significance allows us to reject the null hypothesis about normality. The Jarque
Bera test shows that the returns do not have the normal distribution. This fact should influence
the way of estimation of the model. We can estimate the models assuming another distribution
(e.g. t-Student) or as Bollerslev and Wooldridge show (1992) we can still assume conditional
normality and estimate the model obtaining quasi maximum likelihood estimators, that as shown
by them are consistent.
Following we have checked the autocorrelation of the series of returns. Table 2 shows the
values of the Ljung - Box statistics at lag 5, 10, 20 and 50.
All the p-values are very small and we can conclude that we have the presence of autocorrelation.
The examination of international stock markets movements suggests that there exists a
substantial degree of interdependence among national stock markets. Given the fact that we
analyze the interdependence between the oil prices and stock markets in different countries it is
important to take into account the trading hours of one market relative to other markets in the
real time.
Marten and Poon (2001) have shown that using non-synchronous results in significant downward
bias in correlation, as compared to pseudo-closed, which means simply constructed by
sampling the data at the same time. One of the solutions to this problem would be to construct the weekly returns, but since we are interested in the daily fluctuations we have to take into
account the differences in opening and closing of the stock markets that we have selected to
analyze.
The European and Japanese stock markets are closed when the American markets open -
at day t the American DJIA does not influence neither the NIKKEI nor DAX or FTSE. Those
markets will react on day t + 1 to that what happened in U.S. at day t.
Let us consider first the correlations shown in the Table 3.
In the Table 3 we show the correlation between the series on returns with the corresponding p-values about the statistically significance. We see that the correlation between American stock markets and oil prices is negative, small but statistically significant. Only in the case of NASDAQ and WTI and FTSE and WTI we observe that the correlation is not statistically significant.
There is also (as expected) high correlation between American markets but surprisingly low
correlation between American and European stock markets, which we could expect to be high,
and very low correlation between changes in stock markets and changes in oil prices. Capiello et
al. (2003) obtain very similar results with the average correlation among the European markets
of 0.5289 and the correlation between European and North American markets of 0.3386.
Following we want to see if the correlation between changes in stock prices and oil prices was
changing over time.
In the appendix we present the plots of the correlations between returns on stock markets
and return on oil prices computed in the 3-month-windows. We can observe that the correlation
was not stable during the time we consider. The American markets follow very similar pattern
- we observe high negative spikes at the beginning of 1990s, then around 1992 another spike -
positive and then again there are high changes around 1995 - 1996.
We also observe similar spikes in the European and Japanese market but the magnitude is
of the spikes is smaller.
This analysis demonstrates that one of the empirical evidences is the changing character of
correlations which we can take into account when proposing the multivariate models.
Finally we have computed the average monthly correlations across markets in a very similar
manner as Campbell et al. (2001). First we have calculated monthly non-overlapping correlation
coefficients for each pair of the returns on the stock markets and returns on the oil prices. We
then average the correlations between returns to compute a synthetic equally weighted index of
the average correlation.
The figure shows average monthly correlation between returns on stock markets and oil
prices. We observe changing pattern of the average correlations - there are periods of the smaller
and higher correlations. This will support the idea of using models with dynamic correlation
structure.
4 Empirical Evidence
In this section we present and discuss the empirical results of the estimation of both univariate
and multivariate GARCH models for the data and perform the diagnostic checking tests for the
results we have obtained. First we discuss the model for the returns on the oil prices.
4.1 Univariate model for returns on oil prices
We start by investigating the model for returns on the oil prices.
In the first step we determine the conditional mean part. The predictable part - the conditional
mean we can define as the mixture of the autoreggresive part, independent explanatory
variables and lagged innovations. The lowest value of the BIC criterion we have obtained for
the ARMA(2,3). The model for the mean part is as follows
r_oilt = c + φ1r_oilt−1 + φ2r_oilt−2 + θ1εt−1 + θ2εt−2 + θ3εt−3 + εt
Engle(1982) developed a test for conditional heteroscedasticity in the context of ARCH
models based on the Lagrange Multiplier principle. We present the details of the test in the
appendix.
