1. Supply of and demand for volatility
11/12/2018
On the Causality Between Price Movements in VIX Exchange-traded Funds (ETFs) and VIX Futures Contracts. Do ETFs Increase Volatility?
By O’Neill, Rajaguru and Whaley
Michael O’Neill
FMRC Conference
May 18, 2018
Nashville, Tennessee

2. VIX derivatives markets
Supply of and demand for volatility
11/12/2018
VIX derivatives markets
VIX was launched in 1993, VIX in 2004, options in 2006 and ETPs in 2009 (Whaley, 1993). VIX derivatives are now the most liquid volatility instruments.
Sensitivity (“vega”) of VIX futures and options exceeded that of SPX and SPY options since late 2012 (now 2x).
VIX Futures are the “go-to market”, representing the forward expectation of VIX and leading VIX from 2012 onwards (“tail wags dog”) (Bollen et al, 2016; Dian-Xuan et al, 2017).
Price discovery is likely to occur in the deepest, most liquid market with lower trading costs (Fleming et al, 1996).

3. Supply of and demand for volatility
11/12/2018
VIX closing prices 2004 to 2018

4. Price discovery and lead-lag relations
Supply of and demand for volatility
11/12/2018
Price discovery and lead-lag relations
“Volatility as an asset class” is not well understood, retail investors suffer the “contango trap”, and rebalancing of leveraged ETPs might be front-run (Whaley, 2013).
Futures and ETPs like VXX are largely contemporaneous.
Causal links between futures and inverse/leveraged products such as XIV and TVIX have not been studied.
More attention needs to be focused on the supply and demand dynamics and the price discovery of volatility.
We focus on the most actively traded 1x long, 2x leveraged and -1x short ETPs vs their 30-day VIX futures benchmark.

5. Daily closing prices VIX ETPs
Supply of and demand for volatility
11/12/2018
Daily closing prices VIX ETPs

6. Term structure (spread % contango)
Supply of and demand for volatility
11/12/2018
Term structure (spread % contango)

7. Sources of high frequency intraday data
Supply of and demand for volatility
11/12/2018
Sources of high frequency intraday data
S&P 500 VIX futures data from Thomson Reuters Tick History (TRTH) available through SIRCA (Securities Industry Research Centre of Asia-Pacific). S&P 500 VIX short-term total return index (SPVXSTR).
iPath S&P 500 VIX Short-Term Futures ETN (VXX) launched 29/1/10. Benchmarked to SPVXSTR x1.
VelocityShares Daily 2x VIX Short-Term ETN (TVIX) launched 29/11/10. Benchmarked to SPVXSTR x2.
VelocityShares Daily Inverse VIX Short-Term exchange-traded note (XIV) launched 29/11/10. Benchmarked to SPVXSTER x-1.
Daily NYSE trade and quote data (TAQ) for VXX, XIV and TVIX from WRDS to 31 March 2018.

8. Users of long and short ETPs
Supply of and demand for volatility
11/12/2018
Users of long and short ETPs
Long ETPs (VXX and TVIX) higher retail ownership.
Eg retail buying long-levered ETPs when volatility low selling on VIX spikes, flattening the term structure.
Short ETPs (XIV, SVXY and UVXY) institutional.
Growth in short ETPs and rebalancing risk since 2013, potentially exacerbating changes in volatility (“gamma”).
Eg custodian Credit Suisse covered position as largest shareholder in XIV via the VIX Futures Market and are now subject to a lawsuit. Perhaps a structural change?
Larry Fisher in 1950s.

9. Growth in AUM of ETPs ($’m)
Supply of and demand for volatility
11/12/2018
Growth in AUM of ETPs ($’m)

10. Traded volumes – ETPs and Futures
Supply of and demand for volatility
11/12/2018
Traded volumes – ETPs and Futures

11. Lead-lag relations in nonsynchronous data
Hayashi and Yoshida (2005) correlation using high frequency data.
Correlation estimate includes sum of products of every pair of returns that shares overlap: where 1 is an indicator function that equals one whenever pair of returns has any overlap in time.
Eg.

12. Cross-correlation and the lead-lag ratio

13. LLR of VIX Futures and ETPs 2013-18
Supply of and demand for volatility
11/12/2018
LLR of VIX Futures and ETPs

14. Liquidity events of February 2018

15. Cross correlations 2-6 February 2018

16. Quantile regression VIX Futures / ETPs

17. Unit Root and Cointegration Tests
Supply of and demand for volatility
11/12/2018
Unit Root and Cointegration Tests
All variables in logarithmic transformation are non-stationary I(1) at the 5% level. We also test the unit root of first differences. Results are robust to stationary alternative (ADF and PP and DF-GLS) and non-stationary alternative (KPSS).
Cointegration tests verify that the series have long-term relationships. We use a Gaussian vector autoregression (VAR) process (Johansen and Juselius, 1990).
VIX Futures and ETPs are cointegrated with one cointegrating vector.
There exists a unique long-run equilibrium relationship between VIX Futures and ETPs.

