Dealing with Downside Risk in Energy Markets: Futures versus Exchange-Traded Funds. Panit Arunanondchai

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1 Dealing with Downside Risk in Energy Markets: Futures versus Exchange-Traded Funds Panit Arunanondchai Ph.D. Candidate in Agribusiness and Managerial Economics Department of Agricultural Economics, Texas A&M University Kunlapath Sukcharoen Assistant Professor of Agricultural Business and Economics Department of Agricultural Sciences, West Texas A&M University David J. Leatham Professor, Associate Head for Graduate Programs Department of Agricultural Economics, Texas A&M University Selected Paper prepared for presentation at the Southern Agricultural Economics Association (SAEA) Annual Meeting, Jacksonville, Florida, February 2-6, 2018 Copyright 2018 by Panit Arunanondchai, Kunlapath Sukcharoen, and David J. Leatham. All rights reserved. Readers may make verbatim copies of this document for non-commercial purposes by any means, provided that this copyright notice appears on all such copies.

2 Dealing with Downside Risk in Energy Markets: Futures versus Exchange-Traded Funds Abstract The emergence of energy exchange-traded funds (ETFs) has provided an alternative vehicle for both energy producers and users to hedge their respective exposures to unfavorable energy price movements without opening a relative expensive futures account. While hedging with energy ETFs has been touted as a promising alternative to hedging with traditional energy futures, the question concerning the hedging effectiveness of energy ETFs versus energy futures, especially in terms of their ability to manage downside risk, remains largely unexplored. Accordingly, this study formally compares the hedging effectiveness of the two instruments in a downside risk framework from the perspective of both short and long hedgers. Two estimation methods are applied to estimate the minimum-value at Risk (VaR) and minimum-expected Shortfall (ES) hedge ratios: the empirical distribution function method and the kernel copula method. The empirical application focuses on four different energy commodities: crude oil, gasoline, heating oil, and natural gas. Key words: copulas, downside risk hedging, futures, exchange-traded funds, energy markets 1

3 Introduction Energy is an important part of modern economy. By nature, the energy markets are much more volatile than other commodity markets. Specifically, price risk is one of the main concerns in the energy markets. Energy commodity prices can be affected by a variety of factors, such as weather, changes in tax and legal systems, changes in transportation, and unexpected changes in supply and demand. Therefore, it is desirable to focus on hedging against unexpected price movements of energy commodities. Among derivatives, futures contracts are widely used to hedge price risk because of their liquidity, speed, and low transaction costs. Numerous studies had investigated the hedging effectiveness of futures contracts in hedging price risk of energy commodities (see, e.g., Chang et al., 2011; Alizadeh et al., 2008; Jin and Jorion, 2006a; Juhl et al., 2012; Alexander et al., 2013; Benada and Konecna, 2017). Theoretically, futures contracts can be used to reduce the risk of unfavorable price changes, because spot and futures prices of the same commodity tend to move in the same direction. Subsequently, changes in the value of a futures position could offset undesirable changes in the value of a spot position. Knill et al. (2006) show that oil and gas company uses futures contracts mainly to hedge the downside risk. In addition to futures contracts, exchange-traded funds (ETFs) have been promoted as a promising alternative instrument for hedging due to their low costs, tax efficiency, and stock-like characteristics. Generally, ETFs do not have a maturity date, thus they can be held indefinitely. Nevertheless, their ability to manage downside risk remains largely unexplored. Sukcharoen et al. (2015) investigate the hedging effectiveness of both futures and ETFs on the gasoline market and show that ETF hedging could outperform futures hedging during the high-volatility period, but not during the normal time period. In this study, we investigate and extend the use of both ETFs and futures contracts as an instrument for price risk reduction to four different energy 2

