Strategic Opaqueness: A Cautionary Tale on
Securitization
Ana Babus
Chicago Fed & CEPR
Maryam Farboodi
Princeton University
July 2015
Motivation
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Enormous rise in securitization in the banking sector
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Increase in banks’ interconnectedness
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Overlapping portfolios
Interbank exposures
Run on banks
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Information asymmetry
Research Questions
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Why do banks securitize their assets?
Research Questions
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Why do banks securitize their assets?
I
How much do they choose to securitize?
This Paper
Our framework:
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Banks
I
I
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Issue debt to invest in risky projects
Can securitize their assets
Investors
I
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Have access only to local information about the state of the project
Decide whether to liquidate prematurely or continue
This Paper
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Why do banks securitize their assets?
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Securitization creates information asymmetry
Traditionally: information asymmetry leads to securitization
This Paper
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Why do banks securitize their assets?
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Securitization creates information asymmetry
Traditionally: information asymmetry leads to securitization
How much do they choose to securitize?
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Optimal portfolio: optimal opaqueness
Securitization is welfare reducing and leads to banking crisis
This Paper
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Why do banks securitize their assets?
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How much do they choose to securitize?
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Securitization creates information asymmetry
Traditionally: information asymmetry leads to securitization
Optimal portfolio: optimal opaqueness
Securitization is welfare reducing and leads to banking crisis
Bailouts further increase probability of banking crisis
Outline
Model
Equilibrium
Welfare, optimal securitization and financial crises
Conclusion
The Model
The environment
I
Three dates t = 0, 1, 2
I
Two banks i = 1, 2
I
Two investors I = 1, 2
The Model
The environment
I
Three dates t = 0, 1, 2
I
Two banks i = 1, 2
I
Two investors I = 1, 2
I
Bank i raises one unit of funds from investor I :
I
I
Issues debt contracts at face value D with maturity at date t = 2
Invests in a risky project that returns R̃i per unit of investment at date t = 2
State
θi = L
θi = M
θi = H
Probability
pL
pM
pH
Return t = 2
0
RM
FH (.) = RH
RH > RM > 0
The Model
Securitization
At date 0, banks choose whether to securitize a fraction of their project
I
Bank i , chosen at random, proposes to exchange a fraction (1 − φ) of her project
for a fraction (1 − φ) of bank j ’s project
The Model
Securitization
At date 0, banks choose whether to securitize a fraction of their project
I
Bank i , chosen at random, proposes to exchange a fraction (1 − φ) of her project
for a fraction (1 − φ) of bank j ’s project
I
Bank j can accept or reject
I
I
If she reject, no exchange takes place
If she accepts, bank i’s portfolio is
Vi (φ) = φR̃i + (1 − φ) R̃j
while bank j’s portfolio is
Vj (φ) = φR̃j + (1 − φ) R̃i
The Model
Information
At date 1, perfectly revealing signal θi ∈ {L, M , H } is realized about state of project i
I
Investor I observes signal θi
I
Bank i observes both signals θi and θj if φ ∈ (0, 1)
The Model
Actions and payoffs
At date 1, after observing θi , investor I chooses to liquidate or continue
1 if investor I continues bank i
sI ( θ i ) =
0 if investor I liquidates bank i
The Model
Actions and payoffs
At date 1, after observing θi , investor I chooses to liquidate or continue
1 if investor I continues bank i
sI ( θ i ) =
0 if investor I liquidates bank i
I
Liquidate
I
I
Investor receives an early liquidation value, r < RM .
Bank receives 0
The Model
Actions and payoffs
At date 1, after observing θi , investor I chooses to liquidate or continue
1 if investor I continues bank i
sI ( θ i ) =
0 if investor I liquidates bank i
I
Liquidate
I
I
I
Investor receives an early liquidation value, r < RM .
Bank receives 0
Continue
I
I
Investor receives D at date 2, if Vi ≥ D and zero otherwise
Bank is the residual claimant and receives at date 2
max{Vi − D, 0}.
I
Note: if Vi < D, bankruptcy wipes out Vi and both the bank and the
investor receive 0.
