Studies on Cross-Prediction

Managing investments for an institution is a balancing act between achieving return targets and mitigating solvency risks. These objectives are approached by exploring statistical dependence in institutional equity and fixed income portfolio returns across two dimensions - cross-sectionally and over time.
The analysis focuses on return forecasts generated using cross-prediction methods, which are applied and tested with various models for asset allocation and portfolio optimisation. This approach utilises existing information more effectively and demonstrates its ability to improve predictions of future returns.
The research presents three distinct perspectives on cross-prediction. The first study explores methods for studying both the temporal and cross-sectional dimensions of statistical causality. The second study applies multivariate modelling techniques by making extensive use of variables and parameters for portfolio optimisation. In contrast, the third study focuses on matrix factorisation, which relies on optimising portfolios based on the simplest possible combination of common return drivers.
The first study takes a statistical approach by examining how different equity and fixed income portfolio components correlate cross-sectionally and over time. The findings show that these correlations are time-varying and tend to increase during periods of market turmoil. This study also provides a detailed analysis of interdependencies that exist within and across different asset classes.
Building on these empirical findings the second study integrates cross-prediction with Copula GARCH methodology within the Black-Litterman portfolio allocation framework. This approach is implemented as a daily rebalancing trading strategy using the original model and two of its extensions: Copula Opinion Pooling and Entropy Pooling.
The third study is structured in two parts. The first applies a novel portfolio optimisation concept called Principal Portfolios, which is based on the factorisation of a return prediction matrix constructed to account for cross-prediction. The second part brings together equity and fixed income portfolios by utilising asset pricing factors as return predictors within the context of machine learning models.
These three studies demonstrate that cross-prediction can materially improve the accuracy of return forecasts for both equity and fixed income portfolios and offer substantial benefits for institutional investors in portfolio and risk management. The findings also highlight the time-varying nature of statistical dependence and the predictive relationships between and within these portfolios. Perhaps most importantly the analysis shows that machine learning methods offer substantial potential for financial modelling with large and complex datasets.