850243
research-article20192019
SGOXXX10.1177/2158244019850243SAGE OpenAli et al.
Original Research
Symmetric and Asymmetric GARCH
Estimations and Portfolio Optimization:
Evidence From G7 Stock Markets
SAGE Open
April-June 2019: 1–12
© The Author(s) 2019
https://doi.org/10.1177/2158244019850243
DOI: 10.1177/2158244019850243
journals.sagepub.com/home/sgo
Shahid Ali1 , Junrui Zhang1, Mazhar Abbas2 ,
Muhammad Umar Draz3, and Fayyaz Ahmad4
Abstract
Volatility exchanges between equity markets and oil markets are vital for portfolio designing and risk management. This
study empirically analyses the interdependence of stock and oil market for G7 countries. For econometric estimations, we
used the data of G7 countries’ stock markets for the period of 2000-2016. Dynamic conditional correlation and corrected
dynamic conditional correlation are employed for symmetric estimation. We find differences in the magnitudes of negative
and positive oil price shocks of G7 countries. The study also uses the asymmetric estimations to examine the response of
different shocks, and the variance and covariance series of these estimations are used for portfolio optimization and hedging
of stock and oil assets. The findings of symmetric and asymmetric estimations depict that past news and lagged volatility
have a significant impact on the current conditional volatility of G7 stock markets. On the contrary, the current conditional
volatility in the oil market is less dependent on past news and lagged volatility in the oil market. Our results portray that
G7 stock markets are more sensitive to past news and lagged volatility than oil markets. FIGARCH and FIEGARCH provide
evidence of an intermediate range of persistence of volatility. Finally, portfolio estimations report the importance of oil assets
to form an optimal portfolio that can minimize the portfolio risk without changing the expected return. Based on our findings,
we suggest that investors and portfolio managers of G7 countries should formulate a portfolio of stock and oil assets to
manage their portfolio risk.
Keywords
G7 countries, stock markets, oil market, asymmetric analysis, portfolio optimization
Introduction
In the recent three decades, the stock market returns continue
to remain unpredictable as such affecting both international
and national economies (Degiannakis, Fills, & Arora, 2017).
The volatility of the stock returns has prompted numerous
economists to dedicate resources on analysis of dynamics
influencing the unpredictability. Moreover, the recent financial crisis and management of markets have inspired concern
for many investors, scholars, and financial consultants.
Exploring the dynamics associated with volatility is critical
in the analysis of financial economics since it influences
investment decisions by investors and laws by policy makers. One of the most influential underlying forces in the stock
market is oil prices (Waheed, Wei, Sarwar, & Lv, 2018).
Volatility exchanges between the oil market and equity markets are essential for both portfolio designing and risk management. There is little doubt on the influence of oil prices
on various economic variables of a country or internationally. As such, volatility spillover between oil and stock
markets is vital in analyzing hedging ratios for oil-stock
investment holdings.
The price of oil typically encompasses the spot price of a
barrel of crude oil. There is a differential in the prices of oil
depending on the grade. The price of oil is marked internationally since it is one the most traded commodity in international levels. From the late 1990s to 2008, the prices of oil
rose significantly. Many economists attributed the increase
in oil prices to growing demand in the emerging economies.
The oil prices hit the highest during the 2008 recession at
more than US$140 a barrel (Degiannakis et al., 2017). The
1
School of Management, Xi’an Jiaotong University, P.R. China
COMSATS University Islamabad, Vehari Campus, Pakistan
3
Universiti Teknologi Petronas, Seri Iskandar, Malaysia
4
Lanzhou University, P.R. China
2
Corresponding Author:
Shahid Ali, School of Management, Xi’an Jiaotong University, No. 28,
Xianning West Road, Xi’an, Shaanxi 710049, P.R. China.
Email: Shahidali24@hotmail.com
Creative Commons CC BY: This article is distributed under the terms of the Creative Commons Attribution 4.0 License
(http://www.creativecommons.org/licenses/by/4.0/) which permits any use, reproduction and distribution of
the work without further permission provided the original work is attributed as specified on the SAGE and Open Access pages
(https://us.sagepub.com/en-us/nam/open-access-at-sage).
2
lowest prices of oil were also recorded in the middle of the
recession in December 2008. However, they peaked up
immediately after the crisis. Between 2010 and 2013, the
prices of oil remained between US$90 and US$120.
However, the prices have been declining since 2014 due to a
significant increase in oil production in the United States and
some other reasons.
There is a high level of unpredictability in the oil market.
Studies indicate that the primary cause of fluctuations in oil
prices since the 1980s is explained by the shift in oil demand.
The fast expansion of the global economy illustrates the
increase in the usage of oil (Hamilton, 2009). Similarly, high
inventory demand for oil is frequent during times of geopolitical tension and highly anticipated global economic
upsurge. Domestic conflicts and international issues in oilproducing countries contribute to increase oil prices
(Shahbaz, Sarwar, Chen, & Malik, 2017).
The extent to which stock markets are affected in both
long run and short term by oil price shocks varies considerably. When the price of oil increases, real output is compromised. The upsurge in prices of oil would predictably cause
the decline in stock prices owing to higher expenses hence
lower corporate earnings. In addition, considering oil is an
essential commodity in the production process of various
companies in the G7 countries, it may result in inflationary
pressure and higher interest rates. The adverse effect of an
increase in the price of oils on the stock market returns was
initially confirmed by an experimental study by Jones and
Kaul (1996); this research indicated significantly reduced
returns in inventory market due to crude oil impacts in
Canada and the United States. However, the results were less
evident for the United Kingdom and Japan. Sadorsky (1999)
described oil prices played a significant influence on stock
markets returns in the United States between 1946 and 1996.
Apergis and Miller (2009) analyzed the stock markets for
eight economies, including G7 countries, and reported a nonlinear relationship between prices of oil and stock market
returns.
However, the nonlinear theoretical assumption of the
effect of oil price fluctuations on the stock market does not
always hold. In recent years, many economists cited the bubbles in the crude oil market as the main reason for different
results in various countries. Some studies indicated a linear
relationship between oil prices and stock markets (El-Sharif,
Brown, Burton, Nixon, & Rusell, 2005). Similarly, other surveys show that oil shocks do not influence stock market
returns in either a positive or negative way. Another study
indicated that oil price has no long-term impact in the G7
countries as it does in emerging economies like Brazil, Russia,
India, and China (BRIC) states (Markoulis & Neofytou,
2016). The unrelated results can be explained by the different
degree of dependence on oil in various economies.
