Is the effectiveness of government bonds as a diversifier of equity risk weakened after the Covid-19 crisis?†

Abstract

In this paper, we examine how the relationship between the US stock index and the US Treasury market has changed after the start of the Covid-19 crisis. For that purpose, we compute upside and downside correlations between the index and interest rates of different maturities. Our main findings are as follows: first, we document the correlation asymmetry. The downside correlation is higher than the upside correlation before the crisis but the opposite is true after the start of the crisis for all maturities. The magnitude of the change is large for short-term maturities but small for long-term maturities. It indicates that the benefit of holding the short-term government bonds as a diversifier for stock investors is weakened after the start of the Covid-19 crisis. We also study the economic impact of ignoring the correlation asymmetry and report that the cost increased after the start of the crisis in general.

Keywords:

• Non-normality
• Dynamic Conditional Score models
• DCC models
• Regime-switching models
• Optimal asset allocation

JEL Classification:

• C53
• G11
• G12

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

‡ For example, see Bloomberg article titled with ‘Bonds No Longer Work to Diversify Stock Risk, Credit Suisse Says’ by Joanna Ossinger published on August 25, 2020.

§ The concept of exceedance correlation has been used to understand the asymmetric relationship between two financial markets. For example, González-Pedraz et al. (2015) employ the exceedance correlations to investigate the relationship between the oil, gold, and stock markets during the 1990–2010 period and find the asymmetric relationship between them.

† A bivariate normal mixture, a bivariate t-distribution mixture, and a threshold DCC models are the same as in Sakurai and Kurosaki (2020). We extend the list of estimated models by developing the DCS normal mixture model.

† Although not reported, we have compared the performance of our threshold DCC with the original threshold DCC model developed by Cappiello et al. (2010) by looking at the H statistics. As expected, our threshold DCC generally outperforms the original threshold DCC model, especially at short-term maturities during the Covid-19 crisis where the correlation asymmetry is remarkable, due to the additional term.

‡ We also used another date (September 21, 2010) as the start date of the whole sample, and selected February 1, 2020, as the start date of the Covid-19 crisis. But our main results below do not change qualitatively.

§ The dimension of the EGARCH model is 1. The dimension of the correlation models (i.e. mixture and threshold DCC models) is 2. One dimension for the stock return and another dimension is for the interest rate change for one out of eight maturities.

† Longin and Solnik (2001) find that the empirical downside correlation is higher than the empirical upside correlation between stock indices in the following five countries: US, UK, France, Germany, and Japan.

† The time series of the EPU and its decompositions are available at https://www.policyuncertainty.com.

† We do not use the policy rate and its volatility as the Federal Funds Rate has been stable during the Covid-19 crisis period due to the zero interest rate policy in our regression. We also do not include the level of interest rates as an explanatory variable in our regression because the definition of the exceedance correlation uses the level of interest rates as threshold θ.

† $\text{ZIRP flag}$ is equal to 1 during the zero interest rate policy period and otherwise 0.

‡ The start date is determined by the data availability of the 10-year break even inflation data at the FRED.

† We can see that the FPU case ($-274.09$) is higher than the QE case ($-294.27$) for the first model. Also, the FPU case ($-274.14$) is higher than the QE case ($-291.98$) for the second model.

† The previous studies on joint pricing of stocks and the government bonds under the consumption CAPM include but not limited to: Bakaert et al. (2010) and Lou et al. (2021).

† We note that the empirical exceedance correlations in figure 1 do not change qualitatively even when we replace nominal stock return with real excess stock return and nominal bond return with nominal excess bond return in order to be consistent with equations (19(19) $\begin{array}{rl}\text{E}\left[r_{t+1}^E\right]& =-\frac{1}{2}{\sigma }_E^2+\gamma (1+\lambda (s_t\left)\right){\sigma }_x^2,\end{array}$(19) ) and (20(20) $\begin{array}{rl}\text{E}\left[\mathrm{\Delta }{i}_{t+1}\right]& =\frac{1}{2}{\sigma }_{\mathrm{\Delta }i}^2+\gamma (1+\lambda (s_t\left)\right){\sigma }_x{\sigma }_{\pi }{\rho }_{x,\pi },\end{array}$(20) ). Since the Federal Funds rates are close to zero during the Covid-19 period, we consider that nominal excess return for bond $-\text{E}[\mathrm{\Delta }{i}_{t+1}-r_{ffr,t}]\approx -\text{E}\left[\mathrm{\Delta }{i}_{t+1}\right]$ where $r_{ffr}$ is the Federal Fund rates.

‡ We may also consider the regime-dependent risk aversion parameter to explain the correlation asymmetry but it is more complicated as the sensitivity function $\lambda \left(s_t\right)$ is a nonlinear function of γ.

§ In the simulation, we assume that the regime changes are described by a mixture model and set parameters equal to the following values: ${\sigma }_x={\sigma }_c=1\mathrm{\%}$ and ${\sigma }_{\pi }=1\mathrm{\%}$, $({\sigma }_E^{low},{\sigma }_E^{high})=(0.1,04)$, (${\sigma }_{\mathrm{\Delta }i}^{high},{\sigma }_{\mathrm{\Delta }i}^{low})=(0.4,0.1)$, (${\rho }_{x,\pi }^{good},{\rho }_{x,\pi }^{bad})=(0.95,-0.95)$), $\gamma =2$, ${\theta }_0=0.87$, ${\theta }_1={\theta }_2=0$, and the mixing probability p = 0.5. Since our model is very simple, some parameter values are not plausible. Generating the correlation asymmetry under more realistic parameter values is left for future research.