Equilibrium Collateral Values, Risk-Shifting and Credit
Rationing∗
Christian Kuklick†
University of Münster
March 15, 2012
Abstract
Within many borrower-lender relationships, such as project finance, a borrower’s
endogenously chosen level of risk may affect collateral liquidation values. We explore
this impact, focusing on potential buyers for corporate assets in cases of idiosyncratic
as well as industry-wide defaults. We then use endogenous investment decision and
resale prices to analyze their interaction with ex ante credit rationing. As a result,
provision of collateral does not necessarily solve for the asset substitution problem, but
may even fuel moral hazard and credit rationing in banking. Moreover, our approach
provides an explanation as to why creditors may prefer to lend to borrowers short of
assets. This somewhat surprising result is primarily driven by a negative correlation
between risk and liquidation value, rather than by the bank’s liquidation costs.
Keywords: Asset substitution, collateral, credit rationing, debt, moral hazard.
JEL Classification: D82, G21, G32,G33.
∗
We are deeply indebted to the participants of the 60th Midwest Finance Association (MFA) conference, to two anonymous referees of the 74th Annual Meeting of the German Academic Association for
Business Research 2012 and finally those of the Finance Center Muenster seminar for providing valuable comments that led to a considerable improvement of previous versions of this paper. Remaining
errors and omissions are my sole responsibility.
†
Corresponding author, Finance Center Münster, University of Münster, Universitätsstr. 14-16, 48143
Münster, Germany, phone +49-251-83-22883, fax +49-251-83-22882, [email protected].
I
Introduction
This paper presents a new theory of the asset substitution problem. According to the
latter, increasing risk may be the borrower’s first-best response to a preceding increase in
the loan interest rate by the lender. A rich literature exists on the topic, since financial
economists like Jensen and Meckling (1976) have identified it as a major component of the
agency costs of debt. Pledged internal assets as well as third party (’external’) collateral
usually provide incentives to stop such risk-shifting (Smith and Warner (1979); Stiglitz and
Weiss (1981, 1986)) and diminish credit rationing. Nevertheless, academic research has
neither rationalized (1) the nexus between risk-shifting and collateral liquidation values
nor (2) the interaction of this nexus with credit-rationing so far.
The principal contribution of this paper is to review and theoretically deduce these stylized
facts. We therefore endogenize the ex post collateral liquidation value and set up a general
two-stage equilibrium aspect of asset sales, i.e. the revenue gained for the lender by selling a
pledged asset. Unlike Shleifer and Vishny (1992) and Kiyotaki and Moore (1997), we allow
defaults to occur industry-systematic or idiosyncratic. Resale prices hinge on whether or
not there are potential buyers standing by ready to repurchase the pledged assets. If the
whole industry suffers, there may only remain a few industry outsiders standing by ready
to bid for assets. Corporate asset supply in turn depends on the borrower’s action. The
more risk borrowers take, ceteris paribus, the more likely they will default and the higher
the supply of corporate assets rises. Thus, liquidation values tend to be lower when riskier
projects are undertaken. This theory fits well with empirical studies (e.g. Gupton (2000);
Franks et al. (2004); Grunert (2005)). We show that refraining from collateralization may
under certain circumstances be profit-maximizing for the lender. This result also offers a
novel argument in the light of the debate within the traditional corporate finance literature.
While adverse selection models (Bester (1985); Chan and Kanatas (1985); Besanko and
Thakor (1987)) predict that safe borrowers within a risk pool pledge more collateral than
risky ones, moral-hazard models (Chan and Thakor (1987)), on the contrary, find the
opposite. In a nutshell, our findings suggest that borrowers don’t have to pledge collateral
for loans because banks simply don’t want them to. This result is mainly driven by
the correlation between risk and liquidation value, rather than by the bank’s liquidation
costs. Otherwise, if default primarily occurs due to idiosyncratic reasons, there may remain
enough potential buyers within the same industry. The resale price may then even exceed
the average, which is assumed in one-staged models like Stiglitz and Weiss (1981, 1986)
or Bester and Hellwig (1989). In this case, collateral solves the asset substitution problem
even more reliably. These results rely on rational expectations and at least partial public
I
INTRODUCTION
2
information. As soon as public information becomes private, agency costs of debt go from
bad to worse.
Our analysis is in the tradition of classical credit rationing models, which allow for asset
substitution design. It is closest in spirit to Stiglitz and Weiss (1981, 1986) and Bester and
Hellwig (1989), who, in an incomplete contract framework, stress the fact that increasing
the interest rate may not maximize the lender’s profit as the borrower can in turn increase
project risk. Collateral commonly mitigates risk-shifting incentives within the corporate
finance and credit rationing literature, subject to the constraint that its resale price is an
exogenously given factor.
The second strand of literature stresses the link between an exogenous liquidation value
and debt capacity. The concept applied therein is fairly general: An asset0 s liquidation
value is the amount that lenders receive if they seize the asset from the borrower and
sell it on the open market when the latter fail to make a promised payment. Within
a transaction cost approach, Williamson (1988) emphasizes that debt as a rules-based
claim requires liquidation in adverse states. Redeployable assets, i.e., assets that are not
specialized, will be rather suited to debt-financing. Shleifer and Vishny (1992) focus on
asset illiquidity. Within their industry-equilibrium model, specialized assets, i.e., assets
with only a few potential buyers, are poor candidates for debt finance, since liquidation
is likely to fetch a low price. Benmelech et al. (2005) provide empirical evidence for
these findings. Customers which offer more redeployable assets receive larger loans with
longer maturities, lower interest rates granted by fewer creditors. Nevertheless, a lot of
specialized assets are used for debt finance due to a lack of alternatives. Harris and Raviv
(1990) analyze the information effects of debt. Borrowers are assumed to prefer to avoid
liquidation. Debt can facilitate efficient liquidation since borrowers who miss payments
have to reveal information to lenders. In turn, the latter will choose to liquidate the
firm if such action yields higher returns than a restructuring. In Hart and Moore (1994),
incomplete contracts and non-verifiable cash-flows limit creditors’ claims. But creditors
retain the option to liquidate assets. The larger the liquidation value, the more creditors
are willing to lend. Bolton and Scharfstein (1996) consider the optimal number of creditors.
Borrowing from multiple lenders makes default costly, which disciplines managers. But it
also may lead to inefficient outcomes when default is involuntary. Borrowing from only
one lender is the optimal solution when liquidation vales are high since, in such a case, the
costs of inefficient liquidation are high as well. Diamond (2004) makes a similar prediction,
supposing that an intervention by the lender is costly.
II
BASIC MODEL
3
Nevertheless, this strand of literature does not analyze the dynamic interplay between ex
post liquidation value, risk-shifting incentives and credit rationing at the time the contract
is set. With the exception of Shleifer and Vishny (1992), none of the referenced papers
explore determinants of the liquidation value in any way. Yet, the former merely use their
findings to explain variation in debt capacity across industries and over the business cycle,
as well as the rise in U.S. corporate leverage in the 1980s.
The remainder of the paper is organized as follows: Section II sets up the formal model,
which builds on Stiglitz and Weiss (1981, 1986); Bester and Hellwig (1989). Section III
explores the resale price of corporate assets and the two-way interaction between ex post
liquidation value and ex ante credit rationing and investment choice. Our framework
also allows us to ”revisit” the contributions of the early asset substitution and credit
rationing models. Section IV deals with the role of information in such a setting. Due to
asymmetric information and risk incentives of debt, a first-best solution (e.g. the lender
and the borrower agree on a project which is going to be implemented) is not possible.
When we, in addition, let information turn from public to private, a third-best equilibrium
arises. We analyze the agency costs of debt for the latter. Finally, section V concludes
with a summary of our main insights, as well as possible extensions of the analysis.
II
Basic Model
Model framework
We establish a one-periodic model with a single bank on one side and plenty of borrowers
on the other. The latter are homogenous, e.g. an industry which consists of n symmetric
firms using the same equipment. All subjects act risk-neutral and profit-maximizing. The
entrepreneur is protected by limited liability. He can only choose between a less risky
investment (a) and a riskier one (b). Projects a and b can be interpreted as two contrary
ends of an investment spectrum. Projects intermediate in risk (e.g. a0 ) may lie in between.
