Structure and Asymptotic Theory for Multivariate Asymmetric Volatility: Empirical Evidence for Country Risk Ratings

Following the rapid growth in the international debt of less developed countries in the 1970s and the increasing incidence of debt rescheduling in the early 1980s, country risk has become a topic of major concern for the international financial community. A critical assessment of country risk is essential because it reflects the ability and willingness of a country to service its financial obligations. Various risk rating agencies employ different methods to determine country risk ratings, combining a range of qualitative and quantitative information regarding alternative measures of economic, financial and political risk into associated composite risk ratings. This paper provides an international comparison of country risk ratings compiled by the International Country Risk Guide (ICRG), which is the only international rating agency to provide detailed and consistent monthly data over an extended period for a large number of countries. As risk ratings can be treated as indexes, their rate of change, or returns, merits attention in the same manner as financial returns. For this reason, a constant correlation multivariate asymmetric ARMA-GARCH model is presented and its underlying structure is established, including the unique, strictly stationary and ergodic solution of the model, its causal expansion, and convenient sufficient conditions for the existence of moments. Alternative empirically verifiable sufficient conditions for the consistency and asymptotic normality of the quasi-maximum likelihood estimator are established under non-normality of the conditional (or standardized) shocks. The empirical results provide a comparative assessment of the conditional means and volatilities associated with international country risk returns across countries and over time, enable a validation of the regularity conditions underlying the models, highlight the importance of economic, financial and political risk ratings as components of a composite risk rating, evaluate the multivariate effects of alternative risk returns and different countries, and evaluate the usefulness of the ICRG risk ratings in modelling risk returns.