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

Leverage and Disagreement François Geerolf UCLA September 15, 2015 0 / 39

structure of beliefs / or on the number of agents). among competitive investors with heterogenous beliefs . homebuyers, entrepreneurs, hedge funds, investment banks... model yields two key predictions. 1 / 39 ▶ In this paper, I develop a model of : ▶ Endogenous Leverage ▶ Interest Rates on Collateralized Bonds ▶ Geanakoplos (1997) and subsequent : ▶ Only one leverage ratio (simplifying assumption on the ▶ Counterfactual. Many leverage ratios, even for same asset: ▶ Relaxing the hypotheses leading to one leverage ratio, the

1) When disagreement goes to 0, the upper tail of the distribution of leverage ratios goes to a Pareto with endogenous tail Histogram 2 / 39 density of beliefs. coeffjcient 2 , for any smooth and bounded away from zero ▶ Cross section of Hedge Funds (TASS Lipper, 2006) 0 Slope: -1.95 -1 Log 10 Survivor -2 -3 -4 0 1 2 3 4 Log 10 Leverage Ratio Leverage Ratio Fitted values ▶ Pareto in the upper tail ( l ∈ [ 150 , 3000 ] ) ▶ Point estimate for tail coeffjcient : α = 1 . 95 (std: 0 . 2).

3 / 39 for example October 1989). small belief heterogeneity: ▶ Cross-section of homowners’ initial leverage ratios (Dataquick, Leverage Ratio Distribution of US Homeowners (Leverage Ratio on New Loans) −6−5.5−5−4.5−4−3.5−3−2.5−2−1.5−1 −.5 0 Date: 10/1989 Log 10 Survivor 0 .5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 Log 10 Leverage Ratio ▶ Pareto of leverage ratios found also for: ▶ Entrepreneurs in the SCF. ▶ Firms in Compustat. ▶ ⇒ Pareto for borrowers’ expected / realized returns, however ▶ Pareto Returns to entrepreneurship. ▶ Pareto Returns to speculation in general.

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: Credit Spread Puzzle? / CDS-Bond Basis) 4 / 39 ▶ New determinant for pricing fjxed income securities. ( ⇒ ▶ Investing in high yield not necessarily risk shifting. ▶ High customization / fragmentation of the market = Endogenous OTC structure. ⇒ OTC versus exchanges debate.

Model Ingredients : realized returns. Also gives information on: aversion. Other Theoretical / Methodological contributions: 5 / 39 leverage. Geanakoplos (1997), Simsek (2013). Key Results : ▶ Heterogenous priors asset pricing model with endogenous ▶ Disagreement on mean rather than on default probabilities. ▶ Pareto distributions for leverage ratios / expected and ▶ Representativeness of marginal buyer/ Elements of the belief distribution. ( ⇒ monitoring systemic risk?) ▶ Underlying fjnancial structure. ▶ Credit spreads as hedonic interest rates . ▶ Pyramiding Lending Arrangements. ▶ Endogenous Short-sales: ▶ Endogenous rebate rates, without transactions costs / risk ▶ Endogenous short interest.

Literature Sattinger (1975), Rosen (1981), Teulings (1995), Gabaix, Landier Lusardi (2004). Albagli, Hellwig, Tsyvinski (2012), McQuade (2013). Buraschi, Trojani, Vedolin (2011), Huang and Huang (2012), Kesten (1973), Gabaix (1999), Luttmer (2007). (2008). Fostel, Geanakoplos (2012), Simsek (2013). (1997, 2003), Geanakoplos, Zame (2002), Geanakoplos (2010), Stein (2007), Hong, Sraer (2012). Ofek, Richardson (2003), Hong, Scheinkman, Xiong (2006), Hong, 6 / 39 ▶ Heterogeneous Priors. Miller (1977), Harrison, Kreps (1978), ▶ Heterogeneous Priors & Collateral Constraints. Geanakoplos ▶ Competitive Assignment Models. Roy (1950), Rosen (1974), ▶ Pareto distributions. Champernowne (1953), Simon (1955), ▶ Credit Spread Puzzle. Chen, Colling-Dufresne, Goldstein (2009), ▶ Entrepreneurship. Moscowitz, Vissing-Jorgensen (2002), Hurst,

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 7 / 39 ▶ Two Periods: 0 and 1. ▶ Continuum of agents. Measure 1. ▶ Wealth 1. ▶ Consume in period 1.

Assets Endogenous Price: p . 8 / 39 ▶ Storage’s Return R = 1. → Cash . ▶ Real Asset. Finite Supply normalized to 1. Exogenous p 1 . ▶ 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, p 1 } .

Beliefs on value upon default. 9 / 39 ▶ Agents agree to disagree on p 1 . 1 ∈ [ 1 − ∆ , 1 ] . ▶ Agent i : point expectations p i 1- Δ 1 p i 1 ▶ Key difgerence with Geanakoplos (1997), where agents agree ▶ Generalization: ▶ Agents agree on a probability distribution around mean. ▶ Risk neutral. ▶ Density f ( . ) , c.d.f F ( . ) on [ 1 − ∆ , 1 ] . ▶ Exogenously given. ▶ No learning.

