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Liquidity and Risk Management Author(s): Bengt Holmstrm and Jean Tirole Source: Journal of Money, Credit and Banking, Vol. 32, No. 3, Part 1 (Aug., 2000), pp. 295-319Published by: Ohio State University PressStable URL: http://www.jstor.org/stable/2601167Accessed: 20-03-2015 12:33 UTC

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MONEY, CREDIT, AND BANKING T,E,CTURE

Liquidity and Risk Management

BENGT HOLMSTROM JEAN TIROLE

Firms and financial institutions are best viewed as ongoing entities, whose project completion may require renewed injections of liquidity. This paper proposes a contract-theoretic framework integrating three dimensions of corporate financing and prudential regulation: (1) liquidity management, (b) risk management, and (c) capital structure. It concludes with a preliminary assessment of recent regulatory approaches to the treatment of market risk.

THIS PAPER IS CONCERNED with the corporate demand for liquidity and the various ways in which firms in the real and the financial sectors manage their liquidity needs so as to be able to carry out production and investment plans effectively without being held back by temporary liquidity shortages. Several key decisions impact a corporation's future ability to avail itself of financial funds.

First, the corporation's capital structure sets, among other things, a timetable for reimbursing investors. Short-term debt forces the firm to pay out cash, drying up liquidity. Long-term debt allows the Elrm more room to adjust to liquidity shocks, exerting pressure mainly by the constraints it places on the amount of new debt that can be raised. Preferred stock explicitly embodies a liquidity option (a form of line of credit) by allowing the firm to delay reimbursement. Equity is, of course, the most accommodating claim with no precise timetable for the payment of dividends.

Second, corporations do not invest all their resources in profitable, long-term projects. They also invest in less profitable liquid assets that are held on their balance sheets as buffers against shocks. We define a liquid asset as one that the firm can quickly resell or pledge as collateral at its true value and whose market value is unlikely to be depressed when the firm needs resources. Looking at this dual condition,

This lecture was delivered April 16, 1999, at Ohio State University by the second author. The authors are grateful to the participants for helpful comments.

BENGT HOLMSTROM is Paul A. Samuelson Professor of Economics at MIT. E-mail: [email protected]. JEAN TIROLE is professor of economics at IDEI and GREMAQ, Toulouse, CERAS, Paris, and atMIT. E-mail: [email protected] Journal of Money, Credit, and Banking, Vol. 32, No. 3 (August 2000, Part 1) Copyright 2000 by The Ohio State University


296 : MONEY, CREDIT, AND BANKING

we observe that the first part is just the notion of liquidity emphasized in the literature on market microstructure. The second part is the analog of the covariance condition in the consumption CAPM model stemming from the producers' demand for liquidity [see Holmstrom-Tirole (1998a) for the derivation of liquidity premia in this context and a discussion of how they differ from risk premia in a consumption-based asset pricing model]. The firm's demand for a liquid asset depends on whether and how much the asset will deliver when the firm needs cash. In this respect, corporate equity or commercial real estate may be poor instruments for securing liquidity even when they are liquid in the sense of market microstructure theory. Short-term treasury bonds better satisfy our two conditions as do cash instruments, of course.

Rather than hoarding liquidity themselves, corporations may secure lines of credit from finaricial institutions.l For example, they can contract with a bank or an insurance company for the right to draw a specified amount of cash at a given rate of interest by a given date in exchange for an upfront commitment fee. The associated liability for the financial institution must be backed up by an increase in its liquid assets, sufficient to make it likely that it can deliver on its promise. Liquidity provision is an important activity of banks. For example, roughly 80 percent of commercial and industrial loans at large U.S. banks are take-downs under loan commitments (Greenbaum and Takor 1995).

Third, corporations engage in risk management. They can use derivatives to hedge specific risks (interest rate, currency, raw materials, etc.). For example, a corporation with substantial exports may quickly become short of cash if the exchange rate sud- denly turns unfavorable. Foreign exchange swaps allow the firm to insure against this type of liquidity shortage. Using derivatives and forward and futures markets is only one of many ways in which firms can cover themselves against specific risks: other ways include securitization, insurance against theft, fire or the death of a key employee, trade credit insurance and diversification of various sorts (geographic, product mix, etc.).

Last, corporations also attempt to measure their global risk exposure. Sophisti- cated tools, such as RAROC or Risk Metrics, give an imperfect, but useful picture of a firm's or bank's exposure to various macroeconomic factors. Such Value at Risk (VAR) models, extensively used by banks to control their dealers' and traders' risk taking, and by prudential regulators to monitor banks, estimate the extreme lower tail risk of a portfolio. The value at risk is the level of loss that will be exceeded with some prespecified probability (1 percent, 5 percent, ...) over some time horizon (1 day, 10 days, a year, ....)2 The purpose of such models is to assess the probability that an entity runs into a serious liquidity problem and is forced into a costly liquidation of assets. These models have become popular in the 90s in the wake of recent scan- dals at Barings, Procter & Gamble, Metallgesellschaft, and the Orange County.

1. For more on lines of credit and loan commitments, see Crane (1973) and Greenbaum and Thakor (1995).

2. See Duffie and Pan (1997) and Gordy (1998) for a review of the techniques employed in such models.


BENGT HOLMSTROM AND JEAN TIROLE : 297

The Arrow-Debreu model, the cornerstone of modern finance, offers few clues for understanding the above-mentioned three practices, let alone how they are related. In the Arrow-Debreu model capital structure is irrelevant (Modigliani-Miller). Nor do firms need to hoard liquid assets, since they can issue claims against the full value of the new investments (see below). Finally, claimholders cannot gain by having firms engage in risk management, since reshuffling state-contingent resources in a complete market does not affect the market portfolio.

Two arguments that have been put forward to explain the value of liquidity management are taxes and managerial incentives. Taxes are specific to locality and time and do not appear very helpful in explaining the observed patterns of liquidity management (Stultz 1996). And while risk management techniques could be used to filter out some of the exogenous noise in managerial compensation (Fite-Pfleiderer 1995; Stulz 1984, 1996), Froot, Scharfstein, and Stein (1993) rightly observe that this argument does not make a strong case for risk management, since the same could be accomplished by building the filter directly into the manager's contract. It has also been suggested that corporate risk management reduces the risk of bankruptcy, but without an explanation of why bankruptcy leads to inefficient liquidation and reallocation of assets,3 this point is subsumed in the earlier observation that issu- ing new claims in a complete market will not improve the claimholders' lot.

