Risk appetite and oil prices

Journal Pre-proof Risk appetite and oil prices

Mahmoud Qadan, Yasmeen Edilbi-Bayaa PII:

S0140-9883(19)30390-1

DOI:

https://doi.org/10.1016/j.eneco.2019.104595

Reference:

ENEECO 104595

To appear in:

Energy Economics

Received date:

15 September 2018

Revised date:

25 July 2019

Accepted date:

22 November 2019

Please cite this article as: M. Qadan and Y. Edilbi-Bayaa, Risk appetite and oil prices, Energy Economics(2019), https://doi.org/10.1016/j.eneco.2019.104595

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© 2019 Published by Elsevier.

Journal Pre-proof

Risk Appetite and Oil Prices

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Yasmeen Edilbi-Bayaa Faculty of Social Sciences, University of Haifa University of Haifa Email Address: [email protected]

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Mahmoud Qadan School of Business Administration Faculty of Social Sciences, University of Haifa Tel: +972-4-8249584 Email Address: [email protected]

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Risk Appetite and Oil Prices Abstract

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We demonstrate that oil prices and their volatility are no longer determined solely by real economic shocks to supply of and demand for oil, but are also driven by shocks originating in the economic uncertainty and risk appetite of investors that prevail in the equity market. The contribution of the latter factor has become particularly remarkable since the mid-2000s. To establish these results, we dismantle the squared VIX index, determined in the S&P 500 options market, into the conditional variance in stock returns (to proxy for economic uncertainty) and the equity variance risk premium (to proxy for risk appetite). Using threshold-GARCH, structural vector auto regression and causality models, we provide evidence about the link between risk appetite, oil price returns and volatility. Furthermore, investors’ appetite for risk drives changes in the OVX, which measures perceptions about future oil volatility, but not vice versa. Our results provide a better understanding of the relationship between oil, the VIX and its two proposed components. In particular, we show that changes in the risk appetite of investors are an important determinant not only for the price of equities but also for that of the most important energy resource – oil.

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JEL Classification: G1, Q4

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Keywords: Financialization, Oil Prices, Risk Appetite, Risk Aversion, Uncertainty, Variance risk Premium.

Journal Pre-proof 1. Introduction The terms “risk appetite” or “risk aversion” are frequently used in the literature interchangeably to refer to the willingness of investors to bear risk. Not surprisingly, it has become increasingly acceptable to assume that changes in these measures are an important determinant of asset prices (e.g., among others, Epstein, 1988; Campbell and Cochrane, 1999; Coudert and Gex, 2008). Recent financial econometrics studies suggest the equity variance risk premium measure (VP) as an indicator that captures risk aversion or its counterpart – risk appetite (e.g., Carr and Wu, 2008; Bollerslev et al., 2009). These studies decompose model-free

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implied volatility (the VIX) into a measure of stock market uncertainty, constructed using model-

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free realized volatility from high-frequency intraday data, and a residual that is closely associated with risk aversion. In practice, the variance risk premium is calculated as the difference between

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the squared VIX index and an estimate of the realized variance of the stock market.

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Despite the proliferation in the research on the link between oil and equity prices in the last

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two decades, previous efforts to directly link time-varying variance risk premiums, that is, risk aversion or risk appetite, with oil price movements are limited in scope. Therefore, the purpose of study is to add to the scarce literature on this issue by providing empirical evidence about the

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role of risk appetite in affecting oil returns and their volatility. We do so by using recent data and

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the methods developed by Carr and Wu (2008) and Bollerslev et al. (2009). In this study, we use data for January 1990 to September 2017 to construct future realized

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monthly variances computed using squared 5-minute returns and create a variance risk premium in order to capture the risk appetite prevailing in the equity market. Examining oil prices against just one aggregate risk estimator, the VIX, may mask the relationship between characteristics specific to oil and the two different components comprising the VIX. Hence, the separation of the VIX into the components of uncertainty and implied risk aversion provides a better indication of the nature of the relationship between risk appetite, economic uncertainty and oil price movements. As detailed in the literature review section, previous research confirms significant spillovers from the financial markets, including the VIX, into the oil market. Nevertheless, these studies do not account for the decomposition of the overall market risk into physical volatility and variance in the risk premium, a gap we seek to rectify.

Journal Pre-proof The literature and the participants in the financial markets view the VIX as simultaneously a measure of risk aversion, uncertainty and fear in the market place (e.g., Whaley, 2000). Indeed, many empirical works have suggested the VIX as a proxy for such risks without any distinction between physical expected volatility (i.e., economic uncertainty – Bekaert and Hoerova, 2014) and the variance risk premium. For example, Sari et al. (2011) indicate that global risk perceptions, described by the VIX, have a significant suppressing effect on oil prices in the long run. Bloom (2009) uses the VIX index to measure macroeconomic uncertainty and reports that a heightened VIX reduces employment and output. In Bekaert et al. (2011), as well as in

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Silvennoinen and Thorp (2013), the VIX is regarded either as a proxy for risk aversion or world

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investor sentiment. Cheng et al. (2014) report that financial traders sold positions in response to increases in the VIX as prices fell during the recent financial crisis, with hedgers taking the other

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side. Actually, such results may originate in the variance risk premium rather than in uncertainty

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per se.

This research is also motivated by the increasing tendency of investors to expose their

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portfolios to financial vehicles related to oil for speculative, hedging and investment purposes. The accelerated inclusion of oil and other commodities in investors' portfolios – recently called

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the financialization of commodities – has increased oil price exposure to financial shocks (Tang and Xiong, 2012; Silvennoinen and Thorp, 2013; Hamilton and Wu, 2015). As a result, there is a

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growing interest in understanding the role of risk aversion in influencing oil prices. We posit that periods associated with increased risk appetite, as implied by lower levels of

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the variance risk premium, tend to be associated with increased or higher oil prices, and vice versa. The underlying assumption is that a decline (increase) in risk aversion prompted by more optimistic (pessimistic) judgments about equities is associated with parallel changes in oil prices. This contention may be in line with prior works claiming that a euphoric stock market represented by the S&P 500 index has an impact on oil prices (Bhar and Malliaris, 2011). Preliminary support for our contention is illustrated in Table 1. In this table, we divided the implied risk aversion proxy into ten deciles. The lower deciles are those identified as periods with lower levels of risk aversion (i.e., increased risk appetite), and the upper deciles are those associated with an increased degree of risk aversion. The table demonstrates the association between increased risk aversion (higher variance risk premium

Journal Pre-proof values) and low oil prices, as opposed to an atmosphere of reduced risk aversion (i.e., increased risk appetite), accompanied by high oil prices on average.

[Insert Table 1 here]

In our analysis, we use the Granger causality test, structural VAR, and volatility thresholdGARCH models. We exhibit that implied risk aversion is crucial in setting the price of oil. Specifically, we show that the variance risk premium Granger-causes not only the price of oil,

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but also contributes significantly to the volatility of oil returns. Using threshold-GARCH, we

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document that lagged values of the variance risk premium negatively affect oil returns, but positively affect their conditional volatility. The picture emerges indicates that the results are

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prominently significant mainly after the earlier periods of 2000s. Actually, in this period many international portfolio and hedge fund managers, as well as retail investors, increased their

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exposure to the oil market by holdings oil financial products (ETFs, futures contracts, ETNs, and

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oil derivatives).

We also find that implied risk appetite significantly drives the oil volatility index (OVX),

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which is based on the market price of oil return variance, but not vice versa. This finding clearly indicates that investors’ attitude toward risk affects the forward looking implied volatility in the

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oil market. We confirm the role of the implied risk aversion in affecting and driving not only oil prices, but also the prices of equities involved in the petroleum industry. Finally, we establish

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that unanticipated innovations to the variance risk premium have a persistent and significant effect on oil prices. In addition, unexpected innovations in the conditional variance constructed using 5-minute data, which may potentially serve as a reflection of economic uncertainty, significantly and negatively affect oil prices. This result confirms the macroeconomic “wait and see” stylized fact that arises during uncertain economic times, and negatively impacts economic activity. We reveal that the fluctuations in crude oil prices depend not only on real economic shocks to the supply of and demand for oil, but are also strongly affected by shocks originating from economic uncertainty and the attitudes of market participants toward risk (risk aversion). These four factors jointly account for 17-30% of the short-term variation in oil prices. Furthermore, about 50% of this variation is related to economic uncertainty and implied risk aversion.

