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[World Scientific Handbook in Financial Economics Series] The World Scientific Handbook of Futures...
[World Scientific Handbook in Financial Economics Series] The World Scientific Handbook of Futures Markets Volume 5  Volatility as an Asset Class
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المجلد:
10.1142/89
عام:
2015
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english
DOI:
10.1142/9789814566926_0014
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July 3, 2015 8:28 World Scientific Handbook of Futures Markets. . . 9.75in x 6.5in b1892ch14 CHAPTER 14 The World Scientific Handbook of Futures Markets Downloaded from www.worldscientific.com by LA TROBE UNIVERSITY on 05/21/16. For personal use only. VOLATILITY AS AN ASSET CLASS Tom Nohel and Steven K. Todd Abstract: In this chapter, we discuss the development and evolution of the CBOE’s volatility index or VIX, the correlation structure of VIX with other assets, and we highlight hedge fund strategies that are exposed to volatility and that could therefore potentially beneﬁt from the existence of derivatives that reference VIX. We also describe the development of the markets for VIX derivatives and detail their structure, as well as the development of pricing models for VIX derivatives. Finally, we describe the development of exchangetraded products (ETPs) that reference volatility, and we analyze the structure of these products. We conclude with an analysis of the performance of VIXrelated ETPs, and we test the performance of simple technical trading rules that use ETPs that reference VIX. These have all been crucial to the development of volatility as a separate asset class. Keywords: Volatility, VIX, ETP, implied volatility, VIX derivatives, trading volatility. Economists understand that option prices ought to depend very strongly on the volatility of the underlying asset. Simple strategies like straddles, strangles, and butterﬂy spreads have long been thought of as a means to invest in volatility. But it was not until economists started to develop models that could price options that we could contemplate an estimate of volatility implied by option prices. The seminal model of Black and Scholes (1973), followed by Cox et al. (1979), Heston (1993), and Britten–Jones and Neuberger (2000), among many others, combined with the initiation of options trading at the Chicago Board Options Exchange (CBOE) and other venues brought options trading and the notion of volatility to the masses. In this ch; apter, we discuss the foundations and evolution of trading in volatility, and ultimately, the notion of volatility as an asset class. 437 page 437 July 3, 2015 8:28 The World Scientific Handbook of Futures Markets Downloaded from www.worldscientific.com by LA TROBE UNIVERSITY on 05/21/16. For personal use only. 438 World Scientific Handbook of Futures Markets. . . 9.75in x 6.5in b1892ch14 T. Nohel and S. K. Todd A crucial catalyst for the growing interest in volatility was the creation, and eventual wide dissemination, of the CBOE’s volatility index or VIX. The VIX was the brainchild of Robert Whaley, Professor of Finance at Vanderbilt University (see Whaley, 1993). The VIX uses prices of traded options to construct a measure of the market volatility expected to prevail over the subsequent 30 days. Often referred to as the “fear index” in the popular press, and for that reason widely used as a barometer of market sentiment, what immediately caught the eye of market participants is the fact that VIX appears to be strongly negatively correlated with popular proxies for the market portfolio (e.g., the S&P500). This is especially true during downward market spikes that correspond to upward spikes (jumps) in volatility. It is perhaps no coincidence that the growing awareness of volatility very much dovetails with the growth of hedge fund assets, since many hedge fund strategies are inherently exposed to volatility, with some funds even premising trades based on volatility. Clearly hedge funds engaged in such trades form a natural clientele for products that enable investment in volatility as an asset class. But, alas, the VIX is not tradable. Enter VIX derivatives. Though the VIX itself is not tradable, the CBOE introduced VIX derivatives starting in 2004 with VIX futures (in March), followed by VIX options in February of 2006. The introduction of VIX options helped to increase trading in VIX futures (see Whaley, 2013), but neither of these products was accessible to the vast majority of individual investors, or even to many institutional investors like pension fund managers. This changed with the introduction of the ﬁrst ExchangeTraded Product (hereafter, ETP) referencing the VIX in 2009, followed by numerous permutations of ETPs referencing VIX.1 There are now 30 or more ETPs that reference the VIX, including both levered products and short products. However, while by design the ETPs track their benchmark indices, net of fees, either perfectly (ETNs) or very well (ETFs), the extent to which they track the VIX itself is at best mediocre, and at worst, disastrous.2 While the market cap of VXX (the most popular of the ETPs that reference VIX) stood at just over $1 billion in early December 1 The ﬁrst ETP to reference the VIX is the S&P500 VIX ShortTerm Total Return Futures Index (Ticker: VXX), introduced by Barclays Bank, PLC, on January 29, 2009. 2 Whaley (2013) tabulates returns on various assets over the period December 20, 2005 through March 30, 2012. While the holding period return for SPY (ETF that references the S&P500) was 26.6%, and the holding period return on the VIX was 38.5% over the same period, the comparable return on the ShortTerm VIX Futures Index was −93.2%. page 438 July 3, 2015 8:28 World Scientific Handbook of Futures Markets. . . 9.75in x 6.5in b1892ch14 The World Scientific Handbook of Futures Markets Downloaded from www.worldscientific.com by LA TROBE UNIVERSITY on 05/21/16. For personal use only. Volatility as an Asset Class 439 of 2013, indicative of its continued popularity, cumulative losses for VXX investors since inception are several multiples of that ﬁgure. In fact, the cumulative return on VXX since its inception is a rather disparaging −99.3%. So, what is wrong with ETPs that reference the VIX? A lot of the diﬃculty with ETPs that reference the VIX comes about because VIX itself is not a traded asset. As a result, the ETPs that reference VIX have little choice but to use VIX derivatives as the basis for their trading strategies. And there is little if any agreement among academics and/or practitioners on a model that consistently prices volatility derivatives. One of the true stumbling blocks in this area is to keep in mind that while the VIX itself does not trade, its value is derived from the prices of traded assets, namely options on the S&P500. Therefore, in order for a model to have some semblance of reality, it must be a model that correctly prices options on the index, as well as derivatives that reference volatility derived from options on the index. Only recently have such models begun to emerge and they have yet to gain universal acceptance. In what follows we discuss the development and evolution of the VIX (the ﬁrst section), the correlation structure of the VIX with other assets (the second section) and