a supply chain model of financing: the capital structure of banks and firms
TRANSCRIPT
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A Supply Chain Model of Financing:The Capital Structure of Banks and Firms
William Gornall1 Ilya A. Strebulaev2
1Graduate School of BusinessStanford University
2Graduate School of BusinessStanford University
and NBER
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Bank Leverage is Very High While Firm Leverage is Low
0.0%
25.0%
50.0%
75.0%
100.0%
1998 2002 2006 2010
Aggregate Leverage of US Banks and
Nonfinancial Firms
Nonfinancial Firms Banks
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A Firm’s External Financing
Debt Issuance
Equity Issuance
Firm
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A Firm’s External Financing
Debt Issuance
Equity Issuance
Bank
Firm
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Key Findings
Main Result: Banks have high leverage, firms have low leverage
Model Mechanisms:
I Strategic Substitution
I Strategic Complementarity
I Interbank Competition
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The Firm’s Operating Income
Firms’ operating income Xt ;
dXt = µdt + (RNt − 1)XtdNt
Nt Poisson process with intensity λ
− log(R) ∼ Exponential(1/θ)
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The Firm’s Tradeoff
Tax Costs: τ (1− cf ) Xt
Default Costs: αf R Xt− when R < cf
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The Firm’s Optimal Capital Structure
The firm minimizes taxes and bankruptcy costs:
τ (1− cf ) Xt︸ ︷︷ ︸Tax Costs
+λE[αf R Xt− I
[R < cf
]]︸ ︷︷ ︸Expected Loss in Default
The optimal coupon is
cf =
(τθ
λαf
)θ
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Adding a Financial System
Competitive banking system:
I Competitive banks and debt markets
I Costless loan origination, lender exit and entry
I All firms pursue identical financing policy
I Continuum of nonfinancial borrowing firms
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Systematic Shocks
Shocks hit the economy at rate λ:
I Q: Fraction of firms hit by the shock− log (1− Q) ∼ EXP(1/γ)
I R: Recovery rate of those firms− logR ∼ EXP(1/θ).
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The Bank
Continuum of firms∫X it di = 1:
I cf Xit : Each firm’s coupon
I cf : Bank’s operating income
I cbcf : Bank’s coupon payment
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The Bank
Bank’s Tax Costs: τ cf (1− cb)
Bank’s Default Condition: 1− Q < cb and R < cf
Bank’s Default Cost: αb ((1− Q)cf + QR)
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The Joint Capital Structure Decision
The bank and firms minimize total joint default and tax costs:
τ (1− cf )︸ ︷︷ ︸Total Firm Tax Costs
+ (1− τ)(1− cb) cf︸ ︷︷ ︸Bank Tax Costs
+λE[αf Q R I
[R < cf
]]︸ ︷︷ ︸Total Firm Default Costs
+λE[αb ((1− Q)cf cb + QR) I
[1− Q < cb and R < cf
]]︸ ︷︷ ︸Bank Default Costs
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The Joint Capital Structure Decision
For interior solutions,
c1/θf =
τθcb
λαfγ
1+γ + λαb
(1 + 1
1+γ cbθ)c1/γb
c1γ
b ((1 + γ)(θ − γ − γθ) + (θ − γ)θcb)αb = γ2(1 + θ)αf
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Firm Leverage and Bank Leverage are StrategicSubstitutes
Increasing firm leverage decreases bank leverage and vice versa
For example, impact of τ on cb:
I Direct Impact: Change in cb, holding cf fixed
I Indirect Impact: Change in cb posed by change in cf inresponse to τ
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Varying αf (high αf → firm bankruptcy costs are high)
Α f
11
c f
cb
Hcb + 1L c f
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Varying αb (high αb → bank bankruptcy costs are high)
Αb
11
c f
cbHcb + 1L c f
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Varying γ (high γ → shocks are more systematic)
Γ
11
c f
cb
Hcb + 1L c f
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Varying θ (high θ → shocks are more severe )
Θ
11
c f
cb
Hcb + 1L c f
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Impact of Banking Regulation
I Capital Regulation
I Bailouts
I Deposit Insurance
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Capital Regulation: Limit cb to c̄b
cb
11
c f
cb
Hcb + 1L c f
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Capital Regulation: Limit cb to c̄b
cb
Firm Default Probability
Bank Default Probability
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Bailouts: Reduce αb, possibly to a negative number
Αb
11
c f
cb
Hcb + 1L c f
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Bailouts: Bank defaults if 1− Q < cb/k and R < cf
k
11
c f
cb
Hcb + 1L c f
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Conclusion
I Three mechanisms explain bank leverage: strategicsubstitution, strategic complementarity, interbank competition
I Bank regulation could have unexpected impacts on lending tothe real economy