Delegated monitoring notes(word file) - NYU Stern

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Delegated monitoring notes(word file) - NYU Stern




    B40.3312.30 Spring 2001


I. Despite the inroads that securitization made on financial intermediation in the 1970s and 1980s, bank loans

     remain an important source of business and consumer credit. As of September 27, 2000 there were $1.08

     trillion in commercial and industrial loans outstanding at U.S. banks, and $1.63 trillion in bank real estate

     loans outstanding. Even though many large corporations are able to borrow directly through the securities

     markets, many of them still borrow from banks as well. .

     A. Why do some firms issue debt directly in the markets, while others borrow exclusively from


     B. Why do some firms do both?

II. In the past 15 years a new theory of the banking firm has arisen that is making progress toward answering

     some of these questions. The theory focuses on:

     A. Information asymmetries, which occur when one party to a transaction has more information

     than the other;

     B. The problems that arise from information asymmetries; and

     C. The institutional arrangements that have been developed to solve or at least ameliorate t

     hese problems.

    Suppose information were complete and costless. Then we would probably not need banks. Issuers and

    investors could find, negotiate, and transact with one another directly (possibly over the internet).

    But: Information about borrowers is not costless to gather or analyze, and information in financial markets

    is often incomplete. In particular, it is often prohibitively expensive for investors (who are outsiders to the

    borrowing firm) to stay informed about developments inside the firm.

     Illustration [from M. Berlin (1987)]: Suppose an investor wants to lend directly to a firm. He/she would

     have to:

    1. Find a firm that needs money;

    2. Determine its credit standing;

    3. Negotiate the terms of the loan (How much? For how long? At what interest rate?); and

    4. Find some way to make sure that the firm’s insiders are not diverting resources to themselves

    at his/her expense, or are not making business decisions that make the loan riskier. In other

    words, the investor would have to monitor the firm, which could be difficult and costly.

    III. What kind of contract would arise without monitoring? [Examples mostly from Diamond (1996)]


    1. The firm needs to raise $1 million, henceforth referred to simply as $1;

    2. Investors’ required rate of return is 5%;

    3. Everyone aggress that the firm has a profitable project to finance;

    4. Only the firm (the borrower) will be able to observe how profitable the project turns out to be.

In this case, think of a firm in a far-away locale that is borrowing from an individual investor. A conflict of

    interest exists between the firm’s insiders, who can appropriate resources to themselves, and investors

    (outsiders to the firm).

The project costs $1 to finance. The project has two possible outcomes:

    1. High (H) which can be thought of as occurring during good business conditions, with

    probability of .8, in which it returns $1.4; and

    2. Low (L) which can be thought of as occurring during a recession, with probability of .2, in

    which it returns $1.

How would an equity contract work in these circumstances? It would have to be some sort of profit sharing

    arrangement. Let’s assume it takes the form of a promise on the part of the firm to pay a fraction ? of the

    profits from the project to the investor.

Problem: The payoff to the firm and the investor are not portions of the project’s true value, V, but of the

    value reported by the firm, Z. Therefore, the payoff to the firm is V- ?????With no monitoring, the value of Z that maximizes the payoff to the firm is zero. In other words, the firm has an incentive to report that the

    project has turned out to have a low value as low as zero.

So: Equity contracts do not work well if at all without monitoring.

    Obviously, the investor would like to be able to put some kind of sanction on the firm when it appears it might be under-reporting the project’s value. Here we will assume:

    1. The investor can force the firm into bankruptcy and seize and liquidate the assets of the firm;

    2. But: Bankruptcy is expensive. So expensive, in fact, that the investor recovers only ? percent

    of the value of the firm’s assets, where 0 < ??, 1. (D. Diamond assumes that ? = 0 that the

    bankruptcy consumes all of the firm’s assets, which is an extreme assumption, but one that

    simplifies the example)

    Therefore, the amount recovered by investors is: ?V

    Bankruptcy costs are: (1-?)V.

    The investor would like to set a face value on the loan, f, (principal + interest) that will (a) allow it to meet the required rate of return of 5%, and (b) will somehow induce the borrower to repay the loan if it can.

From now on we will now refer to the investor as the lender because the contract is a loan. Note that the

    only tools available to the lender in the absence of monitoring are the power to force the firm into

    bankruptcy, and the ability to set the face value of the loan.

With bankruptcy and liquidation now possible, the payoffs are:

    Outcome: L (1-P = .2) H (P = .8)

     V: $1 $1.4

    Return to firm: 0 V f

    Return to lender: ?V f

How should the lender set f?