In our analysis, liquidity management derives its rationale from the corporations' concern for refinancing, a concern emphasized in various contexts by Thakor, Hong, and Greenbaum (1981) and Froot, Scharfstein, and Stein (1993) among others. In the Arrow-Debreu world, refinancing is not a concern because the entire benefit from reinvestment can be pledged to outside investors. Consequently, any positive net present value project can be funded at the time the opportunity for investment arises. Even when there is a debt-overhang problem, the initial debtholders can be per- suaded to exchange their claims for more valuable ones in order to raise the needed capital. The situation is very different when claims on the full value of the firm cannot be issued. If part of the corporate cake is nonpledgable, because insiders (managers, workers, owner-monitors, etc.) have to hold a share of that cake in order to behave properly, or if insiders enjoy significant private benefits for some other reason, it is possible that an (ex ante) socially beneficial liquidity need cannot be met unless the firm has secured sufficient liquidity in advance (see, for instance, Holm- strom and Tirole 1998b). Long-term financing is also of value if assets can become temporarily illiquid (nonpledgable) because of adverse selection problems (see, for instance, von Thadden 1995). Information about the true value of a firm's assets is typically limited to a smaller set of experts. If these experts have difficulties raising funds at the same time that the firm needs liquidity, the firm's assets cannot be sold at full value. While adverse selection may be a realistic reason for illiquidity, we will rely on our own moral hazard model to study the three earlier-mentioned aspects of liquidity management because of its greater ease of use.

3. See, however, Caillaud, Dionne, and Jullien (2000) for a model of hedging in the presence of endogenous bankruptcy costs.



The paper is organized as follows: Section 1 models corporate liquidity demand as in Holmstrom and Tirole (1998b) and applies the framework to the analysis of financial structure. Sections 2 through 4 contain the more novel material. Section 2 applies this model to the free cash flow problem and undesired refinancing. Section 3 derives the optimal risk management strategy. Last, section 4 provides a preliminary analysis of the regulatory treatment of market risk in prudential regulation. In 1996 the Basle Committee amended the 1988 international accord on prudential regulation to incorporate market risk, in reaction to the concern that banks' trading book losses might jeopardize their ability to manage their banking book. Section 4 as- sesses recent regulatory approaches to market risk in the light of section 3.

While this paper focuses on microeconomic issues, liquidity considerations are central to a number of other topics such as asset pricing and country-wide liquidity crises, which will not be pursued here (see Caballero and Krishnamurthy 1999).

1. MODELING CORPORATE LIQUIDITY DEMAND

1.1 Roadmap In order to study corporate demand for liquidity we need to extend the standard

two-period model of investment to include an intermediate, third stage at which the firm might need additional funding (see Figure 1 for a representation of the timing of the model). Initially, we assume that the firm does not produce any income at the intermediate stage; rather, it may be hit by an adverse shock and required to plow in some extra cash in order to be able to continue the project. There are two approaches

'tCash poor firtrl'l

/ overruns /reinvestment Cash need

/ \shortfall in earnings

O 1 Continue 2 * / E E

Financing Outcome

Liquidation downsuing

FIG. 1


BENGT HOLMSTROMAND JEAN TIROLE : 299

the firm can take to deal with urgent liquidity needs. The first is to secure some source of liquidity before the shock occurs. For example, the firm may keep liquid assets such as treasury bills on its balance sheet or it can secure a line of credit from a bank. In the second approach the firm waits for the shock to occur before its starts raising funds.

We will show that the wait-and-see approach does not sufElce when liquidity shocks are exogenous. There will be situations where the firm would have been res- cued under an optimal ex ante contract, but will fail without such a contract. Neither initial lenders nor new lenders want to rescue the firm in certain states unless the firm secured liquidity services in advance. This is due to the fact that the borrower must always keep a stake in the firm and hence the firm's full value cannot be pledged to the outsiders. Consequently, the lenders do not internalize the loss incurred by the borrower when the project is stopped, resulting in excessive liquidation.

1.2 Optimal Liquidity Management At date O an entrepreneur (also called the "insider" or the "borrower") can invest

in a project with constant returns to scale. The scale of the project, I, is a continuous variable that can be selected freely.

The entrepreneur initially has "assets" or "net worth" A. These assets could be cash or liquid securities that can be used to cover the cost of investment. To implement a project of scale I > A the entrepreneur must borrow I-A.

A project started at date O and continued at date 1 (see below) either succeeds, that is, yields verifiable income RI > O at date 2, or fails, that is, yields no income at date 2. The probability of success is denoted by p. The project is subject to moral hazard between dates 1 and 2. The entrepreneur can "behave" ("work," "exert effort"), or "misbehave" ("shirk"); or, equivalently, the entrepreneur chooses between a project with a high probability of success and another project which ceteris paribus he prefers (is easier to implement, is more fun, has greater spin-offs in the future for the entrepreneur, benefits a friend, etc.), but has a lower probability of success. Behaving yields probability P = PH Of success and no private benefit to the entrepreneur, and misbehaving results in probability P = PL < PH of success and private benefit BI > O (measured in units of account) to the entrepreneur. Let Ap--PH - PL. In the "effort interpretation," BI can also be interpreted as a disutility of effort saved by the entrepreneur when shirking. Note that the private benefit is proportional to investment. For notational simplicity the rate of interest is taken to be zero. Both the borrower and the potential lenders (or "investors") are risk neutral. The borrower is protected by limited liability. Lenders behave competitively so that loans make zero profit.

After investment I is sunk at date O but before the entrepreneur works on the project, an exogenous liquidity shock p E [O, ) occurs at date 1. A cash infusion equal to pI is needed to cover "cost overruns" and allow the project to continue. If pI is not invested, the project is abandoned and thus yields no income. The fraction p is dis- tributed according to the continuous distribution F(p) on [O, oo), with densityt(p).

Regardless of the required fraction of the cash infusion, the project, if pursued, is still a project of size I, in that the income in case of success is RI and the borrower's



private benefit from misbehaving is BI. One cannot increase the size of the project after the initial stage. The timing is summarized in Figure 2.

