Savings Glut
and Financial
Fragility
Patrick
Bolton, Tano
Santos, José
A.
Scheinkman
Savings Glut and Financial Fragility
Patrick Bolton∗
Tano Santos∗
∗ Columbia
∗∗ Columbia
José A. Scheinkman∗∗
University and NBER
University, Princeton University and NBER
New York University
October, 2015
1/42
Savings Glut
and Financial
Fragility
Patrick
Bolton, Tano
Santos, José
A.
Scheinkman
Some observations
• In period preceding the crisis
• The US financial sector accounted for an increasing
fraction of corporate profits
• Strong growth in compensation in the financial services
industry
• Finance as a favorite occupation
• Deterioration of origination incentives
• Increase in balance sheet size and leverage among some
financial intermediaries (IBs and broker-dealers)
• Growth of the “originate and distribute” model
• With Patrick and Tano: Models that aim to shed light on
these facts
2/42
Savings Glut
and Financial
Fragility
Patrick
Bolton, Tano
Santos, José
A.
Scheinkman
Motivation for this paper
• Relationship between large increases in liquidity and:
Deterioration of origination standards among asset
originators.
2 Across the board drop in asset yields.
3 More debt and increased leverage.
1
3/42
Savings Glut
and Financial
Fragility
Patrick
Bolton, Tano
Santos, José
A.
Scheinkman
Savings Glut
1
Excess savings view: Bernanke (2005):
• World savings glut and current account deficits
• Precautionary savings shocks in the 90s: Asia, Russia,
Germany, ...
• In US, Spain etc.: Asset appreciation, low yields.
2
“Excess elasticity” of financial regimes: Borio and Disyatat
(2011)
• Excess savings view incomplete: What is key is financing:
• The financial crisis reflected disruptions in financing
channels, in borrowing and lending patterns, about which
saving and investment flows are largely silent.
• Adrian and Shin (2010)
4/42
Savings Glut
and Financial
Fragility
Patrick
Bolton, Tano
Santos, José
A.
Scheinkman
Secular rise of institutional cash-pools (Pozsar)
• Surveys indicate that 90% of these pools subject to
written cash policies with safety of principal as dominant
consideration.
5/42
B
Savings Glut
and Financial
Fragility
Patrick
Bolton, Tano
Santos, José
A.
Scheinkman
Percent of loans in private mortgage market with
incomplete documentation (Piskorky et al.)
C
6/42
Fig. 4.4
Evolution of FICO, LTV/CLTV, and percent low documentation loans in
Savings Glut
and Financial
Fragility
Patrick
Bolton, Tano
Santos, José
A.
Scheinkman
Cumulative default path of subprime mortgages
• Source: Corelogic-Blackbox
7/42
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
Savings Glut
and Financial
Fragility
Patrick
Bolton, Tano
Santos, José
A.
Scheinkman
8/42
Broker dealers: Leverage (Assets/equity) and Assets
3500000
25
3000000
2500000
20
2000000
15
1500000
10
1000000
500000
5
0
0
Total Assets
Leverage
Savings Glut
and Financial
Fragility
Patrick
Bolton, Tano
Santos, José
A.
Scheinkman
Outline of model
• Model where financial sector “recycles” savings into assets
of endogenous quality, impacting:
1. The quality of asset origination.
2. The balance sheet of financial intermediaries.
3. Later will consider
• Incentives for distribution
• Financial stability
• Three ingredients:
• Liquidity: cash-in-the-market pricing
• Allen and Gale, “cheap” risk-aversion
• Coexistence of OTC and exchange.
• Endogenous distribution of capital and knowledge
9/42
Savings Glut
and Financial
Fragility
Patrick
Bolton, Tano
Santos, José
A.
Scheinkman
Agents
• Three types of risk-neutral agents
• A unit measure of originators
• A measure N of informed investors.
• In the equilibrium we will describe, informed will look like
“financial intermediaries”.
• A measure M = 1 − N of uninformed investors.
• In the equilibrium we will describe, uninformed will
provide cash pools.
• Two dates τ = 1, 2
• τ = 1: Assets originated and distributed in two markets
• τ = 2: Payoffs are realized
10/42
Savings Glut
and Financial
Fragility
Patrick
Bolton, Tano
Santos, José
A.
Scheinkman
Originators
• At τ = 1 each originator originates one asset of high (xh )
or low quality (xl = 0)
• Originators exert effort e ∈ [e, 1), where e > 0
Pr(x = xh | e ) = e
• Private cost of effort: ψ(e − e )
• ψ(0) = ψ0 (0) = 0, ψ0 > 0, if e > e, ψ00 >> 0 and
lime →1 ψ0 (e − e ) = +∞
•
u o (e, c1 ) = −ψ(e − e ) + c1 , if c1 ≥ 0.