Information is imperfect and asymmetric. The bank is not able to verify the chosen project
after entering the loan contract, but the projects specifications are common knowledge.
Thus, the bank is able to anticipate the borrower’s choice via rational expectations. Later
on, we will alter this assumption (Section IV). Income is verifiable for free ex post. The
bank knows about the borrower’s limited liability as well as his wealth. Further monitoring
is either not possible or too costly. Especially in research and development, moral hazard
II
BASIC MODEL
4
can remain unobserved for a long time (Long and Malitz (1985)). The model consists of
four parts:
E(X̃a ) = pa Xa > E(X̃b ) = pb Xb > I > 0
(II.1)
1 > pa > pb > 0
(II.2)
Xb > Xa > I > 0
(II.3)
W ≥C≥0
(II.4)
0≤β≤1
(II.5)
βC ≤ I ≤ R
(II.6)
π=0
(II.7)
I ≤ L < nI
(II.8)
Ls = Ls (Gi )
Y
Ld = Ld (
)
(II.9)
(II.10)
i
Y
i
(R, C) = pi (Xi − R) − (1 − pi )C , i {a, b}
(II.11)
Gi (R, C) = pi R + (1 − pi )βC − I , i {a, b}
(II.12)
The first part contains information about the projects. Their returns are modeled by two
discrete variates X̃i with i = a, b (II.1). The project either succeeds with probability pi
and yields verifiable income X̃i = Xi > 0, or fails and yields no income (X̃i = 0). Thus,
the project asset is highly specialized and not redeployable (e.g. oil rigs and steel plants)
or it gets lost in production. We see eye in eye to Williamson (1983) that most assets in
the world are specific and investigates 4 categories of asset specificity.
2
Our two cash-
flow model is the simplest framework to reflect that specificity. Furthermore, both projects
require an indivisible and fixed investment size I > 0, as the borrower does not have liquid
2
The author investigates 4 categories of asset specifity. Utilized categories are labeled site specificity,
physical asset specificity, human asset specificity and dedicated assets.
II
BASIC MODEL
5
assets or cash on hand.3 I is the optimal investment size for the firm. As in Jensen and
Meckling (1976), the less risky project a has a higher expected profit, but the expected
profit of the riskier project b is still positive. There has been a long discussion about
whether or not such modeling is feasible because the assumption seems to be at odds
with the financial economic paradigm, namely less risky projects have higher expected
returns and vice versa because efficient riskier projects must have higher expected values
in portfolio theory (Kürsten (1995, 1997)). But the riskier project may be inefficient in
cases of equity finance, and can get efficient if debt is used (Nippel, 1994, 1995). Thus,
a lower expected value of the riskier project may occur if the less risky project a also
has the higher probability of success pa (II.2), but leads to a smaller yield Xa in case
of success (mixed aggravation of risk). We decided to express risk by the probability of
failure of the project (II.3) as this allows us to compare and contrast our results to previous
contributions.
The second part deals with collateralization. As we want to focus on the nexus between
risk and collateral liquidation values, we assume collateral to be internal: Borrowers have
pledgeable wealth (W ) which may (partially) serve as collateral (C) (II.4). Internal collateral may solve for the asset substitution problem, too (Smith and Warner (1979)). At a
first glance, preferential access rights on pledgeable borrowers’ assets don’t seem necessary
due to monopoly. But internal collateral hinders the opportunistic borrower from eroding
liability by selling his assets and squandering the corresponding cash-flows just prior to
default. Thus, there is a raison d’être for collateral in such a setting as well. Additional
external collateral is not available. W is illiquid, i.e. it can not be used to cover the
costs of investment. Lenders value collateral at βC, where 0 ≤ β ≤ 1 when they seize it
(II.5). The reasons for a deadweight loss attached to collateralization via (1 − β)C are
e.g. transaction costs, documentation costs, cost of upkeep, lack of benefits from ownership or realization losses (Chan and Kanatas (1985); Stiglitz and Weiss (1986); Besanko
and Thakor (1987); Bester (1987)). Thus, the lender’s evaluation of C equals βC, which
cannot exceed the borrower’s evaluation (even for β = 1). Let R denote the repayment
demanded by the bank (i. e. interest and loan repayment).4 Because the bank’s claims are
restricted to the contractual repayment (R) in case of a security surplus, βC ≤ R holds
(II.6). Thus, as is common in most legal frameworks, we allow for over-collateralization
up to the bank’s costs.
3
With a few exceptions, e.g. Besanko and Thakor (1987), existing models of collateral assume a fixed
project size.
4
By setting the size of the loan to one, R can be interpreted as (one plus) the interest rate of the loan.
II
BASIC MODEL
6
The third part introduces funding. We neglect the deposit interest rates by π to 0%,
because non-trivial rates do not does not affect general results noteworthily (II.7). Because
funds (L) are scarce and the lender is unable to finance all borrowers at the same time,
(II.8) arises. Some applicants receive a loan and some do not (’type II-rationing’ as in
Keeton (1979) and Stiglitz and Weiss (1981)). According to their definition, a would-be
borrower is rationed if he is not able to obtain the loan he wants even though he is willing
to pay the interest rate the lender is asking, or in some cases even a higher one. In order to
close the model, the supply of credit is introduced as a (positive) function of the lender’s
expected profit G (II.9). The simplest specification corresponds to an infinitely elastic
supply of funds. However, this might bear multiple equilibria. In any case, equilibrium
credit rationing cannot occur when the supply of funds is infinitely elastic, since markets
will clear. The usual assumption of a finite elasticitiy for the deposit supply function,
results in a two-state clearance equilibrium (Stiglitz and Weiss (1981); Freixas and Rochet
(2008)). Loan demand is supposed to be positively correlated to expected profits somehow.
Given an expected profit of zero, borrowers are indifferent about borrowing at all.
Q
At last, (II.11) and (II.12) reflect the borrower’s ( i (R, C)) and the bank’s (Gi (R, C))
expected profits, conditional on the chosen project (a or b). We will refer to them later
on (see e. g. figures 1 and 2).
Initial situation
Figure 1 illustrates the dynamic game in extensive form:
II
BASIC MODEL
7
Figure 1: Initial situation in extensive form.
Initially, the borrower decides whether or not to apply for a loan. Borrowers behave in
the sense that the NPV of the investment, if any, makes at least zero profit. If they
obtain extensive wealth, they will only undertake an investment if lenders agree to a
contractual limitation of their claims. Besides, the lender’s claim in cases of failure is
restricted to the contractual repayment (II.6). Otherwise, the borrower would not be
protected from an unjust enrichment. Due to rational expectations, the bank determines
the profit-maximizing combination of repayment (R) and collateral (C). Of course, C is
zero for W = 0. The bank will only offer a loan if it makes at least zero profit. Depending
on repayment (R) and collateral (C), borrowers maximize their expected profits. If the
latter is negative, they refrain from investing at all. Once again, the project choice itself
is unobservable for the bank (see dotted lines between a and b), but income is verifiable
ex post.
We derive the bank’s optimal strategy (and the borrower’s project choice) by means of
backward induction. Due to limited liability, the riskier investment b potentially increases
the borrower’s return, while expropriating value from the bank in case of bankruptcy
(’asset substitution problem’). As a consequence of incomplete contracts (the borrower
cannot be bound to a certain project, but incentivized to act in accordance with the bank’s
wishes) and asymmetric information, second-best solutions follow. The riskier project b
II
BASIC MODEL
8
is profit-maximizing for the borrower if the repayment R exceeds a critical value Rcrit .
Otherwise, he chooses project a.
Before moving forward, it is helpful to comment on the optimal repayment if project b is
carried out. Subject to the borrower’s zero-profit constraint, the banks claim will amount
to at most Xb . Due to risk-neutrality and transaction costs (1 − β)C, demanding Xb and
refraining from collateralization is the first-best strategy for the bank. We formally prove
this intuitive solution later on (see Proposition 1).
