Leverage and Disagreement Franois Geerolf UCLA September 15, 2015 - - PowerPoint PPT Presentation

Leverage and Disagreement

François Geerolf

UCLA

September 15, 2015

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▶ In this paper, I develop a model of :

▶ Endogenous Leverage ▶ Interest Rates on Collateralized Bonds

among competitive investors with heterogenous beliefs.

▶ Geanakoplos (1997) and subsequent :

▶ Only one leverage ratio (simplifying assumption on the

structure of beliefs / or on the number of agents).

▶ Counterfactual. Many leverage ratios, even for same asset:

homebuyers, entrepreneurs, hedge funds, investment banks...

▶ Relaxing the hypotheses leading to one leverage ratio, the

model yields two key predictions.

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1) When disagreement goes to 0, the upper tail of the distribution

• f leverage ratios goes to a Pareto with endogenous tail

coeffjcient 2 , for any smooth and bounded away from zero density of beliefs.

▶ Cross section of Hedge Funds (TASS Lipper, 2006)

Slope: -1.95

• 4
• 3
• 2
• 1

Log10 Survivor 1 2 3 4 Log10 Leverage Ratio Leverage Ratio Fitted values

▶ Pareto in the upper tail (l ∈ [150, 3000])

Histogram

▶ Point estimate for tail coeffjcient : α = 1.95 (std: 0.2).

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▶ Cross-section of homowners’ initial leverage ratios (Dataquick,

for example October 1989).

Date: 10/1989 −6−5.5−5−4.5−4−3.5−3−2.5−2−1.5−1 −.5 0 Log10 Survivor .5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 Log10 Leverage Ratio (Leverage Ratio on New Loans)

Leverage Ratio Distribution of US Homeowners

▶ Pareto of leverage ratios found also for:

▶ Entrepreneurs in the SCF. ▶ Firms in Compustat.

▶ ⇒ Pareto for borrowers’ expected / realized returns, however

small belief heterogeneity:

▶ Pareto Returns to entrepreneurship. ▶ Pareto Returns to speculation in general. 3 / 39

2) Distribution of interest rates adjusts so that borrowers and lenders are matched assortatively : interest rates are assignment / hedonic prices, disconnected from expected and true default probability:

▶ New determinant for pricing fjxed income securities. (⇒

Credit Spread Puzzle? / CDS-Bond Basis)

▶ Investing in high yield not necessarily risk shifting. ▶ High customization / fragmentation of the market =

Endogenous OTC structure. ⇒ OTC versus exchanges debate.

4 / 39

Model Ingredients :

▶ Heterogenous priors asset pricing model with endogenous

• leverage. Geanakoplos (1997), Simsek (2013).

▶ Disagreement on mean rather than on default probabilities.

Key Results :

▶ Pareto distributions for leverage ratios / expected and

realized returns. Also gives information on:

▶ Representativeness of marginal buyer/ Elements of the belief

• distribution. (⇒ monitoring systemic risk?)

▶ Underlying fjnancial structure.

▶ Credit spreads as hedonic interest rates.

Other Theoretical / Methodological contributions:

▶ Pyramiding Lending Arrangements. ▶ Endogenous Short-sales:

▶ Endogenous rebate rates, without transactions costs / risk

aversion.

▶ Endogenous short interest. 5 / 39

Literature

▶ Heterogeneous Priors. Miller (1977), Harrison, Kreps (1978),

Ofek, Richardson (2003), Hong, Scheinkman, Xiong (2006), Hong, Stein (2007), Hong, Sraer (2012).

▶ Heterogeneous Priors & Collateral Constraints. Geanakoplos

(1997, 2003), Geanakoplos, Zame (2002), Geanakoplos (2010), Fostel, Geanakoplos (2012), Simsek (2013).

▶ Competitive Assignment Models. Roy (1950), Rosen (1974),

Sattinger (1975), Rosen (1981), Teulings (1995), Gabaix, Landier (2008).

▶ Pareto distributions. Champernowne (1953), Simon (1955),

Kesten (1973), Gabaix (1999), Luttmer (2007).

