Instabilities in the relationships and hedging strategies between crude oil and US stock markets: Do long memory and asymmetry matter?

Accepted Manuscript Title: Instabilities in the relationships and hedging strategies between crude oil and US stock markets: Do long memory and asymmetry matter? Author: Walid Chkili Chaker Aloui Duc Khuong Nguyen PII: DOI: Reference:

S1042-4431(14)00114-0 http://dx.doi.org/doi:10.1016/j.intfin.2014.09.003 INTFIN 732

To appear in:

Int. Fin. Markets, Inst. and Money

Received date: Accepted date:

26-3-2014 13-9-2014

Please cite this article as: Chkili, Walid, Aloui, Chaker, Nguyen, Duc Khuong, Instabilities in the relationships and hedging strategies between crude oil and US stock markets: Do long memory and asymmetry matter?.Journal of International Financial Markets, Institutions and Money http://dx.doi.org/10.1016/j.intfin.2014.09.003 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Instabilities in the relationships and hedging strategies between crude oil and US stock markets: do long memory and asymmetry matter? Walid Chkilia,b, Chaker Alouic, and Duc Khuong Nguyend,* a

International Finance Group, Tunisia Faculty of Economic Sciences and Management of Mahdia, University of Monastir, Tunisia c College of Business Administration, King Saud University, Riyadh, Kingdom of Saudi Arabia d IPAG Lab, IPAG Business School, France b

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DCC-FIAPARCH model is used to examine the oil-stock market relationships. Long memory and asymmetric behavior characterize the conditional volatility of returns. Conditional correlations are affected by several economic and geopolitical events. An optimal oil-stock portfolio for US investors should have more than 80% of stocks Lower hedging costs are found when the DCC-FIAPARCH model is used.

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Highlights

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Abstract

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This article uses the DCC-FIAPARCH model to examine the time-varying properties of conditional return and volatility of crude oil and US stock markets as well as their dynamic correlations over the period 1988-2013. Our results indicate that both the long memory and asymmetric behavior characterize the conditional volatility of oil and stock market returns. On the other hand, the dynamic conditional correlations (DCC) between the crude oil and US stock markets are affected by several economic and geopolitical events. When looking at the optimal design of an oil-stock portfolio, we find that investors in the US markets should have more stocks than crude oil asset in order to reduce their portfolio risk. Finally, the use of the DCC-FIAPARCH model that explicitly accounts for long memory and asymmetric volatility effects enables the investors to effectively hedge the risk of their stock portfolios with lower costs, compared to the standard DCC-GARCH model.

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JEL classification: C58, G1, G15, Q43 Keywords: asymmetric volatility, long memory, crude oil, stock returns, hedging strategy.

Abstract

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This article uses the DCC-FIAPARCH model to examine the time-varying properties of conditional return and volatility of crude oil and US stock markets as well as their dynamic correlations over the period 1988-2013. Our results indicate that both the long memory and asymmetric behavior characterize the conditional volatility of oil and stock market returns. On the other hand, the dynamic conditional correlations (DCC) between the crude oil and US stock markets are affected by several economic and geopolitical events. When looking at the optimal design of an oil-stock portfolio, we find that investors in the US markets should have more stocks than crude oil *

Corresponding author: 184 Boulevard Saint-Germain, 75006 Paris, France. Phone: +33 (0)1 53 63 36 00 - Fax: +33 (0)1 45 44 40 46. Email addresses: Walid Chkili ([email protected]), Chaker Aloui ([email protected]), and Duc Khuong Nguyen ([email protected])

asset in order to reduce their portfolio risk. Finally, the use of the DCC-FIAPARCH model that explicitly accounts for long memory and asymmetric volatility effects enables the investors to effectively hedge the risk of their stock portfolios with lower costs, compared to the standard DCC-GARCH model. JEL classification: C58, G1, G15, Q43 Keywords: asymmetric volatility, long memory, crude oil, stock returns, hedging strategy.

1. Introduction

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Research devoted to volatility spillovers and dynamic correlations between crude oil (CO) and stock markets has recently attracted a particular attention from academics and practitioners, especially fol-

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lowing recent heightened fluctuations in crude oil and stock prices. The context of macroeconomic

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and geopolitical uncertainty, and economic and financial crises contributes significantly to these price tendencies in both markets. Recent statistics show that international nominal prices of all major energy

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commodities reached their highest levels in nearly 50 years during the first quarter of 2008, while the

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prices in real terms were the highest in nearly 30 years. These unprecedented increases in oil prices,

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coupled with substantial increases in volatility, reflect uncertain markets and volatile environment.

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The theory predicts the interactions between CO and stock markets by the impact of crude oil

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prices on the present value of a firm’s expected future cash-flows. Indeed, oil price increases can lead

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to higher production cost and thus lower expected cash-flows which in turn depress the firm’s share price. On the one hand, rising oil prices can result in higher consumer price index (inflation) which

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often requires central banks to raise interest rates in order to stabilize the price level and thereby in-

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creases the discount rate used in the stock pricing models. The increase in the discount rate then causes the reduction in the firm’s market value and, all other things being equal, the decrease in stock prices.

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Chang et al. (2010) analyze the impact of CO volatility shocks on stock prices via expected cashflows, the discount rate and the equity pricing model, and assess that the direction of the stock price effect depends on whether the firm under consideration is a producer or a consumer of oil and oilrelated products. The oil prices can also influence stock prices via their effects on company’s operating costs and household’s income. For example, higher energy costs may lead to lower oil usage and

decreases in the productivity of capital and labor (Hamilton, 1983). Equally, higher costs of imported oil would reduce the disposable income of the household (Chang et al., 2013), which has a negative effect on stock investment. Finally, from the demand side, oil prices movements may directly affect the consumer’s discretionary spending on durable goods, which would, in turn, cause changes in corporate earnings and consequently stock prices (Gogineni, 2010). This indirect relationship between consumers’ discretionary spending and stock prices can be explained by the fact that consumers tend to purchase durable goods only after they pay their energy bills (Kilian, 2009). For instance, Edelstein and Kilian (2009) show that, in the United States, the actual share of energy in consumer expenditures

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fluctuates between 4% and 10%. Accordingly, the discretionary spending effect will be large if the

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elasticity of the demand for oil (and energy in general) is low.

