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Nonlinear Asset Covariance Prediction Conditioned on the Financial Environment

Hansson, Alexander LU (2026) In Master's Theses in Mathematical Sciences FMSM01 20261
Mathematical Statistics
Abstract
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... (More)
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. (Less)
Please use this url to cite or link to this publication:
author
Hansson, Alexander LU
supervisor
organization
course
FMSM01 20261
year
type
H2 - Master's Degree (Two Years)
subject
keywords
Covariance estimation, Conditional autoencoder, Nonlinear factor models, Portfolio optimization, Neural networks
publication/series
Master's Theses in Mathematical Sciences
report number
LUTFMS-3574-2026
ISSN
1404-6342
other publication id
2026:E101
language
English
id
9246345
date added to LUP
2026-07-03 09:51:47
date last changed
2026-07-03 09:51:47
@misc{9246345,
  abstract     = {{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.}},
  author       = {{Hansson, Alexander}},
  issn         = {{1404-6342}},
  language     = {{eng}},
  note         = {{Student Paper}},
  series       = {{Master's Theses in Mathematical Sciences}},
  title        = {{Nonlinear Asset Covariance Prediction Conditioned on the Financial Environment}},
  year         = {{2026}},
}