The relationship between oil prices and stock prices

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This article investigates the long-run and short-run dynamics between US stock prices and oil prices over the period from 1 January 1992 to 22 November 2013.
Applied Financial Economics, 2014 Vol. 24, No. 12, 793–800, http://dx.doi.org/10.1080/09603107.2014.907476

The relationship between oil prices and stock prices: a nonlinear asymmetric cointegration approach Panagiotis Rafailidis* and Constantinos Katrakilidis Department of Economics, Aristotle University of Thessaloniki, Thessaloniki, Greece

This article investigates the long-run and short-run dynamics between US stock prices and oil prices over the period from 1 January 1992 to 22 November 2013 using the S&P 500 index and West Texas Intermediate spot oil prices. Unlike the majority of previous studies that are based on the conventional time series analysis, we examine for the presence of different sources of nonlinearities, such as structural breaks and asymmetric adjustments in the dynamic links between the investigated markets. The results from the threshold autoregressive (TAR) and momentum threshold autoregressive (MTAR) models of Enders and Siklos (2001) in conjunction with the Threshold Error Correction Model estimations provide evidence of asymmetric responses towards the equilibrium. Keywords: threshold cointegration TAR and MTAR models; asymmetric error correction model; stock prices and oil prices JEL Classification: C32; G12; Q49

I. Introduction In recent years there has been a growing body of research on the relationship between oil prices and stock prices. Theoretically, this relationship is justified by the fact that asset prices are valuated using the present discounted value of future dividends and earnings. The links between stock and oil prices can be attributed to changes either in expected cash flows or the discount rates. Expected cash flows can be affected by oil prices, as oil is a crucial input in most firms’ production process and leads to changes in costs, affecting earnings and dividends and hence stock prices. On the other hand, discount rates are composed of an expected inflation and a real interest rate component. Higher oil prices may lead to overestimation of the expected inflation and thus higher nominal interest rates; and since discount rates are negatively related with stock prices, increases in interest rates depress stock prices. Furthermore, discount rates can

be affected by monetary policy. Inflationary pressures caused by increased oil prices may lead central banks to raise interest rates and thus to negatively affect stock prices. Since the pioneer research by Jones and Kaul (1996), who using a cash-flow dividend valuation model found that oil-price changes affect the stock price returns negatively in the US and Canadian stock markets, a great amount of relevant researches has followed. However, the relationship between oil-price changes and stock returns still remains a controversial issue. The majority of the empirical work for oil-importing countries failed to detect a long-run relationship, providing only short-run evidence of negative impacts of oil-price changes to stock returns (Cong et al., 2008; Park and Ratti, 2008; Sadorsky, 1999 and others). In contrast, several studies have doubted these results, supporting either that oil-price changes have no impact on asset price valuation or that the relationship between them is positive (Ferson and Harvey, 1994; Huang et al., 1996; Narayan and

*Corresponding author. E-mail: [email protected]

© 2014 Taylor & Francis

793

794 Narayan, 2010). However, demand-side effects could justify a positive relationship between oil and stock market prices (Kilian and Park, 2007; Apergis and Miller, 2009). The majority of the relevant literature applies traditional time series techniques that heavily depend on the integration properties of the involved variables. It is widely accepted that the existence of structural breaks or any other type of nonlinearities distorts the reliability of the conventional unit root and cointegration tests (Phillips, 1986; Perron, 1989). Detection of asymmetries in the adjustment process to longrun equilibrium constitutes a further valuable information that may be exploitable accordingly by investors, authorities and firms to manage their portfolios and strategies, by minimizing their exposure to oil-price risk. In this direction this article contributes to the existing literature by enriching the understanding of the dynamic linkages between oil and stock market prices in the following aspects. It applies comparatively conventional and advanced time series methodologies to (1) reliably identify the integration properties of the examined series; (2) trace out possible significant breaks in the evolution of the price series, since several booms and crashes are reported in both the US stock market and oil-price history, especially over the period under investigation, such nonlinearities might falsely lead to the nonrejection of the null hypothesis of no cointegration; (3) estimate the long- and sort-run dynamic linkages between the considered price series accounting for such break-type nonlinearities; (4) discover hidden possible information due to asymmetric adjustments to long-run equilibrium under the nonlinear cointegration framework; (5) strengthen the evidence accounting for a prolonged sample period that includes the post-crisis period till the end of 2013. The outline of the article is as follows: Section II reviews related literature and presents the findings. Section III briefly presents the adopted empirical methodology. Section IV describes the examined data set and illustrates the results of the empirical analysis. Finally, Section V summarizes and concludes.