Journal Pre-proof Given that energy prices and their volatility are considered very important variables for economies, our study and its results have far-reaching implications for a wide range of issues including oil production, hedging strategies, investors’ investment strategies, and countries’ policy making. The economic literature has established that oil price movements are tightly linked with global inflation, variations in trade deficits worldwide, household incomes, and the likelihood of global recessions. Consequently, it is important to understand the role of risk appetite in influencing oil prices. From the practical point of view, organizations such as central banks, for example, that

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maneuver between supporting demand and containing inflation may find our findings useful in

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their monetary decision making and forecasts for future trends in oil prices. In addition, our findings may provide helpful information for oil market analysts, investors and portfolio

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managers that can potentially help them manage their portfolios and reduce their risks in a much

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more informed manner.

Our analysis also contributes to the debate on the implications of the “financialization” of oil,

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a major concern given the growing importance of commodity market investments among households and institutional investors. The increasing attention of investors to financial vehicles

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related to energy commodities for speculative, hedging and investment purposes has contributed significantly to the evolution of oil from a physical to a financial vehicle that replicates many of

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the price characteristics detected in equities. To summarize, this study emphasizes the sizable contribution of risk appetite in financial

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markets to oil prices since 1990 and to a much larger extent since the mid-2000s. To the best of our knowledge, this study is the first to provide direct evidence about the link between implied risk appetite in the equity market and oil returns and their volatility. Thus, our results enable us to better assess the interplay between the capital market and oil prices. The rest of the paper is organized as follows. Section 2 reviews the literature. Section 3 explains the methods used here. Section 4 reports the data used in the paper. Section 5 details and discusses the empirical findings, and Section 6 concludes.

2. Literature Review

Journal Pre-proof With the gradual transformation of crude oil from a physical to a financial asset in recent years, a great deal of attention has been paid to the impact of equity markets on oil price movements. In particular, the spillover effect of equity returns and their volatility onto the oil market has been widely investigated, revealing significant volatility interactions between the two markets. While the vast majority of studies report that the transmission of returns and volatility is much more apparent from oil to stocks than from stocks to oil (e.g., Sadorsky, 1999; Park and Ratti, 2008), others provide evidence supporting the hypothesis of a bidirectional volatility spillover (e.g., Arouri et al., 2011; Salisu and Oloko, 2015). In this spirit, Thuraisamy et al.

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(2013) demonstrate bidirectional volatility spillovers between the equity, oil and gold futures

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markets, and Mensi et al. (2013) show that past S&P 500 shocks have significant effects on the volatility in the gold and oil markets as well. Broadstock and Filis (2014) report that correlations

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between oil price shocks and stock returns are systematically time varying. The role of speculation in affecting oil prices has been addressed in the literature in recent

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years, but has left this issue with open questions because the findings are not consistent (Irwin

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and Sanders, 2011), and because the data available on trader positions in oil futures contracts are problematic (e.g., Irwin and Sanders, 2012; Hamilton and Wu, 2015). While part of the literature

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supports the role of speculation in affecting oil prices (Hamilton, 2009; Kaufmann and Ullman, 2009; Kaufmann, 2011; Zhang, 2013; Kilian and Murphy, 2014), other studies maintain that there is a limited or weak impact (e.g., Sanders et al., 2004; Sanders and Irwin, 2010). Kilian and

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Lee (2014), for example, report mixed findings, and demonstrate that, conditional on inventory

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specification, speculative demands raised the price in mid-2008, but found no evidence of speculative demand between 2003 and 2008. The measures used in the literature to capture speculative tendencies in the oil market include the ratio of short (or long) positions to total hedging positions in oil futures (e.g., Du et al., 2011), GARCH-in-mean models (e.g., Cifarelli and Paladino, 2010) and the proportion of net long positions of non-commercial traders in US crude oil futures on the NYMEX (Sanders et al., 2004; Chen et al., 2016). Kaufmann (2011) suggests three indicators that together signify speculation: changes in crude oil inventories, repeated and extended break-downs in the cointegration relationship between spot and future prices, and the predictive failures of an econometric model of oil prices that is based on market fundamentals. Other studies use a

Journal Pre-proof survey-based index created by the American Association of Individual Investors (AAII) or the Investor Intelligence Index (e.g., Du and Zhao, 2017; Qadan and Nama, 2018). Other studies indirectly link oil prices to speculation using risk factors originating from the bond, foreign exchange and capital markets. The literature sometimes refers to these factors as speculation factors. They include interest rates (e.g., Barsky and Kilian, 2004; Balcilar et al., 2015), the S&P 500 index (e.g., Ghouri, 2006), the foreign exchange rate (e.g., Amano and van Norden, 1998; Basher et al., 2012; Wen et al., 2018) and the prices of precious metals (e.g.,

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Kumar, 2017; Śmiech and Papież, 2017). Finally, another stream of literature focuses on the dynamics and the extent of information

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transmission between the commodity markets and the VIX. For example, Sari et al. (2011)

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indicate that global risk perceptions, described by the VIX, have a significant suppressing effect on oil prices in the long run and a less important role in explaining the forecast error variance of

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oil prices in the short term. They also suggest that a shock in the VIX has a negative but shortlived initial impact on oil prices. Jubinski and Lipton (2013) reveal that oil has a statistically

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negative response to implied volatility and a marginally negative response to contemporaneous volatility. Cheng et al. (2014) show that high levels of the VIX index reverse the flow from

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financial investors into the commodity markets, thereby depressing prices. The separate consideration of the link between the VIX components and oil prices may stem

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from the recognition that the VIX carries important forward-looking information, which

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improves the precision of conditional market variance estimations (Kanas, 2012). For many commodities, correlations with S&P 500 returns rise when the VIX spikes, pointing to strong financial influences (Silvennoinen and Thorp, 2013). Using Markov chain techniques, Bhar and Malliaris (2011) find that changes in the VIX adversely affected oil price dynamics between 2004 and 2009, which was an extremely volatile period, and that the effects are regime dependent. In this spirit, Cochran et al. (2015) use the VIX as an indicator of threshold regime change and report that the returns of oil and other commodities and volatility in them are threshold regime-dependent. To sum up, as previously stated, although returns and volatility spillovers between stock markets and oil have been examined extensively, research regarding the oil-stock nexus in terms of appetite for risk are still limited.

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3. Method 3.1 Decomposing the VIX index As Carr and Wu (2008) and Bollerslev et al. (2009) suggest, the VIX can be decomposed into a variance risk premium and an uncertainty component. This decomposition requires an estimate of the expected future realized variance, which is constructed and computed using the sum of squared intra-daily returns. Following the literature (e.g., Andersen and Bollerslev, 1998; Andersen et al., 2007), we calculate the daily realized volatility as the sum of squared 5-minute

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returns. The underlying assumption here is that for a liquid market (and the US capital market

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definitely is one), a 5-minute sampling interval is optimal (Andersen et al., 2001). The

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computation of the daily realized volatility reads as follows. 𝐼

2 = ∑ 𝑅𝑖,5−𝑀𝑖𝑛 . (1)

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𝑅𝑉𝑡𝐷

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𝑖=1

Although other papers use S&P 500 futures (e.g., Andersen et al., 2007; Corsi et al., 2010),

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we follow Bekaert and Hoerova (2014) and focus on S&P 500 index returns. The daily realized variance 𝑅𝑉𝑡𝐷 , sums squared 5-minute intraday returns and the squared close-to-open returns. We

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then construct the monthly realized variance (𝑅𝑉𝑀,𝑡 ) measured over the next month (22 trading

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days) using the above-mentioned 5-minute returns. In other words, 22 𝐷 𝑅𝑉𝑀,𝑡 = ∑ 𝑅𝑉𝑡−𝑗+1 . (2) 𝑗=1

On a typical trading day that opens at 9:30 to 16:00, we should have 78 five-minute return observations. Consequently, in a regular month consisting of 22 trading days, we will have 1,716 observations. Following the literature (e.g., Jiang and Tian, 2005, Carr and Wu, 2008), we convert the resulting monthly values to annual terms, and define the variance risk premium is as follows:

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𝑉𝑃𝑡 = 𝑉𝐼𝑋𝑡2 − 𝐸(𝑅𝑉𝑀,𝑡+1 ).

