New York University (NYU) – Courant Institute of Mathematical Sciences; Finance Concepts LLC
NYU Polytechnic School of Engineering – Department of Finance and Risk Engineering
We study the dynamics of VIX futures and ETNs/ETFs. We find that contrary to classical commodities, VIX and VIX futures exhibit large volatility and skewness, consistent with the absence of cash-and-carry arbitrage. The constant-maturity futures (CMF) term-structure can be modeled as a stationary stochastic process in which the most likely state is a 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 multi-factor 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 (see Proposition 3.1). To quantify further, we estimate a 2-factor lognormal model with mean-reverting factors to 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 = 0.5 or less, and high variability over 1-year horizon simulations. This is due to the surges in VIX and CMF backwardations which are experienced sporadically, but also inevitably, in the volatility futures market.