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A common risk factor and the correlation between equity and corporate bond returns

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A growing body of literature documents that security prices within and across asset classes behave similarly highlighting the importance of investors’ common expectations about future risk and returns in the asset pricing. Consequently, variations in the common expectations of investors have a major role in determining the correlation among asset prices. We examine the role of these common expectations in determining the relationship between firm-level equity and bond returns. We use a novel measure of the common expectations defined as the difference in relative frequencies of words signalling excitement and anxiety in a large dataset of articles published by Reuters. Further, we also consider the VIX index and the indices of Baker and Wurgler (J Finance 61(4):1645–1680, 2006) and Huang et al. (Rev Financ Stud 28(3):791–837, 2015) as potential common factors. The results show that changes in common expectations, proxied by our index and the VIX, are significant in predicting variations in the correlation between equity and bond returns. An improvement in investors’ optimism about future risk and returns causes a weaker correlation. The effect is stronger for the riskiest firms and flattens as firms’ credit risk improves. By decomposing our index into the excitement and anxiety components, we find that this predictive power is due to changes in the anxiety components.

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Correspondence to Amer Demirovic.

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The threshold values for the dummy variables are determined in the spirit of Hansen (2000). We basically regress the conditional correlation between equity and bond returns on all potential combinations of models using predetermined threshold increments and select the optimal model based on the Akaike information criterion (AIC).

We assign \(D_{it}^{\text{k}} = I(\tau_{{{\text{k}} - 1}} \le X_{it} < \tau_{\text{k}} )\) as the dummy variables, where \(X_{it}\) is the value of a variable for firm i at time t, \(\tau_{\text{k}}\) are thresholds, and \(I\left( . \right)\) is the indicator function. \(\tau_{0}\) is equal to the variable’s sample minimum, the first threshold, \(\tau_{1}\), is equal to the lower limit \(K_{\text{L}}\), and the last threshold, \(\tau_{\text{n}}\), is equal to the upper limit \(K_{\text{U}}\). The difference between the lower and upper limits covers the large majority of observations. The first threshold, \(\tau_{1}\), increases by an increment of 0.1, and the difference between two thresholds,\(s\), starts at 0.5 and increases by an increment of 0.5, i.e. \(\delta\) = 0.5, 1.0, 1.5,…. The threshold selection procedure involves estimation of models with all possible combinations of the number or thresholds (n), the starting value of \(\tau_{1}\), and the differences between two thresholds (\(\delta\)), which covers the range from \(K_{\text{L}}\) to \(K_{\text{U}}\).

In the case of one threshold, the procedure simplifies to estimating the models with one dummy variable \(D_{it}^{1} = I(X_{it} < \tau_{1} )\) with \(\tau_{1} = K_{\text{L}} ,K_{\text{L}} + 0.1,K_{\text{L}} + 0.2, \ldots .,K_{\text{U}}\).

In the case of two thresholds, where \(\tau_{1} = K_{\text{L}} ,K_{\text{L}} + 0.1,K_{\text{L}} + 0.2, \ldots .,K_{\text{U}} - \delta\) and \(\tau_{2} = \tau_{1} + \delta\).

In the case of n thresholds, \(D_{it}^{1} = I(X_{it} < \tau_{1} )\) and \(D_{it}^{\text{k}} = I\left( {\tau_{{{\text{k}} - 1}} \le X_{it} < \tau_{\text{k}} } \right),\) where \(\tau_{1} = K_{\text{L}} ,K_{\text{L}}\,+\,0.1,K_{\text{L}} + 0.2, \ldots .,K_{\text{U}} - \left( {n - 1} \right)\delta\) and \(\tau_{\text{k}} = \tau_{1}\,+\,\left( {k - 1} \right)\delta\).

Performing the above procedure on the distance to default variable requires estimation of 4753 models with all combinations of the number of dummies (1–26), the starting value of \(\tau_{1} = 0.5\), and the differences between two thresholds \(\delta\) = 0.5, 1, 1.5…, which cover the range from \(K_{\text{L}} = 0.5\) to \(K_{\text{U}} = 13\). The values between these limits cover 98% of the observations. The lowest AIC gives a model with 15 dummy variables or thresholds, and the lowest SSE gives a model with 26 dummy variables. The greatest improvement in AIC (94%) and SSE (90%) is achieved by the best performing model with four dummies. Therefore, we use the best performing four-dummy model in order to present a model that is as parsimonious as possible. Thus, the optimal thresholds for the distance to default dummies are 0.8, 1.8, 2.8, and 3.8. The threshold values for the robustness variables are selected in the same manner.

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Demirovic, A., Kabiri, A., Tuckett, D. et al. A common risk factor and the correlation between equity and corporate bond returns. J Asset Manag (2020). https://doi.org/10.1057/s41260-020-00151-8

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  • Investor sentiment
  • Equity–bond correlation
  • Credit risk
  • Systematic risk