▶ Credit Spread Puzzle. Chen, Colling-Dufresne, Goldstein (2009),

Buraschi, Trojani, Vedolin (2011), Huang and Huang (2012), Albagli, Hellwig, Tsyvinski (2012), McQuade (2013).

▶ Entrepreneurship. Moscowitz, Vissing-Jorgensen (2002), Hurst,

Lusardi (2004).

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Model with Borrowing Contracts Only Setup Equilibrium Defjnition Equilibrium Solution Equilibrium Properties Extension 1: ”Pyramiding” Lending Arrangements Extension 2: Short-Sales Conclusion

6 / 39

Model with Borrowing Contracts Only Setup Equilibrium Defjnition Equilibrium Solution Equilibrium Properties Extension 1: ”Pyramiding” Lending Arrangements Extension 2: Short-Sales Conclusion

6 / 39

Set-up

▶ Two Periods: 0 and 1. ▶ Continuum of agents. Measure 1. ▶ Wealth 1. ▶ Consume in period 1.

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Assets

▶ Storage’s Return R = 1. → Cash. ▶ Real Asset. Finite Supply normalized to 1. Exogenous p1.

Endogenous Price: p.

▶ Borrowing Contracts collateralized by the Real Asset.

▶ No-recourse. ▶ Normalization: 1 unit of Real Asset in Collateral. ▶ φ: Face Value - promised payment in period 1. ▶ Notation for contract: (φ). ▶ Competitive Markets (Anonymous). Price: q(φ). ”Loan

amount”. Implicit interest rate: r(φ) = φ/q(φ).

▶ Payofg: min{φ, p1}. 8 / 39

Beliefs

▶ Agents agree to disagree on p1. ▶ Agent i: point expectations pi 1 ∈ [1 − ∆, 1]. 1-Δ 1 pi

1

▶ Key difgerence with Geanakoplos (1997), where agents agree

• n value upon default.

▶ Generalization: ▶ Agents agree on a probability distribution around mean. ▶ Risk neutral.

▶ Density f(.), c.d.f F(.) on [1 − ∆, 1]. ▶ Exogenously given. ▶ No learning.

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Agents’ Problem

Given (p, q(.)), agent i chooses (ni

A, ni B(.), ni C) to max. expected

wealth (W) in period 1 under:

▶ Budget Constraint (BC). ▶ Collateral Constraint (CC).

max

(ni

A,ni B(.),ni C)ni

Api 1 +

∫

φ

ni

B(φ) min{φ, pi 1}dφ + ni C

(W) s.t. ni

Ap +

∫

φ

ni

B(φ)q(φ)dφ + ni C ≤ 1

(BC) s.t. ∫

φ

max{−ni

B(φ), 0}dφ ≤ ni A

(CC) s.t. ni

A ≥ 0,

ni

C ≥ 0

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Model with Borrowing Contracts Only Setup Equilibrium Defjnition Equilibrium Solution Equilibrium Properties Extension 1: ”Pyramiding” Lending Arrangements Extension 2: Short-Sales Conclusion

10 / 39

Equilibrium

Defjnition (Competitive Equilibrium for Economy EB)

A competitive equilibrium is a price system (p, q(.)), and portfolios (ni

A, ni B(.), ni C) for all i such that: ▶ Given (p, q(.)), agent i chooses (ni A, ni B(φ), ni C) maximizing

(W) under (BC) and (CC),

▶ Markets clear:

∫

i

ni

Adi = 1,

and ∀φ, ∫

i

ni

B(φ)di = 0.

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Model with Borrowing Contracts Only Setup Equilibrium Defjnition Equilibrium Solution Equilibrium Properties Extension 1: ”Pyramiding” Lending Arrangements Extension 2: Short-Sales Conclusion

11 / 39

Agents’ Types

Agents split into three types depending on optimism:

Cash Investors Lenders Borrowers

1-Δ 1 pi

1

𝝊 p ξ

pi

1

1 Borrowers (”Homeowners”, ”Hedge Funds”, ”Entrepreneurs”). ni

C

ni

A

ni

B

pi

1

Lenders. ni

A

ni

C

ni

B

pi

1

1 Cash Investors. ni

A

ni

B

ni

C

w

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Agents’ Types

Agents split into three types depending on optimism:

Cash Investors Lenders Borrowers

1-Δ 1 pi

1

𝝊 p ξ ▶ pi 1 ∈ [τ, 1] → Borrowers (”Homeowners”, ”Hedge Funds”,

”Entrepreneurs”). ni

A > 0

∃φ, ni

B(φ) < 0.

pi

1

Lenders (”Banks”, ”Money-Market Fund”). ni

B

pi

1

1 Cash Investors. ni

C

w

12 / 39

Agents’ Types

Agents split into three types depending on optimism:

Cash Investors Lenders Borrowers

1-Δ 1 pi

1

𝝊 p ξ ▶ pi 1 ∈ [τ, 1] → Borrowers (”Homeowners”, ”Hedge Funds”,

”Entrepreneurs”). ni

A > 0

∃φ, ni

B(φ) < 0. ▶ pi 1 ∈ [ξ, τ] → Lenders (”Banks”, ”Money-Market Fund”).

∃φ, ni

B(φ) > 0.

pi

1

1 Cash Investors. ni

C

w

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Agents’ Types

Agents split into three types depending on optimism:

Cash Investors Lenders Borrowers

1-Δ 1 pi

1

𝝊 p ξ ▶ pi 1 ∈ [τ, 1] → Borrowers (”Homeowners”, ”Hedge Funds”,

”Entrepreneurs”). ni

A > 0

∃φ, ni

B(φ) < 0. ▶ pi 1 ∈ [ξ, τ] → Lenders (”Banks”, ”Money-Market Fund”).

∃φ, ni

B(φ) > 0. ▶ pi 1 ∈ [1 − ∆, ξ] → Cash Investors.

ni

C = 1.

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Borrowers’ Problem

Lemma

A borrower pi

1 chooses (φ) s.t.: φ = arg maxφ

pi

1 − φ

p − q(φ).

▶ Coll. Const. binds: 1 Real asset ⇒ 1 Borrowing Contract. ▶ Number: 1/(p − q(φ)) of Real assets / Borrowing Contracts. p p − q(φ) q(φ) A L E D ▶ Leverage ratio of (φ): l(φ) = p/(p − q(φ)).

1 p − q(φ)(pi

1−φ) = pi 1

p l(φ) − φ q(φ) (l(φ) − 1) = pi

1

p + (pi

1

p − r(φ) ) (l(φ) − 1) .

▶ Promise φ ↗ ⇒ q(φ) ↗ ⇒ q′(φ) > 0

⇒ l′(φ) > 0 ⇒ Leverage rises with face value φ.

▶ Trade-ofg between higher φ but higher r(φ) ⇒ r′(φ) > 0 .

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Lenders

Lemma

A lender with beliefs pi

1 chooses contract (pi 1). ▶ For lenders: Face value of the loan = Beliefs about the Real

Asset.

▶ Why not a higher φ ? Default for sure.

Return: min{pi

1, φ}

q(φ) = pi

1

q(φ) ↘ φ.

▶ Why not a lower φ ?

Return: min{pi

1, φ}

q(φ) = φ q(φ) = r(φ) ↗ φ.

▶ Leverage rises with φ, and φ = pi 1 of lenders ⇒ Leverage

rises with beliefs of lenders.

▶ Lenders think they trade perfectly safe contracts.

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Positive Sorting

▶ Supermodularity of Expected Wealth of a Borrower with

respect to his Beliefs pi

1 and the face value φ:

pi

1 − φ

p − q(φ) = pi

1

p (1 + l(φ)) − φ q(φ)l(φ) ⇒ ∂2 ∂φ∂pi

1

(.) = 1 pl′(φ) > 0.

▶ Complementarity between leverage (φ) and expected return

• n each asset (pi

1). ▶ φ = pi 1 of lenders ⇒ Positive Sorting of borrowers and

lenders . Empirically: Over-The-Counter (OTC) Markets.

▶ Γ(.): Belief of borrower → Belief of lender. Sorting: Γ′(.) > 0.

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2 fjrst-order ODE for Γ(.) and q(.)

