Credit spreads and investment opportunities

Abstract

Do credit spreads signal firm investment opportunities just like Tobin’s q? Because both credit spreads and Tobin’s q are market prices, they should contain similar information about the firm. I develop an investment model in which an analytical relation is established between the marginal q and the credit spreads. Using U.S. firm-level data, I find that credit spreads are a statistically important predictor of firm investment and their explanatory power is higher than that of Tobin’s q. The empirical evidence shows that credit spreads capture the effects of financial frictions, which drive a wedge between marginal and Tobin’s q.

Appendices

Appendix 1: Proof

$$\begin{aligned} log(I)\approx \Gamma +\frac{(n-1)\theta }{\gamma _{-}}log(CDS)-\frac{(n-1)\theta }{\gamma _{-}}log(y+m)(r+m) \end{aligned}$$

with $\gamma _{-}=0.5-\frac{\mu }{\sigma ^{2}}-\sqrt{(0.5-\frac{\mu }{\sigma ^{2}})^{2}+\frac{2(r+m)}{\sigma ^{2}}}$, $\Gamma =log\left[ \beta \left( \frac{n-1}{n\gamma }\right) \left( \frac{c+m}{\frac{c+m}{r+m}-\frac{\beta }{\psi }}\right) ^{\frac{\theta }{\gamma _{-}}}\right] ^{n-1}$, and $n=\{2,4,\ldots \}$.

We want to show the investment is more sensitive to credit spreads for firms with low growth and high volatility, and bonds with longer maturity. It is equivalent to show that $\partial |\frac{1}{\gamma _{-}}|/\partial \mu <0$, $\partial |\frac{1}{\gamma _{-}}|/\partial \sigma ^{2}>0$, and $\partial |\frac{1}{\gamma _{-}}|/\partial m<0$.

First, let $X=0.5-\frac{\mu }{\sigma ^{2}}$ and $C=\frac{2(r+m)}{\sigma ^{2}}$. It immediately follows that $\frac{\partial X}{\partial \mu }<0$, and $\frac{\partial \gamma _{-}}{\partial X}=1-\frac{1}{\sqrt{1+\frac{C}{X}}}$. Since $\sqrt{1+\frac{C}{X}}>\sqrt{1}=1$, we have $\frac{\partial \gamma _{-}}{\partial X}>0$. So $\frac{\partial \gamma _{-}}{\partial \mu }=\frac{\partial \gamma _{-}}{\partial X}\frac{\partial X}{\partial \mu }<0$, $\frac{\partial |\gamma _{-}|}{\partial \mu }=-\frac{\partial \gamma _{-}}{\partial \mu }>0$, and $\frac{\partial |\frac{1}{\gamma _{-}}|}{\partial \mu }<0$.

Second, let $X=0.5-\frac{\mu }{\sigma ^{2}}$, and $Y=\frac{2(r+m)}{\sigma ^{2}}$. It immediately follows that $\frac{\partial X}{\partial \sigma ^{2}}>0$, $\frac{\partial Y}{\partial \sigma ^{2}}<0$, and $\frac{\partial \gamma _{-}}{\partial Y}=-\frac{1}{\sqrt{X^{2}+Y}}<0$. So $\frac{\partial \gamma _{-}}{\partial Y}\frac{\partial Y}{\partial \sigma ^{2}}>0$. We have shown $\frac{\partial \gamma _{-}}{\partial X}>0$, so $\frac{\partial \gamma _{-}}{\partial X}\frac{\partial X}{\partial \sigma ^{2}}>0$. $\frac{\partial \gamma _{-}}{\partial \sigma ^{2}}=\frac{\partial \gamma _{-}}{\partial X}\frac{\partial X}{\partial \sigma ^{2}}+\frac{\partial \gamma _{-}}{\partial Y}\frac{\partial Y}{\partial \sigma ^{2}}>0$ and $\frac{\partial |\frac{1}{\gamma _{-}}|}{\partial \sigma ^{2}}>0$.

Third, let $Y=\frac{2(r+m)}{\sigma ^{2}}$. We have $\frac{\partial Y}{\partial m}>0$. $\frac{\partial \gamma _{-}}{\partial m}=\frac{\partial \gamma _{-}}{\partial Y}\frac{\partial Y}{\partial m}<0$, and $\frac{\partial |\frac{1}{\gamma _{-}}|}{\partial m}<0$.

Appendix 2: Variable definition

The firm accounting data come from the COMPUSTAT file. The sample period is from 1980 to 2011. Firms with a SIC code that is between 4900 and 4999, between 6000 and 6999, or greater 9000, are dropped. Firms with total asset below 10 million dollars (inflation adjusted in year 2004 dollars), with missing value in investment (item#30) or capital stock (item#7), and negative market to book ratio are also dropped.

Total debt is the sum of item#34 and item#9. Total book value of asset is item#6. Market value of asset is (item#6 + item#24 × item#25 − item#60 − item#74). Book leverage is the total debt divided by book value of asset; market leverage is the total debt divided by market value of asset; investment is the ratio of capital expenditures (item#30) to beginning-of-period capital stock (lagged item#7); Tobin’s q is the market value of assets divided by the book value of assets; cash flow is earnings before extraordinary items and depreciation (item#18 + item#14) divided by the beginning-of-period capital stock; payout ratio is the sum of item#21, item#19 and item#115 divided by item#13; equity issuance is item#108 divided by item#6; sales are item#12; cash holding is item#1; profitability is item#13; R&D is item#46. Sales, cash holding, profitability, and R&D are scaled by the beginning-of-period capital stock. All variables are winsorized at 1 % level each tail every year. Item numbers refer to COMPUSTAT annual data items.

Firm rating is S&P Long-Term Domestic Issuer Credit Rating. This item represents the current rating assigned to the company by Standard & Poor’s. The numeric value is 2 (AAA), 4 (AA+), 5 (AA), 6 (AA−), 7 (A+), 8 (A), 9 (A−), 10 (BBB+), 11 (BBB), 12 (BBB−), 13 (BB+), 14 (BB), 15 (BB−), 16 (B+), 17 (B), 18 (B−), 19 (CCC+), 20 (CCC), 21 (CCC−), 23 (CC), and 27 (D).

Volatility is the annualized monthly stock return volatility. The stock return data come from the Center for Research in Security Prices (CRSP). I calculate the standard deviation in month t using the previous 36 month (month t to month t − 35) stock returns, and require at least 24 month non-missing data.