Moreover, a multitude of studies has insisted on the importance of portfolio formation in minimizing risks (Arouri &
Nguyen, 2010; Degiannakis et al., 2017; Khalfaoui, Boutahar,
SAGE Open
& Boubaker, 2015). Portfolio formation is a diversification
technique that reduces risk through the allocation of financial
holdings to various instruments and industries. The model
involves investing in different categories that react differently
to the same event in efforts of maximizing returns. If stock
and oil markets are nonlinear, their diversification maximizes
returns while in the event they are positively correlated,
diversification of the two markets is not necessary. The relevancy of oil prices on stock market returns whether in the
short run or long run displays the influence of oil prices on
portfolio formation and risk hedging (Arouri & Nguyen,
2010). Moreover, oil is the record-used physical commodity
in its capacity; as such, it has a tremendous influence on portfolio formation depending on price fluctuations (Miller &
Ratti, 2009).
Statistics indicate the high interdependence rates between
crude oil prices and the stock market returns in the 1990s
(Markoulis & Neofytou, 2016). This correlation is associated
with the influx in the housing market which influenced the
Organization of the Petroleum Exporting Countries (OPEC)
to stimulate oil production. As such, it is evident that aggregate demand for oil shock increases the correspondence
between oil prices and stock markets. The precautionary oil
demand shock reduces correlation between the oil and equity
markets as evident between the years 2001 and 2006 which
was characterized through several oil demand shocks such as
the Iraq war in 2003 (Ftiti, 2016). The correlation increased
significantly in all the G7 countries during the 2008 financial
crisis which is considered an aggregate demand oil shock.
Despite the level of correlation, there is a relationship
between oil shocks which expectably influences oil prices
and the stock markets in the G7 countries.
The existing studies have not analyzed the optimal strategy to construct an oil-stock portfolio by using econometric
estimation techniques, symmetric and asymmetric spillover
between oil and the stock market. Therefore, the objective of
our study is to fill this gap by examining the portfolio optimization strategies using symmetric and asymmetric estimations for G7 countries. These countries include the United
States, the United Kingdom, Germany, Canada, Italy, France,
and Japan. The motivation behind analyzing G7 countries is
the influence of oil in their economies that shows the relevance of oil price fluctuations in the G7 countries as both oil
importing and exporting countries. Moreover, these countries have the most developed and prestigious stock market
systems that are important in analyzing trends regarding oil
prices and formation of portfolios to hedge risks.
Objective of Study
This article attempts to examine the symmetric and asymmetric effect among the oil market and stock markets by using the
time series data over the period from January 2000 to
December 2016. Our emphasis is on the stock markets of G7
countries. There are three key objectives of the current study.
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Ali et al.
First, this study explores the interdependence among the oil
market and stock markets. It might well be asked how past
news and lagged volatility affect the current conditional volatility of oil and stock markets in its respective markets.
Previously, the studies only emphasized on traditional
approaches such as CCC-GARCH (constant conditional correlation–generalized autoregressive conditional heteroskedasticity) and DCC-GARCH (dynamic conditional
correlation–generalized autoregressive conditional heteroskedasticity); however, this article uses the modern technique
cDCC-GARCH (corrected dynamic condition correlation–
generalized autoregressive conditional heteroskedasticity)
that is introduced by Aielli (2008). This latest method by
Aielli (2008) has reformulated the correlation process.
Second, we examine the presence of an asymmetric effect
in the oil market and G7 stock markets. The asymmetric
analyses look at the range of persistence of lagged volatility
on current conditional volatility. In addition, asymmetric
analyses observe the response of negative and positive
shocks in its respective markets. Earlier studies in the context of G7 countries have not studied the asymmetric effect
such as the persistence of volatility effect on oil and the stock
market. To the best of our knowledge, this study is the first
attempt to examine the persistence of volatility effect on
stock and oil market in the context of G7 countries. Finally,
the study is to evaluate the role of oil assets to form an optimal portfolio. It might well be asked how oil assets can be
used to hedge the portfolio risk.
the stock market. The analysis is conducted by applying the
DCC-GARCH framework. Previously, similar techniques
have been applied by McAleer, Hoti, and Chan (2009) and
Arouri, Lahiani, and Nguyen (2011) for investigating the
relationship between the oil and stock returns. DCC-GARCH
is the most applied method in this study; this method answers
the question of whether the stock market and oil market are
dependent on the past news and lagged volatility, in its
respective markets. The specification of DCC-GARCH is
considered as the generalization of CCC-GARCH model as
proposed by Bollerslev (1990). The dynamic condition correlation in this method is given as follows:
Significance of Study
φ11,t
ϕt =
φ21,t
The article is important as it provides informed insight on
portfolio management that aims to reduce risks and influence
profitable investment decisions. The study will contribute to
the growing literature on the influence of oil price on the
stock markets and portfolio optimization in G7 countries. As
such, investors and portfolio managers may use the suggestions of the study to initiate appropriate diversification and
risk-hedging strategies (Arouri & Nguyen, 2010). The
emphasis on cDCC-GARCH model provides insight on the
link of volatility transmission among the oil and stock markets. The conclusions from the study will provide insight to
policy makers since adverse oil prices fluctuations may
result in extreme influences on the equity markets hence
affecting cash flow in corporate domains. The incorporation
of oil and stock markets volatility transmission provides
long-term analysis. Long-run effects of oil prices on stock
markets are essential in influencing informed decision making (El-Sharif et al., 2005).
Method
DCC-GARCH Model
This study uses the stock index and the oil prices for G7
countries to analyze the relationship between oil prices and
H t = Dt Αt Dt ,
(1)
Where Dt = diag{ hstock , hoil },
stock = China, Japan, India
hii ,t = ωi , 0 + aii εi2,t −1 + bii hii ,t −1 , i = stock , oil
Αt = (diag{ϕt }) −1/ 2 ϕt (diag{ϕt }) −1/ 2
(2)
The dynamic conditional correlation parameters are as
follows:
ϕt = (1 − δ1 − δ 2 )ϕ0 + aπt −1πt’ −1 + δ 2 ϕt −1
φ12,t
φ22,t
(3)
(4)
ϕt in the formula is the time-varying condition correlation between the oil market price and the stock market while
δ1 is used to estimate the previous standardized shocks on
current dynamic conditional correlation and finally δ 2 captures the previous dynamic conditional correlation on current
’
dynamic conditional correlation; πt = (πstock , πoil ) is 2 × 1
vector of standardized residuals which is defined as
ε
πt = t
ϕ
ht ; 0 which is the matrix of unconditional
correlation.
cDCC-GARCH Model
The cDCC-GARCH is a more amenable DCC model. It is
described and heuristically proven to be a consistent model
of examination. This model was introduced by Aielli (2008)
which is similar to the DCC-GARCH model by Engle (2002).
