Savings glut, leverage, and the originate-to-distribute model

Motivation and introduction• The years leading up to the crisis were characterized by several features:I. Progressive deterioration of mortgage underwriting standardsII. Price compressions in tranches of different qualities, at least judging by the 2006 vintage ABXindex.III. Increase leverage among broker dealers driven to some extent by the increase in repo transactionswhere 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, formaltreatments.• Here we focus on a particular source of variation: The growth of cash pools in the hands ofinvestors seeking deposit-like instruments, safe and liquid and that the traditional banking systemcannot supply.– Institutional cash pools: Corporates and mutual funs cash positions, securities lenders, ...• Animportantcharacteristicofthesepoolsisthat,inprinciple, theyarenotbundledwithknowledgeabout, say, real estate risk: Growth of “uninformed funds”

Prices: ABX for 2006 and 2007-1 for AAA and BBB debt. Source: Markit

• Here we propose a simple model where the exogenous source of variation is precisely the growthof funds in the hands of uninformed investors.– We have nothing to say about the origins of this growth.• The model has three ingredients:I. Endogenous origination quality: A moral hazard problem at origination that results in a particulardistribution if risk qualityII. Rich market structure: Flows across different markets of funds and risks(A) “Uninformed exchange,” where uninformed investors acquire risk assets.– Key feature: Cash-in-the-market pricing(B) “Private market,” where informed investors operate and cream skim the best assets.(C) Markets for secured lending, where some of the funds in the hands of uninformed investorsflow to informed investors through leverage.III. Endogenous information acquisition: The amount of capital bundled with knowledge is endogenous.

• In our model the growth of uninformed funds:I. Produces a narrowing of the price spreads across markets due to cash-in-the-market pricingII. This lowers the returns associated with the uninformed exchangeIII. As a result some of the funds “spill over” to other markets:(A) Capital in private markets: Some of these funds become bundled with knowledge andfinance informed transactions in capital markets(B) Repo transactions: Another fraction of these funds flow into markets for secured lendingincreasing the leverage of informed investorsIV. Incentives for origination of good assets are non-motone in the size of the funds of uninformedinvestors:(A) Incentives increase with informed capital(B) Incentives decrease as price spreads narrow

A simple modelI. 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.

II. Agents(A) Originators• There is a unit measure of originators, agents in charge of funding assets in the economy.• We assume that each originator can generate one and only one project, which can be abusiness or consumer loan, a mortgage, or any other asset.• The quality of the asset can be high or low:– An originator can either originate a high quality asset that pays x h at t = 2 with probabilitye or a low quality asset that pays x l < x h , with probability 1−e.• The probability e is a costly decision: Entrepreneurs bear a private cost ψ(e) of choosing alevel 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• There is a measure ι of risk neutral financial intermediaries.• Each intermediary i ∈ [0,ι] is endowed with one unit of capital and a technology to acquireinformation given by ϕ(i) with ϕ(0) ≥ 0 and ϕ i > 0.• These intermediaries provide liquidity to the entrepreneurs at the interim stage and theycan 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 intermediariesonly 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)• Informed intermediaries supply liquidity cream skimming the best assets, those that pay x h .• Price in this market p d : As in Bolton, Santos and Scheinkman (2012)where p is the price in the exchange.p d = κx h +(1−κ)p, (1)• n: Number of good assets acquired by each of the intermediaries in the private market.• Originators distributing asset in this market for a price p d get matched to one informedintermediary with probabilitym = in(2)πe• After cream skimming, the supply of assets available to uninformed investors isS = π(1−em) (3)

(B) Public markets or exchanges• Uninformed intermediaries acquire risks in the exchange• The quantity of good and bad projects flowing into the uninformed exchange is given byS h = πe(1−m) and S l = π(1−e). (4)• The expected payoff of the assets traded in the exchange is given byp max (i,e,n) = S hx h +S l x lS(5)

• Cash-in-the-market pricing:– The cash available to absorb asset sales in the uninformed exchange isι−(1+l)i (6)where l is the amount borrowed by each of the informed intermediaries.– As we have seen the total number of projects flowing to the exchange is givenπ(1−em)– Cash-in-the-market prices, p cim , may obtain and that the price in the exchange isp cim = ι−(1+l)iπ(1−em)(7)• Thus the equilibrium price in the exchange is:p = min{p cim ,p max} (8)

(C) Markets for secured lending• Intermediaries present in the uninformed exchange can led to those in private markets.• Intermediaries present in private markets borrow from those present in exchanges againstthe asset acquired to finance the purchase itself.• l the amount borrowed by each of the intermediaries present in private markets. Leverageconstraint is:(1−η)np ≥ l, with η ∈ (0,1) (9)• The balance sheet of the intermediaries in private markets is:np d = 1+l. (10)• Combining these two expressions:l = (1−η)pp d −(1−η)pand n =1p d −(1−η)p(11)

Payoffs and definition of equilibriumI. Payoffs(A) Originators: Choice variable: eU e (e|i) = −ψ(e)+π [ emp d +(1−em)p ] +(1−π)(ex h +(1−e)x l ) (12)(B) Financial intermediaries: Choice variables: Whether to become informed and, if so, l and n.V ( ĩ ) =⎧⎪⎨⎪⎩r−ϕ ( ĩ ) +R+l(R−r)if ĩ ≤ iif ĩ > i(13)II. Definition of equilibrium• An equilibrium is a measure of intermediaries present in private markets, i ∗ , an equilibriumeffort action, e ∗ , a leverage ratio, l ∗ , number of good assets bought by each intermediarypresent in private markets, n ∗ , prices p d∗ , p ∗ , (and thus returns R ∗ and interest rates r ∗ ) suchthat agents maximize and markets clear.