the markets for VIX derivatives (the third and fourth sections). In the ﬁfth section, we examine pricing models for VIX derivatives. The sixth section analyzes ETP trading strategies and concludes. The Development and Evolution of the VIX When VIX was ﬁrst introduced in 1993, the underlying index was the S&P100 Index (OEX) and the computation for implied volatility relied on Whaley’s model, which assumes constant volatility over the option’s life. The OEX was the most liquid stock index at the time and Black–Scholes implied volatilities were easy to compute quickly and eﬃciently. However, if volatility is stochastic, then the implied volatility from a model that assumes constant volatility will be biased. In 2003, acknowledging the overshadowing of the OEX by the SPX (S&P500), as well as the importance of stochastic volatility and volatility risk, the CBOE changed the index underlying the VIX to the S&P500 Index (SPX) and developed a new computation methodology known as model free implied volatility (MFIV), ﬁrst described in Britten–Jones and Neuberger (2000). Later, Jiang and Tian (2005a, 2005b) developed consistent estimation techniques for MFIV. While the original VIX was based only on nearest to page 439 July 3, 2015 8:28 The World Scientific Handbook of Futures Markets Downloaded from www.worldscientific.com by LA TROBE UNIVERSITY on 05/21/16. For personal use only. 440 World Scientific Handbook of Futures Markets. . . 9.75in x 6.5in b1892ch14 T. Nohel and S. K. Todd the money contracts, the modelfree volatility calculation is based on a full spectrum of option strikes. MFIV eschews the Black–Scholes (1973) model assumptions and instead uses a full set of option prices to estimate the implied volatility. The formula for the MFIV takes the form of an integral over a range of strike prices that represents an expectation of squared returns. This expectation is evaluated using riskneutral probabilities, rather than objective probabilities. If volatility is stochastic and there is a risk premium associated with volatility risk, then the riskneutral and objective expectations of future squared returns diﬀer signiﬁcantly. When investors require a risk premium to hold volatility, then volatility comprises two “prices”: a forecast of future realized volatility and a premium that reﬂects investors’ uncertainty about this forecast. The distinction between expectations under riskneutral probabilities and expectations under objective probabilities is inconsequential in a Black– Scholes (1973) model of constant volatility, or a Hull and White (1987) model of stochastic volatility, where the volatility risk premium is zero. However, there is considerable evidence that market participants do indeed price in a volatility risk premium [see Bakshi and Kapadia (2003) and Chernov (2002) among others]. The implied volatilities that VIX reports still end up being biased predictors of future realized volatility. Consider the following regression equation: RVolt = b0 + b1 IVolt−1 + ut . (14.1) Here, RVol and IVol are realized and implied volatilities, respectively, and u is an error term. The R2 of this regression tells us the percentage of the variation in realized volatility that is explained by implied volatility. If IVol is an unbiased forecast of RVol, then the coeﬃcient, b1 , should be statistically equal to 1. We know from prior research that most estimates of b1 are in the neighborhood of 0.7–0.8, statistically signiﬁcantly less than 1. Moreover, the R2 s indicate that IVol explains only half of the variation in RVol [see Christensen and Prabhala (1998)]. Part of the problem is related to the measurement of realized volatility. Andersen et al. (2003) and Anderson et al. (2005) show the superiority of using highfrequency data to compute realized volatility. Speciﬁcally, by eschewing daily prices in lieu of 5minute pricing, a much better estimate of realized volatility is obtained. However, even with better measurements of realized volatility, estimates of b1 are still statistically below 1. page 440 July 3, 2015 8:28 World Scientific Handbook of Futures Markets. . . 9.75in x 6.5in b1892ch14 The World Scientific Handbook of Futures Markets Downloaded from www.worldscientific.com by LA TROBE UNIVERSITY on 05/21/16. For personal use only. Volatility as an Asset Class 441 If implied volatilities are biased high, then it makes sense for informed traders to take advantage of this “mispricing” by writing put and call options on the S&P500 and maintaining deltaneutrality. In fact, there is evidence that market makers are net short index options [see Garleanu et al. (2009)]. Alternatively, an investor could write call (put) options and buy (sell) the underlying index. Since its introduction in 1993, the VIX has gained steadily in popularity. Its level is routinely quoted alongside the level of the Dow, the S&P500, and the NASDAQ indices, and the business press routinely references it as the “fear gauge”. Finally, the VIX was ubiquitous during the recent ﬁnancial crisis as it spiked dramatically in the fall of 2008 and remained elevated for quite some time. This served as the perfect backdrop for the introduction of ETPs referencing volatility that we discuss later in this article. Correlation of Volatility with Other Assets & Strategies Exposed to Volatility Many hedge funds engage in strategies that either directly involve trading volatility, or are very exposed to volatility risk. Most obviously, the strategy of looking for hefty option premiums, shorting said options, and delta hedging the position, is clearly a trade predicated on making a bet on volatility. According to Lowenstein (2000), a big part of the success of LongTerm Capital Management, as well as a big contributor to its demise, was to short options as a bet against volatility at a time when implied volatilities were thought to be “lofty”. Lowenstein claims that traders at Morgan Stanley dubbed LongTerm Capital the “Central Bank of Volatility”. Though it is widely understood that such strategies can generate substantial alphas over time (see Karakaya, 2013), the strategy has also been dubbed “collecting nickels in front of a steamroller”, given the exposure to volatility jumps. Similar characterizations are applied to other hedge funds strategies like ﬁxed income arbitrage (see Duarte et al., 2007). Figure 14.1 depicts returns on Merrill Lynch’s volatility arbitrage index in 2008: the sudden appearance of the steamroller is quite apparent in the ﬁgure, with the index losing 85% of its value in the fall of 2008. What ﬁnancial economists have come to realize over the recent years of studying such strategies is that volatilityrelated strategies and volatility risks are closely related to liquidity risk. After all, many of the arbitrage strategies that hedge funds employ amount to supplying liquidity where it is lacking and seeking to proﬁt from those services. Perhaps the most obvious page 441 July 3, 2015 8:28 The World Scientific Handbook of Futures Markets Downloaded from www.worldscientific.com by LA TROBE UNIVERSITY on 05/21/16. For personal use only. 442 World Scientific Handbook of Futures Markets. . . 