Forecasting Regime‐Dependent Tail Risk in Digital Asset Portfolios With a Mixture of Hidden Markov Factor Analyzers

This paper proposes the mixture of hidden Markov factor analyzers (MHMFA), a unified framework for jointly forecasting value‐at‐risk (VaR) and expected shortfall (ES) in digital asset portfolios. The model integrates regime‐switching dynamics via a hidden Markov chain, a latent factor structure capturing systematic co‐movements, and regime‐specific Gaussian mixtures to flexibly accommodate non‐Gaussian features in both common and idiosyncratic components. Parameters are estimated using an expectation–maximization algorithm, and joint VaR–ES forecasts are generated through Monte Carlo simulation under a probabilistic soft‐assignment scheme. In a large‐scale out‐of‐sample evaluation on a six‐cryptocurrency portfolio, the MHMFA consistently outperforms all competing models across multiple portfolio strategies and confidence levels according to the Patton–Ziegel–Chen joint loss criterion. The model achieves strong Basel III compliance at α=2.5% and generates a time‐varying ES/VaR ratio that adapts to market conditions, reflecting increased tail risk during turbulent periods. From an economic perspective, the risk‐averse strategy based on MHMFA delivers robust performance after transaction costs, highlighting the practical relevance of the proposed approach for risk management and portfolio allocation.