timothy krause - etf

THE JOURNAL OF DERIVATIVES 7FALL 2014

Implied Volatility Dynamics Among Exchange-Traded Funds and Their Largest Component StocksTIMOTHY A. KRAUSE AND DONALD LIEN

TIMOTHY A. KRAUSE

is a former derivatives trader at the CBOE and is currently an assistant professor at The Sam and Irene Black School of Business at Penn State-Erie in Erie, [email protected]

DONALD LIEN

is the Richard S. Liu Distinguished Chair in Business at the Uni-versity of Texas in San Antonio, [email protected]

This article examines the presence of common fac-tors in the evolution of stock option implied volatili-ties. We analyze the implied volatilities of ETF options and their largest component stocks, and the results strongly suggest the presence of both a market volatility factor and an industry volatility factor. In a cross-section of nine popular industry ETFs, the average volatility “betas” for the industry factors are equal to about one third of the value of the market factor beta. Additionally, implied volatility reverts more strongly to industry long-term averages than it does to a market measure of volatility. Traders, market-makers, and investors may reduce hedging errors by using options on these industry-related products in addition to market-based volatility products. The drivers of implied volatility spill-overs from ETFs to component stocks vary across industries, but the spillovers are most strongly related to turnover in S&P 500 ETF options and those of SPDR industry sector ETFs. Additional important factors in the volatility generating process include deviations from net asset value, ETF flow of funds, and ETF market capitalization.

Stochastic volatility is a well-docu-mented property of stock returns; thus, the dynamic hedging strategy postulated by the Black and Scholes

[1973] option pricing model is not riskless. Green and Figlewski [1999] demonstrate the risk that remains for delta-hedged options portfolios due to f luctuations in implied vola-

tility (vega risk). These f luctuations may be related to a common market-based determi-nant of volatility, and Bakshi and Kapadia [2003] find that for a sample of 25 individual equity options, “only market volatility risk is priced and idiosyncratic risk is unpriced.” Driessen [2009] documents similar results using OEX options and those of its compo-nent stocks. To address this issue, Engle and Figlewski [2014] note that hedging errors due to vega risk may be reduced through the use of VIX futures and/or options. They dem-onstrate that individual stock option-implied volatilities are highly correlated with changes in the VIX index, noting that these “volatility betas” imply a common factor that is linked to the overall level of market volatility. Further, they propose a multivariate EGARCH-M-t model “to explore the dynamics of changes in implied volatilities and the correlations among them.”

This article explores the presence of an additional industry factor in the evolution of stock-implied volatilities as well as how this factor is related to liquidity and other fac-tors involved in the trading in ETF options. Following the one-factor (market) model of Engle and Figlewski [2014], we estimate a two-factor EGARCH-M-t model that includes implied volatility estimates from nine SPDR Industry ETFs (whose com-ponents altogether comprise the S&P 500 Index) and their 10 largest component stocks,

JOD-KRAUSE.indd 7JOD-KRAUSE.indd 7 8/19/14 12:21:54 PM8/19/14 12:21:54 PM

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8 IMPLIED VOLATILITY DYNAMICS AMONG EXCHANGE-TRADED FUNDS AND THEIR LARGEST COMPONENT STOCKS FALL 2014

respectively. In addition to these tests, we also examine potential factors driving linkages in “volatility of vola-tility.” The methodology of Diebold and Yilmaz [2009, 2012] is used to estimate implied volatility spillovers from the S&P 500 Index ETF (SPY) and the industry ETFs to their largest component stocks. Volatility spillovers from SPY and industry sector ETFs to these component stocks are driven primarily by ETF options turnover and the proportion of each stock that comprises the ETF. Individual stock option liquidity is generally negatively related to these spillovers. Other factors that are significant in the implied volatility generating pro-cess include deviations from net asset value (NAV), ETF f low of funds, and ETF market capitalization.

Although numerous studies have examined the risk characteristics of industry sectors,1 very few use implied volatility data, to our knowledge. Wang [2010] demon-strates that industry-specific volatilities exhibit widely varying behaviors and that realized volatility is highly correlated with implied volatility, although it is generally lower.2 The use of industry information is motivated by Peng and Xiong [2006], who find that “investors tend to process more market and sector-wide information than firm-specific information” due to limited attention and resources. Engle and Figlewski [2014] demonstrate that stock option hedging errors are smaller when the hedging strategy uses contracts based on companies in the same industry.

In addition to our examination of industry vola-tility “betas,” we also study the effects of ETF options liquidity. Hegde and McDermott [2004], Yu [2005], and Madura and Ngo [2008] find that the introduction of ETFs improves liquidity in their underlying stocks. Chen and Chung [2012] find that liquidity and price discovery improve after the introduction of SPY options. This article seeks to answer a different research ques-tion, however. We examine the effects of ETF options liquidity on the ability of ETFs to “spill over” implied volatility information to their largest component stocks. Related papers include those of Ben-David et al. [2014] and Madhavan [2012], which examine ETF liquidity during the “f lash crash” of May 6, 2010. Additionally, since we explore the implications of ETF option trading activity on individual stocks, the option to stock ratio (O/S) relationship of Johnson and So [2012] is also relevant.

The topic is relevant to practitioners and regula-tors given the exponential growth in ETF trading over

the past decade. This growth has been accompanied by similar growth in derivatives on these securities, mainly exchange-traded options. Data from the CBOE web-site indicate that volume in options on these products has increased twelvefold from 2005 to 2013, an average annual increase of approximately 38%. Options on SPY and SPDR industry ETFs are particularly liquid. While Engle and Figlewski [2014] use the VIX index as their proxy for the market common volatility factor, we use at-the-money (ATM) volatility for SPY options. One reason for this departure is that, since 2003, the CBOE calculates the VIX using all available strike prices. Our measure of SPY volatility, therefore, does not contain information regarding the volatility skew, although the difference is minor in practice. The correlation between our proxy for market-implied volatility and the VIX is 0.82. The International Securities Exchange recently announced that it will begin trading options on the Nationshares VolDex® Index, which is constructed using SPY ATM options only. Most importantly, VIX daily closing values are published by the CBOE as of 4 p.m. ET, while our option-implied volatility data is a 3:45 p.m. ET “snapshot” provided by Bloomberg. Thus, combining the ETF data with VIX closing prices might induce an asynchronous trading problem.3

