Proceedings of 7th Annual American Business Research Conference
23 - 24 July 2015, Sheraton LaGuardia East Hotel, New York, USA, ISBN: 978-1-922069-79-5
Elucidating the Relationship among Volatility Index,
US Dollar Index and Oil Price
John Wei-Shan Hu* and Hsin-Yi Chang**
Financial tsunamis have caused enormous disruption globally during the past decade.
Particularly, the subprime mortgage loan crisis during 2007 to 2009 and the European
debt crisis that began from 2010 to 2011, both significantly increased the volatility
index (VIX). This study examines the cross causality and long-term equilibrium
relationships among the VIX, US Dollar Index (USDX) and oil price from 2004 to 2011.
This investigation also divides the full sample period into three sub-periods: 2004 to
2006, 2007 to 2009, and 2010 to 2011. Empirical results indicate that long-term
equilibrium relationship among VIX, USDX and oil price exists for both the full sample
period and the first sub-period. Hence, the VECM model was employed for the three
parameters for full sample period and the first sub-period; while VAR model, impulse
response function and forecast error variance decomposition are required for VIX,
USDX and oil price the three parameters for the second and third sub-periods. This
study finds that, VIX is significantly and negatively related with USDX and oil price
throughout the full sample period. Meanwhile, only VIX and oil price are significantly
and negatively related during the first sub-period, while oil price and USDX have a
significantly and mutually causal relationship. This investigation finds that VIX affects
USDX and oil price during the second sub-period. However, VIX only affects USDX
during the third sub-period, suggesting it can serve as a reference instrument for
investors engaged in arbitraging or hedging. This study also finds that each variable is
most strongly affected by itself, and the forecast error variance decomposition of oil
price arises from all three variables. Empirical results suggest spill-over effects from
VIX and oil price, while co-movement occurs in response to large change in USDX.
Empirical findings also show that all three parameters converge rapidly soon after
major changes occur in each of them, indicating market efficiency. This study
concludes that VIX, USDX and oil price are sensitive to increasing market uncertainty.
JEL Codes: G11, G14
__________________________________________________
*Dr. John Wei-Shan Hu, Dep’t of Business Administration and Finance, Chung Yuan Christian University, 200 Zhong Bei
Rd., Zhongli District, Tao Yuen City, Taiwan 32023, E-mail: weishanhu@yahoo.com.
**Ms. Hsin–Yi Chang, MBA graduate and Statistics Assistant, Dep’t of Business Administration, Chung Yuan Christian
University, 200 Zhong Bei Rd., Zhongli District, Tao Yuen City, Taiwan 32023., Email:hingis032002@hotmail.com
Proceedings of 7th Annual American Business Research Conference
23 - 24 July 2015, Sheraton LaGuardia East Hotel, New York, USA, ISBN: 978-1-922069-79-5
1. Introduction
For the past decade, financial tsunamis occurred in succession (namely, the
subprime mortgage loan crisis, bankruptcy of Lehman Brothers, and the
European debt crisis), causing great unease globally. Consequently, investors
are anxiously seeking hedging or arbitraging instrument.
The volatility index (VIX) measures implied volatility for the U.S. market and was
provided by the Chicago Board of Options Exchange (CBOE) in 1993. VIX is a
key measure of market expectations of near-term volatility conveyed by the
S&P500 index option prices. Generally, VIX exceeding 40 suggests investors
unease regarding future stock index trends; meanwhile, VIX smaller than 15
implies stable stock index trends.
Additionally, international oil prices are important influence on global markets.
Since crude oil is a traded commodity, foreign exchange (FX) rate is an essential
reference for crude oil trading nations. Zhang et al.(2008) argued that, in the
long-term, the US exchange rate is a key influence on the price of crude oil.
Since most previous studies examined the relationship between oil price (OIL)
and FX rates or the correlation between VIX and stock index returns, this study
follows a different direction and attempts to examine the long-term equilibrium
relationship among the VIX, OIL and the US dollar index (USDX) to provide a
reference for the hedging or arbitrating strategy of investors, and to examine the
causal relationship among VIX, USDX and OIL.
2. Literature Review
This study classifies previous literature into two categories: (1) Articles on the
relationship between VIX and various stock indexes or commodities; (2) Studies
on the relationship between OIL and FX rate.
