Distribution and Origination Incentives Patrick Bolton Tano Santos Columbia University Jose Scheinkman Princeton University May 23rd-24th, 2013 - 4th Banque de France - Deutsche Bundesbank Macroeconomics and Finance Conference
Motivation and introduction • The years leading up to the crisis were characterized by several features: I. Progressive deterioration of mortgage underwriting standards II. Price compressions in tranches of different qualities, at least judging by the 2006 vintage ABX index. III. Leverage increase among intermediaries partially driven by repo transactions where the counterparties are agents such as money market funds. • There are some narratives trying to make sense of these disparate facts but few, if any, formal treatments.
• Here we focus on a particular source of variation: – The growth of cash pools in the hands of investors seeking deposit-like instru- ments, safe and liquid and that the traditional banking system cannot supply. ∗ Institutional cash pools: Corporates and mutual funds cash positions, secu- rities lenders, ... – Growth of “uninformed funds:” These pools are not bundled with knowledge about, say, real estate risk.
Figure 1: The secular rise of institutional cash-pools (Pozsar, 2011, Figure 1) • Corporate cash, cash collateral for securities lenders, cash pools of long-term mutual funds (excluding MMMF), ... • Surveys indicate that over 90% of the cash pools are subject to written cash- policies, which safety of principal as the dominant consideration.
Figure 2: Percent of payments due after x of origination per year of vintage • Non linearities in quality: Mortgage vintages improved from 2001 to 2003 and then started deteriorating.
Figure 3: ABX 06-1: Prices as a percentage of par for the five different subindices (Source: Fender and Scheicher, 2008, Graph 1) • ABX: Equally weighted portfolios of CDS referencing 20 subprime MBS. • We are interested in the compression in the run-up to the crisis.
Figure 4: Securities broker dealer: Leverage (Total assets over equity) and Total Assets. Quarterly data: 1980Q1-2012Q4 3500000 25 3000000 20 2500000 15 2000000 1500000 10 1000000 5 500000 0 0 1980Q1 1980Q4 1981Q3 1982Q2 1983Q1 1983Q4 1984Q3 1985Q2 1986Q1 1986Q4 1987Q3 1988Q2 1989Q1 1989Q4 1990Q3 1991Q2 1992Q1 1992Q4 1993Q3 1994Q2 1995Q1 1995Q4 1996Q3 1997Q2 1998Q1 1998Q4 1999Q3 2000Q2 2001Q1 2001Q4 2002Q3 2003Q2 2004Q1 2004Q4 2005Q3 2006Q2 2007Q1 2007Q4 2008Q3 2009Q2 2010Q1 2010Q4 2011Q3 2012Q2 Total Assets Leverage • The above data is for broker dealer subsidiaries (not the holding companies) – Holding companies (and leverage can be constructed looking at the 10Ks) show a much milder increase in leverage. • See Adrian and Shin (Journal of Financial Intermediation, 2010).
• Origination incentives and the joint distribution of knowledge and capital. • The model has three ingredients: I. Endogenous origination quality: Moral hazard at origination. II. Rich market structure: Flows across different markets of funds and risks (A) “Uninformed exchange,” – Key feature: Cash-in-the-market pricing (B) “Private market,” (C) Markets for secured lending, III. Endogenous bundling of capital and leverage with knowledge
• In our model the growth of uninformed funds: I. Narrows price spreads across markets due to cash-in-the-market pricing II. which lowers the returns associated with uninformed trading. III. As a result some of the funds “spill over” to other markets: (A) Private markets: Markets for information (B) Repo markets: markets for collateralized lending IV. Non-monotonicity of origination incentives as a function of uninformed capital (A) Incentives increase with informed capital (B) Incentives decrease as price spreads narrow
A simple model I. Timing: Three dates t = 0 , 1 , 2 • t = 0, origination and capital distribution across markets • t = 1, distribution of originated assets • t = 2 payoffs are realized.
Originators: 1 Uninformed Investors: ι Distribution: π Uninformed capital Incentives: e ∗ ι
Originators: 1 Uninformed Investors: ι Distribution: π Uninformed capital Incentives: e ∗ ι { ι p ∗ = min π , e ∗ x h + ( 1 − e ∗ ) x l } e ∗ x h + ( 1 − e ∗ ) x l
Informed investors: i ∗ Originators: 1 Uninformed Investors: ι − i ∗ Distribution: π Incentives: e ∗
Informed investors: i ∗ Originators: 1 Uninformed Investors: ι − i ∗ p d ∗ ℓ ∗ n ∗ p d ∗ ℓ ∗ 1 ℓ ∗ r ∗ x h Distribution: π Uninformed capital Incentives: e ∗ ι − i ∗ ( 1 + ℓ ∗ ) p ∗ = min { ι − i ∗ ( 1 + ℓ ∗ ) π ( 1 − e ∗ m ∗ ) , e ∗ ( 1 − m ∗ ) x h +( 1 − e ∗ ) x l } 1 − e ∗ m ∗ e ∗ ( 1 − m ∗ ) x h +( 1 − e ∗ ) x l 1 − e ∗ m ∗
II. Agents (A) Originators • Unit measure of originators. • Each originator can generate one and only one asset • The quality of the asset can be high or low: – High quality asset that pays x h at t = 2 with probability e or a low quality asset that pays x l < x h , with probability 1 − e. • Originators bear a private cost ψ ( e ) of choosing a level of effort e ∈ ( 0 , 1 ) . – ψ ( 0 ) = 0 and ψ e > 0 and ψ ee ≥ 0. – The quality of the projects is independent across originators.
