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Bond Risk Premiums with Machine Learning

Journal: Review of Financial Studies

Date: 20210201

Author: Bianchi, Daniele; Buchner, Matthias; Tamoni, Andrea

Abstract:
We show that machine learning methods, in particular, extreme trees and neural networks (NNs), provide strong statistical evidence in favor of bond return predictability. NN forecasts based on macroeconomic and yield information translate into economic gains that are larger than those obtained using yields alone. Interestingly, the nature of unspanned factors changes along the yield curve: stock- and labor-market-related variables are more relevant for short-term maturities, whereas output and income variables matter more for longer maturities. Finally, NN forecasts correlate with proxies for time-varying risk aversion and uncertainty, lending support to models featuring both channels.

Link: Google Scholar

Key Findings

Superior Machine Learning Performance

Neural networks and extreme trees detect significant predictable variations in bond returns, outperforming traditional methods with out-of-sample R² values up to 26.4% for single hidden layer networks.

Macro Information Enhances Predictions

Adding macroeconomic variables to forward rates improves prediction accuracy by approximately 10 percentage points across maturities, with certainty equivalent returns up to 5% annually.

Economic Drivers Identified

Neural network forecasts are countercyclical and strongly linked to macroeconomic uncertainty and time-varying risk aversion, supporting both risk prices and time-varying risk channels.

Bond Return Predictability Across Models

  • Neural networks achieve highest predictive accuracy with 26.4% R² out-of-sample
  • Extreme trees show strong performance with 24.6% R²
  • Traditional PCA methods achieve lower R² of 10.2%

Economic Value of Predictions

  • Adding macro variables increases CER from 3.55% to 5.02% annually
  • Economic gains are statistically significant at 5% level
  • Results hold across different utility specifications

Performance Across Economic Cycles

  • Neural networks show strong performance in both expansions and recessions
  • Sharpe ratios are higher during recessions (2.098 vs 1.093)
  • Demonstrates robust performance across economic cycles

Contribution and Implications

  • Demonstrates superior predictive power of neural networks even in low-dimensional bond market settings
  • Provides evidence for unspanned macroeconomic information in bond returns
  • Supports theoretical models featuring both time-varying risk prices and quantities

Data Sources

  • Model comparison chart constructed using data from Table 1, showing out-of-sample R² values for different prediction methods
  • CER comparison based on Table 5, presenting economic value metrics for different modeling approaches
  • Economic cycle performance visualization derived from Table 6, showing Sharpe ratios across different market conditions