The following articles dealt with the correlation between VIX and various stock
indexes or commodities: Copeland and Copeland (1999), Whaley (2000), Giot
(2005), Qadan and Cohen (2011), Sari et al. (2011) and Williams (2011) all found
that the VIX is significantly and negatively related to stock indexes or various
commodities.
Furthermore, the following studies dealed with the relationship between OIL and
FX rates: Sadorsky (2000), Yousefi and Wirjanto (2003), Wirjanto and Yousefi
(2005), Zhang et al. (2008), Lizardo and Mollick (2010), Wang et al. (2010) and
Beckmann and Czudaj (2012) all found a significant relationship between OIL
and FX rates.
Proceedings of 7th Annual American Business Research Conference
23 - 24 July 2015, Sheraton LaGuardia East Hotel, New York, USA, ISBN: 978-1-922069-79-5
3. The Methodology and Model
This study examines the cross causality and long-term equilibrium relationship among
VIX, USDX, and OIL. This investigation uses the prices of West Texas Intermediate
(WTI) Crude Oil to represent OIL because WTI is used as a benchmark in oil pricing.
USDX measures the value of the United States dollar relative to a basket of foreign
currencies. USDX was launched in March, 1973, soon after the dismantling of the
Bretton Woods system.
The sample period runs from January 1, 2004 to December 31, 2011. There are 2,087
daily data available after deleting days on which data for any of the three variables was
missing. Figure 1(a) shows that the VIX increased markedly from the end of 2008
because of the shock of the financial tsunami, and the VIX peaked at 80.86 on
November 20, 2008. The OIL also increased rapidly from 2004 to 2008, and peaked at
US$142.81 per barrel in early 2008. However, the USDX declined from a peak of 92.44
in 2005 to a low of 71.012 in 2008, and then fluctuated significantly.
Figure 1. The trend of VIX, USD and Oil Price from Jan.1, 2001 to Dec.31, 2011
(b) USDX
(a) VIX
90
80
70
First subperiod
Second
sub-period
Third subperiod
95
140
90
120
60
50
(c) OIL
160
85
100
80
80
40
30
20
10
0
60
75
70
40
20
This study further divides the full sample period into three sub-periods to examine the
reaction of a major shock resulting from the VIX. The first sub-period is defined as the
VIX stable period, and runs from January 1, 2004 to December 31, 2006, and it contains
782 daily data. The second sub-period is labeled the VIX rising period, and runs from
January 1, 2007 to December 31, 2009, coinciding with the U.S. subprime mortgage
loan crisis causing the bankruptcies of Lehman Brothers and multiple investment banks
and insurance companies. The second sub-period includes 784 daily data. The third
sub-period runs from January 1, 2010 to December 31, 2011, when the VIX rapidly
increased again because of the European debt crisis. The third sub-period contains 521
daily data. The data sources were CBOE and the Thomas Datastream.
Before implementing the co-integration test, this study examines the stationarity of the
time series variables and the integrated order of variance using the Augmented
Dickey-Fuller (ADF) test. The ADF test model is as follows:
∆Yt = α + β𝑡 + γY𝑡−1 + δ1 ∆Y𝑡−1 + ⋯ + δ𝑝−1 ∆Y𝑡−𝑝+1 + 𝜀𝑡 ,
(1)
Proceedings of 7th Annual American Business Research Conference
23 - 24 July 2015, Sheraton LaGuardia East Hotel, New York, USA, ISBN: 978-1-922069-79-5
where ∆Yt denotes the first-order difference of the Y logarithmic series; 𝛼 is a constant,
β is the coefficient for a time trend t, and p is the lag order of the autoregressive process
that makes the residual white-noises. By including lags of the order p, the ADF
formulation permits a high-order autoregressive process. Notably, εt represents
white-noise in the null hypothesis H0：γ = 0. Failure to reject the null hypothesis implies
a unit root in the event of a regime shift such as an oil shock.
This study then employs the maximum likelihood estimation (MLE) proposed by
Johansen (1988) to examine whether co-integration (long-term equilibrium relationship)
exists among variables, and to determine the number of co-integration vector groups:
𝑡
= ∑𝑞
+ 𝜀𝑡 ,
𝑡−
1
(2)
Equation (2) is then rewritten using the first-order difference function as
∆
𝑡
= ∑𝑞
where
1
∆
𝑡−
+
∑𝑞
=
𝑡−𝑞
1
;
+
𝑡
,
=
(3)
∑
1
, and I is an identity matrix.
