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07.01.2019 | Research Article

Cash flows risk, capital structure, and corporate bond yields

verfasst von: Berardino Palazzo

Erschienen in: Annals of Finance | Ausgabe 3/2019

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Abstract

This paper explores the effects of a firm’s cash flow systematic risk on its optimal capital structure. In a model where firms are allowed to borrow resources from a competitive lending sector, those with cash flows more correlated with the aggregate economy (i.e., firms with riskier assets in place) choose a lower leverage given their higher expected financing costs. On the other hand, less risky firms, having lower expected financing costs, optimally choose to issue more debt to exploit a tax advantage. The model predicts that cash flow systematic risk is negatively correlated with leverage and corporate bond yields.

Vorheriger Artikel Optimal bailouts, bank’s incentive and risk

Nächster Artikel Dynamic portfolio strategies under a fully correlated jump-diffusion process

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Differently from George and Hwang (2010), who focus exclusively on book-leverage, Gomes and Schmid (2010) and Ozdagli (2012) also study the relation between market leverage and equity returns. In both models, investment and financing choices are endogenous, but while in Ozdagli (2012) corporate debt is risk-free, in Gomes and Schmid (2010) firms can issue risky corporate debt.

A more realistic setting with costly debt restructuring at time 1 will only complicate the analysis without changing the key predictions of the model.

The cash flow produced at time $t=1$ is discounted using the factor

$$\begin{aligned} M_1= & {} e^{m_{1}}=e^{-r -\frac{1}{2}\sigma _z^2-\sigma _z \varepsilon _{z,1}}, \end{aligned}$$

where $\varepsilon _{z,1}\sim N(0,1)$ is the aggregate shock at time $t=1$. The above formulation implies $E_0[M_1]=e^{-r}=1/R$. The pay-off produced by the risky asset at time 1 is $e^{x_{1}}$, where $x_{1}$ is equal to

$$\begin{aligned} x_{1}=\mu -\frac{1}{2}\sigma _x^2+\sigma _x \varepsilon _{x,1}. \end{aligned}$$

The cash flow shock, $\varepsilon _{x,1}\sim N(0,1)$, is correlated with $\varepsilon _{z,1}$, thus making the cash flows produced by the asset in place risky. In what follows, we assume that $COV(\varepsilon _{z,1},\varepsilon _{x,1})=\sigma _{x,z}$ and, as a consequence, $COV(x_{1},m_{1})=-\sigma _x\sigma _z\sigma _{x,z}$. As in Berk et al. (1999), the systematic risk of a project’s cash flow, $\beta _{xm}$, is equal to $\sigma _x\sigma _z\sigma _{x,z}$.

See “Appendix A.1” for the derivation.

$\frac{ds_1(N_1)}{dN_1}=(1-\tau )R \left[ \frac{\varPhi _2'(\sigma _x(N_1-\overline{L_1}))^{-1} }{(1-\varPhi _2)^2}\right] >0$, $\frac{ds_1(N_1)}{d\beta _{xm}} =(1-\tau )R\left[ \frac{\varPhi _2'(\sigma _x )^{-1} }{(1-\varPhi _2)^2}\right] >0$, and $\frac{ds_1(N_1)}{d\mu }=(1-\tau )R\left[ \frac{-\varPhi _2'(\sigma _x )^{-1} }{(1-\varPhi _2)^2}\right] <0$.

The first derivative of $\hat{R} +s_1(N_1)$ is $\frac{ds_1(N_1)}{dN_1}$, while the first derivative of $N_1\frac{ds_1(N_1)}{dN_1}$ is $\frac{ds_1(N_1)}{dN_1}+N_1\frac{ds_1(N_1)}{dN_1dN_1} $, which is larger for each value of $N_1>\overline{L_1}$ given the convexity of the credit spread. An alternative argument is the following. Let us assume that there is more than one maximum. It follows that there must be two values of $N_1$, $N_1^a$ and $N_1^b$ with $\overline{L_1}<N_1^a < N_1^b$, such that $B_1(N^a_1)=B_1(N^b_1)=\overline{B}$ and $B_1(N_1)<\overline{B}$ for all $N_1 \in (N_1^a,N_1^b)$. In the interval $(N_1^a,N_1^b)$, $B_1$ is first decreasing and then increasing in $N_1$; it follows that the credit spread $N_1/B_1$ is not increasing at an increasing rate over $(N_1^a,N_1^b)$. This violates the convexity of the credit spread function.

Consider the following result:

$$\begin{aligned} \frac{d\varPhi \left( f(x)-\sigma _x\right) }{dx}=\phi (f(x) -\sigma _x)f_x(x)=\frac{1}{\sqrt{2\pi }}e^{-\frac{(f(x)-\sigma _x)^2}{2}}f_x(x) =\phi (f(x))e^{f(x)\sigma _x-\frac{\sigma _x^2}{2}}f_x(x), \end{aligned}$$

where $\phi $ is the probability distribution of a standard normal variable. If we set $f(x)=\varepsilon _{i}+\frac{\beta _{xm}}{\sigma _x}$, then

$$\begin{aligned} (1-\tau )e^{\mu -\beta _{xm}}\frac{\partial \varPhi _3}{\partial N_1} =\frac{1-\tau }{\sigma _x}\phi \left( \varepsilon _{i}+\frac{\beta _{xm}}{\sigma _x}\right) =(N_1+1)\frac{\partial \varPhi _4}{\partial N_1}. \end{aligned}$$

This allows us to simplify the first-order condition in Eq. (26):

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Titel: Cash flows risk, capital structure, and corporate bond yields
verfasst von: Berardino Palazzo
Publikationsdatum: 07.01.2019
Verlag: Springer Berlin Heidelberg
Erschienen in: Annals of Finance / Ausgabe 3/2019
Print ISSN: 1614-2446
Elektronische ISSN: 1614-2454
DOI: https://doi.org/10.1007/s10436-018-00342-9

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