Essays on Asset Pricing and Portfolio Choice with Time-Varying Uncertainty

In the first essay, I present a parsimonious consumption-based asset pricing model that explains the pricing of equity index options. The model has two key ingredients, a recursive utility function that overweights left-tail outcomes and a process for endowment volatility that allows for shocks with different persistence levels. The utility function produces a high price for tail risks and allows the model to replicate the implied volatility smirk in times of high uncertainty, during which extreme events are more likely. In times of low uncertainty the smirk arises due to mean reversion in volatility, which results in substantial volatility feedback and a conditional return distribution that is strongly left-skewed. The presence of multiple shock frequencies gives the variance premium the ability to predict returns over short horizons and the price-dividend ratio the ability to predict returns over long horizons, as in the data. Consistent with recent empirical evidence, the equity and variance premiums in the model arise predominantly from a high price of tail risk. The second essay (joint with Jan Schneemeier, University of Chicago) investigates the role of time-varying stock return volatility in a consumption and portfolio choice problem for a life-cycle investor facing short-selling and borrowing constraints. Faced with a benchmark investment strategy that conditions on age and wealth only, we find that an investor is willing to pay a fee of up to 1% - 1.5% of total life time consumption in order to optimally condition on volatility. Tilts in the optimal asset allocation in response to volatility shocks are considerably more pronounced than tilts in response to wealth shocks, and almost as important as life-cycle effects. Lastly, we find that the correlation between volatility and permanent labor income shocks may explain the low equity share of young households in the data. The third essay analyzes whether cross-sectional differences in the variance premium and the implied volatility smirk are related to the underlying firms' exposure to market variance risk and common idiosyncratic variance (CIV) risk. Using both cross-sectional regressions and sorts based on firms' loadings I find that firms whose variance co-moves more with market variance have steeper smirks and larger (less negative) variance premia. The latter finding is surprising in light of the fact that the variance premium of the market is believed to be negative. I show that the result persists in different sub-samples and that it is robust to various ways of estimating variance loadings. Exposure to CIV is not related to firm level option prices in a robust way.