Correlated Default and Financial Intermediation

• Date: 01 June 2017
• Published date: 01 June 2017
• Author: GREGORY PHELAN
• DOI: http://doi.org/10.1111/jofi.12493

THE JOURNAL OF FINANCE •VOL. LXXII, NO. 3 •JUNE 2017

Correlated Default and Financial Intermediation

GREGORY PHELAN∗

ABSTRACT

Financial intermediation naturally arises when knowing how loan payoffs are corre-

lated is valuable for managing investments but lenders cannot easily observe that

relationship. I show this result using a costly enforcement model in which lenders

need ex post incentives to enforce payments from defaulted loans and borrowers’ pay-

offs are correlated. When projects have correlated outcomes, learning the state of one

project (via enforcement) provides information about the states of other projects. A

large correlated portfolio provides ex post incentives for enforcement. Thus, inter-

mediation dominates direct lending, and intermediaries are financed with risk-free

deposits, earn positive profits, and hold systemic default risk.

AS IS WELL KNOWN,BANKS AND OTHER financial intermediaries frequently hold

assets whose risks are correlated and hard to value. Thus, while loans are

jointly correlated, either it is unclear how they correlate with easily observable

information or that information has low explanatory power. Moreover, banks

do not simply pool risk: banks’ balance sheets are risky and banks produce

information to efficiently monitor investments, yet banks can nonetheless pro-

duce safe deposits from their assets. This paper proposes a mechanism that

would explain intermediation with this risk exposure.1

The key contribution of this paper is to show that financial intermediation

with correlated risks naturally arises when knowing how loan payoffs are

correlated is valuable for managing investments but lenders cannot easily

observe this relationship (as might be the case for investments in nontraded

securities). When a complete description of a portfolio’s correlation structure is

unknown, an investor with a large portfolio can learn the relevant information

∗Gregory Phelan is with the Department of Economics, Williams College. I have benefited

tremendously from feedback from Quamrul Ashraf, Bruno Biais, William Brainard, Gerard Caprio,

Maximilian Eber, John Geanakoplos, Johannes H¨

orner, Michael Kelly, David Love, Peter Montiel,

Guillermo Ordo ˜

nez, Peter Pedroni, Stanislav Rabinovich, Ashok Rai, Alexis Akira Toda,and anony-

mous referees. The views and errors are my own. I have read the Journal of Finance disclosure

policy and have no conflicts of interest to disclose.

1Economists have developed a number of other explanations for why intermediaries are often

exposed to more correlated, or aggregate, risk than standard models of intermediation would pre-

dict: fixed costs of developing expertise in an industry or asset class provide incentives to specialize;

limited liability gives incentives to take risk, passing downside risk to depositors (Hellwig (1998));

not monitoring as a form of ex ante risk-shifting encourages investment in aggregate risk (Kahn

and Winton (2004)); and banks have strategic incentives to fail at the same time if they expect to

be bailed out (Farhi and Tirole (2012)).

DOI: 10.1111/jofi.12493

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by monitoring or servicing the assets in the portfolio—and the investor has

incentives to do so because this information is valuable. Small investors cannot

learn much from their portfolios as their sample size is small. As a result, it

is natural for an intermediary to borrow from small investors and hold a large

portfolio, which provides incentives to learn the condition of their loans and

improve portfolio performance. In addition to explaining why intermediaries

hold loans with correlated risks, my model rationalizes empirical regularities

regarding returns to scale and the use of hard and soft information in lending

(discussed below).

I develop my results using a simplified costly enforcement model as in Krasa

and Villamil (2000). Lenders must pay a cost to enforce payments from bor-

rowers, and cannot commit to enforce payments (or to monitor, service, or

audit defaulted loans), and so must have ex post incentives to do so. I depart

from their setup in two principal ways. First, I suppose that borrowers’ payoffs

are correlated: there are two “aggregate states” that index the distribution of

payoffs. Knowing the aggregate state (how loan payoffs are related) typically

allows lenders to pursue improved enforcement strategies. Second, I suppose

that enforcement costs are large: if a borrower defaults only in the states in

which the borrower cannot repay the loan, the enforcement cost exceeds the

expected gain. As a result, the borrower defaults stochastically when able to

repay. Knowing the joint condition of loans is valuable when enforcement costs

are low, but even more valuable when costs are high. When costs are high,

without knowing the joint condition of loans, a lender does not have ex post

incentives to enforce payments. But a lender will have incentives to enforce

payments ex post when the likelihood of a “good aggregate state” is sufficiently

high (Proposition 3).

