Interactive relationships between fossil fuels, currencies and
market uncertainty.
(Energy Focus Area)
Name: Julian Alexiou Student number: s3745317 Study programme: MSc Finance
Faculty of Business and Economics, University of Groningen Supervisor: Dr Ioannis Souropanis
Abstract
In this paper, we investigate the important linkages between oil and natural gas futures and Euro and US Dollar indexes, as well the stock market uncertainty (VIX index). Since the year 2000, there have been billions of Dollars of investment flows into energy futures, which may trigger an interaction with the two major currencies and the market sentiment. This work uses a VAR model to provide evidence that the increased interest in energy futures in the last two decades from individual and institutional investors is interconnected with all the variables mentioned above. Oil prices explain natural gas and the VIX index changes. We also found that the uncertainty index affects oil and the US Dollar. There is also a 2-way feedback relationship between fossil fuels but also between currencies. These findings have practical implication for portfolio-building, risk diversification, and hedging.
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1.Introduction
The relationships between oil prices and the US Dollar has got significant attention in the literature. Different empirical strategies have been employed to analyze the link between the two assets, and mainly negative relationship was found, indicating that these two essential assets could be used for hedging strategies and risk diversification. On the other hand, the behavior of the two assets is closely related to the changes in natural gas prices and other major currency exchange rate changes. The two energy prices share an equilibrium relationship and follow the same path in the long-term horizon. Meanwhile, the two exchange rates move in opposite directions. Finally, overall the energy prices and the exchange rates of the main currencies are also significantly affected by the changes in the expected uncertainty of the stock market.
In this research, we aim to investigate the important linkages between the two energy prices and two major currency exchange rates, Euro and US Dollar, as well the stock market uncertainty. In contrast to the existing literature on the topic, our paper is among the first attempts to combine all the asset prices mentioned above and model their dynamic inter-relationships in a Vector Autoregression model. Using the latest available data, we propose a robust VAR model, the results of which can serve as an essential toolkit for market participants for portfolio and risk diversification strategies and hedging.
The literature mainly suggests a significant negative relationship between oil prices and US Dollar exchange rates. We want to re-address this question but also take into account the developments in other energy prices and main currency exchange rates. It is a question whether the rapid investors demand for energy commodities since 2000 linked the commodities market with the two major currencies and the market sentiment. Our findings are consistent with the literature, there is a negative relationship between the US Dollar exchange rate and oil prices, but the effect is significantly moderated after controlling for natural gas prices and the Euro exchange rate. We also found that the currency exchange rates mainly move towards the opposite directions, and the two energy prices share common trends. Finally, the stock market uncertainty is significantly affected by the changes in oil prices and US Dollar exchange rates, meanwhile provides essential feedback to the oil and gas prices and exchange rate developments of the main currencies.
The rest of the paper is structured as follows: in section 2 we review the literature and guide the reader to the recent empirical papers from the field; chapter 3 describes the expected mechanisms and transmission channels; part 4 reveals the details of the employed methodology; section 5 introduces data; section 6 presents the empirical results, and finally in chapter 7 we summarize the main findings and give some ideas about potential extensions of the research.
2.Literature Review
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rate changes contribute to the variation in the prices of both assets simultaneously. They mention that, while the market participants are anticipating an inflation increase, they tend to change their portfolio from dollar-denominated soft assets such as stocks to Dollar-denominated physical assets such as oil and precious metals, which are considered a safe haven in their flight to safety when the US Dollar weakens against the other major currencies, especially the Euro. Sari et al. (2010) also highlight the evidence that depreciated Dollar exchange rate against the Euro can also push up oil prices. Therefore, it will be informative and useful to traders and investors to understand the dynamics and the relationships between precious metals, oil prices and exchange rates.
Cifarelli and Paladino (2010) employed modified CAPM methodology and estimated univariate GARCH(1,1)-M and multivariate CCC GARCH-M model with complex nonlinear conditional mean equations, and found strong evidence of a negative relationship between the US Dollar exchange rate and oil prices. Some other researchers found that this negative relationship is not constant and varies across time. Wu et al. (2012) used dynamic GARCH models, which they claim have better forecasting properties, found an increasingly negative impact after 2003. Coudert and Mignon (2016) employed a nonlinear model to examine the relationships between oil prices and the US Dollar over the period from 1974 to 2015. They found that although the causality is mostly negative and significant, it became positive when the Dollar hit very high values in the mid-2000s.
Furthermore, many scholars argue that the negative relationship between the US currency and oil is not constant and mostly varies across time. The variation was more emphasized in the papers investigating the causality among the two assets before and after the crisis period. Reboredo et al. (2014) examined the link between the oil prices and the US Dollar exchange rate for a panel of countries over different periods through a de-trended cross-correlation analysis. They found a low negative correlation between the two variables for the analyzed sample, with significantly increasing negative impacts after the global financial crisis. Similar conclusions were also achieved by Mensah et al. (2017), who examined the long-run causality between the two variables on the data of oil-dependent countries, and show that there is a significant long-run negative relationship between oil prices and US Dollar exchange rate, which is more evident for oil-exporting countries, especially after the global financial crisis. The relationship between crude oil and natural gas prices is also widely investigated in the literature. Most of the scholars found long-run causality between the two energy prices. Serletis and Herbert (1999) concluded about non-stationarity of the two energy prices based on augmented Dickey-Fuller unit root test procedures. Furthermore, they showed that the prices appeared to share long-run trends due to the application of Engle and Granger (1987) cointegration tests. The author`s estimated error-correcting causality models for the integrated price series, also, they used Vector Auto-Regressive models. Τhey concluded that across these markets, there appear to be effective arbitraging mechanisms for the price of natural gas and oil. Bachmeier and Griffin (2006) analyzed long-term relationships within and between crude oil, coal, and natural gas markets. Based on the daily price data, they support the view that the world oil market is a single, highly integrated economic market. Still, the three energy markets are only very weakly integrated. Hartley et al. (2008) also found long-run cointegration between oil and gas prices.
