Diapositive 1

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Liquidity Risk and Corporate Demand for Hedging
and Insurance
by Jean-Charles ROCHET and Stéphane
VILLENEUVE Toulouse University (Preliminary)
March 2004
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OBJECTIVES

• Develop a tractable theoretical model where
• liquidity management (cash reserves
  dividends) and
• risk management (hedging insurance)
• are determined simultaneously.
• Disentangle the determinants of the decisions
  to hedge
• (or insure) from those of the extent of
  hedging
• (or insurance).

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RELEVANT LITERATURE (THEORY)

• Froot-Scharfstein-Stein (1993) by reducing
  risk on cash
• flows, RM allows firms to depend less on
  external finance
• for their future investments.
• Stulz (1984) Managerial risk aversion.
• Smith and Stulz (1985) Tax optimization.
• De Marzo and Duffie (1991, 1995) Reduction of
  agency costs.

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EMPIRICAL EVIDENCE

• Correlations between liquidity, leverage and risk
  management
• Geczy, Minton and Schrand (1997) currency
  derivatives use
• more liquid firms hedge less
• leverage is not significant.
• Tufano (1996) US good mining industry
• more liquid firms hedge less
• leverage is not significant.
• Haushalter (2000) Oil and gas producers
• leverage is positively correlated with the
  extent of
• hedging but not with the decision to hedge.

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EMPIRICAL EVIDENCE (continued)

• Hoyt and Khang (2000) insurance premiums paid
  by US firms
• leverage is significant but not bankruptcy
  probability
• (Altmans Z score).
• Core (1997) Directors and officers liability
  insurance
• leverage is not significant but bankruptcy
  probability is.

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OUTLINE OF THE PRESENTATION
1- The benchmark model 2- Hedging
decisions 3- Insurance decisions 4- Extensions
4-1 External financing 4-2 Partial
hedging 5- Empirical implications 6- Future
work.
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1- THE BENCHMARK MODEL

• Dynamics (continuous time)
• LT assets and liabilities fixed
• Unique state variable x cash in hand.
• No access to external finance ? liquidation if
  
• (cash flows)
• dividends payments
• Risk neutral shareholders, discount rate r.
• N.B. Could introduce remuneration on
  cash holdings
• (bank deposit)

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• If shareholders were not cash constrained
• First Best Solution
• (No need for cash inside the firm)
• We assume shareholders have no cash
• (later introduce external financing)

cash in hand
Expected NPV of future cash flows
cumulated dividends process
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Optimal Liquity Management

• Threshold x above which dividends are
  distributed
• Below x, value function satisfies a
  classical ODE

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Optimal Liquity Management (continued)
Explicit formulas for
where are the roots of the
characteristic equation
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Value of the firm
Cash holdings
No Dividends
Dividends
Figure 1 The Benchmark Case.
Notice that x measures the cost of financial
frictions.
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COMPARATIVE STATICS
Figure 2 The cost of financial frictions as a
function of and .
Notice that x is not monotonic in .
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2- HEDGING DECISIONS

• Cash flow process perturbed by exogenous risk
• (currency risk, commodity price risk,)
• Two control decisions
• hedging
• dividends cumulated process
• Value function

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Optimal hedging pattern characterized by 2
thresholds
Explicit formulas for V (x),
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Cash poor firms hedge
Value of the firm
No Hedging
Hedging
Dividends
Figure 3 The pattern of optimal hedging
decisions.
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• Two limit cases are interesting
• When
• (Benchmark case with ).
• When

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Gains from hedging
when
Value of the firm
No Hedging
Hedging
Dividends
Figure 4 Gains from hedging.
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3- INSURANCE DECISIONS
Poisson process (intensity )

• Cash flows
• Insurance control with values in
• Controlled cash reserve process
• The value function

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Optimal insurance decisions characterized by 2
thresholds
Gains from insurance Explicit formulas for
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Cash rich firms buy insurance!
Value of the firm
Cash holdings
Insurance
No insurance
Dividends
Figure 3 Gains from insurance.
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Corporate Demand for insurance
Proposition 7 When premiums are fair
, the firm buys insurance if and only
if Proposition 8 When the firm stops
buying any insurance. Large risks are not
insured!
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4- EXTENSION (1) LEVERAGE

• Long Term Debt continuous coupon c
• Credit Line competitive banking sector.
• If
• firm can draw on a credit line (interest
  payment r)
• measures the tangibility of assets
• ( liquidation value for the bank)
• Findings

leverage inverse impact than profitability credi
t line dramatically reduces G.
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EXTENSIONS (2) PARTIAL HEDGING

• Same qualitative pattern but non linear
  differential equation
• no closed form solution
• Companion paper (Rochet Villeneuve 2004)
• continuous portfolio selection by a firm
  (Mertons problem)

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5- EMPIRICAL IMPLICATIONS

• RM modeled as a two stage decision problem for
  the firm
• 1) create a RM unit (cost F)? to hedge or
  not
• 2) If yes, how much to hedge? extent of
  hedging
• Question 2 h(x) decreasing with x (cash in
  hand)
• cash rich firms hedge less
• (h also increases with )
• NB Opposed prediction for insurance i (x)
  increases.
• IS THIS EMPIRICALLY TRUE?

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Question 1 Firm decides to create a RM unit
Gain G gt cost F
empirical evidence
our model
endogenous
endogenous
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6- FUTURE WORK

• Optimal financial contracting
• Bank offers a contract
• (Alternative Risk Transfer Methods)
• Frictions come from
• cash flow verifiability (or Moral Hazard)
• limited commitment by the bank
• otherwise ? FIRST BEST