• Later: τ = 1 distribute a fraction π of those assets at
τ=1
11/42
Savings Glut
and Financial
Fragility
Patrick
Bolton, Tano
Santos, José
A.
Scheinkman
Investors
• Every investor has endowment K in period 1.
• Utility of all investors,
U (c1 , c2 ) = c1 + c2 , if ci ≥ 0.
• Two types of investors
1
Measure N of informed investors. For each project they
can see a signal σ ∈ {σ` , σh }:
Prob (σh |xh ) = 1
and
Prob (σh |xl ) = α,
g := Prob (xh |σh ) =
2
12/42
e
.
e + α (1 − e )
M = 1 − N measure of uninformed investors
α
small.
(1)
Savings Glut
and Financial
Fragility
Patrick
Bolton, Tano
Santos, José
A.
Scheinkman
1. Private markets (OTC)
•
•
•
•
Private deals between an originator and investor.
Only accessible by informed dealers.
Originators only know effort e.
If each informed investor buys q i , originator with a project
with a good signal sells to an informed trader with
probability
Nq i
m := min
;1 .
(2)
e + (1 − e ) α
• Price in this market p d : As in Bolton, Santos and
Scheinkman (2015), if p is price in exchange,
p d = κgxh + (1 − κ )p,
13/42
(3)
Savings Glut
and Financial
Fragility
Patrick
Bolton, Tano
Santos, José
A.
Scheinkman
Public markets or exchanges
• T amount of cash brought to exchange.
• Two candidate prices:
pf =
e ( 1 − m ) xh
T
; p cim =
1 − em − (1 − e )αm
1 − em − (1 − e )αm
• Prices in the exchange
n
o
p = min p cim , p f
• p ≤ p f ⇒ p ≤ gxh or p ≤ p d . (inequalities strict if
m > 1.)
14/42
(4)
Savings Glut
and Financial
Fragility
Patrick
Bolton, Tano
Santos, José
A.
Scheinkman
Market for collateralized lending
• Investors can lend against collateral:
• D: Amount borrowed
• r : Interest (repo) rate
• Leverage constraint: η ∈ (0, 1). An investor that owns q
units of asset can borrow D provided:
(1 − η ) qp ≥ D
15/42
Savings Glut
and Financial
Fragility
Patrick
Bolton, Tano
Santos, José
A.
Scheinkman
Expected payoffs I
• Originator’s expected payoff
h i
−ψ (e − e ) + e mp d + (1 − m)p + (1 − e ) α mp d + (1 − m)p + (1 − α)p
• Uninformed choose q u ≥ 0 and borrows D u = q u p − K .
Leverage constraint implies ηpq u ≤ K . Expected payoff is:
V u (Q u ) := q u pr x − D u r ,
rx =
16/42
e (1 − m )xh
(1 − em − (1 − e )αm)p
Savings Glut
and Financial
Fragility
Patrick
Bolton, Tano
Santos, José
A.
Scheinkman
Expected payoffs II
• Informed investor chooses q i ≥ 0 amount bought in OTC
and y − q i ≥ 0 bought in exchange. Borrows
D i = K − py − (p d − p )q i . Leverage constraint
⇒ ηpy ≤ K − (p d − p )q i . Expected payoff:
V i q i , y = q i p d (R − r ) + p (y − q i )(r x − r ) + Kr
where
R=
17/42
gxh
pd
Savings Glut
and Financial
Fragility
Patrick
Bolton, Tano
Santos, José
A.
Scheinkman
Equilibrium
• Given (K , N, α)
• A vector of equilibrium prices and allocations is a vector
(p, r , p d , m, g , r x , R, q u , D u , q i , y , D i ) such that g , p d and
m satisfy equations (1)-(3) , p satisfies (4) when
T = p (q u + y ), (e, q u , D u , q i , y , D i ) solves the
maximization problems of agents and furthermore,
Mq u + N (q i + y ) = 1; MD u + ND i = 0.
• Focus on equilibria in which capital in the hands of
informed scarce relative to the number of good projects,
that is m < 1.
18/42
Savings Glut
and Financial
Fragility
Patrick
Bolton, Tano
Santos, José
A.
Scheinkman
Strict CIM equilibria
• A strict CIM equilibrium satisfies
R > rx > 1
1
2
19/42
Cash-in-the-Market (CIM) pricing obtains.
