future of shorting vix stock trading strategy

"The CBOE Volatility Index (VIX) is a winder measure out of grocery expectations of near-term unpredictability conveyed by Sdanamp;P 500 stock market index alternative prices. Since its introduction in 1993, VIX has been considered aside many to be the ma's premier barometer of investor sentiment and market volatility."
– Web site of CBOE

Including volatility positions in an investiture portfolio is donein national for portfolio diversification and for hedging purposes. The latter is correct for portfolio managers that are tracking index number equity portfolios and World Health Organization are short volatility. When equity markets suit highly volatile then the portfolio trailing error and the rebalancing costs growth but using volatility futures helps to hedge against these frictional costs. At the else extreme, the unpredictability futures contracts offer a direct exposure to Lope de Vega with no delta involved.

Hence, speculative directive positions rump be taken via VIX and VSTOXX futures. An interesting trading strategy that will be explored later on is based on the correlation between the VSTOXX and VIX. A fund manager may be endless VSTOXX volatility and short VIX volatility. A similar idea is to trade connected the basis between VIX and VSTOXX, given the historical development 'tween the cardinal.

The VIX index was introduced by Whaley (1993) and the methodology was further altered by CBOE in 2003. This index measures the market's implied view of next volatility of the equity SdanAMP;P 500 index, given by the current Sdanamp;P 500 stock index option prices. When constructing the VIX, the put and call options are good and next-term, normally in the first and second Sdanamp;P 500 contract months. "Near-term" options must induce at to the lowest degree 1 calendar week to maturity. This condition is obligatory in order to minimise pricing anomalies that might appear close to going. When this condition is violated VIX "rolls" to the second and thirdly Sdanamp;P 500 contract months. The open sake and trading volume of VIX futures have got hyperbolic rapidly complete the years. As reported in Shu and Zhang (2012), shortly after launch the mean open worry and trading volume was 7,000 contracts and 460 contracts,respectively. During the sub-prime crisis complete the period August 2008-Nov 2008, the average day by day trading volume was 4,800 contracts per 24-hour interval, and the average VIX futures price was $19.20. This implies an mean daily market price of about $92 million dollars.

The EURO STOXX 50 Index is constructed from blue chip companies of sphere leaders in the Eurozone: Oesterreich, Belgique, Finland, France, Federal Republic of Germany, Greece, Ireland, Italy, Luxembourg, Nederland, Portuguese Republic and Spain. The EURO STOXX 50 Volatility Index (VSTOXX) index is comparatively new and provides the implied volatility given past the prices of the options with corresponding matureness, connected the EURO STOXX 50 Index. By choic the VSTOXX index is based happening the square root of implied variance and it calibrates the volatility skew from OTM puts and calls. The VSTOXX does not metre implied volatilities of at-the-money EURO STOXX 50 options, merely the implied variance across all options of a given time to expiry. This model has been jointly developed by Goldman Sachs and Deutsche Börse, such that using linear interpolation of the 2 nearest sub-indices, a rolling index of 30 years to expiration is calculated every five seconds exploitation real number-time EURO STOXX 50 selection bid/ask quotes. The VSTOXX is calculated on the basis of eight expiry months with a maximum clock time to expiry of cardinal years. If in that respect are no such close sub-indices, nearest to the time to expiry of 30 days, the VSTOXX is calculated using extrapolation, victimization the two nearest available indices which are as close to the prison term to expiry of 30 calendar years as possible. The pay-off of VSTOXX futures resembles many the fund-soured of a excitableness swap, existence stubborn past the difference between the realised 30-day implied unpredictability and the predicted 30-day implied volatility at trade initiation, multiplication the numeral of contracts and the monetary size of the index increased (€100).

An important securities industry change occurred on June 2009 when Eurex introduced the Mini-Futures contracts for VSTOXX, followed soon by the ending in July 2009 of the VSTOXX futures. This important shift has been motivated away the erratic mass of trading in VSTOXX futures. Hence, aft this change, investors could use a excitableness futures condense trading at €100 per index point instead than €1000 antecedently.

Thus, the Mini-Futures contracts are size-comparable with the options on VSTOXX. The minimum price change is 0.05 points which is equivalent to €5, and the contract months are the three nearest calendar months and the next quarterly calendar month of the February, May, August, and November cycle. The evolution of the futures and mini-futures contract volume are delineated in Figure.1.

Szado (2009) and Rhoads (2011) highlighted the potential drop benefits of adding excitability derivatives to equity index portfolios. Changing the equity portfolio combine away adding a 10% VIX futures to the Qaeda SdanAMP;P 500 portfolio would have reduced losses over the period August to December 2008 by 80% and also minimized the portfolio standard deviation aside tierce. While this improvement should be expected from the design of the volatility derivatives, the impact of changing the portfolio mix by including excitableness futures is unclear. Ex ante, an investor should expect an erosion of returns for portfolios including VIX futures contracts during normal fourth dimension in equity markets. The opposite is expected in turbulent times.

Hence, IT is ill-defined what an investor should expect for longer time periods. Furthermore, in the consequence of the sub-prime liquid state crisis, other crises such every bit the sovereign bond crisis appeared in the Common Market. It would be therefore of great interest to equity investors not only to have an updated analysis of the protective impact of VIX futures on US equity portfolios but also to know the impact of VSTOXX futures on EU equity portfolios represented by STOXX 50. Equity index number returns are generally negatively skewed, while volatility futures returns expose positive skewness.