DATA DESCRIPTION

The data set includes daily option-implied vola-tility, volume, and open interest from January 10, 2005, to March 31, 2013, obtained via Bloomberg Profes-sional®. The securities include SPY and nine SPDR industry Select Sector ETFs, as well as their respective 10 largest component stocks as of March 31, 2013. The Appendix describes the composition of the sample as well as the cumulative percentage of the 10 largest com-ponent stocks in each ETF. Although these companies comprised the top 10 holdings of the ETFs at the end of March 2013, they were not necessarily top holdings for the entire period of the study. However, they were held in significant amounts by each of their respective ETFs for the entire period. For instance, in the case of SPY, 6 of the components were included in the top 10 at the beginning of the sample, and 3 others were in the top 20. Given that the proportion of each stock held in an ETF is positively related to the spillovers that we document, the fact that some of the components may not have been in the top 10 for the entire period


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actually decreases the likelihood of finding significant spillovers.

The industry ETFs examined here are all sub-com-ponents of the S&P 500 ETF, so each individual stock is a component of both SPY and its respective industry ETF. Thus, the total number of stocks in all of the ETFs is 500. The average cumulative percentage holding of the 10 largest component stocks in each industry ETF is 57.55%. We use only the top 10 stocks in each ETF to maintain tractability in the spillover model, following Madura and Ngo [2008]. During our sample period, on average, these 10 stocks comprise between 41.03% (XLF − Financials) and 66.50% (XLB – Basic Materials) of total ETF value. Many ETF arbitrage strategists use “tracking baskets” that comprise only 25% to 30% of the funds’ total value. Additionally, market-makers and large institutions ensure a close relationship among the implied volatilities of the ETFs and their component stocks through “dispersion” trading. The cumulative percentage of the top 10 components in SPY is signifi-

cantly lower at 18.40% due to the fact that this ETF con-tains 500 stocks, while the industry ETFs contain only 56 stocks on average. The number of stocks in each ETF in our sample ranges from 30 (XLB – Basic Materials) to 82 (XLY – Consumer Staples). The CRSP Mutual Fund Database is used to obtain the proportions of each component stock held in each ETF on a monthly basis. Finally, we obtain daily NAV, market capitalization, and total net asset (TNA) data from Bloomberg.

The sample includes data on option-implied volatil-ities for constant 30-day maturity, at-the-money options, as calculated by Bloomberg.4 The sample begins with the inception of trading of SPY options on January 10, 2005, and summary statistics for the ETF-implied vola-tilities are contained in Exhibit 1. There are 2,064 daily observations, and it is immediately clear that volume and open interest in SPY options dwarf those of the industry ETFs. The existence of pre-existing deep and liquid options markets in the S&P 500 cash index and futures options made these options instantly popular for arbitrage

E X H I B I T 1Summary Statistics

Notes: This exhibit contains daily sample statistics for the S&P 500 Index ETF (SPY) and nine SPDR industry ETFs. The sample period is from January 10, 2005 (the inception of trading in SPY options), to March 31, 2013, and there are 2,064 observations. Volume and open interest figures are presented in thousands of contracts. Options turnover is defined as daily options volume divided by daily options open interest.


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trading and as investment and hedging vehicles. However, industry ETF volumes and open interests are all economi-cally significant. For instance, using an average daily ETF price for XLP (the ETF with the lowest average volume of 6,000 contracts per day), its average daily notional value of open interest is almost a half-billion dollars. The volume and open interest figures for the popular Energy (XLE) and Financials (XLF) ETFs are quite large, even in a relative comparison to SPY.

THE ONE-FACTOR MODEL

In order to evaluate the effect of market vola-tility on the largest component stocks of the ETFs under consideration, we first implement the one-factor EGARCH-M-t model of Engle and Figlewski [2014]. The model is estimated for each component stock as follows, using Newey-West [1987] standard errors with five lags:

ln ln_

_ln( )

ln( )1

1 21

3 1ln(

4 1ln(

vv

v SPYv SPY

SPY

it

iti i2

tYY

tYYln(

ln( _ i)1 t it

⎛⎝⎜⎛⎛⎝⎝

⎞⎠⎟⎞⎞⎠⎠

= θ +θ⎛⎝⎜⎛⎛⎝⎝

⎞⎠⎟⎞⎞⎠⎠

+θ

+ θ + σ ε−_ t−1 ⎠ ⎝

(1)

ln | | ln1 1 3| 4 1i i2 it i ln 4( )2it ( )2

it 1=)2it φ +1 φ ε|2i2 + φ +)1

2it 1 φ ε443i| it (2)

where v_SPYt represents at-the-money, option-implied

volatility for SPY options and vit represents at-the-money

implied volatility for each of its 10 largest component stocks. We include a constant term θ

1 that impounds

the long-term mean, as noted by Engle and Figlewski [2014]. Each stock’s volatility “beta” relative to the S&P 500 ETF is represented by θ

2, and consistent with their

results, we expect to find positive and significant coef-ficients for θ

2 The following two terms, θ

3 and θ

4, quan-

tify the adjustment to the deviation from the long-run equilibrium relationship between the implied volatility of each stock and that of SPY. Essentially, these terms demonstrate reversion to long-term means such that

( ) / ) 01

)) /t S/ ) (1 4) ( 3/) PYtYY+ θ((((( θ ≈) l ( )v) ln(3 S) (3 v) ln(3 PY −. These could be com-

bined into one term in the form of an error correction model, but we follow Engle and Figlewski [2014] to provide more general results that do not restrict such a coefficient to be a single number.