’
However, E (πt −1πt −1 ) is inconsistent. In addition, it has been
shown that the specification of correlation is reformulated in
the cDCC-GARCH model.
The specification of cDCC-GARCH model is the same as
the specification of the DCC-GARCH model. However,
4
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Aielli (2008) reformulated the correlation process as given in
Equation 13.
Qt = (1 − a − b)Q + aπ*t −1π*’
t −1 + bQt −1
(5)
*
1/ 2
Where πt = diag{Qt } πt and πt is the standardized
residuals.
Asymmetric GARCH Estimations
GJR-GARCH (Glosten–Jagannathan–Runkle–generalized autoregressive conditional heteroskedasticity) model. Both the GJR
and the GARCH specification are often used in the finance
and economics literature. However, according to various
researchers such as Mohammadi and Su (2010) and Morana
(2001), the GJR model performs better than the GARCH
specification thereby enhancing forecasting performance.
This model was introduced by Glosten, Jagannathan, and
Runkle (1993) which is used to support the fact that conditional variance oil price return responds asymmetrically to
the shocks of equal magnitude with difference sign (Morana,
2001; Mohammadi & Su, 2010). The GJR-GARCH reads as
follows:
2
stock
stock 2
stock stock
htstock = α stock (ε tstock
Dtstock
ht −1
−1 ) + δ
−1 ( ε t −1 ) + β
htoil = α oil (ε toil−1 ) 2 + δ oil Dtoil−1 (ε toil−1 ) 2 + β oil htoil−1
1
Where, Dt −1 =
0
(6)
(7)
α
(1 − φ( L)(1 − L) d
+ (1 −
1 − β( L)
1 − β( L)
q
φ( L)(1 − L) d ln ht = α + ∑ (β j
j =1
εt −1
ht −1
+γ j
εt −1
ht −1
(9)
Where γ j shows the existence of leverage effects,
FIEGARCH model is stationary if 0 < d < 1 (Bollerslev &
Mikkelsen, 1996). When we include leverage term in the
equation, we allow the conditional variance of the model to
depend on magnitude and sign of expected returns.
FIEGARCH model indicates that stock responds with different manners to negative and positive shocks. Unlike GARCH
and MGARCH functions, the FIGARCH and FIEGARCH
functions are estimated using the Broyden–Fletcher–
Goldfarb–Shanno (BFGS) algorithm. More often, daily
financial returns are minimal in figures. As a result, the algorithm is not properly scaled and it may result in failure in
convergence. Thus, in this study, we used returns in our
empirical research to improve the convergence.
Portfolio Management With Oil Risk-Hedging
Strategies
if , ε t −1 < 0, otherwise
FIGARCH (fractional integrated generalized autoregressive conditional heteroskedasticity) model. This study made use of the
bivariate model of Brunetti and Gilbert (2000) to investigate
the volatility processes for the stock and oil prices. This
model is used to find out the extent to which stock and oil
volatility persists. The primary purpose of the model is to
develop a more complex flexible class of processes for the
conditional variance. The FIGARCH model combines many
features of the fractionally integrated processes for the mean
and the conditional variance for the GARCH process.
σt =
FIEGARCH (fractionally integrated exponential generalized autoregressive conditional heteroskedasticity) model. This model is
similar to the other models of estimation, but the FIEGARCH
simultaneously deals with the finite persistence of the shocks
and the magnitude of positive or negative shocks. The FIEGARCH model was proposed by Bollerslev and Mikkelsen
(1999). This model has the property of positive conditional
variance, and therefore the study had to make use of the
model to estimate the persistence of shocks on volatility and
the magnitude of the stock market deviation.
This section uses the variance and covariance series to calculate, calculated from the above models, and to evaluate
whether oil is a useful asset for portfolio optimization. The
primary objective of this study was to provide risk-hedging
analysis without reducing the expected return. According to
Kroner and Ng (1998), the optimal weight of oil in one dollar
of the stock market at a specified time t can be expressed as
follows:
w12,t =
h1,t − h12,t
h2,t − 2h12,t + h1,t
(10)
Under condition that
(8)
Where d is the parameter that describes the degree of
hyperbolic decay. There are three scenarios: one, if d = 0, it
describes the geometric decay. Two, for 0 < d < 1, it shows
the intermediate range of persistence and confirms that the
process has a unit root. Three, d = 1 expresses the infinite
persistence.
w12,t
0, if
= w12,t , if
1, if
w12,t < 0
0 ≤ w12,t ≤ 1
w12,t > 1
Where w12,t shows the weight of oil in one dollar portfolio
of the oil stock asset at the time t represents the weight of the
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Ali et al.
Table 1. Descriptive Statistics.
Observation
M
SD
Variance
Skewness
Kurtosis
Jarque–Bera
ARCH
Unit root
ADF
Elliott et al.
Unconditional correlation
WTI Oil
Oil
United
States
United
Kingdom
Germany
Canada
Italy
France
Japan
3,504
1.0947
1.7428
1.0021
1.0961
9.5038
7,643**
28.4692**
3,504
0.1523
1.8236
1.0053
1.0532
6.2351
5,832**
43.235**
3,504
0.0523
1.8235
1.5638
1.2035
4.5638
3,618**
35.238**
3,504
0.0342
2.1523
1.0304
0.9235
8.2365
4,691**
84.135**
3,504
0.0152
1.8294
1.4628
1.2365
5.2362
6,385**
24.637**
3,504
0.6234
2.1163
1.1193
0.5314
6.9125
9,531**
19.423**
3,504
0.0523
1.2035
1.0325
1.6352
7.9643
4,761**
109.890**
3,504
0.1237
1.5371
2.0138
1.7152
8.4538
3,511**
94.231*
–35.835**
0.0942
–41.285**
0.0148
–21.341**
0.3297
–47.136**
0.03825
–24.997**
0.0093
–53.824**
0.8936
–41.235**
0.0153
–40.824**
0.0722
0.0352
0.0293
0.0041
0.0165
0.0063
0.0527
0.0316
Note. ARCH = autoregressive conditional heteroskedasticity; ADF = augmented Dickey–Fuller; WTI = West Texas Intermediate.
**represents significance at the 1% level and ***represents significance at 5% level.
stock market in oil stock portfolio at the time. h1,t moreover,
describes the conditional variance of the stock market return
and oil market return, respectively. While h12,t is the conditional covariance of oil-stock at the time t . However, supplementary this method, the study also applied Kroner and
Sultan (1993) method to estimate the optimal hedge ratio for
two studied assets in case of G7 countries. Calculation of risk
hedging is presented in the equation below. However, it symbolizes risk-minimizing hedge for the oil and stock market.