II. Review of the Literature It is widely accepted that oil prices, economic activity and stock prices respond to the same economic forces (Barsky and Kilian, 2002, 2004; Hamilton, 2005; Kilian, 2008a, b) and thus share a common stochastic trend, which supports a long-run causal relationship between the examined variables. 1 

P. Rafailidis and C. Katrakilidis Hammoudeh and Li (2005) and Masih et al. (2011) using the linear cointegration method proposed by Johansen (1991, 1995) found evidence that oil prices and stock prices are cointegrated. On the other hand, Miller and Ratti (2009) investigating the long-run relationship between oil prices and stock prices for six OECD countries suggested that, although a long-run relationship had been detected, it was not stable over all the investigated sub-periods, possibly due to the presence of several structural breaks in the links between the investigated markets. However, there are many researchers who suggest that the relationship between oil prices and stock market is asymmetric. Sadorsky (1999) was among the first researchers who showed that oil price shocks have asymmetric effects on stock returns; specifically, positive oilprice changes have a greater impact on US stock returns than that of negative oil-price changes. In line with Sadorsky (1999), Ferderer (1996) and Lee et al. (1995), attributed the asymmetric response of economic activity on oil-price variations to the adverse relations between increased uncertainty and investment decision. Higher oil prices and the consequent increase in uncertainty lead companies to postpone their investments reducing economic activity and therefore depressing stock price values. Ciner (2001) provided evidence that oil prices affect the US stock market in a nonlinear manner using a nonlinear Granger causality framework. Particularly, rising oil prices may retard aggregate economic activity by more than oil price decreases stimulate it.1 According to Gogineni (2007), a possible explanation for the asymmetric response of stock returns to oil-price changes is provided by Brown et al. (1988) and Campbell and Hentschel (1992) who argued that stock price reactions to unfavourable news events tend to be larger than the reactions to favourable ones. Gogineni (2007) indicated that while small oil-price changes cause positive effects on stock returns, large oil-price changes have negative impacts. Furthermore, according to Kilian and Park (2007), the response of US real stock returns differs significantly depending on whether the increase in the price of oil is driven by demand- or supply-side shocks. The results of their structural VAR analysis imply that the negative response of stock returns to oil-price changes can be attributed only to precautionary demand shocks, driven by the uncertainty about future crude oil supply shortfalls; while, higher oil prices, driven by an unanticipated global expansion, have positive effects on stock returns. Apergis and Miller (2009) following a similar approach confirmed the previous results. However, Kilian and Vigfusson

Among the most possible explanations in the literature about the asymmetric relationship between oil prices and economic activity are the monetary policy proposed by Bernanke et al. (1997), the adverse relationship between investment and uncertainty (Bernanke, 1983; Lee et al. 1995; Ferderer, 1996), the adjustment costs that arise from sectoral imbalances (Hamilton, 1988), or from coordination problems between the firms (Huntington, 2000), or because the energy-to-output ratio is embedded in the capital stock (Atkeson and Kehoe, 1999) and the asymmetry in petroleum product prices (Bacon, 1991; Balke et al., 1998; Huntington, 2000).