We expect to find negative coefficients for θ3 since

it ref lects individual stock volatility mean reversion, while θ

4 should be positive as a consequence of cointe-

gration (i.e., the two volatilities are positively propor-tional to each other in equilibrium). When the implied volatility of an individual stock is too “low” relative to the implied volatility of SPY, it will adjust upward to approach the long-run equilibrium, making θ

4 posi-

tive. The conditional variance equation is estimated as in Nelson [1991], with one significant difference in interpretation. The asymmetric volatility term φ

4 in the

original model is generally negative for stock returns, ref lecting higher volatility following negative returns. But in this specification, the asymmetric term should be positive, since positive (negative) shocks to implied vola-tility have a larger (smaller) effect on future volatility. To account for non-normality in the distribution of the error terms in these models, we utilize the Student-t distribution for purposes of statistical inference.

We estimate EGARCH-M-t models for each of the 10 largest component stocks in the industry ETFs and SPY, resulting in 100 estimations. The results of these estimations are contained in Exhibit 2. First, we note that the constant terms (θ

1) are positive and significant

in 89 of 100 cases. More importantly, the volatility beta coefficients θ

2 are significant for all 100 of the under-

lying component stocks. For SPY, the average coefficient is large (0.502) and highly significant (average t-statistic of 41.130), and comparable to the coefficient of 0.325 that Engle and Figlewski [2014] find for the Dow Jones Industrial companies. Our result confirms their assertion that there is a common market-based volatility factor driving the evolution of single-stock implied volatility. All of the industry ETF component stocks display posi-tive significant market volatility beta coefficients as well, ranging from an average of 0.363 for those contained in XLU (Utilities) to 0.570 for XLF (Financials). The grand average for all of the ETF volatility betas is 0.463, ref lecting the presence of a significant common market-related volatility factor in all 90 of the industry ETF components.

The average coefficient for “stock volatility rever-sion” (average θ

3 = −0.022, t-stat = −14.77) and “market

volatility reversion” (average θ4 = 0.014, t-stat = 6.19)

for SPY are quite similar to those obtained by Engle and Figlewski [2014], who obtain coefficients of −0.022 and 0.018 in their sample of Dow 30 stocks. The mean stock reversion term is negative and significant (average θ

3 = −0.025, t-stat = −28.12) for 98 of the 100 compo-

nent stocks. Regarding reversion to market volatility, the coefficients are positive and significant in 96 cases


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E X H I B I T 2EGARCH-M-t Estimates for Stock-Implied Volatilities with One Common Factor

ln ln_

_ln( ) ln( _ )

11 2

13 1 4 1

v

v

v SPY

v SPYv v SPYit

iti i

t

ti it i it it it

⎛⎝⎜

⎞⎠⎟

= θ + θ⎛⎝⎜

⎞⎠⎟

+ θ + θ + σ ε− −

− −

ln | | ln21 2 1 3 1

24 1it i i it i it i it( ) ( )σ = φ + φ ε + φ σ + φ ε− − −

Notes: This exhibit presents the average coefficients and Newey-West [1987] t-statistics (with five lags) from the one-factor EGARCH-M-t estimations. The equations are estimated for each of the 10 largest component stocks of each industry ETF and SPY.


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(average θ4 = 0.018, t-stat = 21.37). The absolute values

of the coeff icients are relatively small and similar in absolute value, as expected. However, these coefficients represent small fractions of the volatility beta coeffi-cients, on average. Thus, the speed of convergence to the long-run equilibrium relationship in the implied volatility process is quite slow, consistent with the results of Engle and Figlewski [2014]. The coefficients φ

1 through φ

4 are all positive, as expected, although the

asymmetric coefficient φ4 is statistically significant for

only 62 of 100 possibilities. The fact that all of the φ3

coefficients are less than one (both individually and on average) ensures that the EGARCH systems are stable. The shape parameters range from 3.310 for XLK to 4.608 for XLU, with a grand average of 3.730 across all of the ETFs. The implied distributions indicate sig-nificantly fat tails for all of the stock implied volatilities in our sample.

THE TWO-FACTOR MODEL

We extend the EGARCH-M-t model to include an additional industry factor to proxy for industry-wide information. The new model is specified as follows:

ln ln_

_

ln( ) l ( )

ln_

_ln( )

11 2

1

3 1ln( 4 1( _

51

6 1ln(

vv

v SPYv SPY

) ln(4 ln( SPY

v ETFv ETF

ETF

it

iti i2

tYY

tYY

ln( )1 4) 4

itFF

tFFln( _ it it

⎛⎝⎜⎛⎛⎝⎝

⎞⎠⎟⎞⎞⎠⎠

= θ + θ⎛⎝⎜⎛⎛⎝⎝

⎞⎠⎟⎞⎞⎠⎠

+ θ + θ

+ θ⎛⎝⎜⎛⎛⎝⎝

⎞⎠⎟⎞⎞⎠⎠

+ θ + σ ε

−_ t−1 ⎠ ⎝( _) 4

−

(3)

ln | | ln1 1 3| 4 1i i2 it i ln 4( )2

it ( )2it 1=)2

it φ +1 φ ε|2i2 + φ +)12it 1 φ ε443i| it

(4)

Equations (3) and (4) are identical to Equations (1) and (2) except for the additional coefficients θ

5 and θ

6,

which represent industry volatility betas and industry mean reversion terms, respectively.

The results for the two common factor models are presented in Exhibit 3. For this model, we present only results for the nine industry sector ETFs that may be affected by the two common factors (SPY implied volatility and ETF implied volatility). Once again, the constant terms θ

1 are overwhelmingly positive and sig-

nificant (in 81 of 90 cases), ref lecting a positive long-term mean volatility. The coefficient values are smaller on average than in the one-factor model, however, which

is an indication that the inclusion of an industry factor provides additional explanatory information regarding stock implied volatility.

The coefficients for the market volatility betas θ2

are also uniformly smaller than in the one-factor model (grand average coefficient of 0.317 in the two-factor model versus 0.463 in the one-factor model). The inclu-sion of the industry ETF coefficients reduces the sen-sitivity of component stock implied volatility to SPY implied volatility, and 83 of the 90 industry ETF betas (θ

5) are signif icant. The average coeff icient is 0.105;

thus, it is about one-third the level of the market factor. Parallel to the use of SPY to impound market-wide information, common industry-wide information seems to be impounded in the industry ETF implied volatili-ties first and then transmitted to their largest component stocks.

