The thesis contributes to the financial econometrics literature by improving the estimation of the covariance matrix among financial time series. To such aim, existing econometrics tools have been investigated and improved, while new ones have been introduced in the field. The main goal is to improve portfolio construction for financial hedging, asset allocation and interest rates risk management. The empirical applicability of the proposed innovations has been tested trough several case studies, involving real and simulated datasets. The thesis is organised in three main chapters, each of those dealing with a specific financial challenge where the covariance matrix plays a central role. Chapter 2 tackles on the problem of hedging portfolios composed by energy commodities. Here, the underlying multivariate volatility among spot and futures securities is modelled with multivariate GARCH models. Under this specific framework, we propose two novel approaches to construct the covariance matrix among commodities, and hence the resulting long-short hedging portfolios. On the one hand, we propose to calculate the hedge ratio of each portfolio constituent to combine them later on in a unique hedged position. On the other hand, we propose to directly hedge the spot portfolio, incorporating in such way investor’s risk and return preferences. Trough a comprehensive numerical case study, we assess the sensitivity of both approaches to volatility and correlation misspecification. Moreover, we empirically show how the two approaches should be implemented to hedge a crude oil portfolio. Chapter 3 focuses on the covariance matrix estimation when the underlying data show non–Normality and High–Dimensionality. To this extent, we introduce a novel estimator for the covariance matrix and its inverse – the Minimum Regularised Covariance Determinant estimator (MRCD) – from chemistry and criminology into our field. The aim is twofold: first, we improve the estimation of the Global Minimum Variance Portfolio by exploiting the MRCD closed form solution for the covariance matrix inverse. Trough an extensive Monte Carlo simulation study we check the effectiveness of the proposed approach in comparison to the sample estimator. Furthermore, we take on an empirical case study featuring five real investment universes characterised by different stylised facts and dimensions. Both simulation and empirical analysis clearly demonstrate the out–of–sample performance improvement while using the MRCD. Second, we turn our attention on modelling the relationships among interest rates, comparing five covariance matrix estimators. Here, we extract the principal components driving the yield curve volatility to give important insights on fixed income portfolio construction and risk management. An empirical application involving the US term structure illustrates the inferiority of the sample covariance matrix to deal with interest rates. In chapter 4, we improve the shrinkage estimator for four risk-based portfolios. In particular, we focus on the target matrix, investigating six different estimators. By the mean of an extensive numerical example, we check the sensitivity of each risk-based portfolio to volatility and correlation misspecification in the target matrix. Furthermore, trough a comprehensive Monte Carlo experiment, we offer a comparative study of the target estimators, testing their ability in reproducing the true portfolio weights. Controlling for the dataset dimensionality and the shrinkage intensity, we find out that the Identity and Variance Identity target estimators are the best targets towards which to shrink, always holding good statistical properties.
|Titolo della tesi:||COVARIANCE MATRIX CONSTRUCTION AND ESTIMATION: CRITICAL ANALYSES AND EMPIRICAL CASES FOR PORTFOLIO APPLICATIONS|
|Data di discussione:||29-mag-2019|
|Appare nelle tipologie:||Tesi di dottorato|