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Oil sensitivity and its asymmetric impact on the stock market
Energy 36 (2011) 168e174
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Energy journal homepage: www.elsevier.com/locate/energy
Oil sensitivity and its asymmetric impact on the stock market Yen-Hsien Lee a,1, Jer-Shiou Chiou b, * a b
Department of Finance, Chung Yuan Christian University, 200 Chung Pei Rd., Chung Li 32023, Taiwan, ROC Department of Finance and Banking, Shih-Chien University, 70 Ta-Chih Street, Taipei 104, Taiwan, ROC
a r t i c l e i n f o
a b s t r a c t
Article history: Received 30 December 2009 Received in revised form 19 October 2010 Accepted 30 October 2010 Available online 3 December 2010
We develop a two-step methodology to facilitate an examination of the impact of oil shocks on stock returns. Oil price volatility is monitored in this study through the use of a regime-switching model, with the presence of jumps subsequently being taken into consideration to examine the asymmetric effects of oil prices on stock returns. Our analysis provides quite conclusive results based upon the use of a regimeswitching model with consideration of jumps; that is, when there are significant fluctuations in oil prices (West Texas Intermediate; WTI), the resultant unexpected asymmetric price changes lead to negative impacts on S&P 500 returns. However, the same result does not hold in a regime of lower oil price fluctuations. We therefore suggest that the achievement of a well diversified portfolio should involve the consideration of oil price shocks, which, as a consequence, should also help to improve the accuracy of hedging against oil price risks. 2010 Elsevier Ltd. All rights reserved.
JEL classification: C5 G1 Keywords: Asymmetric effects ARJI model Regime-switching
1. Introduction It is already widely recognized that there will be various changes over time in the conditional volatility levels of stock market indices; however, the causes of such changes have intrigued researchers for some considerable time. As a result, a substantial body of literature has emerged on the relationships between oil prices, the stock market and various financial and macroeconomic variables.2 Indeed, various data and statistical approaches have been adopted within the prior studies as a means of verifying the existence and nature of the negative relationship between oil price shocks and the US economy.3 Since asset prices are regarded as the present discounted value of future net earnings (Nandha and Faff [20]), we would reasonably expect to find a significant relationship between oil price shocks and stock market returns. As a result, if oil prices directly affect real output, then oil price increases will depress aggregate stock prices; this clearly suggests that oil prices must be associated with stock
* Corresponding author. Tel.: þ886 2 2538 1111x8927; fax: þ886 2 2538 1111x8714. E-mail addresses: [email protected] (Y.-H. Lee), [email protected] (J.-S. Chiou). 1 Tel.: þ886 3 265 5711. 2 Recent examples include Lee and Chang [15] and Sadorsky [25]. 3 See for example Hamilton [8,9], Loungani [17], Mork [19], and Lee et al. [16]. 0360-5442/$ e see front matter 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2010.10.057
returns (Kaul and Jones [12]; Sadorsky [24]). However, investigations into the linkages between oil prices and the equity markets are relatively few; thus, our analysis in the present study of the time variations in stock returns focuses on oil price volatility spillovers, as opposed to the consideration of general macroeconomic variables. A regime-switching phenomenon is found within most of the existing time-series models when they are applied to real data; thus, any estimations or inferences obtained without consideration of this phenomenon may well lead to unreliable results. Thus, various regime-switching models have emerged as a means of identifying such changing states within economic data generating mechanisms. In the present study, we assume that stock returns are affected by oil price shocks, and also that the state of such shocks will, in turn, have direct impacts on oil price volatility. Oil price volatility is therefore examined here based upon a regime-switching model, with the spillover and asymmetric effects of oil prices on stock returns subsequently being explored with the additional consideration of jumps. Our analysis provides quite a conclusive result, which is that when there are severe fluctuations in oil prices, unexpected asymmetric changes in oil prices (West Texas Intermediate; WTI) will have a negative impact on the S&P 500. The purposes of this research are to examine the relationship between the oil price and stock returns. In contrast to the extant literature, the model of stock returns adopted in the present study
Y.-H. Lee, J.-S. Chiou / Energy 36 (2011) 168e174
incorporates the consideration of expected, unexpected and negatively unexpected oil price fluctuations, whilst also focusing on oil price volatility, as opposed to general macroeconomic variables. Additionally, Maheu and McCurdy [18] proposed that the process of financial innovation has two components e normal innovations, and abnormal or jump innovations. A potential source of jump innovations is important news events. The investor makes incorrect financial and economic decisions when they fail to grasp abnormal information. In considering the impact of the jump characteristics of abnormal information, this study uses GARCH with the autoregressive conditional jump intensity (ARJI) model, which was developed by Chan and Maheu [3]. High and low of oil price fluctuations are incorporated using the regime-switching model, and expected, unexpected and negatively unexpected oil price fluctuations are considered, to study how oil spot and oil futures price fluctuations affect S&P 500 returns. 2. Literature review A considerable body of research has emerged on the relationship between energy prices and stock prices. For example, Ferson and Harvey [7] found evidence to show that oil price risk factors have statistical and significant influences on the equity markets of eighteen countries, whilst Faff and Brailsford [6] reported that oil prices positively and significantly affect the oil and gas industry and the diversified resources industry, with further negative and significant influences on both the paper and packaging industry and the transportation industry. Papapetrou [21] suggested that changes in oil prices affect both employment and real economic activity. However, it is generally accepted that whilst oil prices are important in explaining stock price movements, stock returns do not cause changes in either employment or real economic activity. Indeed, the only study to have found a bi-directional relationship between oil prices and stock prices was the examination of the Saudi Arabian stock market undertaken by Hammoudeh and Eleisa [11]. Using daily and weekly data for the petroleum market, Pindyck [22] developed a structural model of inventories, spot and futures prices capable of explaining oil price volatility. Furthermore, Hammoudeh and Li [10] suggested that in the pricing of oil-sensitive returns, regardless of the direction of the global capital markets, investors should regard systematic risk as being of greater importance than oil sensitivity. Kaufmann and Laskowski [13] confirmed that asymmetric pricing can be generated by efficient markets, thereby suggesting that there is little justification for policy interventions as a means of reducing or eliminating such price asymmetry in the motor gasoline and home heating oil markets. Krey et al. [14] went on to investigate the impact of uncertain energy prices on supply structures as well as their interaction with various measures in the demand sectors. Whilst the majority of the prior studies tend to agree that energy prices influence stock prices, there are, nevertheless, very few examples of studies having been undertaken to investigate the long-run equilibrium between stock and oil markets. Indeed, in the majority of the studies involving the use of traditional time-series models, the tendency has been to assume that the underlying variables exhibit a linear and symmetrical adjustment processes; however, in reality, most macro variables exhibit asymmetrical adjustment. Some research has, nevertheless, been undertaken into the impact on stock prices arising from asymmetric changes in oil prices. For example, both Sadorsky [24] and Basher and Sadorsky [2] provide support for the argument that oil price changes have
169
Table 1 Descriptive statistics. Items
Oil spot
Oil futures
S&P 500
Mean Std. Dev. Max. Min. Skewness Kurtosis JarqueeBera LjungeBox Q2 LjungeBox Q2 LjungeBox Q2 LjungeBox Q2
0.0422 2.2650 17.0918 15.3827 0.3345*** 4.8210*** 3971.9404*** 274.402*** 304.095*** 328.601*** 434.909***
0.0423 2.1631 16.5445 14.2309 0.2599*** 3.4807*** 2076.6466*** 168.2110*** 196.1400*** 223.5850*** 270.2790***
0.0280 1.0139 7.1127 5.5744 0.1545*** 3.8688*** 2525.5466*** 708.8150*** 1141.9340*** 1432.0770*** 1732.7910***
(5) (10) (15) (20)
Note: *** indicates significance at the 1% level.
an asymmetric effect on stock prices. It has, however, been demonstrated in several studies that traditional co-integration tests are of very limited use in situations involving asymmetric adjustment.4 In contrast to the extant literature, the present study adopts a model of stock returns which takes into consideration expected, unexpected and negatively unexpected fluctuations in oil prices. We then apply an ‘ARJI’ model with regime-switching to examine the influence of oil prices on S&P 500 returns.
