Analyzing Stock and Bond Return Correlations: A Dynamic Factor Model Approach

1. The Determinants of Stock and Bond Return Comovements Lieven Baele Tilburg University, CentER, Netspar Geert Bekaert Columbia University, NBER, CEPR Koen Inghelbrecht Ghent University

2. Research questions • Establish stylized facts with respect to stock-bond return correlations. • Explain level and time variation in stock-bond return correlations using dynamic factor model. Only fundamental factors are considered (but we consider wide range) • Consider non-fundamental instruments to explain any residual correlation.

3. Stylized Facts

4. Stylized Facts • Data: • NYSE-AMEX-NASDAQ value-weighted total excess returns from CRSP. • 10-Year excess Bond Returns from CRSP US Treasury and Inflation Module. • Unconditional Correlation:

5. Quarterly Conditional correlations Unconditional Correlation Ex-Post Correlation

6. In search for fundamentals: Explain average stock-bond correlation and its time variation through common exposures to economic state variables.

7. Methodology: intuition State of the Economy CF Uncertainty M Inflation Interest Rate Output Risk Aversion Bond Return Stock Return Comovement

8. Dynamic Factor Model • Consider following model: Stock/Bond returns Expected Stock/Bond returns (Time-Varying) Factor Exposures Model Residuals Shock to economic State variable Diagonal factor VCV

9. Model Implied Correlations • The fundamental-implied correlation is given by: • Implications: • Correlations driven by Betas and Factor Variances. • Positive (negative) correlation if stock/bond betas have same (different) signs.

10. Task List Select relevant Economic State Variables Identify Shocks in State Variables Model Conditional Variance of State Variable Shocks Relate Fundamental Shocks to Stock-bond Returns Constant Factor Exposures Time-Varying Factor Exposures Calculate Model-Implied Stock-Bond Return Correlations

11. Identifying shocks in state variables • We need to identify unexpected shocks in the state variables. • For interpretational purposes, shocks also need to be pure, i.e. stripped of the effects of (shocks to) other state variables. • Two methods: • Standard Vector AutoRegressive model (VAR) • Structural New-Keynesian Model (structural VAR) • Imposes restrictions that come from economic theory • Parameters have ‘interpretation’. • Only for simple model with output, inflation, and interest rate as state variables.

12. Factor Volatility • The model for conditional factor volatility contains two building blocks: • A Regime-Switching Intercept • Lagged information variables • Example of three factor model: shifts variance of exogenous shocks shifts variance of monetary policy (interest rate) shocks

13. Some take-aways from our NK model estimates Smoothed Probability of being in High Volatility Regime

14. Constant vs Time-Varying Betas • Simple affine asset pricing models imply asset returns are constant beta functions of innovations in state variables. • We allow betas to vary through time, but put sufficient structure on betas to avoid picking up non-fundamental sources: • Duration Effects: Interest rate sensitivity increases with duration • Bonds: duration decreases with interest rate level. • Equity: duration decreases with level of dividend yield • Uncertainty:dispersion in beliefs increases the effect of economic shocks on returns (David and Veronesi (04)).

15. Summary of Fundamental Models • Best models explain some of time variation in S-B Correlations • Economically motivated models work better than a-theoretical VAR • Positive Correlations before Great Moderation, then zero to negative correlations. • Risk Aversion – Uncertainty are Key • Yet, even best models fails to fit both magnitude and timing • Our positive correlations are not positive enough. • Our switch to low (negative) correlations is too early • Our negative correlations are not negative enough.

16. Example: 4-factor model • Results from constant beta model: • Joint significance (blue) only for Fundamental Risk Aversion factor. • Comparable performance when Risk Aversion is replaced by economic uncertainty variables. • Allowing betas to vary through time improves fit with ex-post correlatons.

17. Fundamental model versus data

18. In search for alternative explanations

19. Alternative explanations #1 • We relate residual stock-bond return correlations to: • Flight-to-safety • Investors switch from the risky asset, stocks, to a safe haven, bonds, in times of increases stock market uncertainty. • Proxies: VIX Implied Volatility, Conditional equity volatility from statistical model. • Consumer Confidence • Consumer confidence may contain an additional component that proxies for particular behavioral biases. • We measure consumer confidence by the University of Michigan’s Consumer Sentiment Index.

20. Alternative explanations #2 • We relate residual stock-bond return correlations to: • Flight-to-Safety • Consumer Confidence • Cross-Market Liquidity Effects • Flight-to-Liquidity from Stocks to Bonds : Negative effect on stock-bond correlation. This effect is likely to be correlated with flight-to-safety. • Common Liquidity shocks (possibly monetary policy driven) : Positive shock to stock-bond correlations. • Bond liquidity measure based on quoted bid-ask spreads. • Equity liquidity measure based on proportion of zero daily returns/volumes.

21. Alternative explanations: Findings • Residual stock-bond return correlations... • Decrease when there are large shocks in equity market volatility • Consistent with flight-to-safety story. • Are unaffected by shocks to consumer confidence • Feature already captured by fundamental model. • Decrease when liquidity in equity market dries up • Consistent with flight-to-liquidity story. • Increase when liquidity dries up in both equity and bond market • Increase in liquidity risk premiums from common liquidity shock leads to lower returns in both markets, and hence positive correlations.

22. Conclusions • We give maximum flexibility for economic fundamentals to explain the time variation in stock-bond correlations: • Wide range of fundamentals. • Flexible specifications. • Despite flexibility, we do not get close to explaining the average/conditional level of stock-bond correlations. • Alternative (non-fundamental) explanations look more promising.

23. Future Work • How much do fundamental – non-fundamental factors explain of stock – bond return volatility? • Low versus high-frequency components in volatility and correlations. • Incorporate liquidity in the fundamental model. • Stock-bond correlations at different frequencies (daily -> 5 year) • International evidence • Surprising commonality in stock-bond return correlations across markets.

24. International Evidence

25. International Evidence