Cash Investors Lenders Borrowers 1-Δ 1 pi

1

𝝊 p y Γ(y) ξ (Γ(y))

▶ pi 1 = y chooses φ s.t. lender choosing same φ is Γ(y):

Γ(y) = arg max

φ

y − φ p − q(φ) ⇒ q′(φ) y − φ p − q(φ) = 1 ⇒ (y − Γ(y)) q′(Γ(y)) = p − q(Γ(y)).

▶ Market clearing for contract (x):

∫

i

ni

B(x)di = 0

⇒ f(Γ(y))dΓ(y) q(Γ(y)) = f(y)dy p − q(Γ(y)) ⇒ (p − q(Γ(y))) f (Γ(y)) Γ′(y) = q(Γ(y))f(y) .

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▶ Unknowns: q(.) (≡ r(.)), Γ(.), ξ, p, τ. ▶ 2 First-Order ODEs ⇒ Need 5 algebraic equations.

Cash Investors Lenders Borrowers

1-Δ 1 pi

1

𝝊 p ξ

▶ Indifgerence Cash / Lending:

r(ξ) = 1. Indifgerence Lending / Investing: r p . Most pessimistic lenders & borrowers: . Most optimistic lenders & borrowers: M. Market clearing for the real asset: w 1 F Sp.

17 / 39

▶ Unknowns: q(.) (≡ r(.)), Γ(.), ξ, p, τ. ▶ 2 First-Order ODEs ⇒ Need 5 algebraic equations.

Cash Investors Lenders Borrowers

1-Δ 1 pi

1

𝝊 p ξ

▶ Indifgerence Cash / Lending:

r(ξ) = 1.

▶ Indifgerence Lending / Investing:

r(τ) = τ − ξ p − ξ . Most pessimistic lenders & borrowers: . Most optimistic lenders & borrowers: M. Market clearing for the real asset: 1 F p.

17 / 39

▶ Unknowns: q(.) (≡ r(.)), Γ(.), ξ, p, τ. ▶ 2 First-Order ODEs ⇒ Need 5 algebraic equations.

Cash Investors Lenders Borrowers

1-Δ 1 pi

1

𝝊 p ξ

▶ Indifgerence Cash / Lending:

r(ξ) = 1.

▶ Indifgerence Lending / Investing:

r(τ) = τ − ξ p − ξ .

▶ Most pessimistic lenders & borrowers:

Γ(τ) = ξ. Most optimistic lenders & borrowers: 1 . Market clearing for the real asset: 1 F p.

17 / 39

▶ Unknowns: q(.) (≡ r(.)), Γ(.), ξ, p, τ. ▶ 2 First-Order ODEs ⇒ Need 5 algebraic equations.

Cash Investors Lenders Borrowers

1-Δ 1 pi

1

𝝊 p ξ

▶ Indifgerence Cash / Lending:

r(ξ) = 1.

▶ Indifgerence Lending / Investing:

r(τ) = τ − ξ p − ξ .

▶ Most pessimistic lenders & borrowers:

Γ(τ) = ξ.

▶ Most optimistic lenders & borrowers:

Γ(1) = τ. Market clearing for the real asset: 1 F p .

17 / 39

▶ Unknowns: q(.) (≡ r(.)), Γ(.), ξ, p, τ. ▶ 2 First-Order ODEs ⇒ Need 5 algebraic equations.

Cash Investors Lenders Borrowers

1-Δ 1 pi

1

𝝊 p ξ

▶ Indifgerence Cash / Lending:

r(ξ) = 1.

▶ Indifgerence Lending / Investing:

r(τ) = τ − ξ p − ξ .

▶ Most pessimistic lenders & borrowers:

Γ(τ) = ξ.

▶ Most optimistic lenders & borrowers:

Γ(1) = τ.

▶ Market clearing for the real asset:

1 − F(ξ) = p.

17 / 39

Model with Borrowing Contracts Only Setup Equilibrium Defjnition Equilibrium Solution Equilibrium Properties Extension 1: ”Pyramiding” Lending Arrangements Extension 2: Short-Sales Conclusion

17 / 39

Ilustrating examples : f uniform, f increasing

f(.) 1 1-Δ Δ 1/Δ pi 1 f(.) 1 1-Δ Δ 2/Δ pi 1

▶ Uniform : 2 fjrst-order ODE → second-order ODE:

Γ′′ (Γ − x) + Γ′ + Γ′2 = 0 ⇒ Γ(x) = −x − a + b √ x + c.