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frequency of the ADF test decreases substantially. Thus, the ADF test correctly indicates that the constant parameter cointegrating relationship is not appropriate as there exist structural breaks for the long-run relationship between the variables. Villar and Joutz (2006) examined the relationship between the Henry Hub natural gas price and the West Texas Intermediate (WTI) crude oil price. They found a cointegrating link relating Henry Hub prices to the WTI and trend capturing the relative demand and supply effects over the 1989-through-2005 period. Meanwhile, they also mention the structural breaks in the long-run relationship and note that ignoring these structural changes in the cointegrating equation can cause serious failure in forecasting exercises. Ramberg and Parsons (2012) also found long-run relationships between crude oil and gas prices. Still, they claim that the cointegrating link does not appear to be stable through time and can shift dramatically over time. Therefore, Ramberg and Parsons (2012) suggest that although the two-price series may be cointegrated, the confidence intervals for both short and long-time horizons are broad. Brigida (2014) analyzed the cointegrating relationship between natural gas and crude oil prices by endogenously incorporating shifts in the cointegrating vector into the estimation of the cointegrating equation. He found the existence of regime-switching by allowing the cointegrating equation to switch between m states according to a first-order Markov process (he found two as an optimal number of lags). Brigida (2014) concluded that natural gas and crude oil prices are cointegrated, and the long-term equilibrium relationship can be consistently estimated with error correction model.
The energy prices and the exchange rates of the main currencies have also a considerable sensitivity towards the expected uncertainty in stock markets. Sari et al. (2011) use a VAR model to examine the information transmission mechanism between the stock market expectations, oil and metal prices, as well as Dollar and Euro exchange rate markets. Taking the VIX index as a proxy for global risk perceptions, the authors found that there is a unique long run equilibrium relationship between the examined variables, and risk perceptions appear as long-run forcing variables of world oil prices.
Also, shocks in risk perceptions of global investors have a negative but short-lived initial impact on oil prices. Finally, the paper reveals a statistically and economically significant negative relationship between the VIX index and oil prices. Daigler et al. (2014) employed a quantile regression approach to examine the return and volatility relation for foreign exchange on the example of the Euro and the VIX index. They used the Euro‐currency exchange‐traded fund, and its associated option implied volatility index and found a negative asymmetric return and volatility relation for implied volatility, with a strong relationship when large market movements occur. They also concluded about the ambiguity of the sign of the relationship, which can be either a positive or negative. Jubinski and Lipton (2013) examined the influence of implied and contemporaneous equity market volatility, measured by the VIX index and aggregated squared intraday S&P 500 index returns correspondingly, on the oil futures returns, and found that the oil prices have a statistically negative response to implied volatility and a marginally negative response to contemporaneous volatility. They also mention that these effects are amplified during recessionary periods and are robust after controlling for a Dollar index.
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(2010)). There is also an agreement in the literature about the link between the oil and natural gas prices, which frequently is found to share a long-term term cointegrated relationship with structural breaks. Finally, the relationships between the VIX index and the energy prices, as well as the exchange rates, are not straightforward and appeared to have somewhat ambiguous empirical evidence.
3.Hypothesis and Expectation
The purpose of this section is to provide the theoretical framework, the reasons we expect links between oil futures, natural gas futures, Dollar, Euro and the VIX index, and the expected mechanisms and transmission channels between the analyzed variables.
The literature focuses on a single reason why we might expect a relationship between oil prices and the US Dollar. The value of a currency can have an impact on oil futures through financial markets. The direct reasoning for this effect comes from the fact that crude oil and oil futures are denominated in US Dollars. The portfolio effect then implies that a depreciation of the currency will cause a flight of investors to physical assets which can be considered a form of protection against inflation (Kaufmann and Ullman 2009). Beckman and Czudaj (2017) also mention the wealth effect. When oil prices increase, wealth is transferred from oil-importing countries to oil-producing countries, impacting the value of their currencies. Also, oil futures could act as a hedge for investors who are exposed to US Dollar-denominated assets.
The unique position of the US Dollar in regards to oil futures can be contrasted with the position of the Euro. Before the official circulation of the Euro currency in 2002, there were talks regarding the impact of the new currency on the status of the US Dollar. Portes and Rey (1998) mention that the common European currency has the required financial characteristics to threaten the world status of the US Dollar. The Euro has the potential to become the first real competitor of the US currency and shift billions of international investments from Dollars into Euros. The liquidity and the size of the common European financial market determine the global investment role of the Euro. A shift in investment denomination would have a direct effect on the Dollar and would lead to a decline of the US currency. Market psychology is a decisive factor since movements in one currency can impact the value of another. These linkages between currencies have great importance for investors who must measure their exchange rate risk.