Figure 2 visualizes the possible constellations. To keep things simple, C is set zero here.
The bank’s maximum profits, depending on the project choice, are highlighted by a pinhead. One sees that the bank’s expected profit does, ceteris paribus, not monotonically
increase in R. At R = Rcrit , an infinitesimal increase in the repayment leads to a discontinuous drop in G(R,C), as the borrower switches to the riskier project. If the individual
characteristics of project b (line (2)) are as illustrated in figure 2, scenario 1, the bank
should encourage the borrower to run project a by demanding an optimal repayment
R∗ . Consider the following example: For pa = 0.8, pb = 0.5, Xa = 150 and Xb = 160,
Ga = 133 13 > Gb = 80 follows. But even project b can be favorable for the bank: In figure
2, scenario 2, the pinhead of line (2) indicates a higher expected profit than the one for
line (1)). For example, this takes place for pa = 0.8, pb = 0.5, Xa = 150 and Xb = 200,
Ga = 53 13 < Gb = 100.
(a) Scenario 1: Bank prefers project a.
(b) Scenario 2: Bank prefers project b.
Figure 2: Bank’s expected payoff (G) as a function of the contractual repayment R.
II
BASIC MODEL
9
Critical repayment
As we stated earlier, the borrower chooses project a as long as it maximizes his expected
profit, net of interest. We now derive the critical repayment (Rcrit ). According to (II.4),
borrowers may have pledgeable, but illiquid assets W , whereby C ≤ W . Let RwC denote
the critical repayment in cases of collateralization and RoC the one in cases without collateral. Given an infinitesimal rise above Rcrit , the borrower invests in b (risk incentive)
and the bank’s expected profit may be reduced (see figure 2 (a), line (2)). Comparing the
borrower’s expected profits leads to:
pa (Xa − R) − (1 − pa )C ≥ pb (Xb − R) − (1 − pb )C
⇐⇒
(pb − pa )R ≥ pb Xb − pa Xa + (pb − pa )C
Due to pa > pb , we obtain:
R ≤
pa Xa − pb Xb pb − pa
C = RwC
+
pa − pb
pb − pa
|
{z
} | {z }
=RoC
⇐⇒
R ≤
=1
pa Xa − pb Xb
+C
pa − pb
(II.13)
In the limiting case, equality holds:
pa Xa − pb Xb
+ C = RoC + C = RwC
pa − pb
(II.14)
The critical repayment RwC in cases of collateralization exceeds RoC by exactly C.5 If
collateral values do not hinge on the borrower’s action, the bank can increase its repayment
from RoC to RwC . This is well in line with the prevailing view according to which collateral
decreases risk incentives and moral hazard.
Expected profits and credit rationing
In addition, we have to checkc both, the bank’s and the borrower’s zero-profit conditions.
As the bank has insufficient funds for granting a loan to the entirety of potential borrowers
(II.8), whereas the latters’ expected profits and loan demand are correlated positively
(II.10), we have to account for (type II-)credit rationing as well. If the borrowers’ expected
profits are positive, all borrowers will apply for a loan. Credit rationing arises due to
Q
insufficient funds. For i = 0, the borrowers are indifferent about borrowing at all and
credit rationing is not an issue. We will now determine the banks’ optimal strategies
5
Substituting Xb for Xa and vice versa yields RoC ≤ Xa ≤ Xb . Because substitutions are used which
fulfil the inequations even more, RoC < Xa and RoC < Xb hold.
II
BASIC MODEL
10
under rational expectations.6 One arrives at the corresponding scenarios by comparing
the pinheads in figure 2. In scenario 1, the pinhead of line (1) leads to a higher expected
profit than the pinhead belonging to line (2). Thus, project a should be implemented. On
the contrary, project b is favorable for the bank in scenario 2.
Within these scenarios, collateral, if any, must not infringe the borrowers’ zero-profit
condition. Otherwise, they will not engage in any project at all. Thus, pa (Xa − R) −
(1 − pa )C ≥ 0 must hold. Solving the equation leads to a maximal collateralization
C max =
pa (Xa −R)
1−pa .
Of course, collateral cannot exceed the borrower’s wealth W . Thus,
h
i
a −R)
the contractual collateralization is C ∗ = min W, pa (X
. Concluding, we have to
1−pa
compare project a, linked with a repayment RwC and a collateralization C ∗ , to project b.
In cases of a favorable b, R∗ = Xb and C ∗ = 0 are profit-maximizing (for a formal proof
of the latter see scenario 2).
Scenario 1) pa RwC + (1 − pa )βC > pb Xb
Project a is optimal for the bank. The borrower only implements the safer project if the
contractual repayment is at most RwC . As pointed out above, the optimal collateralization
C ∗ depends on the borrower’s wealth. We have to distinguish between two scenarios.
a) W <
pa (Xa − R∗ )
1 − pa
If the borrower’s wealth is a bottleneck with regard to collateralization, i. e. C ∗ = W with
W <
pa (Xa −R∗ )
,
1−pa
the borrower obtains pa (Xa − RwC ) − (1 − pa )W > 0 and credit rationing
follows. The bank’s expected profit amounts to pa RwC + (1 − pa )βW − I > 0. This value
exceeds the bank’s profit in the cases of no collateral by pa (RwC − RoC ) + (1 − pa )βW .
b) W ≥
pa (Xa − R∗ )
1 − pa
If the borrower’s wealth is not that scarce (C ∗ =
pa (Xa −R∗ )
1−pa
and R∗ = RwC ), the borrower’s
expected profit is zero. Credit rationing does not occur. The bank obtains pa RwC +
βpa (Xa − RwC ) − I > 0, which exceeds the bank’s profit in the cases of no collateral
by pa (RwC − RoC ) + βpa (Xa − RwC ). The first addend captures the benefit due to an
increase in the critical repayment, while the latter reflects proceeds gained due to collateral
liquidation.
Scenario 2) pa RwC + (1 − pa )βC < pb Xb
6
We will alter this assumption in section IV.
II
BASIC MODEL
11
Proposition 1: Refraining from collateralization is the optimal strategy if project b is
advantageous to the bank (Gb > Ga ).
Proof: Due to risk-neutrality and transaction costs, one supposes zero-collateralization
as being the first-best strategy to the bank. Maximizing the bank’s profit function
subject to the constraint that the borrower makes at least zero-profit, we receive:
max G = pb R + (1 − pb )βC − I
R,C
subject to:
Fixing
Q
Y
(R, C) ≥ 0
(R, C) = 0 and solving for R, we obtain
R = Xb −
(1 − pb )
C.
pb
(II.15)
Inserting (II.15) into the bank’s profit function (Gi ) reveals that a zero-collateralization
is favorable for 0 ≤ β < 1.
max G = max G = pb Xb −(1 − pb )C + (1 − pb )βC −I.
|
{z
}
R,C
C
< 0 for C > 0
Thus, R∗ = Xb and C ∗ = 0 are optimal in scenario 2. The bank obtains pb Xb − I, whereas
the borrower’s expected profit is zero. Due to the borrowers are indifferent about borrowing
at all, credit rationing does not occur. Figure 3 illustrates the results graphically.
II
BASIC MODEL
12
Figure 3: Credit-rationing in cases of non-project related liquidation values.
The optimal project choice from the bank’s point of view is determined by the level of
endowment (ordinate) and the ratio of the project proceeds (abscissa). In analogy to
the project proceeds, we normalize the ordinate by Xa as well. On the abscissa, the
left limitation ’1’ results from Xb > Xa . The right-hand side limitation is determined by
pa Xa > pb Xb . Credit rationing for borrowers short of wealth (i.e., W = 0) can be found on
the abscissa. Here, credit rationing occurs as long as the repayment does not exceed RoC .