(3)

The realized annual return variance, denoted by 𝑅𝑉𝑀,𝑡+1, can be considered the return resulting from buying variances in a variance swap contract. Since the value of variance risk premium is mostly negative, we follow Carr and Wu (2008) and Bekaert and Hoerova (2014) and define it as appears above in Eq. (3), making it a proxy for implied risk aversion. By creating this difference, as discussed in the above literature, we insure two things. The first is that VP “purifies” the VIX from the impact of economic uncertainty and physical volatility dynamics,

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and the second is keeping the measure of variance risk premium intensely connected to risk

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aversion.

3.2 Structural vector auto regression model (SVAR)

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To study the impact of the market participants’ assessment of risk on oil price fluctuations, we

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use the SVAR model, and specify a number of specifications. We first define 𝑿𝑡 to be a vector that contains the variables of interest. Then, a SVAR model is created based on this vector as: 𝑄

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𝑨𝟎 𝑿𝑡 = 𝜶 + ∑ 𝑨𝑞 𝑿𝑡−𝑞 + 𝜺𝑡 .

(4)

𝑞=1

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𝑨𝟎 , 𝜶 and 𝑨𝒒 are unknown coefficient vectors and matrixes to be estimated. The 𝜶 in the SVAR

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model is a matrix of (𝑘 × 1) constants, Aq is a matrix of (𝑘 × 𝑘) coefficients and 𝜺𝒕 is a (𝑘 × 1) matrix of serially and mutually uncorrelated shocks. "Q," which denotes the lag length of the SVAR, is set using the Schwarz information criterion. The first specification derived from Eq. (4) addresses the unidirectional feedback between oil price movements and risk aversion, measured using the variance risk premium. In other words, (𝑋𝑡 = 𝑝𝑡 , 𝑉𝑃𝑡 )′ , where 𝑉𝑃𝑡 = 𝑉𝐼𝑋𝑡2 − 𝐸(𝑅𝑉𝑀,𝑡+1 ), and 𝑝𝑡 = log(𝑅𝑒𝑎𝑙 𝑂𝑖𝑙 𝑃𝑟𝑖𝑐𝑒𝑡 ). If we assume that A0 is an identity matrix, and use the rate of change of the oil price, we then obtain the Granger causality procedure. 𝑸 𝑶𝒊𝒍 𝑹𝑶𝒊𝒍 = 𝒂𝟎𝟏 + ∑𝑸 𝒕 𝒒=𝟏 𝒂𝒒𝟏 𝑹𝒕−𝒒 + ∑𝒒=𝟏 𝒃𝒒𝟏 𝑽𝑷𝒕−𝒒 + 𝒖𝒕 , (5) 𝑸 𝑶𝒊𝒍 𝑽𝑷𝒕 = 𝒂𝟎𝟐 + ∑𝑸 𝒒=𝟏 𝒂𝒒𝟐 𝑽𝑷𝒕−𝒒 + ∑𝒒=𝟏 𝒃𝒒𝟐 𝑹𝒕−𝒒 + 𝒗𝒕 . (6)

Journal Pre-proof The second specification extends that of Kilian (2009) and suggests including macroeconomic factors as well as the risk aversion variable in the

𝑋𝑡 matrix. In other words,

𝑋𝑡 = (Δ𝑝𝑟𝑜𝑑𝑡 , 𝑟𝑒𝑎𝑡 , 𝑅𝑉𝑡 , 𝑉𝑃𝑡 , 𝑝𝑡 )′, where Δ𝑝𝑟𝑜𝑑𝑡 is the percent change in the global crude oil production of the OPEC countries, reat is the real economic activity index suggested in Kilian (2009), which reflects the demand for oil, 𝑅𝑉𝑡 is the realized volatility referred to as a measure of economic uncertainty, VPt is the variance risk premium proxied to capture the implied risk aversion variable, and 𝑝𝑡 is the natural logarithm of the real price of oil. The reduced form of the

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SVAR reads as follows: 𝑄

𝑞=1

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−1 𝑋𝑡 = 𝐴−1 0 𝛼 + ∑ 𝐴0 𝐴𝑞 𝑋𝑡−𝑞 + 𝑒𝑡 ,

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where 𝑒𝑡 = 𝐴−1 0 𝜀𝑡 is the vector of the estimated residuals in the reduced VAR model. Unlike

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prior studies that focus only on economic fundamentals and overlook investors' attitude toward risk, we include shocks to the implied risk aversion and the realized volatility in the structural

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VAR. Accordingly, the errors 𝑒𝑡 of the reduced form can be decomposed into the following

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components:

𝑜𝑖𝑙 𝑠𝑢𝑝𝑝𝑙𝑦 𝑠ℎ𝑜𝑐𝑘

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Δp𝑟𝑜𝑑 𝜀1𝑡 𝑒𝑡 𝑎11 0 0 0 0 𝑎𝑔𝑔𝑟𝑒𝑔𝑎𝑡𝑒 𝑑𝑒𝑚𝑎𝑛𝑑 𝑠ℎ𝑜𝑐𝑘 𝜀2𝑡 𝑒𝑡𝑟𝑒𝑎 𝑎21 𝑎22 0 0 0 𝐸𝑐𝑜𝑛𝑜𝑚𝑖𝑐 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 𝑒𝑡 ≡ 𝑒𝑡𝑅𝑉 = 𝑎31 𝑎32𝑎33 0 0 . (8) 𝜀3𝑡 𝑎41 𝑎42𝑎43 𝑎44 0 𝑉𝑃 𝑅𝑖𝑠𝑘 𝑎𝑝𝑝𝑒𝑡𝑖𝑡𝑒/𝑎𝑣𝑒𝑟𝑖𝑜𝑛 𝑒𝑡 [𝑎51 𝑎52𝑎53 𝑎54 𝑎55 ] 𝜀4𝑡 𝑃 ( 𝑒𝑡 ) ( 𝜀 𝑜𝑖𝑙 𝑠ℎ𝑜𝑐𝑘 ) 5𝑡

In line with Kilian (2009), we impose a number of restrictions on the A−1 0 matrix motivated by the following assumptions. The crude oil supply curve is assumed to be vertical in the short run, meaning that an inelastic supply does not respond contemporaneously to innovations in the demand for oil within the same month. This assumption is based on the practical observation that oil-producing economies are slow to respond to shocks to demand for two reasons. First, adjusting oil production is very costly. Second, there is a great deal of uncertainty regarding the nature of the shock and the state of the crude oil market.

Journal Pre-proof Consistent with the empirical literature showing the slow reaction of real economic activity globally when oil prices increase (Kilian and Vega, 2011), and given that innovations in oil prices are considered to be predetermined with respect to the economy (e.g., Lee and Ni, 2002), we assume that innovations in real economic activity worldwide that cannot be explained by supply shocks to crude oil will refer to shocks to the aggregate global demand. We also assume that innovations in the price of oil that cannot be attributed to shocks to supply or aggregate demand will reflect changes in the demand for oil driven by future economic uncertainty about economic conditions (captured by realized volatility). Finally, we also assume that innovations in

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the price of oil that cannot be attributed to the shocks listed above can be explained by shocks to investors’ appetite for holding risky assets, captured by the variance risk premium. To sum, we

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propose that shocks to the price of oil (𝑒𝑡𝑝 ) are justified by innovations in oil market

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fundamentals, meaning shocks to the supply of and demand for oil, and shocks originating in economic uncertainty and shocks to investors’ risk appetite.

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We base this assumption on the idea that there are no other plausible candidates for

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exogenous oil-specific demand shocks. Hence, strong reasons drive us to believe that shocks to the real price of oil can be related to exogenous shifts in the demand for oil originating in

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investors' inclinations for incurring risk and speculating. As discussed in the preceding sections,

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4. Data

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a growing body of research has addressed the link between the appetite for risk and asset pricing.

