Imperfect Transparency and the Risk of Securitization

Imperfect Transparency and the Risk of Securitization Seungjun Baek Florida State University June. 16, 2017

1. Introduction

Motivation Study benefit and risk of securitization

Motivation Study benefit and risk of securitization Benefit: relax borrowing constraints ( diversify idiosyncratic risk)

Motivation Study benefit and risk of securitization Benefit: relax borrowing constraints ( diversify idiosyncratic risk) Risk: solvency and funding risk

Motivation Study benefit and risk of securitization Benefit: relax borrowing constraints ( diversify idiosyncratic risk) Risk: solvency and funding risk Build a model of banking with securitization

Motivation Study benefit and risk of securitization Benefit: relax borrowing constraints ( diversify idiosyncratic risk) Risk: solvency and funding risk Build a model of banking with securitization Endogenize solvency and funding risk

Key Innovations Endogenous Solvency and Funding Risk

Key Innovations Endogenous Solvency and Funding Risk Solvency Risk (Quality) : adverse selection between securitizers (originators) and projects (borrowers).

Key Innovations Endogenous Solvency and Funding Risk Solvency Risk (Quality) : adverse selection between securitizers (originators) and projects (borrowers). must exert costly effort.

Key Innovations Endogenous Solvency and Funding Risk Solvency Risk (Quality) : adverse selection between securitizers (originators) and projects (borrowers). must exert costly effort. Funding Risk : imperfect information about the quality (solvency) of assets.

Key Innovations Securitization : create the pool of underlying projects (ABS), then trade ABSs

Key Innovations Securitization : create the pool of underlying projects (ABS), then trade ABSs = diversify idiosyncratic risk : the pledgeability of assets

Preview of the Paper Key Objective : quality Profits = N.P.V leverage funding risk fire-sale price. }{{} losses from funding crises

Preview of the Paper Key Objective : quality Profits = N.P.V leverage funding risk fire-sale price. }{{} losses from funding crises Key Externalities : Externality 1: the benefit of transparency not internalized. - funding risk depends on aggregate transparency of a portfolio (diversification via trade) - transparency also depends on choices of others.

Related Literature/Key Contributions Financial stability and systemic risk. Lorenzoni (2008), Stein (2012) : need to limit the use of short-term liabilities.

Related Literature/Key Contributions Financial stability and systemic risk. Lorenzoni (2008), Stein (2012) : need to limit the use of short-term liabilities. The composition of the asset side of the balace sheet matters : new dimension of macroprudential policy. The recent financial crisis: lax lending standards Originate-to-distribute hypothsis : Diamond and Rajan (2009), Akerlof and Shiller (2010). Objections : Gorton (2008), Acharya, Schnabl, and Suarez (2013), Erel, Nadauld, and Stulz (2014). Irrational optimism: Gennaioli, Shleifer and Vishny (2012,2013).

1. State of Nature 2. Securitizers 3. Inside Investors 4. Outside Investors Model

Overview of the Model 3 dates, and initial wealth of securitizers, inside investors, and outside investors: 1, Y S, Y I respectively. State of Nature Technology Preference

Figure: State of Nature (Securitization)

Figure: Preference, Technology (Securitization)

Securitizer Can choose borrowing d up to the borrowing constraint d q

Definition (Securitization) Pool assets across islands to create ABS.

Definition (Securitization) Pool assets across islands to create ABS. Trade: fully diversifies idiosyncratic risk in the economy.

Definition (Securitization) Pool assets across islands to create ABS. Trade: fully diversifies idiosyncratic risk in the economy. Create safe cash flows -> increases pledgeability

Definition (Securitization) Pool assets across islands to create ABS. Trade: fully diversifies idiosyncratic risk in the economy. Create safe cash flows -> increases pledgeability Source of externality: diversifies the benefit of transparency

Securitizer : Quality and Transparency choice once and for all at t=1 An Individual underlying project defaults in s = b, yielding 0.

Securitizer : Quality and Transparency choice once and for all at t=1 An Individual underlying project defaults in s = b, yielding 0. In s = g, it returns µ (S) > 0.

Securitizer : Quality and Transparency choice once and for all at t=1 An Individual underlying project defaults in s = b, yielding 0. In s = g, it returns µ (S) > 0. Quality Choice : long-term solvency risk λ. Quality : 1 λ Cost of quality: ι 1 λ, where ι > 0. Transparency Choice : The accuracy of signal r i about the individual state s i : f (r i = s i s i ) = α, f (r i = s i s i ) = 1 α.

Inside Investors (Short-term lenders to securitizers) Pursue safety assets.