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The relationships between CO and stock markets have also been the headlines of prestigious financial newspapers such as Financial Times and Wall Street Journal. On August 21, 2006, the Finan-

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cial Times reported for example that U.S. stock prices declined due to an increase in oil prices caused

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by geopolitical risk in the Middle East (including the Iranian nuclear program and terrorist attacks by

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Islamic militants). The Wall Street Journal on March 31, 2013 reported that “the close ties between

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daily movements of commodities and stock markets, which have persisted mostly uninterrupted since

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the financial crisis, have frayed.” It is also noted that the daily correlation between the S&P 500 and

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the S&P GSCI commodities indices has fallen to the lowest level since October 2008. This stylized fact may signal the end of the crisis and associated recession period or a new dynamical phase for

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these markets.

Past studies in the related literature have provided insightful information about the links be-

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tween CO and stock markets (e.g., Jones and Kaul, 1996; Ewing and Thompson, 2007; Driesprong et

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al., 2008; Park and Ratti, 2008; Aloui and Jammazi, 2009; Arouri et al., 2011; Aloui et al., 2012). The majority of these studies generally show that stock price changes can be explained by the movements in the price of oil, but the CO effects typically depend upon the nature of firms, economic sector and market with respect to their dependence on crude oil and oil-related products. Exogenous factors such as macroeconomic conditions, business cycle, geopolitical tensions, and OPEC production quotas have also been found to exert important influences on the behavior of both CO and stock prices.

This article aims to analyze the time-varying interdependence between the CO prices and US stock markets and to discern this interdependence between the bullish and bearish phases in the US economy. For this purpose, we empirically rely on the use of the DCC-FIAPARCH model which al-

lows for capturing the dynamic market linkages through the dynamic conditional correlations (DCC) as well as asymmetric effects and long memory property in the conditional volatility processes. Past studies such as Aloui and Mabrouk (2010), Christensen et al. (2010), and Chkili et al. (2014) have shown that long memory and asymmetry properties are important stylized facts which need to be accounted for when modeling and forecasting the conditional volatility of both stock and commodity

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markets. Moreover, the link between oil and stock markets can greatly differ across market states ow-

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ing to different economic conditions. Under the extreme market state, for example, this link may be severely affected by, in addition to the oil supply and demand shocks, other factors including strong

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herding, differential market power and excessive price regulations imposed by governments (Aloui et

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al., 2013).

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In this way, our study contributes to the related literature in several aspects. First, we investigate

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the dynamic linkage between the CO and US stock markets over a relatively long period from 1988 to

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2013. This period is characterized by the occurrence of successive crises and turbulent episodes including, among others, several geopolitical tensions and social unrest (e.g., the Iraq evasion on 1991,

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the US military intervention in Iraq in 2003, the Arab Spring in 2010), the Mexican crisis in 1994, the Asian financial crisis 1997-1998, the Russian and Brazilian crises 1998-1999, the September 11, 2001

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terrorist attacks, and the last global financial crisis 2007-2009. These events have significant effects on the dynamics of CO and stock prices and may therefore influence their underlying relationships.

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Second, while the interactions between CO and stock markets have been extensively examined in re-

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cent years, none of the previous studies have explicitly accounted for the impacts of the long memory (LM) and volatility asymmetry on these cross-market interactions. Finally, we use the empirical results obtained from our bivariate LM-based model to build optimal and hedged portfolios of stocks that immunize against the oil risk. Using daily price data from January 1988 to April 2013 for the S& P500 index and the two CO

benchmarks (the West Texas Intermediate, and Brent), we mainly find that the DCC-FIAPARCH suc-

cessfully captures the dynamic relationships between the CO and US stock markets. The DCC between the oil and stock markets is found to exhibit shift behavior and significantly affected by major economic and geopolitical extreme events. In addition, from a portfolio management perspective, we uncover that American investors should take more stocks than oil in their investments in order to reduce their portfolio risk and that hedging with Brent oil is slightly more effective than with WTI oil. The rest of this article is organized as follows. Section 2 offers a short overview of the major studies in the related literature. Section 3 introduces the econometric methodology. Section 4 describes the data and their properties. Section 5 reports and discusses the empirical results. Section 6 provides

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some concluding remarks.

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2. Short overview of the literature

There is now an important literature on the issues of shock transmission and volatility spillovers be-

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tween commodity and equity markets, using various datasets and different econometric methods (e.g.,

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Malik and Hammoudeh, 2007; Choi and Hammoudeh, 2010; Arouri et al. 2011, 2012; Vo, 2011, Zhu

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et al. 2011; Jammazi, 2012; Naifar and Al Dohaiman, 2013; Jouini, 2013; Chang et al., 2013; Mensi et

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al. 2013). This growing literature has generally documented significant interactions of return and vola-

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tility between CO and stock markets, but the strength of these interactions typically depends on the

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oil-dependence profiles of the markets under consideration. To start, Jones and Kaul (1996) point out the negative reaction of US, Canadian, UK and Japan

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stock prices to CO price volatility shocks through the effect of oil prices on real cash flows. By using linear and nonlinear causality tests, Ciner (2001) finds significant nonlinear interactions between CO

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prices and real stock market returns. Hammoudeh and Aleisa (2002) provide evidence of volatility

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spillovers between CO markets and stock market indices for oil-exporting countries. Quite similar findings are provided by Driesprong et al. (2008) who document a strong connection between stock market and CO prices. Aloui et al. (2008) analyze the volatility spillovers between WTI (West Intermediate Texas) and Brent oil prices and the major six stock markets using the cross correlation functions suggested by Cheung and Ng (1996). Their findings indicate that oil price volatility has, in gen-

eral, a negative impact on stock market behavior. Also, some asymmetry and persistence on oil price volatility have been detected. Several studies have used vector autoregressive (VAR) and multivariate GARCH models to examine the shock transmission and volatility spillovers between oil and stock markets. For instance, Kaneko and Lee (1995) show that changes in oil prices significantly explain the Japanese stock market returns. Huang et al. (1996) find strong causality running from oil futures prices to stock returns of individual firms, but not to aggregate market returns. Using monthly data, Sadorsky (1999) shows that positive shocks to oil prices depress real stock returns. In addition, the results from the impulse func-

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tion reveal that oil price movements are important in explaining movements in stock returns. Arouri et

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al. (2011) use a generalized VAR-GARCH model to investigate the volatility transmission between oil

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and stock markets in Europe and the United States at the sector level. Their results indicate the existence of strong volatility spillover between oil and sector stock returns. However, the spillover is

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usually unidirectional from oil markets to stock markets in Europe, but bidirectional in the United

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States. In addition, they show that the VAR-GARCH model provides better results in terms of hedging

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strategies than commonly-used multivariate volatility models. Similar results are found in Jouini

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(2013) for the case of Saudi Arabia.