Informed investors obtain higher returns by investing in
private markets than in exchanges.
Savings Glut
and Financial
Fragility
Patrick
Bolton, Tano
Santos, José
A.
Scheinkman
Strict CIM equilibria
• In strict CIM equilibrium uninformed investors must be
indifferent between deploying capital in the exchange or in
the secured lending market
rx = r.
• q i = y and (1 − η ) q i p = D i > 0
• Uninformed provide loans. Informed are intermediaries.
The balance sheet of the intermediaries in private markets
is:
qp d = K + D i .
20/42
Originators: 1
Informed investors: N
pd
Assets
Liabilities
q i pd
D
K
D
gxh
Dr
Uninformed
investors
Incentives: e
MK − ND
p = min
(
e(1−m)xh
M K−N D
,
1−m(e+α(1−e)) 1−m(e+α(1−e))
e(1−m)xh
1−m(e+α(1−e))
Cream skimming
)
Savings Glut
and Financial
Fragility
Patrick
Bolton, Tano
Santos, José
A.
Scheinkman
Remaining time
• Existence of a strict CIM equilibrium
• Comparative statics: How does an increase in K affect
•
•
•
•
Prices in exchange: p
Origination standards: e
Debt: D := D i
Leverage:
K +D
D
` :=
= 1+
K
K
• Increase in capital in hands of all investors, zero supply
response from originators.
• Extensions: Increase in uninformed capital only, mistakes
in α, originate and distribute.
22/42
Savings Glut
and Financial
Fragility
Patrick
Bolton, Tano
Santos, José
A.
Scheinkman
CIM equilibrium equations I
• Given (p, r ) and candidate choices (e, q u , q i ), define:
Nq i
,1
m := min
e + α (1 − e )
e
g :=
e + α (1 − e )
pd
Du
:= κgxh + (1 − κ ) p
e (1 − m )xh
:=
p (1 − m (e + α (1 − e )))
:= q u p − K
Di
:= q i p d − K
rx
23/42
and
R :=
gxh
pd
Savings Glut
and Financial
Fragility
Patrick
Bolton, Tano
Santos, José
A.
Scheinkman
CIM equilibrium equations II
• First order conditions and market clearing: (p, r ) and
candidate choices (e, q u , q i ) form an equilibrium
0
D
i
p
=
ψ 0 (e − e )
=
=
+
+
r
Mq u
MD
24/42
≥
=
u
Du
(1 − η ) pq i
MK − ND i
e (1 − m)xh
min
,
1 − m (e + α (1 − e )) 1 − m (e + α (1 − e ))
(1 − α) mκ (gxh − p )
rx
Nq i = 1
ND i = 0
Savings Glut
and Financial
Fragility
Patrick
Bolton, Tano
Santos, José
A.
Scheinkman
A system of equations in p and e
• If (p, r ) is a strict CIM equilibrium then:
f 1 (p, e, K , N, α)
:=
p − K (M + Nγ) = 0
f 2 (p, e, K , N, α)
:=
(e + α (1 − e )) ψ0 (e − e ) − (1 − α) NK (1 − γ) = 0
where
γ=
ηp
κ (gxh − p ) + ηp
• A “converse” also holds. If (p, e ) solves
f (p, e, K , N, α) = 0 we can calculate (g , m, p d , r x , R ). If
m < 1 and R > r x > 1, can construct strict CIM
equilibrium.
• Do the math with f (·) = 0 but results are necessarily
local.
25/42
Savings Glut
and Financial
Fragility
Patrick
Bolton, Tano
Santos, José
A.
Scheinkman
Existence
Proposition 1. Suppose that
eκxh
< K̃ < exh .
1 − e + eκ
(5)
Then there exists a neighborhood N of (K̃ , 0, 0)
such that for (K , N, α) ∈ N , N > 0 and α ≥ 0,
there exists a unique equilibrium and this
equilibrium is a strict CIM equilibrium with
m < 1.
26/42
Savings Glut
and Financial
Fragility
Patrick
Bolton, Tano
Santos, José
A.
Scheinkman
Prices increase with K
Proposition 2. There exists a continuous
non-increasing function ᾱ : [0, ∞) → (0, 1] with
ᾱ(0) = 1 such that if K1 < K2 and there are
continuous functions p (K ) and r (K ) defined in
(K1 , K2 ) such that (p (K ), r (K )) is a strict CIM
equilibrium for parameters (K , N, α) and
α < ᾱ(K2 N ), then p (K ) is smooth with
p 0 (K ) > 0.