Inside Investors (Short-term lenders to securitizers) Pursue safety assets. Only safe cash flows q are pledgeable to IIs. (no default at t = 2 ).

Inside Investors At date 1, IIs lend up to q.

Inside Investors At date 1, IIs lend up to q. At date 2,

Inside Investors At date 1, IIs lend up to q. At date 2, Receive signal φ (accuracy of which α = α j dj). => Form a posterior about the aggregate state.

Inside Investors At date 1, IIs lend up to q. At date 2, Receive signal φ (accuracy of which α = α j dj). => Form a posterior about the aggregate state. Decide whether to pay χ to learn about the aggregate state. (choose the early resolution of uncertainty)

Outside Investors at t=2

Outside Investors at t=2 Observe the distribution of signal {r i } about the quality of underlying assets.

Outside Investors at t=2 Observe the distribution of signal {r i } about the quality of underlying assets. The first order condition: q i r i di }{{} A = υ (M), (1) q gains from new projects }{{} gains from buying fire-sold assets q = q r i di. We may also introduce unsophisticated OIs who can t distinguish the good signal from the bad signal. q = q g = q b

Equilibrium

Equilibrium : Inside Investors (Lenders to Securitizers) t = 2, roll-over decisions : Lemma (Learning and Funding) (i) In S = M, IIs keep funding if and only if they learn about S.

Equilibrium : Inside Investors (Lenders to Securitizers) t = 2, roll-over decisions : Lemma (Learning and Funding) (i) In S = M, IIs keep funding if and only if they learn about S. Intuition: for risk-averse IIs, E [U(C S 3 ) φ] }{{} expected utility under uncertainty < U (dn) }{{} certain utiliy with the cash withdrawal

Equilibrium : Inside Investors Lemma (i) Let P denote the fraction of IIs who learn about the state with the costly extra information in S = M. Then P α > 0;

Equilibrium : Inside Investors Lemma (i) Let P denote the fraction of IIs who learn about the state with the costly extra information in S = M. Then P α > 0; (ii) Let Λ denote funding risk, which is defined as the fraction of IIs quit funding. Λ M = (1 P(α)) }{{}, IIs who do not learn stop funding Λ L = 1. Intuition: In S = L, learning is less likely with greater transparency. If signal φ is transparent, paying for the additional information does not add much value.

Equilibrium : Securitizer (Fire-sales at t=2) If some IIs stop funding, asset liquidation occurs in a resale market, } Λ {{ d } short-term liabilities = κ q }{{} proceeds from fire-sales, where κ is the fraction liquidated κ = Λd q.

Equilibrium : Securitizer j (t=1) At date 1:

Equilibrium : Securitizer j (t=1) At date 1: choose borrowing, d, quality λ, and transparency α for each project.

Equilibrium : Securitizer j (t=1) At date 1: choose borrowing, d, quality λ, and transparency α for each project. pooling and trading ABS

Taking underlying asset price q and α as given, each chooses borrowing d, quality λ and transparency α to maximize: [E (µ) Rd ι λ (λ) ι α (α)] }{{} E [L(λ, α)]d }{{}, n.p.v. of projects net losses from fire-sales subject to the collateral constraint, E [µ] =pµ + (1 p)(ηµ B + (1 η)(1 λ) µ B ), }{{} quality

Equilibrium ABS price depends on the distribution of signal {r i } q =((1 λ) α + λ (1 α)) q g + ((1 λ) (1 α) + λα) q }{{}}{{} weight on q g weight on q b b.

Equilibrium ABS price depends on the distribution of signal {r i } q =((1 λ) α + λ (1 α)) q g + ((1 λ) (1 α) + λα) q }{{}}{{} weight on q g weight on q b When transparency α is higher, q is closely correlated with its quality q (1 λ) (2α 1) f, where f = q g q b. b.

Constrained Effi ciency Constrained effi ciency: no better information than the private sector. debt must be safe. The social planner s problem: max W = U S + U II + U OI = E [µ λ] Rd ι λ (λ) ι α (α) E [υ(λd) + (A R) (Λd)] }{{} real losses from fire sales subject to the same collateral constraint. υ(λd) : fire-sold assets lose value (Shleifer and Vishny, 1992)

Sources of Ineffi ciency: Imperfect Transparency and Social Marginal Value (SMV) of Quality Proposition (i) (Perfect transparency) SMV of quality λ equals the PMV;

Sources of Ineffi ciency: Imperfect Transparency and Social Marginal Value (SMV) of Quality Proposition (i) (Perfect transparency) SMV of quality λ equals the PMV; Intuition: fully internalized through q (ii) (Imperfect transparency) SMV of quality is strictly greater than the PMV. due to imperfect transparency, only partly internalized through q. q (1 λ) 2α 1 < 1 SMV-PMV is increasing in d. Greater leverage d decreases securitizers stakes in the downturn, causing socially excessive risk-taking.