Our analysis is based on monthly and daily implied and realized volatilities for the S&P 500 index from January 1990 through September 2017. We use US data because the US stock market is considered one of the most important financial markets and has a remarkable influence on other markets, and the S&P 500 index is used as the most representative index of that stock market. For the risk-neutral implied volatility measure, we rely on the VIX index provided by the Chicago Board of Options Exchange (CBOE). The VIX index, available back to January 1990, is based on the S&P 500 index options, and more importantly, is calculated based on the modelfree approach. To demonstrate the impact of risk aversion on oil prices, we use monthly and daily data about West Texas Intermediate (WTI) oil prices for the period from January 1990 until

Journal Pre-proof September 2017. The oil price data come from the U.S Energy Information Administration.1 We also use high frequency data obtained from the π-trading database.2 In addition, our analysis employs data about the demand for oil proxied by the index of real economic activity constructed in Kilian (2009), and data about the supply of oil proxied by OPEC production that is extracted from the official US Energy Statistics website.3 To measure the volatility using high frequency data, Andersen and Bollerslev (1998) propose a robust measure for actual market volatility, called the realized volatility (realized variance). Hence, our realized volatility is based on the summation of the 5-minute squared

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returns of the S&P 500 index within the month.

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Summary statistics are reported in Table 2. The realized volatility is systematically lower than the implied volatility, and its unconditional distribution deviates more from the normal. The

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mean of the variance risk premium, (𝑉𝑃 = (𝑉𝐼𝑋𝑡2 – 𝐸(𝑅𝑉𝑡 )) × 100) represents the average

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dollar profit and loss for each $100 notational investment in the variance swap contract. Thus, longing a 30-day variance swap contract with a notional sum of $100 on the S&P 500 index, and

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holding this contract to maturity, results in an average return of $2.47, or −$2.47 if we consider Carr and Wu's (2008) definition precisely (i.e., (𝐸(𝑅𝑉𝑡 ) – 𝑉𝐼𝑋𝑡2 ) × 100). As discussed in the

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introduction, academics and market participants use the difference between the implied and realized volatilities as a measure of market-implied risk aversion. Figure 1 depicts the evolution

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of the implied and realized volatility, showing that both obviously co-move rather noisy and

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more or less reflect the overall level of volatility. Figure 2 depicts the variance risk premium. [Insert Figure 1 here] [Insert Figure 2 here] Table 2 reports the descriptive statistics of the key variables considered in this study. The data are illustrated in two panels. Panel A reports the daily variable statistics, while Panel B reports the monthly ones. The data are positively skewed and leptokurtic, as we would expect for financial data. Furthermore, the Jarque and Bera (1987) test for normality is rejected for the entire set of variables. 1

https://research.stlouisfed.org/fred2/series/DCOILWTICO/downloaddata https://pitrading.com/historical-market-data.html 3 https://www. eia.gov/ 2

Journal Pre-proof [Insert Table 2 here]

5. Empirical Findings 5.1 Granger Causality Test Results As discussed earlier in this study, the VIX is decomposed into two components. The first is realized volatility, which captures the capital market participants’ perceptions about uncertainty, and the second is the variance risk premium, which proxies for implied risk aversion. In Panel A

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of Table 3, we present the results of Granger (1969) causality tests between implied risk aversion

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captured by the variance risk premium (VP) and daily oil returns. The values reported in both panels are the F-statistics related to the Granger test procedure. Thus, statistically significant F-

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statistic values indicate the rejection of a non-causal relationship between a pair of variables.

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In our analysis, we test two hypotheses. In the first, we hypothesize that the variance risk

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premium does not Granger-cause oil returns, while the second (or alternative) posits that changes in oil price do not Granger-cause the variance risk premium -VP. We conduct the Granger causality test for the full sample period (1990 to 2017), and two subsamples (January 1990 to

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December 2003 and January 2004 to 2017) for robustness purposes. Furthermore, previous research has established that the earlier periods of the 2000s mark the start of the popularity of

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oil futures contracts among different types of investors. Specifically, the related empirical

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literature dates the start of the financialization of commodity futures to around 2004 (e.g., Büyüksahin et al., 2010; Boons et al., 2014; Hamilton and Wu, 2014, among others), and some of these works explicitly test for and confirm a structural break around 2004. Overall, the results reveal that for the period before the early 2000s (1990-2003) there are no feedback effects between the variance risk premium and oil prices. This finding actually means that oil in this period is merely a physical asset rather than a financial asset. However, this picture changes for the subsequent sample period (2004-2017). During this period, oil gradually transformed from a physical to a financial asset, as evident in the strong, significant bidirectional causality between the variance risk premium and oil prices. We find that the variance risk premium Granger-causes oil prices and vice versa. This result is statistically significant for both the daily data, with the relatively higher F-statistic values for causality from the variance

Journal Pre-proof risk premium to oil returns. With respect to monthly data (results are available upon request), the results indicate that the variance risk premium drives the prices of oil, but not vice versa. The results obtained here are in line with previous works that link the variance risk premium to equities. Bollerslev et al. (2009) demonstrate that measures of the variance risk premium can predict stock returns. Furthermore, Bekaert et al. (2013) show that strong interactions exist between monetary policy and the variance risk premium, suggesting that monetary policy can affect market participants' risk aversion. Panel B of Table 3 reports the results of Granger causality test regarding any effect of realized

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volatility on oil prices. The panel indicates bi-directional causality between these two variables.

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The findings are statistically significant for the period 2004-2017. However, the period before financialization does not reveal any feedback effect between these two variables, an indication

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that the link between uncertainty and oil prices has tightened since the latter became widely held by many international hedge funds portfolios (e.g., Irwin and Sanders, 2011). With respect to

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monthly data (results are available upon request), the results indicate that realized volatility

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drives oil prices, but not vice versa.

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[Insert Table 3 here]

Panel A of Table 4 tests for any feedback effects between the variance risk premium and the CBOE’s crude oil volatility index (the OVX). Liu et al. (2013) point out that the OVX is a better

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measure of oil volatility. Aboura and Chevallier (2013) also emphasize the important role of this

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kind of implied volatility of oil prices. The results of the Granger causality test indicate unidirectional causality, implying that the variance risk premium drives changes in the OVX. In other words, the perceived volatility in the oil market is strongly affected by shifts in risk aversion. The findings are robust using either daily data or monthly data. [Insert Table 4 here]

Regarding the interplay between uncertainty and the OVX, Panel B demonstrates bidirectional causality between the two variables. The results of the daily data prove that both variables strongly overlap, maybe because both reflect uncertainty about economic and financial conditions. This finding is in line with the literature that postulates in favor of uncertainty in macroeconomic performance driving oil-price fluctuations (e.g., Bekiros et al., 2015). In this

Journal Pre-proof spirit, Baker et al. (2016) construct a measure of economic policy uncertainty and find that it strongly influences the intensity of recent recessions and recoveries. Qadan and Nama (2018) use this measure of economic uncertainty, and document its role in affecting oil price fluctuations. Panel A of Table 5 reports the feedback effect between the variance risk premium and the S&P 500 equity index. As expected, the variance risk premium strongly drives the S&P 500 index returns and vice versa, as evident in the significant F-statistic values in Panel A. When considering monthly data, we observe that the variance risk premium strongly drives the market index, as evident in the large and significant F-statistic values (results are available upon

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request). Unsurprisingly, as Panel B of Table 5 illustrates, the same findings are obtained with

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respect to the XOI index, which is designed to mirror the performance of the oil industry in the US. The estimated beta of this portfolio relative to the S&P 500 index is 0.48. Previous works

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(Sadorsky, 2001; Diaz and de Gracia, 2017).

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have established that oil price movements have a positive effect on oil and gas stock returns

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[Insert Table 5 here]

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5.2 Assessing the impact of risk appetite on oil price dynamics To assess the impact of implied risk aversion, captured by the variance risk premium, on oil

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returns and volatility in the short term, we use the following simple specification.

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𝐽 𝑂𝑖𝑙 𝑅𝑡𝑂𝑖𝑙 = 𝑤0 + ∑𝐻 𝑖=1 𝑏𝑖 𝑉𝑃𝑡−𝑖+1 + ∑𝑗=1 𝑐𝑗 𝑅𝑡−𝑗 + 𝑢𝑡 .