The Model
Timing
I
Date 0:
I
I
I
Banks borrow from investors and invest in projects
Banks choose their portfolio (φ, 1 − φ)
Face value of debt D set to maximize expected lender surplus
The Model
Timing
I
Date 0:
I
I
I
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Banks borrow from investors and invest in projects
Banks choose their portfolio (φ, 1 − φ)
Face value of debt D set to maximize expected lender surplus
Date 1
I
I
Signals are realized
Investors decide whether to continue or liquidate
The Model
Timing
I
Date 0:
I
I
I
I
Date 1
I
I
I
Banks borrow from investors and invest in projects
Banks choose their portfolio (φ, 1 − φ)
Face value of debt D set to maximize expected lender surplus
Signals are realized
Investors decide whether to continue or liquidate
Date 2, for the bank(s) continued
I
I
The project(s) matures
The debt is paid back, or the bank is destroyed
Outline
Model
Equilibrium
Welfare, optimal securitization and financial crises
Conclusion
Equilibrium
A symmetric equilibrium is given by
I
A portfolio allocation (φ∗ , 1 − φ∗ ) and a face value of debt D ∗
I
A continuation decision sI∗ (θi ) of each investor I given signal θi
such that
Equilibrium
A symmetric equilibrium is given by
I
A portfolio allocation (φ∗ , 1 − φ∗ ) and a face value of debt D ∗
I
A continuation decision sI∗ (θi ) of each investor I given signal θi
such that
I
Investor I ’s decision is optimal:
I
Each investor I ’s expected payoff is maximized at date 1
max {sI (θi ) · D ∗ · Pr(D ∗ ≤ Vi (φ∗ ) |θi ) + (1 − sI (θi )) · r }
sI
I
Face value of debt maximizes investors expected surplus at date 0
max Eθi {sI∗ (θi ) · D · Pr(D ≤ Vi (φ∗ ) |θi ) + (1 − sI∗ (θi )) · r }
D
Equilibrium
A symmetric equilibrium is given by
I
A portfolio allocation (φ∗ , 1 − φ∗ ) and a face value of debt D ∗
I
A continuation decision sI∗ (θi ) of each investor I given signal θi
such that
I
Investor I ’s decision is optimal:
I
Each investor I ’s expected payoff is maximized at date 1
max {sI (θi ) · D ∗ · Pr(D ∗ ≤ Vi (φ∗ ) |θi ) + (1 − sI (θi )) · r }
sI
I
Face value of debt maximizes investors expected surplus at date 0
max Eθi {sI∗ (θi ) · D · Pr(D ≤ Vi (φ∗ ) |θi ) + (1 − sI∗ (θi )) · r }
D
I
Bank i ’s decision is optimal:
I
Portfolio allocation maximizes bank’ expected surplus at date 0
max Eθi ,θj { max[(Vi (φ) − D ∗ ), 0]| sI∗ (θi )}
φ
Equilibrium
2 Steps
1. Solve for investors’ optimal decisions, given φ.
2. Solve for banks’ optimal decisions.
Investors’ Decisions
Face value of debt
Given a continuation decision sI (θi ), the face value of debt is
∗
DsI = arg max Eθi {sI∗ (θi ) · D · Pr(D ≤ Vi (φ∗ ) |θi ) + (1 − sI∗ (θi )) · r }
Investors’ Decisions
Face value of debt
Example 1: φ = 1.
I sI (H ) = 1, and sI (M ) = sI (L) = 0
∗
DH = arg max pH · D · Pr(D ≤ R̃i |θi = H )
=
I
RH ,
sI (H ) = sI (M ) = 1, and sI (L) = 0
∗
DHM = arg max pH · D · Pr(D ≤ R̃i |θi = H ) + pM · D · Pr(D ≤ R̃i |θi = M )
=
RM .
Investors’ Decisions
Face value of debt
Example 1: φ = 1.
I sI (H ) = 1, and sI (M ) = sI (L) = 0
∗
DH = arg max pH · D · Pr(D ≤ R̃i |θi = H )
=
I
sI (H ) = sI (M ) = 1, and sI (L) = 0
∗
DHM = arg max pH · D · Pr(D ≤ R̃i |θi = H ) + pM · D · Pr(D ≤ R̃i |θi = M )
=
Example 2: φ̂ =
I
RM .
RH
pH +pM
RM
.
−(RH −RM )
sI (H ) = 1, and sI (M ) = sI (L) = 0
DH∗ = arg max pH · D · Pr(D ≤ φR̃i + (1 − φ) R̃j |θi = H )
=
I
RH ,
φRH ,
sI (H ) = sI (M ) = 1, and sI (L) = 0
∗
DHM = RM .
Investors’ Decisions
Face value of debt
7
6.5
6
5.5
Ds∗I
5
4.5
4
3.5
3
2.5
∗
DH
0
0.2
0.4
0.6
φ
0.8
1
Investors’ Decisions
Face value of debt
7
6.5
6
5.5
Ds∗I
5
4.5
4
3.5
∗
DH
3
2.5
∗
DHM
0
0.2
0.4
0.6
φ
0.8
1
Investors’ Decisions
Face value of debt
7
6.5
6
5.5
Ds∗I
5
4.5
4
3.5
∗
DH
∗
DHM
∗
DHM
L
3
2.5
0
0.2
0.4
0.6
φ
0.8
1
Investors’ Decisions
Investors’ surplus
Given a continuation decision sI (θi ) and Ds∗I , then investor I ’s surplus is
 ∗
∗
with prob pH
 DsI · Pr(DsI ≤ Vi (φ) |θi = H ) · sI (H ) + r · (1 − sI (H ))
∗
∗
DsI · Pr(DsI ≤ Vi (φ) |θi = M ) · sI (M ) + r · (1 − sI (M ))
with prob pM
 ∗
∗
DsI · Pr(DsI ≤ Vi (φ) |θi = L) · sI (L) + r · (1 − sI (L))
with prob pL
Investors’ Decisions
Investors’ surplus
Example 1 (cont): φ = 1.
