Essays on Tail Risks and Volatility Timing


Student thesis: Doctoral Thesis

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Awarding Institution
  • Jun CAI (Supervisor)
  • Yusen KWOH (External person) (Supervisor)
  • Kuoping CHANG (External person) (External Supervisor)
  • Yusen KWOH (External person) (External Supervisor)
Award date9 Jul 2021


This dissertation examines the relationship between tail risk and individual stock extreme returns in U.S. stock markets, as well as the performance of volatility timing strategies. In this thesis, I attempt to measure the relative risks posed by a multitude of uncertainties. This study mainly answers three questions: how does the tail behavior of a variety of risk factors affect the extreme return of individual stocks, what firm characteristics are associated with tail risk, and how to improve the performance of tail risk related strategies such as momentum.

To begin with, this thesis examines how the tail behavior of risk factors affects the extreme return of more than 7,000 stocks in the U.S. It identifies a total of 35 widely used risk factors from asset pricing literature, including 25 stock market factors, three bond market factors, and seven commodity market factors. By examining the univariate and multivariate conditional exceedance patterns of stocks, I compare the relative importance of risk factors in affecting extreme returns. I also investigate the tail behavior patterns of stocks in multivariate conditional situation, as well as the patterns of co-exceedance. Besides, this thesis also explores firm characteristics associated with extreme returns.

To confirm the robustness and symmetry of findings of the tail risk behavior, I examine US oil market as test samples since the effect is more obvious for oil firms, due to the fact that the volatility of commodity market is closely related to and even bigger than that in the stock and bond markets. The results indicate that the findings are consistent and robust in upper and lower tails.

I further turn to momentum which is the typical strategy related to tail risk, and focus on how to improve its performance. There are two different ways to explore this. One is the double-sort strategy which combines momentum with contrarian. The other is the volatility timing, including three methods, volatility-managed, variance-managed, and dynamic-managed strategy. At last, this thesis does the spanning test for momentum related single- and double-sort strategies.

This thesis makes several major contributions to the literature. This is the first study of the impact of tail behavior of risk factors on the tail behavior of individual stock returns. Previous studies generally focus on the average relationship between risk factors and stock returns. In this study, I aim at the tails' relationship and I find some symmetry findings in upper and lower tails.

First, it reveals the largest impact 7 individual risk factors in affecting stock extreme returns to be: Excess market return (EXMRET), FF security trading sector return(SECUR), FF bank sector stock return (BANKS), FF insurance sector stock return (INSUR), Aggregate volatility factor (DVXO), Earnings price ratio factor (EP), and Cash flow price ratio factor (CP). It also identifies the direction of such impacts.

Second, tail behavior patterns of stocks were explored in multivariate conditional situation. In about 65% (83%) of trading days at least one of risk factors move into their (un)favorable tail which will lead to a positive (negative) outcome for individual stocks return. I also find the multiple tail events have a substantially greater impact on extreme returns than single or less events. For instance, every six or more risk factors moves into their (un)favorable tails, that the average probability of a positive (negative) individual stock extreme return roughly doubles that of the former one.

Third, it also finds the firm characteristics associated with more frequent likelihoods of tail risk. More specifically, firm size (ln(ME)), beta (BETA), idiosyncratic volatility (IVOL), price synchronicity (R2), capital expenditures (CAP), dividend payments (DIV), asset growth (ATG), accruals (ACR), cash flows (CFO), and cash holding (CASH) are important determinants of upper and lower tail risks. For example, small firms with higher betas, lower dividend payments are associated with higher tail risk.

Fourth, the former three findings all show symmetry in upper and lower tails. The robustness tests indicate that it does not depend on the number of risk factors and industries.

Fifth, it is not only confirmed that the double-sort strategies can enhance the performance of momentum in U.S. stock markets, but also measure the effect. Among the four single and double-sort strategies, double-sort momentum-contrarian (Mom-Ctr) and contrarian-momentum (Ctr-Mom) strategies have an average annual return of 20.00% and 20.03%, respectively, which almost triple the momentum with that of 6.80%. Besides, I also confirm that momentum and contrarian can be mutually used as tools to enhance each other's performance in double-sort strategies.

Besides, I provide evidence that the three volatility timing strategies all increase the Sharpe ratio of risk-managed portfolios relative to the original portfolios. More importantly, I find that, generally speaking, dynamic-managed strategy has the best outperformance, volatility-managed strategy next, and variance-managed strategy is the least.

    Research areas

  • Risk Factor, Tail Risk, Extreme Return, Volatility Timing, Momentum and Contrarian