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More recently, Mensi et al. (2013) employ the VAR-GARCH model to research the return rela-

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tionship and volatility spillovers between major international commodity prices and S&P500 index. For energy commodities, the authors find that the past shocks and volatility of the S&P500 strongly

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affect the oil and gold markets. Furthermore, they provide evidence that the highest conditional correlations are obtained between S&P500 and gold and S&P500 and WTI. Similarly, Chang et al. (2013)

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investigate the dynamic correlation and the volatility spillovers between oil and stock market indices

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using various multivariate GARCH models such as CCC-GARCH, VARMA-GARCH, and VARMAAGARCH models. These authors find evidence of time-varying oil-stock market co-movements and some asymmetric volatility effects from the VARMA-AGARCH model. Mollick and Assefa (2013) use a DCC-MGARCH model to investigate at the stability of the stock-oil relationship in the United States given the onset of the recent financial crisis. They show that stock returns are slightly (negative-

ly) affected by oil prices and by the USD/EUR exchange rate over the pre-crisis period. From mid2009 onwards, however, stock returns are positively affected by oil prices. Differently, Zhu et al. (2011) employ a panel threshold cointegration approach to investigate the links between CO prices and stock markets for a sample of OECD and non-OECD countries. They reveal the presence of asymmetric dynamic adjustment between the two markets in the long-run. Accordingly, the speed of adjustment towards equilibrium is faster under negative changes in the deviation than under positive ones. Vo (2011) shows, from a multivariate stochastic volatility structure, that stocks and oil futures returns are interrelated and that their correlation follows a time-varying dynamic

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process and tends to increase when the markets are more volatile. Furthermore, Vo (2011) finds evi-

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dence of cross-market dependence in the volatility. Other studies have used the Markov switching

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regime model to investigate shifts behavior in the relationship between oil prices and stock returns (Aloui and Jammazi, 2009; Choi and Hammoudeh, 2010; Bhar and Hammoudeh, 2011; Jammazi,

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2012; Naifar and Al Dohaiman, 2013). For example, Aloui and Jammazi (2009) employ the Markov-

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switching EGARCH to study volatility spillovers between CO prices, interest rates and stock returns

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for some major developed economies. They find that rises in oil prices have a significant role in de-

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termining both the volatility of stock returns and the probability of transition across regimes. Choi and

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Hammoudeh (2010) investigate the regime-switching behavior in the relationship between oil prices

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(WTI and Brent) and the S&P500 index, and show the existence of regimes in the energy commodity and stock markets. It is also found that the WTI oil prices are more sensitive to regime switching then

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the Brent oil prices. Naifar and Al Dohaiman (2013) focus on the nonlinear relationship between CO prices, macroeconomic activity and stock returns in the Gulf Cooperation Council (GCC) countries.

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They document, from a two-state Markov-switching model and several Archimedean copulas, evi-

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dence of regime-switching behavior for the variables under consideration. Finally, some previous studies have employed the conditional multifactor asset pricing model to

establish an association between oil prices and stock market returns (e.g., Basher and Sadorsky, 2006; Mohanty et al., 2011; Aloui et al., 2012 and references therein). For example, Mohanty et al. (2011) employ a two-factor model to assess the relationship between changes in CO prices and equity returns in the GCC countries using country-level and industry-level stock return data. They provide strong

evidence that oil price changes have asymmetric effects on stock market returns. Aloui et al. (2012) use a three-factor model including the oil risk to study the effects of oil price shocks on stock market returns for three groups of emerging countries: the largest net-oil importing countries, the moderately oil-dependent countries, and the largest net-oil exporting countries. Their empirical results based on an analysis of long-term correlation and a conditional multifactor pricing model show that the oil risk is significantly priced in emerging markets, and that the oil impact is asymmetric with respect to market phases. Our present study enriches the related literature in that we examine the dynamic links between

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the United States’ stock market and two global crude oil markets, while taking both volatility asymme-

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try and long memory into account. In addition to the analysis of optimal portfolio designs and hedging

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effectiveness, it also looks explicitly at the potential shift in behavior of the oil-stock dynamic linkages

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with respect to five major geopolitical events and financial crises.

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2. Empirical framework

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We use a multivariate GARCH-type model to investigate the dynamic relationships between the CO

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and the US stock markets. Past studies such as Arouri et al. (2011) and Chang et al. (2013) show that

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this class of models is flexible enough to gauge the cross-market interactions. Our approach differs

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from the previous studies in that we attempt to incorporate the LM and asymmetric effects into the conditional volatility process and explore these features on portfolio management involving crude oil

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asset and stocks. We also use the Student-t distributions at the estimation stage to accommodate the leptokurtic behavior of return series.

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Tse (1998) proposes the fractional integrated asymmetric power ARCH (FIAPARCH) model as

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an extension of the standard GARCH model. This model simultaneously accommodates not only volatility clustering, but also the long memory property and asymmetric effects in the conditional volatility. Formally, the FIAPARCH(1,d,1) can takes the following form

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 t  1  L  1  1  L 1  L1  L   t   t  1

1

d



(1)

where ω˃0, δ>0, λ<1, β˂1 and -1<γ<1. L is the lag operator. As stressed above, this model introduces the asymmetric reaction of conditional variance to chocks. More precisely, if γ>0, negative shocks will generate more volatility than positive shocks of equal magnitude. The parameter d, 0  d  1 , measures the long range-memory in the conditional volatility. Formally, the FIAPARCH model reduces to the FIGARCH model when δ = 2 and γ = 0, while it becomes an APARCH model when d = 0. Given our objective in this article, a multivariate dynamic conditional correlation FIAPARCH model (DCC-FIAPARCH) which combines the FIAPARCH and the DCC process of Tse and Tsui (2002) is a suitable empirical specification. Conrad et al (2011) has analyzed the applicability of the

