Coarse-graining the cross-section : How Regression-via-Classification improves robustness in high-noise, small-sample-size domains such as cross-sectional asset pricing ; Grovkorniga tvärsnittet : Minska påverkan av brus i finansiell maskininlärning genom att binda svarsvariabeln i kvantiler

In the field of Quantitative Asset Pricing, the task of predicting expected asset returns stands as one of the hardest challenges due to the inherent complexities and uncertainties that lie in the evolving dynamics of financial markets. The prediction of expected returns is a central input parameter for the portfolio optimization problem, a constrained utility-maximization problem that lays the foundations of Portfolio construction. Traditional Machine Learning approaches to the field rely on regression models to predict expected stock returns, treating the problem as a continuous variable forecasting. However, the inherent small sample size of financial data combined with low signal-to-noise ratio, poses substantial difficulties for accurate forecasting. This thesis addresses these challenges by introducing a novel methodology – the application of a coarse-graining technique for the prediction of stock returns. Coarse-graining, commonly applied in statistical physics to simplify complex systems, involves grouping entities into broader categories. In the context of equity selection, this transforms the traditional regression problem - predicting the return of a stock - into a Regression-via-Classification one, predicting the quantile in which each stock is likely to reside within the market’s cross-section and then reverting it back to a continuous prediction through interpolation. The proposed approach of Regression-via-Classification has several motivations : by transforming a regression problem into a classification one, we prove theoretically that the task of classifying simplifies the task of estimating. Also, by categorizing stocks into quantiles we reduce the impact of outliers, extreme market fluctuations and shocks over time, providing a robust framework for prediction. This acknowledges the inherent uncertainty in financial markets and mitigates the noise present in financial time series data. Moreover, the coarse-grained classification facilitates the interpretability of model predictions, helping to ...