β12,t =
h12,t
h1,t
(11)
Data and Preliminary Analysis
The study uses daily base data for econometric analysis over
the period from January 2000 to December 2016. The choice
of information in the past 20 years is based on the availability
of information. The stock price data of G7 stock markets are
collected from their relevant websites. Whereas, the daily base
oil price data for the study are collected from the U.S. Energy
Information Administration (2017). The present study uses the
data of New York stock exchange for the United States, FTSE
100 for the United Kingdom, S&P/TSX Composite for
Canada, FTSE MIB for Italy, CAC 40 for France, DAX 30 for
Germany, and NIKKEI 225 for Japan. For analysis, we utilize
the return series of all the stock prices which is the natural
logarithm of closing prices divided by lagged closing prices.
The formula for the calculation is as follows:
P
Ri ,t = ln i ,t × 100, i = stock , oil
P
i ,t −1
(12)
Where, Ri, t represents the return series of stock i at time t.
Pi, t is the price series of stock i at time t and Pi, t – 1 is the
lagged price of stocks.
Table 1 shows the descriptive statistics of West Texas
Intermediate (WTI) oil return series, US stock return, UK
stock return, German stock return, Canadian stock return,
Italian stock return, French stock market return, and Japanese
returns series. The total number of observations for the return
series is 3,504. WTI oil return series has the maximum average value while the Canadian stock series contains the lowest
average return with 1.0947 and 0.0152, respectively.
However, the oil series and all stock return series present
negative skewness that shows the extreme losses in the oil
market.
Furthermore, the statistics of Kurtosis and Jarque–Bera
indicate the non-normality of oil and stock markets return.
The significance of ARCH effect appears in the oil and
stock markets. This non-normality and presence of ARCH
allow us to apply the GARCH modeling to examine the oil
and stock markets spillover. For stationarity analysis,
Augmented Dickey–Fuller (ADF) and Elliott, Rothenberg,
and Stock (1996) unit root tests have been used which
rejected the null hypothesis of unit root presence in the
return series of oil and stock markets.
Empirical Evidence
Symmetric Analysis
Tables 2 to 8 report the symmetric and asymmetric GARCH
estimations for G7 countries. The findings of the symmetric
DCC-GARCH confirm that past shocks in the US stock market have a significant effect on the current conditional volatility of the US stock market. Moreover, the current
conditional volatility responds to the lagged volatility in US
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Table 2. U.S. Analysis.
Symmetric
Mean(stock)
Mean(oil)
C(stock, stock)
C(oil, oil)
A(stock, stock)
A(oil, oil)
B(stock, stock)
B(oil, oil)
GJR (stock)
GJR (oil)
FIGARCH (stock)
FIGARCH (oil)
EGARCH(Theta1) (stock)
EGARCH(Theta2) (stock)
EGARCH(Theta1) (oil)
EGARCH(Theta2) (oil)
Residual-diagnostics
Log likelihood
Asymmetric—DCC
Asymmetric—cDCC
DCC
cDCC
GJR-GARCH
FIGARCH
FIEGARCH
GJR-GARCH
FIGARCH
FIEGARCH
–0.2841**
–0.1052
0.0253**
0.0356
0.2105**
0.4321
0.5661**
0.9257*
–0.2376**
–0.1124
0.0221**
0.0415
0.2403**
0.3946
0.5941**
0.8468**
–0.0746**
–0.0138
0.0584*
0.0113
–0.0642**
0.0491**
0.6015**
0.8642**
0.3465**
0.09521**
–0.1352**
–0.0141
0.0492**
0.0094
–0.0513*
0.0441*
0.6743**
0.9431**
–0.0495**
–0.0312
0.0629*
0.0163
–0.0558**
0.0381**
0.4138
–0.8847**
–0.0132**
–0.0465
0.0346*
0.0714
–0.0651**
0.6943
0.6814**
0.9133**
0.3024**
0.0846**
–0.0846**
–0.0332
0.0486**
0.0648
–0.0544*
0.7536
0.0943**
0.8943**
–0.0494**
–0.0215
0.0941*
0.0135
–0.0231**
0.6135**
0.4638
–0.9437**
0.8351**
0.8118
0.9306*
0.6094*
–0.0164*
0.651**
–0.0947*
0.2047**
.7,341**
0.9463*
0.9465**
0.6397**
–0.0175*
0.8406**
–0.0118*
0.2445**
–5,219.2110
–5,136.9480
–5,141.4630
–5,141.4630
–5,219.2110 –5,136.9480
Note. DCC = dynamic condition correlation; cDCC = corrected dynamic condition correlation; GJR = Glosten–Jagannathan–Runkle; GARCH =
generalized autoregressive conditional heteroskedasticity; FI = fractional integrated; FIE = fractionally integrated exponential.
**represents significance at the 1% level and ***represents significance at 5% level.
Table 3. UK Analysis.
Symmetric
Mean(stock)
Mean(oil)
C(stock, stock)
C(oil, oil)
A(stock, stock)
A(oil, oil)
B(stock, stock)
B(oil, oil)
GJR (stock)
GJR (oil)
FIGARCH (stock)
FIGARCH (oil)
EGARCH(Theta1) (stock)
EGARCH(Theta2) (stock)
EGARCH(Theta1) (oil)
EGARCH(Theta2) (oil)
Residual-diagnostics
Log likelihood
Asymmetric—DCC
Asymmetric—cDCC
DCC
cDCC
GJR-GARCH
FIGARCH
FIEGARCH
GJR-GARCH
FIGARCH
FIEGARCH
–0.0141
–0.0163
0.0406**
0.0419**
0.0497
0.0623
0.8136
0.7992
–0.0413
–0.0286
0.0121**
0.0502*
0.0428
0.0706
0.9241
0.8943
–0.0208
–0.0137
0.0264*
0.0382
0.0467
0.0528
0.9334
0.8943
0.0804**
0.0172*
–0.0317
–0.0526
0.1052*
0.0428
0.0681
0.0764
0.8436
0.9937
–0.0119
–0.0163**
0.5128**
0.0712**
0.0842**
0.0861**
0.8461**
0.9286**
–0.0106
–0.0637
0.0109**
0.0168
0.0764**
0.0827
0.8931**
0.9020**
0.0840**
0.0194*
–0.0361
–0.0108
0.0861*
0.0374
0.0236
0.0794
0.8264
0.8963
–0.0260
–0.0193**
0.4294
0.0205
0.0649
–0.0596
0.9084
0.8320
0.9067*
0.9142
0.8947**
0.9726*
–0.0864**
0.0301
–0.0628**
0.0141
0.9074*
0.9168**
–5,737.3030
–5,746.1240
0.9864*
0.8943*
–0.0946**
0.0230
–0.0646*
0.0174
–5,722.2960
–5,737.2490
–5,746.0890
–5,722.2790
Note. DCC = dynamic condition correlation; cDCC = corrected dynamic condition correlation; GJR = Glosten–Jagannathan–Runkle; GARCH =
generalized autoregressive conditional heteroskedasticity; FI = fractional integrated; FIR = fractionally integrated exponential.