(9)

We assume that previous variance risk premium values can predict future oil prices. The inclusion of lagged oil returns accounts for autocorrelation. The literature on forecasting the volatility of oil returns usually uses the generalized autoregressive conditional heteroscedasticity - GARCH(p,q) (e.g., Sadorsky, 2006). The standard GARCH model is symmetric in its response to past innovations. However, there are theoretical arguments that suggest a differential response in the conditional variance to past positive and negative innovations. Hence, we follow the literature (e.g., Wei et al., 2010; Hou and Suardi, 2012; Wu et al., 2012) and allow the variance in oil returns to change over time. We also utilize the threshold-GARCH specification which

Journal Pre-proof allows for asymmetric effects of negative and positive shocks in the conditional variance equation (Glosten et al., 1993). The conditional variance equation is formulated as follows. 2 2 2 2 𝜎𝑢,𝑡 = 𝜇0 + ∑𝑃𝑝=1 𝛼𝑝 𝑢𝑡−𝑝 + 𝛾𝑆𝑡−1 𝑢𝑡−1 + ∑𝑄𝑞=1 𝛽𝑞 𝜎𝑢,𝑡−𝑞 + ∑𝐾 𝑖=0 𝜃𝑖 𝑉𝑃𝑡−𝑖 . (10) 2 "St-1" is a dummy variable that receives 1 if 𝑢𝑡−1 < 0; 𝑆𝑡−1 𝑢𝑡−1 captures the asymmetric effects 2 of 𝑢𝑡−1 on the conditional variance; 𝛾 quantifies the leverage effect, and the 𝜃 coefficients

account for any effect of the variance risk premium (VP) on the volatility in oil returns.

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Eqs. (9) and (10) are regressed using five different modeling specifications – M1-M5, and

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their estimation results are reported in Table 6. For the sake of gaining overall picture, we constructed two panels: Panel A with daily data results for 2004-2017, and Panel B with daily

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data results for 1990-2017. We obtained two main results. The first is that implied risk aversion, captured by the variance risk premium, negatively affects oil prices. The second is that the

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variance risk premium positively affects the volatility in oil returns. To save space, we do not

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include the results for 1990-2003, because the variance risk premium did not play any significant role in affecting oil returns and volatility. The results hold true for the various specifications

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used, and support our initial claim that risk aversion plays a significant role in affecting the

[Insert Table 6 here]

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evolution of oil prices and volatility in general, particularly for the period after the mid-2000s.

Finally, we repeated this examination with regard to the realized volatility. In other words, we replaced the variance risk premium (VP) variable in Eqs. (9) and (10) with realized volatility (RV) and utilized several specifications. As Table 7 illustrates, RV negatively drives oil prices mainly at the first lag. We did not find any contemporaneous effect of RV on oil returns. Furthermore, RV positively affects the conditional variance of oil, as evident by the positive and statistically significant coefficients in the variance equation. As previously noted, the results are significant mainly when we consider the period of 2004-2017.

[Insert Table 7 here]

Journal Pre-proof 5.3 Structural vector auto regression While the literature provides empirical support for the role of economic growth and other fundamentals in affecting oil price movements, little if anything is known about the role of risk appetite in explaining oil prices.4 In this subsection, we assess how the real prices of WTI oil respond to shocks in risk aversion as well as to other economic variables. For this purpose, we use the SVAR model as given in Eq. (7). We follow the literature about the oil market and set Q=24 (Kilian, 2009). Such a long lag

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length allows for a potentially long delay in the effects of shocks to oil prices and for removing

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serial correlation. Indeed, prior works have shown that utilizing long lags is beneficial in structural models to account for the infrequent co-movement between the real price of oil and

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economic activity globally. For example, Hamilton and Herrera (2004) claim that Q=24 (months) is sufficient to capture the price dynamics when modeling business cycles in commodity

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to oil prices that persist more than a year.

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markets. Ciner (2013) also highlights the importance of using long lags in understanding shocks

Following Bekaert and Hoerova (2014), we focus on non-crisis observations, and therefore,

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we drop two observations belonging to September and October 2008 in which the variance risk premium equals -10.83 and -39.34, respectively. In fact, there is unlikely to be a sudden increase

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in risk appetite during periods of a major panic and financial stress.

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Figure 3 plots the impulse response of oil prices to one standard deviation in structural innovations. As the figure illustrates, unexpected shocks in supply and demand, economic uncertainty and risk appetite have an impact on oil prices. Most importantly, shocks to the variance risk premium that proxy for the implied risk aversion negatively influence oil prices. These findings are also corroborated in Morana (2013). The author finds that speculation shocks, although captured using a different method, have a significant positive influence on oil prices. [Insert Figure 3 here] We also determined that unexpected shocks to economic uncertainty, captured by the realized volatility of the US equity market, have a permanent negative influence on oil prices. This 4

Fan and Xu (2011) provide a comprehensive literature review of these economic fundamentals.

Journal Pre-proof finding accords with that of Sari et al. (2011). In fact, the uncertainty-output nexus has been studied extensively in the literature (e.g., Bloom, 2009; Bachman et al., 2013), yielding the very important stylized fact that uncertainty does not benefit the economy. In uncertain economic environments, firms tend to “wait and see” how the economy unfolds, putting a pause on their investments and hiring. Such behavior eventually results in a drop in economic activity. Given that such activity is an important factor in affecting oil prices, shocks to realized volatility negatively affect oil prices. As to the other substantial factors, shocks to the demand for oil, proxied by the real activity

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measure proposed by Kilian (2009), significantly and positively influenced the WTI crude oil

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prices in the sample period. As depicted in Figure 3, the demand for oil has a persistent influence on oil prices, while unanticipated innovations in the oil supply tend to lower prices significantly

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in the long run.

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We divided the shocks to oil prices into five different components using the variance decomposition procedure. The results appear in Table 8. The variance decomposition quantifies

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the extent to which the shocks 𝜀1𝑡 , 𝜀2𝑡 , 𝜀3𝑡 , and 𝜀4𝑡 (that account for shocks to the supply, demand, realized volatility and variance risk premium, respectively) contribute on average to oil

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price shocks. Looking at the short-term, meaning periods 1 to 12, we find that the effects of both the realized volatility and the variance risk premium are evident and meaningful. For example, in

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period 6, the four suggested shocks account for 17% of the variability in oil prices, specifically,

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1.07% for supply, 7.32% for demand, 1.43% for uncertainty and 6.77% for risk appetite or risk aversion. In other words, about 50% of the variability in the price of oil that originated from the four shocks comes from both uncertainty and the variance risk premium. As the table demonstrates, the share of these four shocks increases over time. In later periods, say period 24, the contribution of the uncertainty risk component (realized volatility) to oil price fluctuations is 6.56%, while risk aversion/appetite contributes 4.57%. In addition, shocks to the demand for oil account for 30.23%, and those to the supply contribute 16.29% to the oil price fluctuations in our sample. These findings are consistent with Kilian (2008), who found that shocks to the demand are more dominant compared with those to supply. Moreover, Kilian and Murphy (2014) report that the demand for oil, rather than the unexpected drop in oil supplies, can explain the majority of the price movements in crude oil between 2003 and 2008.

Journal Pre-proof [Insert Table 8 here] For the sake of robustness, we investigated the stationarity of the SVAR model by examining its roots. The results depicted in Figure 4 indicate that the estimated SVAR is stable (stationary), because all of the roots are less than one and lie inside the unit circle. [Insert Figure 4 here] In general, the picture depicted here suggests that dismantling the aggregate market variance

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risk, reflected by the VIX, into two different components (economic uncertainty and risk aversion) is important because both components act as additional financial fundamentals in the

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oil market.

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As the main purpose of using the SVAR model is to obtain uncorrelated structural shocks (Amisano and Giannini, 1997), in Table 9 we report the results of the LM test for the serial

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correlation of the structural VAR residuals. For each lag length (Q), we test the hypothesis of no serial correlation of the VAR residuals. We then provide the LM statistics and the significance

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level (Prob.) for this hypothesis. By and large, the results support the absence of serial correlation as evident by the relatively high values of the Prob. Overall, the results reported here

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support our initial claim that risk appetite, captured by dividing the VIX into two components,

[Insert Table 9 here]

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has a significant effect on oil prices mainly in the short run.

6. Concluding Remarks

In this study, we provided evidence about the role that shifts in risk aversion play in affecting oil prices. We established these results using the information embedded in the VIX. While the literature views the VIX as a measure of global risk and uncertainty, in this study we take a different view. Using model-free realized volatility and model-free implied volatility, we construct an estimator of implied risk aversion. Specifically, we dismantle the squared optionimplied volatility-VIX, into two ingredients: the realized variance (RV) of the equity market constructed using 5-minute return data for the S&P 500 index, and the equity variance risk

Journal Pre-proof premium (VP). By this procedure, we expanded the evidence on the role of the realized volatility and variance risk premium in affecting asset prices. We find that the variance risk premium, which proxies for the implied risk aversion, drives both the returns and volatility of oil, and drives the market's expectations about the 30-day volatility of crude oil prices - the OVX. On the other hand, the realized volatility, suggested to measure the implied economic uncertainty, demonstrates bidirectional feedback effect with daily oil returns, confirming by that the macroeconomic “wait and see” stylized fact that arises during

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uncertain economic times. Our findings emphasize the sizable contribution of risk appetite to oil price dynamics since 1990 and to a much larger extent since the mid-2000s.