Figure: Difference between the Social and Private Marginal Value of Quality 0.07 0.07 0.06 0.06 0.05 0.05 0.04 0.04 0.03 0.03 0.02 0.02 0.01 0.01 0 0.5 0.6 0.7 0.8 0.9 1 0 0.05 0.1 0.15 0.2 0.25

Social Marginal Value of Transparency Real costs from opacity Λ d }{{} borrowing υ + (A R) }{{} marginal losses from fire sales

Social Marginal Value of Transparency Real costs from opacity Λ d }{{} borrowing υ + (A R) }{{} marginal losses from fire sales Benefit on funding risk is not internalized: Λ α < 0.

Social Marginal Value of Transparency Real costs from opacity Λ d }{{} borrowing υ + (A R) }{{} marginal losses from fire sales Λ Benefit on funding risk is not internalized: α < 0. Benefit of transparency is also diversified via trading. But it may be internalized to some extent as transparency may benefit via q q Higher q decreases fire-sale losses. α (1 2λ) f. It is smaller if cost of transparency is high (e.g., CDO) solvency risk λ is high (e.g., subprime mortgage markets)

Figure: Private and Socially Optimal Allocation 0.55 0.5 Private Social 0.75 0.7 0.45 0.65 0.4 0.6 0.35 0.55 0.3 0.16 0.18 0.2 0.22 0.24 0.26 0.5 0.16 0.18 0.2 0.22 0.24 0.26

Implementation : Capital Surcharges on Opaque Securities Instrument : Surcharge on opaqueness τ a and solvency risk τ λ.

Implementation : Capital Surcharges on Opaque Securities Instrument : Surcharge on opaqueness τ a and solvency risk τ λ. The socially optimal funding risk does not lead to the socially optimal solvency risk in competitive equilibrium. Proposition Given a constrained-effi cient allocation, there are capital surcharges τ λ and τ α such that the corresponding competitive equilibrium is constrained effi cient.

Financial Autarky and Securitization Summary of Securitization (Trading and diversification) Idiosyncratic state-dependent vs independent funding risk (Λ i versus Λ)

Financial Autarky and Securitization Summary of Securitization (Trading and diversification) Idiosyncratic state-dependent vs independent funding risk (Λ i versus Λ) Funding risk depends on the transparency of assets produced by others. (Asset pooling) Idiosyncratic state-dependent vs independent asset price (q vs q)

Securitization and Funding Risk Global funding crisis in S = L. Securitization: Λ L = 1. Financial Autarky: E [Λ i ] = 1 [1 λ] }{{} P(α). (2) fraction of good islands

Securitization and Funding Risk Global funding crisis in S = L. Securitization: Λ L = 1. Financial Autarky: E [Λ i ] = 1 [1 λ] }{{} P(α). (2) fraction of good islands Securitization spreads out regional risk to other places via diversification Decreases the number of assets yielding more than 1 in the worst state.

Figure: Funding crisis in the middle state

Securitization and Financial Stability Q j = N.P.V j leverage j funding risk j quality j fire-sale price j. (return to projects ) => leverage => generates two counteracting effects on the MB of quality and transparency: 1. MB of quality - fire-sale losses => high quality becomes less valuable. 2. MB of transparency : it decreases fire-sale losses. (1) Funding risk : individual versus aggregate transparency With securitization, this benefit is not internalized.

Figure: Securitization and Financial Autarky 0.5 Securitization Autarky 0.9 0.85 0.45 0.8 0.75 0.7 0.4 0.65 0.6 0.35 0.16 0.18 0.2 0.22 0.24 0.26 0.55 0.16 0.18 0.2 0.22 0.24 0.26

Summary Benefit of transparency is diversified. Securitizers do not fully internalize the benefit of it.

Summary Benefit of transparency is diversified. Securitizers do not fully internalize the benefit of it. A decrease in transparency further exacerbates solvency risk.

Summary Benefit of transparency is diversified. Securitizers do not fully internalize the benefit of it. A decrease in transparency further exacerbates solvency risk. Solvency and funding risks are high particularly when borrowing is high.

Key Objective : Profits = N.P.V quality leverage funding risk fire-sale price. }{{} securitizers losses from funding crises Social Welfare = N.P.V E [υ(λd) + (A R) (Λd)] }{{} real losses from fire sales