Is there a paradox of pledgeability?

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Abstract

We show that in the limited-commitment framework of Donaldson et al. (2019), firm value always increases in the fraction of cash flows that can be pledged as collateral. That is, pledgeability increases investment efficiency and relaxes a firm’s financing constraint. We derive this conclusion using the same contracts considered by the authors and generalize the result to an arbitrary number of states. We also show that the first best can always be implemented by a nonstate-contingent secured debt contract, which differs from the ones they consider.

Introduction

Do firms benefit from having access to a wider set of assets that can be pledged as collateral? The canonical view is that greater cash flow pledgeability should relax a firm’s financing constraint, thereby benefiting firms,1 which is consistent with the empirical findings of Campello and Larrain (2016), Cerqueiro et al. (2016), Calomiris et al. (2017), Mann (2018), and Aretz et al. (2020). However, Vig (2013) shows that greater pledgeability led to an inefficient liquidation bias in India, while Acharya et al. (2011) present cross-country evidence that pledgeability is associated with an excessive reduction in corporate risk taking. Therefore, in light of the tremendous expansion of collaterizable assets in the US and abroad in recent years, it has become important to identify and understand the theoretical conditions under which greater pledgeability can harm a firm.

Donaldson et al. (2019) (henceforth DGP) develop a dynamic model in which collateral (i) provides property rights that accrue to a secured creditor upon default and (ii) gives an initial creditor the right of exclusion, preventing a subsequent creditor from seizing the collateral. DGP identify what they term an inefficient collateral rat race that ensues when only a fraction of the firm’s assets can be pledged as collateral. In this case, the demand for collateral from the initial creditors can be so high that it encumbers the assets, creating a collateral overhang that may inefficiently constrain future borrowing and investments. This is because if the initial creditor does not collateralize at least partially, it is too easy for a future borrower to fund new (possibly negative net present value) projects using collateralized credit that severely dilutes the claims of the initial creditor.

Does it follow from this analysis that being able to pledge a greater fraction of its cash flows may harm a firm? If so, then as DGP’s abstract highlights: “policies aimed at increasing the supply of collateral can backfire, triggering an inefficient collateral rat race.”2 To provide intuition, DGP present a motivating example with two scenarios: a low-pledgeability case, in which the first best is implemented, and a high-pledgeability case in which—supposedly—it is not. This analysis suggests that, counterintuitively, increasing the share of cash flows that a firm can pledge as collateral can make it worse off.

Our paper shows that, in fact, firms can never be hurt by having access to more pledgeable cash flows in DGP’s setting. The intuitive extends beyond their two-state setting and its validity does not require any of their parametric assumptions. To see the logic, consider the effect of an increase in a firm’s pledgeable assets. Regardless of whether the firm was investing efficiently before, absent informational asymmetries, having access to more collateral has an option value that cannot hurt. The firm can always increase the amount of secured debt issued at date zero to offset the increase in pledgeability, if this is needed to impede the financing of negative NPV projects. If not needed, the firm might be able to exploit the greater pledgeability to free some collateral needed to take on future positive NPV projects. Either way, pledgeability does not harm a firm.

We complete our analysis by showing that an alternative, non-state-contingent, debt contract can implement the first best for all parameter values. This contract is designed so that the required collateral falls with the scale of future investments. Our findings suggest that future investigations of the conditions under which pledgeability might hurt a firm should explicitly consider informational asymmetries between the firm and its investors.

In an extension, DGP relax the equivalence between pledgeable and collateralizable assets assumed in their core model. Specifically, Section 4.7 assumes that a fraction of pledgeable assets cannot be used as collateral. DGP then argue that high collateralizability may be associated with underinvestment. In Appendix A we show that this requires the cash flows of negative NPV projects to be more collateralizable than those of positive NPV ones. If the fraction of cash flows that is collateralizable is project-independent—as is assumed to hold for pledgeability—then increased collateralizability can only help a firm.

Section snippets

The motivating example

To provide intuition, DGP first give an example in which a firm requires external debt finance to pursue investment projects at dates 0 and 1, where the date 0 project has a positive NPV but the date 1 project has a negative NPV. They show that when the fraction θ of cash flows that can be pledged is low, unsecured debt can then be used to finance the positive NPV date 0 project, as it does not leave enough pledgeable assets to fund the negative NPV date 1 project.

In this example, the positive

Setup

There are three dates (t=0,1,2) and one consumption good dubbed cash. A borrower B has no cash but has access to two investment projects: one at t=0 and one at t=1. The date 0 project requires investment I0 > 0 at t=0 to generate X0 for sure at t=2. At date 1, a state s ∈ {H, L} realizes, where p:=Pr[s=H] is the probability of a high state. In state s, B can invest in a project that requires borrowing I1s and delivers X1s for sure at date 2. The state L project has a negative NPV and is

Results

Assumption A2 asserts that the project has positive a NPV in state H, but a negative NPV in state L, making the problem interesting. Lemma 1 shows that if A2 holds, then A7 can be satisfied by some θ only if X1H>X1L, which we henceforth assume.

Lemma 1

If X1HX1L, then A7 and A2 do not simultaneously hold for any θ ∈ [0, 1].

Proof

If X1H<X1L, then I1HI1*θI1LI1HX1LX1H. The condition can be satisfied by some θ ∈ [0, 1] only if I1LI1HX1LX1H1 or, equivalently, only if I1LX1LI1HX1H. However, from A2, I1L

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We thank the editor (Darrell Duffie), Michael Gofman, Alan Moreira, Christian Opp, Michael Raith, Pavel Zryumov, and two anonymous referees for helpful suggestions. All errors are our own.

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