**represents significance at the 1% level and ***represents significance at 5% level.
stock market. However, the results for oil series are contradicting the past shocks and conditional volatility have no significant impact on current volatility and supports the findings
of Khalfaoui et al. (2015; Liu, An, Huang, & Wen, 2017).
The robust estimations using the cDCC-GARCH also report
similar results for the United States and oil market.
Table 3 indicates a symmetric estimation of the DCCGARCH and cDCC-GARCH for UK stock market and oil
market. The result shows that the current conditional volatility of stock returns respond to the past news, in its market.
The lagged conditional volatility has a significant impact on
current conditional volatility for the UK stock market. On
7
Ali et al.
Table 4. Germany Analysis.
Symmetric
Mean(stock)
Mean(oil)
C(stock, stock)
C(oil, oil)
A(stock, stock)
A(oil, oil)
B(stock, stock)
B(oil, oil)
GJR (stock)
GJR (oil)
FIGARCH (stock)
FIGARCH (oil)
EGARCH(Theta1) (stock)
EGARCH(Theta2) (stock)
EGARCH(Theta1) (oil)
EGARCH(Theta2) (oil)
Residual-diagnostics
Log likelihood
Asymmetric—DCC
Asymmetric—cDCC
DCC
cDCC
GJR-GARCH
FIGARCH
FIEGARCH
GJR-GARCH
FIGARCH
FIEGARCH
–0.2941**
–0.1152
0.0353**
0.0456
0.2205**
0.4421
0.5761**
0.9357*
–0.2476**
–0.1224
0.02321**
0.0515
0.2503**
0.3046
0.5894**
0.8568**
–0.0846**
–0.0238
0.0684*
0.0213
–0.0742**
0.0591**
0.6115**
0.8742**
0.0365**
0.09621**
–0.1452**
–0.0241
0.0592**
0.0194
–0.0613*
0.0541*
0.6843**
0.9531**
–0.0595**
–0.0412
0.0729*
0.0263
–0.0658**
0.0481**
0.4238
–0.8947**
–0.0232**
–0.0565
0.0446*
0.0814
–0.0751**
0.6843
0.6914**
0.9233**
0.0324**
0.0946**
–0.0946**
–0.0432
0.0586**
0.0748
–0.0644*
0.7636
0.0843**
0.8843**
–0.0594**
–0.0315
0.0841*
0.0235
–0.0331**
0.6235**
0.4738
–0.9537**
0.8451**
0.8218**
0.8906**
0.7814**
–0.0742**
0.1751*
–0.0124**
0.2164**
0.8441**
0.8248**
0.8965**
0.7852**
–0.0836**
0.1906*
–0.0118**
0.2535**
–5,314.6570
–5,271.7410
–5,314.6330
–5,271.8140
–5,285.4460
–5,285.5080
Note. DCC = dynamic condition correlation; cDCC = corrected dynamic condition correlation; GJR = Glosten–Jagannathan–Runkle; GARCH =
generalized autoregressive conditional heteroskedasticity; FI = fractional integrated; FIE = fractionally integrated exponential.
**represents significance at the 1% level and ***represents significance at 5% level.
the contrary, the current conditional volatility of the oil market does not respond to the lagged volatility. Similarly, Table
8 reports the results for the Japanese stock market with similar findings.
Table 4 offers the results of DCC-GARCH for German
stock market; the findings show that past news in the stock
market has a significant effect on the current conditional
volatility. However, the past news in the oil market has no
impact on the current volatility of the oil market. On the contrary, the current conditional volatility in the stock and oil
market significantly responds to the lagged volatility in its
market. Similarly, the estimations of the robust test, cDCCGARCH, confirms that past shocks and lagged conditional
volatility have a significant effect on current conditional
volatility, in its respective markets.
Table 5 illustrates the findings of symmetric DCCGARCH for the Canadian stock market. The results confirm
the significant effect of past news and lagged conditional
volatility on current conditional volatility for the Canadian
stock market. On the contrary, the past news and lagged conditional volatility have proved to be insignificant for oil
series. The cDCC-GARCH supports the results for Canadian
stock market; the current conditional volatility responded to
the lagged news and lagged conditional volatility.
Interestingly, in the cDCC-GARCH analysis, the result
shows that the current conditional volatility of the oil market
significantly responds to the lagged conditional volatility.
Table 6 presents similar results for the Italian stock market, whereas Table 7 shows the estimations for the French
stock market. Column 2 and 3 deal with the symmetric
GARCH techniques, named DCC-GARCH and cDCCGARCH. The results of ARCH and GARCH coefficients
describe that past news and past conditional volatility are
statistically significant at 1% level. Thus, the findings confirm the significant impact of lagged news and lagged conditional volatility on current conditional volatility for stock
and oil markets, in its respective markets. It is also worth
noting that coefficients of ARCH term are smaller than the
coefficients of GARCH term, which suggests that current
conditional volatility responds more quickly as significant
impacts of lagged volatility than as lagged shocks.
Asymmetric Analysis
Tables 2 to 8 present the results of asymmetric GARCH. The
fourth column of each table deals with the GJR-GARCH,
which shows that the current conditional volatility responds
significantly to past shocks in the respective market. The
coefficient of GJR-GARCH for US stock market indicates
that the magnitude of adverse shocks is higher in the US market. The statistical value of FIGARCH shows the persistence
of shocks over the period. For US analysis, the oil and stock
market values confirm that volatility has an intermediate
range of persistence and the process contains a unit root. The
results of FIEGARCH depict the persistence of volatility as
well as the magnitude of negative and positive shocks on
current conditional volatility. The significant value of
FIEGARCH indicates that the US stock market and oil market also provide evidence of an intermediate range of persistence of shocks on conditional volatility. Moreover, the
8
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Table 5. Canada Analysis.