Applied mathematics arbitrage strategies victimization GARCH forecasting
Knowing that the difference betwixt the VIX and VSTOXX is significant and negative the following 'naïve' trading scheme is first investigated. A off-road cattle farm is entered into, short 100 VIX futures and long a number of VSTOXX futures, adjusted daily, much that the size (i.e., place value) of the short and long positions is the same. For example, bestowed that the size of it of one VSTOXX mini-futures contract is €100 per point and the size of one VIX futures is $1000 per point, if the rate of exchange is $1.3 for €1:

($1000/€100) / ($1.3/€1) ≈ 7.69

one would go by long 7.69 VSTOXX futures contracts for apiece VIX contract, which gives a tot position of 100 short VIX futures contracts to 769 long VSTOXX contracts. While the number of VIX contracts stays fixed at 100, the number of VSTOXX contracts is orientated daily such that the sized of both legs of the transaction matches at $100,000 per point.

Fig.2 illustrates the evolution of the come of VSTOXX contracts from 1 June 2010 to 28 December 2012, while Libyan Fighting Group.3A plots the accumulative profits (given in US dollars) that could have been generated by this scheme. It is of note that, if put in place at the first of June 2010, the strategy would have been bankable for roughly half of horizons up to 2.5 years. To make the public presentation of this strategy forthwith comparable to that of the GARCH strategy presented below, in Fig.3C and Fig.3D the additive and daily Pdanamp;L are computed assuming the strategy commences initially of June 2012 (rather than June 2010). This bequeath match to the out-of-sample period employed for the rating of the GARCH strategy.

CLICK ON IMAGE TO ENLARGE

A potential application of the GARCH modelling results is for the forecasting of the VIX- VSTOXX (closest futures price) difference which in turn posterior be exploited to inform trading strategies. Libyan Fighting Group.4 plots the series of one-step-ahead forecasts obtained from a AR(4)-T – GARCH(1,1). The model parameters are re-estimated daily, using a roll sample distribution of 500 observations, with 146 observations used for out-of-sample forecasting. The results depicted in Fig.4 show that the VIX-VSTOXX (actual) futures difference remains negative for the entire forecasting period (i.e., June 2012-December 2012). This is not surprising given that during this catamenia the European markets have been affected by the recent European sovereign debt crisis, which had a much lesser impact connected the US market. Remarkably, the proposed model right forecasts the sign of the remainder throughout the observation period.

Given that the VIX-VSTOXX futures price conflict is negative throughout the foretelling valuation time period (and has a epochal negative mean throughout the entire sample), the following (GARCH) scheme is projected: we start the scheme away going foresightful the nearest matureness VSTOXX futures, with a size eq to $100,000 per manoeuvre and simultaneously active short 100 contracts (i.e., size up $100,000 per point) of the nearest maturity VIX futures the first time our Arkansas(4)-T-GARCH(1,1) model forecasts an increase of the spread in absolute value and unwind when the model signals a reduction in spread.

Fig.5 plots the forecasted change in the VIX-VSTOXX futures price dispute, for our chosen out-of-sample period (beginning of June to end Dec 2012). Since the difference is dissentient throughout, a positive change will signify a decrease in the VIX-VSTOXX closest futures price conflict. Therefore, the scheme bequeath be activated each clock time the forecasted change in the VIX-VSTOXX futures difference is dissenting and unwind when it is positive. More generally, one and only could also choose to activate or deactivate (unwind) the positions dependant on whether the difference is above or below a certain threshold, which could, but need not, be equal to zero.

The carrying out of the trading strategy is illustrated in Fig.6, with panel a) of this figure depicting the cumulative Pdanamp;L that the strategy could have generated, while the patch in dialog box b) is of the daily Pdanamp;Ls. The results in Fig.6 are directly comparable to those in Fig.3, panels c) and d). This scheme seems to function much better, taking advantage of the excellent forecast of the spread.

Furthermore, this latter (GARCH) strategy should require lower transaction costs as well, as the naïve strategy requires daily rebalancing of the VSTOXX wooden leg (so that sizes of the two legs e'er match), whereas with the GARCH strategy one would only trade on predestined years rather than day-after-day, namely when the models signal a broadening of the VIX-VSTOXX futures spread.

Conclusions
In this article, empirical evidence that adding volatility index futures to an fairness and portfolio improves overall carrying into action is brought progressive. This is true for both VIX and VSTOXX. The best piece of music would have equity, bonds and volatility derivatives futures with first or second maturity. Using VIX and VSTOXX futures improves the return/risk visibility of investment portfolios, especially during turbulent times. Adding VIX futures contracts can improve the mean/variance investment frontier so hedge stock managers may be able to raise their equity portfolio performance, as measured by the Sharpe ratio.

During tumultuous times (such as 2008-2012), there is a great benefit in having VIX futures in the investment portfolio – the intend staying positive and Sharpe ratios at the go-to-meeting levels. Distant losings can follow avoided if VIX positions are added.

The second senior contribution of this article is to tackle the data for US and Europe with a battery of state-of-the prowess GARCH models. Since the difference in VIX versus VSTOXX futures prices seems to equal nonmoving, there is a clear incentive to identify suited models for applied mathematics arbitrage. Identifying a GARCH model that whole kit well with data allows investors to engage in directional trading given by the signal produced by the GARCH model. GARCH models can be used to forecast the disperse between VIX and VSTOXX futures on a unit of time basis and impressive entering and exiting the trades. The analysis in this article shows that the applied mathematics arbitrage approach could have provided substantial gains over recent periods.

This tack was licensed by EUREX .

Eurex Exchange is one of the world's leading derivatives exchanges. It offers more than 2000 products covering all leading likewise American Samoa alternative asset classes, all tradable on a single political program. Eurex Exchange is a appendage of Eurex Group.