  We study a series of static and dynamic portfolios of VIX futures and their
effectiveness to track the VIX index. We derive each portfolio using
optimization methods, and evaluate its tracking performance from both empirical
and theoretical perspectives. Among our results, we show that static portfolios
of different VIX futures fail to track VIX closely. VIX futures simply do not
react quickly enough to movements in the spot VIX. In a discrete-time model, we
design and implement a dynamic trading strategy that adjusts daily to optimally
track VIX. The model is calibrated to historical data and a simulation study is
performed to understand the properties exhibited by the strategy. In addition,
comparing to the volatility ETN, VXX, we find that our dynamic strategy has a
superior tracking performance.