We assume that the investment has a positive net present value. That is, under a rule that specifies that the project is abandoned if and only if p ' p for some threshold p, the expected payoff per unit of investment is strictly positive. The positive NPV condition under liquidity shocks is

m-ax{F(p)pHR-1-Jo pf(p)dp} > 0 * (1)

We first look for the optimal loan agreement and later discuss its implementation. It is easy to show that it is optimal to have a "cutoff rule" for the date-l reinvestment. There exists a threshold p* such that it is optimal to continue if and only if

P ' P* (2) The incentive constraint in case of continuation requires that the borrower's stake in case of success, Rb, times the reduction in the probability of success due to shirking be larger than the private benefit from shirking (due to risk neutrality the entrepreneur optimally receives 0 in case of failure):

(P)Rb ' BI. (ICb)

The break-even condition for the investors is

F(p*)[pH(RI-Rb)]-I-A + IP pIt(p)dp (IRe)

The lenders receive a return only if the project is continued, which occurs with probability F(p*). The left-hand side of (IR) is the expected pledgeable income. The right-hand side is the investors' date-0 outlay, I-A, plus the expected liquidity need. From these two constraints, we deduce the "debt capacity" (or more precisely the maximal investment that allows the lenders to break even):

Date 0 Date 1 Date 2 Disbursement

)< )< 3< x )< )( b Loan Investment Need for Moral Outcome agreement I cash infusion hazard

pI realized

No disbursement

V Project is abandoned FIG. 2



I = k(p*)A,

where

1 + JP p+(p)dp-F(P*)[PHR-PH AP I 1 (3)

1 + JP p+(p)dp-F(p*)po Note that the borrower's debt capacity is maximal when the threshold p* is equal to

/ B \ the unit expected pledgeable income Po-PH VR--J .

Given that lenders make no profits the borrower's net utility is the social surplus of the project, namely,

Ub = m(p *)I = m(p *)k( p *)A

where

m(p*)--F(p*)pHR-1-JP p+(p)dp (4)

is the margin per unit of investment. What is the optimal continuation rule? Intuition might first suggest that, given that

liquidity shocks are exogenous, one would want to continue if and only if this is ex post efficient, that is, if and only if p ' pHR. Indeed, p* = pHR = P1, maximizes the margin m(p*). However, at p* = pHR, the multiplier k is decreasing in p*. So one actually ought to choose a lower threshold than the ex post efficient one. It is easily seen from (3) and (4) that

1 + JP* pf(p)dp ub= F(p*) A,

1+JP pf(p)dp / B\ F(p*) \ AP J

and so the optimal threshold minimizes the expected unit cost c(p*) of effective investment:



p * minimizes c(p*) = 1 + lo Pf(p)dp

or

JoP F(p)dp = 1. (6) Condition (6) can be obtained by integrating by parts and rewriting the expected unit cost, of effective investment as

1-JP* F(p)dp

This expression also shows that at the optimum,4 the threshold liquidity shock is equal to the expected unit cost of egffective investment:

c(p*)= p*.

This in turn implies that the borrower's net utility is

P1 -p* Ub=p*_p A. (7)

Next, we observe that this optimal threshold lies between the pledgeable income po and the expected return P1

( /\P ) (8) This follows from the fact that the margin m(p*) and the multiplier k(p*) are both decreasing above P1 and both increasing below pO: see Figure 3.5 Condition (8) is consistent with (7): If p* were to exceed P1, the project could not be financed prof- itably. If p* were lower than pO, the debt capacity and the borrower's utility would be infinite.6

4. It is easy to show that c(-) is quasi-convex (c"(p*) > O if c'(p*) = O). 5. Indeed, m(-) is quasi-concave with a maximum at Pl and k(-) is quasi-concave with a maximum at

Po 6. Note that p* does not depend on pO and Pl as long as it falls between the two. The investment scale

only depends on pO.



investment multiplier >(P)

0 Po p* P1 P pledgeable NPV: liquidity income: maxirnizes shock maximizes profit debt capacity per uIiit of

investment

FIG. 3

We conclude that the pervasive logic of credit rationing applies not only to the choice of initial investment, but also to the continuation decision. In order to be able to invest more ex ante, the borrower accepts a level of reinvestment below the ex post efficient level (p* < pHR). The logic is important. Because the entrepreneur is credit constrained, his return on internal funds (A) exceeds the market rate (O). Therefore, he does not want to buy full insurance against the liquidity shock p (that is, set p* = P1) At full insurance the marginal return for his money is zero, while the marginal return from expanding scale is strictly positive.

Equation (8) implies that a wait-and-see policy, under which the borrower tries to raise funds from the lenders after observing the liquidity shock, is suboptimal. Even under perfect coordination (there is no "debt-overhang" phenomenon), lenders will provide new credit at date 1 only if the pledgeable income exceeds the amount of reinvestment, that is, only if p < pO. Because pO < p*, it is optimal for the borrower to secure in advance more funds than can be raised by a wait-and-see policy. This creates a corporate demand for liquidity. See Figure 4 for a summary of our findings.

Condition (6) has an interesting implication. An increase in the riskiness of the liquidity shock in the sense of a mean-preserving spread of F7 raises the left-hand side of (6) and thus reduces the threshold p*. So, the borrower should hoard more liquidity when the liquidity shock incurs a mean-preserving reduction in risk, as may occur, for example, when a new market opens that allows the firm to insure against a

7. See, for example, Rothschild and Stiglitz (1970, 1971). The distribution G(p) (with density g(p), say) is a mean-preserving spread of distribution F(p) if

lUDO lUDO lUDO lUDO

(i) Jo G(p)dp = Jo F(p)dp ( Jo pg(p)dp = jo p0(p)dp, so the means are the same), and rP rP (ii) J 0 G(p)dp 2 J 0 F(p)dp for all p.



capital inefficient liquidadon market will do under wait-and-see policy

Po P P1 l l I I ,p ' s I ' v '

positirre positiveNPV, negative net pledgeable negative NPV income net pledgeable continuation continuation mcome

continuation FIG. 4

previously uninsurable risk. Furthermore, (7) shows that welfare increases with an increase in the riskiness of p. The reason is the option value of discontinuing the project. Ex ante uncertainty about the liquidity shock p is a key ingredient in the de-

mand for liquidity. Suppose p were deterministic. If p 2 po = pH(R _ B ), then

investors do not want to lend at date 0, since they know that they will have to cover at date 1 a liquidity shock that exceeds the income that can be pledged to them at date 2. There will never be anything to distribute to investors. If p < pO, then the firm is always solvent at date 1, and new claims can be issued at date 1 (that partially di- lute existing ones) in order to meet the liquidity shock and continue; hence there is no need to hoard reserves.

A good way of thinking about this issue is in terms of insurance. A high liquidity shock is similar to an illness or an accident, and a low liquidity shock is similar to an absence of such a mishap. There is no scope for insurance if it is known in advance whether there will be an illness or an accident.