Currency markets and energy markets have become more closely intertwined as futures markets have grown. Commodity futures and mainly energy futures have become a popular asset for investors in the last two decades. The reasons were primarily speculation, hedging and portfolio diversification. Between 2003 and 2008, there were inflows of more than 185 billion Dollars in various commodity instruments according to the Commodity Futures Trading Commission (CFTC). Figure 1 illustrates the ratio between physical and futures market contracts in the crude oil market. In 15 years, the futures market grew to be 12 times the size of the physical market. It is essential to mention that the increased activity in futures the last two decades by far exceeded any growth in actual oil production and any need from commercial producers to hedge their risk (Knoepfel 2011). Rather, this trend reflected the financialization of commodity markets.
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financial asset like stocks and bonds available for all kind of investors. Index investors considered commodities as an alternative to stocks and a new market for returns. According to Gorton and Rouwenhorst (2006), the average excess futures returns for commodities during the period from 1959 to 2004 was 5,23%, compared to the excess returns of the S&P 500 index which was 5,65% in the same period. Hughes (2006) also mentions that all these new investment products based on commodities attracted many billions of dollars from individual and institutional investors. Tang and Xiong (2012) support that price movements of commodities could be linked to the US Dollar exchange rate, to world equity indexes, and also other commodities.
Figure 1: Physical and Futures Markets, 1995-2009
Notes: this graph shows the ratio between physical and financial futures contracts in the oil market.
Oil and natural gas futures can be viewed as a pair that experience price comovements in the energy futures markets. This link can arise first from the commodity market financialization and the constant search of financial institutions for returns. The link also occurs because of the common practice of pricing natural gas based on the price of oil, which acts as a benchmark for commodity indexes, since oil has the highest percentage weight in the index. It seems that oil futures function as a leading indicator for the performance of all other energy futures. Any sharp increase or decrease in the oil futures triggers a move in the same direction for natural gas futures.
It is also essential to understand if the considerable demand for commodity investment products since 2000 had an impact on the equity market and vice versa. There are several reasons why these two markets may be connected. The substantial inflow in mostly commodity indexes, a result of financialization, may alter market factors and commodity returns. Basak and Croitoru (2006) mention cross-market arbitrage as another reason for a link between the two markets. If hedge funds, pension funds and financial institutions participate in the commodity markets, this will weaken the effect of cross-market arbitrage and strengthen the interconnection between commodities and equities. Last but not least, extreme stock market events may affect the commodity markets. In 2008 the S&P 500 index experienced a decline of around 50% of its highs. During the same period, the Standard and Poor's Goldman Sachs Commodity index (S&P GSCI), which is the first major investable commodity index, fell almost 75%, and the VIX index hit historically high levels.1 Extreme
1 S&P GSCI index serves as a benchmark for investments in commodities. The index comprises 24 commodities
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equity falls with high levels of market stress (VIX) force financial institutions and hedge funds to close their positions in the commodity markets in order to have enough liquidity for margin calls. Many scholars also mention that a high level of stress in the financial markets has a direct impact on the US Dollar. According to Cairns et al. (2007), the international status of the US Dollar makes foreign investors view the US currency as a safe haven in periods of financial panic compared to currencies of developing countries. This flight to safety phenomenon (Fratzscher 2009) in times of high uncertainty triggers inflows in the US Dollar and can lead to an appreciation of the US currency.
4.Methodology
This study examines the correlation of the log returns of oil and natural gas futures, Dollar, Euro and the first differences of the VIX index within the period from January 4, 1991, through September 17, 2019. According to the literature there is evidence of connection for some pairs of the variables mentioned above. So, with this paper we want to investigate if there is a wider relationship between these five variables. In order to define the interactive relationship between the variables, unit root test, co-integration test, vector auto-regression model (VAR), granger causality and stability test and impulse response are applied. This procedure has been used by Chang, Huang & Chin (2013) who investigated the correlation of oil, gold and NT Dollar versus the US Dollar exchange rate withing the period from September 9, 2007, through December 28, 2011.
3.1 Unit Root Test
The mean reverting nature of the examined sample is tested through Augmented Dickey and Fuller (1979) and Phillips–Perron (1988) tests for stationarity. The both tests are implemented under the null hypothesis that the variable contains a unit root, and the alternative hypothesis is that the variable was generated by a stationary process. ADF estimates a linear model with least squares estimator where the first difference of the time series at time t is regressed on the level at time t-1, augmented with lag terms of the dependent variable (eq. 1). Then the stationarity is checked based on the significance of the level term. Phillips-Perron test is a generalization of Dickey-Fuller test, without augmenting by lag terms, using the Newey–West (1987) heteroskedasticity and autocorrelation robust standard errors (eq. 2).