We applied the ARCH-LM test to the series of residuals εt that we obtain from the mean
equation. For the valued of q = 1, 5, 10 we have obtained following valued of ARCH-LM test statistic
- ARCH(1)=60.82(0.000), ARCH(5)=140.52(0.000) and ARCH(10)=292.46(0.000), where
in the parenthesis we provide the p − values. So clearly we have the presence of ARCH effects
and this will support modelling the conditional volatility as the GARCH process.
We can further check if there are present the asymmetric GARCH effects by means of the
Sign Bias, Negative Size Bias and Positive Size Bias tests proposed by Engle and Ng (1993)
which we present in appendix.
For the Sign Bias we have obtained the value of the t-statistic for the parameter γ1 of 0.1732
(p-value 0.8624), for Negative Size Bias of -6.4675 (0.0000) and for the case of Positive Size Bias
of of 5.6163 (0.0000). Clearly, there is substantial evidence of asymmetric ARCH effects.
We present the results of the estimation for each of the models - ARMA(2,3) - GARCH(1,1),
ARMA(2,3) - EGARCH(1,1) and ARMA(2,1) - GJR-GARCH(2,3) with normally distributed
errors in Appendix.
The results of the estimation show that although the test for the asymmetric behavior of the
shocks confirms the hypothesis about the presence of asymmetry in the conditional variance the
parameters that govern this asymmetry are not significant in both EGARCH and GJR-GARCH.
So the model we can consider for the return on oil prices is the GARCH(1,1).
The standardized errors zt are assumed to be independent and identically distributed. We
can check the adequacy of the variance model by examining the series {bzt} . The Ljung-Box
statistics of bzt can be used to check the adequacy of the mean equation and that of the bz2
t of the volatility equation. Checking the properties of standardized residuals we can prove if the conditional mean is correctly specified and by analyzing the aquared standardized residuals we
can prove the conditional volatility specification.
The Ljung-Box statistics of the standardized errors of {bzt} give Q(5) = 6.29 with p-value
0.2789 and Q(15) = 19.49 with p-value 0.1949 and those of ©bz2
t ª are Q(5) = 2.07 with p-value
0.8383 and Q(15) = 18.21 with p-value 0.2516. Consequently, the proposed model is adequate
for the data at 5% level of significance.
Lundbergh and Teräsvirta (2002) discuss the framework for testing the adequacy of the
estimated GARCH model. They propose the LM type tests of no ARCH in the standardized
errors.
We have tested for remaining ARCH part taking the value of m = 1, .., 5 , the results of
the test presents the table below - we present the value of the statistic and the corresponding
p-value
For each m we accept at 5% level of significance the null hypothesis about no remaining
ARCH in the model. So that the GARCH(1,1) correctly specifies the conditional variance
equation.
4.2 The univariate GARCH models with the returns on oil prices as the explanatory variable
For each of the six stock market indices we have estimated the univariate GARCH models with
the returns on oil prices as the explanatory variable.
We have proceed as follows - first using the Schwarz Information Criterion we have defined
the model for the mean. With the residuals we obtain from the mean equation we will check
the presence of asymmetric GARCH effects. Once we have detected the asymmetry we will
consider three models for conditional volatility equation - the linear GARCH(p,q) model and two asymmetric models - EGARCH(p,q) and GJR-GARCH(p,q). We will take the returns on
oil prices as the explanatory variable for the mean equation. Then we will jointly estimate the
model and will propose the one with the lowest value of BIC.
For each of the stock market the lowest value of BIC was obtained by taking just the constant
as the only explanatory variable for the mean equation and in case of NASDAQ we have AR(1).
We perform the Sign Bias test, Negative Size Bias and Positive Size Bias in the same way as
in the case of returns on oil prices. The results are presented in the table below - we present
t-statistics and p-values in the case of the SB, PSB and NBS tests and for the joint test we
present F -statistic and corresponding p-value
At 5% level of significance we see that all the markets show the asymmetric behavior of the
squared residuals so that in the next step we have to investigate the asymmetric GARCH model.
Since there is a time difference between USA (we have the price of oil of WTI crude, that is
quoted in New York), Europe and Japan we must account for it. For European and Japanese
market we take the one - lagged returns of the oil prices as the explanatory variable (so that we
have e.g. for the return on day t on DAX, we consider the returns on oil price on the day t − 1,
and for the return on DJIA on day t we take the corresponding return on the oil price on the
day t).