1.3 Implications The first implication of our analysis has already been stated: because the firm may

not be able to raise funds to pursue certain worthwhile projects at date 1, it ought to make sure at date O that it can avail itself of some liquidity. If negotiations run fric- tionessly at date 1, the firm can raise up to the pledgeable income (poI) in the capital market at that date. Thus the minimum amount of liquidity that the firm must secure at date O is the difference between the targeted reinvestment and the pledgeable income, that is, (p*-po)I.

At, this stage, the theory says nothing about the nature of this liquidity buffer. The firm can hold liquid securities on a balance sheet, or contract with an intermediary for a credit line. It is only when liquidity is scarce at the economy level and liquid as-



sets therefore sell at a premium that economic agents must organize the dispatching of liquidity so as not to waste it. Waste occurs when in some state of nature at date 1 assets are held by an economic agent who does not need them while another agent is short of liquidity. The transfer of liquidity between these two agents cannot be arranged at date 1 because the latter agent is unable to pledge enough to make it worthwhile for the former agent to lend. We refer the reader to Holmstrom and Tirole (1998b) for a discussion of wasted liquidity and the role of intermediaries as liquidity pools.

For the moment the theory also says nothing about the maturity of claims on the firm. Since the firm does not produce any cash flow at date 1, all reimbursements/ dividends must be paid at date 2. We now relax this assumption by allowing the firm to generate a profit at the intermediate stage.

2. INTERMEDIATE INCOME, FREE CASH FLOW, AND THE SOFT BUDGET CONSTRAINT

Let us first extend the model by assuming that the firm generates an exogenous (for simplicity), deterministic, and verifiable cash flow, rI, at date 1, where r ' 0: see Figure 5.

To solve for the optimal financing contract, we do not need to redo the analysis of section 1.2. Intuitively, since the pledgeable income as well as the NPV are increased by the amount rI, the unit cost of investment is no longer 1, but 1-r. The formulae above remain unchanged except that the cutoff p* is determined by

tP F(p)dp = 1-r . (9)

Even though the results closely track those of the liquidity shortage model of section 1, it is important to note that the short-term income, while deterministic and

Date 0 . Date 1 . Date 2 *. Disbursement

x x * )< X )( . )< > Loan Investment . * Accrual of Moral Date-2 agreement short-term hazard . income

income rI (RI or 0) * Realization pI No disbursement

of investment need

V .. Project is abandoned

FIG. S



fully pledgeable, is not equivalent to an increase in the borrower's equity A. Such an increase in equity would result in a larger investment (as is the case here), but not in a modification of the continuation rule. By contrast, condition (9) shows that the larger the short-term profit, the lower the optimal threshold p*. To understand this point, recall the scale expansion-insurance trade-off between increasing debt capacity (by reducing p*) and increasing the probability of continuation (by increasing p*). The short-term revenue makes investment more attractive and therefore makes it worth sacrificing continuation more in order to boost debt capacity.

While young firms or firms with substantial investment needs are well depicted by the liquidity-shortage model of section 1, Easterbrook (1984) and Jensen (1986, 1989) considered the opposite situation of "cash-rich firms" that generate large cash inflows exceeding their efficient reinvestments needs. Such firms have excess liquidity that must be "pumped out" in order not to be wasted on poor projects, unwar- ranted diversification, perks, and so forth. Jensen's (1989) list of industries with huge free-cash-flow problems in the 1980s includes oil, steel, chemical, television and radio broadcasting, brewing, tobacco, and wood and paper products.

The liquidity-shortage and free-cash-flow problems are opposite sides of the same coin. The key challenge in liquidity management is to ensure that, at intermediate dates, just the right amount of money is available for payment of operating expenses and reinvestments. Whether this results in a net inflow (the liquidity-shortage case) or outflow (the free-cash-flow case) is important for corporate finance, but from an economic point of view there is no conceptual distinction. Indeed we can merely reinterpret the liquidity-shortage model as a free-cash-flow model without changing the analysis.8

More formally, let us make the following free-cash-flow assumption: r > p*. Under the free-cash-flow assumption, and given that the entrepreneur cannot steal the intermediate income, the entrepreneur would reinvest excessively. He would continue as long as p ' r.

To obtain the optimal reinvestment rule, an amount

P1-(r-p*)I,

must be pumped out of the firm. The payment P1 can be interpreted either as repayment of short-term debt as in

Jensen or as a dividend payment as in Easterbrook. Note, though, that the dividend must be capped by a covenant. Otherwise, investors would want to pay dividends up to (r-po)I > P1 in order to prevent the entrepreneur from reinvesting whenever the liquidity shock exceeds the date- 1 pledgeable income p0. With this interpretation, we see that covenants specifying a maximum of dividend payment serve to protect the entrepreneur against excessive liquidation.9

8. For a related study of free cash flow and liquidity, see Krishnamurthy (1998). 9. This insight complements the standard and important explanation for the existence of such

covenants. They are usually viewed as protecting creditors against expropriation by the equityholders, who could use dividend distributions and share repurchases to leave creditors with an "empty shell."


. .


Until now, we have assumed that the date-l income is exogenously determined. Let us briefly consider the case in which income is influenced by the entrepreneur's date-O effort eO. It is natural to assume that effort shifts the distribution G(r|eO) of the date-l income higher (in the sense of first-order stochastic dominance).l

What is now the optimal liquidity management? Intuitively, there are two ways in which the entrepreneur can be induced to exert effort at date O.The first is standard and consists of increasing the entrepreneur's stake (giving new stock options) in case of a high date- 1 income. Alternatively, the entrepreneur may be given more liquidity when the income is high. This means that the date-l income is not mechanistically pumped out (redistributed to claimholders), but is in part kept by the firm to reinvest if needed. This yields a state-contingent continuation rule

p ' p*(r), (10) where p8( ) is an increasing function of the intermediate income.

Figure 6 depicts the optimal continuation rule as a function of the intermediate income for two cases. When date-O moral hazard is light (the private gain from misbehaving is small and the date-l income is a good indicator of managerial effort), the continuation rule is strictly increasing in date-l income, and it is inefficient to increase the entrepreneur's stake in date-2 income beyond what is needed to induce good date- 1 behavior. Two new features appear when the date-O moral hazard is substantial. First, the continuation function p* (r) is steeper. Second, since a cutoff p* (r) > P1 is inefficient even in first best, it will be optimal to award extra stock options to the entrepreneur after p*(r) hits the ceiling P

p* (r) p* (r)

pl P1 /

/.- pO pO/Sa@-bb

O r r O r r (a) Light moral hazard (b) Substantial moral hazard

at date O at date O FIG. 6

10. The following draws from Rochet and Tirole (1996), which applies the model in Holmstrom and Tirole (1998b) to peer monitoring and systemic risk.



