Double Descent in Portfolio Optimization: Dance between Theoretical Sharpe Ratio and Estimation Accuracy

TL;DR

This paper explores the double descent phenomenon in portfolio optimization, showing how model complexity affects out-of-sample performance and the interplay between theoretical Sharpe ratio and estimation accuracy.

Contribution

It reveals the double ascent behavior of Sharpe ratio in high-dimensional portfolios and explains the mechanisms involving theoretical limits and overfitting.

Findings

Performance initially improves then declines with model complexity

High-dimensional models approach the theoretical Sharpe ratio limit

Overfitting reduces as model complexity increases in high dimensions

Abstract

We study the relationship between model complexity and out-of-sample performance in the context of mean-variance portfolio optimization. Representing model complexity by the number of assets, we find that the performance of low-dimensional models initially improves with complexity but then declines due to overfitting. As model complexity becomes sufficiently high, the performance improves with complexity again, resulting in a double ascent Sharpe ratio curve similar to the double descent phenomenon observed in artificial intelligence. The underlying mechanisms involve an intricate interaction between the theoretical Sharpe ratio and estimation accuracy. In high-dimensional models, the theoretical Sharpe ratio approaches its upper limit, and the overfitting problem is reduced because there are more parameters than data restrictions, which allows us to choose well-behaved parameters based on inductive bias.