Statistical issues in trading and risk management : innovations and applications

Abstract

This thesis analyzes and explores how various innovations and alternative implementations of statistical models can be applied to solve some of the key issues faced by finance academia and practitioners, with a focus on trading and risk management. The main issues to be addressed include sub-optimal design of pairs trading, which produces undue risks; the lack of formal treatments for performance evaluation on the comparison of passive and active investment strategies; inadequate conditional covariance modeling to capture portfolio risk dynamically; and excessive constraints on tail risk construction, which restrict its wide usage in markets other than the US. To tackle the sub-optimal design of pairs trading, an alternative single-stage approach for cointegration is proposed, which combines the augmented Dickey-Fuller (ADF) statistic together with the standardized residuals from equilibrium into a single power statistic. This single-stage approach is shown to have superiority in attaining better reward-to-risk ratios than traditional pairs trading methods. For performance evaluation, the two broad classes of strategies, namely passive and active portfolio management, are given rigorous statistical treatments. The concept of equivalence testing and non-inferiority testing, which are commonly used in biostatistics and clinical studies, are innovatively applied to the evaluation of passive portfolio strategies. Two important performance statistics, the tracking error and the information ratio, are extensively studied and their asymptotic distributions are derived respectively. For active portfolio management, the asymptotic distribution of the difference between two information ratios is notably derived, which allows direct comparison of any two relative strategies. In portfolio risk modeling, a new framework is developed to estimate portfolio Value-at-Risk (VaR) using the Dynamic Conditional Covariance (DCC) model. Various advancements from random matrix theory are also applied to de-noise the variance target within the DCC framework. It is discovered that the choice of de-noising methods plays a critical role for the accuracy of the dynamic portfolio VaR estimates. Finally, with increasing attention to measuring tail risk accurately for risk management purposes and its role as a new pricing factor in the asset pricing theory, a new and more concise construction of non-parametric tail risk is proposed by direct minimization of systematic excess expected shortfall. The new construction process not only avoids unnecessary dimension reduction and risk-neutralization steps, which are employed in current approaches in the literature, but also exhibits higher explanatory power when applied to more liquid stock universes in large-scale empirical studies. The ease of the new construction without the need of certain factor portfolios already in place also allows its wider usage in other markets in addition to the US.