9.75in x 6.5in b1892ch14 T. Nohel and S. K. Todd S&P 500 over the same time period: Figure 14.1. Merrill Lynch Equity Volatility Arbitrage Index which seeks to capture the spread between S&P500 market implied volatility and subsequent realized volatility. and simple example is the ontherun/oﬀtherun arbitrage made famous by Jon Meriwether at Solomon Brothers in the 1980s, and more infamously at LongTerm Capital Management. But strategies like merger arbitrage, convertible arbitrage, closedend fund arbitrage, and index arbitrage are equally predicated on the same principal of markets returning to alignment as liquidity ﬂows in. Any convergence trade relies on convergence of market conditions begetting price alignment. As such, these strategies are exposed to market downturns which tend to correspond to volatility spikes when prices can be misaligned for extended periods of time. For example, Mitchell and Pulvino page 442 July 3, 2015 8:28 World Scientific Handbook of Futures Markets. . . 9.75in x 6.5in b1892ch14 The World Scientific Handbook of Futures Markets Downloaded from www.worldscientific.com by LA TROBE UNIVERSITY on 05/21/16. For personal use only. Volatility as an Asset Class 443 (2001) show how hedge funds engaging in merger arbitrage have very low betas in “normal” markets, but are highly exposed to market downturns with substantial market betas in severe down markets. As volatility spikes, arbitrageurs see their valueatrisk rise dramatically, forcing pullbacks by most funds as their risk management policies often dictate. At the same time, these funds often have investors wanting to redeem shares, and prime brokers refusing to roll over short term repos.3 Such funds would be prime candidates to use securities referencing volatility to lay oﬀ some of their volatility risk. Since most convergence trades are based on wellunderstood relationships that appear to be out of whack, for the most part, hedge funds are pretty good at focusing convergence trades in markets that they understand quite well. However, in many venues, the gains from unlevered convergence trades do not amount to a great deal after transactions costs are factored in, leading to a temptation to use leverage extensively. In this case, the key to convergence trades is ensuring that one has the capital necessary to see the convergence through to fruition. LTCM is a case in point: the large bets in convergence trades that LTCM placed eventually faired pretty well, but along the way, the principals were essentially wiped out. The Structure and Trading of Derivatives that Reference the VIX The CBOE introduced VIX futures trading in March 2004 and VIX option contracts in February 2006. Currently volatility futures trade for up to nine nearterm serial months and ﬁve months on the February quarterly cycle; up to six contract months of VIX options may be listed, provided the time to expiration does not exceed one year. The ﬁnal settlement date for VIX futures is the Wednesday that is 30 days prior to the third Friday in the following month (i.e., the expiration date for the coming month’s S&P500 options, the prices of which are the basis for the calculation of the VIX itself), unless that Friday happens to be a holiday, in which case the VIX futures expire on a date with is precisely 30 calendar days prior to the subsequent S&P500 options expiration. VIX futures contracts 3 The interplay between capital ﬂight and asset market illiquidity can be selfreinforcing, leading to liquidity spirals (see Brunnermeier and Pedersen, 2009). For evidence of this phenomenon, see Mitchel et al. (2007, 2012). page 443 July 3, 2015 8:28 The World Scientific Handbook of Futures Markets Downloaded from www.worldscientific.com by LA TROBE UNIVERSITY on 05/21/16. For personal use only. 444 World Scientific Handbook of Futures Markets. . . 9.75in x 6.5in b1892ch14 T. Nohel and S. K. Todd call for cash settlement based on the futures price in the contract relative to the actual VIX on the settlement day times 1000. The VIX itself is calculated and disseminated in realtime by the CBOE. Theoretically, it is a weighted blend of prices for a range of options on the SPX. All traded strikes are included in the calculation to compute a modelfree implied volatility (MFIV) at each S&P500 option maturity. A weighted average of the nearest and nexttonearest maturity MFIV is computed in such a way that the weighted average maturity is exactly 30 days. Moreover, to avoid microstructure eﬀects, when the nearest term maturity falls to 8 days or less, this contract is dropped and a weighted average of the second and third nearesttomaturity MFIVs are used instead, while maintaining the weighted average maturity at 30 days (i.e., a positive weight on the 2nd nearest to maturity MFIV and a negative weight on the third nearest to maturity MFIV). Note: Since the VIX futures expire precisely 30 days prior to the expiration of the coming month’s S&P500 options, on the settlement date the VIX itself will be calculated based on S&P500 options maturing on a single date (rather than a weighted average of maturities). The calendar for VIX options is identical to that for VIX futures, with expiration occurring on the Wednesday immediately preceding the Friday that is four weeks prior to the third Friday in the following month. Again, like the VIX futures, the contracts are cash settled, but the payout is based on the diﬀerence between the strike price and the VIX level, times 100 (rather than 1000). Strikes may be available in one volatility point increments. It is important to note that for longerdated VIX options, the options whose prices will determine the VIX on the settlement date of the VIX options may not yet exist. An example may be helpful for illustrative purposes. Suppose it is currently December 2013 and you are interested in purchasing VIX options that expire in July of 2014. At expiration of the VIX options in July of 2014, the VIX itself will be determined based on the prices of S&P500 options that expire in August of 2014. At expiration in July of 2014, all traded S&P500 options that expire in August of 2014 will be used to calculate a MFIV that corresponds to the VIX for the purposes of computing the payout on any VIX options contracts that expire in July of 2014. In this sense, when you enter into your VIX options contract in December 2013, the underlying asset for this VIX options contract is the VIX based on S&P500 options expiring in August of 2014. It is conceivable that these options do not yet exist in December of 2013. Since its inception in early 2004, trading in the VIX futures has rapidly gained traction, seemingly driven by two catalysts: the introduction of VIX page 444 July 3, 2015 8:28 World Scientific Handbook of Futures Markets. . . 