In addition to their use as convenient vehicles to take advantage of industry information, there is a potential further explanation for this phenomenon. The ETFs under study are not subject to the “uptick” rule until only recently;5 thus, traders could act on negative market or industry information (via short selling) more quickly than might be possible for individual stocks. The resulting negative price shocks may then f low through to stock ETF options and their implied volatilities. The information transmission process is not uniform, how-ever, as the coefficients vary widely among the ETFs, consistent with the results of Wang [2010], who found that the volatility characteristics of different industries vary widely. At one extreme, the market volatility beta coefficient θ

2 for the Basic Materials ETF (XLE) declines

from 0.448 in the one-factor model to 0.276 in the two-factor model. Its industry volatility beta coefficient θ

5

is comparable at 0.256. For this ETF, common industry volatility information is just as important as market volatility information, a reasonable result given this industry’s broad exposure to the economy. At the other extreme, the market volatility beta for the Technology ETF (XLK) barely declines (from 0.468 to 0.424), and its industry average volatility beta coefficient is only 0.006. Two other high-volume ETFs, XLF (Financials) and XLB (Basic Materials), have average industry volatility betas that are comparable to the level of their market volatility betas.

Additionally, when industry information is included in the model, the size of the average market mean rever-sion coefficients θ

4 declines substantially, from 0.018 to


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0.005. However, this reduction is substantially offset by the inclusion of the coefficient for “industry volatility mean reversion” (θ

6), which averages 0.019, or almost

four times as high as the market reversion coefficients. So, although the industry volatility “betas” are only

one-third the level of those of the market, mean rever-sion is much more strongly inf luenced by the industry factor. Stock implied volatilities are thus driven more in the short term by market factors, but tend to revert to industry levels over longer intervals. Also, short-term

E X H I B I T 3EGARCH-M-t Estimates for Stock-Implied Volatilities with Two Common Factors

ln ln_

_ln( ) ln( _ ) ln

_

_ln( _ )

11 2

13 1 4 1 5

16 1

v

v

v SPY

v SPYv v SPY

v ETF

v ETFv ETFit

iti i

t

ti it i it i

t

ti t it it

⎛⎝⎜

⎞⎠⎟

= θ + θ⎛⎝⎜

⎞⎠⎟

+ θ + θ + θ⎛⎝⎜

⎞⎠⎟

+ θ + σ ε− −

− −−

−

ln | | ln21 2 1 3 1

24 1it i i it i it i it( ) ( )σ = φ + φ ε + φ σ + φ ε− − −

Notes: This exhibit presents the average coefficients and Newey-West [1987] t-statistics (with five lags) from the two-factor EGARCH-M-t estimations. The equations are estimated for each of the 10 largest component stocks of each industry ETF.


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changes in volatility are higher when industry volatility is high. A final observation of these results is driven by Engle and Figlewski [2014], who find that the φ

3i and φ

4i

coefficients decline when moving from a zero-factor to a one-factor (market) model. We observe the same result here when moving from a one-factor to a two-factor model, such that total variance is less persistent and less asymmetrical in the presence of an industry factor.

IMPLIED VOLATILITY SPILLOVERS

Having established a link among the implied vola-tilities of ETFs and their largest component stocks, we seek to quantify this relationship over time. We use the model of Diebold and Yilmaz [2009 and 2012, here-after DY] to generate implied volatility spillovers from the ETFs to their respective component stocks. In this framework, spillover estimates are generated as rolling variance decompositions of 10-day-ahead return variance forecasts based on five daily lags of volatility informa-tion. However, instead of generating estimates of return volatility from daily price ranges as in their papers, we use our estimates of implied volatility. This approach provides time series’ of implied spillover levels that we link to measures of liquidity in the next section.

We are particularly interested in the effect of implied volatility spillovers from SPY and the industry ETFs to their largest component stocks, and DY pro-vide a method to examine these relationships through the calculation of “directional” volatility spillovers. The original spillover model in DY [2009] is sensitive to the ordering of variables, since Cholesky factorization is used to achieve orthogonality. However, the generalized VAR framework of Koop et al. [1996] and Pesaran and Shin [1998], hereafter KPPS, is adopted in DY [2012]. This model is not sensitive to the ordering of variables, and we use the more recent specification to avoid this issue.

The normalized forecast variance shares from the DY model estimate the percentage of spillovers trans-mitted by SPY and the industry ETFs to their largest component stocks. Specifically, for each ETF and its 10 largest component stocks, we use implied volatility data to estimate 11 variable vector autoregressions (VAR(p)) using p equal to five lags to represent one week of trading activity:

, where ( , ),

1

5

x x i i d. .t i t ii

t∑∑φ∑ + ε ε Σ~ (0,=

(5)

The moving average representation of this expres-sion is:

, where0

x At i t ii∑∑ εAiA

=

∞

(6)

1 2 5 5A A1 A A2 5i i11 i 2 52 5φ + φ � φ21 φ (7)

In this setup, A0 is an 11-by-11 identity matrix

where Ai = 0 for i < 0, and the moving average coef-

ficients are used to construct variance decompositions. The fraction of the H-step-ahead error variance in a forecast of x

t is calculated as shocks to x

j ∀

j ≠ i for each i.

We generate 10-day-ahead forecasts from the variance decompositions by setting H = 10. Therefore, own vari-ances shares are defined by DY as “the fractions of the H-step-ahead error variances in forecasting x

i that are

due to shocks to xi for i = 1, 2, …, N, and cross variance

shares, or spillovers, as the fractions of the H-step-ahead error variances in forecasting x

i that are due to shocks

to xj, for i, j = 1, 2, …, N, such that i ≠ j.” Thus, the

implied variance decomposition of each firm’s H-step-ahead forecast is denoted by ( )ij

gθ :

( )1 2

0

1

0

1ij

jj h

H

h

H

∑∑

( )e A ei hA j∑( )e A A ei hA h je∑

θ =( )ijg

σ

A A∑−

=

−

=

− (8)

The implied variance matrix for the error vector ε is denoted by Σ and the standard deviation of the error term for the jth equation is σ

jj. The selection vector e

i

contains one as its ith element and zeroes otherwise. As mentioned previously, this implied generalized variance decomposition framework does not orthogonalize inno-vations from the implied volatility error term; therefore, the contributions to the variance of the forecast error may not sum to unity. Thus, we follow DY and nor-malize each entry in the decomposition matrix (own and cross variance shares) by the row sum as follows:

� ( )( )

( )1

ijijg

ijg

j

N∑θ =( )ij

g θ

θ=

(9)

Therefore, by def inition, � ( ) 11 ijj

N∑ θ =( )ijg

= and

( ), 1

Niji j,

N �∑ θ =( ))ijg . DY observe in their 2012 study that

this “is the KPPS analog of the Cholesky factor-based measure used by Diebold and Yilmaz (2009).” All of the spillover tests in this article are repeated using nor-


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malization by column instead of row, and the results are qualitatively similar. Going forward, we focus on the individual directional spillover contributions (cross variance shares) from the implied volatilities of the ETFs to those of their largest component stocks.

