#
An Econometric Analysis of ETF and ETF Futures in Financial and Energy Markets Using Generated Regressors^{ †}

^{1}

^{2}

^{3}

^{4}

^{5}

^{6}

^{7}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

“Fifty-one North American oil-and-gas producers have already filed for bankruptcy since the start of 2015, cases totaling $17.4 billion in cumulative debt, according to law firm Haynes and Boone LLP. That trails the number from September 2008 to December 2009 during the global financial crisis, when there were 62 filings, but is expected to grow: About 175 companies are at high risk of not being able to meet loan covenants, according to Deloitte LLP.”

^{®}S&P 500

^{®}ETF, issued by State Street Bank & Trust Company, tracks the performance of the S&P 500 Index. In contrast to investing in a single stock, ETFs invest in a basket of stocks or commodities, thereby diversifying the non-systematic risk and decreasing the levels of risk and volatility. Furthermore, unlike actively-managed mutual funds, most ETF managers take a passive management style and collect lower managing fees. Whereas mutual funds are limited to trades based on end-of-day prices, ETFs are traded like stocks.

- (i)
- ETFs offer greater transparency compared with mutual funds in the sense that ETFs are required to reveal their holdings data on a daily basis, whereas mutual funds are mandated only to disclose holdings data on a quarterly basis.
- (ii)
- ETFs are more flexible than mutual funds because investors can short sell them when they are bearish on the market. Although short selling may be considered risky compared with conventional investing, it can be a useful strategy if executed by savvy investors when the market is overvalued.

## 2. Brief Literature Review

## 3. Methodology

- (1)
- a brief discussion of the most widely-used univariate conditional volatility model;
- (2)
- the definition of three novel spillover effects;
- (3)
- a discussion of the most widely-used multivariate model of conditional volatility.

#### 3.1. Univariate Conditional Volatility Models

#### Random coefficient autoregressive process and GARCH

#### 3.2. Multivariate Conditional Volatility Models

#### 3.3. Full and Partial Volatility and Co-Volatility Spillovers

- (1)
- Full volatility spillovers:$$\partial {Q}_{iit}/\partial {\epsilon}_{kt-1},k\ne i$$
- (2)
- Full co-volatility spillovers:$$\partial {Q}_{ijt}/\partial {\epsilon}_{kt-1},i\ne j,k\ne i,j$$
- (3)
- Partial co-volatility spillovers:$$\partial {Q}_{ijt}/\partial {\epsilon}_{kt-1},i\ne j,k=eitheriorj$$

#### 3.4. Diagonal and Scalar BEKK

#### 3.5. Triangular, Hadamard and Full BEKK

#### 3.6. Generated Regressors

- (1)
- Financial Select Sector SPDR Fund (XLF);
- (2)
- Generic 1st S&P 500 index futures (SP1); and
- (3)
- Generic 1st FTSE 100 index futures (Z1).

- (1)
- Energy Select Sector SPDR Fund (XLE);
- (2)
- Generic 1st Crude Oil WTI futures (CL1); and
- (3)
- Generic 1st Natural Gas futures (NG1).

_{1}, θ

_{2}and θ

_{3}are the weights attached to one-period lagged financial ETF, Generic 1st S&P 500 index futures and Generic FTSE 100 index futures, respectively.

## 4. Data and Variables

^{®}). The index represents the performance of the U.S. financial industry. Components of the Financial Select Sector are weighted by their float-adjusted market capitalization, and the Select Sector Indices are rebalanced quarterly. The three largest constituents of the financial sector are Berkshire Hathaway B, Wells Fargo & Co and JP Morgan Chase & Co. The related ETF tracking IXM is the Financial Select Sector SPDR Fund (Ticker: XLF), as listed on the New York Stock Exchange.

^{®}). This index represents the performance of the U.S. energy industry. Components of the Energy Select Sector are weighted by their float-adjusted market capitalization, and the Select Sector Indices are rebalanced quarterly. The related ETFs tracking IXE is the Energy Select Sector SPDR Fund (Ticker: XLE), as listed on the New York Stock Exchange.

