Paper: arXiv 2212.01048

Authors: Damir Filipović, Puneet Pasricha

Abstract

We introduce an ensemble learning method based on Gaussian Process Regression (GPR) for predicting conditional expected stock returns given stock-level and macro-economic information. Our ensemble learning approach significantly reduces the computational complexity inherent in GPR inference and lends itself to general online learning tasks. We conduct an empirical analysis on a large cross-section of US stocks from 1962 to 2016. We find that our method dominates existing machine learning models statistically and economically in terms of out-of-sample $R$-squared and Sharpe ratio of prediction-sorted portfolios. Exploiting the Bayesian nature of GPR, we introduce the mean-variance optimal portfolio with respect to the prediction uncertainty distribution of the expected stock returns. It appeals to an uncertainty averse investor and significantly dominates the equal- and value-weighted prediction-sorted portfolios, which outperform the S&P 500.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 6.0/10 (capped from 8.5: transaction costs not modelled; see penalty flags)
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces a novel ensemble Gaussian Process Regression approach to handle computational complexity in non-parametric asset pricing. It combines rigorous Bayesian uncertainty quantification with extensive empirical validation on US equities over a 50+ year sample, yielding superior out-of-sample portfolio performance.

Research Flowchart

  flowchart TD
    A[Research Goal: Predict US stock returns & optimize portfolios using Ensemble GPR] --> B[Data Inputs: US Stocks & Macro Variables 1962–2016]
    B --> C[Methodology: Ensemble Gaussian Process Regression]
    C --> D[Computational Step: Divide Data & Perform Low-Complexity Online Inference]
    D --> E[Portfolio Construction: Uncertainty-Averse Mean-Variance Optimization]
    E --> F[Key Outcomes: Outperforms ML benchmarks in OOS R² & Sharpe Ratio vs S&P 500]