Discussion of Calomiris Kahn. Economics 542 Spring 2012

Transcription

1 Discussion of Calomiris Kahn Economics 542 Spring

2 Two approaches to banking and the demand deposit contract Mutual saving: flexibility for depositors in timing of consumption and, more specifically, in the implicit insurance of unobservable risk outcomes (Diamond and Dybvig) Mutual investment: enforcement of manager performance and, more specifically, in situations of costly monitoring (Calomiris and Kahn). 2

3 What does demand feature of the contract accomplish? Mutual saving: allows high need individuals to access consumption in an incentive compatible manner (allowing their behavior to transfer their private information about need) Mutual investment: allows lender to forestall intensified agency problems, arising from the unobservability of borrower actions or outcomes. 3

4 Background from prior lectures If only borrower can see outcome, then a debt claim is an outcome if there is a method ( ex post state verification or ex post monitoring a technology for determining the nature of outcomes). We reviewed this idea previously, attributing it to Townsend and Williamson. This is a bankruptcy situation: borrower signals that he cannot make payments and is verified. [Examples: mortgage default (individual borrower), Lehman banktuptcy. Each situation may have taken a year or more to resolve value of underlying assets] But there is really no time dimension to this, there is no ongoing evaluative activity on the lender s side, lender is passive 4

5 CK model In order for lenders to access higher return projects, they must relinguish control over resources to borrowers. An agency problem occurs: the borrower will take actions that are desirable from his perspective but not necessarily from the lenders. Stealing (absconding with) resources. Example?: MF global Taking on more risky projects than was initial common understanding There are limits to direct punishment of borrower ex post (also in the basic debt model) 5

6 Structure Lender has one unit, opportunity cost of S Borrower needs one unit (no resources, standing in for not enough), and has a project (comparative advantage at evaluating some group of investments) that has uncertain returns Return outcomes are T 2 >T 1 ; prob(t 2 )=. (Greek g for good) 6

7 Borrower commitment problem Borrower learns return prospects Cannot directly commit not to take action that hurts lender Formalized as absconding with a portion of assts. Banker gets fraction (1 A) when he departs, so that he compares his promised repayment (T P) if doesn t abscond to (1 A)T if does abscond. He absconds if P>AT If we think of absconding as fraud, then this indicates that absconding is more of a difficulty if returns are low. 7

8 Liquidation Liquidation (termination) is a means of forestalling bad outcomes CK assume that this is court enforced Amount which is recoverable per unit of initial investment is M Liquidation is useful, but not always so, if AT 2 >M>AT 1. Latter inequality implies it forestalls bad outcomes 8

9 Information production After initial investment, depositor can obtain at cost I, a signal that sharpens information if there is a good signal ( =g) then the likelihood of the good outcome increases (from to g ). If there is a bad signal, then the probability falls from from to b ). 9

10 Time line Period 0: contract, investment. Contract must produce incentive for borrower to fund Period 1: costly information production Contract must produce incentive for borrower(s) to produce information Period 2 liquidation Contact of interest demand contract must produce incentives for borrower to require liquidation for bad signals Period 2.5 lenders can abscond with stuff Period 3 payoffs 10

11 1. No monitoring, No liquidation (roughly page 502) At last stage of game, the borrower will not abscond if the price of the bond exceeds Ati. Hence, the following payouts are credible (outcome of sequential equilibrium given the bond price P) as follows. Payment in both states if P <AT 1 assumption is that borrower pays if indifferent Payment in just good state if AT 1 <P<AT 2 Payment in neither state if P >AT 2 11

12 Borrower proposes contract: I will pay P (the price of this bond is P). Lender accepts if expected payout is at least S Expected payout requirement S min( P, AT2 ) (1 ) min( P, AT ) Borrower maximizes his expected payout subject to this constraint (getting funding) 1 12

13 What s borrower objective? Maximize expected value of his own future payouts max( T P,(1 A) T ) 2 2 (1 ) max( T P,(1 A) T ) 1 1 If project is run, choose smallest possible price P such that lender participation constraint is induced (constraint above binds) 13

