Common Factors and the Correlation between the Equity and Bond

Common factors are generally expected to influence the correlation between asset returns. Longin and Solnik (2001), and Ang and Bekaert (2002) find that the correlation between the returns in international equity markets tends to increase in turbulent times. In a recent study, Bartram and Bodnar (2009) document a sharp increase in the correlation between international equity markets during the recent financial crisis in 2008. Ben-David, Franzoni and Moussawi (2012) report that hedge funds rushed to exit equity markets during the 2007-2009 crisis which implies that the average correlation

These studies suggest that common factors influence the correlation between equities and that their importance increases in turbulent times when investors tend to decrease their exposure to equity markets in general. If investors attempt to cut their risk exposure in all markets then prices in equity and bond markets will be subject to downward pressure. As a result, the correlation between equity and bond returns will increase. Belke and Gokus (2011) provide some evidence that this effect is present in the returns of different securities issued by the same firm. They examine the volatility patterns of the credit default swap spreads, the bond yield spreads and the equity returns of four large banks, and report that the correlations strongly vary over time and increase in absolute values after the outbreak of the recent financial crisis in 2007. The conditional correlations between the values of equity and debt were negative before the crisis and turned positive during the crisis.

Scheicher (2009) documents a significant increase in the conditional correlation between the equity and credit default swap markets during the market turmoil of May 2005 caused by the S&P’s decision to downgrade General Motors and Ford to the speculative status. Besides the firm-level equity volatility, the slope of the swap curve (defined as the 10 year swap rate minus the three-month money market rate) is reported to be a significant determinant of the correlation. Therefore, the author concludes that the correlation is determined by both firm-level and common factors. The impact of common factors on the correlation between equity and bond returns can also be analysed at the micro level. The structural model implies that the equity and bond returns are both the functions of the value of firm’s assets. Campello, Chen and Zhang (2008) show that the equity premium equals the bond risk premium multiplied by the unobservable elasticity of the equity value with respect to the bond value. Since the equity premium depends on the exposure to systematic risks, it follows that the bond premium also depends on systematic factors. Elton et al. (2001) show that the common equity pricing factors of Fama and French (1993) are significant in explaining the bond credit spread. Campbell and Taksler (2003) report that both excess equity market return and market volatility are significant determinants of the credit spread. The risk-free rate is the only common variable in the structural model. It is assumed that the value of firm’s assets grows at the risk-free rate. Therefore, an increase in the risk-

free rate leads to an increase in the value of assets which positively affects the value of equity. On the other hand, a higher risk-free interest rate implies a higher discount rate for the future coupon and principal payments and therefore a lower bond value. This induces a negative correlation between the equity and bond returns. Furthermore, if considered as an indicator of the health of the overall economy, the risk free-rate should have a negative impact upon the correlation between equity and bond returns as a higher risk-free rate is associated with better macroeconomic conditions.

Based on the above discussion, the following hypotheses are put forward:

H5: Systematic risk has a positive impact upon the correlation between the equity and bond returns.

The empirical testing is conducted by regressing the conditional correlation between the equity and bond returns on the risk-free rate, the S&P 500 index returns and volatility. Let be the conditional correlation between the equity and bond returns at time t, be the estimated volatility of the S&P 500 index, and be the return of the same index at time t. Then Hypothesis 5 is tested by assessing the statistical significance of coefficients b and c in the following regression:

= + + + (6.6)

The above model ignores different exposures of firms to systematic risks (i.e. different firm betas) and therefore may bias the importance of systematic risks downward. To examine this, the returns and volatility of the S&P 500 index are replaced by firm-level measures of systematic equity returns and the volatility of systematic equity returns, which are estimated by the three factor model of Fama and French (1993)5_.

= + + + (6.7)

H6: The risk-free rate has a negative impact upon the correlation between the equity and bond returns.

To test this hypothesis empirically, Model 6.6 is extended as follows.

= + + + + + (6.8)

where is the risk-free rate and is the difference between the redemption yields on 10-year and 2-year Treasury bonds. Significantly negative coefficients d and e lead to the acceptance or rejection of Hypothesis 6.

6.3. Methodology