Equation (3) denotes a VAR model with first-order difference plus an error correction
item
represents the short-term dynamic information, and the matrix
𝑡−𝑞 , where
reflects the long-term relevant information.
According to Persaran and Shin (1988), the co-integration relationship must be included
in the VAR model (i.e., the vector error correction model, VECM) to estimate the
dynamic price relationship among variables. Based on the co-integration Eqn. (3), a
VECM examines the short-term adjustment as follows:
∆𝑋𝑡 = ∑
𝑞−1
1
∆𝑋𝑡− + 𝑋𝑡−𝑞 + 𝜀𝑡 ,
where 𝑋𝑡−𝑞 is an error correction term;
(4)
= αβ, which is the coefficient matrix of the
adjustment speed of error correction. If α differs significantly from zero, then the
variable which deviates from equilibrium in the short-term will immediately move
toward long-term equilibrium. Furthermore, if α > 0, the parameter was under-estimated
in the short-term and will be upward corrected in t+1; otherwise, it will be downward
corrected in t+1.
Although there are two main methods (i.e., the trace and maximum eigenvalue tests) to
examine variable co-integration, this study uses the maximum eigenvalue test because
Lûtkepohl et. al (2001) found the powers of the corresponding trace and maximum
eigenvalue tests to be very similar. The null hypothesis of the maximum eigenvalue test
is as follows:
H0: There are r groups of co-integration vectors;
H1: There are r +1 groups of co-integration vectors.
The maximum eigenvalue test statistic is
𝜆𝑚𝑎𝑥 𝑟, 𝑟 + 1 =
𝑇 𝑙𝑛(1
𝜆̂𝑟+1 ),
(5)
Proceedings of 7th Annual American Business Research Conference
23 - 24 July 2015, Sheraton LaGuardia East Hotel, New York, USA, ISBN: 978-1-922069-79-5
where λ𝑚𝑎𝑥 represents the statistic value of the Johansen maximum eigenvalue.
This study then employs the Vector Autoregressive (VAR) model to capture the linear
interdependence among multiple time series. This investigations uses two time series
=
variables,
,
, to illustrate the simplified VAR model, as follows:
𝑡
= 𝑎 𝑜 + ∑𝑝 1 𝛼
= 𝑏𝑜 + ∑
𝑝
1𝛾
𝑡−
+ ∑𝑝 1 𝛽
+∑
𝑝
1𝛿
𝑡−
+ 𝜀𝑥𝑡 ,
(6)
+ 𝜀𝑦𝑡 ,
(7)
where 𝑎𝑜 and 𝑏𝑜 are intercepts, 𝛼 & 𝛽 are the coefficients of the lags of 𝑡 and 𝑡
of Eqn. (6); 𝛾 & 𝛿 are the coefficients of the lags of 𝑡 and 𝑡 of Eqn. (7); and 𝜀𝑥𝑡
and 𝜀𝑦𝑡 are error terms.
𝑡
𝑡−
𝑡−
Generally, optimal lag period selection of the VAR model is important; this study
uses the Schwartz Bayesian Information Criterion (SBC) rule which has the lowest SBC
value:
SBC = T × ln 𝜎𝜀2 + 𝑃 × ln T ,
(8)
where P is the number of parameters to be estimated; T is the number of observation;
𝜎𝜀2 is the error variance.
The Granger causality test is then used to determine whether a time series Y is caused by
X, in which the forecasts are linear and based on the information in series 𝑡 and 𝑡 .
If no long-term equilibrium (co-integration) relationship exists between either VIX
and OIL or USDX, a study on short-term interactions is necessary. This study applies the
Granger causality test based on the VAR model in equations (6) and (7).
The impulse response function (IRF) describes the reaction of the dynamic system
in response to external change involving an endogenous variable as a function of time.
After obtaining the VAR(1) model, the IRF is
𝑋𝑡 = 𝜛𝑜 + 𝜛1 𝑋𝑡−1 + 𝜀𝑡 .
(9)
Equation (9) can be transformed to obtain the following moving average form:
𝑋𝑡 = 𝜇 + 𝜀𝑡 + Ψ1 𝜀𝑡−1 + Ψ1 𝜀𝑡−2 + Ψ1 𝜀𝑡−3 + ⋯ + 𝜀𝑡 .