To the left of the blue surface, credit rationing does not occur because the bank is able to
push the borrower where he is indifferent whether to apply for a loan or not. Within the
blue surface, the lender prefers project a, but the borrower’s wealth W is insufficient to
appropriate the entire surplus. Credit rationing follows. The bottom right corner of the
blue triangle sits at pa RoC , where the borrower still implements project a and obtains a
positive expected profit due to zero collateralization. For parameter constellations to the
right of the blue surface the implementation of project b is favorable for the bank. Credit
rationing does not occur here. Finally, there is no credit rationing above the blue triangle.
The bank prefers project a and is able to push the borrower to the point where he is
indifferent about borrowing at all. In this basic approach, an increase in assets (W/Xa )
ceteris paribus diminishes credit rationing and risk-shifting issues.
III
EQUILIBRIUM DETERMINATION OF LIQUIDATION VALUES
III
13
Equilibrium determination of liquidation values
Williamson (1988); Harris and Raviv (1990); Hart and Moore (1994); Bolton and Scharfstein (1996) as well as Diamond (2004) present models in which liquidation values appear
as an exogenous factor for the determination of debt capacity. Stiglitz and Weiss (1981,
1986) determined collateral benefits with regard to credit rationing issues. Section II of
this paper took a similar approach. We will now go beyond previous observations by explicitly modeling the two-way interaction between ex post liquidation value and ex ante
credit rationing and investment choice. Therefore, we endogenize the liquidation value.
Let us adduce at least three good reasons why the value of the borrower’s pledged position
may depend on his project choice:
1. The last section came up with the result that the lender rather grants loans to
borrowers with pledgeable assets because his expected profit increases. Suppose a
majority of our n (homogenous) borrowers have to put (similar) assets on the market
because they are in distress. All other things being equal, this is more likely for highrisk projects. Limited demand and competition between the defaulted borrowers
brings down the liquidation value. At the same time, riskier projects may go along
with less collateralization and less supply of pledged assets in equilibrium. Thus, it is
ambiguous whether an increase in risk goes along with higher or lower resale prices.7
Kiyotaki and Moore (1997) trace distress back to industry-wide shocks, while Shleifer
and Vishny (1992) analyze the firms’ industries and the valuation of specialized
assets. We endogenize the liquidation value with the aid of both approaches.
2. Igawa and Kanatas (1990) state that collateral liquidation values are affected by the
borrower’s level of ’care’ in the use of the asset. Borrowers may privately receive
signals that indicate a forthcoming distress. They either have low incentives for
adequate maintainance of assets well or spend too little time for such supervision
because they want to prevent going bankrupt at any price. Asset depletion follows.
3. Finally, the borrower’s investment strategy may simply affect his wealth for other
reasons. Imagine, for instance, the borrower’s project consists of a plant extension.
If increasing project risk is equivalent to an extreme customization, this may affect
the expected resale price of existing company grounds as a whole.
7
In Section II, we assumed that there are only two kinds of projects. For the riskier one, C ∗ = 0
was optimal for the bank due to exploitation costs. Thus, no assets will be put on the market in
distress. In reality, there may be a broader spectrum of possible investments, such as a, a0 and b
with probabilities of success pa > pa0 > pb . In analogy to Section II, the optimal contract (R,C) will
include less collateral than project a, but more than b.
III
EQUILIBRIUM DETERMINATION OF LIQUIDATION VALUES
14
In light of these considerations, Stiglitz and Weiss (1981, 1986) took the easy way out by
assuming collateral to be external. We will now follow the line of argumentation presented
in (1) and treat liquidation values, investment decisions and credit rationing in its entirety.
This also enables us to critically review previous results . Thereby, we will in the following
suppose the parties involved to have rational and homogenous expectations. We will relax
this assumption in section IV.
Demand side of pledged assets
As long as there has been no initial contract that specifies a transfer price paid by a
third party in the case of distress, the resale price depends on whether there are buyers
standing by ready to repurchase the pledged assets. This in turn hinges on whether or
not potential bidders are also financially constrained. We see eye to eye with Shleifer and
Vishny (1992) that most assets in the world are quite specialized (e.g. pharmaceutical
patents, an uncommon set of professional know-how, unique physical facilities etc.) and
therefore hardly redeployable. Such assets need to be sold to someone able to use them in
approximately the same way and has accumulated the knowledge for proper management.
We now analyze the general equilibrium aspect of such asset sales.
Two major types of potential buyers should exhaust the relevant set for most specialized
assets. At first, there are firms within the same industry. These may either have enough
cash on hand or rely on debt financing. Secondly, there may be ’deep pocket’ financial
investors outside the industry with extensive wealth or resources, which do not face debt
overhang. The prime-value is probably provided by other firms within the same branch of
industry (high-valuation industry specialists). However, unless the borrower got in trouble
for some idiosyncratic reason (e.g. mismanagement), firms within the same industry are
likely to experience cash flow problems of their own and are not able to stem the payoffs
in the first place (e.g. due to debt overhang).8 Deep pocket investors compris of astute,
low-valuation industry outsiders who often do not know how to manage such assets appropriately. As a matter of fact, they face costs for hiring experts to run these assets, e.g.
parts of the management of the distressed borrower. Furthermore, financial investors fear
overpayment as they cannot value assets properly and apply an eligible valuation haircut.
Additionally, they are interested in making a snatch due to their bargaining power.
Let us consider the following example for the different types of potential buyers: Imagine
the pledged asset is an airplane, and the distressed borrower is an airline. Then, the high8
But even if they can raise funds, antitrust and government regulation may prevent such bidders from
purchasing. We will abstain from these issues for the remainder of the paper.
III
EQUILIBRIUM DETERMINATION OF LIQUIDATION VALUES
15
valuation industry specialists would consist of other airlines. In this case, deep pocket
investors may be financiers who purchase airplanes simply to lease or sell them to other
airlines.
Let PIns (P out ) denote industry insiders’ (outsiders’) maximal willingness to pay (WTP).
Industry investors, though, will not pay more funds than what they will receive from
their expansion. This competitive price is commonly known as the increase in pledgeable
income. To maintain our previous denotations, the increase in pledgeable income is the
yield of a project with present value cash flow X and probability of success 0 < p < 1. In
case of failure, the project yields zero. We restrict our analysis to only one available project
for the potential buyer because we don’t want to introduce a ’double asset substitution
problem’. In order to render the acquired assets operational, the acquiring firm needs
to (re)invest. In analogy to section II, we denote the (re)investment I. We assume that
acquiring managers do not get a surplus out of the transactions so that further agency
problems are not introduced. To keep things simple, a quantity of industry insiders (Inse )
either has enough equity, e.g. cash on hand to stem the payoffs or they do not and have to
rely on debt financing (Insd ). Investors who are not able to raise funds are redlined from
the auction. As their opportunity costs are assumed to be zero, industry insiders with
cash on hand pay no more than pX − I. Debt financing investors are willing to pay less,
at most pX − R, whereby pX − R denotes the increase in pledgeable income net of interest
and repayment. As elucidated before, outsiders pay less than insiders (P Out < P Ins ).
Without loss of generality of our analysis, we suppose that the outsiders’ WTP is even
less than that of debt financing industry insiders.
The aggregated demand (x)as a function of the asset price (P ) is:

0
f or P > pX − I > pX − R > P Out





 Inse
f or
pX − I ≥ P > pX − R > P Out
x(P ) =


f or
pX − I > pX − R ≥ P > P Out
 Inse + Insd



Inse + Insd + Out f or
pX − I > pX − R > P Out ≥ P
(III.1)
To add up individual’s demand curves, we use horizontal summation. Figure 4 illustrates
both, single as well as aggregated demand of potential buyers.
As usual, the resulting demand curve has a negative slope. We start with an auction
price equal to the yield of the asset in use net investment. At such a price, up to all
insiders within the industry sector in possession of enough cash on hand (Inse = critical
investment value for industry insiders) are going to bid for the seized assets. As the price
III
EQUILIBRIUM DETERMINATION OF LIQUIDATION VALUES
P
P
P
P
pX − I
pX − I
pX − R
pX − R
P Out
Inse
x
16
Insd
x
P Out
Out
x
Out Inse+d All
x
Figure 4: Single and aggregated demand for different types of potential buyers.
declines below the yield of the investment net amount to be invested and interest, the
industry insiders, who are able to raise debt, will make offers, too. Finally, only at prices
P Out or lower, all potential buyers (All = Inse + Insd + Out) are supposed to make offers,
i.e. even the industry outsiders.
