COVARIANCE MATRIX CONSTRUCTION AND ESTIMATION: CRITICAL ANALYSES AND EMPIRICAL CASES FOR PORTFOLIO APPLICATIONS
Creators: name: NEFFELLI, MARCO
Publisher: name: Universit� degli studi di Genova
Year: 2019

description: 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.