3. Methodology 3.1. Markov regime-switching model iid
Consider the time series yt ¼ mst þ 3t , where 3t w Nð0; s2 Þ, st ¼ 1, ., N indicates the market regime at time t. Note that the variable st ¼ i, which can be referred to as a regime indicator, is a random variable with its own distribution and cannot be observed. We begin with the case where N ¼ 2.5 In addition to aiding intuition, the two-regime case is a popular specification in applied work. Two states of the market are provided through a first-order Markov process with the following transition probabilities matrix:
P ¼
p11 p12
p21 p22
(1)
where P is the transition probabilities matrix and the transition probability P11 and P12 (P21 and P22) gives the probability that state 1 (2) will be followed by state 1 and 2 (2 and 1). The ht show the two density function:
2
3 ) ( 2 m 1 ðy Þ t 6 7 1 7 6 pffiffiffiffiffiffiffi exp 6 2ps1 7 2s21 f ðyt jst ¼ 1;Yt1 ; qÞ 6 )7 ( ht ¼ ¼6 2 7 f ðyt jst ¼ 2;Yt1 ; qÞ ðyt m2 Þ 7 6 1 4 pffiffiffiffiffiffiffi exp 5 2s22 2ps2
(2)
where q ¼ ðm1 ; m2 ; s21 ; s22 ;p11 ;p22 Þ0 , m1 and s21 (m2 and s22 ) are the conditional mean and variance on state 1 (2), and then P12 and P21 ^
are transition probability. Collect these forecast in a vector x t , which is a vector whose jth element represent Pðst ¼ jjY t1 ; qÞ for j ¼ 1, 2. ^
Thus, x tþ1jt is defined as:
4 See for example Pippenger and Goering [23], Balke and Fomby [1], Enders and Granger [4] and Enders and Siklos [5]. 5 Limiting the number of the regimes to two improves the model's tractability and, intuitively, a two-state process corresponds to periods of high- and lowvolatility in the markets.
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Y.-H. Lee, J.-S. Chiou / Energy 36 (2011) 168e174
Fig. 1. (a) S&P 500 prices and returns. (b) Oil spot prices and returns. (c) Oil futures prices and returns.
Y.-H. Lee, J.-S. Chiou / Energy 36 (2011) 168e174
171
Table 2 Unit root and stationarity tests for the stock price indices. Items
Model
ADF
PP
KPSS
Level
Differencea
Level
Differencea
Levela
Difference
S&P 500
C C/T
1.6332 0.5955
51.0573*** 51.0909***
1.6290 0.5618
70.5228*** 70.6429***
5.6095*** 1.0205***
0.3483 0.1118
Oil spot
C C/T
1.3546 1.8883
30.5616*** 30.5587***
1.3769 2.0430
69.3101*** 69.3024***
5.3515*** 1.2557***
0.0924 0.0985
Oil futures
C C/T
1.3205 1.8470
30.2615*** 30.2587***
1.3635 1.9945
69.4799*** 69.4720***
5.3577*** 1.2620***
0.0958 0.1020
a
*** indicates significance at the 1% level.
^
^
x tþ1jt ¼ P$x t ¼
p11
p21
p12
p22
Pðst ¼ 1jYt1 ; qÞ $ Pðst ¼ 2jYt1 ; qÞ
Et ¼ Roil;t
" *# p p21 Pðstþ1 ¼ 1jYt ; qÞ $ 1* ¼ p22 Pðstþ1 ¼ 2jYt ; qÞ p2 (3) P1 Pðstþ1 ¼ 1jYt ; qÞ ¼ ¼ P2 Pðstþ1 ¼ 2jYt ; qÞ
¼
p11 p12
qffiffiffiffiffiffiffiffiffiffi hoil;t 3oil;t
(7)
qffiffiffiffiffiffiffiffiffiffi From Eq. (7), Et and hoil;t 3oil;t are expected- and unexpected-oil price growth rate, respectively. Defining up t ¼ Minðupt ; Eðupt ÞÞ as the negatively unexpected (up t ) changes in spot or futures within the stock returns model, we then take the expected (Et), unexpected (upt) and negatively unexpected (up t ) changes in spot or futures into consideration within the stock returns model, as shown in Eq. (8).
We can obtain the log likelihood function:
( LðqÞ ¼ log
T Y
3.3. The ARJI model6
) f ðyt jY t1 ; qÞ
t ¼1
9 8 =
Following Chan and Maheu [3], we use the ARJI model which postulates that jump intensity follows an autoregressive moving average (ARMA) process and incorporates the generalized autoregressive conditional heteroskedasticity (GARCH) effect of the returns series.7 Given the set of returns at time t 1 and the two stochastic innovations, 31, t and 32, t, the ARJI model of returns (Rt) can then be written as:
t
(4) where 2 P x tjt1 Qht Þ ¼ f ðyt jst ;Yt1 ; qÞ$Pðst jYt1 ; qÞ and f ðyt jY t1 ; qÞ ¼ 10 ðb st ¼1
3
2
Rt ¼ m þ
m X
fi Rti þ 41 Et þ k1 upt þ k DLow 1 upt
i¼1
DHigh þ 31;t þ 32;t þ 42 Et þ k2 upt þ k 2 upt
(8)
) ( 1 ðyt m1 Þ2 7 6 pffiffiffiffiffiffi ffi exp 7 6 7 6 2ps1 2s21 q b )7 ( x tjt1 Qht ¼ Pðst ¼ 1jYt1 ; Þ Q6 2 7 Pðst ¼ 2jY t1 ; qÞ 6 ðyt m2 Þ 7 6 1 5 4 pffiffiffiffiffiffiffi exp 2s22 2ps2
where Et defines the expected changes in oil spot and futures; upt and up t are the respective unexpected and negatively unexpected changes in oil spot and futures returns; Rti refers to the S&P 500 returns in period t i; and 31, t is a zero mean innovation with a normal stochastic process, which is assumed to be:
3.2. The ARMAeGARCH model
31;t ¼ st Zt ;
Expected (Et), unexpected (upt) and negatively unexpected (up t ) changes (for which the value is less than the average of the unexpected indices) are constructed for each of the states, as follows:
Roil;t ¼ moil þ
p X
foil;i Roil;ti þ
qffiffiffiffiffiffiffiffiffiffi hoil;t 3oil;t ; 3oil;t wNIDð0; 1Þ
¼ uþ
Zt wNIDð0; 1Þ;
p X i¼1
ai 32ti þ
q X
and
bsjtj
st (9)
j¼1
These 31, t and 32, t two innovations are contemporaneously independent of one another. From Eq. (8), 32, t is the stochastic jump process (which is assumed to have Poisson distribution with
(5)
i¼1
hoil;t ¼ uoil þ
p X i¼1
boil;i hoil;ti þ
q X j¼1
aoil; j 32oil;tj
(6)
where Roil,ti denotes the change in oil spot or futures prices in period t i. Therefore, the expected changes can be taken as the difference between the changes in oil prices and estimated residual:
6 Conventional volatility models smooth persistent in volatility, but such models are not suitable for elucidating large discrete changes in asset prices. Conventional volatility models ignore the effect of anomalous information; therefore, studies of the development of econometric models have combined diffusion with the jump process. When investors fail to comprehend the true features, they will make incorrect decision. 7 The ARMA model states that the current value of a variable depends linearly on its own pervious values plus a combination of current and previous values of a white noise error term. The GARCH model allows the conditional variance to depend on a lagging squared error and previous lags.