I
sI (H ) = 1, and sI (M ) = sI (L) = 0
pH · RH + (pM + pL ) r
I
sI (H ) = sI (M ) = 1, and sI (L) = 0
(pH + pM ) · RM + pL r
Example 2 (cont): φ̂ =
I
RH
pH +pM
RM
.
−(RH −RM )
sI (H ) = 1, and sI (M ) = sI (L) = 0
pH · φRH + (pM + pL ) r
I
sI (H ) = sI (M ) = 1, and sI (L) = 0
pH · (pH + pM ) RM + pM · (pH + pM ) RM + pL r
Investors’ Decisions
Investors’ surplus
5
4.5
4
Investor Surplus
3.5
3
2.5
2
1.5
1
∗
ISH
0.5
0
0
0.2
0.4
0.6
φ
0.8
1
Investors’ Decisions
Investors’ surplus
5
4.5
4
Investor Surplus
3.5
3
2.5
2
1.5
1
∗
ISH
∗
ISHM
0.5
0
0
0.2
0.4
0.6
φ
0.8
1
Investors’ Decisions
Investors’ surplus
5
4.5
4
Investor Surplus
3.5
3
2.5
2
1.5
1
∗
ISH
∗
ISHM
∗
ISHM
L
0.5
0
0
0.2
0.4
0.6
φ
0.8
1
Investors’ Decisions
Continuation decision
5
4.5
4
Investor Surplus
3.5
3
2.5
2
HML
HM
HM
H
1.5
∗
ISH
∗
ISHM
∗
ISHM
L
IS Optimal
1
0.5
0
0
0.1
0.2
0.3
0.4
0.5
φ
0.6
0.7
0.8
0.9
1
Investors’ Decisions
Continuation decision
H&M&L
H&M
H
H&M
H
H&M
φ
0
φ1
φ2
φ3
φ4
φ5
1
Intuition: for each φ, the investor chooses over compound lotteries
I
The inner lotteries: the choice of D for each continuation decision
I
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Small D is a safe lottery;
High D is a risky lottery.
Investors’ Decisions
Continuation decision
H&M&L
H&M
H
H&M
H
H&M
φ
0
φ1
φ2
φ3
φ4
φ5
1
Intuition: for each φ, the investor chooses over compound lotteries
I
The inner lotteries: the choice of D for each continuation decision
I
I
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Small D is a safe lottery;
High D is a risky lottery.
The outer lotteries: the continuation decision
I
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Continuation in H&M: smaller expected payoffs in each state;
Continuation in H: higher expected payoff in state H, but only r in state M.
Banks’ Decisions
Banks surplus
Given a continuation decision sI (θi ), then bank i ’s surplus

∗

 Eθj {max[(φsI RH + (1 − φsI ) R̃j − Ds∗I ), 0]} · sI (H )
Eθj {max[(φsI RM + (1 − φsI ) R̃j − DsI ), 0]} · sI (M )

 E {max[(0 + (1 − φ ) R̃ − D ∗ ), 0]} · s (L)
sI
j
I
θj
sI
with prob pH
with prob pM
with prob pL
Banks’ Decisions
Banks surplus
Example 1 (cont): φ = 1
I
If (pH + pM ) RM > pH RH + pM r
∗
∗
∗
∗
sI (H ) = sI (M ) = 1, sI (L) = 0, and D = RM .
pH (RH − RM ) .
Example 2 (cont): φ̂ =
I
RH
pH +pM
RM
.
−(RH −RM )
If φpH RH + pM r > (pH + pM )2 RM
∗
∗
∗
∗
sI (H ) = 1, sI (M ) = sI (L) = 0, and D = φRH
pH · (1 − φ) (pH RH + pM RM )
Banks’ Decisions
Banks surplus
5
∗
BSH
4.5
4
Borrower Surplus
3.5
3
2.5
2
1.5
1
0.5
0
0
0.2
0.4
0.6
φ
0.8
1
Banks’ Decisions
Banks surplus
5
∗
BSH
∗
BSHM
4.5
4
Borrower Surplus
3.5
3
2.5
2
1.5
1
0.5
0
0
0.2
0.4
0.6
φ
0.8
1
Banks’ Decisions
Banks surplus
5
∗
BSH
∗
BSHM
∗
BSHM
L
4.5
4
Borrower Surplus
3.5
3
2.5
2
1.5
1
0.5
0
0
0.2
0.4
0.6
φ
0.8
1
Banks’ Decisions
Optimal securitization
5
∗
BSH
∗
BSHM
∗
BSHM
L
BS Optimal
4.5
4
Borrower Surplus
3.5
HML
3
HM
H
HM
2.5
2
1.5
1
0.5
0
0
0.1
0.2
0.3
0.4
0.5
φ
0.6
0.7
0.8
0.9
1
Outline
Model
Equilibrium
Welfare, optimal securitization and financial crises
Conclusion
Welfare
Proposition 1
Securitization decreases welfare.
