Brief Introduction



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Liquidity and Risk Management


Bengt Holmström; Jean Tirole

Journal of Money, Credit and Banking,

Vol. 32, No. 3, (Aug., 2000), pp. 295-319

A presentation by Twinemanzi Tumubweinee

Fin 7310


Spring 2007

Brief Introduction


Presents a Principal-Agent framework to analyze the following three aspects of corporate financing:

  • Liquidity management

  • Risk management

  • Financing structure ( debt versus equity financing)

Factors affecting corporate liquidity:



  • Financing structure; short versus long term debt, equity finance

  • Liquid asset holdings: loan commitments, short term instruments and cash reserves

  • Risk management strategies: forwards and futures contracts, insurance, hedging instruments (to hedge basis risk, interest rate risk, currency, default risk, market risk etc)

  • Measures of risk exposure: use of Risk metrics, Value at Risk etc

Note: Rationale for liquidity management is the corporate need for refinancing (short and long term) thus discounting the taxes and managerial incentives arguments.


Initial Assumptions;

  • Extends Holmstrom and Tirole (1997) to include an intermediate third stage, when firm might receive an adverse shock and require additional funding.

  • No income is produced at intermediate stage

  • Moral hazard can set in at

  • Rate on interest is zero

  • Risk neutral borrowers and investors

  • Borrowers behave competitively and borrowers are protected by limited liability.


The Model; (Extends Holmstrom and Tirole (1997)
Exogenous shock occurs at t=1 and requires amount to continue, else it stalls and no return is realized at t=2. Note that

is continuously distributed with pdf and CDF


  • Initially a fixed project size I, which gets abandoned if, some threshold shock.

  • Incentive Compatibility for borrower

Breakeven condition for investors,



(1)

Investors receive return only if project is continued with probability.

Rearranging Eqn (1), we have, where
(2)
Debt capacity is maximal when, the unit pledgeable income.

Since lenders behave competitively, the borrowers net utility is the social surplus of the project = margin per unit of investment times the maximal investment.


, where
(3)

Using (3) and (2) we have,


where


minimizes , or alternatively .

Integrating by parts the expression for expected unit cost of effective investment, Holmstrom and Tirole, show that at the optimum, the threshold liquidity shock is equal to the expected unit cost of effective investment



From which it follows that


(4)
And that, the wait and see approach to liquidity shocks is sub optimal.
We relax one of the initial assumptions and allow for verifiable, exogenous and deterministic income at the intermediate stage, the new threshold is

Assuming free cash flow, then the optimal re-investment rule is



.
If the intermediate income is a function of the borrower’s effort i.e. endogenously determined then the continuation rule becomes,

being an increasing function of the intermediate income.
Finding: firms require insurance against liquidity shocks, as long as they cannot pledge the full value of their activity to new investors.
Secondly: firms should fully hedge, if it is costless to do so, even if the idiosyncratic shocks are outside their control.
Assume a unit hedging cost and hedging ratio and exogenous shock to date 1 income
Then the firm has enough liquidity to continue at date 1, If and only if
.

If date 1 income is, per unit cost of investment at date 0 becomes


, and investors break even constraint in expectation, implies that investors total outlay is equal to their benefit. [similar to Eqn (1)]
(5)
And just like in Eqn (3), entrepreneur’s utility is equal to the project NPV

If we define the unit cost of effective investment (cost of obtaining, in expectation, one unit of unliquidated investment) as
(6)
Then the entrepreneur objective function is to maximize net utility (social surplus of the project)
(7)
The extent of hedging , and liquidity hoarding are determined by
Min {

{}


Hedging ratio is invariant to changes in variables that affect only date 2 total benefits , and pledgeable income.
Normalizing the model to a uniform distribution
,
Then (8)

where is the variance of .


Note that , giving us

, since we are minimizing
In the uniform case, the optimal hedging ratio decreases with the unit cost of hedging.
If we substitute into (8) and set the least cost, we have



  • The threshold liquidity shock is depends on date 1 income .Furthermore an increase in the cost of hedging, reduces the hedging ratio, decreases the hoarding of liquidity and raises the cost.

  • Increase in r, increases amount of short term debt per unit of investment

  • Hedging may or may not depend on factors that affect liquidity management like short and long run leverage.

Banking and risk management:



  • 1996 amendment to 1986 Basle Accord imposed extra Capital Adequacy Requirements on banks trading books, by differentiating between credit and market risk; by specifying a Value At Risk of 99%, adding the CAR for the trading book to that for the banking book etc.

Basic model assumptions:

  • Trading book serves as hedge for the banking book

  • and are the income shocks at date 1 on the banking and trading book respectively.



Hypothesis 1: Both income shocks are observed by regulators.

  • Expropriation of bank surplus when both shocks are favorable.

  • Penalties assessed when realizations of both shocks are positively related

  • Bank is rewarded if the realization of both shocks are negatively rewarded

Punishments are hard to implement when the bank is under capitalized.
Hypothesis 2: Only the sum of the shocks is observed by regulators. Since regulators cannot differentiate between shocks, and have no way of knowing if the trading book is being used to hedge risks or gamble, banks have the incentive to carry out transfers between the two books to avoid punishment or minimize charges, leading to “double moral hazard”;

  • They exert effort to shift the distribution of income towards higher values.

  • Take risks or hedge against the uncertain income, thus distorting the riskiness of the income distribution.

Hypothesis 3: Only the shock to trading book income is observed. According to Holmstrom and Tirole, this is a situation is which information about the banking and trading books accrues at different frequencies. More specifically shocks to the trading book reveal themselves faster than shocks to the banking book, by the very nature of the two portfolios.


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