Supply side of pledged assets
According to (II.8), there are n homogenous borrowers which apply for a loan (I). Due
to insufficient funds (L), only L/I borrowers obtain credit. Once these received a credit,
they run a project out of their available investment spectrum. As already illustrated in
equilibrium, there exists a relatively safe project a with collateralization on the one side
and a riskier one (b) without collateralization, but with a higher repayment R on the other
side of this spectrum. Projects intermediate in risks (e.g. a0 ) and collateralization may
lie in between. Ceteris paribus, the supply of pledged assets in the market increases with
the quantity of funds (L) and, of course, borrowers seeking for a source of funding (L/I).
Intuitively, one may suggest that risk-shifting, i.e. an active increase in the probability of
failure (1 − pi ) of a project, also increases market supply for associated assets. We will
now investigate whether or not this intuition holds..
Interpreted very loosely, the ’law of large numbers’ induces that the higher the probability
of failure (1 − pi ), the more likely the project fails.9 If the wealth, and thus the optimal
∗
a −R )
), then, all
collateralization C ∗ is smaller than the maximum level of collateral ( pa (X
1−pa
else being equal, the supply of pledged assets on the market increases.
However, if C ∗ =
on
9
R∗ ,
via
∂R
∂pi .
pa (Xa −R∗ )
1−pa
holds, one has to consider the effect of an increase in (1 − pi )
Subsequently, we consider an increase in risk for a
Diamond (1984); Hellwig (2000) treat the ’law of large numbers’ more carefully, with a finite number
of projects going to infinity.
III
EQUILIBRIUM DETERMINATION OF LIQUIDATION VALUES
17
from a safe project a to a riskier one a0 , i.e. the probability of success decreases from pa
to p0a , while Xa < Xa0 holds. Project a0 is riskier than a, but, in contrast to project b, still
contains collateralization. Because we want to derive ex post project-related liquidation
values, we have to utilize RoC or RwC .10 Because we calculate the derivative
not matter whether we apply
Roc
or
∂R
∂pa0
it does
RwC .
pa Xa − pa0 Xa0
Xa0
∂R
=
−
2
∂pa0
(pa − pa0 )
pa − pa0
pa Xa − pa Xa0
⇐⇒
(pa − p0a )2
Due to Xa < Xa0 ,
∂R
∂pa0 ,
(III.2)
< 0 holds. As a result, R∗ increases with a rise in risk (1 − p0a ). As a
consequence, the maximum level of collateralization
pa (Xa −R∗ )
1−pa
decreases. This reduction
in assets may even overcompensate the increase in defaults. For example, we consider
Xa = 150, Xa0 = 180. (1 − pa ) = 0.5 then yields C ∗ = 200, while (1 − p0a ) = 0.51 leads to
C ∗ = 189, 68. Thus, the supply of corporate assets (1 − pi )C ∗ is 100 for 1 − pa = 0.5 and
92, 94 for 1 − pa0 = 0.51. Hence, an increase in risk (1 − pi ) may even lower the supply of
corporate assets on the market due to less collateralization.
The analysis of the supply side raises a number of additional questions. At first, why does
not the lender wait until market conditions improve once he has repossessed the assets?
This fits well with Asquith et al. (1994) who find that, when industry conditions are bad, a
debt work-out is more likely than a liquidation. But in such times, banks are not supposed
to hold all of the repossessed assets on hand until market conditions improve far enough.
Some assets, such as airplanes cannot be held for longer periods as they cause enormous
maintenance costs.
The other way round, is it not possible for firms firms to benefit from colluding ex ante
and committing to put only a fraction of distressed assets on the market? We don’t have
to debate on the issue of whether or not cartelization is an efficient policy to redistribute
income toward the corparate sector. Because assets are pledged as internal collateral,
borrowers do not have any fredom of action to sell assets on their own. Banks, in turn,
are not able to hold all of the assets on hand.
In the third place, why does the borrower not renegotiate or issue new shares in order
to avoid a sale of pledged assets? The reason is that these alternatives are hardl to
10
If we took the Radj introduced later on, we would assume different values for C instead of deriving
them ex post.
III
EQUILIBRIUM DETERMINATION OF LIQUIDATION VALUES
18
implement: On the one hand, debt rescheduling requires costly coordination (Gertner
and Scharfstein (1991)). Moreover, managers will take extra risks if the loan maturities
are extended (Jensen and Meckling (1976)). On the other hand, even new shares are
not an alternative if there is severe debt overhang. Besides, the tremendous anxiety of
new security buyers about the value of the assets also raises the costs of security issues
(Myers and Majluf (1984)). Finally, buyers of new shares have to worry that managers will
squander gained liquidity rather than use it productively, while asset sales are exclusively
used for repayment. Concluding this line of thought, we assume that banks are not able
to hold any collateral on hand. Thus, supply is inelastic.
Market equilibria of collateral liquidation values
We are now able to illustrate ideal-typical equilibria for liquidation values. We start
with idiosyncratic reasons for default. As we mentioned, one has to differentiate whether
collateral is scarce (C ∗ <
pa (Xa −R∗ )
),
1−pa
or not. As long as borrowers defaulted due to
idiosyncratic reasons and collateral is scarce, there may be enough industry peers with
cash on hand (see figure 5, case 1). The resale price remains unchanged. It should be
pointed out that this is the scenario previous theoretical models, as well as our own basic
model described in section II, refer to.
P
pX − I
pX − R
P Out
(1 − pa )L/I (1 − pa0 )L/I
Figure 5: Idiosyncratic reasons for default: Case 1 (C ∗ <
x
pa (Xa −R∗ )
).
1−pa
Additionally, we showed that the supply of corporate assets may even decline if risk has
been increased. This will take place if the borrower’s wealth is no bottleneck for collateralization (C ∗ =
pa (Xa −R∗
)
1−pa
. An increase in risk then corresponds to a decrease in
contractual collateralization. As a result, corporate assets may even fetch a higher resale
price (see figure 5, case 2).
III
EQUILIBRIUM DETERMINATION OF LIQUIDATION VALUES
19
P
pX − I
pX − R
P Out
(1 − pa0 )L/I
x
(1 − pa )L/I
Figure 6: Idiosyncratic reasons for default: Case 2 (C ∗ =
pa (Xa −R∗ )
).
1−pa
If default occurred due to some industry-systematic reason, the equilibrium price of seized
assets may decline. Imagine that all borrowers increase risk and the whole industry suffers.
As soon as the minor demand of the surviving high-WTP buyers, i.e. industry insiders
with cash on hand, is satisfied, assets will fetch a lower equilibrium resale price. Strictly
speaking, the price drops to the WTP of the outsiders. For example, in figure 7, the
equilibrium price of assets declines from pX − I to P Out as borrowers implement a riskier
project (see red pinheads). If the demand side is almost completely exhausted, even a
decrease in contractual collateralization is not able to outweigh the disadvantages with
regard to the resale price.
11
P
pX − I
pX − R
P Out
(1 − pa )L/I
(1 − pa0 )L/I
x
Figure 7: Industry-systematic reasons for default.
11
The same would be true if potential buyers were not homogenous, e.g. if there were different (opportunity) costs for cash on hand, or debt among the insiders or outsiders had different expenditures for
hiring managers.
III
EQUILIBRIUM DETERMINATION OF LIQUIDATION VALUES
20
Model Adaptions
The last section elaborated that liquidation values in equilibrium (P ∗ ) crucially depend
on the endogenously chosen level of risk as well as on the potential buyers. As the market
value of the pledged position for the bank is the equilibrium liquidation value, P ∗ = C ∗
holds. We will now consider our previous explanations in our model framework.