(10)
This investigation then partially differentiates Eqn. (11) using the 1 lag error term to
derive
𝜕𝑋𝑡
𝜕𝜀𝑡−1
= Ψ1 ,
(11)
Specifically, matrix Ψ1 includes four impulse responses:
1
Ψ1 = [
1
Ψ11
Ψ12
Ψ21
Ψ22
1
1
where Ψ11
1
on 𝑋𝑡 ; Ψ21
1
]=[
𝜕𝑋𝑡
𝜕𝑋𝑡
𝜕𝜀𝑥𝑡−1
𝜕𝜀𝑦𝑡−1
𝜕𝑌𝑡
𝜕𝑌𝑡
𝜕𝜀𝑥𝑡−1
𝜕𝜀𝑦𝑡−1
],
(12)
is the extent of the impact of external shock of one lag term of 𝑋𝑡 (𝜕𝜀𝑥𝑡−1
1
is that of external shock of one lag term of 𝑋𝑡 on 𝑌𝑡 ; Ψ12 is that of
Proceedings of 7th Annual American Business Research Conference
23 - 24 July 2015, Sheraton LaGuardia East Hotel, New York, USA, ISBN: 978-1-922069-79-5
1
external shock of one lag term of 𝑌𝑡 on 𝑋𝑡 ; and Ψ22 is that of external shock of one
lag term of 𝑌𝑡 (𝜕𝑞𝑦𝑡−1 on 𝑌𝑡 .
Equation (12) shows that other variables can be included in IRF to obtain
cross-impacts. Furthermore, the influence of the speed adjustment can be assessed when
one standard error shock of a parameter on the reaction of itself and other variables at
t+1. Restated, the sign of Ψ1 can indicate the reaction direction.
According to Sari et al., (2011), the generalized forecast - error variance
decomposition (FEVD) demonstrates the extent to which the variance of a particular
variable can be explained by a shock to itself and another variable.
First, this study derives the expectation value of 𝑋𝑡 as follows:
Ε 𝑋𝑡 = Φ0 1 + Φ1 + Φ12 + ⋯ + Φ1𝑛−1 + Φ1𝑛 𝑋𝑡 .
(13)
The forecast error of the n-th term is
Ε 𝑋𝑡+𝑛 = 𝜀𝑡 + Φ1 𝜀𝑡−1 + ⋯ + Φ1𝑛 𝜀𝑡−𝑛−1 ,
𝑋𝑡+𝑛
(14)
where Ε 𝑋𝑡+𝑛 represents the possible forecast error of the n-th term when forecasting
the t+n-th term. The variance matrix of the n-th term forecast error can be observed as
Ω𝑓 = 𝑣𝑎𝑟 𝜀𝑡 1 + Φ12 + ⋯ + Φ12𝑛 ,
(15)
where Ω𝑓 = Ω𝑥 Ω𝑦 ′.
The forecast error variance of all the terms before the n-th term can be expressed using
the linear function combination of 𝜎𝑦2 +𝜎𝑥2 as follows:
Ω𝑥 = Ω𝛽 𝜎𝑥2 + Ω𝛼 𝜎𝑦2 .
(16)
Equation (16) can be rewritten as
Ω𝛽 𝜎𝑥2
Ω𝑥
+
Ω𝛼 𝜎𝑦2
Ω𝑥
= 100%.
(17)
Equation (17) demonstrates that the variance of each variable can be expressed as the
sum of all the variances, and that can be used to assess the degree to which explanatory
power of a specific variable contributes to itself and to other variables.
4. The Findings
This investigation applies the ADF test for the full sample period and three sub-periods.
Table1 indicate that most original data are non-stationary. After applying the first-order
difference all the data become stationary.
Proceedings of 7th Annual American Business Research Conference
23 - 24 July 2015, Sheraton LaGuardia East Hotel, New York, USA, ISBN: 978-1-922069-79-5
Table 1: ADF test result: The full sample period and three sub-periods
1st sub-period
Full Sample Period
p-value
Variables Original
2nd sub-period
3rd sub-period
p-value
p-value
p-value
p-value
p-value
p-value
p-value
First-order
Difference
Original
First-order
Difference
Original
First-order
Difference
Original
First-order
Difference
LVIX
0.00**
0.00**
0.00**
0.00**
0.24
0.00**
0.06*
0.00**
LUSD
0.24
0.00**
0.24
0.00**
0.45
0.00**
0.54
0.00**
LOIL
0.22
0.00**
0.22
0.00**
0.57
0.00**
0.20
0.00**
Note: *denotes 10%; **represents 5% significance levels
After employing the maximum eigenvalue test of Johansen (1988) to examine the
existence of the long-term equilibrium relationship for all variables, this study finds
that, during the full sample period and the first sub-period, the VIX, USDX and OIL
have at least one co-integration relationship (Table 2). A VECM test is then performed
and Table 3 summarizes the empirical result.