▶ Closed form: p, ξ, τ, r(.), q(.), L(.), a, b, c. Example:

p = 1 + ∆ + 2∆2 + 2∆3 − √ (−1 + ∆)2 (1 + 2∆2) 2∆ + ∆2 + 4∆3 + 2∆4 = 1 − O(฀2).

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Cutofgs as a function of ∆ (f uniform)

Lenders Borrowers Cash Investors 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 0 %ile 10 %ile 20 %ile 30 %ile 40 %ile 50 %ile 60 %ile 70 %ile 80 %ile 90 %ile 100 %ile Disagreement Δ Percentile (Ranked by Degree of Optimism) Cutoff τ Price of Real Asset p Cutoff ξ

True across bounded away from zero density function: p = 1 − O(∆2), τ = 1 − O(∆2), and ξ = 1 − O(∆).

19 / 39

Limiting Pareto Tail of Endogenous Tail Coeffjcient 2

▶ In uniform case, truncated Pareto with coefg 2:

p p − Q(y) = p √2ξ √ p − ξ τ − ξ 1 √

(p+ξ)τ−ξ(p−ξ) 2ξ

− y .

Proposition (Limiting Pareto Distribution for Leverage Ratios

• f Optimists for smooth f(.))

Let f(.) difgerentiable, f′ continuous, f(.) bounded away from 0. G∆(.) distribution function for the leverage of borrowers for f∆(.): ∃A∆,

• l2(1 − G∆(l)) − A∆
• [L∆(1)/2,L∆(1)]

∞ ∆→0

− − − → 0,

▶ Heuristically:

1 − G∆(l) ∼ A∆ l2 .

▶ Upper tail behavior: not dependent on f(.).

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Pareto Distributions for Leverage Ratios, Uniform Distribution

Coeffjcient: 2.

Disagreement Δ=10% Disagreement Δ=5% Disagreement Δ=2% 1.0 1.5 2.0 2.5 3.0

• 1.5
• 1.0
• 0.5

0.0 Log10 Leverage Ratio Log10 Survivor Function

21 / 39

Pareto Distributions for Leverage Ratios, Increasing Distribution

Still Coeffjcient: 2.

Disagreement Δ=10% Disagreement Δ=5% Disagreement Δ=2% 1.0 1.5 2.0 2.5 3.0

• 1.5
• 1.0
• 0.5

0.0 Log10 Leverage Ratio Log10 Survivor Function 22 / 39

Empirical Counterpart

TASS Hedge Fund Database, August 2006.

Slope: -1.95

• 4
• 3
• 2
• 1

Log10 Survivor 1 2 3 4 Log10 Leverage Ratio Leverage Ratio Fitted values

Calibration: disagreement ≈ 1.8%.

23 / 39

Non Bounded away from 0.

▶ If f(x) ∼ (1 − x)ρ ⇒ Pareto with coeffjcient 2 + ρ. ▶ Scale Independence Remains.

Δ=5%, ρ=0 Δ=5%, ρ=1 1.4 1.6 1.8 2.0 2.2 2.4 2.6

• 2.5
• 2.0
• 1.5
• 1.0
• 0.5

0.0 Log10 Leverage Ratio Log10 Survivor Function 24 / 39

Returns to Entrepreneurship ?

▶ Expected Returns are Pareto from envelope condition:

R′(y) = 1 p − Q(y) = Leverage(y) p .

Disagreement Δ=10% Disagreement Δ=5% Disagreement Δ=2% 0.00 0.05 0.10 0.15 0.20 0.25

• 3.0
• 2.5
• 2.0
• 1.5
• 1.0
• 0.5

0.0 Log10 Expected Returns Log10 Survivor Function 25 / 39

Hedonic Interest Rates

Disagreement Δ=10% Disagreement Δ=5% Disagreement Δ=2% 0% 1% 2% 3% 4% 5% 6% 7% 0bps 10bps 20bps 30bps 40bps 50bps 60bps 70bps 80bps 90bps 100bps 110bps 120bps 130bps 140bps 150bps Haircuts (%) Spreads on Collateralized Bonds (Basis Points)

▶ Hedonic Interest rates r(.) on safe bonds for lenders. Can

be substantial. Example with f(x) = 2(1 − x)/∆.