The relationship between oil prices and stock prices (2009, 2011) doubt previous findings, suggesting that there are even little or no evidence of asymmetric response of oil prices to economic activity in the US. Under a nonlinear cointegration framework, Huang et al. (2005) used a multivariate model based on Sadorsky (1999) and examined the impacts of oil-price changes on real economic activity and stock returns for US, Canada and Japan. They employed a Multivariate Threshold Model and found that the responses of output changes and stock returns are greater when oil-price changes exhibit a threshold level. Jawadi et al. (2010) investigated the links between oil and stock markets for US, France, Mexico and Philippines using the nonlinear cointegration framework and particularly, the Exponential Switching Transition Error Correction Model. They found evidence of a nonlinear cointegration relationship and that stock prices are meanreverting towards the oil-price equilibrium with the adjustment speed depending on the size of disequilibrium.

Bai and Perron (1998, 2003) test To address the issue of possible structural breaks in the cointegration relationship, we employ the Bai and Perron (1998, 2003) multiple structural break approach. Α group of SupF(l + 1|l) tests are employed to statistically identify the appropriate number of breaks. The tests are based on the following model with m breaks (m + 1 regimes): 0

yt ¼ α 1 þ α 2 xt þ

r X

βΔxtj þ ut

(2)

j¼q

Enders and Siklos cointegration Enders and Granger (1988) have shown that all tests for unit roots and cointegration have low power in the presence of asymmetries. Enders and Granger (1988) and Enders and Siklos (2001), have developed two different nonlinear cointegration models, which allow for tests of asymmetries, the threshold autoregressive (TAR) and the momentum threshold autoregressive (MTAR). TAR model can be described by the following equation: Δ μt ¼ It ρ1 μt1 þ ð1  It Þρ2 μt1 þ

p1 X

γi Δ μtj þ εt

where εt , iidð0; σ 2 Þ

(3)

j¼1

where μt are the residuals of the DOLS cointegration approach, the lagged values of Δμ are meant to yield uncorrelated residuals and It is the heaviside indicator such that It ¼ 1 if μt1  τ and zero otherwise, while MTAR is given by the equation:

III. Methodology

0

yt ¼ δj zt þ βxt þ ut ; for t ¼ Tj1 þ 1; . . . ; Tj ; j ¼ 1; . . . m þ 1

795

(1)

where yt is the dependent variable in period t, zt is a constant term and xt is the independent variable and β and δj are the corresponding coefficients and ut is the disturbance at time t. T1,…, Tm are indices that represent the break points, which by assumption are unknown. Dynamic ordinary least squares (DOLS) analysis If the variables under investigation are integrated of order one, I(1), the Dynamic Ordinary Least Squares (DOLS) methodology introduced by Stock and Watson (1993) is asymptotically equivalent to the Maximum Likelihood (ML) approach developed by Johansen (1988) (Phillips and Park, 1988; Phillips, 1991; Watson, 1994). The potential simultaneity bias among the regressors is dealt with by including q lags and r leads of the first differences of the I(1) regressors. Hence, the estimation of the long-run relationship between two series yt and xt has the following general specification:

Δ μt ¼ It ρ1 Δ μt1 þ ð1  It Þρ2 Δ μt1 þ

p1 X

γi Δ μtj þ εt

where εt , iidð0; σ 2 Þ

(4)

j¼1

and It ¼ 1 if Δ μt1  τ and zero otherwise. The coefficients ρ1 and ρ2 represent the different speeds of adjustment for the deviations from the long-run equilibrium. In both models, the null hypothesis of no cointegration can be tested by the restriction ρ1 ¼ ρ2 ¼ 0, by means of an F-test. Enders and Siklos (2001) have tabulated the appropriate critical values for both TAR and MTAR specifications. In addition, if a cointegration relationship exists, the null hypothesis of symmetric adjustment (ρ1 ¼ ρ2 ) can be tested by applying a standard F-test. Thus, if a cointegration relationship with MTAR adjustment exists, the following asymmetric error correction model can be estimated: Δyt ¼ a þ β1 It Δμt1 þ β2 ð1  It ÞΔμt1 p p X X þ γj Δytj þ δj Δχ tj þ et j¼1

(5)

j¼1

IV. Data and Empirical Results Daily data, collected from the Bloomberg database and covering the time period from 1 January 1992 to 22