(B) Financial intermediaries • ι : Measure of risk neutral financial intermediaries. • Each intermediary i ∈ [ 0 , ι ] is endowed with – one unit of capital – and a technology to acquire information given by φ ( i ) with φ ( 0 ) ≥ 0 and φ i > 0. • Intermediaries provide liquidity to originators at the interim stage and they can do so, as we will see, in either a public exchange or a private market. – It is access to this private market that entails incurring the cost φ ( i ) . – Finally intermediaries only consume at date t = 2.
III. Markets (A) Private markets • An intermediary i ∈ [ 0 , ι ] gains access to this market by paying the cost φ ( i ) • They cream skim the best assets, those that pay x h . • Price in this market p d : As in Bolton, Santos and Scheinkman (2012) p d = κ x h + ( 1 − κ ) p , where p is the price in the exchange. • n: Number of good assets acquired by each of the intermediaries in the private market. • Originators get matched to one informed intermediary with probability m = in π e
(B) Public markets or exchanges • Uninformed intermediaries acquire risks in the exchange • Quantity of good and bad projects flowing into the uninformed exchange S h = π e ( 1 − m ) and S l = π ( 1 − e ) . • The expected payoff of the assets traded in the exchange is given by p max ( i , e , n ) = S h x h + S l x l S S : Supply of assets available to uninformed investors after cream skimming S = π ( 1 − em )
• Cash-in-the-market pricing: – The cash available to absorb asset sales in the uninformed exchange is ι − ( 1 + ℓ ) i where ℓ is the amount borrowed by each of the informed intermediaries. – Total number of projects flowing to the exchange is given S = π ( 1 − em ) – Cash-in-the-market prices, pcim, pcim = ι − ( 1 + ℓ ) i π ( 1 − em ) • Thus the equilibrium price in the exchange is: pcim , p max p = min
(C) Markets for secured lending • Intermediaries in the uninformed exchange can lend to those in private mar- kets against collateral. • ℓ the amount borrowed by each of the intermediaries present in private markets. Leverage constraint is: ( 1 − η ) np ≥ ℓ, with η ∈ ( 0 , 1 ) • The balance sheet of the intermediaries in private markets is: np d = 1 + ℓ. • Combining these two expressions: ( 1 − η ) p 1 ℓ = and n = p d − ( 1 − η ) p p d − ( 1 − η ) p
Payoffs and definition of equilibrium I. Payoffs (A) Originators: Choice variable: e U e ( e | i ) = − ψ ( e ) + π emp d + ( 1 − em ) p [ ] + ( 1 − π ) ( ex h + ( 1 − e ) x l ) • Interpretation of π : Skin in the game: Extent of distribution (B) Financial intermediaries: Choice variables: Information acquisition, ℓ and n. r if trading in the uninformed exchange ( ˜ ) V i = ( ˜ ) − φ i + R + ℓ ( R − r ) if trading in the private market where R = x h r = e ( 1 − m ) x h + ( 1 − e ) x l and p d p ( 1 − em )
II. Definition of equilibrium • A measure of intermediaries present in private markets, i ∗ , • an effort action, e ∗ , • a leverage ratio, ℓ ∗ , • a number of good assets bought by each intermediary present in private mar- kets, n ∗ , • prices, p d ∗ and p ∗ , (and thus returns R ∗ and interest rates r ∗ ) such that agents maximize and markets clear. III. Comparative statics ι = ∂ e ∗ • Comparative statics with respect to the measure of intermediaries ι : e ∗ ∂ι
The effect of the pool of uninformed funds, ι , on the measure of informed capital i ∗ • Marginal informed intermediary: Indifferent between trading in the exchange or in the private market: r ∗ = − φ ( i ∗ ) + R ∗ + ℓ ∗ ( R ∗ − r ∗ ) (1) • We are interested in ∂ι ( R ∗ − r ∗ ) + ( 1 + ℓ ∗ ) ∂ ∂ι ( R ∗ − r ∗ ) ∂ℓ ∗ ∂ i ∗ ∂ι = φ i • Given that φ i > 0 and that under some conditions ∂ℓ ∗ ∂ ∂ι ( R ∗ − r ∗ ) , ∂ι > 0 and an increase in an uninformed funds increases the amount of informed capital.
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