Long‐term dynamics of the VIX index and its tradable counterpart VXX

• Published date: 01 March 2019
• DOI: http://doi.org/10.1002/fut.21974
• Date: 01 March 2019

Received: 14 December 2017

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Revised: 10 September 2018

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Accepted: 15 September 2018

DOI: 10.1002/fut.21974

RESEARCH ARTICLE

Long‐term dynamics of the VIX index and its tradable

counterpart VXX

Milan Bašta

1

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Peter Molnár

2,3

1

Department of Statistics and Probability,

Faculty of Informatics and Statistics,

University of Economics, Prague, Czech

Republic

2

UiS Business School, University of

Stavanger, Stavanger, Norway

3

Department of Monetary Theory and

Policy, Faculty of Finance and

Accounting, University of Economics,

Prague, Czech Republic

Correspondence

Peter Molnár, UiS Business School,

University of Stavanger, 4036 Stavanger,

Norway.

Email: peto.molnar@gmail.com

Abstract

We study the relationship of the VIX index and the exchange‐traded note VXX

on various timescales. We find that changes of VIX and VXX are correlated only

contemporaneously on timescales of days, but VIX leads VXX on timescales of

months. Next, we construct a simple joint model for VXX and VIX which

replicates all the key characteristics of these two time series, but in which VIX

and VXX are related only via a correlated error term. Therefore, VIX cannot be

used as a predictor of VXX and there is no apparent trading profit opportunity.

KEYWORDS

comovement, implied volatility, predictability, VIX, VXX

1

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INTRODUCTION

This paper studies the long‐term relationship between the VIX index (volatility implied by options on the S&P 500

index), and a derivative instrument VXX, which seeks to provide investors with exposure to the VIX index. The

exchange‐traded note VXX is practically 30‐day futures on the VIX index. Most financial futures have a very close

relationship with their underlying asset due to the no‐arbitrage condition. For example, the S&P 500 index and futures

on the S&P 500 index are moving closely together. Moreover, there is basically no lead–lag relationship between the

S&P 500 index and futures on the S&P 500, or such a lead–lag relationship exists only on very short timescales and can

be found only in high‐frequency data.

Contrarily, the situation is very different for the VIX index and VIX futures (or alternatively, the exchange‐traded

note VXX). The no‐arbitrage condition cannot be applied, because the VIX index is not tradable (cannot be bought or

sold). Therefore, the relationship between the nontradable VIX index and VXX, which is tradable as easily as a simple

stock, is not governed by any immediate arbitrage, but by risk perceptions and expectations about the future of the

financial markets. As a result, it is not obvious what the joint dynamics between VIX and VXX should look like.

The Chicago Board Options Exchange (CBOE) Market Volatility Index with ticker VIX was launched by the CBOE

back in 1993. The VIX index is nowadays one of the most followed financial indicators in the world. Following the huge

success of the VIX index, many other volatility indices have been introduced not only for equity markets (Bugge,

Guttormsen, Molnár, & Ringdal, 2016), but also for various commodities, including electricity (Birkelund, Haugom,

Molnár, Opdal, & Westgaard, 2015).

Figure 1 illustrates the relation between the VIX index and its underlying S&P 500 index in the period from January

2007 to July 2016. As this figure illustrates, implied volatility was high during the Financial crisis of 2007–2009.

Moreover, there is a strong negative correlation between changes in the S&P 500 index and changes in the VIX index.

Due to its strong negative correlation (see Figure 1) with the overall stock market, the VIX index would be a very

valuable instrument for portfolio diversification if it was a traded instrument. However, it is not traded. Direct trading

J Futures Markets. 2019;39:322–341.wileyonlinelibrary.com/journal/fut322

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© 2018 Wiley Periodicals, Inc.

of volatility started in 2004 when the CBOE introduced futures contracts on the VIX index. These futures allow

investors to trade volatility directly. However, futures contracts were not suitable for small investors. In 2009, futures

indices were introduced. These indices are constructed by rolling futures contracts in such a way that the average

maturity of all the contracts in the index remains constant. Most importantly, futures indices enabled the creation of

exchange‐traded products that replicate the performance of these indices. The first VIX exchange‐traded product, VXX,

was introduced in 2009. It replicates the performance of the S&P 500 VIX Short‐Term Futures Index, which has a

constant 30‐day maturity. The popularity of the VIX exchange‐traded products, and VXX in particular, has been

increasing tremendously (Figure 2, where the natural logarithm of the traded volume of SPDR S&P 500 ETF [SPY] and

the natural logarithm of the traded volume of VXX are depicted for the period from January 2009 to July 2016). This

figure illustrates that VXX experienced almost exponential growth in its traded volume during the period shown (the

traded volume has increased by about 20,000 times), whereas the traded volume of the most popular exchange‐traded

fund, the SPY, replicating the S&P 500 index, has not changed much.

Recently, VIX exchange‐traded products have been studied from the perspective of risk‐return tradeoff,

diversification, and trading strategies in several academic studies. Most of these studies have concluded that VIX

exchange‐traded products are not suitable for diversification, because of the high negative expected return of the VIX

short‐term futures index (Alexander & Korovilas, 2013; Alexander, Korovilas & Kapraun, 2016; Whaley, 2013). On the

other hand, this high negative expected return offers a possibility for highly profitable trading strategies (Bordonado,

Molnár, & Samdal, 2017). An excellent overview of trading and investment in volatility products is provided in

Alexander, Kapraun, and Korovilas (2015).

The relationship between VIX and VIX futures is another important topic that has recently attracted increasing attention.

One strand of literature (Lu & Zhu, 2010; Zhang, Shu, & Brenner, 2010) focuses on the relationship between VIX and its

derivatives from the perspective of derivatives pricing. The goal of these models is to explain the price of VIX derivatives for a

given level of the VIX index. Another strand of the literature studies whether VIX or its derivatives react faster to new

information and whether VIX leads its derivatives, or vice versa. This relationship has been studied at daily and high‐

frequency (15‐sor1‐min) timescales. At the daily scale, changes of the VIX index and returns of VXX (or equivalently

returns of VIX futures) are highly correlated (Zhang et al., 2010). Contrarily, at 15‐s scale contemporaneous correlation in the

changes of VIX and changes of its futures is close to zero (Frijns, Tourani‐Rad, & Webb, 2016).

FIGURE 1 The natural logarithm of VIX (logVIX, gray, left vertical axis) and the natural logarithm of the S&P 500 close price (log S&P

500, black, right vertical axis)

FIGURE 2 Natural logarithm of the traded volume of VXX (gray, left vertical axis) and the natural logarithm of the traded volume of

SPY (black, right vertical axis) in the period from January 2009 to July 2016

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