P. Rafailidis and C. Katrakilidis

796 Table 1. Unit root tests ADF Levels S&P 500 WTI spot prices First differences S&P 500 WTI spot prices

PP

−1.50 (α) −1.12 (α)

−1.73 (β) −3.38 (β)

−57.62 (α)*** −76.76 (α)***

KPSS

−0.98 (α) −0.87 (α)

−57.62 (β)*** −76.75 (β)***

−3.14 (β) −2.79 (β)

−81.80 (α)*** −77.18 (α)***

−81.81 (β)*** −77.17 (β)***

6.16 (α)*** 8.93 (α)***

1.50 (β)*** 0.80 (β)***

0.17 (α) 0.05 (α)

0.11 (β) 0.04 (β)

Notes: All variables are in natural logs. ADF is the Augmented Dickey–Fuller test. PP is the Phillips Perron test and KPSS the Kwiatkowski–Phillips–Schmidt–Shin test. (α) indicates a model with constant and without deterministic trend, (β) indicates a model with constant and deterministic trend. *** denotes rejection of the null hypothesis at 1% significance level.

November 2013, are used in the need of our empirical effort. The time series included in our data set consist of 5713 observations of the S&P 500 index and the West Texas Intermediate (WTI) spot oil prices. The S&P 500 index, focuses on the large-cap sector of market companies, represents about 75% of the total US equities market and is the most widely accepted barometer of the US stock market. As for oil prices, the WTI, also known as Texas light sweet spot prices, is used. Both series are used in logarithmic form. It is a standard practice in the literature on cointegration modelling to test for the integration properties of the involved variables. Consequently, we examine the variables for stationarity, by applying the Dickey and Fuller (1979) unit root test (ADF), the Phillips and Perron (1988) test (PP) and the Kwiatkowski et al. (1992) stationarity test (KPSS). The results from all tests, reported in Table 1, suggest that both variables are nonstationary in levels while they turn stationary in first difference form; and thus, we can proceed with testing for cointegration. In the first step of our analysis we use the well-known ML Johansen’s (1991, 1995) cointegration technique which provides two likelihood tests for the presence of cointegrating vectors; the trace and the maximum

Table 2. Johansen cointegration test results

H0

5% Max critical eigenvalue value

HA

r = 0 r = 1 4.405154 r ≤ 1 r = 2 2.139520

Note: The critical values are calculated using the approach in MacKinnon et al. (1999).

eigenvalue tests. The estimation results, reported in Table 2, suggest that we fail to reject the null hypothesis of no cointegration between the examined variables, at the 5% significance level. However, conventional cointegration techniques such as the Johansen’s (1991, 1995) approach may lead to unreliable inference if significant structural breaks in the evolution of the investigated series are ignored. According to Miller and Ratti (2009), the occurrence of several structural breaks in the stock market history and in the oil-price evolution have resulted in a nonstable cointegration relationship between stock and oil prices. Figure 1 below,

Prices

3.0 2.5 2.0 1.5

92

94

96

98

00

5% critical value

14.26460 6.544674 15.49471 3.841466 2.139520 3.841466

3.5

1.0

Trace test

02

04

06

08

10

12

Time LSP500

LWTI

Fig. 1. Stock prices and oil-prices evolution (prices are in logarithmic form)

The relationship between oil prices and stock prices

797

Table 3. Bai–Perron test of multiple structural changes in the long-run relationship Panel A. Test statistics Sup FT(1) 7895.17*** Sup FT(2|1) 758.62***

Sup FT(2) 5374.63*** Sup FT(3|2) 1329.53***

Sup FT(3) 5694.46*** Sup FT(4|3) 1077.46***

Sup FT(4) 6151.92*** Sup FT(5|4) 434.31***

Sup FT(5) 5756.27*** Sup FT(6|5) 124.62***

Sup FT(6) 5025.69*** Sup FT(7|6) −2602.56

Sup FT(7) 0.00

Panel B. Break dates estimates T1

T2

T3

T4

T5

Τ6

7 February 1996 12 November 1998 14 August 2001 14 May 2004 27 February 2008 4 January 2011 [2 February 1996 to [11 November 1998 to [23 July 2001 to 22 [10 May 2004 to 26 [15 February 2008 [1 November 2010 to 13 February 1996] 24 November 1998] August 2001] November 2004] to 7 March 2008] 21 January 2011] Notes: The critical values are taken from Bai and Perron (1998), table II. 95% confidence intervals in brackets. *** denotes rejection of the null hypothesis at 1% significance level.