14 Three possible outcomes: contract form depends on S, A and T Payments in both states with low expected return (S<AT 1 ). Contract is be based on payments in both states and the smallest face value is P=S. Expected payoff to borrower is (T 1 S)+ (1 )(T 2 S) = S T 1 + (1 )T 2 Note that low is defined relative to bad outcome, so that greater volatility (lower T 1 holding expected T constant) makes this condition harder to satisfy. Trust is harder to produce when volatility is greater Note also that low is defined relative to return on bad outcome, so that a lower A (more absconding) also makes this condition harder to satisfy. Trust is harder to produce when the rewards to misbehavior are greater. 14

15 Contract forms cont d Payments just in good state with intermediate expected return (AT 1 <S<AT 2 ) Contract is based on payment just in good state and smallest face value is determined by S= P. Defaults occur with probability (1 ). Expected payoffs for borrower are (T 2 P)+(1 )(AT 1 ) = S+ T 2 +(1 )(AT 1 ) Note that a small move in S over boundary value AT 1 leads to a much higher value of P (cost of funding is higher). No project if required expected return is high S>AT 2. This can occur even though it would be socially desirable to undertake even with absconding, because there is no credible way for the borrower to transfer necessary resources to the lender (this situation arises if T 2 +(1 )AT 1 >S> AT 2 ). 15

16 2. Adding Liquidation Liquidation destroys a portion L of returns to project (firm running under bankruptcy) Purpose of liquidation is recovery of lender resources. CK assume that this is an amount M that satisfies (CK_1): AT M AT 2 1 This implies that can be is desirable to have contracts that involve liquidation (right hand inequality) but is not always so. 16

17 Investment in information without agency problems Expected return if information not produced R T (1 ) T 2 1 Expected return if information is produced B q *[ T (1 ) T ] g g 2 g 1 q *max[ T (1 ) T, M] b b 2 b 1 Probability of good signal (q) must satisfy prob( T T ) q * q 2 prob( T T i); q prob( i) q i 2 g g b b 1 q ( )/( ) g b b g b i 17

18 Some comments If M< conditional expected return with bad signal, then B = R (information is not valuable). Can check this by using probability relations on prior page. Investment in information requires B I>R, where I is the cost of information. How much higher does M have to be for given I? or what is largest I for given M at which investment is reasonable? 18

19 Contracts with information production Now can have two payments. P is payment with signal. Contracts must provide incentive for information production. Information production will occur only if P b <P g by a sufficient amount to warrant investment If there is no liquidation incentive in contract then must be concerned about absconding P b <AT 1 P g <AT 2 [These limits would make total sense if signal is perfect (defined below): I am not so sure that they do if it is not perfect, but see top of page 504 right hand column]. Now suppose that signal is in fact perfect ( g =1 and b =0, implying q=g]). The highest expected return that can be promised to the lender is AT 2 +(1 AT 1 I. This is better than AT 2 if I is not too large. So there may be value to information production even if there is not liquidation. Projects can be undertaken for higher required returns than without information production, if the signals are pretty informative and the costs are not too high. Information lets borrower get higher expected profits, as he does not need to pay prices that are as high as above, if the lender s expected return requirement is not high. 19

20 Why have liquidating contract? Let s continue the above example, in which the signal is perfect. Let s also assume that there are NO returns in the bad state (T1=0). But we ll think of the return in the good state as quite high, so that the project can be worthwhile. Its not good enough that we can rationalize doing it if we can t terminate it. That is, S> AT 2 typo corrected in last line 20

21 What does a liquidating contract do? It means that the lender gets M if the bad signal is realized and if the project is liquidated. So, under this contract, the lender s expected return can be as high as AT2 (1 ) M I If (1 )M I>0, then this is an improvement. Demand debt expands feasible investment activity, by reducing damage in worse case scenario. It is necessary when required returns are relatively high. But if they are really high, then it is not desirable to do project at all. 21

22 Notation 1 = endowment of lender S = required expected return of lender 1 = project funding requirement for borrower Ti = return to project in state I A = fraction of return that borrower can take = unconditional probability of good state (2) P = face value of bond Pg,Pb = face value of bond L M = recoverable in event of liquidation 22