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multivariate constant conditional correlation (CCC) version of this model and find that it is generally

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applicable when financial time series exhibit power, leverage and long-memory effects. The DCC

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version of this model has been used by Dimitriou et al. (2013) to investigate the contagion effects between the BRICS (Brazil, Russia, India, China and South Africa) and the US stock markets around the

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(2)

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 H t  Dt Rt Dt  1/ 2 1/ 2  Dt  diag h11t ...hNNt   R  1     R      R 1 2 1 t 1 2 t 1  t

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recent global financial crisis. The multivariate conditional variance-covariance matrix is given by

The conditional variance hiit can follow any univariate GARCH-class model. In our study, it is

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modeled by the univariate FIAPARCH (1,d,1) model. R is a (N×N) symmetric matrix of dynamic con-

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ditional correlations (DCC) with ρii = 1. θ1 and θ2 are non-negative parameters and they satisfy the

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condition that the sum of the two parameters is less than unity. Ψt-1 is the (N×N) correlation matrix of ɛτ, for τ = t – M, t – M+1,…, t – 1, with the (i,j)th element given by M

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 ij ,t 1 



 m  1 u i ,t  m u j ,t  m

M m 1

u i2,t  m  hM1 u 2j ,t  m 

(3)

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where uit   it / hiit and ɛt is the vector of residuals from the conditional mean equation. Indeed, the Ψt-1 can be presented as follows:

t 1  Bt11Lt 1 L't 1 Bt11

(4)

where Bt 1 is a (N×N) diagonal matrix with ith diagonal element given by ( hM1 u 2 )1 / 2 and Lt-1 is a i ,t  h (N×N) matrix expressed as ut1 ,...,utM  with ut  uit , u2t ,..., uNt  . With respect to Eq. (4), the non'

negativity of Ψt-1 and therefore Rt require that M ≥ N. In our case, N is equal to 2 (bivariate model). Finally, the dynamic correlation coefficient in a bivariate case can be defined as follows: M

12 ,t  1  1   2  12   2  12,t 1  1

 u u  u  m 1

1,t  m

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2 m 1 1,t  m

2 ,t  m M h 1

u 22,t  m



(5)

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where m (m = 1, 2,…, M) refers to the time lag (Bauwens et al., 2006).

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3. Data

We use daily spot closing prices for the US stock market index (S&P500) and two global crude oil

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markets (Brent and WTI). While both prices are the leading global price benchmarks for international

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oil trading, the Brent oil price is currently used to price two thirds of the world’s internationally traded

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crude oil supplies. As shown in Table 1, these two price benchmarks differ in terms of unconditional

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risk-return trade-off (i.e., the Brent oil has greater return and lower volatility than WTI oil) and of

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unconditional correlation with the S&P500 market index (i.e., the Brent oil has lower correlation with S&P500 than the WTI oil). In a recent paper that focuses on the weak-form efficiency of the Brent and

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WTI crude oil markets over the period from May 20, 1987 to March 6, 2012, Mensi et al. (2012) find that the efficiency of the two oil markets varies over time, but exhibits different time trends. In par-

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ticular, the WTI market is found to be less efficient than the Europe Brent market. This result is also consistent with the evidence provided in Charles and Darné (2009). Thus, considering both crude oil

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markets will permit a thorough analysis of the oil-stock market relationships in the United States and

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provide valuable insights for commodity portfolio investors, hedgers and policymakers. We obtain the stock market indices from the Datastream International. The CO price data are

extracted from the US Energy Information Administration database. Our study period spans from January 4, 1988 to April 30, 2013, yielding 6,306 daily observations. We compute the daily percentage returns by taking the difference in the natural logarithm of two consecutive prices, multiplied by 100.

Table 1 shows the summary descriptive statistics for the daily returns of the S&P500 index and the two selected CO price indices. Panel A shows that the daily average returns are positive for all the series and range from 0.0263% (WTI) to 0.0290% (S&P500). While the crude oil markets realized relatively similar returns as the US stock market, their volatility as measured by the standard deviation nearly doubled the volatility level of the US market. The values of the skewness and kurtosis coefficients indicate that the probability distributions of both the stock and crude oil returns are skewed to the left and have fatter tails than corresponding normal distributions. This departure from normality is confirmed by the Jarque-Bera test. The Ljung-Box test for autocorrelation applied to the squared re-

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turns at 10 lags shows that the squared returns are serially correlated. The Engle (1982) test uncovers

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the presence of ARCH effects, which thus justifies our choice of GARCH models type for modeling

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the conditional volatility.

Panel B reports the results of some conventional tests that examine the stationarity of return se-

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ries. We see that the Augmented Dickey-Fuller (ADF) test rejects the null hypothesis of a unit root at

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the 1% level, while the KPSS test cannot reject the null hypothesis of stationarity at 1% level. As in

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Arouri et al. (2011), we also employ the Zivot and Andrews (1992)’s unit root test to check whether

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the results provided by the ADF and KPSS tests are robust to the occurrence of a potential structural

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break in the data generating processes. As it can be seen, the Zivot-Andrews test confirms the findings

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of the ADF and KPSS tests in that return series are stationary at conventional levels, and therefore

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they can be used in further statistical analysis

Panel C reports the unconditional correlations between the US and crude oil markets over the

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study period. These correlations are positive but generally low (0.036 between the US and Brent mar-

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kets, and 0.086 between the US and WTI markets). These findings suggest that the US investors may achieve portfolio diversification benefit by allocating some of their funds to the crude oil futures markets, which is expected to be higher for the Brent oil. We investigate this issue in a more careful manner in subsection 5.4 as the unconditional correlations may not be relevant in business decision making owing to their inability to take the market conditions into account.

