Expanding the risk horizon: an integrated framework for managing uncertainty and risk in portfolio selection

Portfolio optimization requires accurate estimates of expected returns and covariances. For return prediction, combining multiple forecasting models improves accuracy, but traditional methods assume model reliability can be quantified through past performance. This assumption fails when predictive relationships undergo structural breaks, creating epistemic uncertainty about which models will prove reliable. For covariance estimation, realized covariance models using high-frequency data offer precision gains, but computational barriers limit their applications to approximately 5 assets, far below diversification requirements. This paper addresses both challenges through a unified framework that combines principled uncertainty management in returns forecasting with scalable high-frequency covariance estimation. We develop a knowledge-based system using Dempster-Shafer Theory that learns to combine multiple forecasting models while explicitly representing uncertainty about their reliability. We derive a computationally tractable framework for estimating realized covariance models that capture asymmetric volatility dynamics for portfolios of 25-30 assets. Integrating these within Black-Litterman, our approach achieves an annualized certainty-equivalent return of 5.6% over 2011-2020, substantially exceeding both naive diversification and standard Black-Litterman, with benefits extending to traditional benchmark strategies.