Essays on Risk Management and Portfolio Allocation Using Tail Measures
Date
2024-07-09
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University of Southampton
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.
Description
Keywords
Forecasting, Risk Management, high-dimensional, optimisation, portfolio, weights, VaR, score function, CoVaR, backtesting, systemic risk, robust estimation, huber loss function