A Supply Chain Model of Financing: The Capital Structure of Banks and Firms
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Transcript of A Supply Chain Model of Financing: The Capital Structure of Banks and Firms
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
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
A Firm’s External Financing
Debt Issuance
Equity Issuance
Firm
A Firm’s External Financing
Debt Issuance
Equity Issuance
Bank
Firm
Key Findings
Main Result: Banks have high leverage, firms have low leverage
Model Mechanisms:
I Strategic Substitution
I Strategic Complementarity
I Interbank Competition
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)
The Firm’s Tradeoff
Tax Costs: τ (1− cf ) Xt
Default Costs: αf R Xt− when R < cf
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
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
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).
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
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)
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
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
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
Varying αf (high αf → firm bankruptcy costs are high)
Α f
11
c f
cb
Hcb + 1L c f
Varying αb (high αb → bank bankruptcy costs are high)
Αb
11
c f
cbHcb + 1L c f
Varying γ (high γ → shocks are more systematic)
Γ
11
c f
cb
Hcb + 1L c f
Varying θ (high θ → shocks are more severe )
Θ
11
c f
cb
Hcb + 1L c f
Impact of Banking Regulation
I Capital Regulation
I Bailouts
I Deposit Insurance
Capital Regulation: Limit cb to c̄b
cb
11
c f
cb
Hcb + 1L c f
Capital Regulation: Limit cb to c̄b
cb
Firm Default Probability
Bank Default Probability
Bailouts: Reduce αb, possibly to a negative number
Αb
11
c f
cb
Hcb + 1L c f
Bailouts: Bank defaults if 1− Q < cb/k and R < cf
k
11
c f
cb
Hcb + 1L c f
Conclusion
I Three mechanisms explain bank leverage: strategicsubstitution, strategic complementarity, interbank competition
I Bank regulation could have unexpected impacts on lending tothe real economy