Four essays on risk assessment with financial econometrics models

Resumen

This thesis includes four essays on risk assessment with financial econometrics models. The first chapter provides Monte Carlo evidence on the efficiency gains obtained in GARCH-base estimations of VaR and ES by incorporating dependence information through copulas and subsequently using full maximum likelihood (FML) estimates. First, individual returns series are considered; in this case, the efficiency gain stems from exploiting the relationship with another returns series using a copula model. Second, portfolio returns series obtained as a linear combination of returns series related with a copula model, are considered; in this case, the efficiency gain stems from using FML estimates instead of two-stage maximum likelihood estimates. Our results show that, in these situations, using copula models and FML leads to a substantial reduction in the mean squared error of the VaR and ES estimates (around 50\% when there is a medium degree of dependence between returns) and a notable improvement in the performance of backtesting procedures. Then, chapter 2 analyzes the impact of the COVID-19 pandemic on the conditional variance of stock returns. In this work, we look at this effect from a global perspective, employing series of major stock market and sector indices. We use the Hansen’s Skewed-t distribution with EGARCH extended to control for sudden changes in volatility. We oversee the COVID-19 effect on the VaR. Our results show that there is a significant sudden shift up in the return distribution variance post the announcement of the pandemic, which must be explained properly to obtain reliable measures for financial risk management. In chapter 3, we assess VaR and ES estimates assuming different models for standardised returns such as Cornish-Fisher and Gram-Charlier polynomial expansions, and well-known parametric densities such as normal, skewed Student-t family of Zhu and Galbraith (2010), and Johnson. This paper aims to check whether models based on polynomial expansions outperform the parametric ones. We carry out the model performance comparison in two stages. First, a backtesting analysis for VaR and ES, and second, using the loss function approach. Our backtesting results in our empirical exercise suggest that all distributions, but the normal, perform quite well in VaR and ES estimations. Regarding the loss function analysis, we conclude that the Cornish-Fisher expansion usually outperforms the others in VaR estimation, but Johnson distribution is the one that provides the best ES estimates in most cases. Although the differences among all distributions (excluding the normal) are not great. Finally, chapter 4 assess whether accounting for asymmetry and tail-dependence in returns distributions may help to identify more profitable investment strategies in asset portfolios. Three copula models are used to parameterize the multivariate distribution of returns: Gaussian, C-Vine and R-Vine copulas. Using data from equities and ETFs from the US market, we find evidence that, for portfolios of 48 constituents or less, the R-Vine copula is able to produce more profitable portfolios with respect to both, the C-Vine and Gaussian copulas. However, for portfolios of 100 assets, performance of R- and C-Vine copulas is quite similar, being both better than the Gaussian copula