Symmetric
Mean(stock)
Mean(oil)
C(stock, stock)
C(oil, oil)
A(stock, stock)
A(oil, oil)
B(stock, stock)
B(oil, oil)
GJR (stock)
GJR (oil)
FIGARCH (stock)
FIGARCH (oil)
EGARCH(Theta1) (stock)
EGARCH(Theta2) (stock)
EGARCH(Theta1) (oil)
EGARCH(Theta2) (oil)
Residual-diagnostics
Log likelihood
DCC
cDCC
–0.2841**
–0.1042
0.0243**
0.0366
0.2115**
0.4331
0.5671**
0.9267*
–0.2386**
–0.1134
0.0221**
0.0425
0.2413**
0.3956
0.5961**
0.8478**
Asymmetric—DCC
GJR-GARCH
–0.0756**
–0.0148
0.0594*
0.0123
–0.0652**
0.0481**
0.6025**
0.8652**
0.3075**
0.09531**
–5,141.4730
FIGARCH
Asymmetric—cDCC
FIEGARCH
GJR-GARCH
FIGARCH
FIEGARCH
–0.1362**
–0.0151
0.0482**
0.0084
–0.0523*
0.0451*
0.6753**
0.9441**
–0.0485**
–0.0322
0.0639*
0.0173
–0.0568**
0.0391**
0.4148
–0.8857**
–0.0142**
–0.0475
0.0356*
0.0724
–0.0661**
0.6953
0.6824**
0.9143**
0.3034**
0.0956**
–0.0856**
–0.0342
0.0496**
0.0658
–0.0554*
0.7546
0.0953**
0.8953**
–0.0484**
–0.0225
0.0951*
0.0145
–0.0241**
0.6145**
0.4648
–0.9447**
0.8361**
0.8128**
0.9316**
0.6084**
–0.0652**
0.3677*
–0.0957**
0.2074**
0.8642**
0.9473**
0.9475**
0.6387**
–0.0746**
0.3616*
–0.1028**
0.2445**
–5,219.2210
–5,136.9580
–5,141.4730
–5,219.2210 –5,136.9580
Note. DCC = dynamic condition correlation; cDCC = corrected dynamic condition correlation; GJR = Glosten–Jagannathan–Runkle; GARCH =
generalized autoregressive conditional heteroskedasticity; FI = fractional integrated; FIE = fractionally integrated exponential.
**represents significance at the 1% level and ***represents significance at 5% level.
Table 6. Italy Analysis.
Symmetric
Mean(stock)
Mean(oil)
C(stock, stock)
C(oil, oil)
A(stock, stock)
A(oil, oil)
B(stock, stock)
B(oil, oil)
GJR (stock)
GJR (oil)
FIGARCH (stock)
FIGARCH (oil)
EGARCH(Theta1) (stock)
EGARCH(Theta2) (stock)
EGARCH(Theta1) (oil)
EGARCH(Theta2) (oil)
Residual-diagnostics
Log likelihood
Asymmetric—DCC
Asymmetric—cDCC
DCC
cDCC
GJR-GARCH
FIGARCH
FIEGARCH
GJR-GARCH
FIGARCH
FIEGARCH
–0.2840**
–0.1053
0.0254**
0.0357
0.2106**
0.4322
0.5662**
0.9258*
–0.2377**
–0.1123
0.0222**
0.0416
0.2404**
0.3947
0.5942**
0.8469**
–0.0747**
–0.0139
0.0585*
0.0114
–0.0644**
0.0492**
0.6016**
0.8643**
0.1766**
0.0842**
–0.1353**
–0.0142
0.0493**
0.0095
–0.0514*
0.0442*
0.6744**
0.9432**
–0.0496**
–0.0313
0.0628*
0.0164
–0.0559**
0.0382**
0.4139
–0.8848**
–0.0133**
–0.0466
0.0347*
0.0715
–0.0652**
0.6944
0.6815**
0.9134**
0.1725**
0.0847**
–0.0847**
–0.0333
0.0487**
0.0649
–0.0545*
0.7537
0.0944**
0.8944**
–0.0495**
–0.0216
0.0942*
0.0136
–0.0232**
0.6136**
0.4639
–0.9438**
0.9352**
0.8119**
0.9307**
0.6096**
–0.1643**
0.4652*
–0.0948**
0.2065**
0.9462**
0.9464**
0.9466**
0.6398**
–0.1737**
0.4607*
–0.1019**
0.2436**
–5,218.2110
–5,137.9480
–5,218.2110
–5,137.9480
–5,142.4730
–5,142.4630
Note. DCC = dynamic condition correlation; cDCC = corrected dynamic condition correlation; GJR = Glosten–Jagannathan–Runkle; GARCH =
generalized autoregressive conditional heteroskedasticity; FI = fractional integrated; FIE = fractionally integrated exponential.
**represents significance at the 1% level and ***represents significance at 5% level.
conditional volatility of stock and oil markets has a higher
response to the adverse shocks than the positive shocks. The
asymmetric results further show that the magnitude of negative shocks in the stock market is higher than in the oil
market.
The values of GJR-GARCH for UK stock market and
oil market indicate the higher magnitude of adverse shocks
on current conditional volatility in its market. The
GJRGARCH results further confirm that a negative shock
profoundly affects the stock market than the oil market.
9
Ali et al.
Table 7. France Analysis.
Symmetric
Mean(stock)
Mean(oil)
C(stock, stock)
C(oil, oil)
A(stock, stock)
A(oil, oil)
B(stock, stock)
B(oil, oil)
GJR (stock)
GJR (oil)
FIGARCH (stock)
FIGARCH (oil)
Asymmetric—DCC
DCC
cDCC
–0.3841**
–0.2052
0.1253**
0.1356
0.3105**
0.5321
0.6661**
0.8257*
–0.3376**
–0.2124
0.1221**
0.1415
0.3403**
0.4946
0.6941**
0.9468**
EGARCH(Theta1) (stock)
EGARCH(Theta2) (stock)
EGARCH(Theta1) (oil)
EGARCH(Theta2) (oil)
Residual-diagnostics
Log likelihood
GJR-GARCH
FIGARCH
–0.0746**
–0.0138
0.0584*
0.0113
–0.0642**
0.0491**
0.6015**
0.8642**
0.0105**
0.1821**
Asymmetric—cDCC
FIEGARCH
–0.2352**
–0.1141
0.1492**
0.1094
–0.1513*
0.1441*
0.7743**
0.8431**
–0.1495**
–0.1312
0.1629*
0.1163
–0.1558**
0.1381**
0.5138
–0.9847**
0.8351**
0.9118**
0.8306**
0.7094**
GJR-GARCH
–0.1132**
–0.1465
0.1346*
0.1714
–0.1651**
0.7943
0.7814**
0.8133**
0.0124**
0.1846**
FIGARCH
FIEGARCH
–0.1846**
–0.1332
0.1486**
0.1648
–0.1544*
0.8536
0.1943**
0.9943**
–0.1494**
–0.1215
0.1941*
0.1135
–0.1231**
0.7135**
0.5638
–0.8437**
0.8341**
0.8463**
0.8465**
0.7397**
–0.2642**
0.1651*
–0.1947**
0.3064**
–6,141.4630
–6,219.2110
–6,136.9480
–0.2736**
0.1806*
–0.2018**
0.3435**
–6,141.4630
–6,219.2110
–6,136.9480
Note. DCC = dynamic condition correlation; cDCC = corrected dynamic condition correlation; GJR = Glosten–Jagannathan–Runkle; GARCH =
generalized autoregressive conditional heteroskedasticity; FI = fractional integrated; FIE = fractionally integrated exponential.