4 commodity markets: crude oil, gasoline, heating oil, and natural gas. According to Cotter and Hanly (2006), the choice of performance measures is related to hedger s objectives and trading position (either short or long). Hence, this study formally compares the hedging performance of the two instruments from the perspective of both short and long hedgers. Two downside risk measures, value at risk (VaR) and expected shortfall (ES), are employed under two different estimation methods: the empirical distribution function method and the kernel copula method. The remainder of this paper is organized as follows. Section II describes the data and preliminary analysis. Section III describes the hedging models Section IV discusses the empirical results of the different hedging models with different hedging instruments. Lastly, the conclusions drawn from this study are provided in Section V. Data and Preliminary Analysis The empirical analysis is based on daily spot, futures, and ETF prices for four different energy commodities: crude oil, gasoline, heating oil, and natural gas. The spot and futures price data used include daily spot and futures prices for West Texas Intermediate (WTI) crude oil, New York Harbor Regular gasoline, New York Harbor No. 2 heating oil, and Henry Hub natural gas. With respect to the ETF price data, we employ daily ETF prices for the United States Oil (USO) Fund, United States Gasoline (UGA) Fund, United States Diesel-Heating Oil (UHN) Fund, and United States Natural Gas (UNG) Fund. The spot and futures price data are drawn from the U.S. Energy Information Administration (EIA), and the ETF price data are obtained from Thomson Reuters Datastream. For each commodity we use the ETF launch date as the first date of the spot, futures and ETF time series. Accordingly, daily log returns are calculated using the price data from April 10, 2006 to August 31, 2017 for crude oil, from February 27, 2008 to August 31, 3

5 2017 for gasoline, from April 9, 2008 to August 31, 2017 for heating oil, and from April 18, 2007 to August 31, 2017 for natural gas. To construct each continuous series of futures returns, we use the nearby futures contract and switch to the next contract month at expiration. Care has been taken to ensure that the log returns of futures prices are calculated using the same futures contract. Altogether, we have a total of 2,862 observations for crude oil, 2,389 observations for gasoline, 2,360 observations for heating oil, and 2,606 observations for natural gas. Table 1 reports summary statistics for daily spot, futures, and ETF log returns for crude oil, gasoline, heating oil, and natural gas. Over the time period studied, the means of all return series are negative but close to zero. The spot returns are found to be more volatile than the futures and ETF returns for all four commodities, with the natural gas market being the most volatile. All return series are slightly skewed and display high excess kurtosis (especially the gasoline and natural gas spot returns). This implies that all return series are not normally distributed. The Augmented Dicky-Fuller (ADF) test results indicate that each return series is stationary. For crude oil and heating oil markets, there is a stronger correlation between the spot and futures returns than between the spot and ETF returns, but the opposite is observed for gasoline and natural gas markets. The lowest correlation of is between the natural gas spot and futures returns. <Table 1> Minimum-Downside Risk Hedging Problem Methodology 4

6 !! Let R! and R! respectively denote the per-period returns on the spot and futures positions at time t, and h denote the hedge ratio. The per-period return on the hedged portfolio for the case of futures hedging is given by: R!! = R!!! hr! (1) for short hedgers (commodity producers), and by: R!! = R!!! + hr! (2) for long hedgers (commodity users). For the case of ETF hedging, the per-period ETF return at period t, denoted as R!"#!, is used in place of R!!. In this study, we assume that the hedger s objective is to minimize the downside risk of the hedged portfolio return. The hedger s problem is then to select the optimal hedge ratio h that minimize the downside risk of the hedged position. The following equation formally presents the hedger s problem: h = arg min! RM R!! (3) where RM denotes the risk measure. In this paper, we consider the two most popular downside risk measures: Value at Risk (VaR) and Expected Shortfall (ES). For a given confidence level, α, VaR is defined as the largest potential loss on a hedged portfolio over a given time horizon and given by: VaR! R!! = F!! (1 α) (4) where F is the cumulative distribution function of R!!. On the other hand, the ES is defined as the expected loss on a hedged portfolio conditional on the amount of losses exceeding the VaR of the portfolio. More specifically, the ES at the confidence level α over a given time horizon is given by: 5

7 For both VaR and ES, we consider α = 0.90, 0.95, and ES! R!! = E R!! R!! VaR! (5) Estimation of the Optimal Hedge Ratios To find the minimum-var and minimum-es hedge ratios, we solve the optimization problem in Equation (3) numerically. Two nonparametric approaches are used to estimate the distribution of the portfolio returns: the empirical distribution function and kernel copula methods. The empirical distribution method (also known as the historical simulation technique) uses historical return data to generate a distribution of portfolio returns without making any specific distribution assumption about portfolio return distribution. Specifically, for any given hedge ratio, h, we use! an empirical distribution function to estimate the distribution of R! and then calculate the VaR and ES of the resulting hedged portfolio. The optimal hedge ratios are then derived through a numerical optimization procedure. In this study, we also consider a kernel copula method to estimate the joint distributions!! of R! and R! and thus the distribution of R!!. The kernel copula approach is based on the Sklar s theorem (Sklar, 1959). For the case of two random variables, the Sklar s theorem states that any bivariate distribution can be decomposed into two parts: two individual marginal distributions and a copula that describes their dependence structure. More formally, F x!, x! = C F! x!, F! x! (6) where F! x! and F! (x! ) are marginal distributions of random variables x! and x!, respectively, and C: 0,1! [0,1] is a copula function. If F! x! and F! x! are differentiable, the joint density function, f x!, x!, can be expressed as: f x!, x! = f! x! f! x! c F! x!, F! x! (7) 6

