Publication Date
11-29-2025
Document Type
Article
Organizational Units
Daniels College of Business, Business Information and Analytics, Reiman School of Finance
Keywords
Machine learning, Bias-variance trade-off, Principles of parsimony, Virtue of complexity
Abstract
(Kelly et al., 2024) show that increasing complexity in linear models, with potentially thousands of predictors, is "virtuous". Their work contradicts the dogma of model selection, including the Principles of Parsimony and Occam's Razor. They find that when the number of predictors far exceeds the number of observations, the bias-variance trade-off breaks down, the variance declines, and the Sharpe ratio increases. In the context of ridge regression, we find that very high complexity coupled with large penalty terms (excessive shrinkage) generate forecasts that converge to a rolling window of past returns. For example, we show the past twelve-month moving average of actual returns is 97.5% correlated to the forecasts from a twelve-month rolling window of random Fourier features with a large penalty. This finding is consistent with the theory of ridge regression. As the penalty term increases, the forecasts closely approximate the mean, and ignore the explanatory variables. Thus, increasing complexity does not outperform the standard ridge regression, and increasing complexity does not generate high Sharpe ratios, abnormal returns, utility gains or profitable investment strategies.
Copyright Date
12-3-2025
Copyright Statement / License for Reuse
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Rights Holder
Ryan Elmore and Jack Strauss
Provenance
Received from Elsevier
File Format
application/pdf
Language
English (eng)
Extent
6 pgs
File Size
1.81 MB
Publication Statement
Copyright is held by the Authors. User is responsible for all copyright compliance. This article was originally published as
Elmore, R., & Strauss, J. (2025). Is Complexity Virtuous? Economics Letters, 258. https://doi.org/10.1016/j.econlet.2025.112749
Publication Title
Economics Letters
Volume
258
First Page
112749
ISSN
0165-1765
Recommended Citation
Elmore, Ryan and Strauss, Jack, "Is Complexity Virtuous?" (2025). Business Information and Analytics: Faculty Scholarship. 6.
https://digitalcommons.du.edu/business_info_fac/6
https://doi.org/10.1016/j.econlet.2025.112749
Included in
Business Analytics Commons, Economics Commons, Finance and Financial Management Commons, Statistics and Probability Commons