^{®}Fund (Ticker: XLF), issued by SSGA Funds Management, Inc. and listed on the New York Stock Exchange since 16 December 1998, is the most representative financial ETF, with the largest total assets and average trading volume in the financial sector. This ETF seeks to replicate the performance of the Financial Select Sector Index. As of 31 May 2016, the industry allocation of XLF consisted of banks (34.47%), Real Estate Investment Trusts (REITs) (18.30%), insurance (16.83%), diversified financial services (13.04%), capital markets (12.01%), consumer finance (4.92%), real estate management and development (0.29%) and unassigned (0.10%). The top three holdings of XLF are Berkshire Hathaway Inc. Class B (8.84%), JPMorgan Chase & Co. (8.04%) and Wells Fargo & Company (7.87%).

^{®}Fund (Ticker: XLE), issued by SSGA Funds Management, Inc. and listed on the New York Stock Exchange since 16 December 1998, is the most representative energy ETF, with the largest total assets and average trading volume in the energy sector. This ETF seeks to replicate the performance of the Energy Select Sector Index. As of 31 May 2016, the industry allocation of XLE consisted of oil gas and consumable fuels (83.19%), energy equipment and services (16.66%) and unassigned (0.15%). The top three holdings of XLE are Exxon Mobil Corporation (18.85%), Chevron Corporation (14.68%) and Schlumberger NV (8.37%).

^{®}Fund (XLF), Generic 1st S&P 500 index futures (Bloomberg ticker: SP1) and Generic 1st FTSE 100 index futures (Bloomberg ticker: Z1). The Generic 1st S&P 500 index futures is the continuous contract constructed by the front-month futures contract of S&P 500 index futures (Ticker: SPX), the latter having been introduced by the Chicago Mercantile Exchange (CME) in 1982. Meanwhile, the Generic 1st FTSE 100 index futures is the continuous contract constructed by front-month futures contract of FTSE 100 index futures, the latter having been launched by the London International Financial Futures and Options Exchange (LIFFE) in 1984.

^{®}Fund, SP1 is Generic 1st S&P 500 index futures, Z1 is Generic 1st FTSE 100 index futures, and t-ratios are shown in parentheses. As stated previously, the t-ratios do not have the standard asymptotic normal distribution as the variables are non-stationary, but the extremely high value of ${\overline{\mathrm{R}}}^{2}$ suggests that the generated variable is a useful construction of the latent variable.

^{®}Fund (XLE), Crude Oil futures (CL1) and Natural Gas futures (NG1). The Generic 1st Crude Oil futures is the continuous contract constructed by the front-month futures contract of Crude Oil WTI futures (Ticker: CL), listed in the New York Mercantile Exchange (NYMEX). The Generic 1st Natural Gas futures is the continuous contract constructed by the front-month futures contract of Natural Gas futures (Ticker: NG) listed in the New York Mercantile Exchange (NYMEX).

^{®}Fund, CL1 is Generic 1st Crude Oil WTI futures, NG1 is Generic 1st Natural Gas futures, and t-ratios are shown in parentheses. As stated previously, the t-ratios do not have the standard asymptotic normal distribution as the variables are non-stationary, but the extremely high value of ${\overline{\mathrm{R}}}^{2}$ suggests that the generated variable is a useful construction of the latent variable.

## 5. Empirical Results for Co-Volatility Spillovers

#### 5.1. Hypothesis Testing of Co-Volatility Spillovers

_{0}, as shown in the definition of the test of co-volatility spillover effects in Section 3, indicates the significance of the co-volatility spillovers from the returns shocks of asset j at time t − 1 to the co-volatility between assets i and j at time t.

#### 5.2. Calculating Average Co-Volatility Spillovers

- Asymmetric spillover effects were found in all cases of spot-spot and futures-futures across sectors (see Groups 1 and 2).
- Symmetric spillover effects were found in all cases of spot-spot between the financial ETF and financial index, as well as between the energy ETF and energy index in all periods (see Group 4).
- Asymmetric spillover effects were found in all cases of spot-futures ETF within sectors. Moreover, in all cases, spillover effects of ETF futures on its co-volatility with the corresponding ETF are stronger than in the reverse case (see Group 5).
- The co-volatility spillovers in all groups over all time periods are statistically significant, except for Cases 3.c.1 to 3.d.2 during-GFC.
- Additionally, with the exception of the insignificant cases, the co-volatility spillovers are stronger during-GFC than for the other time periods (see Groups 1, 2 and 4).
- In terms of the current relationship between the financial and energy sectors, the After-GFC spillovers are of greater relevance than the spillovers of the three sub-periods combined into a single sample.