**represents significance at the 1% level and ***represents significance at 5% level.
Table 8. Japan Analysis.
Symmetric
Mean(stock)
Mean(oil)
C(stock, stock)
C(oil, oil)
A(stock, stock)
A(oil, oil)
B(stock, stock)
B(oil, oil)
GJR (stock)
GJR (oil)
FIGARCH (stock)
FIGARCH (oil)
EGARCH(Theta1) (stock)
EGARCH(Theta2) (stock)
EGARCH(Theta1) (oil)
EGARCH(Theta2) (oil)
Residual-diagnostics
Log likelihood
Asymmetric—DCC
Asymmetric—cDCC
DCC
cDCC
GJR-GARCH
FIGARCH
FIEGARCH
GJR-GARCH
FIGARCH
FIEGARCH
–0.2952**
–0.1163
0.0364**
0.0467
0.2216**
0.4432
0.5772**
0.9368*
–0.2487**
–0.1235
0.0332**
0.0526
0.2514**
0.3857
0.5852**
0.8579**
–0.0857**
–0.0249
0.0695*
0.0224
–0.0753**
0.0582**
0.6126**
0.8753**
0.0576**
0.09632**
–0.1463**
–0.0252
0.0583**
0.0185
–0.0624*
0.0552*
0.6854**
0.9542**
–0.0586**
–0.0423
0.0738*
0.0274
–0.0669**
0.0492**
0.4249
–0.8958**
–0.0245**
–0.0576
0.0457*
0.0825
–0.0762**
0.6854
0.6925**
0.9244**
0.0504**
0.0957**
–0.0957**
–0.0443
0.0597**
0.0759
–0.0655*
0.7647
0.0854**
0.8854**
–0.0585**
–0.0326
0.0852*
0.0246
–0.0342**
0.6246**
0.4749
–0.9548**
0.8962**
0.8229**
0.9417**
0.6185**
–0.0563
0.0762*
–0.0856**
0.2175**
0.8057**
0.9574**
0.9576**
0.6488**
–0.0163
0.0917*
–0.1129**
0.2546**
–5,635.3720
–5,610.3880
–5,613.3870
–5,613.3780
–5,635.3580 –5,610.3840
Note. DCC = dynamic condition correlation; cDCC = corrected dynamic condition correlation; GJR = Glosten–Jagannathan–Runkle; GARCH =
generalized autoregressive conditional heteroskedasticity; FI = fractional integrated; FIE = fractionally integrated exponential.
**represents significance at the 1% level and ***represents significance at 5% level.
Asymmetric FIGARCH is significant for both stock and
oil market, with the values greater than zero and less than
one, which indicates that the lagged shocks have an intermediate range of persistence on current conditional volatility, the same is true for FIEGARCH. Similarly, the adverse
shocks in the UK stock market and oil market have a higher
magnitude than the positive shock and this further confirms the previous findings. Furthermore, this magnitude is
higher for the stock market as compared with the oil
market.
10
SAGE Open
Table 9. Portfolio Analysis.
cDCC-GARCH
Average of W
Average of B
GJR-GARCH
Average of W
Average of B
FIGARCH
Average of W
Average of B
FIEGARCH
Average of W
Average of B
United States
United Kingdom
Germany
Canada
Italy
France
Japan
0.2258
0.1652
0.1748
0.1135
0.4025
0.0836
0.1183
0.2031
0.3351
0.1821
0.4351
0.0462
0.3306
0.2642
0.2301
0.1596
0.1893
0.1252
0.4158
0.0901
0.1205
0.2205
0.3621
0.1934
0.4218
0.0504
0.3416
0.2587
0.2203
0.1624
0.1763
0.1172
0.4056
0.0736
0.1197
0.2263
0.3579
0.1786
0.4304
0.0499
0.3451
0.2614
0.2287
0.1504
0.1886
0.1305
0.4104
0.0952
0.1103
0.2146
0.3568
0.1905
0.4251
0.0463
0.3508
0.2577
Note. cDCC = corrected dynamic condition correlation; GARCH = generalized autoregressive conditional heteroskedasticity; GJR = Glosten–
Jagannathan–Runkle; FI = fractional integrated; FIE = fractionally integrated exponential; W = Weights; H = Hedge.
Table 4 provides the results of the asymmetric analysis for
the German stock market and oil market. The significance of
GJR-GARCH provides evidence that negative lagged shocks
in the German stock market and oil market have a higher
magnitude than positive shocks. However, in contrast to the
US and UK findings, the oil market shows a higher response
to the negative shocks. The FIGARCH presents the intermediate range of volatility persistence in German stock and oil
market with the values of 0.84 and 0.82, respectively.
Moreover, the FIEGARCH estimations support the result of
FIGARCH indicating that the significant parametric values
0.89 and 0.78 for the German stock market and oil market,
respectively. However, the FIEGARCH also confirms the
results of GJR-GARCH that negative shocks in the markets
have a higher influence on current conditional volatility, in
its market.
In the case of Canada, Italy, France, and Japan, the significance of GJR-GARCH specifies that the negative
shocks have a higher magnitude in its respective markets;
the statistical values for stock markets are 0.30, 0.17, 0.41,
and 0.15 for Canada, Italy, France, and Japan, respectively,
whereas; the GJR-GARCH coefficients for Canada, Italy,
France, and Japan are 0.095, 0.084, 0.18, and 0.09, respectively. Moreover, the parameters of FIGARCH indicate the
intermediate range of persistence for Canada, Italy, France,
and Japan. The FIEGARCH estimations also support the
results of FIGARCH that the volatility in stock markets and
oil market has an intermediate range of persistence.
However, the results of Canada, Italy, France, and Japan
represent that the negative shock in stock and oil market
answer back more powerfully in its market than positive
shocks. Also, in Canada and Italy, this magnitude is higher
in stock markets as compared with the oil markets. Despite
this, the results of France and Japan report that the adverse
shocks have a higher influence on oil markets than stock
markets.
The aforementioned results show that G7 markets hold an
asymmetric effect. The findings for United States, United
Kingdom, Germany, Canada, and Italy confirm that the magnitude of negative shocks is higher in stock markets than the
oil market. While France and Japan indicate contradicting
results, the negative shocks have a higher influence on conditional volatility of the oil market than the stock market.
