Nonlinear Asset Covariance Prediction Conditioned on the Financial Environment - Hansson,Alexander (Master's Theses in Mathematical Sciences, 2026)
The thesis studies the problem of predicting large covariance matrices, a central challenge in modern portfolio theory. In portfolios with many assets, the large number of covariance terms makes prediction difficult, often causing traditional methods to suffer from either substantial estimation bias or variance. To address this, the thesis proposes an approach that adapts conditional autoencoders, originally developed in asset pricing theory. The framework decomposes asset movements nonlinearly into a diagonal idiosyncratic component and a low-dimensional systematic component, conditionally on the financial environment. These are then forecast separately using dynamic covariance models. This setup enables nonlinear latent factor construction and, unlike traditional autoencoder approaches, allows the covariance structure to adapt to the changing financial environment through time-varying factor loadings. Out-of-sample performance was evaluated on large-capitalization U.S. equities, using a value-weighted portfolio and minimum-variance portfolios constructed using covariance estimates from the proposed framework, a Ledoit-Wolf shrinkage estimator, and a traditional autoencoder. The models were compared using the Sharpe ratio and resulting transaction costs. Furthermore, each model's forecasting accuracy was evaluated against a target covariance matrix constructed from out-of-sample high-frequency return data. Results show that the proposed framework consistently outperforms the benchmarks across both statistical and economic metrics, most notably a higher Sharpe ratio for the minimum-variance portfolio. While the proposed framework leads to higher portfolio turnover, the net Sharpe ratio remains higher than the benchmarks under realistic transaction costs and weight restrictions. Overall, the results suggest that conditional autoencoders are a promising framework for high-dimensional covariance forecasting.
Keywords: Covariance estimation; Conditional autoencoder; Nonlinear factor models; Portfolio optimization; Neural networks