presents the evolution of the investigated time series. As we can observe, over the examined period, there are several potential structural breaks. Considering the above, we proceed with the empirical analysis by applying the Bai and Perron (1998, 2003) test which accounts for possible structural break(s) in the relationship between US stock and oil prices in levels. The results of the SupF(l + 1|l) tests, reported in Table 3, suggest six structural breaks, identified in 7 February 1996, 12 November 1998, 14 August 2001, 14 May 2004, 27 February 2008 and 4 January 2011. Then, using Stock and Watson’s (1993) DOLS, and accounting for the previously detected structural breaks, we test for cointegration. The DOLS estimates along with the ADF unit-root test on the residuals are reported in Table 4. DOLS estimation Coefficients Panel A. Long-run elasticities from DOLS LWTI 0.039159*** Constant 2.553225*** Trend 0.000126*** 0.148276*** T1 T2 0.099266*** −0.212888*** T3 −0.014297*** T4 −0.192872*** T5 T6 0.018939*** Panel B. Cointegration test for DOLS −5.335572*** Ut

t-Statistic 3.829180 210.9619 42.63092 40.40548 32.70002 −58.40718 −4.874950 −47.18932 7.457624

Notes: Ut is the innovation series obtained by dynamic ordinary least squares (DOLS) cointegration equation. Leads and lags are chosen based on Schwarz information criterion (SIC). *** denotes rejection of the null hypothesis at 1% significance level.

Table 4 and reveal a positive long-run equilibrium relationship between stock and oil prices. The estimated coefficients, which represent elasticities, imply that a 1% increase in oil prices increases stock prices by nearly 0.04%. The positive relationship between the two price series probably indicates that oil-price changes are more likely to be driven by demand-side shocks. So far, the possibility of asymmetry in the adjustment process has not been considered explicitly. In this direction, following Enders and Siklos (2001), we estimate the TAR and the MTAR models. Initially, as described in the ‘Dynamic ordinary least squares (DOLS) analysis’ section, we decompose the DOLS residuals and then we test for cointegration and asymmetry in both the TAR and MTAR specifications. In particular, we test the null hypothesis of no cointegration, H0:ρ1 ¼ ρ2 ¼ 0 and that of symmetry, H0:ρ1 ¼ ρ2 . The results, reported in Table 5, show that in both models, the null hypothesis of no cointegration can be rejected since the F-values for the TAR and MTAR models are found to be 14.48 and 17.08, respectively. Furthermore, the results from the TAR model suggest that the null hypothesis of symmetry cannot be rejected (F-statistic = 1.98). However, considering that the speed of adjustment depends on the previous period’s change (MTAR model), the results imply that the null hypothesis of a symmetric adjustment towards the long-run equilibrium could now be rejected at the 5% significance level (F-statistic = 7.15). Besides, the results from the MTAR model further reveal that the adjustment process is statistically significant only for negative deviations from the equilibrium, with the point estimate of the threshold equal to 0.0029. Since there is no presumption on the use of the TAR or the MTAR model, the recommendation is to choose the best adjustment mechanism using a

P. Rafailidis and C. Katrakilidis

798 Table 5. Tests of cointegration and symmetry (TAR and MTAR models) τ TAR model −0.0402 MTAR model 0.0029

ρ1

ρ2

ρ 1 ¼ ρ2 ¼ 0

ρ1 ¼ ρ2

Lags

AIC

SIC

−0.0080*** (0.0026)

−0.0136*** (0.0031)

14.4851***

1.9828

2

−7.18702

−7.18236

−0.0010 (0.0040)