8 where f! x! and f! (x! ) are the density of F! x! and F! (x! ), and c( ) is the density of the copula function. This decomposition implies that the modeling of the two marginal distributions can be separated from the modeling of the dependence structure.!!! Accordingly, the procedure for constructing the joint distributions of R! and R! (and R! and R!"#! ) using the kernel copula approach can be briefly summarized in four steps. First, we estimate the marginal distribution for each return series using an empirical distribution function, and then transform the return series into a standard uniform variable (also known as copula data). Second, the copula density, c F! x!, F! x!, is estimated nonparametrically using a kerneltype copula density estimator of Geenens et al. (2017). Third, we generate 10,000 Monte Carlo draws of the two standard uniform variables from the estimated copula density. Finally, the draws from the copula are converted to spot and futures (or ETF) return series by applying the inverse of the corresponding marginal distribution function of each return series. Then, for any! given h, we use the simulated return series to generate the distribution of R! as well as its VaR and ES. Similar to the empirical distribution function method, the minimum-var and minimum- ES hedge ratios are computed using a numerical optimization approach. Hedging Effectiveness To analyze hedging effectiveness of two alternative hedging instruments, we apply a rolling window analysis. Specifically, we compute the minimum-var and minimum-es hedge ratios for both short and long hedgers using the first 250 return observations (i.e., a rolling window of 250 trading days). To capture the out-of-sample hedging performance, the next 250 observations are used to measure the hedging effectiveness. Following Ederington (1979), hedging effectiveness 7

9 is measured as a percentage reduction in the risk of the unhedged (spot) position relative to the risk of the hedged portfolio. That is, hedging effectiveness is defined as: HE = 1 RM R!!! RM R! (8)! where RM is the risk measure, R!! is the returns on hedged portfolio, and R! is the returns on unhedged portfolio or spot returns. In this study, four risk measures are considered: Variance, Semivariance (assuming that the target return is zero as the basic goal of hedging is to avoid loss), VaR, and ES. We then move the rolling window by one day and recalculate the hedge ratios and out-of-sample hedging effectiveness. This moving window procedure results in 2,363 test windows for crude oil, 1,890 observations for gasoline, 1,861 observations for heating oil, and 2,107 observations for natural gas. Empirical Results This section presents our empirical findings for optimal crude oil, gasoline, heating oil, and natural gas hedge ratios calibrated through the empirical distribution function and kernel copula methods. Then, the results of out-of-sample hedging effectiveness for all commodities under different hedging objectives and hedging instruments are presented and compared. Optimal Hedge Ratios <Table 2> Table 2 presents the average minimum-var, and minimum-es hedge ratios for all commodities calibrated under the empirical distribution function (Panel A) and kernel copula (Panel B) methods. Overall, the optimal hedge ratios for all commodities except natural gas under all 8

10 hedging objectives are consistently in a range from 0.8 to 1.5. For natural gas, on the other hand, the optimal hedge ratios are between 0.2 and 0.5. Out-of-Sample Hedging Effectiveness <Tables 3-10> Table 3-10 present the out-of-sample hedging effectiveness of the minimum-var, and the minimum-es portfolios for long and short hedging objectives under the two different estimation methods. For each commodity and estimation method, we present the mean percentage reductions from the perspective of the hedged position to the unhedged position. The mean values are estimated across the 2,363 out-of-sample test windows for crude oil, 1,890 windows for gasoline, 1,861 windows for heating oil, and 2,107 windows for natural gas. The best performing hedging instrument for each hedging objective and each hedging effectiveness measure is highlighted in bold type. Crude Oil Overall we find evidence that futures hedging outperforms ETF hedging in terms of the portfolio VaR and ES reduction. This is consistent with the preliminary findings from Table 1 where the correlation coefficient between spot and futures log returns (0.934) is higher than that between spot and ETF log returns (0.903). For the minimum-var objective, futures hedging is more effective than ETF hedging in terms of the portfolio VaR reduction across all confidence levels under the empirical distribution function and kernel copula methods. From Table 3 and 4, all the mean values of VaR reductions are positive for both futures and ETF hedging, which suggests that it is reasonable for those who 9