However, Table 2 also shows that, during the second and third sub-periods, the VIX,
USDX and OIL have no co-integration relationship for the second and third
sub-periods. This study thus uses the VAR to analyze all three variables and examine
the impulse response and variance decomposition for the second and third
sub-periods.
Table 2. Co-integration test: The full sample period and three sub-periods
st
Full Sample Period
Eigen
Max
-value
stat.
None
0.01
21.99
At most 1
0.01
At most 2
0.00
E.V.
**
1 sub-period
nd
rd
2 sub-period
3 sub-period
Eigen
Max E.V.
Eigen
Max E.V.
Eigen
Max
-value
stat.
-value
stat.
-value
stat.
**
0.04
34.39
0.02
18.91
0.04
19.00
11.68
0.02
11.49
0.02
13.86
0.02
9.05
3.67
0.01
4.30
0.00
2.52
0.01
4.14
E.V.
Note: **denotes 5% significance level
Regarding the adjustment speed of error correction, Table 3 shows that the error
correction significantly and negatively affects VIX and OIL during the full sample period.
However, the adjustment speed coefficients of the VIX and OIL are minimal, suggesting
that it takes extended adjustment for error correction to bring the VIX and OIL to
equilibrium. Meanwhile, Table 3 demonstrates that the error correction significantly and
negatively affects VIX during the first sub-period. However, the absolute value of
adjustment speed of the VIX is greater than that of the full sample period, implying that it
will take less time during the first sub-period than the full sample period to return to
equilibrium.
Proceedings of 7th Annual American Business Research Conference
23 - 24 July 2015, Sheraton LaGuardia East Hotel, New York, USA, ISBN: 978-1-922069-79-5
Table 3: The Adjustment Speed for Error Correction
(b) The 1st sub-period
(a) Full Sample Period
VIX
USDX
OIL
VIX
USDX
OIL
Adjustment speed
-0.008
-0.000
-0.002
-0.019
0.000
-0.003
t value
-3.331***
-1.547
-2.079***
-4.839*** 1.118
-1.831
Table 4 shows that OIL affects the USDX, while VIX affects OIL for the full sample
period and the second sub-period. Furthermore, USDX affects OIL for the first and
second sub-periods. This study also finds that VIX affects USDX for all three
sub-periods, but does not influence USDX for the full sample period. The empirical
findings demonstrate that neither USDX nor OIL influence VIX except for the third
sub-period.
Table 4. Causality among VIX、USDX and OIL: Full Sample Period and three
sub-periods
Full Sample Period 1st sub-period
USDX does not cause OIL
OIL does not cause USDX
F
pStatistics value
F
pStatistics value
0.01
3.26
0.04**
3.04
**
5.15
0.91
**
0.02
**
0.05
2nd sub-period
3rd sub-period
F
pStatistics value
F
pStatistics value
3.82
0.02**
0.15
0.70
2.74
**
0.00
0.99
**
0.07
VIX does not cause OIL
5.24
0.02
1.86
0.16
3.80
0.02
0.09
0.76
OIL does not cause VIX
1.01
0.31
1.52
0.22
1.81
0.16
3.24
0.07*
VIX does not cause USDX
0.63
0.43
2.31
0.10*
3.50
0.03**
15.61
0.00**
USDX does not cause VIX
0.51
0.48
0.76
0.47
0.31
0.73
3.20
0.07*
Notes: * denotes 10%; **shows 5%; ***represents 1% significance levels.
Since VIX, USDX and OIL do not have co-integration relationship for the second and
third sub-periods, the impulse response function and forecast error variance
decomposition tests are then examined for the second and third sub-periods.
Figures 2(a) and 3(a) show that 100% influence on VIX resulting from VIX itself in the
first term, then changes from being positive to negative from the second term, and
thereafter gradually converges. This investigation also finds some influences on VIX
arising from OIL and USDX from the second term.
Figures 2 (b) and 3(b) denote that a shock of USDX affecting the reaction of USDX
itself is the most significant among all three variables in the first term. However, a shock
of USDX arising from VIX is also significant in the first term.
