Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)


Mathematics and Statistics

First Advisor

Liang Peng

Second Advisor

Gengsheng Qin

Third Advisor

Yichuan Zhao

Fourth Advisor

Ruiyan Luo


The dissertation concentrates on risk measures and fund performance analysis. It begins with the uncertainty comparison between two risk measures, Value-at-Risk (VaR) and Expected Shortfall (ES). Chapter 2 examines the effect of heavy tail and dependence on comparing these two risk measures using independent data as well as AR models with normal or t distributions. Theoretical analyses, simulation, and empirical study all support the conclusion that VaR at 99% level is better than ES at 97.5% level for distributions with heavier tails.

Chapter 3 and Chapter 4 concentrate on mutual fund analysis. More specifically, Chapter 3 uses daily mutual fund returns to estimate market timing. Because some econometric issues such as heteroscedasticity, correlated errors, and heavy tails bias the traditional least squares estimation in Treynor and Mazuy (1966) and Henriksson and Merton (1981), a new estimate – weighted least square estimate is proposed to ensure a normal limit and random weighted bootstrap method to quantify uncertainty in the empirical study.

As an extension of Chapter 3, Chapter 4 explores the association between stock picking skill and the median of error in models including the one-factor model in Jensen (1968), three-factor model in Fama and French (1996), and four-factor model in Carhart (1997), using daily and monthly mutual fund returns. The dissertation presents a negative association between them.

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