Volatilities vary. This matters for asset pricing, asset allocation, and risk- management. Combining S&P index option prices at different maturities and strike prices provides a model free spot curve of expected returns variances (VarSC), while market prices of futures on the volatility index VIX gives a for- ward curve of expected returns volatilities (VolFC). I compare the two volatility term structures and show evidence of lack integration between the options and the futures markets. First, if options and futures markets are integrated, the same pricing kernel should apply to both, and the VarSC and VolFC can be combined to give the risk-neutral market expectation of the variance-of-volatility.
But taking together the two volatility term structures often implies a negative variance-of-volatility, a mathematical impossibility. Second, the slopes of the two curves are often at odds with each other. The inconsistencies documented are economically significant and not simply due to measurement errors, since trading strategies designed to profit from them reap high risk adjusted returns.