Agents’ Problem n i n i n i s.t. (CC) A s.t. (BC) n i n i (W) C s.t. 10 / 39 A p i wealth (W) in period 1 under: Given ( p , q ( . )) , agent i chooses ( n i A , n i B ( . ) , n i C ) to max. expected ▶ Budget Constraint (BC). ▶ Collateral Constraint (CC). ∫ max 1 + B ( φ ) min { φ, p i 1 } d φ + n i ( n i A , n i B ( . ) , n i C ) n i φ ∫ A p + B ( φ ) q ( φ ) d φ + n i C ≤ 1 φ ∫ max {− n i B ( φ ) , 0 } d φ ≤ n i φ A ≥ 0 , C ≥ 0

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 (W) under (BC) and (CC), n i i and n i i 11 / 39 Defjnition (Competitive Equilibrium for Economy E B ) A competitive equilibrium is a price system ( p , q ( . )) , and portfolios ( n i A , n i B ( . ) , n i C ) for all i such that: ▶ Given ( p , q ( . )) , agent i chooses ( n i A , n i B ( φ ) , n i C ) maximizing ▶ Markets clear: ∫ A di = 1 , ∫ ∀ φ, B ( φ ) di = 0 .

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 p i Lenders. n i A n i C 0 n i B 0 1 p i 1 Cash Investors. n i A n i B 0 n i C w 1 0 Agents split into three types depending on optimism: n i p i B 1 Borrowers (”Homeowners”, ”Hedge Funds”, ”Entrepreneurs”). 1 C n i 0 12 / 39 0 A n i p 𝝊 1- Δ ξ 1 p i 1 Cash Investors Lenders Borrowers

Agents’ Types Agents split into three types depending on optimism: w C n i Cash Investors. 1 1 p i 0 B n i Lenders (”Banks”, ”Money-Market Fund”). 1 p i n i 12 / 39 n i ”Entrepreneurs”). p 𝝊 1- Δ ξ 1 p i 1 Cash Investors Lenders Borrowers 1 ∈ [ τ, 1 ] → Borrowers (”Homeowners”, ”Hedge Funds”, ▶ p i A > 0 ∃ φ, B ( φ ) < 0 .

Agents’ Types ”Entrepreneurs”). w C n i Cash Investors. 1 1 p i n i n i Agents split into three types depending on optimism: n i 12 / 39 p 𝝊 1- Δ ξ 1 p i 1 Cash Investors Lenders Borrowers 1 ∈ [ τ, 1 ] → Borrowers (”Homeowners”, ”Hedge Funds”, ▶ p i A > 0 ∃ φ, B ( φ ) < 0 . 1 ∈ [ ξ, τ ] → Lenders (”Banks”, ”Money-Market Fund”). ▶ p i ∃ φ, B ( φ ) > 0 .

Agents’ Types ”Entrepreneurs”). n i n i n i Agents split into three types depending on optimism: n i 12 / 39 p 𝝊 1- Δ ξ 1 p i 1 Cash Investors Lenders Borrowers 1 ∈ [ τ, 1 ] → Borrowers (”Homeowners”, ”Hedge Funds”, ▶ p i A > 0 ∃ φ, B ( φ ) < 0 . 1 ∈ [ ξ, τ ] → Lenders (”Banks”, ”Money-Market Fund”). ▶ p i ∃ φ, B ( φ ) > 0 . 1 ∈ [ 1 − ∆ , ξ ] → Cash Investors. ▶ p i C = 1 .

Borrowers’ Problem 1 1 1 1 Lemma 13 / 39 A borrower p i p i 1 − φ 1 chooses ( φ ) s.t.: φ = arg max φ p − q ( φ ) . ▶ Coll. Const. binds: 1 Real asset ⇒ 1 Borrowing Contract. ▶ Number: 1 / ( p − q ( φ )) of Real assets / Borrowing Contracts. ▶ Leverage ratio of ( φ ) : l ( φ ) = p / ( p − q ( φ )) . A L φ p − q ( φ ) E p − q ( φ )( p i 1 − φ ) = p i p l ( φ ) − q ( φ ) ( l ( φ ) − 1 ) p ( p i ) q ( φ ) D = p i p + 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 .

Lenders Return: rises with beliefs of lenders. Return: Lemma 1 p i 14 / 39 Asset. A lender with beliefs p i 1 chooses contract ( p i 1 ) . ▶ For lenders: Face value of the loan = Beliefs about the Real ▶ Why not a higher φ ? Default for sure. min { p i 1 , φ } = ↘ φ. q ( φ ) q ( φ ) ▶ Why not a lower φ ? min { p i 1 , φ } φ = q ( φ ) = r ( φ ) ↗ φ. q ( φ ) ▶ Leverage rises with φ , and φ = p i 1 of lenders ⇒ Leverage ▶ Lenders think they trade perfectly safe contracts .