Moreover, FIGARCH and FIEGARCH report the evidence
of an intermediate range of volatility persistence in all G7
stock markets.
Portfolio Analysis
Table 9 reports the results of portfolio weights and hedge
ratios. The series of cDCC-GARCH shows the optimal
weight for the United States is 0.2258 which demonstrates
that the US investors can form an optimal portfolio by using
20 cents to buy oil assets out of US$1. The asymmetric series
provide similar findings; the statistical values of optimal
weights under GJR-GARCH, FIGARCH, and FIEGARCH
are 0.2301, 0.2203, and 0.2287, respectively. After optimal
weights, we emphasize on hedge ratio that assistance to take
a long or short position for oil/stock assets. The result of
hedge suggests that the US investors should sell (short position) oil assets of US$1 and buy US stock assets for 16.52
cents. Asymmetric series also presents parallel results with
slightly different values; the values of hedge ratios are
0.1596, 0.1624, and 0.1504 for GJR-GARCH, FIGARCH,
and FIEGARCH, respectively.
In case of United Kingdom, the symmetric series for
cDCC-GARCH presents that the optimal weight and hedge
ratio are 0.1748 and 0.1135, respectively. The optimal weight
suggests that the investors in the UK market should spend
17.48 cents to buy oil assets out of US$1. Whereas, the hedge
ratio indicates that the investors in the UK stock market
should take a short position in oil assets and the extended
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Ali et al.
position of 11.35 cents in UK stock assets. Asymmetric
series also offers similar results for optimal portfolio weights
and hedge ratios. For the German stock market, the optimal
weight is 0.4025 which indicates that the German investors
should spend 40.25 cents on oil assets out of US$1. The
hedge ratio suggests that investor should take a short position
in the oil and a long position of 8.36 cents in German stocks.
In the case of the Canadian stock market, the optimal weight
and hedge ratio are 0.1183 and 0.2031, respectively. For
Italy, the optimal portfolio weight and hedge ratio are 0.3351
and 0.1821, respectively. The results of France are 0.4351
and 0.0462 for optimal weight and hedge ratio, respectively.
For the Japanese stock market, the optimal weight is 0.3306
and hedge ratio is 0.2642. Asymmetric series reports the
marginally different findings for optimal weights and hedge
ratios.
The overall findings of optimal weights and hedge ratios
establish the importance of oil assets to minimize the portfolio risk for G7 countries. Especially, the weighted average
for Japan, Italy, Germany, and France are 0.3306, 0.3351,
0.4025, and 0.4351, respectively, which suggests that oil
assets are more important for the investors in Japan, Italy,
Germany, and France. The closer look at hedge ratios for G7
countries also endorse that oil assets are significant to hedge
portfolio risk. In a nutshell, average weights and hedge ratios
report that investors and portfolio managers should choose
oil assets as well as stock assets to minimize the risk without
changing the expected returns.
Conclusion
This study attempts to investigate the symmetric and asymmetric volatility spillover among stock and oil assets and
portfolio optimization for G7 countries. For symmetric analysis, we use DCC and cDCC approaches, whereas GJR,
FIGARCH, and FIEGARCH are utilized for asymmetric
estimations. Later, the conditional variance series and conditional covariance series are used for average weights and
hedge ratios. Kroner and Ng (1998) and Kroner and Sultan
(1993) methodologies are used for optimal weights and
hedge ratios, respectively. This empirical study attempts to
examine the role of oil assets for portfolio optimization.
The symmetric and asymmetric estimations provide evidence of interdependence among the oil market and G7 stock
markets. However, current conditional volatility of all the
stock markets responded to the past news and lagged conditional volatility in its respective stock markets. United States,
Germany, Canada, Italy, and France report the insignificant
impact of lagged volatility on current conditional volatility
in oil markets. The findings further confirm that conditional
volatility for oil market in case of the United States, United
Kingdom, and Japan is not affected by the lagged conditional
volatility in oil markets. The important point to note is that
G7 stock markets are more sensitive to their lagged news and
volatility.
More detailed asymmetric estimations, FIGARCH and
FIEGARCH, show that oil markets and G7 stock markets
present an intermediate range of persistence of volatility.
While focusing on our key objective of the study, the
weighted average and hedge ratios provide the evidence that
oil assets play significant importance to hedge the portfolio
risk without minimizing the expected returns. Consequently,
investors and portfolio managers in G7 countries should
take oil assets to optimize portfolio risk. For further research,
the study can be divided according to the precrisis, during
crisis and postcrisis period to better understand the role of
oil as assets. Future research can investigate the volatility
spillover among stock, oil assets, gold asset, and portfolio
optimization.
Declaration of Conflicting Interests
The author(s) declared no potential conflicts of interest with respect
to the research, authorship, and/or publication of this article.
Funding
The author(s) received no financial support for the research, authorship, and/or publication of this article.
ORCID iDs
Shahid Ali
Mazhar Abbas
https://orcid.org/0000-0001-9242-2136
https://orcid.org/0000-0003-2629-0424
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Author Biographies
Shahid Ali is a PhD student in the School of Management, Xi’an
Jiaotong University, China. His area of research interest is Portfolio
Management, corporate finance, corporate governance, corporate
social responsibility, executives compensation, and audit fees.
Currently, his PhD research work revolves around Portfolio
Management, Corporate Social Responsibility, and Subnational
institutions.
Junrui Zhang is a professor of accounting and finance in School of
Management, Xi’an Jiaotong University, China. His area of
research interest is the cost of capital, employees’ quality, corporate
governance, corporate social responsibility, executive compensation, and audit quality. His research work has been published
(accepted) in international journals of good repute e.g. Applied
Economics, Economics Letters, Management Decision, Business
Ethics: A European Review, etc.
Mazhar Abbas Holds Ph.D. from UUM working as an Assistant
Professor at Department of Management Sciences COMSATS
University ISLAMABAD, Vehari Campus Punjab Pakistan. His
area of research interest is Entrepreneurship, corporate governance,
corporate social responsibility, environmental performance.
Muhammad Umar Draz is a Senior Lecturer in the Department of
Management and Humanities, Universiti Teknologi PETRONAS,
Malaysia. Previously, he served as an Assistant Professor in the
Faculty of Business and Information Science, UCSI University,
Kuala Lumpur, Malaysia. Dr. Draz received gold medals at the university level in his bachelor and master degree examinations; subsequently, the China Scholarship Council awarded him a full scholarship for pursuing Ph.D. His research interests include accounting
reforms, financial accounting, financial crises, foreign investment,
and macroeconomics.
Fayyaz Ahmad is a Lecturer in the School of Economics, Lanzhou
University, Gansu China. His research interests include Development
Economics, foreign investment, and macroeconomics.