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Benign Overfitting and its Applications in Finance

Cassio, Tommaso

(2024)

Details

Supervisors

Lassance, Nathan

Faculty

Louvain School of Management

Degree label

Master [120] : ingénieur de gestion, à finalité spécialisée

Abstract

Benign overfitting is a complex and recently discovered phenomenon that remains not fully understood. It describes scenarios where a model fits perfectly the training data and performs well on unseen testing data. This phenomenon contradicts the traditional belief that overfitting normally results in poor data generalisation. In this master’s thesis, we will explore the current literature on this theory and apply these insights to finance. Firstly, we tested some benign overfitting conditions on multiple linear regression and ridge regression models. We evaluated the presence of possible benign overfitting by examining the excess risk and utilizing a pre-established taxonomy. Secondly, we introduced the concept of the double descent curve, an extension of the bias-variance trade-off curve in scenarios of overfitted models. We analysed this phenomenon in regression models and we divided the risk into its variance and bias components to understand their respective influences. Lastly, we investigated overfitting in modern portfolio theory by comparing four portfolio models across various performance metrics. We also assessed the portfolios’ variance as the number of variables increased. Our findings indicate that most of the benign overfitting conditions on our datasets were met. The regression models also demonstrated a small excess risk, suggesting possible benign overfitting. The double descent curve was evident, showing reduced risk when the model was overfitted and reinforcing our hypothesis of benign overfitting. Furthermore, the double descent curve is mostly due to increased variance and bias at a certain point. We also observed that shrinkage can be beneficial in certain situations to reduce risk even in overfitted models. However, for modern portfolio theory, we could not conclusively determine the presence of benign overfitting in any model. We only noted that portfolio variance decreased when the number of assets exceeded the number of observations. In conclusion, we observed that benign overfitting can be applied to financial datasets, but its applicability depends on both the dataset and the model. Even if the conditions are met, the model’s role is crucial in determining the presence of benign overfitting. It is also possible that benign overfitting conditions may not be extended beyond regression models.