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Missing Values Handling for Machine Learning Portfolios

Journal: Journal of Financial Economics

Date: 20240501

Author: Chen, Andrew Y.; McCoy, Jack

Abstract:
We characterize the structure and origins of missingness for 159 cross-sectional return predictors and study missing value handling for portfolios constructed using machine learning. Simply imputing with cross-sectional means performs well compared to rigorous expectation-maximization methods. This stems from three facts about predictor data: (1) missingness occurs in large blocks organized by time, (2) cross-sectional correlations are small, and (3) missingness tends to occur in blocks organized by the underlying data source. As a result, observed data provide little information about missing data. Sophisticated imputations introduce estimation noise that can lead to underperformance if machine learning is not carefully applied.

Link: Google Scholar

Key Findings

Simple Mean Imputation Works Well

Imputing missing values with cross-sectional means performs similarly to more sophisticated imputation methods for machine learning portfolios, with potential equal-weighted returns of 66% per year.

Limited Information in Missing Data

The observed predictors provide little information about missing values due to block missingness patterns and low cross-sectional correlations between predictors.

Sophisticated Imputation Can Underperform

Complex imputation methods like EM can introduce estimation noise that leads to underperformance if machine learning is not carefully applied.

Portfolio Returns Across Imputation Methods

  • Equal-weighted returns around 65-68% annually across different imputation methods
  • Value-weighted returns around 37-43% annually
  • Neural network (NN1/NN3) forecasts show consistently strong performance regardless of imputation method

Predictor Correlations Distribution

  • Most correlations cluster near zero (-0.25 to +0.25)
  • First 10 principal components explain only 40% of total variance
  • Low correlations suggest limited information gain from sophisticated imputation

Imputation Error by Market Cap

  • Higher imputation errors for small-cap stocks (RMSE > 0.70)
  • Error magnitude approaches that of simple mean imputation (RMSE = 1.0) for smallest stocks
  • More reliable imputations for large-cap stocks

Contribution and Implications

  • Provides rigorous justification for the common practice of mean imputation in machine learning asset pricing studies
  • Demonstrates that sophisticated imputation methods may not improve performance despite theoretical advantages
  • Highlights the importance of careful implementation when using complex imputation methods with machine learning

Data Sources

  • Portfolio returns visualization based on Table 4 showing performance across imputation and forecasting methods
  • Correlation distribution chart based on Figure 3 showing empirical distribution of predictor correlations
  • Imputation error chart based on Figure 4 showing out-of-sample RMSE by market equity decile