## 6. Concluding Remarks

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Crude oil prices: West Texas Intermediate (WTI) (1986–2016), Federal Reserve Economic Data.

Variable Name | Definitions | Exchange | Source |
---|---|---|---|

IXM | Financial Select Sector Index | Non-tradable | Bloomberg |

IXE | Financial Select Sector Index | Non-tradable | Bloomberg |

XLF | Financial Select Sector SPDR Fund | NYSE | Yahoo Finance |

XLE | Energy Select Sector SPDR Fund | NYSE | Yahoo Finance |

XLFf | financial ETF futures | Generated Regressors | |

XLEf | energy ETF futures | Generated Regressors | |

Constituents of Financial ETF futures (XLFf) | |||

XLF | Financial Select Sector SPDR Fund | NYSE | Yahoo Finance |

SP1 | Generic 1st S&P 500 futures | CME | Bloomberg |

Z1 | Generic 1st FTSE 100 futures | LIFFE | Bloomberg |

Constituents of Energy ETF futures (XLEf) | |||

XLE | Energy Select Sector SPDR Fund | NYSE | Yahoo Finance |

CL1 | Generic 1st Crude Oil WTI futures | NYMEX | Bloomberg |

NG1 | Generic 1st Natural Gas futures | NYMEX | Bloomberg |

Variables | Mean | Maximum | Minimum | Std. Dev. | Skewness | Kurtosis |
---|---|---|---|---|---|---|