9.75in x 6.5in b1892ch14 The World Scientific Handbook of Futures Markets Downloaded from www.worldscientific.com by LA TROBE UNIVERSITY on 05/21/16. For personal use only. Volatility as an Asset Class 445 options in early 2006, and the introduction of VIXreferencing ETPs in 2009. Focusing on the November contract each year, in the 30 days leading up to expiration of the November 2004 VIX futures contract, trading volume totaled 10,618 contracts, with a peak volume of 1,066 contracts traded on November 1, 2004, and open interest peaking on November 4 at 7,400 contracts (expiration of the contract was November 16, 2004). Total volume in the analogous contract in 2005 was 12K contracts in the 30 calendar days prior to expiration, and then ballooned to 53K in 2006 following the introduction of VIX options. Comparable ﬁgures for the ensuing years were 118K, 53K, 125K, 376K, 516K, 1,533K and 1,841K contracts traded on the analogous contract in the 30 calendar days prior to November expiration in the years 2007–2013, respectively. Open interest follows a similar pattern. The volume of trading in this contract on the most active day in 2013 was more than 130X the volume of trading in the analogous contract in 2004 on its peak volume day (137,121 contracts versus 1,066 contracts). The inﬂuence of the introduction of VIX options and VIXreferencing ETPs on the popularity of the VIX futures is also noted by Whaley (2013). VIX options have seen similarly dramatic growth since their inception in February of 2006. Using trading in VIX options in the 30 calendar days leading up to the November expiration date (for ease of comparison with futures), in 2006 there were 0.65M contracts traded. In the ensuing years volumes grew dramatically to 3.7M, 2.3M, 4.7M, 6.8M, 8.6M, 10.2M and 9.7M in 2007–2013, respectively. In comparing with futures volumes reported above, it is important to keep in mind that the multiplier for options is 100, while for futures it is 1000. Moreover, the reported options volume is for all strikes and all maturities, while the futures volume reported above is simply for one contract. In examining the trading of options that reference the VIX, it is also interesting to consider the relative trading of puts versus calls. Figure 14.2 depicts put volume relative to call volume in three diﬀerent types of options: SPX options, equity options, and VIX options, over the period December 2010 through May 19, 2011. In looking at Figure 14.2, what is immediately apparent is that interest in calls far exceeds interest in puts, with the putcall ratio well below one. In this regard, the patterns are similar, though more volatile, than the trading of individual equity options, and the exact opposite of SPX options, where demand for puts far exceeds the demand for calls in most periods. The opposite patterns for SPX and VIX options make sense since volatility tends to spike (beneﬁtting a call position in VIX options) when page 445 July 3, 2015 8:28 The World Scientific Handbook of Futures Markets Downloaded from www.worldscientific.com by LA TROBE UNIVERSITY on 05/21/16. For personal use only. 446 World Scientific Handbook of Futures Markets. . . 9.75in x 6.5in b1892ch14 T. Nohel and S. K. Todd Figure 14.2. Putcall ratios on options on SPX, VIX, and equity options. equity values plunge (beneﬁtting a put position in index options). This is additional evidence in support of the work of Garleanu et al. (2009), who ﬁnd that the demand for index puts aﬀords option market makers the opportunity to earn excess returns by a willingness to short index puts, thereby supplying much needed liquidity to the option markets, and hedging out the risk. ETPs that Reference VIX VXX, the ﬁrst volatility exchange traded product (ETP) was launched by Barclays in January 2009. VXX oﬀers exposure to a daily rolling long position in the ﬁrst and second month VIX futures contract. In the last 4 years, more than 30 other volatility ETPs have been launched. Figure 14.3 provides a complete list of volatility ETPs. The products currently available span a range of maturities and directional strategies, with and without leverage. Many of these volatility products are not actively traded. Among the most actively traded are VXX, TVIX, XIV (all ETNs) and UVXY (an ETF). ETPs include exchange traded funds (ETFs) and exchange traded notes (ETNs). Both ETFs and ETNs can be bought, sold or shorted intraday on a stock exchange. ETFs are structured so that a shareholder owns a basket of securities. Should the ETF sponsor go bankrupt or shutdown, the shareholder will usually receive cash for the market value of the basket of securities. In this sense, there is no default risk with an ETF, however, there page 446 July 3, 2015 8:28 World Scientific Handbook of Futures Markets. . . 9.75in x 6.5in b1892ch14 The World Scientific Handbook of Futures Markets Downloaded from www.worldscientific.com by LA TROBE UNIVERSITY on 05/21/16. For personal use only. Volatility as an Asset Class Figure 14.3. 447 VIX ETPs. is no guarantee that the basket of securities held by the fund will exactly track the index to which it is pegged. In contrast, exchange traded notes are senior, unsecured, unsubordinated debt securities. By construction, ETN net asset values (NAVs) track their underlying index exactly (net of fees), though whether the price tracks the NAV is potentially another matter. However, ETNs have a maturity date and are backed only by the credit of the issuer, and as such are subject to default risk. These are the major design diﬀerences between ETFs and ETNs. ETFs do not sell or redeem their individual shares at NAV. Instead, large institutions purchase and redeem ETF shares directly from the sponsor, but only in large blocks, called creation units. The ability to purchase and redeem creation units gives ETFs an arbitrage mechanism that should minimize the deviation between market prices and NAVs. If an ETF trades at a premium to its NAV, then arbitrageurs should step in, purchase additional creation units from the ETF sponsor and sell the component ETF shares in the open market. The additional supply of ETF shares puts downward pressure on the market price, eventually eliminating the premium over NAV. A similar page 447 July 3, 2015 8:28 The World Scientific Handbook of Futures Markets Downloaded from www.worldscientific.com by LA TROBE UNIVERSITY on 05/21/16. For personal use only. 448 World Scientific Handbook of Futures Markets. . . 9.75in x 6.5in b1892ch14 T. Nohel and S. K. Todd process applies when there is weak demand for an ETF and its shares trade at a discount to NAV. ETNs give investors a broadbased index with little to no tracking error, unlike some ETFs which may deviate from their benchmarks due to constraints placed on holdings. ETN issuers often guarantee investors a return that is an exact replica of the underlying index, minus expense fees. Although volatility ETFs and ETNs are able to keep their benchmark tracking errors low, there is no mechanism to force volatility futures to track VIX. VIX itself is a complex function of the prices (implied volatilities) of a large set of options on the S&P500. This set includes puts and calls of diﬀerent strike and maturity combinations. If an arbitrageur sought to take advantage of a “mispricing” of volatility futures, relative to VIX, then he would have to combine long or short positions in volatility futures with short or long positions in S&P500 options. The transaction costs incurred from the purchase and sale of options might be so high that the arbitrageur would not pursue the activity unless the mispricing was quite large. So, here we have a very binding limit to arbitrage. The relation between implied and realized volatilities is similar to the relation between forward rates and future realized spot rates. Forward rates are biased high — they tend to exceed future realized spot rates. An investor who anticipates a future investment can lock in the forward rate today by shorting a shortterm Treasury and buying a longerterm Treasury. Like the term structure of volatility, the Treasury yield curve tends to slope