In the interest of brevity, we present only one rep-resentative spillover table (Exhibit 4 for XLE) to dem-onstrate the output of the spillover model. The volatility spillovers from SPY and XLE to its largest component stocks are presented in the f irst two columns of the Exhibit. Each row in these two columns represents the percent share of the variance forecast provided by SPY or XLE to each other and to the component stocks. In general, the spillovers are decreasing in market capital-ization of the components, since the stocks are sorted so that the top percentage holding (for XLE it is XOM) is contained in the third row, while the smallest holding is at the bottom of the column. Own volatility spillovers are presented on the diagonal and are naturally larger than spillovers from the ETFs or the other component stocks. The total spillovers contributed from SPY and XLE are contained in the last row of the table. In this

case, total spillovers from XLE are slightly larger than those from SPY (82% versus 78%).

We present the condensed volatility spillover results for all nine of the industry ETFs in Exhibit 5. To con-struct this table, we combine the first two columns from each of the nine individual spillover tables in a summary table, since we are ultimately interested in spillovers from SPY and the industry ETFs to their component stocks. Once again, the spillovers generally decline with the proportion of each stock represented in the ETFs, but the results vary widely depending on industry. In six out of nine cases, the total spillovers to component stocks are greater for SPY than for the industry ETFs. The greatest discrepancy occurs for XLP (Consumer Staples), where SPY contributes 114% (approximately) to the variance forecasts of the component stocks, while the industry ETF contributes only 11%.

Conversely, stocks in the Financials ETF (XLF) receive 19% more spillovers from the industry ETF than from SPY, an even stronger result than we observe earlier regarding XLE (Energy). The industry spillovers are also greater than the market spillovers for XLY (Consumer

E X H I B I T 4XLE Volatility Spillovers

Notes: This exhibit presents a “volatility spillover table” for XLE that is generated as in Diebold and Yilmaz [2009, 2012]. The figures represent the percent of 10-day-ahead variance forecasts of implied volatility based on five daily lags of volatility information. The contributions “from” each security are presented in columns and the contributions “to” each security are in rows.


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on.


EX

HI

BI

T 5

Vol

atil

ity

Sp

illo

vers

fro

m S

PY

an

d th

e In

du

stry

ET

Fs to

ET

F C

omp

onen

t Sto

cks

Not

es:

Thi

s ex

hibi

t pre

sent

s a

cond

ense

d “v

olat

ility

spi

llove

r tab

le”

that

is c

reat

ed fr

om th

e fir

st tw

o co

lum

ns o

f eac

h of

the

indi

vidu

al v

olat

ility

spi

llove

r tab

les

for e

ach

ET

F in

our

sam

ple.

T

hus,

it p

rese

nts

spill

over

s on

ly fr

om S

PY a

nd th

e E

TFs

to e

ach

of th

eir 1

0 la

rges

t com

pone

nt s

tock

s.


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of F

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is il

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oriz

ed c

opie

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icle

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d to

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use

r or

to p

ost e

lect

roni

cally

with

out P

ublis

her

perm

issi

on.


Durables). Additionally, for four of the other ETFs (XLI, XLB, XLK, and XLU), the industry spillovers represent a significant proportion of the market spillovers. Overall, the results generally parallel the volatility beta results of the prior section in that both market and industry common volatility factors affect the evolution in implied volatility of the stocks to varying degrees.

IMPLIED VOLATILITY SPILLOVERS, OPTIONS LIQUIDITY, AND ARBITRAGE

A useful feature of the DY estimations is that they provide time series of volatility spillovers that are cal-culated on a 200-day moving average basis. In order to examine the potential drivers of the transmission of implied volatility information from a common market factor, we estimate the following Newey-West [1987] regression with five lags:

β⎛

⎝⎜⎛⎛

⎝⎝

⎞

⎠⎟⎞⎞

⎠⎠+ β

⎛

⎝⎜⎛⎛

⎝⎝

⎞

⎠⎟⎞⎞

⎠⎠+ β

⎛

⎝⎜⎛⎛

⎝⎝

⎞

⎠⎟⎞⎞

⎠⎠

+ β + β + β + β + ε

ln( ) l= α + β n_

ln_

ln_, 1β) α + β ,

,2

,

,3

,

,

4 , 5 , 6 , 7 , ,

l p llOPTVLMVV

OPT OI

OPTVLMVV

OPT OI

OPTVLMVV

OPT OI

Proportion D+ β5 evNAV E+ β6 TFFT undFF sFd low E+ β7 TFMkF tCapCC

i ,i t,

i t,

ETF t,TT

ETF t,TT

SPY t,

SPY t,

t, t, t, t, i t,

(10)

The directional volatility spillovers from the industry ETFs and SPY to each of its component stocks are defined as Vol Spill

i,t, as in the model of DY [2012].

We define OPTVLMi,t to be the total combined daily

call and put option volume for each stock, and OPT_OIi,t

as the total daily call and put open interest. Thus, the variables inside the parentheses of the terms β

1 to β

3 rep-

resent daily options turnover for each component stock, its industry ETF, and SPY, respectively. To control for other variables that may impact the implied volatility spillover process, we also include the proportion of each stock represented in the fund, deviations from net asset value, ETF f low of funds, and ETF market capitaliza-tion. Flow of funds for each ETF j is calculated from the raw TNA data from Bloomberg as follows:

(1 )1 ,(1

Flowof FundFF sddTNA TNN NAT r

TNANNj t,j t, j t, j t,

j t,

=+(11(1TNATT j t− (11)

All of the variables are aggregated into 200-day moving averages to be consistent with the calculation

of volatility spillovers, and logarithms are taken for ease of interpretation.