C = C|i = Ci , i {a, b}
(III.3)
C a , Cb < I
∂Ci
∈R
∂pi
(III.4)
(III.5)
Let Ca (Cb ) denote the collateral resale prices if projects a (b) fail (III.3). The cash flow
from liquidating the collateral only partially repays the loan (III.4). Otherwise, granting
loans would not be risky for the bank. Equation (III.5) takes into account the previous
results according to which risk-shifting may affect resale prices positively or negatively.
We now analyze the consequences of endogenous liquidation values as a whole. We must
distinguish three possible parameter constellations:
1) The borrower’s wealth is very large, which necessarily results in a limitation of collateralization (not depending on whether or not liquidation values are correlated).
2) The borrower’s assets drop below both corresponding maximum levels of collateralization.
3) The borrower’s wealth is so large that the maximum level of collateralization is binding
for project-related liquidation values, but not for uncorrelated ones or vice versa.
Constellation 1 can be analyzed in the same way as in section II. No further explanations
in the form of additional scenarios have been deemed necessary against this background.
Instead, we distinguish two cases depending on whether risk shifting leads to either higher
or lower resale prices. In analogy to section II, we start our analysis by examining the
critical repayment for risk-shifting in each case. Within these analyses, we include constellations 2 and 3.
III
EQUILIBRIUM DETERMINATION OF LIQUIDATION VALUES
21
Critical repayment
The borrower’s profit function is now given by:
Y
(R, C) = pi (Xi − R) − (1 − pi )Ci
i
(III.6)
Proposition 2: The critical repayment in cases of project-related liquidation values
may decline and drop below the one in cases without any collateralization.
Proof: Comparing the borrower’s profit functions as done in section II, we determine
the critical repayment in cases of risk-adjusted liquidation values (Radj ):
pa (Xa − R) − (1 − pa )Ca ≥ pb (Xb − R) − (1 − pb )Cb
⇐⇒
(pb − pa )R ≥ pb Xb − pa Xa + Ca − Cb − pa Ca + pb Cb
Solving for the limiting case, we obtain:
pa Xa − pb Xb (1 − pb )Cb − (1 − pa )Ca
(1 − pb )Cb − (1 − pa )Ca
+
= RoC +
= Radj
pa − pb
pa − pb
pa − pb
{z
} |
{z
}
|
I
II
(III.7)
If II < 0, i.e. for
Ca
Cb
>
1−pb
1−pa
> 1, the critical repayment decreases and a negative risk
effect induced by pledgeable assets appears (Radj < RoC ). Risk-related liquidation
values do not influence risk-shifting if the proportion of Ca to Cb corresponds to
the reciprocal proportion of the default probabilities. In common models, the quite
unrealistic assumption of independence between project risk and liquidation values,
justified by external collateral, yields the same results.
Subsequently, we term Radj < RwC a ’negative risk incentive effect’. The borrower’s loss
relatively increases if he implements investment a because of the correlation between ex
ante risk-taking and ex post liquidation value. A high liquidation value is equivalent to a
higher loss, because the borrower is not able to realize this market value in a discretionary
sale. Moral hazard increases. As soon as the rational borrower anticipates this, he will a
fortiori increase risk by choosing project b. Astonishingly, risk-shifting occurs earlier, i.e.
at lower repayments, than in cases without collateral. The reason for this is that poor
borrowers do not have any assets to lose. For them, it does not matter whether project
risk and liquidation values are correlated or not.
III
EQUILIBRIUM DETERMINATION OF LIQUIDATION VALUES
22
Expected profits and credit rationing
With regard to the bank’s profit-maximizing strategies, we still have to distinguish whether
project a or b is favorable (c.f. section II). We are going to start with a positive risk
incentive effect, i.e. a positive correlation between risk and liquidation values (Radj >
RwC > RoC ). If the borrower invests in project a and fails, his assets are worth less
than in cases of miscarriage with project b. Thus, the critical repayment increases. We
have already traced this phenomenon back to a decreased amount of collateralization in
equilibrium which overcompensates higher default rates (see Figure 6).
I. Positive
risk incentive effect 1−pb
a
Radj > RwC > RoC ; C
Cb < 1−pa
Scenario 1) pa Radj + (1 − pa )βCa > pb Xb
Due to Radj > RwC , Radj ≥ Xa is possible. Unless the bank demands a repayment larger
than Xa , the borrower will never undertake project b. The bank’s optimal contract is
R∗ = Xa and C ∗ = 0. Its expected profit amounts to pa Xa − I. The borrower’s expected
profit is exactly zero. Credit rationing is not necessary (c.f. light blue area in Figure 9
afterwards).
If Xa is larger than Radj , a limitation of the demanded repayment is unnecessary. C ∗ = Ca
and R∗ = Radj are optimal.12 The bank’s expected profit is pa Radj + (1 − pa )βCa − I.
The borrower’s expected profit is pa (Xa − Radj ) − (1 − pa )Ca . Credit rationing follows (c.f.
dark blue area in Figure 9 afterwards).
Scenario 2) pa Radj + (1 − pa )βCa < pb Xb
As derived above, R∗ = Xb and C ∗ = 0 are optimal. The borrower’s profit remains
zero. The bank’s profit still amounts to pb Xb − I. Ceteris paribus, scenario 2) occurs
more seldom than before because of Radj > RwC > RoC .
II. Negative risk incentive effect 1−pb
a
Radj < RoC < RwC ; C
Cb > 1−pa
Scenario 1) pa Radj + (1 − pa )βCa > pb Xb
12
a
The critical repayment decreases as the ratio C
increases. We restrict the critical repayment Radj
Cb
to at least zero. A negative repayment does not make sense economically. If Radj is negative, project
b is also optimal for the bank because the borrower will only run project b.
III
EQUILIBRIUM DETERMINATION OF LIQUIDATION VALUES
23
We are now going to analyze a negative impact of project risk on liquidation values.
The more borrowers increase risk, the more borrowers are likely to default. If there
aren’t sufficient potential buyers, the equilibrium resale price decreases (as seen in Figure
7). In such a setting, Radj > Xa is impossible. The optimal repayment is R∗ = Radj .
The optimal collateralization level is C ∗ = Ca . The bank’s expected profit amounts to
pa Radj + (1 − pa )βCa − I. To determine whether a given negative risk incentive effect may
lead to even lower expected profits than lending money to borrowers without any assets,
we assess the critical, permissible level of costs (1 − β).
Proposition 3: Banks may prefer to lend to borrowers short of assets if costs of liquidating collateral are sufficiently high.
Proof: Comparing the bank’s expected profit in case of risk-related liquidation values
to the scenario without collateral yields
pa Radj + (1 − pa )βCa − I = pa RoC − I.
Applying (III.7), we obtain pa Radj + β[(RoC − Radj )(pa − pb ) + (1 − pb )Cb ] = pa RoC .
For β = 0, i. e. liquidation costs devour all liquidation proceeds, the bank always
obtains a smaller expected profit than in cases without any pledgeable assets. We can
determine a critical β, which leads to equal expected profits:
β crit =
⇐⇒
β crit =
⇐⇒
β crit =
(RoC
pa (RoC − Radj )
− Radj )(pa − pb ) + (1 − pb )Cb
(III.8)
b )Cb )
pa (1−pa )Cpaa−(1−p
−pb
(1 − pa )Ca
pa (RoC − Radj )
>0
(1 − pa )Ca
(III.9)
Due to Radj < RoC , β crit always exceeds zero. Whether β crit it is equal to or smaller
than 1 depends on the individual case. If β < β crit < 1 holds, the bank’s expected
profit decreases and banks prefer low quality borrowers.
We will now comment on this result and its requirements. A relatively high loss of assets
results in smaller critical repayments. These may not be fully compensated by pledged
liquidation values. As a result, the risky investment b becomes more favorable. The bank’s
expected profit sinks lower than in cases without any collateralization at all. We show two
appropriate numerical examples in the appendix, where we chose β1 = 70% and β2 = 40%.
III
EQUILIBRIUM DETERMINATION OF LIQUIDATION VALUES
24
Those values are not far-fetched, as empirical studies have shown. In the U.K., a β of
88% was reported, while Germany (73%) and France (35%) had considerably lesser net
realization values (Franks et al. (2004)).