upward. Compared to shortterm investors, longterm Treasury investors demand a risk premium as compensation for additional interestrate risk or for the event risks associated with monetary policy changes. As the economy overheats, the Treasury yield curve often inverts, signaling a recession is on the horizon. Essentially, ﬁxedincome investors are forecasting that the central bank’s medicine of higher shortterm rates will cure the disease of an overheating economy. Somewhat analogously, most of the time the volatility futures curve slopes upward, a circumstance known as “contango”. Compared to shortterm investors, longterm volatility investors demand a risk premium as compensation for additional equity market uncertainty or for the event risks associated with monetary policy changes. If the equity market crashes, the volatility futures curve likely inverts, signaling expectations of future stability. Essentially, volatility investors are forecasting that the central bank’s medicine of lower rates, asset purchases, restrictions on naked short page 448 July 3, 2015 8:28 World Scientific Handbook of Futures Markets. . . 9.75in x 6.5in b1892ch14 The World Scientific Handbook of Futures Markets Downloaded from www.worldscientific.com by LA TROBE UNIVERSITY on 05/21/16. For personal use only. Volatility as an Asset Class 449 sales or lower margin requirements will cure the disease of a downturn in equity values. Persistent contango in the volatility futures market presents similar opportunities for informed traders as a typically upwardsloping treasury yield curve. Bull calendar spreads which combine a short position in a fardated volatility futures contract with a long position in a neardated contract may be proﬁtable, given the high roll yield. Perhaps it is possible to engineer a similar trade by taking short positions in certain volatility ETPs? Pricing Models for Volatility Derivatives The seminal papers of Black and Scholes (1973) and Merton (1973) were premised on ideas like replication and selfﬁnancing trading strategies. These are fundamental ideas that underlie all modern derivative pricing models, and for which Scholes and Merton were awarded the Nobel Prize in Economics in 1997. These early models, as well as subsequent, more sophisticated models, such as Heston (1993), Britten–Jones and Neuberger (2000), and others, begin with some exogenous price process for the underlying asset and price derivatives relative to that price process. The underlying price processes are treated in a manner of everincreasing sophistication, to include stochastic volatility, jumps, etc., but the models rarely if ever endogenize the price process for the underlying asset. The evolution of pricing models for volatility derivatives have proceeded along a similar development path, except that the most basic models had to begin within a paradigm of stochastic volatility, because it makes no sense to talk about volatility derivatives when volatility is deterministic. Early models, such as Grünbichler and Longstaﬀ (1996) and Brenner et al. (2006), and Zhang and Zhu (2006) use a Hestontype model as a depiction of the underlying stock and volatility process, and they develop models to price derivatives on the VIX. More recently, Lin and Chang (2009, 2010) develop a model for pricing volatility derivatives that recognizes the importance of volatility jumps and the possibility of interaction between volatility jumps and asset price jumps. However, Lin and Chang (2009, 2010) fail to recognize that merely acknowledging the importance of jumps and the correlations in the stochastic processes driving the evolution of both stock price and volatility is insuﬃcient. Instead, to ensure an internally consistent framework, it is also crucial that any pricing model/framework that is developed not only needs to correctly price volatility derivatives, but it also needs to correctly page 449 July 3, 2015 8:28 The World Scientific Handbook of Futures Markets Downloaded from www.worldscientific.com by LA TROBE UNIVERSITY on 05/21/16. For personal use only. 450 World Scientific Handbook of Futures Markets. . . 9.75in x 6.5in b1892ch14 T. Nohel and S. K. Todd price options on the underlying whose implied volatility represents the asset underlying the volatility derivatives themselves. Cheng et al. (2012) prove that the formula in Lin and Chang (2009, 2010) is only an approximation, and in fact the approximation performs poorly in a simpliﬁed test based on the Heston (1993) model (i.e., no jumps). Lian and Zhu (2011) also question the validity of the Lin and Chang (2009, 2010) formula. Sepp (2008) derives an exact formula for pricing volatility derivatives in a setting that allows for jumps in volatility and correlation of the volatility and asset price processes, but asset price jumps are not allowed. Only recently has a model been developed that can accommodate interactions between the SPX and its volatility, jumps in both level and volatility of the SPX, and that prices SPX options and VIX derivatives consistently: the model of Cont and Kokholm (2013). They start with an assumption of aﬃne Lévy processes for a discrete tenor of forward variance swap rates, as in Bergomi (2005, 2008). This speciﬁcation allows for Fourierbased pricing of European style volatility derivatives, as in Carr and Madan (1999). Having assumed the dynamics of the forward variance swap rates, Cont and Kokholm (2013) then specify jump diﬀusion dynamics for the underlying asset that are compatible with the variance swap rate dynamics. The jumps in volatility and underlying are assumed to stem from the same process with opposite sign. This allows for additional tractability and also lines up well with observed behavior. The combination of jump and diﬀusion components allows the authors to match values and volatilities of options on the underlying across the entire term structure, as well as volatility derivative pricing. The model of Cont and Kokholm (2013) looks promising as it is able to reproduce several salient empirical features of variance swap dynamics, while at the same time it consistently prices various plain vanilla options on volatility as well as on the underlying index itself. However, this model has yet to garner wide acceptance in the profession, and the lack of a viable and wellaccepted model to price VIX derivatives is likely to hold back more widespread use of existing VIX derivatives contracts for the foreseeable future. Volatility Trading Strategies using ETPs In this section, we examine seven ETPs which provide exposure to VIX shortterm volatility futures. Summary data for the ETPs appears in Table 14.1. Three of the ETPs (VXX, XIV and TVIX) are ETNs. Compared to ETFs, page 450 July 3, 2015 vxx xiv tvix uvxy vixy svxy viix Type Multiplier Fee TR/ER ETN 1 0.89% TR ETN −1 1.35% ER ETN 2 1.65% ER ETF 2 0.95% ER ETF 1 0.85% ER ETF −1 0.95% ER ETF 1 0.89% ER Assets Trading Volume (millions of shares) Inception 955 17.8 415 11.8 138 4.2 231 9.7 305 0.9 152 0.6 11 0.2 January 29, 2009 −3.4 November 29, 2009 3.38 November 29, 2010 −6.4 October 4, 2011 −6.93 January 3, 2011 −3.43 October 4, 211 3.35 November 29, 2010 −3.44 Beta World Scientific Handbook of Futures Markets. . . ETP ETP summary data. 9.75in x 6.5in Notes: TR denotes total return; ER denotes excess return. Source: http://etfdb.com/etfdbcategory/volatility. 