Essays on Volatility Risk and Security Returns
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This dissertation studies the determinants of expected option returns and equilibrium determinants of variance risk and the variance risk premium. In the first essay, I analyze the relation between expected option returns and the volatility of the underlying securities. In the Black-Scholes-Merton and stochastic volatility models, the expected return from holding a call (put) option is a decreasing (increasing) function of the volatility of the underlying. These predictions are strongly supported by the data. In the cross-section of stock option returns, returns on call (put) option portfolios decrease (increase) with underlying stock volatility. This strong negative (positive) relation between call (put) option returns and volatility is not due to cross-sectional variation in expected stock returns. It holds in various option samples with different maturities and moneyness, and it is robust to alternative measures of underlying volatility and different weighting methods. Time-series evidence also supports the predictions from option pricing theory: Future returns on S&P 500 index call (put) options are negatively (positively) related to S&P 500 index volatility. In the second essay, I show that in many consumption-based general equilibrium models with Epstein-Zin-Weil preferences, the market variance risk premium is related to the leverage effect, defined as the conditional covariance between market returns and changes in the conditional market variance. The sign of the relation between the market variance risk premium and the market leverage effect depends on the coefficient of relative risk aversion and the elasticity of intertemporal substitution. I find a statistically significant negative intertemporal relationship between the variance risk premium and the leverage effect for the S\&P 500 from 1996 to 2014. This implies an elasticity of intertemporal substitution less than one and a preference for the early resolution of uncertainty. Exploiting the relation between the variance risk premium and the leverage effect also allows me to characterize the historical behavior of the variance risk premium going back to 1926.