Expected return to lender = .8f + .2?V = $ 1.05 (the required rate of return);

Therefore: f = ($1.05 .2?V)/.8

This will depend on the expected recovery rate on the assets in the event of a liquidation. The higher the

    recovery rate, the lower the face value (and therefore interest rate) has to be on the loan. For the following

    recovery rates the face value is:

     Recovery rate, ? Face value of loan, f

    1 $1.0625

    .5 $1.1875

    .25 $1.25

    0 $1.3125

The last case, where the recovery rate is zero and the contractual interest rate on the loan is 31.125%, is the

    example given in the Diamond article.

    For this loan contract to work, the lender must always put the firm into liquidation if any offer is made to repay less than the full face value of the loan regardless of whether it thinks a bad outcome (L) has occurred or the borrowers are simply not being truthful. Look at the payoff structure to the transaction

    above. The only way the borrower makes any money on the transaction is if the outcome is good (H) and

    by being truthful (in which case it will get to keep an amount equal to V f). This contract is incentive

    compatible it has provided the borrower with the incentive to repay the loan if it can.

What does this tell us about the kinds of contracts that will arise when monitoring is not possible?

    1. They will be debt contracts with fixed face values;

    2. Covenants of the debt contracts will be written tightly;

    3. The debt contracts will be inflexible. If the covenants of the loan are violated the firm will be

    placed into bankruptcy, period. No other factors will be taken into account.

    IV. Loan contracts with monitoring.

     Why don’t investors engage in monitoring?

    1. If there a few large investors monitoring may make sense. But if there are many potential

    investors, each with only a relatively small amount to invest, it is likely to be too costly, both

    individually and collectively.

    For example, suppose the firm wants to borrow $1 million and there are 10,000 investors,

    each with $100 to invest. If the monitoring cost is $200, no one will monitor too


    2. There is a free rider problem. Why should an investor monitor (and incur the expense) when

    he or she knows that someone else is monitoring. In this case, it is possible that insufficient

    monitoring will occur (monitoring is a public good it as third party effects).

Enter banks: Investors could delegate the monitoring function to a single market participant (we’ll call it a

    bank), saving each investor the cost of doing it on his or her own.

With monitoring, it may is no longer necessary automatically to throw a firm into bankruptcy and

    liquidation when the firm is unable to make pay the full face value of the loan. Recall: Without monitoring

    the lender could not tell if the borrower’s representation that a bad outcome had occurred was the truth.

    With monitoring, the bank can tell whether or not the borrower is actually in a position to pay. The lender

    knows the true value of the project. It can accept a partial payment on a loan.

With monitoring, the lender can use the threat of liquidation to induce the borrower to pay as much as

    possible. Specifically, the lender can now accept a payment of $1 when V = $1 (the value of the project in

    a Low outcome), which before would have triggered a bankruptcy. The borrower will be no worse off

    repaying $1 than going through liquidation.

    Assuming that the recovery rate ??) is zero, with monitoring:

    Expected return to the lender = .8f + .2($1) = $1.05

Where .2(1) is the expected savings in financial distress costs.

     So: f = ( $1.05 - .2($1))/.8 = $1.0625

The lender can now either make a higher rate of return, or set a lower loan rate (6.25%). The value of the

    monitoring is the expected savings in distress costs.

Note that there are both private and social gains from monitoring: the deadweight loss of bankruptcy costs

    is eliminated with monitoring.

    V. Quis custodiet ipsos custodes?

Who will monitor the monitors (banks)? Hasn’t the delegation of the monitoring function merely added

    one more market participant that will have to be monitored to the transaction?

Investors (depositors) will face every problem in monitoring banks that they do in monitoring direct credit

    extensions to nonbank borrowers. In effect, monitoring of banks is not possible . This has two


     A. Bank liabilities will generally take the form of debt instruments with a fixed face value the

     kind of contract shown above to be feasible when monitoring is not possible. This provides the

     same incentives to banks as faced by the firms that borrow from banks. The banks are always

     better off paying a sufficient amount to avoid bankruptcy and liquidation.

     Banks in fact do fund themselves principally with debt instruments. As of 3Q 2000, debt

     instruments (deposits, subordinated debt, and other borrowed funds) represented 91% of the total

     liabilities of banks insured by the FDIC.

     B. Banks will be forced to diversify their assets. If they do not, they will be just as risky as their

     loan customer (in which case there is no point in using a bank as an intermediary.)