On the other hand, for r small, a prescribed continuation rule p8(r) < pO is not credible. The investors and the entrepreneur are better off renegotiating the closure of the firm if p < pO. The entrepreneur always prefers continuation, while the investors gain (pO-p)I. This explains the flat part of the dotted line in Figure 6(b).ll

This is just the standard soft budget constraint problem: the entrepreneur is optimally threatened with closure in case of bad performance; however, the firm may be illiquid but solvent, which gives the investors an incentive to renege on their commitment and to rescue the firm. This, naturally, impacts negatively the entrepreneur's initial incentive.

3. OPTIMAL RISK MANAGEMENT

We have seen that, even in a world of universal risk neutrality, firms ought to obtain some insurance against liquidity shocks as long as capital market imperfections prevent them from pledging the entire value of their activity to new investors. Fol- lowing Froot, Scharfstein, and Stein (1993), we can use this idea to derive an ele- mentary explanation of corporate hedging.l2

In this section, we focus on optimal risk management when the investors can observe that the firm is indeed hedging and they understand the correlation between the derivative instrument and the rest of the firm's portfolio. In practice, investors may have trouble knowing whether the entrepreneur uses the derivatives for hedging or gambling purposes; we will study the corresponding issues in section 4.

3.1 Costless Hedging To build intuition, let us begin with the case in which the firm can at no cost hedge

against a shock on its date- 1 income. We extend the model of section 2 by adding an exogenous shock E to the date-l income, which becomes r-, with E(E|p) = O. For example, E may represent the uncertainty in the exchange rate of a country in which the firm produces or sells. An FX derivative allows the firm to stabilize its income to r which, for simplicity, we assume deterministic.

It can be shown (and this will be a special case of the result obtained in section 3.2) that it is optimal for the entrepreneur and the investors to agree to fully hedge the risk. Intuitively, the extra noise imposes undue variation in the liquidity available to the firm and there is in this model no reason to create ambiguity as to the continua-

11. In Figure 6(b), the dark line represents the optimal continuation policy when renegotiation can be ruled out. The optimal policy under renegotiation is depicted by the dotted line.

12. Other explanations have been offered in the literature. Stultz (1984) argues that corporate hedging allows managers to obtain some insurance for their risky portfolio (stock options, ....) against shocks that they have no control over. While this point is well taken Froot, Scharfstein, and Stein (1993) note that managers could obtain such diversification by going to the corresponding markets themselves, and so Stulz' argument relies on a transaction cost differential. Tax reasons have also been discussed in the literature. See Smith and Stulz (1985) and Stulz (1996) for more complete discussions.

Froot, Scharfstein, and Stein (1993) assume that capital markets are imperfect (firms are unable to borrow or issue equity in case of a shortfall), so that "internal finance" is cheaper than "external finance." They argue that the hedging activity shifts internal funds from excess cash scenarios toward deficit scenarios. Our treatment follows their idea while endogenizing the capital market imperfection.



tion rule. For a given amount of liquid assets, the continuation rule is p ' p* under hedging, and p + E < pt in the absence of hedging. The absence of hedging will lead to reinvestment in some states of nature with liquidity shock above pt and closure in other states with liquidity shock under p* (but higher than p0). This is inefficient because the marginal value of liquidity decreases with p. The entrepreneur should not be held accountable for a shock she does not control, provided it can be hedged at a fair rate.

Two important remarks are in order. First, the investors may need to check that the entrepreneur indeed hedges. For small FX shocks E the entrepreneur wants to hedge only if the distribution of liquidity shocks F(p) is concave. For large FX shocks, the umbrella provided by the soft budget constraint (the willingness of investors to finance p < p0) makes it less likely that the entrepreneur will want to abide by her promise to hedge. Similarly, if information accrued to the entrepreneur between dates 0 and 1 concerning the date- 1 liquidity shock p, hedging could become prob- lematic. In case of bad news and knowing that the project is unlikely to be continued, the entrepreneur would want to undo the hedge in order to "gamble for resurrection."

Second, the reader may be puzzled by the fact that the entrepreneur is risk loving with respect to reinvestment needs p see section 1-but risk averse with respect to cash-flow shocks e. The reason is that reinvestment embodies an option value. The firm can forgo reinvestment for bad realizations p, which makes variation in p valuable. In contrast, there is no scope for opting out of a bad realization of the cash-flow shock e.

To sum up, we have argued that firms should be insulated from all shocks that can be costlessly hedged in capital markets. Even firms owned and financed by risk neutral investors should purchase insurance against fire, theft, and other indiosyncratic events in order to reduce the variability in the reinvestment rule. Note that the interest in this fair-rate case is limited in that it does not make any prediction as to which firms should hedge: They should all fully hedge indiosyncratic shocks outside the entrepreneur's control! We now extend the risk management model to allow for partial hedging.

3.2 Costly Hedging While the death of a key employee is an idiosyncratic shock, a number of other

contingencies, such as interest rate fluctuatioIls, against which the firm can hedge in well-organized markets, are macroeconomic in nature. Thus even with perfect markets, such risk cannot be covered at a fair rate. To the extent that the firm's risk is positively correlated with aggregate risk, the firm must pay a premium in order to hedge. It is then optimal for firms to engage in partial hedging. Intuitively, entrepreneurs/insiders should want their fair share of aggregate uncertainty. In practice, hedging by the corporate sector is indeed quite incomplete (Culp, Miller, and Neves 1998).

What kinds of firms should hedge more?l3 One potential determinant is the firm's leverage. Stulz (1996) argues that firms with little debt or highly rated debt have no

13. We abstract from the fact that some types of hedging are subject to increasing returns (due in particular to the need for expertise), and so are best performed by large banks or firms.



need to hedge because such firms are better able to raise new funds on the capital market in case of a liquidity shock. Scholesl4 in contrast argues that such Elrms should hedge and borrow more. One goal of this section is to revisit this debate in the light of our model of optimal liquidity management. Importantly, a firm's leverage is endogenous, and may interact with factors that impact its liquidity and hedging strategy. The same point applies to other determinants of hedging. For example, Tufano (1996), studying mining corporations, finds that firms in which management has a bigger stake hedge more. Rationalizing this observation requires looking at the factors that impact the share of management.

