Trends in stock-bond correlations

ABSTRACT

Previous studies document the existence of long-run trends in comovements in the stock and bond markets. Following these findings, this article examines possible trends in stock-bond return correlations. To this end, we introduce a trend component into a smooth transition regression (STR) model including the multiple transition variables of Aslanidis and Christiansen (2012). The results indicate the existence of significant decreasing trends in stock-bond correlations for many advanced safer countries. In addition, although stock market volatility continues to be an important factor in stock-bond correlations, the short rate and yield spread become only marginally significant once we introduce the trend component. Our out-of-sample analysis also demonstrates that the STR model, including the volatility index and time trend as the transition variables, dominates other models. Furthermore, we find a significant increase in stock-bond correlations for riskier euro countries around the beginning of the euro crisis. Our findings of decreasing and increasing trends in stock-bond correlations can be considered a consequence of the decreasing effects of diversification and more intensive flight-to-quality behaviour that have taken place in recent years and after the euro crisis.

KEYWORDS:

• Comovement
• flight-to-quality
• diversification effect
• smooth transition

JEL CLASSIFICATION:

• C22
• G15
• G17

Acknowledgements

We thank the editor and an anonymous referee for thoughtful comments and suggestions which improved the article considerably. We are also indebted to seminar participants at Research Institute of Economy, Trade and Industry (RIETI), Hitotsubashi University, Workshop on Financial Engineering and Financial Econometrics and Workshop on New Development in Statistics of Economic Risk. A part of this research was conducted while the second author was a visiting fellow at RIETI. The second author thanks the RIETI for their support and hospitality during his stay.

Notes

¹ As a realized correlation, Aslanidis and Christiansen (2012) use the weekly sample correlation calculated from 5-minute high frequency stock and bond returns without demeaning, whereas we use monthly sample correlations based on daily data with demeaning.

² More precisely, ${\rho }_1$ is the average ‘Fisher-transformed correlation’. In what follows, we simply refer to this as ‘correlation’.

³ In practice, all transition variables are standardized to have a mean of 0 and a variance of 1 as Aslanidis and Christiansen (2012).

⁴ Specifically, we assume ${\gamma }_1$ associated with VIX is positive for all estimated models.

⁵ We confirm that the German and UK VIX indices are highly correlated with the US VIX, with a correlation that is greater than 0.8. We also confirm that we can obtain quantitatively similar results even if we use each country’s VIX data with a shorter sample period.

⁶ Time trend for the correlations is calculated as follows. First we calculate the time trend in FRC as

$TTFR{C}_t=\frac{{\hat{\rho }}_1\{1-\hat{F}(s_{t-1})\}+{\hat{\rho }}_2\hat{F}(s_{t-1})}{1-\hat{\varphi }}$

holding the all transition variables other than a time trend variable constant at their mean values of zero. Then, we applied the inverse of Fisher transformation (2) to $TTFR{C}_t$ to obtain the time trend component for the correlation.

⁷ Since the WGBI 7–10 year total return index for PO is not available, we use the WGBI all maturities index.

⁸ Specifically, we use stock index returns from ASX 200 (AU), SPTSX 60 (CA), CAC 40 (FR), SMI (SW), MIB (IT), PSI (PO) and IBEX 35 (SP).

⁹ If the transition function looks like a step function, ${\gamma }_2$ associated with time trend becomes very large and is not well determined, since the log-likelihood becomes insensitive with ${\gamma }_2$. In these cases (for JP, IT, PO and SP), we have fixed ${\gamma }_2$ at an upper bound equal to 300 and have re-estimated the model. Additionally, if ${\gamma }_1$ related to VIX reaches its lower limit of 0, specifically for PO and SP, we have fixed ${\gamma }_1$ at 0 and have re-estimated the model. For these cases, the parameter’s standard errors are denoted by NA.

Additional information

Funding

The authors would like to acknowledge the financial support of this work from the Japan Center for Economic Research.