Δ𝑋𝑡= 𝛼0+ 𝛽𝑋𝑡−1+ 𝛿𝑇 + ∑𝑃𝑖=1𝛾𝑖Δ𝑋𝑡−𝑖+ 𝜀𝑡 (1) Δ𝑋𝑡= 𝛼0+ 𝛽𝑋𝑡−1+ 𝛿𝑇 + 𝜀𝑡 (2)
Where 𝑋𝑡−1 and Δ𝑋𝑡 are the level and the first difference of the tested variable at time (t-1) and (t), 𝛿 is a time trend, ∑𝑃𝑖=1𝛾𝑖Δ𝑋𝑡−𝑖 are corresponding lag terms up to order P, 𝜀𝑡 is the
error term. Also 𝛼0 denoted the intercept and 𝛽 represented the coefficient of interest testing
the hypothesis 𝛽 = 0, is equivalent to testing that 𝑋𝑡 follows a unit root process. Hamilton
(1994) discuss four different cases for implementation of unit-root tests, from which we will employ test specification with and without time trends. The latter is equivalent testing equations (1) and (2) with the restriction that 𝛿 = 0.
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minimum values of AIC and SBC criteria. The functional form of the AIC and SBC criteria are given as follows:
𝐴𝐼𝐶 = 2𝑘 − 2 ln ( 𝐿̂) (3) 𝑆𝐵𝐶 = ln( 𝑇) 2𝑘 − 2 ln ( 𝐿̂) (4)
Where 𝐿̂ is the maximized value of the likelihood function, 𝑘, is the number of estimated parameters, 𝑇 is the number of observations.
3.2 The Co-Integration Test
The co-integration test is applied for variables that follow I(1) processes, are stationary after the first difference. The existence of co-integration proposes that the examined variables share a common long-term relationship and their linear combination follows a mean reverting process (Engle & Granger, 1987). The test was implemented through Johansen (1988) trace statistic and maximum Eigen value statistic methods. The null hypothesis of both tests is that there are no more than r co-integrating vectors. The distribution of the trace statistic is given by:
𝜆𝑡𝑟𝑎𝑐𝑒(𝑟) = −𝑇 ∑𝑛 ln(1 − 𝜆̂ ) 𝑖
𝑖=𝑟+1 (5)
Where 𝑇 stands for the number of used observations is, 𝑟 denoted the number of co-integrated vectors, 𝜆̂ represented the estimated value of ith Eigen value and n is the resultant 𝑖
of Eigen values that follows an 𝜒2 distribution. The corresponding lag order can be chosen based on different statistics, including AIC and SBC, described in the previous section. The Co-integration test will provide evidence of possible long-run association between the variables.
3.3 Vector Auto-Regression (VAR)
Vector auto-regression models provide tools to investigate whether some of the examined variables are useful in forecasting other variables. Vector auto-regression approach is a system of a multivariate time-series where each of the dependent variable is regressed on its own lags and the lags of all the other dependent variables. VAR approach can also be extended by including exogenous variables (VARX). The 𝑝𝑡ℎ order vector Autoregression has the following representation:
𝒀𝑡= 𝜶 + 𝚽1𝒀𝑡−1 + ⋯ + 𝚽𝑝𝒀𝑡−𝑝 + 𝜺𝑡 𝜺𝑡 ∼ 𝑊𝑁(𝟎, 𝛀) (6)
Where 𝒀𝑡 is the vector of endogenous variables (for our analyses 𝒀𝑡 contains oil, natural gas,
US dollar and Euro index returns and VIX index first differences) 𝚽𝑖 is the matrix of estimated
coefficients at lag order p, 𝜺𝑡 is the vector of error terms, which follow white noise process
with mean 0, and variance covariance matrix 𝛀.
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3.4 Granger Causality Test
The Granger Causality Test is a concept which investigates whether one variable is useful for forecasting another. A variable X Granger causes series Y, if the lags of X are significant for predicting the values of Y. Under the null hypothesis, series X fails to Granger cause the series of Y if there is no significant improvement in the mean squared error of the projection of Y conditional on the information of X.
𝑀𝑆𝐸 (𝑃𝑟𝑜𝑗(𝒀𝑡+ℎ|𝒀𝑡, ⋯ , 𝒀𝑡−𝑝, 𝑿𝒕, ⋯ , 𝑿𝑡−𝑝)) = 𝑀𝑆𝐸 (𝑃𝑟𝑜𝑗(𝒀𝑡+ℎ|𝒀𝑡, ⋯ , 𝒀𝑡−𝑝)) (7) If we fail to reject the null hypothesis series X does not Granger cause series Y.2
3.5 VAR Stability Test
As discussed earlier, many time series analyses require variables to be covariance stationary, meaning that their first two moments exist and are independent of time. However, VAR models require more strict stability conditions. A VAR model is stable if it is invertible and has an infinite-order vector moving-average representation. Lütkepohl (1991) and Hamilton (1994) show that if each Eigen value of the companion matrix is strictly less than one, the estimated VAR model is stable. VAR stability will be tested by observing whether all the roots of the companion matrix are inside the unit circle, which act as a stability indicator.