Let us return to our canonical model, and denote by u ' O the unit cost of hedging (in section 3.1 we assumed u = 0). That is, to eliminate risk eI, the firm must pay Iu at date 0. We will still be able to write the investors' break-even condition in terms of an expected rate of return.l5 Let X denote the hedging ratio (0 < X c 1). The initial investment then costs (1 + Bu)I at date 0, and the firm has enough liquidity to continue at date 1 if and only if pI < [pt-e(1 -B)]I, where pt is, as earlier, the planned level of available liquidity.

As in section 2, we allow for a (deterministic for simplicity) date-l income rI. As we noted there, this date- 1 income in effect reduces the per unit cost of investment at date 0, here to 1 + Bu-r. The aggregate shock E can be viewed as a shock on date- 1 income, for example. The investors' break-even constraint states that, in expectation the investors' total outlay is equal to their benefit:

(1 + Bu-r)I-A + E[|P ( ) pf(p)dp] I = E [F(p 8-8(1-))]poI * (1 1)

As usual, the entrepreneur's utility is equal to the firm's NPV:

[ ( ))]plI-[1 + Xu-r+ E [lP8-(l-4P+( )d ]

Let

1 + Xu - r + E [I0 p+(p)dp] ' E [F(p 8-8(1 ))]

14. Cited on page 16 of "A Survey of Corporate Risk Management," The Economist, February 10, 1996.

15. One may think of this model as being embedded in a model of aggregate liquidity premia, as in Holmstrom and Tirole (1998a). But it can also be embedded in a CAPM-type model in which premia are associated with investors' risk aversion: The investors' break-even condition can then be written in the equivalent risk-neutral form, with u denoting the price of aggregate risk and the other uncertainty being firm specific and diversified away.



denote the unit cost of eXective investment, that is, the cost of obtaining (in expectation) one unit of unliquidated investment. It is equal to the net expected investment cost divided by the probability of continuation.

Using (11 ) and (12), the entrepreneur's objective filnction is

b C(p8,)_po (13)

The extent of hedging X and the hoarding of (other) liquidity pt are determined by a cost-minimization program:

min {c(pt, ) } . {p8 k}

This immediately yields the following separability result: The extent, of hedging (X) is invariant to changes in variables that affect only date-2 total benefit (Pl) and pledgeable income (p0).

Thus, suppose that moral hazard increases (B increases, and therefore p0 decreases). The entrepreneur's share in date-2 profit goes up, investment is reduced and presumably leverage also goes down.l6 Similarly, if we identify the rating of the long-term (date-2) debt with the probability, PH, Of reimbursement, then the extent of hedging is unrelated to the rating of the firm's debt.

We now turn to factors that potentially affect the firm's hedging behavior. Note first that for u = 0, the derivative of the cost function c with respect to the hedging ratio X is equal to 0 at X = 1. We thus verify the intuition given in section 3.1: If hedging is costless, the firm should fully hedge. On the other hand, for u > 0, the derivative of c at X = 1 is positive, and so partial hedging is optimal.

Rather than attempting a general analysis, we specialize the model to a uniform distribution: F(p) = p on [0, 1], say. Then

1 + Bu-r +-[(pe)2 + (1-)2a2 ] c(pt, >,) = 2

Pt

where o2 is the variance of e. In the uniform case, the optimal hedging ratio decreases with the ratio of the cost of hedging over the variance of the noise, that is, with the unit cost of hedging:

16. "Presumably" refers to the fact that there are several possible definitions of leverage (in this model as in reality), depending on what is on and off the balance sheet (is the extra liquidity (p*-po)I invested in securities or is it a credit line secured from a bank?) and on how the maturity composition of outsiders' claims is accounted for. We looked (in a non-exhaustive way) at a couple of accounting conventions, for which the leverage ratio was indeed increasing in the pledgeable income pO.



=1- 2.

T

In contrast, pt depends also on the date-l (expected) income r:

(p8)2 = 2(1-r + u) _ u

An increase in the cost of hedging u reduces the hedging ratio and (in the relevant range X ' O) decreases the hoarding of liquidity, (pt-r)I, if positive. It also raises the cost c.

Last, consider the impact of an increase in short-term income r. This increase does not affect the hedging ratio, but increases the amount of short-term debt per unit of investment (r-p8), if positive.l7

To conclude, hedging may or may not depend on factors that affect other dimensions of liquidity management including short- and long-term leverage. Any covari- ation between these endogenous variables requires a detailed analysis of the factors that create within-sample heterogeneity.

4. BANKING REGULATION AND RISK MANAGEMENT

4.1 Brief Overview of the Debate A famous accord designed by the Basle committee and passed in 1988 provides an

international harmonization of prudential rules. This accord focuses on credit risk. Its main objective is to define minimum capital requirements for the banks' on- and off-balance-sheet activities that depend on the identity and on the value of the assets of the borrower (government, other banks, private sector, . . .). This regulation of the banks' banking book raises a number of practical as well as conceptual issues regarding the nature of the risk, the lack of correlation measures, the choice of historical cost versus market value accounting, the incentive to securitize, and the definition of equity. [See Dewatripont and Tirole (1994) for a description of the 1988 regulations and a theoretical analysis of these issues.]

We will here focus on a specific but crucial issue: the treatment of the bank's trading book and market risk. The trading book "means the bank's proprietary positions in financial instruments (including positions in derivative products and off-balance-sheet instruments) that are intentionally held for short-term resale and/or that are taken on by the bank with the intention of benefitting in the short term from ac- tual and expected differences between their buying and selling prices, or from other price or interest rate variations, and positions in financial instruments arising from

17. The short-term debt can alternatively be measured as [r-(p*-pO)] if dilution is permitted, but this does not affect the conclusion.



matched principal brokering and market making, or positions taken in order to hedge other elements of the trading book.''l8

Derivative products (for example, swaps) that are clearly intended to hedge positions in the banking book can be classified by the banks as belonging to the banking book; they are then excluded from the market risk measure, but become subject to the credit risk (counterparty default risk) capital requirements.

When the initial accord was passed, it was already clear to the regulators that the absence of a coherent treatment of market risk was a serious shortcoming. The 1996 amendment to the 1988 Basle accord imposed a second capital adequacy requirement (CAR) for the trading book. Banks were now subject to two separate CARs, one on the banking book based on credit risk, and the other on the trading book based on market risk.