The effect of the pool of uninformed funds, ι, on the measure of informed capital i ∗• The condition that determines the marginal intermediary that is indifferent between trading in theexchange or in the private market:r ∗ = −ϕ(i ∗ )+R ∗ +l ∗ (R ∗ −r ∗ ) (14)• We are interested in∂l∂i∂ι = ∂ι (R−r)+(1+l) ∂ ∂ι (R−r)ϕ i• Given that ϕ i > 0 and that under some conditions∂l∂ι > 0 and ∂∂ι (R−r),an increase in an uninformed funds increases the amount of informed capital.

The effect of the pool of uninformed funds, ι, on originations incentives, e ∗• Consider the first order condition for effort:ψ e = πm ( p d −p ) +(1−π)(x h −x l ) (15)• Then the effort as a function of the measure of intermediaries ι is such thate ι = ∂e∂ι ∝ m (ι p d −p ) +m ( p d )ι −p ι(16)ψ ee• Under simple conditions one can show thatm ∗ ι> 0 and pd∗ ι −p ∗ ι < 0• Thus the increase in the size of the funds of uninformed investors has an ambiguous effect on theincentives to originate good assets.

Example• Consider the following parametric assumptions– First,π = 1 η = .5 κ = .1,– The effort function is given byψ(e) = θ 2 e2 with θ = .01– The costs of becoming informed are given by• π = 1: ”Originate-and-distribute” economyϕ(i) = .05+βi for i ∈ [0,ι] with β = 1.75• We characterize this economy as a function of the measure of intermediaries ι ∈ [.2,1].

0.050.0450.040.035Measure of intermediaries in private markets, i ∗0.030.0250.020.0150.010.00500.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Measure of intermediaries, ιFigure 1: Measure of intermediaries present in private markets, i ∗ as a function of the measure of intermediaries, ι• As the measure of uninformed intermediaries increase, more of those with better informationacquisition technologies migrate to private markets.• That is, more capital flows into private market transactions.

0.350.30.25Matching probability, m ∗0.20.150.10.0500.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Measure of intermediaries, ιFigure 2: Matching probability, m ∗ as a function of the measure of intermediaries, ι• As a result the fraction of good risks funded with informed capital increases.– As a result m ∗ is an increasing function of ι.• This results in an improvement on incentives: as ⇑ m ∗⇒ ⇑ e ∗

0.10.090.08Spread in prices between private markets and exchanges0.070.060.050.040.030.020.010.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Measure of intermediaries, ιFigure 3: Price spread, p d∗ −p ∗ , as a function of the measure of intermediaries, ι• But the increase in the funds available to absorb risk in the exchange pushes prices, p ∗ upwardsand closes the spread between the informed and the uninformed price:– ⇑ ι ⇒ ⇓ p d∗ −p ∗• This effect decreases incentives for good origination. What is the net effect?

0.40.350.30.25effort level, e *0.20.150.10.0500.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Measure of intermediaries, ιFigure 4: Equilibrium level of effort, e ∗ as a function of the measure of intermediaries, ι• In the absence of informed capital there are no incentives for good origination, i ∗ = 0• After a certain threshold the most efficient intermediaries start acquiring information and creamskimming the good projects: ⇑ m ∗– This results in an improvement of origination incentives and so ⇑ e ∗• Eventually the price spread effect“catches up” and then origination incentives start go down: ⇓ e ∗

1.81.71.6Rates of return in private markets and interest rates1.51.41.31.21.110.65 0.7 0.75 0.8 0.85 0.9 0.95 1Measure of intermediaries, ιFigure 5: Rates in private markets, R ∗ (dashed), and interest rates r ∗ as a function of the measure of intermediaries, ι• The rates move in opposite direction to the measure of of intermediaries.• The spread though increases: The rate in private markets R ∗ drops at a slower rate than the riskfree rate r ∗ .• This results in an increase in leverage.

10.90.80.70.6Leverage, l ∗0.50.40.30.20.100.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Measure of intermediaries, ιFigure 6: Equilibrium level of leverage, l ∗ as a function of the measure of intermediaries, ι• Leverage is obviously 0 when agents are not present in private markets and only lever up, l ∗ > 0whenever i ∗ > 0.

• Conclusion:– An increase in the funds of uninformed investors:I. Increases uninformed prices and depresses price spreadsII. pushing efficient intermediaries to private marketsIII. which first increases incentives for origination but, eventually, incentives deteriorate.IV. Simultaneously interest rates drop and repo transactions, as well as leverage, increase.– Thus the model can help rationalize several features of the data apparent in the last cycle.– The question though still remains: Origins of the savings glut?