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