Nonlinear dynamics of exchange rates and portfolio risk management of international assets with regime switching and asymmetric return distributions

Abstract

The study is devoted to the quantitative analysis of complex behavior of key exchange rates and its impact on the quality of international portfolio risk management, where standard models based on the normal distribution of returns prove to be inadequate. The purpose of the research is to assess the extent to which accounting for conditional volatility, heavy tails, and market regime shifts improves the accuracy of risk measurement and the effectiveness of portfolio strategies. The empirical base consists of daily closing quotes for the EUR USD, GBP USD, and USD JPY pairs for the period from 2005 to 2023, on the basis of which logarithmic returns and descriptive statistics are calculated. The initial statistical analysis reveals negative skewness, substantial positive kurtosis, and volatility clustering, while normality tests reject the Gaussian hypothesis, justifying the transition to more flexible modeling. The methodological section employs models of the GARCH family, including asymmetric modifications, with various assumptions about the conditional distribution of errors, among which are the normal, Student’s t, and generalized error distributions, as well as their extension with Markov switching, allowing for the description of low- and high-volatility states with endogenously estimated transition probabilities. Based on the estimated parameters, forecasted values of the Value at Risk measure at the 99 percent confidence level are calculated using historical and parametric approaches, and then backtesting is performed via the Kupiec test to verify the consistency between expected and actual exceedance frequencies. The results show that models based on the normal distribution or ignoring regime shifts systematically underestimate tail risks, whereas the specification with the Student’s t distribution and Markov switching provides an exceedance rate close to the target level and the highest significance of the coverage test. At the final stage, a portfolio of the analyzed currency assets is constructed, and passive strategy, naive diversification, and active optimization strategies based on Conditional Value at Risk estimated by the GARCH and regime-switching models are compared. It is shown that incorporating advanced risk estimates into the optimization criterion simultaneously increases average return, reduces volatility, improves the Sharpe ratio, and decreases maximum drawdown, with the greatest improvement achieved when using the regime-switching model, confirming its practical relevance for international portfolio risk management.