But can the result of proposition 3 really be traced back to insufficient liquidation abilities?
Or is it rather caused by the effect of project risk on collateral liquidation values? In order
to address that issue, we plot two graphs. On the ordinate, we track the relation of
project-related collateral liquidation values. On the abscissa, we plot the project revenues
Xb /Xa . The blue areas highlight the cases in which collateralization increases the lender’s
expected profit. Thus, the white area characterizes those scenarios in which refraining from
collateralization is favorable for the bank. The permissible solutions lie within the green
dashed borders. In Figure 8 (a) , liquidation costs are supposed to be zero (β = 1),
as opposed to β = 0.5 in Figure 8 (b). A substantial increase in liquidation costs does
not create as many additional scenarios, as the introduction of correlation for liquidation
values (see white areas in Figure 8(a)).
In order to illustrate the differences in numbers, we calculated particular scenarios. For this
purpose, we fixed pa = 0.8, pb = 0.5, Xa = 150, Cb = 50 and increased Ca and Xb stepwise
to such an extent that the values do not violate our model assumptions. In total, the
number of scenarios amounts to 106, 377. All correlations are treated equiprobable here.
For β = 1, the expected profit diminishes in 11, 27% of the cases due to collateralization.
For a substantial increase in liquidation costs (β = 0.5), the ratio increases only slightly
to 12.69%. The differences do not base on changes with regard to the borrower’s project
choice.
(a) Advantageous collateralization in cases of ß = 1.
III
EQUILIBRIUM DETERMINATION OF LIQUIDATION VALUES
25
(b) Advantageous collateralization in cases of ß=0.5.
Figure 8: Reasons for refraining from collateralization.
Scenario 2) pa Radj + (1 − pa )βCa < pb Xb
If project b is favorable for the bank, the borrower obtains zero profit. Credit rationing
does not occur. Figure 9 illustrates the results of the two-way interaction between project
related liquidation values and credit rationing.
Figure 9: Credit-rationing in cases of risk-related liquidation values.
IV
AGENCY COSTS AND THE ROLE OF INFORMATION
26
The ratio of liquidation values is displayed on the ordinate, the project revenues Xb on
the abscissa. As in Figure 3, we normalize the axes by Xa . The light and dark blue areas
denote those cases in which the borrower implements project a. Even given a negative
risk incentive (Radj < RoC ), banks may prefer project a over project b (see area above the
vertical dashed line at
1−pb
1−pa ).
Within the light blue surface, Radj > Xa holds. Demanding
Radj and Ca would cause a negative profit for the borrower. For R∗ = Xa and C ∗ = 0,
the borrower’s expected profit is zero. Credit rationing does not occur. Within the dark
blue area, Radj ≤ Xa holds. Project a is favorable for the bank. R∗ = Radj and C ∗ = Ca
coincide with credit rationing because the borrower’s profit is strictly positive. The blue
areas end at pa Radj +(1−pa )βCa = pb Xb at the bottom right. To the right of the dark blue
surface, the bank prefers project b, because Radj is too small. Radj even turns negative if
the ratio Ca /Cb increases far enough. Nonetheless, negative repayments do not make sense
economically. Solving the problem by limiting R∗ to zero and demanding collateral also
results in the implementation of project b because the borrower increases risk immediately,
i.e. even for R = 0. The striking difference in the slopes at the top of the dark blue area
is based on the fact that the lender’s collateral claim (βC) is restricted to the contractual
repayment (Radj ). If project b gets more attractive for the borrower (Xb /Xa rises), the
critical repayment Radj diminishes and so does the lender’s collateral claim.13
IV
Agency costs and the role of information
Section III came up with the result that banks may in certain situations prefer to refrain
from collateralization. Credit rationing may increase. We now analyze whether these
results go from bad to worse (from a bank’s point of view), if the assumption of rational
expectations were abandoned. In reality, banks supposedly do not know all possible investment alternatives of a borrower. In the following, we determine agency costs which arise
for a totally naive lender, who does not know about the existence of a riskier project b at
all. Of course, this a very severe form of information asymmetries. But if there are any
positive agency costs for the principal, i. e. the bank, then other scenarios, which are arbitrary as well (e. g. only the liquidation value of collateral in cases of project b is unknown)
should lie in between. Now, the bank offers a loan only on grounds of common knowledge
project a, while the borrower chooses the project on basis of private information. Jensen
and Meckling (1976) define agency costs as the sum of:
13
Apart from this, the exact slopes also depend on the absolute values of Ca and Cb . The same holds
for different β. For a comparison to credit rationing in cases of independence between liquidation
values and project risk see Figure 3.
V
CONCLUDING REMARKS
27
1. the monitoring expenditures by the principal,
2. the bonding expenditures by the agent,
3. the residual loss.’
We do not consider any monitoring expenditures, because monitoring activity is supposed
either to be impossible or too costly. Moreover, there are no bonding expenditures by the
agent, because the latter cannot be bound to a project but is able to choose the risky
project b. Thus, agency costs are equal to the residual loss. Jensen and Meckling (1976)
suggest to measure the loss monetarily: ’... there will be some divergence between the
agent’s decisions and those decisions which would maximize the welfare of the principal.
The dollar equivalent of the reduction in welfare experienced by the principal due to this
divergence is also a cost of the agency relationship, and we refer to this latter cost as the
’residual loss’.’ The authors link the definition to the principal, i. e. the bank.14 We will
now analyze a third-best equilibrium.
Proposition 4: Being a completely naive bank increases agency costs of debt and thus
enlarges credit rationing issues.
Proof: A naive lender will demand R∗ = Xa and C ∗ = 0 due to costs of collateralization. As Xa > Rcrit holds, the borrower always chooses project b. He obtains
pb (Xb − Xa ) as Xa > Rcrit . If he agreed upon R > Xa , the borrower would reveal the
existence of his alternative investment. The bank has to bear resulting agency costs.
The latter hinge on which project would be favorable for the bank if the bank knew
about the existence of project b. If the bank knew about project b and the latter was
favorable, the agency costs amounted to pb (Xb − Xa ) . If project a was favorable (even
in the case where the bank knew about project b), agency costs would amount to the
decrease in profit due to the lack of knowledge, pa Radj + (1 − pa )βCa − pb Xa .
V
Concluding Remarks
The asset substitution problem and its relationship to leverage ratio has been addressed
frequently in economic literature. Collateralization commonly provides a solution to this
problem as it increases the critical repayment for risk-shifting, while credit rationing diminishes. Nevertheless, previous contributions (e.g. the well-known papers by Stiglitz and
14
For a further discussion cf. Kürsten (1994),pp. 180-183.
V
CONCLUDING REMARKS
28
Weiss (1981, 1986)) draw an incomplete and skewed picture by assuming collateral to be
external and its liquidation value to be exogenous.
We consider a more realistic framework as we endogenize this value. This accords well with
many borrower-lender relationships, such as project finance, where a borrower’s chosen
level of risk may affect collateral values (c.f. Chan and Thakor (1987)). We therefore
link the market equilibrium for corporate assets to the risk-shifting and credit-rationing
decision. First, our analysis shows that increasing project risk may affect liquidation
values in both directions, depending on reasons for default and the composition of market
participants. We then used these findings to analyze risk-shifting and credit rationing
issues. In case of a negative correlation between risk and liquidation values, financiers
may even prefer borrowers short of assets, while credit rationing issues exacerbate. Thus,
our model provides an explanation for financing poor projects, a phenomenon which also
arose in the latest financial crisis. There is not only a question of whether or not pooror high-quality borrowers pledge collateral as described in the corporate finance literature
so far, but also whether the bank itself requires collateral or not. If a positive correlation
between risk and the asset resale price is apparent, collateral solves the asset substitution
problem even better than in traditional models without any correlation.
What are the policy implications of this primarily theoretical contribution? We showed
that our results are mainly driven by the extent of the correlation between liquidation
values and project risk rather than by the lender’s liquidating abilities. As our examples
coincide with contemporary empirical studies, negative effects of collateralization do not
occur ’once in a blue noon’ but may become a serious problem. Thus, banking regulation
should consider possible correlations of collateral, not only in order to solve the credit
rationing puzzle.