18. Multivariate Analysis of Granger Causality
Long-run Granger causality between indices is established through Yamamoto and Kurzoumi (2006) framework.
Spurious long-run Granger causality is further filtered and fixed using the sign rule (Rajaguru and Abeysinghe, 2008).
Key findings:
Bidirectional negative causality between VXX/XIV but not TVIX/XIV.
Bidirectional positive causality between VXX/TVIX.
Weak bidirectional positive causality between VXX/SPXVIXSTR.
BUT Strong bidirectional causality between SPXVIXSTR and ETPs in the last 30 minutes of trading (3:45-4:15pm), particularly since 2015.

19. Multivariate Analysis – Full Sample
Analysis uses Yamamoto and Kurozumi (2008).
Note: Entries indicates the rejection frequencies, where:
-1 : presence of negative Granger Causality
0 : No Granger Causality
1 : Positive Granger Causality

20. Multivariate Analysis – 3:45 to 4:15pm
Note: Entries indicates the rejection frequencies, where:
-1 : presence of negative Granger Causality
0 : No Granger Causality
1 : Positive Granger Causality

21. Time Variance – Regime Shifting Model

22. Time Variance – Regime Shifting Model
Ln(TVIX)
Ln(VXX)
L(XIV) SD
ECM (-1)
-0.12
-0.05
Table shows Markov Switching VECM Model: Estimates.
Regime 1: Low mean (intercept) and Low Volatility (SD)
Regime 2: High mean (intercept) and High Volatility (SD)

23. Regime Shifting Model Findings
Speed at which the markets reach equilibrium is faster in low-mean low-volatile regime than high-mean high-volatile regime (based on ECM).
SPXVIXSTR is more sensitive to Ln(VXX) in regime 1 (1.09) than in regime 2 (0.71).
Ln(XIV) also has a similar impact in negative causal domain.
TVIX has a much lower effect on SPXVIXSTR though the effect is stronger in regime 2.

24. Standardised Estimates
Regime 1
Regime 2
VXX->SPXVIXSTR
-0.09
0.01
TVIX->SPXVIXSTR
0.21
0.05
XIV->SPXVIXSTR
-1.03
-1.46
SPXVIXSTR->VXX
-11.14
TVIX->VXX
2.35
-6.72
XIV->VXX
-11.47
179.18
SPXVIXSTR->TVIX
4.74
19.51
VXX->TVIX
0.42
-0.16
XIV->TVIX
4.87
28.57
SPXVIXSTR->XIV
-0.97
-0.68
VXX->XIV
0.006
TVIX->XIV
0.04
Table shows Markov Switching VECM Model: Standardised Estimates.
Regime 1: Low mean (intercept) and Low Volatility (SD)
Regime 2: High mean (intercept) and High Volatility (SD)
All Coefficients are statistically significant at the 1% level of significance

25. *Regime Classification Map – full sample
Regime 1: Low mean (intercept) and Low Volatility (SD)
Regime 2: High mean (intercept) and High Volatility (SD)

26. *Regime Classification Map – 3:45-4:15pm
Regime 1: Low mean (intercept) and Low Volatility (SD)
Regime 2: High mean (intercept) and High Volatility (SD)

27. *Regime Estimates Based on LLR
Regime 1
Regime 2
VXX->SPXVIXSTR
-0.09
0.01
TVIX->SPXVIXSTR
0.21
0.05
XIV->SPXVIXSTR
-1.03
-1.46
SPXVIXSTR->VXX
-11.14
TVIX->VXX
2.35
-6.72
XIV->VXX
-11.47
179.18
SPXVIXSTR->TVIX
4.74
19.51
VXX->TVIX
0.42
-0.16
XIV->TVIX
4.87
28.57
SPXVIXSTR->XIV
-0.97
-0.68
VXX->XIV
0.006
TVIX->XIV
0.04
Regime 1: Significant LLR
Regime 2: Insignificant LLR
All estimates are statistically significant at the 1% level of significance

28. Further Observations
ETPs increase volatility consistent with traders switching between buying (selling) VXX and selling (buying) XIV in response to movements in the VIX Futures curve.
Volume tends to be greater and term structure slopes more likely negative on days where XIV leads.
Days in which Futures lead ETPs are not materially different in terms of volume and term structure.
ETPs provide liquidity in low volatility regimes, but arbitrage relations can break down when volatility expectations change, most notably on 5 February 2018 when XIV collapsed.

29. Supply of and demand for volatility
11/12/2018
Summary
The impact of VIX ETPs on volatility in VIX Futures varies.
Causal relations between VXX and VIX Futures are well established with leads and lags generally short-lived.
Relations between inverse / leveraged products are not yet established.
We analyse time variance in relations between VXX, XIV, TVIX and SPXVIXSTR for different volatility regimes and VIX term structures.
Quantile regressions highlight elasticity of VIX Futures to ETP prices.
Regime shifting models further demonstrate the changes in causation with the volatility of volatility and relate this back to the term structure of VIX Futures.

30. Supply of and demand for volatility
11/12/2018
Further work
“Uberisation” of markets: price stability and role of algorithmic traders and market makers in different regimes.
Incorporating liquidity variables such as bid-ask spreads, traded volume, time between trades, term structure of VIX futures, and perhaps identity of traders (CTFC data).
Incorporating skew of in-the-money versus out-of-the-money SPX options, ETP short gamma exposures and “vol-of-vol”.
Separating rebalancing impact of leveraged ETPs from price discovery.