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a time-varying conditional intensity parameter, lt). The Poisson distribution, with parameter lt being conditional on Ut1, is assumed to describe the arrival of a discrete number of jumps, where nt ˛f0; 1; 2; .g over the interval [t 1, t]. The conditional j density of nt is expressed aspðnt ¼ jjUt1 Þ ¼ elt lt =j!; j ¼ 0; 1; 2; .. The conditional jump intensity, lt, is the expected number of jumps conditional on the information set Ut1, which is parameterized as:
lt ¼ l0 þ rlt1 þ gzt1
(10)
where lt > 0, l0 > 0, r g and g 0. The lt is related to both the conditional jump intensity and ztj. The zt1 represents the change in the econometrician’s conditional forecast of n 1 as the information set is updated. The jump size, pt,k, is assumed to be independently drawn from 2 a normal distribution of the following form pt;k wNIDðq; d Þ. The Pn t p . jump component affecting returns from t 1 to t is Jt ¼ k ¼ 1 t;k The jump innovation associated with period t is therefore Pn t p qlt .8 The condiexpressed as 32;t ¼ Jt E½Jt jUt1 ¼ k ¼ 0 t;k tional density of returns is normal distribution and j jumps is normally distributed as
f ðRt jnt ¼ j; Ut1 Þ ¼
1=2 2 2p st þ jdt
N X
Variables
p1 p2 m1 m2 s21 s22
Oil spot
Oil futures
Coefficients
Standard error
Coefficients
Standard error
0.1612*** 0.0252*** 0.0036* 0.0011*** 0.0418*** 0.0178***
0.0205 0.0036 0.0020 0.0003 0.0012 0.0002
0.0979*** 0.0201*** 0.0020 0.0009*** 0.0350*** 0.0177***
0.0208 0.0058 0.0014 0.0003 0.0010 0.0003
Specification tests Mean test 1.6669 Variance test 2536.3156***
0.5713 2235.8163***
Note: *** indicates significance at the 1% level; and * indicates significance at the 10% level.
dependence and strong GARCH effects, indicating that GARCH families are present in the modeling. The respective prices and returns for the S&P 500, oil spot contracts and oil futures contracts, are illustrated in Fig. 1aec. The results of both the application of the augmented DickeyeFuller (ADF) and the Phillips and Perron (PP) unit root tests on
!2 9 8 2 P > > > > > > m ql q R a R þ j t > > i t1 < t = i¼1 exp 2 > > > > 2 st þ jdt > > > > : ;
Following the exclusion of all jumps occurring during a single unit interval, the conditional probability density function can be expressed as:
f ðRt jUt1 Þ ¼
Table 3 Markov switching investigation.
f ðRt jnt ¼ j; Ut1 Þpðnt ¼ jjUt1 Þ
(12)
j¼0
Therefore, the likelihood function can be written as LLðJÞ ¼ log f ðRt jUt1 ; JÞ, where J ¼ (m, a1, u, a, b, q, d2, l0, r, g, X) and X represent endogenous variables.
PT
t¼1
4. Data and empirical results
the prices are presented in Table 2, along with the first-order differences with regard to S&P 500, oil spot and oil futures prices. In order to ensure the completeness of our confirmatory data analysis, the table also lists the results of the Kwiatkowski et al. (KPSS) stationarity tests. Table 4 ARJI model of S&P 500 oil spot and futures with Markov switching. Variables
m1 f1
Our sample period runs from 1 January 1992 to 14 March 2008, with the retrieval of the daily S&P 500 and WTI oil transaction data in this study, as well as the subsequent transformation of the data into daily returns, ultimately yielding a total of 4053 observations; the daily data were obtained from Bloomberg. The returns are defined in logarithmic form, as Rt ¼ ln(Pt/Pt1) 100, where Pt denotes the closing price at time t. 4.1. Descriptive statistics The descriptive statistics for the oil spot, oil futures and S&P 500 returns, including JarqueeBera, Skewness and Kurtosis statistics, are provided in Table 1. The LjungeBox Q2 test statistics examining the serial correlation of the square returns are significant at below the 1 per cent level. The returns exhibit autocorrelation, linear
8 The conditional variance of returns is decomposed into two separate components. The first is a smoothly developing conditional variance component associated with the diffusion of past news impacts. The second is the conditional variance component relating to the heterogeneous information arrival process which generates the jumps, conditional on j jumps occurring during the normal conditional density of returns.
(11)
f2
u a b q d2 l0 r g
Oil spot
Oil futures
Coefficients
Standard error
Coefficients
Standard error
0.0139* 0.0038 0.0251 0.0028*** 0.0239*** 0.9611*** 0.7205*** 0.3576*** 0.0214*** 0.9454*** 0.5552
0.0081 0.0165 0.0156 0.0004 0.0008 0.0010 0.0427 0.0490 0.0020 0.0052 0.0611
0.0092 0.0034 0.0253 0.0028*** 0.0234*** 0.9618*** 0.7124*** 0.3691*** 0.0213*** 0.9459*** 0.5539***
0.0081 0.0165 0.0156 0.0004 0.0008 0.0010 0.0422 0.0501 0.0020 0.0052 0.0610
0.1260 0.0043 0.0159
0.1942 0.0156 0.0211
0.0151 0.0012 0.0181
0.1882 0.0154 0.0206
0.1152 0.0050 0.0489**
0.2082 0.0154 0.0192
0.1087 0.0061 0.0534***
0.2191 0.0159 0.0198
Low oil regime f1
k1 k 1 High oil regime f2
k2 k 2
Function value 5075.5322 LjungeBox Q2 (5) 6.1150 2 7.3220 LjungeBox Q (10) 11.4910 LjungeBox Q2 (15) 13.0790 LjungeBox Q2 (20) ARCH-LM test 7.6038
5074.8899 6.1550 7.4040 11.6270 13.0370 7.6980
Note: *** indicates significance at the 1% level; ** indicates significance at the 5% level; and * indicates significance at the 10% level.
Y.-H. Lee, J.-S. Chiou / Energy 36 (2011) 168e174
173
Fig. 2. Jump intensity in oil spot prices on the S&P 500 using the ARJI model with Markov switching.