11 invest in crude oil to hedge. The mean values of VaR reduction from using futures contracts are at least 77%, 70%, and 63%, while the mean values of VaR reductions from using ETFs are at least 63%, 61%, and 47% at the 90%, 95%, and 99% confidence levels respectively. Similarly, under the minimum-es objective, futures hedging is more effective than ETF hedging in terms of ES reduction. All the mean values of ES reduction are positive for both futures and ETF hedging. We can see from Table 3 and 4 that almost all the mean values of ES reduction from using futures are higher than from using ETFs under the empirical distribution function and kernel copula methods at all confidence levels. The only exception is the case at the 99% confidence level under the kernel copula method, where the mean value of ES reduction from using futures is lower than that from using ETF. Overall, the mean values of ES reduction from using futures contracts are at least 65%, 60%, and 48%, while the mean values of ES reductions from using ETFs are at least 56%, 52%, and 44% at the 90%, 95%, and 99% confidence levels respectively. Gasoline In contrast to crude oil, we find evidence that ETF hedging outperforms futures hedging in terms of the portfolio VaR and ES reduction. In Table 1, the correlation coefficient between spot and ETF log returns (0.601) is higher than that between spot and futures log returns (0.518). From Table 5 and 6, the mean values of VaR reduction from using ETF are at least 18%, 16%, and 7%, while the mean values of VaR reductions from using futures contracts are at least 11%, 5%, and -2% at the 90%, 95%, and 99% confidence levels respectively. Moreover, the mean values of ES reduction from using ETFs are at least 14%, 11%, and 8%, while the mean values of ES reductions from using futures contracts are at least 2%, -2%, and -5% at the 90%, 10

12 95%, and 99% confidence levels respectively. That is, in some cases, we find evidence that futures hedging is very ineffective and yields negative downside risk reduction. On the other hand, ETF hedging yield only positive downside risk reduction, which is desirable. Heating Oil Similar to crude oil, we find evidence that futures hedging outperforms ETF hedging in terms of the portfolio VaR and ES reduction. Consistently, Table 1 reports the correlation coefficient between spot and futures log returns (0.896), which is higher than that between spot and ETF log returns (0.845). For the minimum-var objective, futures hedging is more effective than ETF hedging in terms of the portfolio VaR reduction across all confidence levels under the empirical distribution function and kernel copula methods. From Table 7 and 8, the mean values of VaR reduction from using futures contracts are at least 55%, 54%, and 46%, while the mean values of VaR reductions from using ETFs are at least 51%, 48%, and 33% at the 90%, 95%, and 99% confidence levels respectively. Similarly, under the minimum-es objective, futures hedging is more effective than ETF hedging in terms of ES reduction. All the mean values of ES reduction are positive for both futures and ETF hedging. We can see from Table 7 and 8 that almost all the mean values of ES reduction from using futures are higher than from using ETFs under the empirical distribution function and kernel copula methods at all confidence levels. The mean values of ES reduction from using futures contracts are at least 51%, 49%, and 37%, while the mean values of ES reductions from using ETFs are at least 43%, 39%, and 31% at the 90%, 95%, and 99% confidence levels respectively. 11

13 Natural Gas Unlike other commodities, we do not find clear evidence on which instrument is better in terms of portfolio VaR and ES reduction under both the empirical distribution function and kernel copula methods. In fact, we find that most mean values of the downside risk reduction from using either futures contracts or ETFs are very low or even negative. Moreover, Table 1 shows that the correlation coefficients between spot and futures log returns and that between spot and ETF log returns are and respectively, which are very low. From Table 9 and 10, the mean values of VaR reduction from using futures contracts are at least -20%, -13%, and -15%, while the mean values of VaR reductions from using ETFs are at least -16%, -5%, and -9% at the 90%, 95%, and 99% confidence levels respectively. Moreover, the mean values of ES reduction from using futures contracts are at least -14%, -13%, and -15%, while the mean values of ES reductions from using ETFs are at least -7%, -7%, and -10% at the 90%, 95%, and 99% confidence levels respectively. Hence, we conclude that hedging using either futures contracts or ETFs does not seem to yield desirable outcomes for natural gas. Conclusions We find evidence supporting that ETF hedging outperforms futures hedging only for the case of gasoline. On the other hand, hedging with futures contracts are more effective than with ETFs for crude oil and heating oil. For natural gas, unlike other commodities, we do not find clear evidence on which instrument is better in terms of portfolio downside risk reduction. In fact, we find that hedging natural gas with either futures contracts or ETFs do not yield a desirable outcome. Furthermore, we find that correlation coefficients between the spot returns and the instrument returns are also consistent with our results. They can be used as a preliminary 12