Figure 1 displays the price series (left panel) and returns (right panel) for the markets under consideration. We observe that the two CO prices experienced a continuously increasing trend over the study period except the sharp declines during the recent global financial crisis 2008-2009. The two CO markets achieved their highest values in 2008, which are followed by a break point in mid-2008, owing to the effects of the global financial crisis. The US stock market index also experienced an increasing movement with two important bearish phases. The first phase occurred in the aftermath of the terrorist attack of September 11, 2001, and the second after the advent of the subprime crisis. Regarding the return series, the graphs show that volatility clustering is definitively present for

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all the series, i.e., large (small) changes are followed by large (small) changes of either sign. This fea-

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ture reveals the presence of ARCH effects. In particular, the time-paths of crude oil returns testify the

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presence of an important change in 1991, which coincides with the aerial bombardment on 17 January

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1991 by the coalition forces to expel Iraqi troops from Kuwait.

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4. Results and interpretations

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4.1 Long memory tests

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We start our analysis by testing the presence of long memory in the conditional variance of return

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series. For this purpose, we apply the two commonly-used long memory (LM) tests, the log periodo-

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gram regression (GPH) test of Geweke and Porter-Hudak (1983) and the Gaussian semiparametric (GSP) test of Robinson (1995), to absolute and squared returns. These tests have been used by several

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studies in the literature focusing on stock and/or energy markets (Choi and Hammoudeh, 2009; Arouri et al., 2012; Aloui and Mabrouk, 2011; Mabrouk and Saadi, 2012; and Chkili et al., 2012).

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The results of the two LM tests are reported in Table 2.1 The null hypothesis of no long-range

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memory for the stock and CO market (absolute and squared) returns is clearly rejected at the 1% significance level whatever the test used. We also report in Table 2 the rescaled variance test of Giraitis et al. (2003), applied to both squared and absolute returns. The results of this test confirm those provided by the GPH and GSP tests. Taken together, these findings suggest the presence of long memory effects

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The selected bandwidths (m) are based on previous studies (see, e.g. Dimitriou et al., 2013; Chkili et al., 2012; Mabrouk and Saadi, 2012; Aloui, 2011; Aloui and Mabrouk, 2011).

for both the US stock market and the crude oil markets, which need to be accounted for when modeling their conditional volatility. Notes: m denotes the bandwidth for the Geweke and Porter-Hudak (1983) (GPH) test, the Gaussian semiparametric (GSP) test of Robinson (1995) and the rescaled variance test. The values in parentheses are standard errors. T is the sample size. ** denotes the statistical significance at the 1% level.

4.2 Stock-oil market relationships We estimate the bivariate DCC-FIAPARCH model to explore the dynamic return relationships between the US stock market and each of the two crude oil markets (Brent and WTI).2 As stated earlier, this model offers the flexibility to straightforwardly infer the dynamic conditional correlations be-

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tween the two markets in the bivariate system, while explicitly accounting for the long memory and

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asymmetric volatility effects in their respective volatility processes. Moreover, to the extent that we consider the instable period of 1988-2013 which covers a number of important economic, social, polit-

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ical and geopolitical events, we are also able to investigate the underlying impact of such events on the

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dynamic links between the stock and oil markets.

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We report the estimation results in Table 3. When looking at the variance equation parameters,

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we see that the fractional differencing parameters (d) are highly significant in all cases, thus confirm-

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ing the evidence of long memory in the conditional volatility provided by the LM tests in subsection 4.1. More interestingly, the estimate values of the long memory parameters are similar across the stock

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and crude oil markets we consider. The corresponding LM coefficients are 0.339 and 0.449 for the

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S&P500-Brent pair and 0.339 and 0.417 for the S&P500-WTI pair.

The estimates of the ARCH and the GARCH coefficients in the DCC-FIAPARCH setting are

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highly significant at the conventional levels for all the markets. The power term (δ) is positive and also highly significant. Moreover, there is also evidence of asymmetric volatility effects in two out of the

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three markets (US stock market and Brent oil market) as the estimated value of the  coefficient is positive and significant at the conventional levels. It means that negative shocks have greater impacts 2

It is worth noting that as a preliminary analysis, we estimate the univariate GARCH, FIGARCH, FIAPARCH models with Student-t distributions for the US stock and crude oil markets. Our results, which can be made entirely available upon request to the corresponding author, show that the FIAPARCH model outperforms the GARCH and FIAPARCH models under the Student-t distribution, regardless of the series under consideration, with respect to the likelihood function values and the two information criteria (AIC and BIC). The same results are obtained for the case of bivariate models when we compare the performance of the bivariate DCC-GARCH, DCC-FIGARCH and DCC-FIAPARCH. The interested readers can refer to Chkili et al. (2014) for more details on the forecasting ability of the FIAPARCH model.

on volatility than positive shocks of the same magnitude. These findings thus indicate that our empirical model is suitable and flexible enough to accommodate the most important stylized facts of stock and crude oil market returns including the volatility clustering, long memory and asymmetric volatility. Note finally the appropriateness of the Student-t distribution in volatility modeling because the Student-t degrees of freedom parameters are significant in all cases. The average conditional correlations (ρ) are positive and highly significant for the two empirical specifications. These coefficients, 0.091 for the S&P500-Brent pair and 0.207 for the S&P500/WTI pair, are substantially higher than the unconditional correlations reported in Table 1. The cross-market

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linkage is greater for the S&P500/WTI pair because the WTI crude oil prices are the benchmark prices

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for the US oil and they are the main driver in the valuation of the US oil companies. According to

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these results, while there is still room for portfolio diversification by adding the oil asset into the portfolios of stocks, the expected benefits are smaller. Arouri et al. (2011) also find a significant correla-

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tion between the S&P’s 500 index and the Brent oil index from a VAR(1)-CCC-GARCH(1,1). How-

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ever, their model does not allow the conditional correlation to change through time.

