Multivariate GARCH models and risk minimizing portfolios: The importance of medium and small firms

Abstract

This paper re-examines the relationship among different firms using a combination of multivariate GARCH models (symmetric and asymmetric with structural changes) and the IBEX 35, IBEX MEDIUM CAP, and IBEX SMALL CAP indexes as the benchmarks to track the performance of large, medium and small firms, respectively. Our findings show the existence of a significant difference in the transmission of volatility when the asymmetric behavior and structural changes are considered. After calculating the risk minimizing portfolio weights, we show that the minimum-volatility portfolio is composed of medium and small indexes with a higher weight of medium firms for a set of different scenarios.