Note: Welfare = Investors’ + Banks’ surplus
Welfare
Proposition 1
Securitization decreases welfare.
Note: Welfare = Investors’ + Banks’ surplus
I
Ineffective liquidation and continuation
I Lender cannot effectively liquidate bad projects
Welfare
Proposition 1
Securitization decreases welfare.
Note: Welfare = Investors’ + Banks’ surplus
I
Ineffective liquidation and continuation
I Lender cannot effectively liquidate bad projects
I (Potential) countervailing force: downward adjustment in face value by
investor → not enough
Welfare
Proposition 1
Securitization decreases welfare.
Note: Welfare = Investors’ + Banks’ surplus
I
Ineffective liquidation and continuation
I Lender cannot effectively liquidate bad projects
I (Potential) countervailing force: downward adjustment in face value by
investor → not enough
I
Too-frequent liquidation
I With perfect info, the investor is able to set a face value he obtains with
high probability if his bank is in state H or M.
I With less info, he cannot do that: he obtains the same face value with lower
probability when his bank is in state M, or H.
I Liquidate more often to break the tie: choose the riskier lottery
Welfare
5.5
5
4.5
Total Surplus
4
3.5
3
2.5
2
1.5
1
0.5
0
TS
0
0.2
0.4
0.6
φ
0.8
1
Optimal Securitization
Proposition 2
The banks always have an incentive to securitize and set φ ∈ (0, 1).
Intuition: division of the surplus favors the bank
Optimal Securitization
Proposition 2
The banks always have an incentive to securitize and set φ ∈ (0, 1).
Intuition: division of the surplus favors the bank
I
Full securitization (φ = 0) and no securitization (φ = 1) are identical: the bank
obtains surplus (RH − RM ) only in state H ;
I
Total surplus decreases when φ < 1, but the share of investors’ decreases more.
Optimal Securitization
Proposition 2
The banks always have an incentive to securitize and set φ ∈ (0, 1).
Intuition: division of the surplus favors the bank
I
Full securitization (φ = 0) and no securitization (φ = 1) are identical: the bank
obtains surplus (RH − RM ) only in state H ;
I
Total surplus decreases when φ < 1, but the share of investors’ decreases more.
I
Compound lottery
I Conditional on signal: dispersion
I Revision in face value of debt
Optimal Securitization
5.5
5
4.5
Division of Surplus
4
3.5
3
2.5
TS
LS
BS
2
1.5
1
0.5
0
0
0.2
0.4
0.6
φ
0.8
1
Financial Crises
Proposition 3
There exist equilibria in which securitization increases the probability of financial crises.
Intuition: the bank chooses over a continuum of compound lotteries to offer the
investor (one fore each φ)
Financial Crises
Proposition 3
There exist equilibria in which securitization increases the probability of financial crises.
Intuition: the bank chooses over a continuum of compound lotteries to offer the
investor (one fore each φ)
I
Each compound lottery translates to two outcomes for the bank:
I
I
Continued in both state H and M, but with smaller expected payoffs;
Continued in state H, with higher expected payoff in state H (because of
∗
lower D ), but only 0 in state M and L.
Financial Crises
Proposition 3
There exist equilibria in which securitization increases the probability of financial crises.
Intuition: the bank chooses over a continuum of compound lotteries to offer the
investor (one fore each φ)
I
Each compound lottery translates to two outcomes for the bank:
I
I
I
Continued in both state H and M, but with smaller expected payoffs;
Continued in state H, with higher expected payoff in state H (because of
∗
lower D ), but only 0 in state M and L.
Banks solves a max-min problem
I Twist: total surplus is also affected
Outline
Model
Equilibrium
Welfare, optimal securitization and financial crises
Conclusion
Conclusions
I
Model of optimal choice of securitization
I
Securitization determines surplus division between investors and banks
I
Banks securitize to maximize their share
I
Excessive runs
I Lenders act on their information more aggressively
I Bank chooses to be run on
Related Literature
I
Dang, Gorton, Holmstrom, Ordonez (2014), Dang, Gorton, Holmstrom (2015)
I
Gorton and Pennacchi (1990)
I
DeMarzo (2005), Duffie (2008)
I
Stanton, Walden, Wallace (2014)