## 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*.

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## Notes

Perhaps the most prominent example of the empirical failure of

*q*-theory is the investment cash-flow sensitivity. Since the seminal work of Fazzari et al. (1988) and summarized by Hubbard (1998), a lot of empirical papers show that investment responds strongly to movements in internal funds (proxied by cash flow) even after one controls for Tobin’s*q*. However, the recent literature (e.g., Kaplan and Zingales 1997; Erickson and Whited 2000; Alti 2003) finds that cash-flow sensitivity may not be the direct evidence for the failure of*q*-theory. Chen and Chen (2012) find that its effects diminish over time.Lehman Brothers collects bid prices from its dealers for bonds that are either traded by the firm or tracked by one of its published bond indices. In months where no bid is posted, a matrix price is recorded as a “best guess”.

Gurkaynak et al. (2007) estimate the U.S. Treasury yield curve from 1961 to date and their daily continuously compounded zero-coupon yields range from 1 to 30 years. I interpolate those yields to get monthly data using cubic method so that on each transaction day we know the risk free discount factors for those cash flows. The data are available at http://www.federalreserve.gov/pubs/feds/2006/200628/200628abs.html.

The numeric values for bond ratings are 1 (Aaa), 2 (Aa1), 3 (Aa2), 4 (Aa3), 5 (A1), 6 (A2), 7 (A3), 8 (Baa1), 9 (Baa2), 10 (Baa3), 11 (Ba1), 12 (Ba2), 13 (Ba3), 14 (B1), 15 (B2), 16 (B3), 17 (Caa1), 18 (Caa2), 19 (Caa3), 20 (Ca), 21 (C), and 25 (D).

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## Acknowledgments

I thank Murray Frank, Raj Singh, Philip Bond, Robert Goldstein, Frederico Belo, Tracy Wang, Santiago Bazdresch, Jianfeng Yu, Jeremy Graveline, Erica Li, Si Guo, Chaoqun Chen, Xin Li, and seminar participants at the University of Minnesota, the Georgia Institute of Technology, the 2011 China International Conference in Finance, and the 2011 Financial Management Association Annual Meeting for their comments and suggestions. I also gratefully acknowledge financial support from the Carlson School of Management at the University of Minnesota Twin Cities. All errors are my own.

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## Appendices

### Appendix 1: Proof

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.

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Shen, T. Credit spreads and investment opportunities.
*Rev Quant Finan Acc* **48**, 117–152 (2017). https://doi.org/10.1007/s11156-015-0545-x

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DOI: https://doi.org/10.1007/s11156-015-0545-x