Statistical Methods in Finance

Abstract

This dissertation focuses on statistical methods in finance, with an emphasis on the theories and applications of factor models. Past studies have generated fruitful results applying statistical techniques in various cross-sectional and time-series analyses, yet better econometric methods are always called for to deal with more involved financial economic settings. To start with, ultra-large data sets which contain high-dimensional variables are increasingly common in recent decades, and make the initial screening of factors both important and necessary. In Chapter 1, a nonparametric independence screening method is proposed for high-dimensional varying coefficient models, a broad class of models used to explore the dynamic impact of factors that evolves over time or with certain characteristics. Another challenge facing financial research is the search and interpretation of factors especially when the underlying process is more volatile. With the 2008 financial crisis included in the period of study, Chapter 2 identifies the risk factors of the volatility risk premium in financial markets, and provides insight into how investors hedge their downside risk and how market intermediates provide liquidity. Meanwhile, the way proxy for factors is chosen may also play an important role in financial studies. We analyze in Chapter 3 how our proposed statistic, the fraction of forecasts that miss on the same side, better measures the market surprise than traditional consensus error, and show its power in capital market event studies. Finally, conventional approaches may no longer be robust when some factors are unobserved, as in the case of risk adjusted fund evaluation. In Chapter 4, we propose a method to more precisely evaluate mutual fund performance in the presence of herding effects and latent factors, and the results improve our understanding of what fraction of fund managers are truly generating alphas.