Figures 2(c) and 3(c) indicate that a shock of OIL on the effect of itself is the most
significant among all three variables in the first term, then decreases in the second term.
However, the shocks to OIL arising from USDX and VIX are also significant during the
first term. Additionally, Figures 2 and 3 show that all three parameters rapidly
converge shortly after their dramatic change for the second and third sub-periods.
One S.D. Innovations
80
800
800
60
600
Proceedings of 7th Annual American Business Research Conference
23 - 24 July 2015, Sheraton LaGuardia East Hotel, New York, USA,400ISBN: 978-1-922069-79-5
400
60040
200
20
0
200 0
-20
Figure 2. Impulse Response of
Parameters to Cholesky
1 std. dev.
-200 Three
0
1
2
innovations - The second sub-period
3
4
5
DLVIX
6
7
8
DLUSDX
9
1
10
DLOIL
-200
2
Response
of DLUSDX to Cholesky
(b) DLUSDX
One S.D. Innovations
800
80
600
60
4
5
3
6
7
8
DLUSDX
4
5
6
7
9
10
DLOIL
8
9
10
Response
of DLOIL to Cholesky
(c) DLOIL
DLVIX
DLUSDX
One S.D.
Innovations DLOIL
300
Response of DLUSDX to Cholesky
One S.D. Innovations
200
Response of DLVIX to Cholesky
One S.D. Innovations
40
400
3
DLVIX
1
(a) DLVIX
Response
of DLVIX to Cholesky
One S.D. Innovations
2
50
100
800
40 0
20
200
600
30
-100
0
0
400
20
-20
-200
1
2
3
4
5
6
7
8
9
-200
1
10
2
3
4
5
6
7
8
9
10
DLUSDX
DLVIX
DLOIL
DLUSDX
3
4
5
DLVIX
6
7
8
DLUSDX
Response of DLOIL to Cholesky
One S.D. Innovations
300 1
Response of DLVIX to Cholesky
One(a)
S.D.
Innovations
DLVIX
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
10
DLOIL
Response of DLOIL to Cholesky
One
Innovations
(c)S.D.
DLOIL
200
50
0
9
10
Response of DLUSDX to Cholesky
One
Innovations
(b)S.D.
DLUSDX
0
800
10
-10
Figure 3. Impulse Response of Three parameters to Cholesky 1 std. dev.
DLVIXinnovation.
DLUSDX
200
60
DLVIX
DLUSDX
DLOIL
- The
third sub-period
40
100
20
9
DLOIL
0
-200
80
2
DLOIL
0
Response of DLUSDX to Cholesky
One S.D. Innovations
1
10
200
DLVIX
-100
150
40
600
-20
-200
1
2
3
4
5
6
7
8
9
10
400
DLVIX
DLUSDX
DLOIL
30
1
2
3
4
5
DLVIX
20
6
7
8
DLUSDX
9
10
DLOIL
100
50
200
Response of DLOIL to Cholesky
One S.D. Innovations
0
300
-200
200
100
10
0
0
-50
-100
-10
1
2
3
DLVIX
4
5
6
7
8
DLUSDX
9
DLOIL
10
1
2
3
DLVIX
4
5
6
7
DLUSDX
8
9
DLOIL
10
1
2
3
DLVIX
4
5
6
7
DLUSDX
0
to Cholesky decomposition (FEVD) analyzes the influence of each
The Response
forecastof DLUSDX
error variance
Response of DLOIL to Cholesky
One S.D. Innovations
One S.D. Innovations
50
structure
shock on the endogenous
variables, including the parameter itself and
-200
200
1
2
3
4
5
6
7
8
9
10
40
other
variables.
Table
5
lists
the
150 explanatory power on the shocks to each variable
DLVIX
DLUSDX
DLOIL
30
100
for
the second and third sub-periods
as follows:
20
50
(1) Regarding the FEVD of VIX,
the only explanatory power on the shocks to VIX
10
in the first term arises from0VIX itself (100%). Although the explanatory power
0
-50
arising from VIX decreases slightly from the second term, it converges from the
-10
-100
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
7
8
9
10
third term.
DLVIX
DLUSDX
DLOIL
DLUSDX
DLOIL
(2) Regarding the FEVD of USDX, DLVIX
the most
significantly
explanatory power on
the
shocks
to toUSDX
Response
of DLOIL
Cholesky at the first term arises from USDX itself and decreases
-100
One S.D. Innovations
from the second term to the third term, then converges from the fourth term.