14 indicator for investors to make a decision on which instrument should be used to hedge a particular commodity. References Ederington, L.H The Hedging Performance of New Futures Markets. Journal of Finance, 34(1): Geenens, G., Charpentier, A. Paindaveine D Probit Transformation for Nonparametric Kernel Estimation of the Copula Density. Bernoulli, 23(3): Sklar, Abe Fonctions de Répartition à n Dimensions et Leurs Marges. Publications de l' Institut Statistique de l'université de Paris, 8: Table 1. Summary statistics of daily spot, futures, and ETF log returns for crude oil, gasoline, heating oil, and natural gas. Spot Futures ETF Crude Oil Mean (%) Standard Deviation (%) Minimum (%) Maximum (%) Skewness Excess Kurtosis ADF * * * Correlation (with Spot) Gasoline Mean (%) Standard Deviation (%) Minimum (%) Maximum (%) Skewness Excess Kurtosis ADF * * * Correlation (with Spot) Heating Oil Mean (%) Standard Deviation (%) Minimum (%) Maximum (%) Skewness Excess Kurtosis ADF * * * Correlation (with Spot)

15 Natural Gas Mean (%) Standard Deviation (%) Minimum (%) Maximum (%) Skewness Excess Kurtosis ADF * * * Correlation (with Spot) Note: ADF is the Augmented Dickey-Fuller test statistic, where * denotes the rejection of the null hypothesis of a unit root (non-stationarity). 14

16 Table 2. Average minimum-value at Risk (VaR) and minimum-expected Shortfall (ES) hedge ratios for the case of ETF (futures) hedging Hedging Short Hedgers Long Hedgers Objectives Crude Oil Gasoline Heating Oil Natural Gas Crude Oil Gasoline Heating Oil Natural Gas Panel A: The Empirical Distribution Function Method (1.024) (0.984) (0.966) (0.419) (0.985) (0.995) (0.958) (0.231) (1.022) (0.981) (0.949) (0.399) (1.005) (1.007) (0.915) ( (1.027) (0.990) (0.893) (0.429) (0.983) (1.129) (0.870) (0.411) (1.011) (1.050) (0.957) (0.368) (1.002) (1.044) (0.908) (0.279) (0.993) (1.035) (0.947) (0.316) (1.010) (1.082) (0.875) (0.288) (0.991) (1.045) (1.080) (0.371) (1.041) (1.233) (0.925) (0.028) Panel B: The Kernel Copula Method (0.972) (0.789) (0.969) (0.242) (0.975) (0.742) (0.948) (0.190) (0.968) (0.804) (0.979) (0.208) (0.989) (0.752) (0.957) (0.248) (0.963) (0.924) (0.998) (0.379) (1.008) (0.918) (0.946) (0.422) (0.962) (0.834) (0.989) (0.247) (0.999) (0.792) (0.934) (0.250) (0.961) (0.865) (0.998) (0.272) (1.009) (0.837) (0.921) (0.293) (0.851) (0.963) (1.040) (0.298) (0.961) (1.007) (0.916) (0.375) Notes: The optimal hedge ratios for both short and long hedgers are estimated using a rolling window approach with a rolling window of 250 trading days. The total number of rolling windows is 2,363 windows for crude oil, 1,890 windows for gasoline, 1,861 windows for heating oil, and 2,107 windows for natural gas.

17 Table 3. Out-of-sample crude oil ETF (futures) hedging effectiveness (in percentage) empirical distribution function method Hedging Hedging Effectiveness Measures Objectives Variance Semivariance VaR (90%) VaR (95%) VaR (99%) ES (90%) ES (95%) ES (99%) Panel A: Long Hedgers (92.317) (92.207) (88.658) (85.108) (68.948) (78.535) (73.436) (59.939) (92.145) (92.114) (87.952) (84.643) (68.563) (78.173) (73.190) (59.965) (86.706) (86.676) (77.751) (75.514) (63.222) (70.339) (66.530) (55.079) (92.493) (92.441) (89.405) (85.976) (69.077) (79.090) (73.878) (60.409) (92.380) (92.377) (89.281) (85.899) (69.265) (79.104) (73.985) (60.581) (88.930) (88.785) (80.145) (78.241) (65.977) (72.855) (68.942) (57.369) Panel B: Short Hedgers (92.194) (92.073) (88.617) (84.831) (72.309) (78.400) (73.120) (57.271) (92.083) (92.001) (89.063) (85.351) (72.017) (78.597) (73.121) (56.861) (90.793) (90.616) (85.495) (81.956) (69.373) (75.564) (70.412) (55.272) (92.220) (92.113) (89.061) (84.905) (72.136) (78.493) (73.056) (57.108) (92.188) (92.168) (88.905) (84.862) (71.925) (78.421) (73.052) (57.207) (89.481) (89.227) (83.544) (80.303) (68.751) (74.331) (69.532) (54.857) Notes: The table reports the mean out-of-sample hedging effectiveness for both long and short hedgers. The mean hedging effectiveness is calculated across 2,363 test windows. The best performing hedging instrument for each hedging objective and each hedging effectiveness measure is highlighted in bold type. 16