     1. Suppose the bank makes and monitors a single loan, with the same distribution

     of returns as in section III above. When the project returns $1 in a Low outcome, the

     bank can monitor and collect $1 without forcing the borrower into liquidation.

     2. However: The depositors would now force the bank into liquidation. Why? Because

     they cannot monitor the bank, they will deposit money into the bank only under a tightly-

     written debt contract that provides for automatic liquidation whenever the borrower (in

     this case the bank) cannot pay the full face value of the deposit otherwise they will not

     be able to earn the required 5% return on their deposits. In other words, depositors act

     just like lenders in a situation in which monitoring is not possible.

     3. The upshot is that undiversified bank lending (modeled here as a loan to a single

     borrower) does not work. Without diversification, the bank will be liquidated as often as

     the borrower, and nothing is gained.

How do we know that diversification can solve this problem?


     1. Bank makes two loans, $1 million each.

     2. The borrowers’ returns are independently distributed, but otherwise just like that of

     the single borrower considered above. Each loan has a .8 probability of returning $1.4

     million, and a .2 probability of returning $1 million.

     3. The bank attracts $2 million in deposits from 20,000 depositors. The deposits are

     unmonitored debt. Let B represent the face value (principal plus interest) of bank

     deposits per loan. There are $2B in total deposits.

     4. The bank lends to two borrowers under a debt contract with a face value (principal and

     interest) of F ($ F million). It collects F when the project returns $1.4 million, and

     monitors to collect $1 million when the project is worth only $1 million. No liquidation

     is necessary to enforce the loan contracts.

     There are three possible outcomes:

     1. Neither loan defaults.

     2. One loan defaults.

     3. Both loans default.

Distribution of payments to the bank:

    Prob. That payment

    Probabilityis > or = this value

    2Neither loan defaults P = 0.640.64

    (both pay F)

    One loan defaults 2P(1- P) = .320.96 = .64 + .32

    (one pays $1, one pays F)

    Both loans default(1 - P)2 = .041.0 = .64 + .32 + .04

    (both pay $1)

    Note that there are two ways that only one loan can default. One is that loan A defaults and loan B pays in

    full; the probability of which is (1 P)P. The other is that loan A pays in full and loan B defaults, the

    probability of which is P(1 P). The sum of the two possible outcomes is 2P(1 P), which in the example

    is 2(.2)(.8) = .32.

    Assume that liquidating the bank consumes all of its assets: ? = 0. Can the bank survive the default of one loan, on which it collects $1? (For simplicity, assume the units are

    in millions.) If so, its probability of collapse can be reduced to only .04 (see table of outcomes above)

    the case when both loans default at once.

    If it can, then:.

    Total payments to depositors = $2B with probability .96

     = 0 with probability .04.

Required rate of return on deposits = 5%, so the expected repayment to depositors is $2(1.05)

    In this case, .96($2)B = $2(1.05)

    So: B = $2.1875 This is the most the bank should promise to repay to depositors if it knows there is

    a .96 probability that, at worst, one loan will default (or, alternatively, that there is only a .04 probability

    that both loans will go bad at once).

    Let R be the promised interest rate of the deposits, such that $2B = $2(1 + R) BB

    Then $2.1875 = $2(1 + R), B

    and R = 2.1875/2 1 = 9.375% B

    So: The bank must be able to pay $2.1875 when one loan defaults (and the bank recovers $1 on that loan).

    When one loan defaults and the other pays the full face value, F, the bank’s earnings are 1 + F.

    So: 1 + F must be equal to $2.1875. Therefore, the bank should set a face value of each loan of F = $1.1875. If the bank makes loans with this face value in other words, if it charges an interest rate equal

    to 18.75% on its loans, it will have the ability and incentive to meet its deposit obligations with a

    high (.96) probability.


    (1) Banks can operate with a diversified portfolio with a low (though nonzero) probability of default. (2) This arrangement permits only a few agents (banks) to engage in monitoring; thousands of depositors need not monitor on their own (which is probably too costly for them to do anyway).

    (3) Banks monitor loans, but will finance themselves with unmonitored debt.

    (4) Banks will diversify their assets (if permitted to do so by law). Diversification makes bank deposits safer than bank loans.

    (5) Laws that limit diversification remove much of the advantage of banks as intermediaries, and makes deposit riskier. Banks subject to such laws (such as restrictions on branching, which will limit the geographic diversification of bank loan portfolios) will lobby for deposit insurance.

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