Full Sample Results

Directional volatility spillovers are calculated for both the industry ETFs and SPY, and these spillovers are used as dependent variables in Equation (10). The results of these estimations are presented in Exhibit 6. The first significant result to note is the negative relationship between stock option liquidity6 and ETF spillovers in the first column of the table. Increased liquidity in a par-ticular stock option’s turnover reduces the ability of its industry ETF to transmit implied volatility information. However, as indicated by the positive and significant coefficients on ETF and SPY liquidity β

2 and β

3, spill-

overs are positively related to liquidity in these securities. The economic effects of SPY liquidity are more than

three times as important as those of the industry ETFs, ref lecting the importance of common market volatility information and consistent with the prior section.

ETF spillovers are also positively related to the proportion of each stock in its ETF, since the beta coef-ficient β

4 is positive and significant. Deviation from net

asset value (β4) is a proxy for arbitrage activity among

the ETFs and their largest underlying component stocks, and it is negatively related to implied volatility spill-overs. It seems that when ETFs are mispriced relative to their underlying securities, the ability of ETFs to transmit implied volatility information to their compo-nents is attenuated. This could be the result of options traders slowing their trading activity (and impounding volatility information) when there is uncertainty sur-rounding ETF value. It may also ref lect the choice of traders to trade directly in the ETF when it is mispriced, and to use options when the security is fairly valued. The coefficient for the absolute value of f low of funds is positive and significant, and is an additional proxy for the ETF creation/redemption process. When there are large positive or negative f lows into the underlying


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ETFs, ETF options provide increased volatility infor-mation to their component stocks. This may also be related to the hedging activities of ETF options market makers as they trade shares to offset the risks of options order f low. Finally, we include ETF market capitaliza-tion as a variable, since Madura and Ngo [2008] and Clifford et al. [2014] find differential effects regarding ETF market capitalization and component stock valua-tion and fund f lows, respectively. This variable is posi-tively related to ETF volatility spillovers, since they are stronger for larger ETFs.

In the second column of Exhibit 6, we examine the ability of SPY options liquidity to spill over infor-mation to the largest ETF component stocks, which are also some of the largest stocks in SPY itself. One major difference between the ETF and SPY results is that both the β

1 and β

2 coefficients are negative and sig-

nificant in this specification. Thus, the ability of SPY to transmit volatility information is attenuated in the pres-ence of high stock and industry ETF options liquidity. The other coefficients are generally consistent with the earlier results, although the coefficients for funds f low and market cap are small and/or insignificant, which is reasonable, given that they are not directly related to trading in SPY or its options.

Robustness: Subsample Results

In order to examine how the volatility gener-ating process is driven at the individual ETF level, we conduct a parallel analysis to the previous section for each individual ETF. The results of these estimations are contained in Exhibit 7, and here the most relevant coefficient is β

2, the sensitivity of ETF volatility spill-

overs to ETF options turnover. All but two of these coefficients are positive and significant, indicating that industry volatility information is being impounded via the industry ETFs and then transmitted to the compo-nent stocks. The coefficients are highest for the Tech-nology ETF (XLK, β

2 = 0.72) and Basic Materials (XLB,

β2 = 0.66). Additionally, the explanatory power of the

models is greater relative to the SPY spillover model in all but two cases. In some cases, the adjusted R-squareds are substantially higher. ETF implied volatility spill-overs therefore generally increase during times of higher ETF options turnover, although there are two excep-tions (Consumer Discretionary – XLY, β

2 = −0.56 and

Consumer Staples – XLP, β2 = −0.52).

The results for the individual stock options volume coeff icients β

1 are mixed, although all of the coeff i-

cient values are relatively small compared to the other turnover variables. It seems that in this specification, the industry and market turnover coefficients subsume idiosyncratic effects. But as in the previous specifica-tion, the coefficients for market volatility information β

3 are generally positive and significant. They are also

generally larger and hold more statistical significance than in the previous specification. Thus, the ability of

E X H I B I T 6ETF Implied Volatility Spillovers, Liquidity, and Arbitrage

= α + β⎛

⎝⎜⎞

⎠⎟+ β

⎛

⎝⎜⎞

⎠⎟

+ β⎛

⎝⎜⎞

⎠⎟+β +β

+ β + β + ε

ln( ) ln_

ln_

ln_

, 1,

,2

,

,

3,

,4 , 5 ,

6 , 7 , ,

Vol SpillOPTVLM

OPT OI

OPTVLM

OPT OI

OPTVLM

OPT OIProportion DevNAV

ETFFundsFlow ETFMktCap

i ti t

i t

ETF t

ETF t

SPY t

SPY ti t i t

i t i t i t

Notes: This table presents the results of Newey-West [1987] regressions (with five lags) of industry ETF and SPY volatility spillovers on liquidity variables for the pooled sample of stocks the industry ETFs, and SPY. We also include variables related to ETF arbitrage: the proportion of each individual stock in each ETF, deviations from NAV, ETF f low of funds, and ETF market capitalization. *, **, and *** indicate statistical sig-nificance at the 10%, 5%, and 1% levels, respectively.


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ublis

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issi

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the ETFs to impound volatility information into the options of their component stocks is enhanced in the presence of higher SPY options liquidity. This may be a further indication of the tightly interwoven arbitrage relationships among these securities, and it is consistent with Peng and Xiong [2006] in that investors are more apt to consider market and industry volatility informa-tion as opposed to information regarding individual stock volatility. The coefficients for proportion are once again generally positive and significant, and the constant terms are all strongly significant. The remaining control variables are generally consistent with the results of the pooled regressions, although there are significant excep-tions at the individual ETF level that ref lect differing characteristics.