3.6 Impulse Responses and Variance Decompositions
Impulse response functions trace the effect of a one-time unexpected shock on the dynamic adjustment path of the other variables. This concept can be usefull for our analysis since it can provide evidence of a wider relationship between the five variables. To analyze the dynamic response of the variables to one-time unexpected shock, initial reduced form VAR is converted to a 𝑚𝑜𝑣𝑖𝑛𝑔 𝑎𝑣𝑒𝑟𝑎𝑔𝑒(𝑀𝐴) representation
𝒀𝑡= 𝜺𝑡+ 𝚿1𝜺𝑡−1+ 𝚿2𝜺𝑡−2+ ⋯ (8)
Where 𝚿𝑖 is the matrix at the corresponding lag order and captures the effect of shocks to 𝜺𝑡 on 𝒀𝑡+𝑖, as it has the following interpretation:
𝜕𝒀𝑡+𝑖
𝜕𝜺𝑡 = 𝚿𝑖 (9)
The line graph of elements of 𝚿𝑖 against 𝑖 is called an impulse response function.
Another useful tool from VAR models is the forecast error variance decomposition, which is also obtained from 𝑀𝐴 representation. Consider the forecast error at time t + h,
𝒀𝑡+ℎ− 𝒀̂𝑡+ℎ|𝑡 = 𝜺𝑡+ℎ+ 𝚿1𝜺𝑡+ℎ−1+ , ⋯ , 𝚿2𝜺𝑡+1 (10) Then
𝑀𝑆𝐸(𝒀̂𝑡+ℎ|𝑡) = 𝐸 ((𝒀𝑡+ℎ− 𝒀̂𝑡+ℎ|𝑡)(𝒀𝑡+ℎ− 𝒀̂𝑡+ℎ|𝑡)′) = 𝛀 + 𝚿1𝛀𝚿1′+, ⋯ , +𝚿ℎ−1𝛀𝚿ℎ−1′ (11)
Assuming that 𝛀 is a diagonal matrix, then
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𝑀𝑆𝐸(𝒀̂𝑡+ℎ|𝑡) = ∑𝑚 𝜎𝑖𝑖2(𝐤i𝐤i′+ 𝚿1𝐤i𝐤i′𝚿1′+, ⋯ , +𝚿ℎ−1𝐤i𝐤i′𝚿ℎ−1′ )
𝑖=1 (12)
Where 𝐤i is a vector of zeros with a one in entry 𝑖.
Finally, the contribution of 𝑖𝑡ℎ shock to MSE will be
𝜎𝑖𝑖2(𝐤i𝐤i′ + 𝚿1𝐤i𝐤′i𝚿1′+, ⋯ , +𝚿ℎ−1𝐤i𝐤i′𝚿ℎ−1′ ) (13)
5.Data
Our data set comprises daily price data within the period from January 4, 1991, through September 17, 2019.3 It consists of oil futures, natural gas futures, the Dollar index, the Euro
index and the VIX index with a total of 7078 observations. Following Buncic and Piras (2016) this study analyses the returns of fossil fuels and currencies and we transform the VIX index by getting the first differences. The returns were calculated based on the logarithmic price changes. The Dollar and the Euro index measure the value of the US Dollar and the Euro in relation to a basket of the strongest currencies in the world.4 The VIX index is a useful
sentiment predictor in the market, representing the expected volatility in the S&P 500. The VIX index price derives from the options of the S&P 500 index. High levels of the VIX index are a signal of uncertainty and market stress while low VIX index levels indicate complacency in the market. In this paper, we aim at extending the work of Jia Liao et al. (2018) who investigated the relationship of crude oil futures with the US Dollar and the VIX index. Next to oil futures, we introduce the natural gas futures since natural gas has increasing importance in the energy market and according to the Energy Outlook 2017 of the Energy Information Administration, natural gas use will rise more than any other fossil fuel. Next to the US Dollar index and the VIX index, the Euro index variable should act as a proxy for the second most traded currency in the world. For the period before the introduction of the Euro currency January 1, 1999, an exchange rate 1 Euro = 1.95583 German Mark was calculated. Next, we provide a brief motivation regarding the specific variables.
(1) Futures: Our set includes oil and natural gas futures, which are commonly used because of their high trading volumes (Wang, Wu & Yang, 2008).
(2) Indixes: We select the Dollar and Euro indexes as proxies for the two most-traded currencies in the world. Also, we consider the VIX index, which allows us to access financial stress in the market. (Liao, Shi & Xu, 2018)
All the sourced data are specified in US Dollars and are available at Thomson Reuters/Eikon. The following tables present basic descriptions of the data.
3 The starting date was restricted by the data availability of the Euro index.
4 The Dollar index consists of a weighted average of a basket of currencies against the US Dollar (Euro 57,6%,
10 Table 1: Description of variables
Variable Explanation Variable Explanation
𝑂𝑖𝑙 Oil futures 𝑔𝑂𝑖𝑙 Oil futures returns
𝐺𝑎𝑠 Gas futures 𝑔𝐺𝑎𝑠 Gas futures returns
𝐷𝑜𝑙𝑙𝑎𝑟 Dollar index 𝑔𝐷𝑜𝑙𝑙𝑎𝑟 Dollar index returns
𝐸𝑢𝑟𝑜 Euro Index 𝑔𝐸𝑢𝑟𝑜 Euro index returns
𝑉𝛪𝛸 VIX index 𝛥𝑉𝛪𝛸 VIX index first differences
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Table 2 provides the summary statistics for the returns and the first differences of the VIX index as the results of the Augmented Dickey-Fuller (ADF) test (Dickey & Fuller, 1979). The means of 𝑔𝑂𝑖𝑙, 𝑔𝐺𝑎𝑠, 𝑔𝐷𝑜𝑙𝑙𝑎𝑟, 𝑔𝐸𝑢𝑟𝑜, 𝛥𝑉𝑖𝑥 are around zero, which means that the yield of all five variables is around zero. However, the VIX index, although having a mean return of -0.01%, had the highest volatility among all variables with a standard deviation of 6.58%. On the other hand, the Euro index was the variable with the lowest volatility (0.48%) during the observed period. Also, we can notice that the average volatilities for fossil fuels are much larger than the average volatilities for currencies.