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Finally, in light of the enhanced global financialization of oil and other commodities, the structural VAR analysis demonstrates that the price of oil is no longer determined solely by real

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economic shocks to supply and demand, but is also significantly affected by aggregate implied

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risk aversion and the economic uncertainty.

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Investors in oil commodities may benefit from the suggested separation of market-wide risk into two components, because it improves hedging activities and price forecasts. In fact, both are crucial for policy makers in terms of inflation targeting, constructing production facilities and

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improving the timing of their investment in oil inventories.

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Wen, F., Xiao, J., Huang, C., & Xia, X. (2018). Interaction between oil and US dollar exchange rate: nonlinear causality, time-varying influence and structural breaks in volatility. Applied Economics, 50(3), 319-334. Whaley, R. E. (2000). The investor fear gauge. Journal of Portfolio Management, 26(3), 12-17. Wu, C. C., Chung, H., & Chang, Y. H. (2012). The economic value of co-movement between oil price and exchange rate using copula-based GARCH models. Energy Economics, 34(1), 270282. Zhang, Y. J. (2013). Speculative trading and WTI crude oil futures price movement: an empirical analysis. Applied Energy, 107, 394-402.

Journal Pre-proof

of

Figure 1 – Implied Volatility and Realized Volatility for 1990-2017

ro

Notes: The figure depicts the evolution of the VIX and the realized volatility for January 1990-September 2017. The dotted line is the realized volatility calculated as the total of the 5-minute squared returns on the S&P 500 index within the month, and the continuous line is the VIX.

na

lP

re

-p

Figure 2 - Variance Risk Premium Evolution for 1990-2017

Jo

ur

Notes: The figure depicts the time series of the equity variance risk premium (the variance risk premium) for January 1990- September 2017. The variance risk premium measure is computed as the difference between the corresponding realized and implied variance measures, namely, 𝑉𝑃𝑡 = 𝑉𝐼𝑋𝑡2 − 𝐸(𝑅𝑉𝑀,𝑡+1 ).

Journal Pre-proof Figure 3 – Response of WTI Oil Prices to Structural one S. Dev. Innovations

of

Notes: The vertical axis represents the logarithm value if the price of oil changes. The horizontal axis is time in terms of months. The broken red lines are ±2 standard error bands. The sample covers the period January 1990September 2017. Inverse Roots of AR Characteristic Polynomial Figure 4: Inverse Roots of the SVAR Model’s Characteristic Polynomials

ro

1.5

-p

1.0

0.5

re

0.0

-1.0

na

-1.5 -1.5

lP

-0.5

-1.0

-0.5

0.0

0.5

1.0

1.5

Jo

ur

Notes: The figure depicts the inverse roots of the SVAR model calculated according to Lütkepohl and Poskitt (1991). The results indicate that the estimated VAR is stable (stationary), because all of the roots are less than one and lie inside the unit circle.

Journal Pre-proof Table 1 – Decile Analysis Panel A –Daily Data (1990-2017) Oil Prices S.D. Min.

Avg. VP

Avg.

Med.

Max.

1

-2.52

66.11

65.75

27.78

20.40

136.54

2

0.75

63.75

58.95

24.60

14.09

141.06

3

1.05

54.30

49.76

31.23

13.98

139.96

4

1.30

46.50

36.18

31.45

13.89

136.91

5

1.65

42.67

29.54

29.40

13.44

145.31

6

2.06

43.52

28.66

31.55

13.96

143.74

7

2.55

39.56

24.73

29.42

11.12

141.47

8 9 10

3.27 4.36 8.03

38.85 37.44 35.15

24.69 24.52 28.11

28.42 26.86 21.70

11.03 10.86 10.82

134.63 145.16 110.03

-p

ro

of

Decile

Oil Prices S.D. Min.

re

Panel B –Daily Data (1990-2017) without 2008

Avg. VP

Avg.

1

-1.21

61.06

60.45

24.59

20.40

107.07

2

0.77

63.17

58.64

23.93

14.09

113.39

3

1.06

51.81

47.65

30.19

13.98

113.03

4

1.31

45.59

34.30

30.44

13.89

107.94

1.65

41.51

29.11

28.08

13.44

110.62

2.05

41.31

27.97

29.01

13.96

112.27

2.54

36.82

24.25

26.17

11.12

107.08

3.26 4.33 7.37

36.84 35.78 33.93

24.00 24.15 27.21

25.92 24.90 21.50

11.03 10.86 10.82

104.71 101.25 102.59

7

Jo

8 9 10

na

6

ur

5

Med.

lP

Decile

Max.

Notes: We sort the variance risk premium (VP) into ten deciles, from Decile 1 (the lowest) to Decile 10 (the highest). For each decile, we report the average of the VP and the corresponding statistical determinants of oil prices including the average (Avg), median (Med), standard deviation (S.D.), maximum (Max) and minimum (Min) of oil prices. The picture emerged indicates that higher values of variance risk premiums (reflecting high degrees of risk aversion) are associated with lower oil prices. Panel A of the table shows that at low levels of implied risk aversion (the variance risk premium), meaning increased risk appetite, the price per barrel of oil fluctuates on average around $66 per barrel. However, for higher levels of risk aversion, the average price of a barrel drops to $35. The difference between the average oil prices in deciles 1 and 10 is statistically significant (T-stat=23.13). Each decile in Panel A contains 694 observations. In Panel B, we repeat the check but without the data from 2008, because of the exceptional levels of the variance risk premium recorded in that year (see Figure 2). As Panel B of the table illustrates, these findings remain qualitatively unchanged even if we omit the period of 2008 during which abnormal variance risk premium levels were recorded.

Journal Pre-proof Table 2 - Descriptive Statistics Panel A: Daily Data ∆OIL

∆VIX

∆OVX

∆XOI

2.247

0.01

-0.008

-0.003

0.021

1.854

0.051

-0.328

-0.319

0.036

RVM

VIX

VP

Avg.

12.179

19.474

Med.

9.824

17.59

S.D.

8.245

7.862

3.447

2.5

6.389

4.881

1.456

Min.

4.061

9.31

-39.346

-40.64

49.601

-43.991

-15.868

Max.

74.634

80.86

40.173

18.868

-35.059

42.497

15.446

Skew.

2.739

2.105

-1.909

-0.707

0.694

0.662

-0.308

10.702

41.053

17.784

7.420

13.086

14.114

49049.04

22284.11

422989.4

63776.94

6205.89

10403.54

35833.27

#Obs Period

6,941 1990:1 to 2017:09

6,941 1990:1 to 2017:09

6,941 1990:1 to 2017:09

6,940 1990:1 to 2017:09

6,940 1990:1 to 2017:09

2,413 2007:5 to 2017:09

6,941 1990:1 to 2017:09

∆OIL

∆VIX

∆OVX

∆XOI

12.176

19.392

Med.

2.192

0.259

-0.160

0.606

0.468

8.223

7.683

S.D.

9.908

17.5

3.823

9.331

18.689

4.431

5.628

1.809

0.698

-1.237

0.313

0.652

re

Avg.

lP

VIX

ro

VP

Panel B: Monthly Data RVM

of

14.815

Jarque-Bera

-p

Kurt.

4.187

9.89

-39.346

-39.117

95.195

17.949

-18.395

Max.

74.293

68.51

31.677

36.469

-53.810

-18.153

15.682

na

Min.

2.788

Kurt.

15.746

Jarque-Bera

2677.25

#Obs

332 1990:1 to 2017:09

Jo

Period

2.045

-2.579

-0.105

0.634

0.066

-0.366

10.309

55.498

4.653

5.064

6.297

3.739

970.44

38493.37

38.5

81.17

56.25

15.01

332 1990:1 to 2017:09

333 1990:1 to 2017:09

332 1990:1 to 2017:09

124 2007:5 to 2017:09

333 1990:1 to 2017:09

ur

Skew.