Having all this requirements into account we have found following models - for DJIA - ARMAX(0, 0, 1)−EGARCH(1, 1), for S&P500 - ARMAX(0, 0, 1)−EGARCH(1, 1), for NASDAQ - ARMAX(1, 0, 1) − EGARCH(1, 1), for FTSE - ARMAX(0, 0, 1) − GARCH(1, 1), for DAX - ARMAX(0, 0, 1) − EGARCH(1, 1) and for NIKKEI - ARMAX(0, 0, 1) − EGARCH(1, 1).
We present the resutls and diagnostic checking in Appendix.
The analysis of the Ljung-Box statistics for the correlations up the lag 5 and 10 in the
standardized and squared standardized errors in the models shows that at 5% level of significance
there is no remaining correlation in the standardized and squared standardized residuals and we
can state that the proposed models are accurate.
In this part of the analysis we want to answer the question if the stock markets react to
changes in the oil prices. The results show that the changes in oil prices affect the American
markets (DJIA and S&P500). In the rest of the markets the influence of the changes in oil prices
on the stock markets are not statistically significant at 5% level of significance.
In the case of the markets where the returns on oil prices were statistically significant we
observe that the impact is negative - so the increase in oil prices (positive returns) diminishes
the return on the stock index. On both markets where the changes in oil prices have impact on
the stock markets (DJIA and S&P500) the magnitude of the impact is very similar.
As the by-product of this analysis we have obtained the asymmetric behavior of reaction of
the markets to positive and negative shocks (which is in line with other empirical findings). In all
the markets but FTSE we have obtained the parameter γ1 negative and statistically significant
which explains that positive return shocks generate less volatility then negative return shocks,
all else being equal. In all the markets this effect is very similar in the magnitude.
We have also checked if the lagged returns on the oil prices have any influence on the returns
on the given stock market and we have not detected any such dependencies. In the appendix we
present the results for DJIA and S&P500 (the markets where we have detected the dependence
between returns on stock markets and returns on oil prices).
Finally we have estimated another bunch of models adding as the explanatory variable the
dummy variable Dt that takes the value of 1 when the return on oil prices is negative. Testing such specification we can investigate if there is any asymmetry in the relationship between
returns on stock markets and returns on oil prices. In all the models we have obtained that the
dummy variable is not statistically significant so that the relationship between returns on stock
markets and oil prices (if any) does not have any asymmetric behavior.
4.3 The univariate GARCH models with the volatility of the returns on oil prices as the explanatory variable
The aim of this analysis is to investigate the impact of volatility of the oil prices on the returns
on the stock markets.
In the first part of the chapter we have estimated the model for the returns on the oil prices.
We will consider the estimated conditional volatility, evaluated at the estimated parameters,
as the explanatory variable in the mean equation for the returns on oil prices. We present the
results of the estimation in appendix. The specification includes the returns on oil prices and
the volatility of oil prices - in this way we can compare both effects.
The results of the analysis show that the volatility of the returns on oil prices do affect
the American stock markets (the NASDAQ as well) leaving the European and Japanese stock
markets unaffected. These results are very similar to the previous analysis of the impact of the
returns on oil prices on the stock markets.
Comparing both effects we see that the volatility of oil prices has the positive impact while
the returns on oil prices have a negative one. The magnitude of the effect of volatility is higher
than the effect of the second component. We can try to explain this by claiming that the
volatility of oil prices moves investors to change their portfolio decomposition (they shift from
one company to another one) and the stock index that tracks the spectrum of companies rises
as the volatility of oil prices increases. We could probably see it immediately when analyzing
sector indices. In this case we could detect the sectors which benefit from the changes in oil
prices and give hints about the best portfolio management strategies.
4.4 Multivariate models
In this section we will present and discuss the multivariate models. We will estimate the models
for the daily series of returns on the stock markets and the series of returns on the oil price. We
need to account for the time differences between opening and closing hours of the stock markets
we consider.