We begin with an ADF test to identify if the variables contain a unit root or a stationary process generated the variables. The null hypothesis states that the variable contains a unit root. ADF estimates an OLS model where the first difference of the time series at time t is regressed on the level at time t-1, augmented with lag terms of the dependent variable. Then the stationarity is checked based on the significance of the level term. Based on the unit root results, we conclude that the returns of all four variables and the first differences of the VIX index are integrated of order one and follow a stationary process.
Table 2: Descriptive statistics & Augmented Dickey-Fuller test
mean median min max std p-value
𝑔𝑂𝑖𝑙 0.0001 0.0006 -0.4005 0.1641 0.0235 0.0000 𝑔𝐺𝑎𝑠 0.0001 0.0000 -0.2600 0.3244 0.0341 0.0000
𝑔𝐷𝑜𝑙𝑙𝑎𝑟 0.0000 0.0001 -0.0372 0.0283 0.0053 0.0000
𝑔𝐸𝑢𝑟𝑜 0.0001 0.0001 -0.0277 0.0262 0.0048 0.0000 ΔV𝑖𝑥 -0.0001 -0.0036 -0.3505 0.7679 0.0658 0.0000 Notes: Descriptive statistics present daily returns (January 4, 1991 to September 17, 2019). Augmented Dickey-Fuller tests the null hypothesis that a unit root is present.
6.Results
The general conclusions from the unit root tests suggest that all the return variables and the first differences of the VIX index appear stationary. The lag order of the unit root tests was selected based on AIC and SBC criteria. In all the cases, we reject the null hypothesis of the existence of a unit root and conclude that the examined variables are stationary.
Co-integration test
Table 3 presents the results of the Johansen test for co-integration and indicates that at any level of 𝑟 we fail to reject the null hypothesis of no co-integration, and should conclude that the examined variables do not share a common long-term relationship.5
13 Table 3: Johansen Co-integration test
Johansen test for co-integration
Trend: trend Number of obs. = 7076
Sample: 3 - 7078 Lags = 2
maximum rank Parms. LL eigenvalue trace statistic critical value
𝑟 = 0 24 -13877.3 . 46.8823* 54.64
𝑟 ≤ 1 31 -13866.4 0.00308 25.0489 34.55
𝑟 ≤ 2 36 -13860.5 0.00166 13.2581 18.17
𝑟 ≤ 3 39 -13855 0.00155 2.287 3.74
𝑟 ≤ 4 40 -13853.9 0.00032
Notes: If the trace statistic at 𝑟 = 𝑖 exceeds its critical value, we reject the null hypothesis of r co-integrating equations.
VAR model
The results in Table 4 (view Appendix Table 6 for the optimal lag selection) suggest that the autoregressive terms are most important predictors in each of the equations.6 This means that
the history of each variable has strong explanatory power for its changes. Οil is a significant variable for explaining the price changes in natural gas and the VIX index. It is clear that the growth of commodity-linked investments explains the process of commodity market financialization. The substantial money inflows in mostly index investments in the energy market made oil and natural gas more correlated to each other. Trading commodity indexes become a new asset class for investors in a constant search for yields. It is evident that investors monitor commodities as equities, both of which get influenced by market sentiment. We found that the VIX index serves as a market timing indicator, which causes portfolio rebalancing in times of increased uncertainty in the market. High levels of stress in the market cause investors to liquidate positions in the commodities market and drive them to safe assets like the US Dollar. The Dollar and the Euro price changes mutually affected one another. The significant negative correlation between the two major currencies shows how useful this pair is for investors aiming to diversify their risk. It is noteworthy that the results of the VAR(2) model don’t show a significant relationship between oil and the Dollar, contrary to results discussed in the literature.