Based upon the use of the ADF, PP and KPSS tests, we provide the results on the non-stationarity for the level, as well as the results obtained on the stationarity for the first difference. The results presented in Table 2 indicate that all of the series are nonstationary in level, but stationary in first-order difference, suggesting that all of the series are integrated, with an order of 1, I(1). 4.2. The ARJI model and Markov switching The maximum likelihood estimates obtained from our Markov switching investigation are presented in Table 3. The m1 (s21) of the first state is 0.0036 (0.0418) with a standard error of 0.0020 (0.0012); the t-statistic for s21 is significantly different from zero, indicating that this state is in a regime of high oil price fluctuations. The m2 (s22) of the second state is 0.0011 (0.0178) with a standard error of 0.0003 (0.0002); the t-statistic for s22 is again significantly different from zero, indicating that this state is in a regime of low oil price fluctuations.
The Wald statistics for the null hypothesis are presented in the lower portion of Table 3. Since the critical significance values for c(1) are 6.63 (1 per cent), 3.84 (5 per cent) and 2.71 (10 per cent), the null hypothesis is rejected in each case; two-state first-order Markov modeling is thus identified as being appropriate. The results of our application of the ARJI model on S&P 500 returns, including a Markov switching investigation, are listed in Table 4, incorporating expected (Et), unexpected (upt) and negatively unexpected (up t ) changes in oil spot and futures prices into the model of stock returns. Based upon our measurements of the oil price fluctuations, the ARCH and GARCH effects (u, a, b) for S&P 500 returns are found to be significant for each state. Thus, a strong GARCH effect is found to exist, as well as persistence in the conditional variance, as evidenced in the parameters a þ b ¼ 0.985 (a þ b ¼ 0.9852) for oil spot (oil futures) contracts. The persistence of returns fluctuations also holds; for every state, the average value of the jump q and the jump variance in
Fig. 3. Jump intensity in oil futures process on the S&P 500 using the ARJI model with Markov switching.
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Y.-H. Lee, J.-S. Chiou / Energy 36 (2011) 168e174
returns d2 is statistically significant; as regards jump intensity, l0, r and g are also found to be statistically significant; therefore, the intensity of the jumps is confirmed as being time varying. Fig. 2 provides an illustration of the jump intensity in the ARJI model with Markov switching for oil spot prices on the S&P 500, whilst Fig. 3 provides the corresponding illustration for oil futures prices on the S&P 500. As the figures show, the asymmetric unexpected occurrences of changes in oil spot and futures prices have negative impacts on the S&P 500 under a regime of high oil price fluctuations. Surprisingly, the expected, unexpected and asymmetrical unexpected occurrences of changes in oil spot and futures prices have no significant impacts on the S&P 500 based on the assumption of a regime of low oil price fluctuations (as low oil regime shows in Table 4). Not only do our results provide support for the existing studies in which a rise in oil prices has been shown to have direct, negative and statistically significant effects on stock returns, but more importantly, they also reveal that the statistical significance of the asymmetric effect exists only in a regime of high oil price fluctuations for both oil spot and oil futures contract prices (as k 2 shows in Table 4).
5. Conclusions This study distinguishes itself from the prior studies in the oil and financial literature insofar as we not only examine the asymmetric effects of oil prices on stock returns, but also explore the role played by the state of the regime in this dependency relationship. We retrieved daily transaction data on the S&P 500 covering the period from 1 January 1992 to 14 March 2008, as well as WTI oil transaction data, all of which were subsequently transformed into daily returns. Quite a conclusive result is obtained from our use of the regimeswitching model with consideration of jumps; we find that when there are significant fluctuations in oil prices, asymmetric unexpected changes in oil prices will have a negative impact on S&P 500 returns, although this result does not hold for a regime state of low oil price fluctuations. Our results verify the existence of a negative and statistically significant impact of oil prices on stock returns, and more importantly, identify that the statistical significance of this asymmetric effect exists only in a regime of high oil price fluctuations for both oil spot and oil futures contracts. The findings of this study emphasize the importance of oil shocks in driving economic fluctuations, with the evidence indicating that with changes in oil price dynamics, oil price volatility shocks will have asymmetric effects on stock returns. The consideration of shock exposure could provide a broader perspective for decision making processes. A well diversified portfolio, which
includes the consideration of oil price shocks can help to increase the accuracy of hedging against oil price risks.
References [1] Balke NS, Fomby TB. Threshold cointegration. International Economic Review 1997;38(3):627e46. [2] Basher SA, Sadorsky P. Oil price risk and emerging stock markets. Global Finance Journal 2006;17(2):224e51. [3] Chan W, Maheu J. Conditional jump dynamics in stock market returns. Journal of Business and Economic Statistics 2002;20:377e89. [4] Enders W, Granger CWJ. Unit-root tests and asymmetric adjustment with an example using the term structure of interest rates. Journal of Business and Economic Statistics 1998;16(3):304e12. [5] Enders W, Siklos PL. Cointegration and threshold adjustment. Journal of Business and Economic Statistics 2001;19(2):166e77. [6] Faff RW, Brailsford TJ. Oil price risk and the Australian stock market. Journal of Energy Finance and Development 1999;4:69e87. [7] Ferson WW, Harvey CR. Predictability and time-varying risk in world equity markets. Research in Finance 1995;13:25e88. [8] Hamilton JD. Oil and the macroeconomy since World War II. Journal of Political Economy 1983;88:829e53. [9] Hamilton JD. A new approach to the economic analysis of non-stationary time series and the business cycle. Econometrica 1989;57:357e84. [10] Hammoudeh S, Li H. Oil sensitivity and systematic risk in oil-sensitive stock indices. Journal of Economics and Business 2005;57:1e21. [11] Hammoudeh S, Eleisa L. Dynamic relationships among GCC stock markets and NYMEX oil futures. Contemporary Economic Policy 2004;22(2):250e69. [12] Kaul G, Jones CM. Oil and the stock markets. Journal of Finance 1996;51: 463e91. [13] Kaufmann RK, Laskowski C. Causes for an asymmetric relation between the price of crude oil and refined petroleum products. Energy Policy 2005;33: 1587e96. [14] Krey V, Martinsen D, Wagner HJ. Effects of stochastic energy prices on longterm energy-economic scenarios. Energy 2007;32(12):2340e9. [15] Lee CC, Chang CP. The impact of energy consumption on economic growth: evidence from linear and non-linear models in Taiwan. Energy 2007;32 (12):2282e94. [16] Lee K, Ni S, Ratti RA. Oil shocks and the macroeconomy: the role of price variability. Energy Journal 1995;16:39e56. [17] Loungani P. Oil price shocks and the dispersion hypothesis. Review of Economics and Statistics 1986;68:536e9. [18] Maheu JM, McCurdy TH. News arrival, jump dynamics and volatility components for individual stock returns. Journal of Finance 2004;59:755e93. [19] Mork KA. Oil and the macroeconomy when prices go up and down: an extension of Hamilton’s results. Journal of Political Economy 1989;91:740e4. [20] Nandha M, Faff R. Does oil move equity prices? A global view. Energy Economics 2008;30:986e97. [21] Papapetrou E. Oil price shocks, stock market, economic activity and employment in Greece. Energy Economics 2001;23:511e32. [22] Pindyck RS. Volatility and commodity price dynamics. Journal of Futures Market 2004;24(1):1029e47. [23] Pippenger MK, Goering GE. A note on the empirical power of unit root tests under threshold process. Oxford Bulletin of Economics and Statistics 1993;55 (4):473e82. [24] Sadorsky P. Oil price shocks and stock market activity. Energy Economics 1999;21:449e69. [25] Sadorsky P. Assessing the impact of oil prices on firms of different size: its tough being in the Middle. Energy Policy 2008;36:3854e61.
