Essays On The Term Structure Of Volatility And Option Returns

The first essay studies the dynamics of equity option implied volatility and shows that they depend both upon the option's time to maturity (horizon) and slope of the implied volatility term structure for the underlying asset (term struc ture). We propose a simple, illustrative framework which intuitively captures these dynamics. Guided by our framework, we examine a number of volatility trading strategies across horizon, and the extent to which profitability of trading strategies is due to an interaction between term structure and realized volatility. While profitable trading strategies based upon term structure exist for both long and short horizon options, this interaction requires that positions in long horizon options be very different than those required for short horizon options. Equity option returns depend upon both term structure and horizon, but for index options, implied volatility term structure slope negatively predicts returns. While the carry trade has been applied profitably across asset classes and to index v volatility, given this difference in index and equity implied volatility dynamics, I examine the carry trade in the equity volatility market in the second essay. I show that the carry trade in equity volatility produces significant returns, and unlike the returns to carry in other asset classes, is not exposed to liquidity or volatility risks and negatively loads on market risk. A long volatility carry portfolio, after transactions costs, remains significantly profitable and negatively loads on market risks, challenging traditional asset pricing theories. Overwriting an index position with call options creates a portfolio with fixed exposures to market and volatility risk premia. I allow for time-varying allocations to volatility and the market by conditioning on the slope of the implied volatility term structure. I show that a three asset portfolio holding a VIX futures position, the SandP 500 Index and cash triples the returns of the index and more than doubles the risk-adjusted returns of the covered call while maintaining a return volatility roughly equal to that of the SandP 500 Index.