18 Table 4. Out-of-sample crude oil ETF (futures) hedging effectiveness (in percentage) kernel copula method Hedging Hedging Effectiveness Measures Objectives Variance Semivariance VaR (90%) VaR (95%) VaR (99%) ES (90%) ES (95%) ES (99%) Panel A: Long Hedgers (92.608) (92.474) (90.326) (86.283) (69.228) (79.459) (74.071) (60.374) (92.624) (92.534) (90.390) (86.352) (69.096) (79.486) (74.083) (60.482) (91.687) (91.650) (87.465) (83.980) (67.649) (77.518) (72.485) (59.392) (92.537) (92.493) (89.939) (86.046) (68.871) (79.251) (73.920) (60.451) (92.349) (92.339) (88.910) (85.321) (68.508) (78.682) (73.529) (60.304) (80.380) (80.323) (73.335) (70.888) (57.190) (65.034) (60.593) (49.179) Panel B: Short Hedgers (92.540) (92.610) (90.741) (86.550) (72.178) (79.672) (73.912) (57.515) (92.490) (92.576) (90.430) (86.393) (72.134) (79.526) (73.852) (57.497) (91.672) (91.790) (88.551) (84.751) (71.382) (78.111) (72.684) (56.769) (92.371) (92.459) (89.908) (85.963) (72.029) (79.226) (73.634) (57.385) (92.225) (92.314) (89.358) (85.579) (71.852) (78.859) (73.360) (57.256) (81.596) (81.771) (77.194) (73.922) (62.442) (67.950) (63.104) (48.335) Notes: The table reports the mean out-of-sample hedging effectiveness for both long and short hedgers. The mean hedging effectiveness is calculated across 2,363 test windows. The best performing hedging instrument for each hedging objective and each hedging effectiveness measure is highlighted in bold type. 17

19 Table 5. Out-of-sample gasoline ETF (futures) hedging effectiveness (in percentage) empirical distribution function method Hedging Hedging Effectiveness Measures Objectives Variance Semivariance VaR (90%) VaR (95%) VaR (99%) ES (90%) ES (95%) ES (99%) Panel A: Long Hedgers (22.110) (19.054) (21.175) (13.536) (1.556) (9.808) (5.456) (0.452) (20.636) (17.540) (20.884) (13.115) (1.200) (9.031) (4.365) (-1.942) (5.665) (1.071) (11.061) (6.074) (-2.854) (1.918) (-2.060) (-6.851) (23.543) (20.918) (21.692) (14.721) (1.977) (10.284) (5.640) (0.172) (20.395) (17.489) (20.239) (13.138) (1.142) (8.767) (4.096) (-1.686) (4.323) (2.271) (10.880) (5.873) (-2.318) (2.390) (-1.067) (-5.766) Panel B: Short Hedgers (21.316) (22.647) (22.467) (17.364) (7.896) (12.830) (8.600) (-1.373) (22.606) (25.106) (24.229) (18.154) (8.652) (13.761) (9.380) (0.857) (12.632) (15.783) (18.089) (13.919) (7.013) (10.005) (6.559) (-3.830) (20.627) (23.666) (23.940) (17.378) (7.994) (13.096) (8.542) (-0.880) (19.411) (23.022) (22.511) (17.013) (8.436) (12.879) (8.611) (-0.753) (11.122) (14.347) (17.700) (14.423) (6.149) (9.320) (5.289) (-5.056) Notes: The table reports the mean out-of-sample hedging effectiveness for both long and short hedgers. The mean hedging effectiveness is calculated across 1,890 test windows. The best performing hedging instrument for each hedging objective and each hedging effectiveness measure is highlighted in bold type. 18