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Figure 2 illustrates the evolution of the DCC estimates between the US stock market and CO

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markets over time. Some important facts can be observed from these dynamics. First, the behavior of

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the two DCC series is relatively similar, suggesting the US stock market has the same co-movement

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with the Brent and WTI crude oil markets. Second, the dynamic conditional correlations between the stock and crude oil markets fluctuate widely over the study period and typically vary between -0.349

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and 0.486 for the S&P500-Brent pair and between -0.462 and 0.655 for the S&P500-WTI pair. These variations seem to be explained by the major economic, financial and geopolitical events. Indeed, they

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are low when international economies entered into crisis and recession periods such as the 1990-1991

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second Gulf war, the 1997-1998 Asian financial crisis, the Russian and Brazilian economic crises between 1998 and 1999, the terrorist attacks of September 11, 2001, the US subprime crisis between 2007 and mid-2008, the European debt crisis, and the Arab wave of social and political unrest. The linkages between the US stock market and international crude oil markets generally increased since the late 2008, following signs of economic recovering. These findings suggest that a deeper analysis of

the DCC behavior is essential to better understand the volatility spillovers between the oil and US markets over time. 4.3 The DCC behavior around geopolitical and financial crisis Economic turbulences and financial crises have a significant impact on the dynamic interactions between different types of markets. Chkili et al. (2011) reveal that volatility spillovers between foreign exchange and stock markets are higher during crisis periods than during normal times. In a related study, Aloui and Jammazi (2009) find similar results for the dynamic relationship between oil price changes and stock market volatility. They suggest that financial crises and geopolitical events play a

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significant role in explaining the relationship between the oil and stock markets. For this purpose, we

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attempt to explicitly explain the potential shift behavior of the DCCs between the US stock market and

thus specify the dynamics of the DCC over time as follows: K k 1

(6)

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p 1

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P

 ij ,t  c 0   p  ij ,t  p   k dummyk ,t   ij ,t

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the two crude oil markets with respect to major geopolitical events and financial crisis periods. We

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where ρij is the pairwise conditional correlation between the US stock and CO markets which is in-

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ferred from the DCC-FIAPARCH models. In this specification, i denotes the US stock market while j denotes the Brent or WTI crude oil market. The dummy variables, which reflect the geopolitical ten-

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sion and crisis periods, take the value of one during the crisis period and zero otherwise. We consider five important financial and geopolitical events that affect both stock and CO markets: the 1991 Iraq

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invasion, the 1997-1998 Asian financial crisis, the 1998-1999 Brazilian and Russian crises, the September 11, 2001 terrorist attacks and the 2007-2009 US subprime and global financial crisis.3

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To the extent that the DCCs exhibit ARCH effects in their variance process, a GARCH(1,1)

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model is used to specify the conditional variance equation.4 Following Chiang et al. (2007), we also introduce the crisis dummy variables to capture any structural changes as follows

3

The choice of these five episodes is based on two main observations. First, several previous studies suggest that these events significantly affected the stock markets (e.g., Vivian, 2006; Dufrénot et al., 2011, Bianconi et al., 2013) and CO markets (e.g., Ewing and Malik, 2010; Vivian and Wohar, 2012; Salisu and Fasanya, 2013). Second, as shown in Figure 4, both stock and CO markets have responded to these geopolitical tensions, and economic and financial events. 4 The results regarding the ARCH tests applied to the DCC series can be made entirely available upon request to the corresponding author.

K

hij ,t   0   1 hij ,t 1   2  ij2,t 1    k dummy k ,t

(7)

k 1

The geopolitical tension and crisis periods are defined in Table 4. We report the estimation results of Eqs. (6)-(7) in Table 5. We globally find evidence of significant effects of geopolitical tensions and economic and financial events on the mean and variance of the DCC coefficients between the US stock market and each of the crude oil market, but the effects are more pronounced in the case of the variance. More precisely, shifts in the average dynamic correlations occurred over the periods of the first Gulf war, the September 11 terrorist attack and the recent US subprime and global financial

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crisis. While the first events led to lower the average oil-stock dynamic correlations, the third event

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contributed to increase the average oil-stock dynamic correlations. These results are expected given that the first Gulf war severely perturbed the US economy due to its strong relations with the Gulf

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region in terms of oil imports and that the unexpected September 11 terrorist attack paralyzed the US

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industrial activity.

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It is also worth noting that the S&P500-Brent market linkages are not significantly affected by the September 11 terrorist attack, which can be explained by the global nature of the Brent market.

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Mollik and Assefa (2013) find similar results for the links between the CO and US stock markets over

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the period 2008-2009. The economic and financial crises in Southeast Asia, Brazil and Russia have no

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significant effects on the relationship between the US stock markets and the two crude oil markets. Regarding the variance equations, the coefficients associated with the dummy variables are negative

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and significant in all cases, suggesting that the volatility of the oil-US stock market linkages is reduced

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during the geopolitical tension and crisis periods. This finding can be explained by the lower economic activity at both local and global levels. Overall, our findings confirm those of Choi and Hammoudeh (2010) in the sense that the links between crude oil and S&P500 equity markets vary through time and are sensitive to major global economic and geopolitical events. As the Brent oil market is more global than the WTI one, its links with the US stock markets are less affected by local and regional events such as the Asian financial

crisis. Policymakers and portfolio managers can, therefore, adopt appropriate actions to optimize respectively their crude oil policy and portfolio allocation decisions. 4.4 Portfolio management and risk hedging implications Our results reported in previous sections show that appropriate models of the oil-stock market relationships in the United States need to account for asymmetric volatility effects and long memory. The use of these models thus has practical implications on portfolio management as they may help in producing better asset allocations. This section shows how optimal weights and hedge ratios can be estimated from our proposed DCC-FIAPARCH model. We also consider the standard DCC-GARCH

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model for comparison purpose.

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More precisely, we determine the optimal weights of a two-asset portfolio held by an investor

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whose objective is to minimize the portfolio risk without lowering the portfolio returns. In our case, we consider a portfolio composed of an oil asset (WTI or Brent) and the S&P index that represents a

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synthetic asset of the US stock markets, and compute the optimal weight of the crude oil asset as fol-

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h22,t  h12,t h11,t  2h12,t  h22,t

(8)

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w12,t 

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lows (Kroner and Ng, 1998):

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with w12 ,t

 0 if w12 ,t  0     w12,t if 0  w12,t  1  1 if w  1  12 ,t  

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The weight of the S&P500 market index in the considered portfolio is equal to (1-w12,t). h12,t is the conditional covariance between crude oil and stock market returns. h11,t and h22,t are, respectively,

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the conditional volatility of crude oil market and stock markets at time t. The reduction of the portfolio’s overall risk after the inclusion of crude oil asset means that the investor can improve the risk-

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adjusted return of the diversified (oil-stock) portfolio. We also compute the optimal hedge ratio as it shows whether the inclusion of the oil asset in the portfolio of stocks can provide a hedge against the investment risk in stock markets. We typically seek the dollar amount of the short position taken in the crude oil market  12 ,t in order to minimize the

risk of a long position of one dollar invested in the stock market. Following Kroner and Sultan (1993), we obtain the dynamic hedge ratio as follows

12,t 

h12,t h22,t

(9)

As shown in Ku et al. (2007) and Arouri et al. (2011), the hedging effectiveness (HE) index can be evaluated by analyzing the realized hedging errors. The higher the HE index, the greater the hedging effectiveness in terms of portfolio risk reduction. In our case, the HE index is given by

 Varunhedged  Varhedged  HE    Varunhedged  

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(10)

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where Varhedged refers to the variance of the stock-CO portfolio with optimal weights and Varunhedged

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denotes the variance of the unhedged portfolio which is composed of only stocks. These variances are obtained from the DCC-FIAPARCH and DCC-GARCH models.

