There's been an exciting debate on whether higher model complexity might be the holy grail for ML factor-driven models to predict returns championed by AQR's B.T. Kelly and other authors as described in the 2021 paper "The Virtue of Complexity in Return Prediction" .
Occam's Razor principle of finding an elegant solution grounded on simplicity was challenged by this new tenet rooted in increasing model complexity by brute force to boost a model performance even without fully understanding the reasons behind why this is occurring.
A few weeks ago, Oxford-Man Institute of Quantitative Finance's Cartea, Jin, Shi released a new paper "The Limited Virtue of Complexity in a Noisy World" challenging the aforementioned "complexity is truth" movement. The authors showcased a critical view on embracing naively higher complexity based on their words:
" We conjecture that as model complexity increases, including more factors allows the model to fit more complex patterns, but in the meantime, each factor becomes noisier, on average, due to re-estimation on the same data sample. As the average level of noise in each factor increases with model complexity, the harm to model performance from increased noise may ultimately outweigh the gains from increased model complexity"
Key takeaways of "The Limited Virtue of Complexity in a Noisy World":
• In a high-dimensional factor space, increasing model complexity under proper regularization can enhance the predictability of asset returns; however, the Sharpe ratio of a portfolio of assets and the R-squared of the prediction of the asset returns decrease monotonically and are convex as the noise level in factors increases.
• When only a subset of factors is observed, there is an optimal level of complexity beyond which incorporating additional factors can degrade portfolio performance due to the effect of noise in the factors.
• Authors underscore a limited virtue of complexity in financial forecasting, where the performance of portfolios depends on the noise level in factors, and where more complex models do not necessarily lead to better performance when factors are not perfectly observed.
Feel free to provide any thoughts or additional research that delves into this fascinating topic linked to Factor Investing and ML/AI research.
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Carlos Salas
Portfolio Manager & Freelance Investment Research Consultant
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