▶ Corr(r(.), l(.)) > 0 from disagreement. But: no risk shifting

⇒ Difgerent regulatory implications.

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Hedonic Interest Rates

▶ Non monotonic relationship between leverage and

realized returns of borrowers, because of spreads.

Expected Returns Realized p1=1 Realized p1=0.9995 Realized p1=0.999 0.9980 0.9985 0.9990 0.9995 1.0000

• 30%
• 20%
• 10%

0% 10% 20% 30% 40% 50% Beliefs of Borrowers Expected or Realized Returns of Borrowers (%) 27 / 39

Model with Borrowing Contracts Only Setup Equilibrium Defjnition Equilibrium Solution Equilibrium Properties Extension 1: ”Pyramiding” Lending Arrangements Extension 2: Short-Sales Conclusion

27 / 39

Pyramiding Lending Arrangements

▶ Allow Borrowing Contracts to be used as collateral.

Cash Investors Lenders

• f Type 2

Lenders

• f Type 1

Borrowers 1-Δ 1 pi

1

ν ξ 𝝊 p Γ2(y) Γ1(y) y (Γ2(y))(2) (Γ1(y))

▶ Hedonic interest rates ⇒ Lenders want to leverage into

them !

▶ Example for houses, loans to SMEs: securitization. Or

rehypothecation of collateral, repos of mortgage-backed securities, etc.

▶ Price p increases even more.

28 / 39

Balance Sheets

q1(ɸ)-q2(ɸ') q1(ɸ) q2(ɸ') L A p-q1(ɸ) p q1(ɸ) L A

▶ Akin to tranching. The lender of type 2 is repaid until φ′,

then lender of type 1 is repaid on φ − φ′, then the borrower gets p1 − φ.

29 / 39

Pyramiding Lending Arrangements

▶ Pareto Coeffjcients decrease (leverage distributions are

multiplied) ⇒ Leverage Ratio distribution shifted to the right.

▶ Price expresses the opinion of superoptimists.

Slope:-3.98556 Slope:-3.26585

Borrowing Economy Pyramiding Economy 2.0 2.5 3.0 3.5

• 3.5
• 3.0
• 2.5
• 2.0
• 1.5
• 1.0
• 0.5

0.0 Log10 Leverage Ratio Log10 Survivor Function

30 / 39

Empirics

▶ Leverage Ratios on New Loans. Source: Dataquick. ▶ ≈ 100,000 - 500,000 new loans per month.

• 6 -5.5 -5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1
• .5

Log10 Survivor .5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 Log10 Leverage Ratio October 1989 31 / 39

Empirics

▶ Leverage Ratios on New Loans. Source: Dataquick. ▶ ≈ 100,000 - 500,000 new loans per month.

• 6 -5.5 -5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1
• .5

Log10 Survivor .5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 Log10 Leverage Ratio October 1989 October 2001 31 / 39

Empirics

▶ Leverage Ratios on New Loans. Source: Dataquick. ▶ ≈ 100,000 - 500,000 new loans per month.

• 6 -5.5 -5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1
• .5

Log10 Survivor .5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 Log10 Leverage Ratio October 1989 October 2001 October 2006 31 / 39

Empirics

▶ Leverage Ratios on New Loans. Source: Dataquick. ▶ ≈ 100,000 - 500,000 new loans per month.

• 6 -5.5 -5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1
• .5

Log10 Survivor .5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 Log10 Leverage Ratio October 1989 October 2001 October 2006 October 2012 31 / 39

Pyramiding Lending Arrangements

50 100 150 200 House Prices (S&P index) .5 1 1.5 Pareto Coefficient 1985m1 1990m1 1995m1 2000m1 2005m1 2010m1 2015m1 Month Pareto Coefficient House Prices (S&P index)

▶ Video: the leverage ratio distribution from 1987 to 2012. ▶ Link: http://www.econ.ucla.edu/fgeerolf/research/

geerolf-leverage-video.avi

32 / 39

▶ The model allows to recover the corresponding increase in

borrowers’ expected returns.