Contents lists available at ScienceDirect
Energy journal homepage: www.elsevier.com/locate/energy
Oil sensitivity and its asymmetric impact on the stock market Yen-Hsien Lee a,1, Jer-Shiou Chiou b, * a b
Department of Finance, Chung Yuan Christian University, 200 Chung Pei Rd., Chung Li 32023, Taiwan, ROC Department of Finance and Banking, Shih-Chien University, 70 Ta-Chih Street, Taipei 104, Taiwan, ROC
a r t i c l e i n f o
a b s t r a c t
Article history: Received 30 December 2009 Received in revised form 19 October 2010 Accepted 30 October 2010 Available online 3 December 2010
We develop a two-step methodology to facilitate an examination of the impact of oil shocks on stock returns. Oil price volatility is monitored in this study through the use of a regime-switching model, with the presence of jumps subsequently being taken into consideration to examine the asymmetric effects of oil prices on stock returns. Our analysis provides quite conclusive results based upon the use of a regimeswitching model with consideration of jumps; that is, when there are significant fluctuations in oil prices (West Texas Intermediate; WTI), the resultant unexpected asymmetric price changes lead to negative impacts on S&P 500 returns. However, the same result does not hold in a regime of lower oil price fluctuations. We therefore suggest that the achievement of a well diversified portfolio should involve the consideration of oil price shocks, which, as a consequence, should also help to improve the accuracy of hedging against oil price risks. 2010 Elsevier Ltd. All rights reserved.
JEL classification: C5 G1 Keywords: Asymmetric effects ARJI model Regime-switching
1. Introduction It is already widely recognized that there will be various changes over time in the conditional volatility levels of stock market indices; however, the causes of such changes have intrigued researchers for some considerable time. As a result, a substantial body of literature has emerged on the relationships between oil prices, the stock market and various financial and macroeconomic variables.2 Indeed, various data and statistical approaches have been adopted within the prior studies as a means of verifying the existence and nature of the negative relationship between oil price shocks and the US economy.3 Since asset prices are regarded as the present discounted value of future net earnings (Nandha and Faff [20]), we would reasonably expect to find a significant relationship between oil price shocks and stock market returns. As a result, if oil prices directly affect real output, then oil price increases will depress aggregate stock prices; this clearly suggests that oil prices must be associated with stock
* Corresponding author. Tel.: þ886 2 2538 1111x8927; fax: þ886 2 2538 1111x8714. E-mail addresses: [email protected] (Y.-H. Lee), [email protected] (J.-S. Chiou). 1 Tel.: þ886 3 265 5711. 2 Recent examples include Lee and Chang [15] and Sadorsky [25]. 3 See for example Hamilton [8,9], Loungani [17], Mork [19], and Lee et al. [16]. 0360-5442/$ e see front matter 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2010.10.057
returns (Kaul and Jones [12]; Sadorsky [24]). However, investigations into the linkages between oil prices and the equity markets are relatively few; thus, our analysis in the present study of the time variations in stock returns focuses on oil price volatility spillovers, as opposed to the consideration of general macroeconomic variables. A regime-switching phenomenon is found within most of the existing time-series models when they are applied to real data; thus, any estimations or inferences obtained without consideration of this phenomenon may well lead to unreliable results. Thus, various regime-switching models have emerged as a means of identifying such changing states within economic data generating mechanisms. In the present study, we assume that stock returns are affected by oil price shocks, and also that the state of such shocks will, in turn, have direct impacts on oil price volatility. Oil price volatility is therefore examined here based upon a regime-switching model, with the spillover and asymmetric effects of oil prices on stock returns subsequently being explored with the additional consideration of jumps. Our analysis provides quite a conclusive result, which is that when there are severe fluctuations in oil prices, unexpected asymmetric changes in oil prices (West Texas Intermediate; WTI) will have a negative impact on the S&P 500. The purposes of this research are to examine the relationship between the oil price and stock returns. In contrast to the extant literature, the model of stock returns adopted in the present study
Y.-H. Lee, J.-S. Chiou / Energy 36 (2011) 168e174
incorporates the consideration of expected, unexpected and negatively unexpected oil price fluctuations, whilst also focusing on oil price volatility, as opposed to general macroeconomic variables. Additionally, Maheu and McCurdy [18] proposed that the process of financial innovation has two components e normal innovations, and abnormal or jump innovations. A potential source of jump innovations is important news events. The investor makes incorrect financial and economic decisions when they fail to grasp abnormal information. In considering the impact of the jump characteristics of abnormal information, this study uses GARCH with the autoregressive conditional jump intensity (ARJI) model, which was developed by Chan and Maheu [3]. High and low of oil price fluctuations are incorporated using the regime-switching model, and expected, unexpected and negatively unexpected oil price fluctuations are considered, to study how oil spot and oil futures price fluctuations affect S&P 500 returns. 2. Literature review A considerable body of research has emerged on the relationship between energy prices and stock prices. For example, Ferson and Harvey [7] found evidence to show that oil price risk factors have statistical and significant influences on the equity markets of eighteen countries, whilst Faff and Brailsford [6] reported that oil prices positively and significantly affect the oil and gas industry and the diversified resources industry, with further negative and significant influences on both the paper and packaging industry and the transportation industry. Papapetrou [21] suggested that changes in oil prices affect both employment and real economic activity. However, it is generally accepted that whilst oil prices are important in explaining stock price movements, stock returns do not cause changes in either employment or real economic activity. Indeed, the only study to have found a bi-directional relationship between oil prices and stock prices was the examination of the Saudi Arabian stock market undertaken by Hammoudeh and Eleisa [11]. Using daily and weekly data for the petroleum market, Pindyck [22] developed a structural model of inventories, spot and futures prices capable of explaining oil price volatility. Furthermore, Hammoudeh and Li [10] suggested that in the pricing of oil-sensitive returns, regardless of the direction of the global capital markets, investors should regard systematic risk as being of greater importance than oil sensitivity. Kaufmann and Laskowski [13] confirmed that asymmetric pricing can be generated by efficient markets, thereby suggesting that there is little justification for policy interventions as a means of reducing or eliminating such price asymmetry in the motor gasoline and home heating oil markets. Krey et al. [14] went on to investigate the impact of uncertain energy prices on supply structures as well as their interaction with various measures in the demand sectors. Whilst the majority of the prior studies tend to agree that energy prices influence stock prices, there are, nevertheless, very few examples of studies having been undertaken to investigate the long-run equilibrium between stock and oil markets. Indeed, in the majority of the studies involving the use of traditional time-series models, the tendency has been to assume that the underlying variables exhibit a linear and symmetrical adjustment processes; however, in reality, most macro variables exhibit asymmetrical adjustment. Some research has, nevertheless, been undertaken into the impact on stock prices arising from asymmetric changes in oil prices. For example, both Sadorsky [24] and Basher and Sadorsky [2] provide support for the argument that oil price changes have
169
Table 1 Descriptive statistics. Items
Oil spot
Oil futures
S&P 500
Mean Std. Dev. Max. Min. Skewness Kurtosis JarqueeBera LjungeBox Q2 LjungeBox Q2 LjungeBox Q2 LjungeBox Q2
0.0422 2.2650 17.0918 15.3827 0.3345*** 4.8210*** 3971.9404*** 274.402*** 304.095*** 328.601*** 434.909***
0.0423 2.1631 16.5445 14.2309 0.2599*** 3.4807*** 2076.6466*** 168.2110*** 196.1400*** 223.5850*** 270.2790***
0.0280 1.0139 7.1127 5.5744 0.1545*** 3.8688*** 2525.5466*** 708.8150*** 1141.9340*** 1432.0770*** 1732.7910***
(5) (10) (15) (20)
Note: *** indicates significance at the 1% level.
an asymmetric effect on stock prices. It has, however, been demonstrated in several studies that traditional co-integration tests are of very limited use in situations involving asymmetric adjustment.4 In contrast to the extant literature, the present study adopts a model of stock returns which takes into consideration expected, unexpected and negatively unexpected fluctuations in oil prices. We then apply an ‘ARJI’ model with regime-switching to examine the influence of oil prices on S&P 500 returns.