6 Lag order was selected based on the lag order selection criteria in an initial VAR model, see the results in the
14 Table 4: VΑR model results (1) (2) (3) (4) (5) VARIABLES g𝑂𝑖𝑙 g𝐺𝑎𝑠 g𝐷𝑜𝑙𝑙𝑎𝑟 𝑔𝐸𝑢𝑟𝑜 Δ𝑉𝐼𝑋 g𝑂𝑖𝑙 = 𝐿1 -0.0304** -0.0511*** -0.000689 -0.00406 0.0189** (0.0123) (0.0179) (0.00279) (0.00253) (0.00805) g𝑂𝑖𝑙 = 𝐿2 -0.0478*** 0.0366** -0.00341 0.00101 -0.00312 (0.0123) (0.0180) (0.00280) (0.00253) (0.00806) g𝐺𝑎𝑠 = 𝐿1 0.00296 -0.0383*** -0.000585 -0.000458 0.00374 (0.00834) (0.0121) (0.00189) (0.00171) (0.00545) g𝐺𝑎𝑠 = 𝐿2 0.0197** -0.0272** -0.00195 0.00117 -0.0111** (0.00834) (0.0121) (0.00189) (0.00171) (0.00544) g𝐷𝑜𝑙𝑙𝑎𝑟 = 𝐿1 0.109 -0.0160 -0.171*** -0.0335* 0.0245 (0.0887) (0.129) (0.0201) (0.0182) (0.0579) g𝐷𝑜𝑙𝑙𝑎𝑟 = 𝐿2 -0.123 -0.0415 -0.00938 -0.0439** -0.0142 (0.0877) (0.128) (0.0199) (0.0180) (0.0573) g𝐸𝑢𝑟𝑜 = 𝐿1 0.0213 0.0935 -0.210*** -0.0496** 0.0230 (0.0978) (0.142) (0.0221) (0.0201) (0.0639) g𝐸𝑢𝑟𝑜 = 𝐿2 -0.0745 0.0143 -0.0121 -0.0492** 0.00267 (0.0981) (0.143) (0.0222) (0.0201) (0.0640) Δ𝑉𝐼𝑋 = 𝐿1 -0.0628*** -0.0213 0.0109*** 0.00469 -0.103*** (0.0184) (0.0268) (0.00417) (0.00378) (0.0120) Δ𝑉𝐼𝑋 = 𝐿2 -0.0335* -0.00560 -0.00118 0.00581 -0.0849*** (0.0185) (0.0269) (0.00418) (0.00379) (0.0120)
Constant 0.000123 6.29e-05 2.19e-05 -2.94e-06 -2.77e-05
(0.000278) (0.000405) (6.30e-05) (5.71e-05) (0.000182)
Observations 7,075 7,075 7,075 7,075 7,075
Notes: Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1
Stability test
15 Figure 3: VAR model stability test
Notes: Roots of the companion matrix outside the unit circle are the sign of non-stability.
Granger causality test
Table 5 shows the results of the granger causality test, and Figure 4 presents a relationship summary of all variables. The resulting graph shows how the variables included in analysis are interconnected. The rapid growth of commodity investments since 2000, commodity market financialization, attracted the interest of institutional and individual investors. This process not only increased the correlation between energy futures which have a 2-way feedback relationship according to Figure 4. Also, commodity market financialization linked energy futures with the financial market, since commodity investments became a new asset class that could provide yield for investors. Energy futures and especially crude oil futures play a critical role for market participants since both Granger cause the VIX index according to Figure 4. It seems that oil acts as a recession barometer, which affects financial stability and the equity market sentiment, increasing the levels of uncertainty investors face. Increased risk and fear in equity markets trigger capital inflows in the US Dollar, which acts as a safe haven for investors. Periods of high market uncertainty force investors to liquidate Euro related investments and flight to the safety of the US Dollar. However, when stability comes back to the markets, this process is reversed. It is noteworthy to mention that although the granger causality test finds a significant connection between the VIX index and the oil, the risk indicator index seems not to affect natural gas.
16 Table 5: Granger causality test
Equation Excluded chi2 df Prob > chi2
𝑔𝑂𝑖𝑙 𝑔𝐺𝑎𝑠 5.6534 2 0.059 𝑔𝑂𝑖𝑙 𝑔𝐷𝑜𝑙𝑙𝑎𝑟 4.2854 2 0.117 𝑔𝑂𝑖𝑙 𝑔𝐸𝑢𝑟𝑜 0.71096 2 0.701 𝑔𝑂𝑖𝑙 Δ𝑉𝑖𝑥 13.889 2 0.001 𝑔𝑂𝑖𝑙 𝐴𝐿𝐿 25.158 8 0.001 𝑔𝐺𝑎𝑠 𝑔𝑂𝑖𝑙 12.484 2 0.002 𝑔𝐺𝑎𝑠 𝑔𝐷𝑜𝑙𝑙𝑎𝑟 0.11 2 0.946 𝑔𝐺𝑎𝑠 𝑔𝐸𝑢𝑟𝑜 0.43204 2 0.806 𝑔𝐺𝑎𝑠 Δ𝑉𝑖𝑥 0.64888 2 0.723 𝑔𝐺𝑎𝑠 𝐴𝐿𝐿 14.723 8 0.065 𝑔𝐷𝑜𝑙𝑙𝑎𝑟 𝑔𝑂𝑖𝑙 1.5402 2 0.463 𝑔𝐷𝑜𝑙𝑙𝑎𝑟 𝑔𝐺𝑎𝑠 1.14 2 0.566 𝑔𝐷𝑜𝑙𝑙𝑎𝑟 𝑔𝐸𝑢𝑟𝑜 91.691 2 0 𝑔𝐷𝑜𝑙𝑙𝑎𝑟 Δ𝑉𝑖𝑥 7.1777 2 0.028 𝑔𝐷𝑜𝑙𝑙𝑎𝑟 𝐴𝐿𝐿 107.93 8 0 𝑔𝐸𝑢𝑟𝑜 𝑔𝑂𝑖𝑙 2.7573 2 0.252 𝑔𝐸𝑢𝑟𝑜 𝑔𝐺𝑎𝑠 0.55305 2 0.758 𝑔𝐸𝑢𝑟𝑜 𝑔𝐷𝑜𝑙𝑙𝑎𝑟 7.9608 2 0.019 𝑔𝐸𝑢𝑟𝑜 Δ𝑉𝑖𝑥 3.5712 2 0.168 𝑔𝐸𝑢𝑟𝑜 𝐴𝐿𝐿 16.476 8 0.036 Δ𝑉𝑖𝑥 𝑔𝑂𝑖𝑙 5.6988 2 0.058 Δ𝑉𝑖𝑥 𝑔𝐺𝑎𝑠 4.7266 2 0.094 Δ𝑉𝑖𝑥 𝑔𝐷𝑜𝑙𝑙𝑎𝑟 0.2909 2 0.865 Δ𝑉𝑖𝑥 𝑔𝐸𝑢𝑟𝑜 0.13076 2 0.937 Δ𝑉𝑖𝑥 𝐴𝐿𝐿 12.151 8 0.145
17 Figure 4: Granger causality results
Notes: The arrows show the directions of the causality based on Granger causality test.