332 1990:1 to 2017:09

Notes: Table 2 illustrates the statistics of the daily (Panel A) and monthly (Panel B) data. RVM denotes the realized volatility, VIX is the CBOE volatility index, VP is the variance risk premium, ∆OIL is the rate of change in the WTI oil price, ∆VIX and ∆OVX are the first differences (rate of change) in the VIX and the CBOE oil volatility index, respectively; and ∆XOI is designed to mirror the performance (weighted returns) of US companies operating in the petroleum industry. Bold values indicate that they are statistically significant at the 1% level.

Journal Pre-proof Table 3- Feedback Effects between the VIX Components and Oil Returns Panel A: Feedback Effects between VP and Oil Returns Sample: 1990-2017

VP  R𝑂𝑖𝑙 R𝑂𝑖𝑙  VP

Sample: 1990-2003

Sample: 2004-2017

#Lags=1

#Lags=2

#Lags=3

#Lags=1

#Lags=2

#Lags=3

#Lags=1

#Lags=2

#Lags=3

3.453*

5.447***

3.864***

0.967

0.986

1.473

9.286***

14.853***

11.283***

7.654

***

2.526

*

7.284

***

0.048

0.942

0.902

10.068

***

3.572

**

7.293***

Panel B: Feedback Effects between RVM and Oil Returns

R𝑂𝑖𝑙  RVM

#Lags=1

#Lags=2

***

***

8.54

6.86***

5.21

4.79***

#Lags=3

#Lags=1

**

0.06

4.98***

3.19*

3.62

#Lags=2

0.04

Sample: 2004-2017

of

RVM 

R𝑂𝑖𝑙

Sample: 1990-2003 #Lags=3

0.06

ro

Sample: 1990-2017

1.79

1.502

#Lags=1

#Lags=2

#Lags=3

***

***

5.96***

8.41***

8.88***

14.30

4.51**

9.17

lP

re

-p

Notes: Panels A illustrates the results of the Granger-causality test between the daily variance risk premium (VP) and oil returns (𝑅𝑂𝑖𝑙 ), while Panel B demonstrates the results of the Granger-causality test between the daily realized volatility (𝑅𝑉𝑀 ) and oil returns (𝑅𝑂𝑖𝑙 ). The values reported in the tables are the F-statistics. By FG we mean that there is a feedback effect form F to G, or simply F drives or Granger-causes G. The purpose is to understand whether risk appetite drives oil prices. "***," "**" and "*" denote statistical significance at the 1%, 5% and 10% levels, respectively.

Table 4- Feedback Effects between the VIX Components and the OVX

ur

na

Panel A: Feedback Effects between the VP and the OVX Sample: 2007-2017 #Lags=1

#Lags=2

#Lags=3

***

***

9.815***

14.566

ΔOVX  VP

1.879

Jo

VP  ΔOVX

14.554

0.076

0.806

Panel B: Feedback Effects between the RVM and the OVX Sample: 2007-2017 #Lags=1

#Lags=2

#Lags=3

***

***

6.381***

RVM  ΔOVX

9.458

ΔOVX  RVM

10.91***

9.754

13.932***

14.499***

Notes: Panel A reports the Granger (1969) causality test results between the daily variance risk premium (VP) and the rate of change in the OVX (ΔOVX), while Panel B reports the Granger (1969) causality test results between the realized volatility (RVM) and the rate of change in the OVX (ΔOVX). The oil volatility index (OVX) reflects the expectations of the US oil-market participants regarding the near 30-day volatility in crude oil prices by applying the VIX methodology to options spanning a wide range of strike prices. By FG we mean that F drives G. OVX data are available starting from May 10, 2007. "***" and "*" denote statistical significance at the 1% and 10% levels, respectively.

Journal Pre-proof Table 5 - Feedback Effects between the VP and Equity Portfolios Panel A – Feedback Effects between the VP and the S&P 500 Sample: 1990-2017 VP  ∆SP ∆SP VP

Sample: 1990-2003

Sample: 2004-2017

#Lags=1

#Lags=2

#Lags=3

#Lags=1

#Lags=2

#Lags=3

#Lags=1

#Lags=2

#Lags=3

217.13***

109.59***

85.82***

53.87***

27.40***

18.52***

163.71***

83.31***

67.60***

41.91

***

6.00

***

2.25

*

4.59

**

8.47

***

18.52

***

36.00

***

4.35

**

1.84

Panel B – Feedback Effects between the VP and ∆XOI Sample: 1990-2003

#Lags=2

#Lags=3

***

***

***

VP  ∆XOI

132.78

∆XOI  VP

46.14***

71.21

9.93***

54.52

8.16***

#Lags=1 7.59

***

2.68

#Lags=2 4.42

***

2.84*

#Lags=3 3.65

**

2.32*

ro

#Lags=1

Sample: 2004-2017 #Lags=1

#Lags=2

#Lags=3

***

***

49.32***

of

Sample: 1990-2017

117.7

36.6***

60.90

6.72***

4.86***

-p

Notes for Panel A: Granger (1969) causality test between the variance risk premium (VP) and the rate of change in the S&P 500 index (∆SP).

Jo

ur

na

lP

re

Notes for Panel B: Granger (1969) causality test between the variance risk premium (VP) and the ∆XOI, which computes the weighted returns of US companies in the oil industry. "***," "**" and "*" denote statistical significance at the 1%, 5% and 10% levels, respectively.

Journal Pre-proof Table 6- Effects of the VP on Oil Returns and Volatility (from 2004-2017) Panel A –Daily Data (2004-2017) M3 -0.023 -0.453*** 0.28*** 0.196***

-0.04**

-0.029*

-0.044*** 0.006

-0.049***

0.038*** 0.0171*** 0.046*** 0.956*** -0.013***

0.042*** 0.018*** 0.052*** 0.952*** 0.164*** -0.177***

0.057*** 0.025*** 0.044*** 0.948*** 0.178*** -0.197***

0.057*** 0.025*** 0.045*** 0.947*** 0.179*** -0.199***

-7376.5 8.21 11.73

-7311.2 11.6** 13.93

0.036*** 0.018*** 0.05*** 0.955*** 0.342*** -0.559*** 0.205*** -7298.2 12.93** 15.83

-7362.9 8.46 12.36

-7362.2 8.35 12.11

M2 0.009 -0.237*** 0.24***

M3 -0.004 -0.192*** 0.103*** 0.098***

M4 -0.017

M5 -0.021

-0.066*** 0.083***

-0.018

-0.017

-0.022* -0.02*

-0.02*

-0.067*** 0.031 0.061* -0.006 -0.021* -0.019

0.052*** 0.074*** 0.006 0.918*** -0.002

0.0567*** 0.077*** 0.007 0.914*** 0.047*** -0.048***

0.057*** 0.079*** 0.003 0.915*** 0.049*** -0.051***

0.057*** 0.079*** 0.006 0.914*** 0.05** -0.052***

-15213.2 5.75 15.2

-15184.3 5.374 14.91

0.05*** 0.078*** 0.005 0.915*** 0.103*** -0.221*** 0.12*** -15171.3 5.38 15.04

-15208.1 5.5 15.77

-15201.6 5.1 15.26

Panel B: Daily Data (1990-2017)

na

lP

M1 0.035 -0.012

ur

Intercept 𝑉𝑃𝑡 𝑉𝑃𝑡−1 𝑉𝑃𝑡−2 𝑉𝑃𝑡−3 𝑉𝑃𝑡−4 𝑂𝑖𝑙 𝑅𝑡−1 𝑂𝑖𝑙 𝑅𝑡−2

Jo

µ0 ARCH(1) (ut-1<0)*ARCH(1) GARCH(1) 𝑉𝑃𝑡 𝑉𝑃𝑡−1 𝑉𝑃𝑡−2 Log likelihood QLB(k=5) QLB(k=10)

ro

re

µ0 ARCH(1) (ut-1<0)*ARCH(1) GARCH(1) 𝑉𝑃𝑡 𝑉𝑃𝑡−1 𝑉𝑃𝑡−2 Log likelihood QLB(k=5) QLB(k=10)