20 Table 6. Out-of-sample gasoline ETF (futures) hedging effectiveness (in percentage) kernel copula method Hedging Hedging Effectiveness Measures Objectives Variance Semivariance VaR (90%) VaR (95%) VaR (99%) ES (90%) ES (95%) ES (99%) Panel A: Long Hedgers (27.164) (24.438) (22.778) (16.011) (3.833) (12.392) (8.147) (4.514) (26.708) (24.041) (22.370) (15.637) (3.940) (12.164) (7.985) (4.213) (22.890) (20.214) (21.219) (13.638) (3.148) (10.073) (6.008) (1.072) (26.650) (23.939) (22.252) (15.394) (4.105) (12.039) (7.883) (3.634) (25.747) (23.082) (21.935) (14.774) (3.891) (11.466) (7.462) (2.858) (21.111) (18.483) (20.123) (13.362) (2.867) (9.238) (5.200) (0.093) Panel B: Short Hedgers (26.700) (29.059) (24.323) (18.611) (10.766) (15.479) (12.069) (5.415) (26.403) (29.026) (24.519) (18.827) (10.535) (15.304) (11.850) (5.496) (23.699) (26.145) (23.595) (18.778) (8.466) (14.035) (10.021) (2.009) (26.636) (29.181) (24.589) (19.666) (10.199) (15.392) (11.739) (5.087) (26.147) (28.666) (24.377) (19.722) (9.533) (15.155) (11.360) (4.321) (22.866) (25.079) (23.589) (18.549) (7.844) (13.598) (9.440) (0.617) Notes: The table reports the mean out-of-sample hedging effectiveness for both long and short hedgers. The mean hedging effectiveness is calculated across 1,890 test windows. The best performing hedging instrument for each hedging objective and each hedging effectiveness measure is highlighted in bold type. 19

21 Table 7. Out-of-sample heating oil ETF (futures) hedging effectiveness (in percentage) empirical distribution function method Hedging Hedging Effectiveness Measures Objectives Variance Semivariance VaR (90%) VaR (95%) VaR (99%) ES (90%) ES (95%) ES (99%) Panel A: Long Hedgers (79.791) (77.222) (67.599) (64.581) (50.450) (57.803) (52.924) (38.497) (79.513) (77.570) (66.318) (63.840) (50.954) (57.685) (53.313) (40.545) (78.053) (75.975) (63.032) (61.399) (48.337) (55.611) (51.593) (40.106) (80.236) (78.291) (67.574) (64.565) (51.190) (58.509) (53.806) (40.904) (79.678) (78.180) (65.836) (63.295) (50.304) (57.614) (53.428) (42.055) (75.597) (73.184) (60.624) (59.304) (47.192) (53.792) (49.961) (38.450) Panel B: Short Hedgers (79.957) (81.702) (66.989) (65.039) (54.498) (60.336) (57.154) (44.848) (79.906) (81.610) (66.498) (65.053) (54.315) (60.235) (57.149) (44.764) (77.162) (79.314) (63.282) (61.523) (52.333) (57.537) (54.895) (44.341) (80.263) (82.120) (66.939) (65.279) (54.676) (60.706) (57.662) (45.176) (79.788) (81.979) (66.781) (65.032) (54.434) (60.543) (57.535) (45.357) (68.725) (72.361) (55.969) (54.139) (46.652) (51.691) (49.786) (41.998) Notes: The table reports the mean out-of-sample hedging effectiveness for both long and short hedgers. The mean hedging effectiveness is calculated across 1,861 test windows. The best performing hedging instrument for each hedging objective and each hedging effectiveness measure is highlighted in bold type. 20

22 Table 8. Out-of-sample heating oil ETF (futures) hedging effectiveness (in percentage) kernel copula method Hedging Hedging Effectiveness Measures Objectives Variance Semivariance VaR (90%) VaR (95%) VaR (99%) ES (90%) ES (95%) ES (99%) Panel A: Long Hedgers (80.060) (77.176) (68.051) (64.897) (50.746) (58.164) (53.152) (38.872) (80.009) (77.155) (68.103) (64.867) (50.669) (58.165) (53.156) (38.902) (78.387) (75.217) (65.825) (63.448) (49.531) (56.713) (52.057) (37.446) (79.890) (77.360) (67.598) (64.712) (50.636) (58.000) (53.169) (39.098) (79.415) (77.160) (66.415) (63.776) (50.135) (57.441) (52.919) (39.382) (77.420) (74.810) (63.278) (61.336) (49.188) (55.349) (51.260) (37.911) Panel B: Short Hedgers (80.067) (82.281) (67.716) (65.768) (55.239) (61.044) (57.792) (45.074) (79.661) (82.220) (67.683) (65.691) (55.336) (60.969) (57.731) (45.017) (79.084) (81.808) (67.375) (65.280) (54.919) (60.536) (57.266) (44.830) (79.508) (82.164) (67.713) (65.614) (55.223) (60.897) (57.647) (45.025) (79.207) (82.023) (67.622) (65.372) (55.099) (60.754) (57.485) (44.969) (77.341) (80.872) (65.858) (63.798) (53.514) (59.485) (56.380) (44.583) Notes: The table reports the mean out-of-sample hedging effectiveness for both long and short hedgers. The mean hedging effectiveness is calculated across 1,861 test windows. The best performing hedging instrument for each hedging objective and each hedging effectiveness measure is highlighted in bold type. 21