−0.0133*** (0.0023)

17.0813***

7.1506**

2

−7.18792

−7.18326

Notes: τ represents the threshold value. ρ1 ¼ ρ2 ¼ 0 is the null hypothesis of no cointegration with critical values obtained from Enders and Siklos (2001, p. 172, Table 5). ρ1 ¼ ρ2 is the null hypothesis of symmetry in ρ1 and ρ2 . The critical values are 7.31 and 4.08 for 1% and 5% significance level, respectively. SE are in parentheses and *** and ** denote rejection of the null hypothesis at 1% and 5% significance level, respectively.

model-selection criterion such as the AIC or Schwarz information criterion. For our analysis, both criterions favoured the MTAR specification. Finally, Table 6 reports the estimates of the asymmetric error correction models described by Equation 5. Although, the Wald test suggests that the null hypothesis of symmetry cannot be rejected (p-value = 0.19), the fact that stock returns seem to respond significantly only to deviations below the threshold value implies the presence of asymmetry. Regarding the short-run dynamics, the results support a Granger type causality effect from ΔWTI to ΔS&P500 (p-value = 0.04). The lagged changes were determined for a maximum lagged order j = 12 and were sequentially reduced to comprise only the significant ones. Furthermore, the cumulative effect δj of the lagged oilprice changes on stock returns, imply that oil-price increases cause an overall negative impact on stock prices which could be explained by the increasing uncertainty regarding future oil supply-side shocks2 (Σδj = −0.036 with p-value = 0.015).

Table 6. Estimation of the asymmetric error correction Equation 5 threshold value τ = 0.0029 Δ S&P 500 Depended variable Constant β1 β2 δj Wald tests Cointegration (Η0: β1 = β2 = 0) Asymmetry (Η0: β1 = β2) Short-run causality (Η0: δj = 0)

Coefficients

Statistics

0.00012** −0.00247 −0.00771*** −0.003620***

t = 1.9728 t = −0.7138 t = −3.5712 F = −2.42892

Wc = 6.58418

p-value = 0.001

Wa = 1.68021

p-value = 0.194

Ws = 3.04519

p-value = 0.047

Notes: δj represents the cumulative effect of ΔWTItj . *** and ** denote rejection of the null hypothesis at 1% and 5% significance level, respectively. 2 

V. Conclusions In this article, we investigated the links between oil prices and stock prices over the period from 1 January 1992 to 22 November 2013. In particular, we focused on the linkages between oil and stock prices in both the long-run and short-run horizons under both the linear and nonlinear cointegration framework. The results from the conventional Johansen’s (1991, 1995) cointegration approach suggested that we cannot reject the null hypothesis of no cointegration. However, using the Bai and Perron (1998, 2003) approach, we found significant structural breaks in the relationship between US stock prices and oil prices that are likely to have distorted the results on cointegration. To cope with this, we applied the DOLS cointegration method, considering for the detected structural breaks in the form of dummy variables. The new results revealed the existence of a positive long-run relationship between the two variables implying that ignoring the presence of structural breaks, leads to spurious results. Thereafter, using the MTAR specification we found evidence of asymmetry in the adjustment process to equilibrium. The results from the respective Threshold Error Correction Model revealed that the stock returns react to oil-price changes only in deviations from the long-run equilibrium below a threshold value. Turning our analysis to the shortrun dynamics, the results were substantially different as oil-price changes were found to significantly affect stock returns though negatively. This negative response can be attributed to investors’ reaction, probably caused by precautionary demand shocks, driven by the uncertainty about future crude oil supply shortfalls; while in the long-run oil prices and stock prices may commove due to expectations regarding future economic activity and shifts in aggregate demand. The above findings could be important for further understanding the relationship between oil and stock prices and could be useful to investors and other market participants, such as, financial managers, analysts and firms in order to manage their investments and minimize their portfolio risks.

For more details see Kilian and Park (2007) and Apergis and Miller (2009); they refer to these shocks as precautionary demand shocks.

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