Impulse response & variance decomposition
18 Figure 5: Impulse response
Notes: The diagrams show the adjustment of time path of the variables when one of the variables is shocked.
19 Figure 6: Variance decomposition
Notes: The bars illustrate the contributions of separate variables to the forecast error variance decomposition.
7. Conclusion
20
This study explores whether the massive investment flows since 2000 into energy futures triggered an interconnection between energy prices, the two major currencies, and the VIX index. The results of the study imply that commodity market financialization, which happened mainly through commodity index investments, led to a closer link between oil and natural gas futures. Commodity indexes attracted the interest of index investors, who considered energy futures as a new asset class that could provide returns. There is evidence that the VIX index acts as a time indicator in periods of market stress, causing investors to sell their energy futures positions in order to raise liquidity. This increased liquidity is invested in the US Dollar, which is considered a safe haven in periods of market uncertainty.
We also showed evidence of Granger causality between the two currencies. We found that VIX index changes have significant impact on oil and Dollar returns, and are affected by oil and natural gas price changes. The impulse response analysis revealed that when a variable is shocked, the impulse response effect on the other analyzed variables lasts not longer than five lags. The estimation results also showed that all the examined variables show significant levels of persistence, with autoregressive terms explaining much of the variation. Although the impacts of own lag coefficients appeared to be relatively small, the forecast error variance decomposition showed that, except for Euro returns, the main parts of forecast error variance are explained by their own lags.
We believe that the results of this study may have practical implications for investors. We have built a robust VAR framework, which models the relationship of energy price returns, main currency price returns and market uncertainty changes. Our results can serve as an important toolkit for portfolio-building, risk diversification, and hedging.
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Appendix
Table 6: AIC, SBC criteria for lag order selection in the stationarity tests
AIC SBC Lag 𝑔𝑂𝑖𝑙 𝑔𝐺𝑎𝑠 𝑔𝑈𝑆𝐷 𝑔𝐸𝑈𝑅 Δ 𝑉𝐼𝑋 𝑔𝑂𝑖𝑙 𝑔𝐺𝑎𝑠 𝑔𝑈𝑆𝐷 𝑔𝐸𝑈𝑅 Δ 𝑉𝐼𝑋 1 -38109.3 -32944.2 -58982.2 -60507.3 -44711.7 -38088.7 -32923.7 -58961.6 -60486.7 -44691.1 2 -41228 -36011.8 -61872.8 -63456.2 -48253.4 -41200.6 -35984.3 -61845.3 -63428.8 -48225.9 3 -43436.7 -38134.5 -63916.9 -65544.9 -50818.6 -43402.4 -38100.2 -63882.6 -65510.6 -50784.3 4 -45075.5 -39770.6 -65493 -67088.3 -52905.7 -45034.3 -39729.4 -65451.8 -67047.1 -52864.6 5 -46455.7 -41171.9 -66795.7 -68327.5 -54603.8 -46407.6 -41123.9 -66747.6 -68279.5 -54555.8 6 -47656.4 -42354.4 -67900 -69407.8 -56106.5 -47601.5 -42299.5 -67845.1 -69352.9 -56051.6 7 -48700.9 -43321.1 -68842.2 -70339.1 -57472.2 -48639.1 -43259.3 -68780.5 -70277.3 -57410.5 8 -49633.6 -44198.3 -69652.1 -71142.1 -58665.1 -49565 -44129.7 -69583.5 -71073.5 -58596.5 9 -50471.9 -44991.2 -70382.3 -71879.6 -59673.9 -50396.4 -44915.8 -70306.8 -71804.1 -59598.4 10 -51243.9 -45680.7 -71058.5 -72571.5 -60513.9 -51161.6 -45598.3 -70976.1 -72489.2 -60431.5 11 -51928.2 -46303.1 -71650.6 -73190.6 -61286.1 -51839 -46213.9 -71561.4 -73101.4 -61196.9 12 -52538.5 -46848.1 -72195.4 -73742.5 -62006.3 -52442.4 -46752 -72099.4 -73646.5 -61910.2 Notes: The values are AIC and SBC values for lag length model of the examined variables. The model with
24 Table 7: Lag order selection for VAR model.
Selection-order criteria
Sample: 13 - 7078 Number of obs. = 7066
lag LL LR df p FPE AIC HQIC SBIC