Return (%) | ||||||

IXM_Return | −0.00001 | 7.47123 | −8.09431 | 0.85274 | −0.07166 | 18.32649 |

IXE_Return | 0.00992 | 7.61806 | −7.51765 | 0.75370 | −0.37323 | 12.69031 |

XLF_Return | 0.00324 | 11.85519 | −8.28167 | 0.86750 | 0.33284 | 24.25198 |

XLE_Return | 0.01286 | 6.62314 | −6.77485 | 0.75686 | −0.41494 | 12.02135 |

XLFf_Return | 0.00329 | 11.83412 | −8.26734 | 0.86482 | 0.33368 | 24.23240 |

XLEf_Return | 0.01290 | 6.61355 | −6.76537 | 0.75571 | −0.41562 | 12.02699 |

ADF Test | |||

Variables | No Trend and Intercept | With Intercept | With Trend and Intercept |

IXM_Return | −74.8746 * | −74.8663 * | −74.8584 * |

IXE_Return | −52.3193 * | −52.3291 * | −52.3299 * |

XLF_Return | −75.4704 * | −75.4632 * | −75.4554 * |

XLE_Return | −52.2382 * | −52.2581 * | −52.2579 * |

XLFf_Return | −75.5023 * | −75.4951 * | −75.4872 * |

XLEf_Return | −52.2497 * | −52.2692 * | −52.2693 * |

PP Test | |||

Variables | No Trend and Intercept | with Intercept | with Trend and Intercept |

IXM_Return | −76.5683 * | −76.5589 * | −76.5513 * |

IXE_Return | −72.0880 * | −72.1263 * | −72.1402 * |

XLF_Return | −77.5130 * | −77.5103 * | −77.5032 * |

XLE_Return | −71.8730 * | −71.9392 * | −71.9946 * |

XLFf_Return | −77.5604 * | −77.5577 * | −77.5502 * |

XLEf_Return | −71.9054 * | −72.0151 * | −72.0267 * |

Group 1: Cross-Sector Spot-Spot | |||||||

Case | Asset 1 | Asset 2 | A | Before-GFC | During-GFC | After-GFC | All |

1.a | IXE | IXM | A1(1,1) | 0.191 * | 0.310 * | 0.225 * | 0.227 * |

A1(2,2) | 0.262 * | 0.226 * | 0.247 * | 0.253 * | |||

1.b | XLE | XLF | A1(1,1) | 0.202 * | 0.290 * | 0.224 * | 0.235 * |

A1(2,2) | 0.320 * | 0.230 * | 0.244 * | 0.272 * | |||

1.c | XLE | IXM | A1(1,1) | 0.192 * | 0.290 * | 0.225 * | 0.227 * |

A1(2,2) | 0.261 * | 0.227 * | 0.249 * | 0.253 * | |||

1.d | IXE | XLF | A1(1,1) | 0.204 * | 0.312 * | 0.224 * | 0.236 * |

A1(2,2) | 0.323 * | 0.228 * | 0.243 * | 0.273 * | |||

Group 2: Cross-Sector Futures-Futures | |||||||

Case | Asset 1 | Asset 2 | A | Before-GFC | During-GFC | After-GFC | All |

2.a | XLEf | XLFf | A1(1,1) | 0.202 * | 0.291 * | 0.224 * | 0.234 * |

A1(2,2) | 0.320 * | 0.230 * | 0.242 * | 0.271 * | |||

Group 3: Cross-Sector Spot-Futures | |||||||

Case | Asset 1 | Asset 2 | A | Before-GFC | During-GFC | After-GFC | All |

3.a | IXM | XLEf | A1(1,1) | 0.267 * | 0.254 * | 0.301 * | 0.286 * |

A1(2,2) | 0.178 * | 0.272 * | 0.188 * | 0.191 * | |||

3.b | XLF | XLEf | A1(1,1) | 0.352 * | 0.249 * | 0.297 * | 0.337 * |

A1(2,2) | 0.174 * | 0.275 * | 0.185 * | 0.191 * | |||

3.c | IXE | XLFf | A1(1,1) | 0.165 * | 0.313 * | 0.260 * | 0.234 * |

A1(2,2) | 0.365 * | −0.037 | 0.189 * | 0.251 * | |||

3.d | XLE | XLFf | A1(1,1) | 0.161 * | 0.307 * | 0.259 * | 0.233 * |

A1(2,2) | 0.362 * | −0.041 | 0.187 * | 0.250 * | |||

Group 4: Within-Sector Spot-Spot | |||||||

Case | Asset 1 | Asset 2 | A | Before-GFC | During-GFC | After-GFC | All |

4.a | IXM | XLF | A1(1,1) | 0.301 * | 0.471 * | 0.313 * | 0.299 * |

A1(2,2) | 0.299 * | 0.439 * | 0.313 * | 0.300 * | |||

4.b | IXE | XLE | A1(1,1) | 0.187 * | 0.408 * | 0.278 * | 0.257 * |

A1(2,2) | 0.186 * | 0.403 * | 0.271 * | 0.253 * | |||

Group 5: Within-Sector Spot-Futures | |||||||

