Essays on risk management and portfolio allocation using tail measures

Abstract

This thesis delves into effective methods for managing risks and decision-making processes in finance. The research comprises three main chapters, each addressing critical challenges in time series analysis, portfolio optimization, and risk assessment. Chapter 2 introduces the Robust Model Averaging Marginal Regressions (RMAMAR) procedure, a novel approach that combines one-dimensional marginal regression functions to approximate conditional regression functions robustly. By employing local linear estimation and robust M-estimators, RMAMAR addresses the curse of dimensionality and enhances parameter estimation accuracy, particularly in high-dimensional datasets. Chapter 3 extends dynamic portfolio choice methodologies under Expected Utility (EU) frameworks to incorporate investors’ quantile preferences, focusing on specific quantiles of the returns distribution. Through empirical applications and simulations, this chapter demonstrates the effectiveness of constructing optimal portfolios under quantile preferences with multiple conditioning variables, showcasing superior performance during market crises. Chapter 4 proposes a new approach to backtesting risk measures by introducing a univariate score function that combines the marginal/conditional score functions for forecasting Value-at-Risk (VaR) and Systemic Risk (SR). This method ensures an equitable and comprehensive assessment of both risk measures, overcoming the limitations of existing methods that prioritize one measure over the other based on the equality of VaR across models. Furthermore, Chapter 4 conducts a comparative analysis of different identification functions for backtesting, including the one-dimensional function proposed by Banulescu-Radu et al. (2021) and the two-dimensional function introduced byFissler and Hoga (2023), to evaluate the potential risk associated with employing identification functions that are not strictly defined for backtesting purposes. Overall, this thesis contributes to advancing risk management and decision-making methodologies by providing robust and practical strategies.

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Identifiers

ORCID for Jose Olmo: orcid.org/0000-0002-0437-7812

ORCID for Huifu Xu: orcid.org/0000-0001-8307-2920

ORCID for Zudi Lu: orcid.org/0000-0003-0893-832X

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