3. Methodology 3.1. Markov regime-switching model iid
Consider the time series yt ¼ mst þ 3t , where 3t w Nð0; s2 Þ, st ¼ 1, ., N indicates the market regime at time t. Note that the variable st ¼ i, which can be referred to as a regime indicator, is a random variable with its own distribution and cannot be observed. We begin with the case where N ¼ 2.5 In addition to aiding intuition, the two-regime case is a popular specification in applied work. Two states of the market are provided through a first-order Markov process with the following transition probabilities matrix:
P ¼
p11 p12
p21 p22
(1)
where P is the transition probabilities matrix and the transition probability P11 and P12 (P21 and P22) gives the probability that state 1 (2) will be followed by state 1 and 2 (2 and 1). The ht show the two density function:
2
3 ) ( 2 m 1 ðy Þ t 6 7 1 7 6 pffiffiffiffiffiffiffi exp 6 2ps1 7 2s21 f ðyt jst ¼ 1;Yt1 ; qÞ 6 )7 ( ht ¼ ¼6 2 7 f ðyt jst ¼ 2;Yt1 ; qÞ ðyt m2 Þ 7 6 1 4 pffiffiffiffiffiffiffi exp 5 2s22 2ps2
(2)
where q ¼ ðm1 ; m2 ; s21 ; s22 ;p11 ;p22 Þ0 , m1 and s21 (m2 and s22 ) are the conditional mean and variance on state 1 (2), and then P12 and P21 ^
are transition probability. Collect these forecast in a vector x t , which is a vector whose jth element represent Pðst ¼ jjY t1 ; qÞ for j ¼ 1, 2. ^
Thus, x tþ1jt is defined as:
4 See for example Pippenger and Goering [23], Balke and Fomby [1], Enders and Granger [4] and Enders and Siklos [5]. 5 Limiting the number of the regimes to two improves the model's tractability and, intuitively, a two-state process corresponds to periods of high- and lowvolatility in the markets.
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Fig. 1. (a) S&P 500 prices and returns. (b) Oil spot prices and returns. (c) Oil futures prices and returns.
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171
Table 2 Unit root and stationarity tests for the stock price indices. Items
Model
ADF
PP
KPSS
Level
Differencea
Level
Differencea
Levela
Difference
S&P 500
C C/T
1.6332 0.5955
51.0573*** 51.0909***
1.6290 0.5618
70.5228*** 70.6429***
5.6095*** 1.0205***
0.3483 0.1118
Oil spot
C C/T
1.3546 1.8883
30.5616*** 30.5587***
1.3769 2.0430
69.3101*** 69.3024***
5.3515*** 1.2557***
0.0924 0.0985
Oil futures
C C/T
1.3205 1.8470
30.2615*** 30.2587***
1.3635 1.9945
69.4799*** 69.4720***
5.3577*** 1.2620***
0.0958 0.1020
a
*** indicates significance at the 1% level.
^
^
x tþ1jt ¼ P$x t ¼
p11
p21
p12
p22
Pðst ¼ 1jYt1 ; qÞ $ Pðst ¼ 2jYt1 ; qÞ
Et ¼ Roil;t
" *# p p21 Pðstþ1 ¼ 1jYt ; qÞ $ 1* ¼ p22 Pðstþ1 ¼ 2jYt ; qÞ p2 (3) P1 Pðstþ1 ¼ 1jYt ; qÞ ¼ ¼ P2 Pðstþ1 ¼ 2jYt ; qÞ
¼
p11 p12
qffiffiffiffiffiffiffiffiffiffi hoil;t 3oil;t
(7)
qffiffiffiffiffiffiffiffiffiffi From Eq. (7), Et and hoil;t 3oil;t are expected- and unexpected-oil price growth rate, respectively. Defining up t ¼ Minðupt ; Eðupt ÞÞ as the negatively unexpected (up t ) changes in spot or futures within the stock returns model, we then take the expected (Et), unexpected (upt) and negatively unexpected (up t ) changes in spot or futures into consideration within the stock returns model, as shown in Eq. (8).
We can obtain the log likelihood function:
( LðqÞ ¼ log
T Y
3.3. The ARJI model6
) f ðyt jY t1 ; qÞ
t ¼1
9 8 =
Following Chan and Maheu [3], we use the ARJI model which postulates that jump intensity follows an autoregressive moving average (ARMA) process and incorporates the generalized autoregressive conditional heteroskedasticity (GARCH) effect of the returns series.7 Given the set of returns at time t 1 and the two stochastic innovations, 31, t and 32, t, the ARJI model of returns (Rt) can then be written as:
t
(4) where 2 P x tjt1 Qht Þ ¼ f ðyt jst ;Yt1 ; qÞ$Pðst jYt1 ; qÞ and f ðyt jY t1 ; qÞ ¼ 10 ðb st ¼1
3
2
Rt ¼ m þ
m X
fi Rti þ 41 Et þ k1 upt þ k DLow 1 upt
i¼1
DHigh þ 31;t þ 32;t þ 42 Et þ k2 upt þ k 2 upt
(8)
) ( 1 ðyt m1 Þ2 7 6 pffiffiffiffiffiffi ffi exp 7 6 7 6 2ps1 2s21 q b )7 ( x tjt1 Qht ¼ Pðst ¼ 1jYt1 ; Þ Q6 2 7 Pðst ¼ 2jY t1 ; qÞ 6 ðyt m2 Þ 7 6 1 5 4 pffiffiffiffiffiffiffi exp 2s22 2ps2
where Et defines the expected changes in oil spot and futures; upt and up t are the respective unexpected and negatively unexpected changes in oil spot and futures returns; Rti refers to the S&P 500 returns in period t i; and 31, t is a zero mean innovation with a normal stochastic process, which is assumed to be:
3.2. The ARMAeGARCH model
31;t ¼ st Zt ;
Expected (Et), unexpected (upt) and negatively unexpected (up t ) changes (for which the value is less than the average of the unexpected indices) are constructed for each of the states, as follows:
Roil;t ¼ moil þ
p X
foil;i Roil;ti þ
qffiffiffiffiffiffiffiffiffiffi hoil;t 3oil;t ; 3oil;t wNIDð0; 1Þ
¼ uþ
Zt wNIDð0; 1Þ;
p X i¼1
ai 32ti þ
q X
and
bsjtj
st (9)
j¼1
These 31, t and 32, t two innovations are contemporaneously independent of one another. From Eq. (8), 32, t is the stochastic jump process (which is assumed to have Poisson distribution with
(5)
i¼1
hoil;t ¼ uoil þ
p X i¼1
boil;i hoil;ti þ
q X j¼1
aoil; j 32oil;tj
(6)
where Roil,ti denotes the change in oil spot or futures prices in period t i. Therefore, the expected changes can be taken as the difference between the changes in oil prices and estimated residual:
6 Conventional volatility models smooth persistent in volatility, but such models are not suitable for elucidating large discrete changes in asset prices. Conventional volatility models ignore the effect of anomalous information; therefore, studies of the development of econometric models have combined diffusion with the jump process. When investors fail to comprehend the true features, they will make incorrect decision. 7 The ARMA model states that the current value of a variable depends linearly on its own pervious values plus a combination of current and previous values of a white noise error term. The GARCH model allows the conditional variance to depend on a lagging squared error and previous lags.