451 b1892ch14 Volatility as an Asset Class The World Scientific Handbook of Futures Markets Downloaded from www.worldscientific.com by LA TROBE UNIVERSITY on 05/21/16. For personal use only. 8:28 Table 14.1. page 451 July 3, 2015 8:28 The World Scientific Handbook of Futures Markets Downloaded from www.worldscientific.com by LA TROBE UNIVERSITY on 05/21/16. For personal use only. 452 World Scientific Handbook of Futures Markets. . . 9.75in x 6.5in b1892ch14 T. Nohel and S. K. Todd these funds do not provide owners a direct claim on the assets of the underlying portfolio. Moreover, these ETNs, which expose owners to the credit risk of the sponsor, do not generally disclose how the fund mimics the underlying benchmark and what risk management strategies are used to reduce tracking error. VXX and XIV are the most actively traded ETPs, with average daily volumes of 17.8 and 11.8 million shares respectively. Two of the ETPs (XIV and SVXY) promise investors −1 * the daily return on the S&P500 VIX shortterm excess futures index (ticker SPVXSP).4 These inverse ETFs allow investors to short volatility directly instead of taking a short position in an ETF with a positive multiplier. Two of the ETPs (TVIX and UVXY) are levered funds promising twice the returns on the SPVXSP index. Annual fund expenses on ETPs that reference volatility vary from 85 basis points (for VIXY) to 165 basis points (for TVIX), with the levered funds generally charging the highest fees. VXX, an ETN, was the ﬁrst fund to launch on January 29, 2009. Nearly two years later, UVXY and SVXY, both ETFs, were launched. As of December 17, 2013, the total number of VIX ETPs stands at 30. Performance data for the ETPs appears in Table 14.2. Only the inverse ETPs have generated positive returns since their inception dates, with SVXY besting XIV by more than 15 basis points per day, on average. Daily return statistics have been quite variable with minimum returns of nearly −30% (on TVIX) and maximum returns of more than 40% (on UVXY). Since their inception dates, 5 of the ETPs (VXX, UVXY, TVIX, VIXY and VIIX) have lost more than 90% of their original values. In contrast, VIX has declined by nearly 65% over the period January 29, 2009 to December 17, 2013. In Table 14.3, we examine the correlation structure of the ETPs using daily price returns over the period that begins with a fund’s inception date and ends on December 17, 2013. All of the ETP correlation measures exceed 94% in absolute value terms, suggesting near perfect alignment. Alignment with VIX, however, is less perfect, with pairwise correlation values nearly 10% lower (in absolute value terms). SPVXSTR serves as the benchmark for VXX. Its performance nearly mirrors the performance of SPVXSP, which 4 SPVXSP serves as the benchmark index for all of the ETPs we examine, except for VXX, which uses the benchmark SPVXSTR, the S&P500 VIX shortterm total return futures index. These two indices are quite similar, especially when shortterm interest rates are low. The total return index adds the return on the riskfree rate (a 91day Treasury bill) to the return on SPVXSP. page 452 July 3, 2015 xiv World Scientific Handbook of Futures Markets. . . vxx ETP performance data. tvix uvxy vixy svxy viix vix Average Daily Return standard Deviation Minimum Maximum −0.33% 0.24% −0.97% −0.61% −0.26% 0.40% −0.29% 0.16% 3.84% 4.04% 7.21% 8.08% 4.09% 3.98% 4.05% 7.09% −14.26% −19.98% −29.80% −26.66% −13.13% −19.16% −13.37% −29.57% 20.70% 13.18% 37.36% 40.79% 20.68% 13.15% 20.78% 50.00% Return: 1 year Return: 3 year Return: since origination −59.50% −92.26% −99.29% 61.69% −89.21% −88.99% −59.39% 163.87% −99.86% 218.59% −99.91% −99.88% −91.80% 60.97% −59.44% −1.90% −92.47% −0.50% 439.18% −93.69% −64.78% 9.75in x 6.5in 453 b1892ch14 Volatility as an Asset Class The World Scientific Handbook of Futures Markets Downloaded from www.worldscientific.com by LA TROBE UNIVERSITY on 05/21/16. For personal use only. 8:28 Table 14.2. page 453 July 3, 2015 uvxy vixy svxy viix vix −99.60% 95.24% 99.84% 99.92% −99.47% 97.99% 88.59% 100.00% −94.75% −99.36% −99.69% 99.66% −97.67% −88.45% −99.36% 95.26% 100.00% 99.84% −99.35% 97.90% 89.03% −94.75% 100.00% 95.26% 95.26% −94.64% 95.14% 84.49% −99.69% 95.26% 99.84% 100.00% −99.50% 98.43% 89.24% 99.66% −94.64% −99.35% −99.50% 100.00% −99.46% −88.35% −97.67% 95.14% 97.90% 98.43% −99.46% 100.00% 87.04% −88.45% 84.49% 89.03% 89.24% −88.35% 87.04% 100.00% −95.82% 91.25% 96.47% 96.43% −95.02% 94.48% 89.70% spvxstr 96.78% −95.82% 96.47% 91.25% 96.43% −95.02% 94.48% 89.70% 100.00% Note: SPVXSTR is the S&P 500 VIX shortterm total return futures index. This is the benchmark index for VXX. 9.75in x 6.5in b1892ch14 The World Scientific Handbook of Futures Markets Downloaded from www.worldscientific.com by LA TROBE UNIVERSITY on 05/21/16. For personal use only. 100.00% −99.60% 99.84% 95.24% 99.92% −99.47% 97.99% 88.59% 96.78% tvix World Scientific Handbook of Futures Markets. . . vxx xiv uvxy tvix vixy svxy viix vix spvxstr xiv T. Nohel and S. K. Todd vxx ETP correlation data. 8:28 454 Table 14.3. page 454 July 3, 2015 8:28 World Scientific Handbook of Futures Markets. . . 9.75in x 6.5in b1892ch14 Volatility as an Asset Class 455 Table 14.4. VXX versus its benchmark index, SPVXSTR. The World Scientific Handbook of Futures Markets Downloaded from www.worldscientific.com by LA TROBE UNIVERSITY on 05/21/16. For personal use only. ReturnVXX −ReturnSPVXSTR Mean Minimum Median Maximum Mean Absolute Deviation −0.02% −10.61% 0.01% 8.63% 0.71% serves as the benchmark for all the ETPs except VXX. Here, we see that VXX is nearly perfectly positively correlated with SPVXSTR. In Table 14.4, we examine the performance of VXX compared to its benchmark index. On average, VXX generates a daily return that is 2 basis points lower than the return earned on the index. Since VXX charges investors an annual fee of 89 basis points, we would expect a performance drag of 0.35 (89/252) basis points per day. The remaining performance diﬀerential results from tracking error. If the ETP creation/destruction arbitrage mechanism is eﬃcient, we would expect small daily tracking errors. In fact, the average daily mean absolute deviation (MAD) in returns is 71 basis points and there are quite a few days (295 or approximately 24% of all trading days) when the tracking error exceeds 100 basis points in absolute value terms. Since VXX is an ETN, closing prices should equal fund indicative values and tracking errors should be zero. Over the full sample period, this appears to be nearly true. However, it is not strictly true on any given day. In general, tracking error stems from imperfect hedging. The ETNs use positions in futures, options and swaps to manage volatility risk. Perfectly mimicking benchmark returns is virtually impossible. For the ETFs, perfect hedging requires the portfolio manager to rebalance VIX futures positions at exactly the same settlement prices that S&P uses to compute their index values. Since settlement prices are determined after the market is closed, and ETF portfolio managers can only trade when the market is open, the ETFs cannot achieve zero tracking error. Moreover, all the ETPs potentially suﬀer from disturbances in the arbitrage mechanism, such as that experienced by TVIX when Credit Suisse (the sponsor) stopped issuing new shares in the