In this setup, correlation increases portfolio values because lenders must

take costly actions to manage their investments (Proposition 4), and financial

intermediation endogenously arises when borrowers have correlated payoffs. I

show that intermediation can arise when intermediaries diversify idiosyncratic

risks in order to isolate correlated (sectoral/aggregate) risks (Proposition 6). By

diversifying away all risks except correlated risks, the intermediary can commit

to monitor more frequently than a single investor can, and as a result borrowers

repay more frequently. Intermediation serves to decrease monitoring costs in

the economy because correlation minimizes expected monitoring costs when

investors cannot commit to monitor. As a result, intermediaries earn positive

expected profits and hold correlated risk.2

2This result is closely related to the literature on diversification and intermediation. Diamond

(1984) and Williamson (1986) show that when multiple lenders are needed to fund a single project

and there is costly state verification, financial intermediation decreases monitoring costs. The

intermediary diversifies idiosyncratic risks, which allows an intermediary to offer risk-free de-

posits to its investors, thus eliminating the need to “monitor the monitor.” In Diamond (1984)

and Williamson (1986), intermediaries earn sure portfolio returns and zero profits. Compared to

Hellwig (1998), in my model the demand for aggregate risk is not driven by limited liability; it

is instead a feature that enables intermediaries to offer risk-free deposits. In contrast to Kahn

and Winton (2004), the decision to monitor in my paper is ex post rather than ex ante. My paper

Correlated Default and Financial Intermediation 1255

The model simplifies many important features to illustrate the point, and

it is worth understanding some of the richer features of the real world we

have in mind. First, information about current conditions is useful for manag-

ing investments. In general, any loan that requires interim or ex post monitor-

ing will benefit from having information regarding the appropriate action. In

particular, knowing the likely condition of defaulted borrowers provides useful

information for monitoring or auditing those loans. Lenders have many options

available when dealing with defaulted borrowers (e.g., restructuring the loan,

delaying foreclosure, Chapter 11 vs. 7) and the best choice may depend non-

trivially on current conditions. Servicing a loan to restructure payments (e.g.,

deferring interest payments or decreasing the principal value of a loan) may

improve the value to the lender, but servicing is a costly process that could

prove fruitless. The liquidation value of a borrower’s assets depends on the

market for those assets—the market value of a firm’s assets depends on the

condition of the industry, while the market value of a house depends on the lo-

cal housing market.3In a corporate default, it may be obvious that proceedings

must wipe out equity holders, but should a restructuring also take the costly

decision of replacing management? If the default were caused by aggregate

conditions rather than bad management, then no.

Second, valuable components of the correlation structure of some assets are

difficult to learn. Even when an investor can perfectly observe aggregate condi-

tions, the way investment payoffs depend on that state may still be uncertain—

in other words, investors may not know the sensitivities of their investments to

what is easily measured. (In contrast, the standard assumption is that “know-

ing the aggregate state” means knowing the aggregate state and all the impli-

cations of that state.) For instance, an investor may know that the economy is

in a boom or a recession without knowing what that means for the loans in her

portfolio. Will her loans weather the storm, or will they turn south? There is no

doubt that an aggregate shock occurred in 2007 to 2009, but economists have

spent years debating its implications.4The issue is further complicated when

investors must also discern the appropriate action for managing an investment,

also relates to Boyd and Prescott (1985), in which intermediaries naturally arise as coalitions to

address an information problem.

3Bernstein, Colonnelli, and Iverson (2016) highlight the importance of local markets and asset

specificity in resolving financial distress: the cases in which indirect costs of Chapter 7 bankruptcy

exceed those of Chapter 11 are concentrated in thin local asset markets with few potential buyers;

in contrast, no differences occur in thick asset markets. Cantor and Varma (2005) show that

recovery rates depend on contemporaneous industry effects, such as capacity utilization, and that

macro factors are more important for Chapter 11. Importantly, Gupton, Gates, and Carty (2000)

find no ex ante difference in recovery rates by industry, providing evidence that contemporary

“aggregate” information is useful. Woo(2009) shows that whetherresidential developers should file

Chapter 7 or Chapter 11 depends on aggregate conditions. Acharya, Bharath, and Srinivasan (2007)

find that creditors of defaulted firms recover significantly lower amounts in present value terms

when the industry of defaulted firms is in distress.

4For an interesting example, Lubben (2013) argues that observing an aggregate shock, even

one as clear as Lehman, nonetheless is insufficient to know how to proceed for liquidation or

reorganization for related complex firms. Lubben examines the legal and financial structure of

Bank of America and argues that no matter how complex Lehman was, the remaining “too big to