We want to consider the CC-MVGARCH model of Bollerslev (1990) and DCC-MVGARCH
model of Engle and Sheppard (2001). The advantages of this models are that they are mostly
used in the applied work due to their low numbers of parameters we need to estimate, few
restriction we need to impose in order to guarantee the conditional correlation matrix to be
positive definite and suitable estimation procedure as shown by Engle and Sheppard (2001) that
can be done in two stages.
In the first step of the estimation we have filtered the series by substracting the deterministic
component for each of the series to obtain pure stochastic errors from the model. Then we have
constructed the matrix of the errors of the following form
[DJ IAt−1 S&Pt−1 NASDAQt−1 F T SEt DAXt N IKKEIt W T It−1]
using this specification we will control for the time differences.
Engle and Sheppard (2002) propose a test for constant correlation. They point out that testing
models for constant correlation has proven to be a difficult problem, as testing for dynamic
correlation with data that has time-varying volatilities can result in misleading conclusions and
rejection of constant correlation when it is true due to the misspecified volatility model. They
propose a test that only requires consistent estimate of the constant conditional correlation, and
can be implemented using a vector autoregression. We discuss the details of the test in the
appendix.
Below we present the results of the test for the specification of the GARCH(1,1) model at
lags from 1, ..., 5. We present the results for the bivariate models (returns on oil prices and
returns on stock markets) and then the full models (p-value in parenthesis).
For each bivariate model we accept the hypothesis about the constant correlation structure
at 5% level of significance and in the case of the full model we reject the hypothesis about
the constant correlation structure of the conditional correlation. The explanation for this fact is
that the dynamics of the correlation between stock markets has stronger effect than the constant
correlation between stock markets and oil prices.
Following the results of the test we consider the CC-MVGARCH model for the bivariate case
and the DCC-MVGARCH model to describe the dynamics between all the series of returns. The
fact of using the dynamic correlation structure for the full model is in line with other empirical
findings (Hafner and Franses (2003) the analysis the DAX and FTSE, Tse and Tsui (2000)).
Each univariate GARCH models estimated for conditional variances was selected by finding the
minimum of the BIC (for all the model we have GARCH(1,1)).
First, below we present the results of the estimation of the volatility part for each of the
market (in parenthesis the standard error, ∗ significant at 5% level of significance).
And the parameters for the conditional correlation between returns on each stock market
and the returns on oil prices for each bivariate model (in the appendix we present full matrix of
correlations estimated with the CC-MVGARCH model).
In appendix we present the plots of estimated conditional volatility.
All the parameters or the conditional volatility part are statistically significant (except the
ω for S&P and FTSE). The volatility equations show quite high level of persistence in volatility.
The volatility linkages are evident especially during the periods of crises - there are spikes
in volatility around the October 1987 (black Tuesday), the Gulf war (reflected as well in the
volatility of oil prices), during the financial crises of 1997 and dotcom bubble (especially visible
in the case of the volatility of NASDAQ - we observe very high variations during the period
2000 - 2002). The spikes that we observe in the case of DAX (but not as visible as in the case
of other stock markets) is the period of 1992 -1993, when there was a tension within European
Monetary System with resulting increases of interest rates and exchange rate realingnments.
In the case of the volatility of returns on oil prices we clearly see a very high spike around
the time when Iraq attacked Kuwait and then the following Gulf war
Looking at the results of the estimation of the conditional correlation equations we observe
that in each of the bivariate case (the return on oil prices and returns on the given stock market)
the estimated conditional correlations are very low, near zero and not statistically significant. At
5% level of significance we can may claim that in all the cases but DAX there is no transmission
of shocks from oil prices to stock markets.
Although the test for contant correlation structure indicates that in the bevariate cases
we should use CC-MVGARCH model instead of DCC-MVGARCH model we will estimate
DCC(1,1)-MVGARCH(1,1) model to have a look at the evolution of correlation between oil
prices and stock markets.
For the full model both parameters, that govern the dynamics of the conditional correlation
matrix, are highly significant. The parameter α that governs shocks to the conditional volatility
is very small (0.0094), from the other side we have high persistent in the conditional correlation
expressed by β iqual 0.9855. Since the sum of both parameters is smaller than one we have
mean reversion in the conditional correlation.