An additional analysis is undertaken for SPY vola-tility spillovers, and the results of these estimations are contained in Exhibit 8. First, we examine the coefficients most likely to be related to spillovers from SPY options to those of its component stocks: the coefficients for SPY option liquidity β

3. All but one of the significant coeffi-

cients are positive, an indication that volatility spillovers are strongest during periods of high options turnover in SPY. Given the high levels of dispersion trading and volatility arbitrage in these products, it is reasonable that trading in SPY options is used to impound market vola-tility information that is then transmitted to component stocks. Since proportion is a percentage and all of the other variables in the equation are expressed in logs, the coefficients represent approximate changes in volatility spillovers given a 1% increase in implied volatility. Thus, for example, a 1% increase in options turnover in SPY implies a 0.41% increase in volatility spillovers to each of the largest component stocks in XLY. The largest coef-ficients are observed for XLK (Technology – 1.06) and XLP (Consumer Staples – 0.98). These relatively large coefficients imply that market-related volatility infor-mation is important in the evolution of the component stocks of these ETFs.

Additionally, all of the significant terms for the pro-portion of each stock in its respective ETF (β

4) are posi-

tive, consistent with higher arbitrage activity in stocks that are represented in greater amounts in the ETFs. The constant terms are also positive and signif icant, but the coefficients vary considerably across the ETFs (from a low of 0.94 for XLI to a high of 9.36 for XLE), consistent with prior results showing volatility variation

EX

HI

BI

T 7

ET

F Im

pli

ed V

olat

ilit

y S

pil

love

rs, L

iqu

idit

y, a

nd

Arb

itra

ge b

y E

TF

Not

es:

Thi

s ex

hibi

t pre

sent

s th

e re

sults

of N

ewey

-Wes

t [19

87]

regr

essio

ns (

with

five

lags

) of i

ndus

try

secto

r ET

F vo

latil

ity s

pillo

vers

on

liqui

dity

var

iabl

es fo

r the

indi

vidu

al s

tock

s, th

e E

TFs

, an

d SP

Y, a

s w

ell a

s th

e pr

opor

tion

of e

ach

indi

vidu

al s

tock

in th

e E

TFs

, de

viat

ions

from

NA

V,

ET

F flo

w o

f fun

ds,

and

ET

F m

arke

t cap

italiz

atio

n. *

, **

, an

d **

* in

dica

te

stat

istica

l sig

nific

ance

at t

he10

%,

5%,

and

1% le

vels,

resp

ectiv

ely.


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earc

h on

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is il

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e un

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oriz

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opie

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art

icle

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ost e

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ublis

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issi

on.


across industries. In contrast, the significant terms for individual stock option liquidity (β

1) and industry ETF

option liquidity (β2) are negative in all but one case.

All of the negative β1 and β

2 coefficients are statistically

significant, indicating that spillovers from SPY to the component stocks are weaker in the presence of high stock and/or ETF options volume. These results indicate that when market participants use these instruments to impound industry and/or idiosyncratic volatility infor-mation, the ability of SPY to impound common market volatility information is attenuated. Trading based on fundamental stock or industry volatility information impedes the ability of market volatility information to be impounded into stock implied volatilities.

We are also interested to see how the explanatory variables affect stocks of different sizes, since even in the top 10 components of the ETFs, there is significant variation in market capitalizations. Therefore, we sepa-rate the sample into three groups according to the pro-portions of each stock contained in each industry ETF: the top three, middle four, and lowest three component stocks in terms of their proportions in each ETF. Equa-tion (10) is re-estimated for each of the three groups, and the results are presented in Exhibits 9 and 10. The results are generally consistent with the full-sample results of Exhibit 6, but there are a few discrepancies that are explained by size.

First of all, in Exhibit 9, the coefficients for stock, ETF, and SPY liquidity are generally consistent with the full-sample results for all three groups (first column of Exhibit 6). However, the results for proportion diverge in the subsamples. Although all of the coefficients are positive, the effects are more economically significant for the smaller stocks. Thus, the proportion of stock held in an industry ETF is more important in its volatility process for relatively smaller stocks. Additionally, the f low of funds coefficients are larger for the smaller stocks in the sample. Finally, the positive effects of ETF market capitalization on volatility spillovers are stronger for smaller stocks as well. All of these results are consistent with Madura and Ngo [2008] and Clifford et al. [2014], who find differential size effects regarding ETF compo-nent stock valuation and fund f lows, respectively.

Exhibit 10 contains the results for SPY implied volatility spillovers. As in the full sample, there is a nega-tive relationship between stock liquidity and spillovers, but the effects are stronger for smaller stocks. The same

EX

HI

BI

T 8

SP

Y I

mp

lied

Vol

atil

ity

Sp

illo

vers

, Liq

uid

ity,

an

d A

rbit

rage

by

ET

F

Not

es:

Thi

s ex

hibi

t pre

sent

s th

e re

sults

of N

ewey

-Wes

t [19

87]

regr

essio

ns (

with

five

lags

) of i

ndus

try

secto

r ET

F vo

latil

ity s

pillo

vers

on

liqui

dity

var

iabl

es fo

r the

indi

vidu

al s

tock

s, th

e E

TFs

, an

d SP

Y, a

s w

ell a

s th

e pr

opor

tion

of e

ach

indi

vidu

al s

tock

in th

e E

TFs

, de

viat

ions

from

NA

V,

ET

F flo

w o

f fun

ds,

and

ET

F m

arke

t cap

italiz

atio

n. *

, **

, an

d **

* in

dica

te

stat

istica

l sig

nific

ance

at t

he10

%,

5%,

and

1% le

vels,

resp

ectiv

ely.


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rnal

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ivat

ives

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earc

h on

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is il

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e un

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oriz

ed c

opie

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icle

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ost e

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ublis

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issi

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E X H I B I T 9ETF Implied Volatility Spillovers, Liquidity, and Arbitrage by Proportion

Notes: This table presents the results of Newey-West [1987] regressions (with five lags) of industry sector ETF implied volatility spillovers on liquidity variables for the individual stocks, ETFs, and SPY, as well as the proportion of each individual stock in the ETFs, deviations from NAV, ETF f low of funds, and ETF market capitalization. In this table, the results are separated by the proportion of each stock held by the fund. Results are presented for the top three, middle four, and lowest three stocks in terms of their proportional holdings by the fund. *, **, and *** indicate statistical significance at the 10%, 5%, and 1% levels, respectively.