ETN on February 21, 2012 “. . . due to internal limits on the size of ETNs.” When arbitrage activities are constrained, the ETN share price can deviate from its NAV. By March 21, 2012, TVIX was priced at an 89% premium to its NAV. The next day, Credit Suisse announced it would allow a limited page 455 July 3, 2015 8:28 456 World Scientific Handbook of Futures Markets. . . b1892ch14 T. Nohel and S. K. Todd Table 14.5. Futures price data. 2009 The World Scientific Handbook of Futures Markets Downloaded from www.worldscientific.com by LA TROBE UNIVERSITY on 05/21/16. For personal use only. 9.75in x 6.5in 2011 2012 2013 Total days 1230 Mean Price Diﬀerential 7.19% Std. Dev. 6.60% Minimum −21.34% Median 7.97% Maximum 33.75% 234 252 5.18% 3.00% 6.29% 7.82% −8.23% −21.34% 5.62% 4.62% 21.09% 22.14% 250 10.14% 5.21% −1.86% 9.64% 33.75% 242 7.36% 3.82% −9.65% 7.51% 17.13% Price Diﬀerential >=0 Total days Mean Std. Dev. Minimum Median Maximum 181 7.66% 4.72% 0.00% 7.42% 21.09% 174 7.37% 4.03% 0.00% 7.52% 22.14% 247 10.27% 5.09% 0.26% 9.73% 33.75% 231 7.81% 3.23% 0.00% 7.58% 17.13% 53 78 −3.31% −6.75% 2.21% 4.85% −8.23% −21.34% −3.14% −5.92% −0.13% −0.48% 3 −1.28% 0.95% −1.86% −1.79% −0.18% 11 −2.12% 2.80% −9.65% −0.94% −0.30% Price Diﬀerential <0 Total days Mean Std. Dev. Minimum Median Maximum 1068 9.00% 4.74% 0.00% 8.93% 33.75% 162 −4.75% 4.23% −21.34% −4.24% −0.13% Note: Mean Price Diﬀerential is the 2month futures price minus the 1month futures price. number of new creation units. Shortly thereafter, the TVIX price aligned with its NAV.5 Term structure data for VIX volatility futures appears in Table 14.5. We examine the price diﬀerential between the 2month (next month) and the 1month (current month) contracts, expressed as a ratio of the current month futures price. Here we see that the term structure of VIX futures prices is upward sloping during most of the sample period, and the mean premium is 7.19%. Futures prices are in contango approximately 87% of all trading days during the sample period (January 29, 2010 to December 17, 2013).6 ETPs which need to meet a targeted volatility must rebalance their holdings in two adjacent futures contracts on a daily basis. An ETP which 5 See “Chaos over a plunging note,” The Wall Street Journal (March 29, 2012) by Tom Lauricella, Jean Eaglesham and Chris Dietrich. 6 We use the term “contango” loosely here. Strictly speaking, a market is in contango only when futures prices exceed expectations of future spot prices. page 456 July 3, 2015 8:28 World Scientific Handbook of Futures Markets. . . 9.75in x 6.5in b1892ch14 The World Scientific Handbook of Futures Markets Downloaded from www.worldscientific.com by LA TROBE UNIVERSITY on 05/21/16. For personal use only. Volatility as an Asset Class 457 takes a long position in volatility will need to sell near month futures contracts and purchase next month futures contracts each trading day, so that the priceweighted average maturity maintains a constant maturity.7 If the futures market is in contango, then the ETP which takes a long position in volatility will end up underperforming a long position in the cash index. Suppose the term structure is upward sloping with 2month futures trading at 105% of the price of 1month futures. Suppose, further, that the term structure is static over the month. Then, daily rebalancing will result in a 5% loss over the month, as 1month futures contracts are sold and 2month futures contracts are purchased to maintain a constant 30day maturity. In this case, a −5% rollyield prevails. Now assume these conditions persist for a fullyear. Then we would incur losses of 5% of invested capital for 12 consecutive months, resulting in an annual loss of approximately 60% (ignoring compounding eﬀects). This example is not so farfetched. In 2013 the term structure of VIX futures was upward sloping 231 out of 242 days, and the average price diﬀerential was 7.36%. Not surprisingly, over the last year, VXX generated a return of −59.50%. A stochastic price process that mean reverts will return over time to a longrun average value. Mean reversion has been documented in interest rates, realized stock return volatilities (Bali and Demirtas, 2008) and implied volatilities (Cont and Da Fonseca, 2002). In contrast, exchange rates and stock prices do not exhibit the tendency to mean revert. Over the period 1990–2008, the mean (median) VIX level was 19.70 (18.26), with a standard deviation of 7.88. VIX reached its minimum value of 9.31 on December 22, 1993; the peak value of 80.86 was registered on November 20, 2008. There is a growing body of evidence that certain technical trading strategies can be proﬁtable (see, for example, Sullivan et al. (1999)). Traders who rely on technical trading strategies identify support and resistance price levels. A contrarian investor might take a long position in an asset when its price falls below a support level and a short position in an asset when its price rises above a resistance level. A trading strategy motivated by mean reversion in the VIX generalizes to [a,b] where a = µ+n1 σ, b = µ−n2 σ, where µ represents the empirically observed mean VIX level over a prior period, σ represents the empirically observed standard deviation of VIX levels over a 7 See S&P Dow Jones Indices: S&P500 VIX Futures Indices Methodology, July 2012. page 457 July 3, 2015 8:28 The World Scientific Handbook of Futures Markets Downloaded from www.worldscientific.com by LA TROBE UNIVERSITY on 05/21/16. For personal use only. 458 World Scientific Handbook of Futures Markets. . . 9.75in x 6.5in b1892ch14 T. Nohel and S. K. Todd prior period, and n1 and n2 are positive numbers. Since VIX prices are not symmetric around the mean (the lower price bound is zero and spikes are quite common), it might be reasonable to set n1 < n2 .8 We ﬁrst examine a naive strategy where n1 = n2 = 1. Implementing this strategy, we take a short position in volatility whenever VIX closes above 27.58 (19.70 + 7.88) and a long position in volatility whenever VIX closes below 11.82 (19.70 − 7.88). Our trading strategy requires a rule for exiting positions. One such rule might have us exit a long (short) position when VIX rises above (falls below) its mean. We examine this strategy in Table 14.6, but we ﬁrst consider a simpler rule that has us exit our positions whenever VIX returns to the absorbing state described by (11.82, 27.58). The results we report in Table 14.7 assume all trades occur at closing prices, short positions are not restricted and transaction costs are zero. The assumption about unrestricted short positions is not necessary, provided inverse ETPs are available. In Panel A, we examine the period October 4, 2011 to December 16, 2013, when all the ETPs were trading. Using our simple technical trading strategy, we execute six roundtrip trades during this period: four short volatility positions and two long volatility positions. The average trade holding period is short, at 7.5 days and the trades generate average returns of 8–9% for the unlevered ETPs and 16–17% for the twicelevered funds. The returns on the unlevered funds are remarkably similar, as are the returns on the levered funds. Note that VIX posts a compound annual growth rate (CAGR) of more than 39%, nearly double the performance of the unlevered ETPs. These results illustrate that the ETPs underperform VIX. Among the unlevered funds, SVXY outperforms VIXY and VXX, which both outperform XIV. Among the levered funds, UVXY outperforms TVIX. In general, the ETFs outperform the ETNs and the funds with lower expenses enjoy better performance. In Panel B, we examine performance since fund inception. Four of the funds (XIV, TVIX, VIXY and VIIX) complete an additional short volatility trade, and VXX (the ﬁrst ETP) completes an additional 11 short volatility trades. Over the full sample period, UVXY enjoys the best performance (a CAGR of 40.17%) and XIV performs worst (a CAGR of −12.07%). VIX generates a 14.93% return per year over the full sample period. 