Date of Graduation


Document Type


Degree Type



College of Business and Economics



Committee Chair

K. Victor Chow

Committee Co-Chair

Naomi Boyd

Committee Member

Naomi Boyd

Committee Member

Alexander Kurov

Committee Member

Eric Olson


This dissertation comprises three separate chapters on both risk-neutral and physical probability spaced equity tail risk for both the market index and in the cross-section of individual stocks.

The first chapter is titled “Does VIX Truly Measure Return Volatility?” This chapter studies the bias of the VIX index as a volatility measure. Particularly, VIX undervalues (overvalues) volatility when market return is expected to be negatively (positively) skewed. Alternatively, we develop a model-free generalized volatility index (GVIX). This chapter further derives the risk-neutral tail risk estimated from the VIX index.

The second chapter is titled “Decomposing the VIX: Implications for the Predictability of Stock Returns” This chapter studies the tail risk for the market index (S&P 500 index) in both risk-neutral and physical probability space and subsequently quantifies the market tail risk premium. Market tail risk premium also is a driving force of the VIX index, especially during a nervous market condition. The VIX decomposed market tail risk premium possesses significant prediction power for the equity market index (S&P500 index), Fama and French style portfolios, and industry portfolios with a prediction range that varies from one month to 12 months.

The third chapter is titled “The Predictive Power of Tail Risk Premia on Individual Stock Returns” This chapter studies both the risk-neutral and physical probability space tail risk for the cross-section of individual stocks and examines the characteristics of this premium in the cross-section of stock returns. The tail risk premium for individual stocks is statistically and economically priced in the cross-section of individual stock returns. Specifically, the existence of a premium for bearing negative tail risk is significantly associated with negative returns up to one month in the future. In contrast, the premium for bearing positive tail risk has no significant predictive power. This phenomenon cannot be explained by size, book-to-market ratio, market beta, idiosyncratic volatility, momentum, illiquidity, or lottery effect (maximum and minimum monthly returns).

Overall, the results from the three chapters indicate that equity tail risk is an important factor for the market index in both risk-neutral and physical probability spaces, and its premium carries strong return predictability for multiple market-level portfolio assets. Furthermore, equity tail risk and its premium carry significant return prediction power in the cross-section of individual stock returns. This phenomenon is robust to previously documented asset pricing factors.