Case | Asset 1 | Asset 2 | A | Before-GFC | During-GFC | After-GFC | All |

5.a | IXM | XLFf | A1(1,1) | 0.267 * | 0.272 * | 0.256 * | 0.277 * |

A1(2,2) | 0.331 * | 0.531 * | 0.373 * | 0.321 * | |||

5.b | XLF | XLFf | A1(1,1) | 0.321 * | 0.171 * | 0.296 * | 0.315 * |

A1(2,2) | 0.306 * | 0.477 * | 0.257 * | 0.291 * | |||

5.c | IXE | XLEf | A1(1,1) | 0.211 * | 0.274 * | 0.233 * | 0.228 * |

A1(2,2) | 0.192 * | 0.609 * | 0.336 * | 0.304 * | |||

5.d | IXM | XLEf | A1(1,1) | 0.267 * | 0.254 * | 0.301 * | 0.286 * |

A1(2,2) | 0.178 * | 0.272 * | 0.188 * | 0.191 * |

Group 1: Cross-Sector Spot-Spot | |||||

Case | Asset | Before-GFC | During-GFC | After-GFC | All |

1.a | IXE | −0.011204 | −0.071687 | −0.008686 | −0.011357 |

IXM | −0.006777 | −0.072454 | 0.001743 | −0.020297 | |

1.b | XLE | −0.011494 | −0.065577 | −0.007675 | −0.011257 |

XLF | −0.007065 | −0.065807 | 0.002071 | −0.020948 | |

1.c | XLE | −0.010616 | −0.062126 | −0.008207 | −0.010482 |

IXM | −0.006639 | −0.069262 | 0.001767 | −0.019909 | |

1.d | IXE | −0.012103 | −0.074886 | −0.008168 | −0.012156 |

XLF | −0.007285 | −0.069917 | 0.002027 | −0.02138 | |

Group 2: Cross-Sector Futures-Futures | |||||

Case | Asset | Before-GFC | During-GFC | After-GFC | All |

2.a | XLEf | −0.01166 | −0.067914 | −0.007756 | −0.011694 |

XLFf | −0.007 | −0.057135 | 0.002322 | −0.021018 | |

Group 3: Cross-Sector Spot-Futures | |||||

Case | Asset | Before-GFC | During-GFC | After-GFC | All |

3.a | IXM | −0.010596 | −0.08784 | −0.000715 | −0.0222 |

XLEf | −0.005352 | −0.043396 | −0.009213 | −0.000729 | |

3.b | XLE | −0.012874 | −0.091973 | −0.001053 | −0.024498 |

XLEf | −0.005131 | −0.04453 | −0.008712 | −0.000712 | |

3.c | IXE | −0.009224 | −0.071131 | −0.009599 | −0.014442 |

XLFf | −0.003639 | 0.001534 | 0.006691 | −0.013987 | |

3.d | XLE | −0.010088 | −0.064578 | −0.009295 | −0.014803 |

XLFf | −0.004424 | 0.000471 | 0.006743 | −0.014104 | |

Group 4: Within-Sector Spot-Spot | |||||

Case | Asset | Before-GFC | During-GFC | After-GFC | All |

4.a | IXM | −0.011165 | −0.08912 | 0.003486 | −0.018308 |

XLF | −0.012522 | −0.086464 | 0.003553 | −0.01781 | |

4.b | IXE | −0.007966 | −0.075882 | −0.007843 | −0.014385 |

XLE | −0.007481 | −0.072072 | −0.007864 | −0.014581 | |

Group 5: Within-Sector Spot-Futures | |||||

Case | Asset | Before-GFC | During-GFC | After-GFC | All |

5.a | IXM | −0.010662 | −0.066578 | 0.005485 | −0.020032 |

XLFf | −0.000539 | 0.001660 | −0.000476 | 4.67E-06 | |

5.b | XLF | −0.014975 | −0.045831 | 0.002275 | −0.024073 |

XLFf | 2.41E-05 | 0.000424 | −6.16E-05 | 1.01E-05 | |

5.c | IXE | −0.005847 | −0.064652 | −0.007429 | −0.012769 |

XLEf | 0.000311 | 0.003213 | −0.000369 | −0.000497 | |

5.d | XLE | −0.009237 | −6.82E-06 | −3.66E-08 | −0.016685 |

XLEf | 1.10E-06 | −2.69E-05 | −3.84E-07 | −6.85E-06 |

Group 1: Cross-Sector Spot-Spot Spillover Effects | ||||||

Case | Asset i | Asset j | Before-GFC | During-GFC | After-GFC | All |

1.a.1 | IXE | IXM | −0.000561 | −0.005022 | −0.000483 | −0.000652 |

1.a.2 | IXM | IXE | −0.000339 | −0.005076 | 0.000097 | −0.001166 |

1.b.1 | XLE | XLF | −0.000743 | −0.004374 | −0.000419 | −0.000720 |