M4 -0.044

M5 -0.047

-0.085** 0.135***

-0.089** 0.099* 0.055 -0.014 -0.05*** 0.007

of

M2 -0.007 -0.464*** 0.478***

-p

M1 0.045 -0.02*

Intercept 𝑉𝑃𝑡 𝑉𝑃𝑡−1 𝑉𝑃𝑡−2 𝑉𝑃𝑡−3 𝑉𝑃𝑡−4 𝑂𝑖𝑙 𝑅𝑡−1 𝑂𝑖𝑙 𝑅𝑡−2

Notes: The table reports the estimation results for Eqs. (9) and (10). The regression model is: 𝑅𝑡𝑜𝑖𝑙 = 𝑤0 + 𝐽 𝑂𝑖𝑙 𝐾 2 2 2 2 ∑𝐻 𝑖=1 𝑏𝑖 𝑉𝑃𝑡−𝑖+1 + ∑𝑗=1 𝑐𝑗 𝑅𝑡−𝑗 + 𝑢𝑡 and 𝜎𝑢,𝑡 = 𝜇0 + 𝛼1 𝑢𝑡−1 + 𝛾𝑆𝑡−1 𝑢𝑡−1 + 𝛽1 𝜎𝑢,𝑡−1 + ∑𝑖=0 𝜃𝑖 𝑉𝑃𝑡−𝑖 . For 19902003, the VP does not play any significant role in affecting oil returns or volatility for both daily and monthly data. Increased implied risk aversion negatively affects oil returns and positively affects the volatility of crude oil. QLB refers to the Q-statistic of Ljung-Box’s (1978) test for the hypothesis of no serial correlation in the squared residuals at the kth lagged order.

Journal Pre-proof Table 7 - Effects of RVM on Oil Returns and Volatility (from 2004-2017) Panel A –Daily Data (2004-2017)

-0.04** 0.004

-0.042***

-0.009 0.02*** 0.053*** 0.942*** 0.005***

-0.009 0.008** 0.046*** 0.963*** 0.214*** -0.211***

-0.008 0.008** 0.046*** 0.963*** 0.22*** -0.217***

-0.009 0.008** 0.047*** 0.962*** 0.213*** -0.21***

-7379.3 5.19 8.78

-7363.4 8.05 12.06

-0.005 0.007* 0.045*** 0.965*** -0.475*** 1.175*** -0.698*** -7351.6 7.76 12.59

-7361.8 8.13 12.09

-7360.8 8.4 12.35

M5 0.089

-0.188** 0.182**

-0.242** 0.306** -0.002 -0.068 -0.041** 0.008

ro M3 0.012 0.064 -0.14* 0.077

-0.017

-0.017

-0.017 -0.016

-0.018

0.019** 0.081*** 0.001 0.906*** 0.006***

0.016** 0.072*** 0.005 0.915*** 0.128*** -0.123***

0.017** 0.072*** 0.005 0.915*** 0.129*** -0.124***

0.017** 0.073*** 0.005 0.914*** 0.127*** -0.122***

-15198.7 5.3 14.68

-15193 6.51 15.78

0.017** 0.071*** 0.005 0.916*** -0.067*** 0.271*** -0.199*** -15180.8 6.46 15.76

-15191.5 6.52 15.86

-15185.9 6.47 15.67

na

M2 0.016 -0.035 0.035

ur

µ0 ARCH(1) (ut-1<0)*ARCH(1)) GARCH(1) 𝑅𝑉𝑀,𝑡 𝑅𝑉𝑀,𝑡−1 𝑅𝑉𝑀,𝑡−2 Log likelihood QLB(k=5) QLB(k=10)

M4 0.084

of

-0.04

M1 0.021 -0.0004

Jo

Intercept 𝑅𝑉𝑀,𝑡 𝑅𝑉𝑀,𝑡−1 𝑅𝑉𝑀,𝑡−2 𝑅𝑉𝑀,𝑡−3 𝑅𝑉𝑀,𝑡−4 𝑂𝑖𝑙 𝑅𝑡−1 𝑂𝑖𝑙 𝑅𝑡−2

-0.037**

lP

Panel B: Daily Data (1990-2017)

M3 0.091 -0.084 -0.072 0.15

-p

µ0 ARCH(1) (ut-1<0)*ARCH(1) GARCH(1) 𝑅𝑉𝑀,𝑡 𝑅𝑉𝑀,𝑡−1 𝑅𝑉𝑀,𝑡−2 Log likelihood QLB(k=5) QLB(k=10)

M2 0.092 -0.117 0.11

re

M1 0.093 -0.007

Intercept 𝑅𝑉𝑀,𝑡 𝑅𝑉𝑀,𝑡−1 𝑅𝑉𝑀,𝑡−2 𝑅𝑉𝑀,𝑡−3 𝑅𝑉𝑀,𝑡−4 𝑂𝑖𝑙 𝑅𝑡−1 𝑂𝑖𝑙 𝑅𝑡−2

M4 0.01

M5 0.015

-0.072 0.072

-0.075 0.085 0.023 -0.032 -0.018 -0.016

𝐽 𝑂𝑖𝑙 2 2 Notes: The regression model is: 𝑅𝑡𝑜𝑖𝑙 = 𝑤0 + ∑𝐻 𝑖=1 𝑏𝑖 𝑅𝑉𝑀,𝑡−𝑖+1 + ∑𝑗=1 𝑐𝑗 𝑅𝑡−𝑗 + 𝑢𝑡 and 𝜎𝑢,𝑡 = 𝜇0 + 𝛼1 𝑢𝑡−1 + 𝐾 2 2 𝛾𝑆𝑡−1 𝑢𝑡−1 + 𝛽1 𝜎𝑢,𝑡−1 + ∑𝑖=0 𝜃𝑖 𝑅𝑉𝑀,𝑡−𝑖 . The 𝜃 coefficients account for any effect of the realized volatility (RV) on the conditional volatility in oil returns. For 1990-2003, RVM does not play any significant role. The rest of the notations are as in the former table.

Journal Pre-proof

Table 8 –Decomposition of the Variance in the Structural VAR

0.084 0.852 0.643 0.537 0.586 1.070 1.125 3.392 5.500 8.625 11.137 13.231 19.155 16.295

6.417 8.825 9.768 8.832 7.567 7.325 7.002 6.520 6.719 7.613 8.070 8.529 13.735 30.239

0.008 1.673 2.178 1.767 1.524 1.433 1.338 2.088 2.560 2.518 2.510 2.355 2.591 6.567

OIL 91.249 84.809 82.676 82.653 83.623 83.401 84.271 81.998 79.664 76.156 73.518 71.389 60.478 42.322

of

1 2 3 4 5 6 7 8 9 10 11 12 18 24

ro

Demand

Variance Risk Premium (VP) 2.242 3.842 4.735 6.211 6.700 6.771 6.264 6.002 5.556 5.088 4.765 4.496 4.042 4.578

-p

Supply

re

Horizon

Economic Uncertainty (RVM)

na

lP

Notes: The table reports the decomposition of the variance in the shocks in oil prices. The shocks considered are those in the supply of and demand for oil, uncertainty--captured by realized volatility--and the risk aversion/appetite captured by the volatility in the variance risk premium.

Table 9: Results of the LM Test for the Serial Correlation of the VAR Residuals

ur

LM-Stat. 24.571 26.534 21.451 25.543 19.486 18.630 18.172 16.654 19.341 17.730 23.799 25.563

Jo

Lags (Q) 1 2 3 4 5 6 7 8 9 10 11 12

Prob. 0.486 0.379 0.667 0.432 0.773 0.814 0.835 0.893 0.780 0.853 0.531 0.431

Lags (Q) 13 14 15 16 17 18 19 20 21 22 23 24

LM-Stat. 23.163 33.867 25.004 34.176 33.794 18.275 20.225 21.987 29.467 21.828 27.642 28.360

Prob. 0.568 0.110 0.462 0.104 0.112 0.830 0.734 0.636 0.244 0.645 0.324 0.291

Notes: The table reports the results of the LM test for the serial correlation of the VAR residuals. The null hypothesis postulates no serial correlation at lag order Q. This hypothesis is not rejected, as evident by the relatively high Prob. values.

Journal Pre-proof

Risk Appetite and Oil Prices

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We examine the link between oil prices, risk appetite and economic uncertainty We decompose the VIX into two components: economic uncertainty and implied risk appetite The contribution of risk appetite to oil prices has become remarkable since the mid-2000s Risk appetite drives the OVX as well as oil-sector share prices but not vice versa Uncertainty negatively affects oil prices but positively affects conditional volatility

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