Essays on High Order Systematic Risk

My dissertation aims at understanding the high order systematic risks in the cross-section of equity returns. It contains two chapters.
Chapter One extends Bollerslev, Tauchen, and Zhou (2009) to derive an market-based equilibrium asset pricing model in which, along with market return volatility, the volatility of market-return volatility (volatility-of-volatility) is a state variable and important for pricing individual stocks. While investors are averse to high market volatility, there is possibility that high market volatility could fluctuate even further, which could drive investors to hedge the increasing uncertainty by buying defensive stocks and dumping crash-prone stocks. To test the model, we use the high-frequency S&P 500 index option data to estimate a time series of the variance of market variance. Consistent with the model, we find that defensive stocks (i.e., returns co-move more positively with volatility-of-volatility) have lower expected returns. A hedge portfolio long in defensive stocks and short in crash-prone stocks yields a significant 10.5 percent average annual return. Furthermore, the volatility-of-volatility risk largely subsumes the valuation effect of volatility risk documented in previous studies. In sum, our model and test results provide a unified framework to better understand the importance of volatility-of-volatility risk in asset pricing.
Chapter Two studies the feature of nonlinear risk-return trade-off. If market returns have high order risk premiums, expected stock returns should comprise compensation for bearing the corresponding high order systematic risks. Allowing for non-normality in market moments, this paper presents an approximate capital asset pricing model in which high order risks are important for pricing individual stocks. Our results show that the second-order risk is significantly and negatively priced and contributes to an inverse-U shaped relation between cross-sectional expected returns and systematic risks. Stocks with high exposure to the second-order risk are volatile and are capable of earning the upside variance potential implied by the negative market variance risk premium. We develop trading strategies to mimic the second-order risk premium and we show that the resulting mimicking factor, on average, per year is −12.00% estimated from the first-order co-moment risks, −15.60% from the second-order co-moment risks, and −16.08% from the risk-neutral variance beta. Based on the mimicking factors, we find evidence consistent with our model that the second-order risk premium (1) is related to market variance risk premium, (2) accounts for the total volatility puzzle, the idiosyncratic volatility puzzle, and the MAX puzzle, and (3) helps explain the betting-against-beta premium. Our study provides a unified framework for better understanding of high order risk-return tradeoff and sheds light on the role of the second-order risk premium.