Abstract

What determines the maturity structure of debt? In this article, I develop a simple model to explore how the optimal maturity of debt issued by a firm (or a country) depends both on the firm's cyclical state and other features of the economic environment in which it operates.

I find that firms with better current earnings and better growth prospects issue debt with longer maturity, while firms operating in more-volatile environments issue debt with shorter maturity. Yield to maturity is a poor indicator of the risk of debt issued by a firm. The reason is simple: Yield to maturity captures both default risk and a component that is a pseudo term premium. In the model, the market does require a term premium and one appears only because of the risk of default. It is not possible to separate the impact of maturity and risk.

Rodolfo E. Manuelli is a professor of economics at Washington University in St. Louis and a research fellow at the Federal Reserve Bank of St. Louis. The author thanks Sid Sanghi for excellent research assistance and the Federal Reserve Bank of St. Louis for financial support.

INTRODUCTION

It is a standard view that borrowing short term exposes debtors—both firms and countries—to potential refinancing shocks. In some cases, the existence of short-term debt has been blamed for the subsequent poor performance of the borrower. In the case of the domestic financial system, the mismatch between (short) liabilities and (long) assets is sometimes viewed as a factor that explains the deep Financial Crisis of 2007-09 (see, for example, Brunnermeier and Oemkhe, 2013). Kacperczyk and Schnabl (2010) review the evidence of the role that commercial paper (which is short-term debt) played in the Finacial Crisis. In the case of sovereign debt, Rodrik and Velasco (1999) argue that short-term debt increases the likelihood of a crisis. Benmelech and Dvir (2011) document how East Asian countries shortened the maturity of their debt before the financial crisis in the 1990s. Broner, Lorenzoni, and Schmukler (2013) find that during crisis times it is optimal for countries to issue short-term debt.

Why do some firms (and countries) borrow short and others long? There is some evidence that shows that firms (or countries) that find themselves in a "weak" position at the time they need to borrow—for example, when their current income is relatively low—tend to issue relatively short-term debt. In some cases, this has been interpreted as the cause of a subsequent default. This simplistic interpretation hinges on the observation that, since default is caused by the inability of a firm or a country to repay its debt and had the firm or country issued long-term debt, it would have had "more time" to recover and default could have been avoided.

If we are going to go beyond simplistic interpretations of observed correlations, a theory of the factors that determine the choice of maturity is needed. In addition to such a theory's ability to rationalize the evidence, having it is important from the point of view of a policymaker to the extent that it describes the supply of debt for different maturities as a function of economic variables.

The literature on firms' choice of maturity includes the early work by Diamond (1991) and Leland and Toft (1996). Recent work on default risk over the cycle in the corporate sector includes Chen et al. (2017). In the sovereign debt literature, Arellano and Ramanarayanan (2013) determine maturity as a function of the costs of different types of debt. Aguiar et al. (2019), following Arellano and Ramanarayanan (2013), show that a country that has issued long and short bonds and needs to reduce its debt should not intervene in the market for long bonds and make the adjustment using exclusively short-term debt.

In this article, I develop a simple model of the choice of the structure of debt by a risk neutral firm that needs to raise a certain level of funds. I restrict the analysis to the case of a pure discount bond. I assume that the borrower and the financial market share exactly the same discount factor, that they are both risk neutral, and that information is complete. Thus, the choice of debt structure does not depend on differences in the valuation of risks between borrowers and lenders. Finally, I consider the case in which the borrower issues one bond. This eliminates the incentive that borrowers might have to issue short-term debt to dilute the value of long-term liabilities. I do not believe that strategic factors and differences in valuation criteria between borrowers and lenders are unimportant. Rather, I want to emphasize that factors other than those related to valuation and strategic considerations are also relevant to determine the maturity of the debt.

Even though the analysis could be applied to the study of sovereign debt (in this interpretation the borrower in the model is a country), I will assume that the borrower is a firm. This is mostly for convenience and to keep the presentation simple.

I find that there are several factors that influence the optimal (from the point of view of the borrower) maturity of the debt:

(i) The cyclical component. Firms that have better prospects (as measured by their current earnings) issue longer-term debt, as do firms with better growth prospects.

(ii) The market environment. Firms that operate in more-volatile environments choose to issue shorter-term debt.

(iii) Asset saleability. Firms that have high collateral—measured as the market value of their assets in the case of default—also issue longer-term debt. 

The intuition underlying these results is somewhat complex. Consider first the impact on the market value of a debt instrument of a given maturity and face value of an increase in current income of the issuer. To the extent that income is positively serially correlated, the increase in current income increases expected future income, lowering the risk of default and, consequently, increasing the market value of the debt. However, a borrower that needs to raise a given amount has the opportunity to redesign the debt instrument to lower the debt's market value to match the financing needed. To this end, the borrower can (and does) increase the maturity (and the face value of the bond), reducing the market value of the debt to the desired level. In the context of the economy that I study, causality runs from the state of the borrower (in this case, the level of current earnings) to maturity: Lower current income induces the borrower to issue shorter-term debt, even when it was possible to issue longer-term debt. This choice is not driven by risk aversion on the part of lenders but rather by the changes in the default risk associated with lower current income.

The impact of higher uncertainty about the growth rate of the firm's income has exactly the opposite effect as an increase in earnings. Higher uncertainty increases the risk of default, lowering the market value of the debt. For a given financing need, the borrower has to change the structure of the debt to restore the debt's market value, which can be accomplished by lowering the expected maturity.

Finally, a higher level of collateral increases the market value of the debt (it lowers the cost of default from the point of view of the debt holders and, hence, the price of risk). In order to reduce this value to match the financing needed, the firm finds it optimal to increase the price of risk by lengthening the expected maturity of the debt it issues.

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