Statistics of VIX futures and their applications to trading volatility exchange-traded products

Marco Avellaneda and Andrew Papanicolaou

Abstract

In this paper, we study the dynamics of Chicago Board Options Exchange volatility index (VIX) futures and exchange-traded notes (ETNs)/exchange-traded funds (ETFs). We find that, unlike classical commodities, the VIX and VIX futures exhibit high volatility and skewness, consistent with the absence of cash-and-carry arbitrage. The constant-maturity futures (CMFs) term structure can be modeled as a stationary stochastic process in which the most likely state is contango with VIX ≈ 12% and a long-term futures price V ^∞ ≈ 20%. We analyze the behavior of ETFs and ETNs based on constant-maturity rolling futures strategies, such as VXX, XIV and VXZ, assuming stationarity, and through a multifactor model calibrated to historical data. We find that buy-and-hold strategies consisting of shorting ETNs that roll long futures, or buying ETNs that roll short futures, will produce theoretically sure profits if it is assumed that CMFs are stationary and ergodic. To quantify further, we estimate a two-factor lognormal model with mean-reverting factors for VIX and CMF historical data from 2011 to 2016. The results confirm the profitability of buy-and-hold strategies but also indicate that the latter have modest Sharpe ratios, of the order of SR 6 0:5, and high variability over one-year horizon simulations. This is due to the surges in VIX and CMF backwardations that are experienced sporadically, but also inevitably, in the volatility futures market.