E X H I B I T 1 0SPY Implied Volatility Spillovers, Liquidity, and Arbitrage by Proportion

Notes: This table presents the results of Newey-West [1987] regressions (with five lags) of SPY implied volatility spillovers on liquidity variables for the individual stocks, ETFs, and SPY, as well as the proportion of each individual stock in the ETFs, deviations from NAV, ETF f low of funds, and ETF market capitalization. In this table, the results are separated by the proportion of each stock held by the fund. Results are presented for the top three, middle four, and lowest three stocks in terms of their proportional holdings by the fund. *, **, and *** indicate statistical significance at the 10%, 5%, and 1% levels, respectively.


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relationships hold for ETF liquidity, SPY liquidity, pro-portion, and deviation from NAV as in the full sample (second column of Exhibit 6). However, once again, the results are strongest for the smallest stocks. The coefficient for f low of funds was insignificant in the full sample, but when separated into subsets by size, it is positive for the smallest stocks in the sample and negative for the stocks that are held in relatively larger proportions. Similar results are obtained for the coef-ficients on ETF market capitalization, once again con-sistent with prior studies showing differential results for relatively smaller companies that are held in ETFs. In summary, the liquidity and trading activity variables are more strongly related to volatility spillovers for smaller ETF holdings.

In order to examine potential differential effects due to the financial crisis that is included in our sample, we once again divide the sample into three parts. The first “pre-crisis” period is from January 10, 2005, to June 30, 2007; the “crisis” period is from July 1, 2007, to

E X H I B I T 1 1ETF Implied Volatility Spillovers, Liquidity, and Arbitrage by Timeframe

Notes: This table presents the results of Newey-West [1987] regressions (with five lags) of industry sector ETF implied volatility spillovers on liquidity vari-ables for the individual stocks, ETFs, and SPY, as well as the proportion of each individual stock in the ETFs, deviations from NAV, ETF flow of funds, and ETF market capitalization. In this table, the results are separated into sub-periods including before, during, and after the financial crisis, which is defined as the period from July 1, 2007, to December 31, 2008. *, **, and *** indicate statistical significance at the 10%, 5%, and 1% levels, respectively.

December 31, 2008; and the “post-crisis” period covers the remainder of the data until March 31, 2013. The results of the re-estimations of Equation (10) for ETF implied volatility spillovers are presented in Exhibit 11. Most of the results are similar to those in the full sample, although the size of the coefficients generally declines over the sample period, indicating that the spillover effects were larger during the rise in ETF trading volume that peaked during the financial crisis. Two exceptions to the generally consistent results are that stock liquidity was positively related to spillovers during the pre-crisis period, and SPY liquidity became negatively related to spillovers during the post-crisis period. The first result may be again related to the buildup in ETF trading, while the second result may ref lect the decline in ETF trading in the post-crisis period and the increased importance of common market volatility information. In Exhibit 12, the results for SPY spillovers are generally consistent in all three time frames with the full-sample results.


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CONCLUSION

In order to reduce hedging errors, traders and market-makers should consider the presence of both a market volatility factor and an industry volatility factor in the evolution of individual stock option implied volatilities. The volatility “betas” for industry factors in this study are economically signif icant in a cross-section of 90 large capitalization stocks, and implied volatility reverts much more strongly to an industry long-term mean than it does to a market mean. Implied volatility spillovers from ETFs to component stocks vary across industries, but the spillovers are most strongly related to options turnover in the S&P 500 Index ETF and SPDR industry ETFs. The spillovers are also positively related to the proportion that each stock represents in the fund’s total holdings. Additional information regarding the evolution of stock-implied

volatilities is provided by deviations from NAV, f low of funds, and ETF market capitalization. New vola-tility information is f irst ref lected in the market- and industry-based products, then impounded into indi-vidual stock-implied volatilities. The results also indi-cate that implied volatility spillovers from both SPY and the industry ETFs are negatively related to indi-vidual stock option turnover, albeit with a lesser effect. Larger volumes in the individual stock options may represent the impounding of fundamental informa-tion that curbs the ability of the ETFs to pass along more “macro” volatility information. The results are generally consistent for individual ETFs, across stocks with differing proportions in their industry ETFs, and during different time frames. As ETF options volume continues to grow, the sensitivity of individual stock-implied volatilities to those of their respective ETFs warrants continued observation.

E X H I B I T 1 2SPY Implied Volatility Spillovers, Liquidity, and Arbitrage by Timeframe

Notes: This table presents the results of Newey-West [1987] regressions (with five lags) of SPY implied volatility spillovers on liquidity variables for the individual stocks, ETFs, and SPY, as well as the proportion of each individual stock in the ETFs, deviations from NAV, ETF f low of funds, and ETF market capitalization. In this table, the results are separated into sub-periods including before, during, and after the financial crisis, which is defined as the period from July 1, 2007, to December 31, 2008. *, **, and *** indicate statistical significance at the 10%, 5%, and 1% levels, respectively.


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A P P E N D I X

SPY, SPDR Sector Select ETFs and their 10 Largest Component Stocks of ETFs, as of March 31, 2013


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ENDNOTES

1See, for example, Roll [1992]; Heston and Rouwen-horst [1994]; Cavaglia et al. [2000]; Campbell et al. [2001]; and Carrieri et al. [2004].

2See also Bakshi and Kapadia [2003] and Carr and Wu [2009].

3In unreported results, we conduct the factor model estimations using VIX data, and the results are qualitatively similar.

4Further information regarding the Bloomberg implied volatility calculations are available from the authors or via the Bloomberg service.

5In February 2011, the SEC adopted Rule 201, which reinstates the uptick rule for equity securities that fall 10% on an intraday basis. As that rule notes, since ETFs are generally diversif ied, the likelihood of a one-day 10% drop is fairly remote. Therefore, an exemption for ETFs was not provided as under the previous Rule 10a-1 of Regulation SHO.

6The use of “liquidity” in this section refers to options liquidity.

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