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a time-varying conditional intensity parameter, lt). The Poisson distribution, with parameter lt being conditional on Ut1, is assumed to describe the arrival of a discrete number of jumps, where nt ˛f0; 1; 2; .g over the interval [t 1, t]. The conditional j density of nt is expressed aspðnt ¼ jjUt1 Þ ¼ elt lt =j!; j ¼ 0; 1; 2; .. The conditional jump intensity, lt, is the expected number of jumps conditional on the information set Ut1, which is parameterized as:
lt ¼ l0 þ rlt1 þ gzt1
(10)
where lt > 0, l0 > 0, r g and g 0. The lt is related to both the conditional jump intensity and ztj. The zt1 represents the change in the econometrician’s conditional forecast of n 1 as the information set is updated. The jump size, pt,k, is assumed to be independently drawn from 2 a normal distribution of the following form pt;k wNIDðq; d Þ. The Pn t p . jump component affecting returns from t 1 to t is Jt ¼ k ¼ 1 t;k The jump innovation associated with period t is therefore Pn t p qlt .8 The condiexpressed as 32;t ¼ Jt E½Jt jUt1 ¼ k ¼ 0 t;k tional density of returns is normal distribution and j jumps is normally distributed as
f ðRt jnt ¼ j; Ut1 Þ ¼
1=2 2 2p st þ jdt
N X
Variables
p1 p2 m1 m2 s21 s22
Oil spot
Oil futures
Coefficients
Standard error
Coefficients
Standard error
0.1612*** 0.0252*** 0.0036* 0.0011*** 0.0418*** 0.0178***
0.0205 0.0036 0.0020 0.0003 0.0012 0.0002
0.0979*** 0.0201*** 0.0020 0.0009*** 0.0350*** 0.0177***
0.0208 0.0058 0.0014 0.0003 0.0010 0.0003
Specification tests Mean test 1.6669 Variance test 2536.3156***
0.5713 2235.8163***
Note: *** indicates significance at the 1% level; and * indicates significance at the 10% level.
dependence and strong GARCH effects, indicating that GARCH families are present in the modeling. The respective prices and returns for the S&P 500, oil spot contracts and oil futures contracts, are illustrated in Fig. 1aec. The results of both the application of the augmented DickeyeFuller (ADF) and the Phillips and Perron (PP) unit root tests on
!2 9 8 2 P > > > > > > m ql q R a R þ j t > > i t1 < t = i¼1 exp 2 > > > > 2 st þ jdt > > > > : ;
Following the exclusion of all jumps occurring during a single unit interval, the conditional probability density function can be expressed as:
f ðRt jUt1 Þ ¼
Table 3 Markov switching investigation.
f ðRt jnt ¼ j; Ut1 Þpðnt ¼ jjUt1 Þ
(12)
j¼0
Therefore, the likelihood function can be written as LLðJÞ ¼ log f ðRt jUt1 ; JÞ, where J ¼ (m, a1, u, a, b, q, d2, l0, r, g, X) and X represent endogenous variables.
PT
t¼1
4. Data and empirical results
the prices are presented in Table 2, along with the first-order differences with regard to S&P 500, oil spot and oil futures prices. In order to ensure the completeness of our confirmatory data analysis, the table also lists the results of the Kwiatkowski et al. (KPSS) stationarity tests. Table 4 ARJI model of S&P 500 oil spot and futures with Markov switching. Variables
m1 f1
Our sample period runs from 1 January 1992 to 14 March 2008, with the retrieval of the daily S&P 500 and WTI oil transaction data in this study, as well as the subsequent transformation of the data into daily returns, ultimately yielding a total of 4053 observations; the daily data were obtained from Bloomberg. The returns are defined in logarithmic form, as Rt ¼ ln(Pt/Pt1) 100, where Pt denotes the closing price at time t. 4.1. Descriptive statistics The descriptive statistics for the oil spot, oil futures and S&P 500 returns, including JarqueeBera, Skewness and Kurtosis statistics, are provided in Table 1. The LjungeBox Q2 test statistics examining the serial correlation of the square returns are significant at below the 1 per cent level. The returns exhibit autocorrelation, linear
8 The conditional variance of returns is decomposed into two separate components. The first is a smoothly developing conditional variance component associated with the diffusion of past news impacts. The second is the conditional variance component relating to the heterogeneous information arrival process which generates the jumps, conditional on j jumps occurring during the normal conditional density of returns.
(11)
f2
u a b q d2 l0 r g
Oil spot
Oil futures
Coefficients
Standard error
Coefficients
Standard error
0.0139* 0.0038 0.0251 0.0028*** 0.0239*** 0.9611*** 0.7205*** 0.3576*** 0.0214*** 0.9454*** 0.5552
0.0081 0.0165 0.0156 0.0004 0.0008 0.0010 0.0427 0.0490 0.0020 0.0052 0.0611
0.0092 0.0034 0.0253 0.0028*** 0.0234*** 0.9618*** 0.7124*** 0.3691*** 0.0213*** 0.9459*** 0.5539***
0.0081 0.0165 0.0156 0.0004 0.0008 0.0010 0.0422 0.0501 0.0020 0.0052 0.0610
0.1260 0.0043 0.0159
0.1942 0.0156 0.0211
0.0151 0.0012 0.0181
0.1882 0.0154 0.0206
0.1152 0.0050 0.0489**
0.2082 0.0154 0.0192
0.1087 0.0061 0.0534***
0.2191 0.0159 0.0198
Low oil regime f1
k1 k 1 High oil regime f2
k2 k 2
Function value 5075.5322 LjungeBox Q2 (5) 6.1150 2 7.3220 LjungeBox Q (10) 11.4910 LjungeBox Q2 (15) 13.0790 LjungeBox Q2 (20) ARCH-LM test 7.6038
5074.8899 6.1550 7.4040 11.6270 13.0370 7.6980
Note: *** indicates significance at the 1% level; ** indicates significance at the 5% level; and * indicates significance at the 10% level.
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173
Fig. 2. Jump intensity in oil spot prices on the S&P 500 using the ARJI model with Markov switching.