Our results are generally based on rational expectations. Increasing asymmetries (e. g.
by assuming a naive lender) diminishes bank’s expected profit even more. An interesting
extension to our research would be to allow liquidation costs (1−β) to additionally depend
on the borrower’s action or the kind of collateral. Also, an examination of how equilibrium
project choices change under ambiguity aversion or (linear) partial information might
provide further insights.
A
APPENDIX
A
29
Appendix
Numerical Examples
Variable
Example 1
Example 2
pa
0,8
0,8
pb
0,5
0,5
Xa
150
150
Xb
160
160
Ca
42,67
89
Cb
10
10
I
50
50
β
0,7
0,4
RoC
133,33
133,33
Radj
121,55
90,67
Bank’s expected profit in cases of low bor-
106,67 - I = 56,67
106,67 - I = 56,56
rower quality
(with project a)
(with project a)
Bank’s expected profit with correlated collat-
103,22 - I = 53,22
81 - I = 31
eral values
(with project a)
(with project b)
13,33
13,33
14,22
0
Borrower’s expected profit in cases of low
borrower quality
Borrower’s expected profit with correlated
collateral values
In example 1, a negative incentive for risk (Radj < RoC ) leads to a reduced profit for the
bank, while it rises for the borrower. For the bank and the borrower, project a is optimal.
Example 2 points out that bank’s liquidation costs can cause reduced expected profits
for the bank and the borrower, because project b becomes favorable. Thus, we don’t
inevitably have a trade-off between the bank’s and the borrower’s profits.
REFERENCES
30
References
Asquith, P., R. Gertner, and D. Scharfstein (1994). Anatomy of financial distress: An
examination of junk-bond issuers. The Quarterly Journal of Economics 109 (3), pp.
625–658.
Benmelech, E., M. J. Garmaise, and T. J. Moskowitz (2005). Do liquidation values affect
financial contracts? evidence from commercial loan contracts and zoning regulation.
The Quarterly Journal of Economics 120 (3), pp. 1121–1154.
Besanko, D. and A. V. Thakor (1987). Collateral and rationing: Sorting equilibria in
monopolistic and competitive markets. International Economic Review 28 (3), pp. 671–
689.
Bester, H. (1985). Screening vs. Rationing in Credit Markets with Imperfect Information.
American Economic Review 75 (4), pp. 850–855.
Bester, H. (1987). The role of collateral in credit markets with imperfect information.
European Economic Review 31 (4), pp. 887–899.
Bester, H. and M. F. Hellwig (1989). Moral hazard and equilibrium credit rationing:
An overview of the issues. In G. Bamberg and K. Spremann (Eds.), Agency Theory,
Information, and Incentives, pp. 135–166. Berlin: Springer-Verlag.
Bolton, P. and D. S. Scharfstein (1996). Optimal debt structure and the number of
creditors. Journal of Political Economy 104 (1), pp. 1–25.
Chan, Y.-S. and G. Kanatas (1985). Asymmetric valuations and the role of collateral in
loan agreements. Journal of Money, Credit and Banking 17 (1), pp. 84–95.
Chan, Y.-S. and A. V. Thakor (1987). Collateral and competitive equilibria with moral
hazard and private information. Journal of Finance 42 (2), pp. 345–363.
Diamond, D. W. (1984). Financial Intermediation and Delegated Monitoring. Review of
Economic Studies 51 (3), pp. 393–414.
Diamond, D. W. (2004). Presidential address, committing to commit: Short-term debt
when enforcement is costly. Journal of Finance 59 (4), pp. 1447–1479.
Franks, J., A. de Servigny, and S. Davydenko (2004). A comparative analysis of the recovery process and recovery rates for private companies in the Uk, France and Germany.
Technical Report, Standard & Poor‘s Risk Solutions Report.
REFERENCES
31
Freixas, X. and J.-C. Rochet (2008). Microeconomics of Banking, Volume 2. MIT Press,
Cambridge, Mass.
Gertner, R. and D. Scharfstein (1991). A theory of workouts and the effects of reorganization law. Journal of Finance 46 (4), pp. 1189–1222.
Grunert, J. (2005). Empirische Evidenz zur Prognose der Ausfallwahrscheinlichkeit und
der Recovery Rate von Bankkrediten an deutsche Unternehmen. Dissertation Universität Mannheim.
Gupton, G. M. & Gates, D. . C. L. V. (2000). Bank Loan Loss Given Default. Technical
report, Moody‘s Investors Service, Special Comment November 2000.
Harris, M. and A. Raviv (1990). Capital structure and the informational role of debt.
Journal of Finance 45 (2), pp. 321–349.
Hart, O. and J. Moore (1994). A theory of debt based on the inalienability of human
capital. The Quarterly Journal of Economics 109 (1), pp. 841–79.
Hellwig, M. (2000). Financial intermediation with risk aversion. Review of Financial
Studies 67, pp. 719–742.
Igawa, K. and G. Kanatas (1990). Asymmetric information, collateral and moral hazard.
Journal of Financial and Quantitative Analysis 25 (3), pp. 469–490.
Jensen, M. C. and W. H. Meckling (1976). Theory of the firm: Managerial behavior,
agency costs and ownership structure. Journal of Financial Economics 3 (4), pp. 305–
360.
Keeton, W. R. (1979). Equilibrium Credit Rationing. Garland, New York.
Kiyotaki, N. and J. Moore (1997).
Credit Cycles.
The Journal of Political Econ-
omy 105 (No. 2.), pp. 211–248.
Kürsten, W. (1994). Finanzkontrakte und Risikoanreizproblem. Gabler, Wiesbaden.
Kürsten, W. (1995).
Finanzkontrakte und Risikoanreizproblem. Missverständnisse
im informationsökonomischen Ansatz der Finanztheorie.
Zeitschrift für betrieb-
swirtschaftliche Forschung 47 (10), pp. 366–369.
Kürsten, W. (1997). Zur Anreiz-Inkompatibilität von Kreditsicherheiten, oder: Insuffizienz
des Stiglitz/Weiss-Modells der Agency-Theorie. Zeitschrift für betriebswirtschaftliche
Forschung 49 (10), pp. 819–857.
REFERENCES
32
Long, M. and J. Malitz (1985). The investment-financing nexus: Some empirical evidence.
Midland Corporate Finance Journal 3 (Fall), pp. 53–59.
Myers, S. C. and N. S. Majluf (1984). Corporate financing and investment decisions
when firms have information that investors do not have. Journal of Financial Economics 13 (2), 187–221.
Nippel, P. (1994). Rezension der Habilitation ”Finanzkontrakte und Risikoanreizproblem”
von Wolfgang Kürsten. Zeitschrift für betriebswirtschaftliche Forschung 46 (10), pp.
885–887.
Nippel, P. (1995). Erwiderung zur Stellungnahme von Wolfgang Kürsten. Zeitschrift für
betriebswirtschaftliche Forschung 47 (10), pp. 370–372.
Shleifer, A. and R. W. Vishny (1992). Liquidation values and debt capacity: A market
equilibrium approach. Journal of Finance 47 (4), pp. 1343–1366.
Smith, C. W. and J. B. Warner (1979). On financial contracting : An analysis of bond
covenants. Journal of Financial Economics 7 (2), pp. 117–161.
Stiglitz, J. E. and A. Weiss (1981). Credit Rationing in Markets with Imperfect Information. The American Economic Review 71 (3), pp. 393–410.
Stiglitz, J. E. and A. Weiss (1986). Credit rationing and collateral. In E. et al. (Ed.),
Recent Developments in Corporate Finance, pp. 101–143. The Press Syndicate of the
University of Cambridge.
Williamson, O. E. (1983). Credible commitments: Using hostages to support exchange.
American Economic Review 73 (4), 519–40.
Williamson, O. E. (1988). Corporate finance and corporate governance. Journal of Finance 43 (3), pp. 567–91.