Borrowing Economy Pyramiding Economy 0%ile 20%ile 40%ile 60%ile 80%ile 100%ile 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 110% 120% 130% 140% 150% 160% 170% 180% 190% 200% Quantile of Borrowers' Optimism Expected Excess Returns of Borrowers (%)

▶ In a model with a little bit of risk aversion: more risk taking?

33 / 39

Model with Borrowing Contracts Only Setup Equilibrium Defjnition Equilibrium Solution Equilibrium Properties Extension 1: ”Pyramiding” Lending Arrangements Extension 2: Short-Sales Conclusion

33 / 39

Short-Sales

▶ Unlike existing disagreement models, the model allows the

treatment of short-sales.

Short-Sellers Lenders Borrowers 1-Δ 1 pi

1

𝝊 p y Γ(y) ξ (Γ(y)) Lenders Securities 𝞽 y (Γs(y))s Γs(y)

▶ Price = pessimists’ valuations ⇒ Systematic undervaluation -

similar to noise trader risks in De Long et al. (1990), but risk

• neutrality. Equity premium, discount of closed-end funds, etc.

▶ Endogenous rebate rates - apparent short-selling costs not

evidence of constraints: about 100 bps, larger with more disagreement.

▶ Endogenous Short-interest (a few percent).

34 / 39

Short-Sales

Lenders Borrowers Short-Sellers Securities Lenders 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 0 %ile 10 %ile 20 %ile 30 %ile 40 %ile 50 %ile 60 %ile 70 %ile 80 %ile 90 %ile 100 %ile Disagreement Δ Percentile (Ranked by Degree of Optimism) Cutoff σ Cutoff τ Price of Real Asset p Cutoff ξ 35 / 39

Endogenous Rebate Rates and Cash Collateral

▶ No short-selling costs or costs of default.

Disagreement Δ=10% Disagreement Δ=5% Disagreement Δ=2% 102% 103% 104% 105% 106% 107% 108% 10bps 20bps 30bps 40bps 50bps 60bps 70bps 80bps 90bps 100bps 110bps 120bps Cash Collateral as a Fraction of Value (%) Extra Return of Asset Lenders (Basis Points) 36 / 39

Endogenous Short Interest

▶ Only a few percent of stocks are on loan in equilibrium, even

though all are potentially available.

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 0 %ile 10 %ile 20 %ile 30 %ile 40 %ile 50 %ile 60 %ile 70 %ile

Disagreement Δ Short Interest (% of Real Asset on Loan)

37 / 39

Larger Spreads on Bonds, even the safest (AAA)

Disagreement Δ=10% Disagreement Δ=5% Disagreement Δ=2% 2% 3% 4% 5% 6% 7% 8% 9% 200bps 300bps 400bps 500bps 600bps 700bps 800bps 900bps Haircuts (%) Spreads on Collateralized Bonds (Basis Points)

38 / 39

Model with Borrowing Contracts Only Setup Equilibrium Defjnition Equilibrium Solution Equilibrium Properties Extension 1: ”Pyramiding” Lending Arrangements Extension 2: Short-Sales Conclusion

38 / 39

Conclusion

▶ Homeowners / Entrepreneurs’ / Hedge Funds data lend

support to a very stylized model.

▶ New (static) source of Pareto distributions in returns

independent from Gibrat’s law/ random growth.

▶ New intuitions on key fjnancial prices / quantities:

▶ Returns on Bonds. ▶ Short-selling ”costs”. ▶ Short interest

Potential for future work:

▶ Empirical work on short interest, rebate rates, distributions of

leverage ratios to recover disagreement.

▶ Financial regulation:

▶ Costs of moving OTC onto exchanges. ▶ Monitoring fjnancial system through ultimate borrowers’

leverage ratio distribution ?

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Thank you

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Leverage Ratios of Entrepreneurs

Slope: -2.02

• 4
• 3
• 2
• 1

Log10 Survivor .5 1 1.5 Log10 Leverage Ratio Leverage Ratio Fitted values

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