23 Table 9. Out-of-sample natural gas ETF (futures) hedging effectiveness (in percentage) empirical distribution function method Hedging Hedging Effectiveness Measures Objectives Variance Semivariance VaR (90%) VaR (95%) VaR (99%) ES (90%) ES (95%) ES (99%) Panel A: Long Hedgers (2.839) (2.162) (1.893) (2.772) (1.210) (2.249) (2.152) (1.335) (0.156) (-0.382) (-1.137) (0.964) (1.153) (1.022) (1.741) (1.141) ( ) ( ) (-7.262) (-5.625) (-4.355) (-5.547) (-4.564) (-6.795) (4.202) (3.668) (2.344) (2.887) (2.025) (3.002) (3.041) (2.226) (3.259) (3.307) (1.902) (1.755) (2.827) (2.614) (2.842) (2.175) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Panel B: Short Hedgers (1.239) (0.980) (5.466) (0.082) (-0.792) (0.929) (-0.832) (0.425) (-1.225) (-1.542) (4.532) (-0.022) (-2.887) (-0.539) (-2.347) (-1.620) (-1.149) (-3.211) (2.356) (-1.702) (-4.645) (-1.491) (-3.321) (-1.265) (4.429) (3.849) (5.744) (1.703) (0.664) (2.037) (0.644) (1.428) (2.439) (1.983) (3.998) (0.877) (-0.886) (0.973) (-0.454) (0.112) ( ) ( ) (-6.759) (-6.568) (-3.701) (-4.969) (-4.540) (-1.209) Notes: The table reports the mean out-of-sample hedging effectiveness for both long and short hedgers. The mean hedging effectiveness is calculated across 2,107 test windows. The best performing hedging instrument for each hedging objective and each hedging effectiveness measure is highlighted in bold type. 22

24 Table 10. Out-of-sample natural gas ETF (futures) hedging effectiveness (in percentage) kernel copula method Hedging Hedging Effectiveness Measures Objectives Variance Semivariance VaR (90%) VaR (95%) VaR (99%) ES (90%) ES (95%) ES (99%) Panel A: Long Hedgers (3.794) (3.525) (3.343) (2.439) (1.364) (2.579) (2.271) (1.472) (5.037) (5.029) (3.995) (1.792) (3.049) (3.229) (3.312) (2.536) ( ) ( ) ( ) (-9.439) (-9.511) (-9.672) (-8.314) (-9.612) (4.630) (4.619) (3.569) (2.494) (2.089) (3.256) (3.067) (2.240) (3.661) (3.794) (2.554) (1.972) (2.623) (2.899) (2.982) (2.116) (-4.937) (-4.597) (-3.651) (-1.983) (0.159) (-0.848) (0.239) (0.696) Panel B: Short Hedgers (3.955) (3.278) (5.396) (3.218) (-0.548) (1.906) (0.349) (1.198) (2.439) (2.362) (4.305) (2.006) (-0.112) (1.416) (0.074) (0.497) (-8.299) (-7.275) (-3.326) (-4.008) (-1.935) (-2.782) (-2.888) (0.340) (3.683) (3.350) (5.248) (2.795) (0.497) (1.951) (0.435) (1.355) (3.569) (3.391) (5.258) (1.886) (0.828) (1.920) (0.415) (1.688) (-1.087) (-1.808) (1.503) (-0.667) (-1.399) (-0.503) (-1.471) (0.530) Notes: The table reports the mean out-of-sample hedging effectiveness for both long and short hedgers. The mean hedging effectiveness is calculated across 2,107 test windows. The best performing hedging instrument for each hedging objective and each hedging effectiveness measure is highlighted in bold type. 23