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Table 6 reports the average values of the optimal weight of the oil asset, the hedge ratios and the

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HE index based on the DCC-FIAPARCH and DCC-GARCH estimations. We see that the optimal

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weights vary from 15.88% for the WTI to 18.23% for the Brent. This suggests that the optimal holding

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of Brent in a one dollar oil-stock index portfolio is 18.23% while the remaining wealth of 84.12%

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should be invested in the US stock market. Similarly, for the portfolio of the WTI and stock market

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index, the optimal investment weights are 15.88% and 84.12%, respectively. The US investors thus obtain diversification benefits by holding more stocks than oil in their portfolios as they can reduce the

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risk of their portfolio without affecting the expected return. Arouri et al. (2011) find a quite similar

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result when looking at the volatility transmission between oil and sector stock markets in Europe and the United States, based on several multivariate GARCH models (VAR-GARCH, BEKK-GARCH,

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DCC-GARCH and CCC-GARCH).

The average values of the hedge ratios derived from the DCC-FIAPARCH model are low in all cases suggesting the potential of hedging strategies concerning oil and stock markets. For the BrentS&P500 index portfolio, a hedge ratio of 0.019 indicates that one dollar long in the US stock market should be hedged by a short position of about 2 cents in the Brent oil market. Similarly, a hedge ratio

of 0.066 for the WTI-S&P500 portfolio means that investors can hedge a long position of one dollar in the stock market by shorting 6.61 cents in the WTI oil market. Arouri et al. (2011, 2012) provide similar evidence for European and American sector stock markets. In the related literature, Hammoudeh et al. (2009) and Chang et al. (2010), among others, also document that adding oil in a diversified portfolio of stocks improves the risk-adjusted performance of the considered portfolio. This diversification and hedging with the oil asset has become much easier over the last decade following a sharp increase in financialization and liquidity of commodity futures markets. Commodity futures are also traded for 24 hours.

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Finally, the average values of the HE index in Table 6 show that the hedging strategies involv-

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ing the US stocks and the oil asset lead to portfolio’s risk reduction, regardless of the oil markets un-

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der consideration. This risk reduction is however greater for the WTI oil market than for the Brent oil market, but at a higher hedging costs as indicated by the higher optimal hedge ratio. The comparison

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of the HE indices across models suggests that the DCC-FIAPARCH model enables to reduce the va-

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riance better than the DCC-GARCH model, which thus confirms the importance of taking both the

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asymmetry and long memory into account when modeling the conditional volatility of crude oil and

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the US stock markets.

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5. Conclusion

This paper investigates the dynamic relationships between the US stock market and two interna-

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tional crude oil markets. Our results from a DCC-FIAPARCH model which accommodate asymmetric volatility and long memory effects over the period 1987-2013 show strong evidence of time-varying

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correlations between the considered markets. This changing pattern in the dynamic conditional corre-

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lations is also found to react to major geopolitical tensions and economic and financial crisis periods, particularly the first Gulf war and the US subprime and global financial crisis 2007-2009. We also find that the DCC-FIAPARCH outperforms the corresponding FIGARCH and GARCH models in analyzing the dynamic interactions between crude oil and stock markets. Finally, we show the implications of our results on portfolio management and risk hedging. It can be seen that investors can improve the risk-adjusted performance of their portfolios by exploiting the diversifying and hedging potential of

the crude oil asset through taking appropriate actions in the crude oil futures markets. For instance, we find that American investors should allocate more weights to stocks than to crude oil, and that stock market risk can be hedged by taking short positions (selling) in the crude oil futures markets. Regarding the hedging strategy, the use of the proposed DCC-FIAPARCH model helps to reduce the cost of hedging, compared to the standard DCC-GARCH model.

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Figure legends Fig. 1: Prices and returns for S&P500 and CO markets. Fig. 2: The DCC between the US stock market and the CO markets.

Table 2: Long memory test results

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Table 1: Statistical proprieties and unit root tests for daily returns S&P500 Brent WTI Panel A: descriptive statistics Mean 0.0290 0.0275 0.0263 Standard deviation 1.157 2.345 2.516 Skewness -0.284 -0.699 -0.828 Kurtosis 11.529 17.574 18.710 JB 19199.42+ 56311.31+ 65561.5+ Q2(10) 4483.6+ 641.59+ 495.07+ + + ARCH(2) 516.36 43.978 56.997+ + + ARCH(10) 198.50 46.056 33.174+ Panel B: stationarity tests ADF -60.575+ -47.101+ -58.886+ KPSS 0.1978 0.0629 0.0450 Zivot-Andrews test -38.756+ -37.043+ -38.511+ Panel C: unconditional correlation matrix S&P 500 1.00 Brent 0.036 1.00 WTI 0.086 0.596 1.00 Notes: JB is the Jarque-Bera test for normality. Q2(10) is the Ljung-Box tests for autocorrelations of order 10 applied to squared returns. ARCH(2) and ARCH(10) refers to the empirical statistics of the Lagrange multiplier test for conditional heteroscedasticity with 2 and 10 lags, respectively. ADF and Zivot-Andrews tests are the Augmented Dickey-Fuller and Zivot and Andrews’s (1992) unit-root tests, while KPSS is the KwiatkowskiPhillips-Shmidt-Shin test for stationarity. The Zivot-Andrews test is robust to the potential structural breaks. + indicates the rejection of the null hypotheses of normality (Jarque-Bera), no autocorrelation (Ljung-Box), unit root (ADF and Zivot-Andrews), and stationarity (KPSS) at the 1% level.