Based upon the use of the ADF, PP and KPSS tests, we provide the results on the non-stationarity for the level, as well as the results obtained on the stationarity for the first difference. The results presented in Table 2 indicate that all of the series are nonstationary in level, but stationary in first-order difference, suggesting that all of the series are integrated, with an order of 1, I(1). 4.2. The ARJI model and Markov switching The maximum likelihood estimates obtained from our Markov switching investigation are presented in Table 3. The m1 (s21) of the first state is 0.0036 (0.0418) with a standard error of 0.0020 (0.0012); the t-statistic for s21 is significantly different from zero, indicating that this state is in a regime of high oil price fluctuations. The m2 (s22) of the second state is 0.0011 (0.0178) with a standard error of 0.0003 (0.0002); the t-statistic for s22 is again significantly different from zero, indicating that this state is in a regime of low oil price fluctuations.
The Wald statistics for the null hypothesis are presented in the lower portion of Table 3. Since the critical significance values for c(1) are 6.63 (1 per cent), 3.84 (5 per cent) and 2.71 (10 per cent), the null hypothesis is rejected in each case; two-state first-order Markov modeling is thus identified as being appropriate. The results of our application of the ARJI model on S&P 500 returns, including a Markov switching investigation, are listed in Table 4, incorporating expected (Et), unexpected (upt) and negatively unexpected (up t ) changes in oil spot and futures prices into the model of stock returns. Based upon our measurements of the oil price fluctuations, the ARCH and GARCH effects (u, a, b) for S&P 500 returns are found to be significant for each state. Thus, a strong GARCH effect is found to exist, as well as persistence in the conditional variance, as evidenced in the parameters a þ b ¼ 0.985 (a þ b ¼ 0.9852) for oil spot (oil futures) contracts. The persistence of returns fluctuations also holds; for every state, the average value of the jump q and the jump variance in
Fig. 3. Jump intensity in oil futures process on the S&P 500 using the ARJI model with Markov switching.
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returns d2 is statistically significant; as regards jump intensity, l0, r and g are also found to be statistically significant; therefore, the intensity of the jumps is confirmed as being time varying. Fig. 2 provides an illustration of the jump intensity in the ARJI model with Markov switching for oil spot prices on the S&P 500, whilst Fig. 3 provides the corresponding illustration for oil futures prices on the S&P 500. As the figures show, the asymmetric unexpected occurrences of changes in oil spot and futures prices have negative impacts on the S&P 500 under a regime of high oil price fluctuations. Surprisingly, the expected, unexpected and asymmetrical unexpected occurrences of changes in oil spot and futures prices have no significant impacts on the S&P 500 based on the assumption of a regime of low oil price fluctuations (as low oil regime shows in Table 4). Not only do our results provide support for the existing studies in which a rise in oil prices has been shown to have direct, negative and statistically significant effects on stock returns, but more importantly, they also reveal that the statistical significance of the asymmetric effect exists only in a regime of high oil price fluctuations for both oil spot and oil futures contract prices (as k 2 shows in Table 4).
5. Conclusions This study distinguishes itself from the prior studies in the oil and financial literature insofar as we not only examine the asymmetric effects of oil prices on stock returns, but also explore the role played by the state of the regime in this dependency relationship. We retrieved daily transaction data on the S&P 500 covering the period from 1 January 1992 to 14 March 2008, as well as WTI oil transaction data, all of which were subsequently transformed into daily returns. Quite a conclusive result is obtained from our use of the regimeswitching model with consideration of jumps; we find that when there are significant fluctuations in oil prices, asymmetric unexpected changes in oil prices will have a negative impact on S&P 500 returns, although this result does not hold for a regime state of low oil price fluctuations. Our results verify the existence of a negative and statistically significant impact of oil prices on stock returns, and more importantly, identify that the statistical significance of this asymmetric effect exists only in a regime of high oil price fluctuations for both oil spot and oil futures contracts. The findings of this study emphasize the importance of oil shocks in driving economic fluctuations, with the evidence indicating that with changes in oil price dynamics, oil price volatility shocks will have asymmetric effects on stock returns. The consideration of shock exposure could provide a broader perspective for decision making processes. A well diversified portfolio, which
includes the consideration of oil price shocks can help to increase the accuracy of hedging against oil price risks.
References [1] Balke NS, Fomby TB. Threshold cointegration. International Economic Review 1997;38(3):627e46. [2] Basher SA, Sadorsky P. Oil price risk and emerging stock markets. Global Finance Journal 2006;17(2):224e51. [3] Chan W, Maheu J. Conditional jump dynamics in stock market returns. Journal of Business and Economic Statistics 2002;20:377e89. [4] Enders W, Granger CWJ. Unit-root tests and asymmetric adjustment with an example using the term structure of interest rates. Journal of Business and Economic Statistics 1998;16(3):304e12. [5] Enders W, Siklos PL. Cointegration and threshold adjustment. Journal of Business and Economic Statistics 2001;19(2):166e77. [6] Faff RW, Brailsford TJ. Oil price risk and the Australian stock market. Journal of Energy Finance and Development 1999;4:69e87. [7] Ferson WW, Harvey CR. Predictability and time-varying risk in world equity markets. Research in Finance 1995;13:25e88. [8] Hamilton JD. Oil and the macroeconomy since World War II. Journal of Political Economy 1983;88:829e53. [9] Hamilton JD. A new approach to the economic analysis of non-stationary time series and the business cycle. Econometrica 1989;57:357e84. [10] Hammoudeh S, Li H. Oil sensitivity and systematic risk in oil-sensitive stock indices. Journal of Economics and Business 2005;57:1e21. [11] Hammoudeh S, Eleisa L. Dynamic relationships among GCC stock markets and NYMEX oil futures. Contemporary Economic Policy 2004;22(2):250e69. [12] Kaul G, Jones CM. Oil and the stock markets. Journal of Finance 1996;51: 463e91. [13] Kaufmann RK, Laskowski C. Causes for an asymmetric relation between the price of crude oil and refined petroleum products. Energy Policy 2005;33: 1587e96. [14] Krey V, Martinsen D, Wagner HJ. Effects of stochastic energy prices on longterm energy-economic scenarios. Energy 2007;32(12):2340e9. [15] Lee CC, Chang CP. The impact of energy consumption on economic growth: evidence from linear and non-linear models in Taiwan. Energy 2007;32 (12):2282e94. [16] Lee K, Ni S, Ratti RA. Oil shocks and the macroeconomy: the role of price variability. Energy Journal 1995;16:39e56. [17] Loungani P. Oil price shocks and the dispersion hypothesis. Review of Economics and Statistics 1986;68:536e9. [18] Maheu JM, McCurdy TH. News arrival, jump dynamics and volatility components for individual stock returns. Journal of Finance 2004;59:755e93. [19] Mork KA. Oil and the macroeconomy when prices go up and down: an extension of Hamilton’s results. Journal of Political Economy 1989;91:740e4. [20] Nandha M, Faff R. Does oil move equity prices? A global view. Energy Economics 2008;30:986e97. [21] Papapetrou E. Oil price shocks, stock market, economic activity and employment in Greece. Energy Economics 2001;23:511e32. [22] Pindyck RS. Volatility and commodity price dynamics. Journal of Futures Market 2004;24(1):1029e47. [23] Pippenger MK, Goering GE. A note on the empirical power of unit root tests under threshold process. Oxford Bulletin of Economics and Statistics 1993;55 (4):473e82. [24] Sadorsky P. Oil price shocks and stock market activity. Energy Economics 1999;21:449e69. [25] Sadorsky P. Assessing the impact of oil prices on firms of different size: its tough being in the Middle. Energy Policy 2008;36:3854e61.