The second significant explanatory power at the first term arises from VIX and
150
100
increases from the second to the third term, and then converges from the fourth
50
term.
0
(3) Regarding the FEVD of OIL, for both the second and third sub-periods, the
-50
most significantly explanatory power on the shocks of OIL in the first term
-100
1
2
3
4
5
6
7
8
9
10
arises
from
the
OIL
itself,
which then decreases and converges from the fourth
DLVIX
DLUSDX
DLOIL
term.
However,
for the
second sub-period, the second most significant influence
200
8
9
DLOIL
10
Proceedings of 7th Annual American Business Research Conference
23 - 24 July 2015, Sheraton LaGuardia East Hotel, New York, USA, ISBN: 978-1-922069-79-5
on OIL shocks is USDX, and converges from the third term; while for the third
sub-period, the second significantly explanatory power at the first term arises
from VIX and converges from the third term.
Table 5. Variance decomposition：The second and third sub-periods
2nd Sub-period
3rd Sub-period
Parameter Terms DLVIX DLUSDX DLOIL Terms DLVIX DLUSDX DLOIL Terms DLVIX DLUSDX DLOIL Terms DLVIX DLUSDX DLOIL
1
100.00 0.000
0.000
4
99.28
0.082
0.639
1
100.00 0.000
0.000
4
98.72
0.815
0.463
2
99.64
0.012
0.350
5
99.28
0.082
0.639
2
99.10
0.500
0.403
5
98.72
0.816
0.463
3
99.33
0.082
0.593
6
99.28
0.082
0.640
3
98.72
0.815
0.461
6
98.72
0.816
0.463
1
1.760
98.24
0.000
4
2.614
96.99
0.397
1
22.552 77.45
0.000
4
24.010 75.55
0.436
DLUSDX 2
2.604
97.01
0.390
5
2.615
96.99
0.397
2
23.789 75.87
0.337
5
24.009 75.55
0.438
3
2.608
97.00
0.395
6
2.615
96.99
0.397
3
24.014 75.56
0.429
6
24.009 75.55
0.438
1
5.293
10.22
84.49
4
5.372
10.50
84.13
1
18.11
5.803
76.09
4
18.10
6.022
75.88
2
5.301
10.49
84.21
5
5.373
10.50
84.13
2
18.17
5.828
76.01
5
18.10
6.022
75.88
3
5.372
10.50
84.13
6
5.373
10.50
84.13
3
18.09
6.017
75.90
6
18.10
6.022
75.88
DLVIX
DLOIL
5. Summary and Conclusions
The conclusions are summarized as follows:
1. The co-integration test indicates that VIX, USDX and oil price have long-term
equilibrium relationships for both the full sample period and the first sub-period.
2. The Granger causality test shows that, during the full sample period, oil price affects
USDX and VIX affects oil price. However, VIX and USDX have no causal
relationship. During the first sub-period, USDX and oil price exhibit mutual causality.
During the second sub-period, USDX affects oil price; while VIX affects USDX and
oil price.
3. The impulse response function and the FEVD demonstrate that each variable is most
significantly affected by itself. All variables rapidly converge after being shocked,
suggesting an efficient market. Additionally, this study finds that, for both the second
and third sub-periods, VIX has high independence. The FEVD of USDX arises from
itself and VIX. However, that of oil price arises from all three variables.
4. The error correction result shows that VIX, USDX and oil price are significantly and
negatively related throughout the full sample period, suggesting that the oil price rises
as the US dollar devalues; demand for oil increases, with decreasing VIX, decreasing
oil price. However, VIX and oil price are significantly and negatively related during
the first sub-period, implying that the prospect for the global economy are promising,
increasing demand for oil, and thus increasing oil price. This study also finds that, it
takes a longer time to achieve equilibrium in error correction for the full sample
period than that for the first sub-period.
This investigation concludes that VIX, USDX and oil price are sensitive to increasing
Proceedings of 7th Annual American Business Research Conference
23 - 24 July 2015, Sheraton LaGuardia East Hotel, New York, USA, ISBN: 978-1-922069-79-5
market uncertainty. Investors may observe the change in VIX to determine whether they
should invest or hedge USDX or oil price.
End Notes
The authors would like to thank Ted Knoy for his excellent editorial assistance, and the
precious remarks on the first draft provided by Chungfang Ho Chang and Catherina Y. F.
Ku at the 88th WEA Conference at Seattle, Washington.
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