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S&P500 Brent WTI GPH test applied to absolute return 0.409 [0.00] 0.463 [0.00] 0.483 [0.00] m  T 0.5 0.654 [0.00] 0.302 [0.00] 0.327 [0.00] m  T 0.6 GPH test applied to squared return 0.638 [0.00] 0.738 [0.00] 0.740 [0.00] m  T 0.5 0.6 0.636 [0.00] 0.522 [0.00] 0.535 [0.00] m T GSP test applied to absolute return 0.463 [0.00] 0.274 [0.00] 0.230 [0.00] m  T /8 m  T / 16 0.546 [0.00] 0.246 [0.00] 0.258 [0.00] GSP test applied to squared return 0.472 [0.00] 0.363 [0.00] 0.358 [0.00] m  T /8 m  T / 16 0.543 [0.00] 0.413 [0.00] 0.432 [0.00] rescaled variance test applied to absolute return m5 2.004 [0.00] 1.412 [0.00] 1.438 [0.00] m  10 3.364 [0.00] 1.941 [0.00] 1.865 [0.00] rescaled variance test applied to squared return m5 2.027 [0.00] 1.652 [0.00] 1.814 [0.00] m  10 3.441 [0.00] 2.445 [0.00] 2.706 [0.00] Notes: m denotes the bandwidth for the Geweke and Porter-Hudak (1983) (GPH) test, the Gaussian semiparametric (GSP) test of Robinson (1995) and the rescaled variance test. The values in parentheses are standard errors. T is the sample size. ** denotes the statistical significance at the 1% level.

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Table 3: Estimation results of the bivariate FIAPARCH(1,d,1) model S&P500/Brent S&P500/WTI Stock market Brent Stock market WTI Panel A: Estimation results C(m) 0.051*** (0.010) 0.059** (0.023) 0.051*** (0.010) 0.060*** (0.023) ** *** ** AR(1) -0.025 (0.012) 0.039 (0.012) -0.025 (0.012) -0.020 (0.012) C(v) 2.107*** (0.521) 5.997*** (2.135) 2.106*** (0.520) 7.224*** (2.012) * *** * ARCH 0.152 (0.083) 0.153 (0.055) 0.152 (0.082) 0.187**(0.085) *** *** *** GARCH 0.438 (0.105) 0.542 (0.071) 0.438 (0.104) 0.473*** (0.093) *** *** *** d 0.339 (0.043) 0.449 (0.046) 0.339 (0.042) 0.417*** (0.044) *** * *** APARCH(γ) 0.782 (0141) 0.086 (0.049) 0.782 (0.140) -0.055 (0.061) APARCH(δ) 1.296*** (0.077) 1.935*** (0.086) 1.296*** (0.077) 1.959*** (0.098) Panel B: Dynamic conditional correlations Average correlations 0.091* (0.059) 0.207** (0.092) Panel C: Model’s statistics and diagnostic tests Student-df 7.830*** (0.434) 7.434*** (0.393) Log L -21708 -21961 AIC 6.9152 7.0132 Hannan-Quinn 6.9212 7.01917 Q2(10) 10.408 [0.405] 7.820 [0.646] 10.138 [0.428] 10.066 [0.434] Q2(20) 15.053 [0.773] 18.03 [0.585] 15.16 [0.767] 22.145 [0.332] Notes: C(m) and C(v) are the constants of the mean and variance equations, respectively. AR(1) refers to the autoregressive parameter of the mean equation. The optimal lag length of the mean equations was selected by using the AIC and BIC information criteria. Q2(.) is the Ljung-Box test for autocorrelation applied to squared standardized residuals. Standard deviations are reported in parentheses. p-values of statistical tests are presented in brackets. *, ** and *** denote significance at the 10%, 5% and 1% levels, respectively.

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Table 4: Geopolitical events and crisis periods Events Periods First Gulf war (dummy1) January 1991 – December 1991 Asian financial crisis (dummy2) July 1997 – December 1997 Russian and Brazilian economic crises (dummy3) August 1998 – December 1999 September 11, 2001 terrorist attack (dummy4) September 2001 – December 2001 Subprime and global financial crisis (dummy5) August 2007 – March2009

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Table 5: Impact of major events on the dynamic correlations between crude oil and stock markets S&P500-Brent S&P500-WTI Panel A: mean equation c0 0.0164 (0.920) 0.0591 (1.289) Ø1 0.997*** (246.72) 0.979*** (179.24) λ1 (dummy1) -0.0326*** (-2.790) -0.0519*** (-3.224) λ2 (dummy2) 0.0086 (0.821) -0.0278 (-0.612) λ3 (dummy3) -0.0105 (-0.276) -0.0155 (-0.442) λ4 (dummy4) -0.0094 (-0.270) -0.0201*** (-11.608) λ5 (dummy5) 0.0148*** (4.051) 0.0166*** (3.355) Panel B: variance equation α0 0.0096*** (7.074) 0.0179*** (5.727) ** α1 0.3756 (1.986) 0.419** (2.128) *** α2 -0.0130 (-4.954) -0.0195*** (-6.025) *** γ1 (dummy1) -0.0095 (-7.076) -0.0177*** (-5.736) *** γ2 (dummy2) -0.0095 (-7.056) -0.0175*** (-5.694) *** γ3 (dummy3) -0.0094 (-7.062) -0.0176*** (-5.732) *** γ4 (dummy4) -0.0095 (-7.071) -0.0177*** (-5.731) *** γ5 (dummy5) -0.0096 (-7.085) -0.0175*** (-5.716) * ** *** Notes: , , and denote significance at the 10%, 5% and 1% levels, respectively.

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Table 6: Portfolio optimal weights, hedge ratios, and hedging effectiveness (HE) Portfolios ω12 β12 HE DCC-FIAPARCH S&P500-Brent 0.1823 0.0196 12.85 S&P500-WTI 0.1588 0.0661 13.52 DCC-GARCH S&P500-Brent 0.1861 0.0341 12.78 S&P500-WTI 0.1564 0.0892 12.33

List of Figures

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