The 1996 amendment has drawn criticism, and is viewed by its designers only as an intermediate step toward a better framework. There are several problems.

First, it is sometimes hard to distinguish between credit risk and market risk. Sup- pose a borrower pledges real estate or equity as collateral for a loan. The value of this collateral is subject to significant market risk. Yet, for the bank, the risk is a credit risk (how much will the bank receive if the borrower defaults?). Similarly, a loan to a highly leveraged institution, such as Long Term Capital Management or to an emerging country, involve a fair amount, of market risk, even though formally the risk is one of counterparty default. As a last example, a loan take-down is not a ran- dom event in the business cycle, since borrowers are much more likely to draw on their credit facilities in bad times. Some of these examples also show how conceptu- ally difficult it can be to distinguish between the trading and the banking books (even though in practice the division is usually quite easy since the two activities are car- ried out in separate units within the bank). This raises a concern about using a piecemeal approach, a concern we will come back to.

Second, there is an issue regarding the measurement of the trading portfolio's overall risk. Unlike the regulation of the banking book, which by and large ignores any correlation between its component risks, the capital adequacy requirement for the trading book is meant to be based on an aggregate view of the trading portfolio. Measuring such risk requires sophisticated econometric techniques and good data concerning the volatility of the elements in the portfolio (bonds of various maturi- ties, currencies, derivative instruments, etc.), of the covariance matrix, and of the ef- fectiveness of the state-contingent portfolio reallocations. There are also problems with using historical simulations to predict future movements, relying on a small amount of data about extreme lower tail events (Gaussian approximations have thin- ner tails than the empirical returns) and choosing the time horizon.

The 1996 Amendment specifies a ten-day Value-at-Risk (VaR) with a 99 percent confidence level. That is, the capital requirement for the trading book (to be added to that on the banking book) is proportional to the maximum loss in the bank's portfo-

18. Basle Committee on Banking Supervision (1996), Amendment to the Capital Accord to Incorpo- rate Market Risks.



lio that can occur within ten days with probability more than 1 percent. The bank must meet, on a daily basis, a capital requirement on the trading book expressed as the higher of (i) its previous day's VaR number and (ii) an average of the daily VaR numbers on each of the preceding sixty business days, multiplied by a factor that is at least 3 and can be brought up to 4 depending on the outcome of backtesting.

How is this VaR computed? The Basle committee allows banks to use their own internal model, provided this model is approved by the regulators. The approval process is based on a number of criteria: skill of the staff (in risk control and back of- fice management), track record on accuracy in measuring risk, and stress testing to cover a range of factors than can create extraordinary losses. The use of an internal model is therefore a priori limited to sophisticated (and often large) banks. Other banks use the default option, the so-called "standardized measurement method" de- scribed in the amendment, which relies on a more prescriptive and mechanical treatment of risk.

It is also worth noting that another approach, the Precommitment Approach (PCA), originating at the U.S. Federal Reserve (see Kupiec and O'Brien l995a and b),was proposed as an alternative to this Internal Model Approach (IMA). The PCA proponents argued that the IMA requires substantial regulatory expertise and inde- pendence, and that the disclosure of the internal model is useful only if the risk structure is highly correlated over time. They argued in favor of a more flexible and lighter regulatory approach in which the bank itself would assess its maximum possible loss, which in turn would determine the capital requirement. Incentive compat- ibility would then be ensured by ex post penalties. The PCA proposal has been criticized on grounds that ex post penalties are particularly limited in situations of undercapitalization .

We refer to Rochet (1999) for a theoretical perspective on the relationship between IMA and PCA (as Rochet notes, the PCA is an "indirect mechanism" while the IMA is "direct mechanism" in the terminology of mechanism design. The two ought to be equivalent if the risk structure changes quickly over time and the regulators lack expertise to see through internal models). The criticism leveled at PCA concerning the difficulty of implementing ex post punishments applies as well to IMA to the extent that the inspection of the model does not suffice to ensure truth telling. The benefit of the PCA is its greater flexibility in letting the bank announce private information about future innovations in the risk structure and in relying less on regulatory expertise and benevolence. The benefit of the IMA is that if either the risk structure is highly correlated over time or/and the regulators are sufficiently staffed and com- petent and are able to see through a complex model, backtesting and inspection allow early action by the supervisory body. There is then a lower reliance on a difficult ex post intervention.

19. See Daripa, Jackson, and Varotto (1997). For general discussions of the dangers of and limit to ex post penalties, see the Federal Deposit Insurance Corporation Improvement Act (1991), Goodhart et al. (1998), and Dewatripont and Tirole (1994). Monetary penalties, public disclosures of financial conditions, and increases in the deposit insurance premium are likely to trigger gambling for resurrection or runs on the interbank market. Capital charges, inspections, and line-of-business restrictions are likely to be more effective punishments.



4.2 What Is It About? The introduction of a CAR on the trading book is motivated by a concern that

large losses on the trading book may dry up the bank's liquidity and thereby jeopardize the banking book. This spillover from the trading book onto the banking book raises the first question: Why is there a trading book in a first place? After all a bank's proprietary trading could be performed through a separate affiliate with no possibility for cross-subsidization between the two arms. The trading arm of the bank would then be just another securities firm. This question is rarely asked in the debate on the prudential regulation of market risk, but seems important when thinking about desirable rules.

There are two possible responses to the separation point. The first is that there are returns to scale in trading activities, in particular, due to the need for expertise. Thus, the knowledge used to hedge the banking book can be used for other purposes as well. It would be interesting to measure the extent of increasing returns of this kind.

Second, the trading book may really be about hedging the banking book, or, more precisely, about providing non-obvious hedges that insure against risk of the overall banking portfolio (we have seen that financial transactions that are clearly meant to hedge a specific risk can be switched to the trading book). In our view, this is an important argument in favor of an integrated or "whole bank" approach. A weaker ver- sion of this argument is that, even if the two books are stochastically independent rather than negatively related, the bank might still reduce its capital requirements by cross-pledging their outcomes (as in Diamond 1984).

Either way, it is hard to see the rationale for a piecemeal approach: Either the two activities are unrelated and then they are best separated into independent entities, which cannot cross-subsidize each other; or they are linked and then a whole-bank (integrated) approach would be preferable.