1.b.2 | XLF | XLE | −0.000457 | −0.004389 | 0.000113 | −0.001339 |

1.c.1 | XLE | IXM | −0.000532 | −0.004090 | −0.000460 | −0.000602 |

1.c.2 | IXM | XLE | −0.000333 | −0.004560 | 0.000099 | −0.001143 |

1.d.1 | IXE | XLF | −0.000797 | −0.005327 | −0.000445 | −0.000783 |

1.d.2 | XLF | IXE | −0.000480 | −0.004974 | 0.000110 | −0.001377 |

Group 2: Cross-Sector Futures-Futures Spillover Effects | ||||||

Case | Asset i | Asset j | Before-GFC | During-GFC | After-GFC | All |

2.a.1 | XLEf | XLFf | −0.000754 | −0.004545 | −0.000420 | −0.000742 |

2.a.2 | XLFf | XLEf | −0.000452 | −0.003824 | 0.000126 | −0.001333 |

Group 3: Cross-Sector Spot-Futures Spillover Effects | ||||||

Case | Asset i | Asset j | Before-GFC | During-GFC | After-GFC | All |

3.a.1 | IXM | XLEf | −0.000504 | −0.006069 | −0.000040 | −0.001213 |

3.a.2 | XLEf | IXM | −0.000254 | −0.002998 | −0.000521 | −0.000040 |

3.b.1 | XLF | XLEf | −0.000789 | −0.006298 | −0.000058 | −0.001577 |

3.b.2 | XLEf | XLF | −0.000314 | −0.003049 | −0.000479 | −0.000046 |

3.c.1 | IXE | XLFf | −0.000556 | Insignificant | −0.000472 | −0.000848 |

3.c.2 | XLFf | IXE | −0.000219 | Insignificant | 0.000329 | −0.000822 |

3.d.1 | XLE | XLFf | −0.000588 | Insignificant | −0.000450 | −0.000862 |

3.d.2 | XLFf | XLE | −0.000258 | Insignificant | 0.000327 | −0.000822 |

Group 4: Within-Sector Spot-Spot Spillover Effects | ||||||

Case | Asset i | Asset j | Before-GFC | During-GFC | After-GFC | All |

4.a.1 | IXM | XLF | −0.001005 | −0.018427 | 0.000342 | −0.001642 |

4.a.2 | XLF | IXM | −0.001127 | −0.017878 | 0.000348 | −0.001598 |

4.b.1 | IXE | XLE | −0.000277 | −0.012477 | −0.000591 | −0.000935 |

4.b.2 | XLE | IXE | −0.000260 | −0.011850 | −0.000592 | −0.000948 |

Group 5: Within-Sector Spot-Futures Spillover Effects | ||||||

Case | Asset i | Asset j | Before-GFC | During-GFC | After-GFC | All |

5.a.1 | IXM | XLFf | −0.000942 | −0.009616 | 0.000383 | −0.001781 |

5.a.2 | XLFf | IXM | −0.000048 | 0.000240 | −0.000033 | 0.000000 |

5.b.1 | XLF | XLFf | −0.001471 | −0.003738 | 0.000173 | −0.002207 |

5.b.2 | XLFf | XLF | 0.000002 | 0.000035 | −0.000005 | 0.000001 |

5.c.1 | IXE | XLEf | −0.000237 | −0.010788 | −0.000582 | −0.000885 |

5.c.2 | XLEf | IXE | 0.000013 | 0.000536 | −0.000029 | −0.000034 |

5.d.1 | XLE | XLEf | −0.000615 | −0.000001 | −2.25E-09 | −0.001069 |

5.d.2 | XLEf | XLE | 7.32E-08 | −0.000003 | −2.36E-08 | −4.39E-07 |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Chang, C.-L.; McAleer, M.; Wang, C.-H.
An Econometric Analysis of ETF and ETF Futures in Financial and Energy Markets Using Generated Regressors. *Int. J. Financial Stud.* **2018**, *6*, 2.
https://doi.org/10.3390/ijfs6010002

**AMA Style**

Chang C-L, McAleer M, Wang C-H.
An Econometric Analysis of ETF and ETF Futures in Financial and Energy Markets Using Generated Regressors. *International Journal of Financial Studies*. 2018; 6(1):2.
https://doi.org/10.3390/ijfs6010002

**Chicago/Turabian Style**

Chang, Chia-Lin, Michael McAleer, and Chien-Hsun Wang.
2018. "An Econometric Analysis of ETF and ETF Futures in Financial and Energy Markets Using Generated Regressors" *International Journal of Financial Studies* 6, no. 1: 2.
https://doi.org/10.3390/ijfs6010002