8 Between 1990 and 2008, VIX levels exceeded µ + σ on 831 trading days (13.7% of the sample). In contrast, VIX levels fell below µ − σ on only 422 trading days (7.0% of the sample). page 458 July 3, 2015 Trades 74 74 74 74 74 74 74 World Scientific Handbook of Futures Markets. . . Avg. Holding Period Trading strategy performance data. 74 Returns Panel A: October 14, 2011–December 16, 2013 January 20, 2012 October 4, 2011 Neutral Short 46.23% 47.62% 76.73% 77.52% 46.63% 53.25% 46.20% 55.22% Panel B: January 29, 2009–December 16, 2013 March 16, 2011 October 11, 2010 May 6, 2010 December 22, 2009 January 30, 2009 Short Neutral Short Neutral Short Vol CAGR Average Return Avg. Holding Period Trades 42.20% 42.15% 68.10% vxx 10.51% 3.81% 14.0 56.42% xiv −12.07% −3.02% 12.6 tvix 3.70% 3.72% 12.6 uvxy 40.17% 16.87% 7.5 vixy −3.60% −0.08% 12.6 svxy 20.91% 8.99% 7.5 viix −4.37% −0.37% 12.6 vix 14.93% 13.14% 14.0 Returns 9.75in x 6.5in Note: Short volatility if VIX closes above 27.58; long volatility if VIX closes below 11.82. Exit a long volatility position if VIX rises above 19.70; exit a short volatility position if VIX falls below 19.70. 459 b1892ch14 Volatility as an Asset Class The World Scientific Handbook of Futures Markets Downloaded from www.worldscientific.com by LA TROBE UNIVERSITY on 05/21/16. For personal use only. 8:28 Table 14.6. page 459 July 3, 2015 tvix uvxy vixy svxy viix vix spvxstr Panel A: October 14, 2011–December 16, 2013 March 18, 2013 March 14, 2013 March 12, 2013 March 11, 2013 December 9, 2011 December 5, 2011 December 1, 2011 November 9, 2011 November 8, 2011 October 31, 2011 October 27, 2011 October 4, 2011 CAGR Average Return Avg. Holding Period Trades Neutral Long Neutral Long Neutral Short Neutral Short Neutral Short Neutral Short 20.74% 8.66% 7.5 19.45% 8.37% 7.5 39.79% 16.29% 7.5 40.25% 16.87% 7.5 20.74% 8.69% 7.5 20.95% 8.99% 7.5 20.37% 8.62% 7.5 38.87% 16.62% 7.5 Returns 5.11% 5.17% 7.93% 10.16% 5.25% 5.09% 5.60% 18.23% 1.54% 1.56% 2.82% 1.52% 1.77% 1.43% 6.14% 0.20% −0.51% 0.93% 0.85% 0.20% −0.77% 0.30% 5.24% 15.87% 14.73% 31.25% 31.22% 15.73% 24.20% −1.77% −4.42% −1.41% −1.44% −1.95% −4.65% −2.19% 8.28% 31.03% 33.70% 56.23% 57.58% 15.91% 31.23% 15.14% 37.39% 37.63% 57.58% −25.23% 37.39% −26.47% 19.58% 3.74% 2.99% 10.31% Panel B: January 29, 2009–December 16, 2013 October 27, 2011 August 8, 2011 March 17, 2011 Neutral Short Neutral −26.17% −41.37% −21.44% 3.06% 3.71% 5.98% 9.75in x 6.5in 30.87% 23.31% World Scientific Handbook of Futures Markets. . . b1892ch14 The World Scientific Handbook of Futures Markets Downloaded from www.worldscientific.com by LA TROBE UNIVERSITY on 05/21/16. For personal use only. xiv T. Nohel and S. K. Todd vxx Trading strategy performance data. 8:28 460 Table 14.7. page 460 July 3, 2015 5.11% World Scientific Handbook of Futures Markets. . . 0.60% 7.81% 4.83% 5.09% 3.82% 4.25% Short Neutral Short Neutral Short Neutral Short Vol 1.97% 1.23% 32.20% Note: Short volatility if VIX closes above 27.58; long volatility if VIX closes below 11.82. Exit position if VIX returns to the absorbing state of (11.82, 27.58) 9.75in x 6.5in 461 b1892ch14 The World Scientific Handbook of Futures Markets Downloaded from www.worldscientific.com by LA TROBE UNIVERSITY on 05/21/16. For personal use only. 8:28 Short Neutral Short Neutral Short Neutral Short Neutral Short Neutral Short Neutral Short Neutral Volatility as an Asset Class March 16, 2011 July 7, 2010 June 26, 2010 June 15, 2010 May 14, 2010 May 12, 2010 May 6, 2010 November 5, 2009 October 30, 2009 October 29, 2009 October 28, 2009 October 5, 2009 October 1, 2009 September 3, 2009 September 1, 2009 August 18, 2009 August 17, 2009 July 13, 2009 July 2, 2009 June 25, 2009 February 1, 2009 page 461 July 3, 2015 8:28 The World Scientific Handbook of Futures Markets Downloaded from www.worldscientific.com by LA TROBE UNIVERSITY on 05/21/16. For personal use only. 462 World Scientific Handbook of Futures Markets. . . 9.75in x 6.5in b1892ch14 T. Nohel and S. K. Todd The reduced performance of VXX, XIV, TVIX, VIXY and VIIX stems mostly from the poor performance of the short volatility position initiated on August 4, 2011. Between that date and November 27, 2011 (the date when the short position is closed), VIX generates a return of 19.58%, whereas VXX, XIV, TVIX, VIXY and VIIX generate returns of −26.17%, −41.37%, −21.44%, −25.23% and −26.47% respectively. During this period, the VIX futures curve moved from ﬂat to sharply downward sloping. In Table 14.6, we examine a similar trading strategy with revised exit rules. Here we exit a long volatility position whenever VIX rises above 19.70 and we exit a short volatility position whenever VIX falls below 19.70. In Panel A, we examine the period October 4, 2011 to December 16, 2013, when all the ETPs were trading. Note that this strategy results in longer holding periods and fewer trades. During this period, there is only one roundtrip trade: a short volatility position initiated on October 4, 2011 and terminated on January 20, 2012. The trade holding period is 74 days. For the unlevered funds, this trade generates average returns from 46.20% for VIX to 53.25% for SVXY. The levered funds earn returns of 76.73% (TVIX) and 77.52% (UVXY). Over the same period, VIX generates a return of 55.22%. In Panel B, we examine performance since fund inception, which ends up lowering the performance of all funds except VXX. Four of the funds (XIV, TVIX, VIXY and VIIX) complete an additional short volatility trade, and VXX completes an additional three short volatility trades. Over the full sample period, UVXY enjoys the best performance (a CAGR of 29.56%) and XIV performs worst (a CAGR of −8.03%). VIX generates a return of 34.32% per year over the full sample period. The reduced performance for most funds stems from the poor performance of the short volatility position initiated on August 4, 2011. Between that date and January 2, 2012 (the date when the short position is closed), VIX generates a return of 42.26%, whereas XIV, VIXY and VIIX generate returns of −35.26%, 2.81% and 1.58% respectively. While more intricate technical trading strategies may produce better results, this simple analysis illustrates several key points. First, the unlevered ETPs will likely underperform VIX due to persistent negative roll yields in the VIX futures market. Second, most of the time, similarly benchmarked ETPs will perform similarly. However, when the term structure of VIX futures changes dramatically, similarly benchmarked ETPs may perform quite diﬀerently, due to large diﬀerences in the way risks are managed. Third, the inverse ETPs beneﬁt from contango. 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