Let us pursue this whole-bank approach using the second rationale for integration: The trading book serves to hedge the banking book. In the framework of this paper, assume that the bank is subject to a dual income shock at date 1: rb on the banking book and rt on the trading book. We can entertain three different hypotheses:

(H1) Both rb and rt are observed. (H2) Only the sum rb + rt is observed. (H3) rt is observed, rb is not. In all cases, we will assume that the regulators are unable to verify that the bank is hedging. Let us look at the implications of each hypothesis:

(H1) If both income shocks are separately observed by the regulators, then the bank should be, ceteris paribus, punished when the realizations of the shocks are positively related and rewarded when they are negatively related. An implication of this is that the bank should see some of its surplus expropriated when both shocks to the banking book and to the trading book are favorable. The amendment in contrast focuses on the extreme lower tail and is unable to yield discipline through action in states of nature (very favorable ones) in which discipline is easiest to enforce (as we have seen, punishments are hard to implement when the bank is undercapitalized).



(H2) In the polar case, the regulator cannot tell the two income shocks apart. The bank is able to carry out transfers between the two books, perhaps through arrange- ments with a third party such as a highly levered institution. The bank may have an incentive to carry out such transfers either to avoid punishment or to minimize capital charges. The scope for this fungibility depends on what counts as hedging. In the most narrow definition, there is little scope for switching income from one book to the other. But then, of course, there is little recognition of the role of the trading book as a hedge against uncertainty in the banking book. Conversely, a broad definition of a hedge recognizes this role, but is subject to manipulations.

Under (H2), the regulators should again adopt a whole bank approach. The difficulty is that the regulators may not know whether the bank is using the financial instruments (the trading book) for hedging or gambling purposes.

Formally, the issue is one of "double moral hazard." The bank affects its income in two ways: through effort it shifts the distribution of income toward higher values (in the sense of first-order stochastic dominance); through risk-taking or hedging, it affects the riskiness of the distribution (in the sense of second-order stochastic dominance). The literature on this type of agency problem is unfortunately quite small.20

Alger (1999) considers a simple example with a two-date (no liquidity shock) structure. A risk-averse banking entrepreneur with capital/assets A, invests an amount I borrowing I-A at date 0, and then selects some effort e, together, possi- bly, with a choice of riskiness. The date- 1 final income is given by

y = (e + 8 + 68)I,

where E is a shock that can be insured in derivatives markets. Regulators lack expertise to control the bank's hedging behavior. If allowed to play with derivatives, the banking entrepreneur can select to hedge (6 =-1) or to gamble (6 = + 1). So 6 is a second dimension of moral hazard. Alternatively, the entrepreneur may be prohibited from playing the derivatives game, which automatically results in 6 = O (this is equivalent to a full separation between the banking and trading books in this model).

The entrepreneur has expected utility E[U(Rf)]-g(e), where Ut ) is a concave function of the banking firm's profit Rf, and g( ) is the disutility of effort. In Alger's example, e E {O, 1}, and E E {-1,0, 1}. Entrepreneurial risk aversion argues in favor of removing the noise E through hedging. However, the entrepreneur may then shirk and gamble so as to benefit from the upper tail of the distribution. Alger character- izes the minimum capital requirement when derivatives are allowed and when they are not.

Intuition suggests that a higher capital requirement should be imposed when the bank wants to use derivatives. Alger shows that this intuition may or may not be cor- rect. The possibility of hedging may increase the signal-to-noise ratio and allow a better control of the first form of moral hazard. So introducing the risk dimension of

20. See, however, Bester and Hellwig (1987) and Bolton and Harris (1999) for structured examples.



moral hazard may actually help control the effort dimension of moral hazard and lower the CAR.21

While the effect unveiled by Alger is quite robust the conclusion that a lower CAR may be associated with the use of derivatives still seems a bit counteractive. The development of more general frameworks combining both types of moral hazard is eagerly awaited.

(H3) Last let us consider the case in which only rt is observed. To be certain, this case can only be a metaphor. Regulators do measure capital ratios for banking books and therefore are able to assess their evolution.

What (H3) is a metaphor for is a situation in which information about the banking and trading books accrue at different frequencies. Information about the quality of loans for example accrues much more slowly than information about the market value of the trading book. A more plausible (but still highly stylized) representation of (H3) in the context of our model would then be one in which rb is learned at date 1 while there are two realizations of rt (shocks on the trading book value) at date 1/2 and 1, say. The exploration of models in which different portfolios (or at least their measurability by the regulator) move at different frequencies seems a fruitful avenue for research.

5. CONCLUDING REMARKS

The paper has developed a unified and optimal contracting approach to the choice of capital structure, liquidity, and risk management, and their relationship to the soft budget constraint and free-cash-flow theories. It has investigated the determinants of hedging and analyzed the incorporation of the market risk in banking regulation. Much remains to be done, though. As discussed in section 47 little is known about risk management when the risk structure is unknown to outsiders (investors for a firm, regulators for a bank). This important policy issue actually raises a much more general question of how to monitor a corporation's use of liquidity. This and other important microeconomic issues concerning liquidity and risk management await future research.

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21. To take an extreme, if unpalatable case, suppose that e E { 0, l }, but, unlike in Alger's paper, is a continuous variable. Then, y = 1 for sure under {e = 1, hedging} and with probability 0 under any other policy. Hence, any deviation from {e = 1, hedging} is detected with probability 1, and so the use of derivatives completely eliminates moral hazard (the first best obtains).



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Article Contentsp. [295]p. 296p. 297p. 298p. 299p. 300p. 301p. 302p. 303p. 304p. 305p. 306p. 307p. 308p. 309p. 310p. 311p. 312p. 313p. 314p. 315p. 316p. 317p. 318p. 319

Issue Table of ContentsJournal of Money, Credit and Banking, Vol. 32, No. 3, Part 1 (Aug., 2000), pp. 295-442Front MatterMoney, Credit, and Banking LectureLiquidity and Risk Management [pp. 295-319]

Political Regime Change and the Real Interest Rate [pp. 320-334]Household Credit and the Monetary Transmission Mechanism [pp. 335-356]International Lending by U.S. Banks [pp. 357-381]The Cyclical Relationship between Output and Prices: An Analysis in the Frequency Domain [pp. 382-399]Perfect Competition and the Effects of Energy Price Increases on Economic Activity [pp. 400-416]Interest Rates, Inflation, and Federal Reserve Policy Since 1980 [pp. 417-434]Does a Bias in FOMC Policy Directives Help Predict Intermeeting Policy Changes? [pp. 435-441]Erratum: Are Banks Risk Averse? Intraday Timing of Operations in the Interbank Market [p. 442]Back Matter

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