We can use the regression-based diagnostics suggested by Wooldridge (1990,1991), where
he proposed the regression-based diagnostics that can be applied to test for many possible
misspecification. Since we concentrate on the conditional volatility we will use the standardized
squared errors and the cross products of the standardized squared errors. The details of the test
for checking both the misspecification in the conditional volatility and conditional correlation
we present in the appendix.
First we check for misspecification in the conditional volatility equation. The results of the
test for Q = 3 presents the table below
The test statistic is distributed χ23, which for the level of significance 5% has the value of
7.81. For each of the models we accept the null hypothesis at 5% level of significance about no
model misspecification in the conditional volatility equation.
The estimated conditional correlations show the pattern of the dependencies between stock
markets and oil prices. For all the markets we observe the condition correlations that range
between -0.3 and 0.3 and fluctuate around the value that we have obtained for the bivariate
models.
We present the plots of estimated conditional correlations in the appendix.
In the case of the correlation between American stock markets and oil prices we observe a
very similar pattern in each of the market. DJIA and S&P500 have similar mean and the mean
in the case of NASDAQ is smaller, what can be explained by the specific construction of this
index as the index of new technology, of the sector not as much sensitive to the oil prices. The
timing of spikes in the plots corresponds again to the periods of crises - there is a drop to the
higher negative correlation (around -0.2 in all the cases) in the moment of the Iraqui invasion
to Kuwait and then the first Gulf war in 1990/1991 or in the moment of the second Gulf war.
The conditional correlation between returns on DAX and returns on oil prices and between
FTSE and oil prices show a similar pattern with the difference that there is more variability
in the case of conditional correlation between DAX and oil prices. In the case of FTSE and
NIKKEI the average conditional correlation in the period we consider was positive with similar
spikes as in the case of American markets.
5 Conclusions
In this work, using the daily data for the period 1984 - 2005, we analyze and assess the relation
between oil prices and oil price volatility and main stock index prices. We consider the prices
of WTI crude and main world stock indexes - DJIA, NASDAQ, S&P500, DAX, FTSE100 and
NIKKEI225.
The results show that oil prices have impact on all the stock markets but this influence takes
different form. We have obtained that only DJIA and S&P500 react to the changes in oil prices.
This impact is negative and very low. There are no asymmetric effects of the changes of oil
prices on the stock markets and already one day lag does not have any influence more. The return on American stock markets are influenced by the volatility of oil prices as well and this
effect seems to be more significative than the reaction to the changes in the returns on oil prices.
Using multivariate GARCH models we can analyze the transmission of shocks between markets.
Analyzing the dynamic of correlation between each stock market index and oil prices
separately, using CC-MVGARCH model, we see that in all the cases but DAX, the estimated
correlation was very small and not statistically significant, so that we may claim that there is
no transmission of shocks from oil prices to stock markets (in the daily data framework).
The dynamic correlation model shows that the correlations was changing over time, we
observe periods of higher and lower correlation between stock markets and oil prices but all the
markets follows very similar pattern.
In the future research we want conider the weekly and monthly returns. This idea is motivated
by the fact that in the daily data framework there is a lot of noise and other factors that
have much more significant impact on the stock markets.
Another idea for the future research possibilities is to consider the asymmetric multivariate
models, in which we may allow for the asymmetry in both conditional variance and conditional
correlation equations.
Much more interesting would be a very similar analysis for the sector indices. In the case
of the stock market indices we have considered here the almost no impact of the oil prices
can be due to the composition of the stock markets indices. Analyzing the sector indices (e.g.
transportation, energy, banks) we could analyze the reaction of different groups of companies
on the changes in the oil prices and this could be a good tool when optimizing the portfolio
composition since we could give hints which portfolio management strategies could be considered when there are changes in oil prices.
* I have benefited from comments by Gabriel Pérez Quirós and Rebeca Jíemenez. I thank to Magda Jurecka
for her help. I acknowledge the financial support from Ministerio de Educación, Cultura y Deporte under the
project AP2003-2252.
[1] We have perform the unit root tests (Augmented Dickey Fuller test) first on the series in levels and in each
case we had to accept the hypothesis of the unit roots. Considering the continuously compounded returns, which
correspond to the first log differences, we have obrained I(0) series.