27/42
Savings Glut
and Financial
Fragility
Patrick
Bolton, Tano
Santos, José
A.
Scheinkman
Rates of return in OTC and exchange
3.5
3
r x (K), R(K)
2.5
2
1.5
1
0.5
28/42
1
1.2
1.4
1.6
Capital
1.8
2
2.2
Savings Glut
and Financial
Fragility
Patrick
Bolton, Tano
Santos, José
A.
Scheinkman
Effort
• The first order condition for effort
ψe = m p d − p = mκ (xh − p )
• The two sides of liquidity:
• Informed liquidity: An increase in m increases origination
incentives
• Uninformed liquidity: An increase in p decreases
origination incentives
29/42
Savings Glut
and Financial
Fragility
Patrick
Bolton, Tano
Santos, José
A.
Scheinkman
Effort is single peaked
Proposition 3. (Single peakedness of effort ) Let
K1 < K2 and suppose that there are continuous
functions p (K ) and r (K ) defined in (K1 , K2 ) such
that (p (K ), r (K )) is a strict CIM equilibrium for
parameters (K , N, α) with α < ᾱ(K2 N ). Then if
η < κ the function e (K ) = e (p (K ), r (K )) is
either monotone or has a single global maximum.
• Recall g is monotone on e.
30/42
Savings Glut
and Financial
Fragility
Patrick
Bolton, Tano
Santos, José
A.
Scheinkman
e,p and m.
Panel B
Panel A
4.5
m
α=0
0.8
(xh − p)
4
0.5
m(K)
p(K)
e(K)
0.75
3.5
0.7
0.4
3
α = .2
0.65
0.6
31/42
1
1.5
Capital
2
2.5
1
1.5
Capital
2
0.3
Savings Glut
and Financial
Fragility
Patrick
Bolton, Tano
Santos, José
A.
Scheinkman
Leverage
• Proposition 4. In a strict CIM equilibrium, If either (i )
e 0 (K ) < 0 or (ii ) α is small, then The leverage ratio D/K
satisfies
D (K ) 0
> 0.
K
• Reasons for increase in leverage ratio: Demand
• An increase in p increases debt capacity
• In addition, p d goes up by less than p: Less equity needed
to buy assets
• Supply: An increase in p, lowers r x and investors
reallocate part of the funds to the repo market.
32/42
Savings Glut
and Financial
Fragility
Patrick
Bolton, Tano
Santos, José
A.
Scheinkman
Financial Fragility
• Total assets and leverage ratios correlate positively
• When liquidity is abundant, additional liquidity:
1
2
Increases leverage
and leads to a deterioration of origination standards
• Moreover the worse the quality of the information of
informed investors (high α), the higher the leverage
33/42
Savings Glut
and Financial
Fragility
Patrick
Bolton, Tano
Santos, José
A.
Scheinkman
Fragility
Panel B: Liability
Panel A: Asset
0.8
0.92
0.75
0.915
0.7
α = .2
0.65
ℓ(K)
K
g(K)
0.91
0.905
0.6
0.55
0.9
0.5
α = 0
0.45
0.895
0.4
0.89
34/42
1
1.5
Capital
2
0.35
1
1.5
Capital
2
Savings Glut
and Financial
Fragility
Patrick
Bolton, Tano
Santos, José
A.
Scheinkman
Extensions: Effect of “dumb” capital
Proposition 5. (For α small ?), in a strict CIM
equilibrium, (a) the price p is an increasing
function of the proportion of capital held by
uninformed investors, M and (b) origination
incentives, e, are a decreasing function of the
proportion of capital held by the uninformed
investors, M.
35/42
Savings Glut
and Financial
Fragility
Patrick
Bolton, Tano
Santos, José
A.
Scheinkman
Extensions: Mistakes by a single intermediary
• Informed investor believes that her b
α < αtrue .
• The rest of the market has the correct beliefs: α = αtrue
• Mistaken investor bids more aggressively in OTC; chooses
qb =
K
κ (gb xh − p ∗ ) + ηp ∗
and
b=
D
(1 − η ) p ∗ K
.
κ (gb xh − p ∗ ) + ηp ∗
• The equity capital at τ = 2 under the wrong beliefs is
b
Equity Capitalwrong = qbgbxh − r ∗ D
• Comparison of true capital and capital under wrong beliefs
b < Equity Capital
Equity Capitaltrue = qbg ∗ xh − r ∗ D
wrong .
• The mistaken intermediary has
• lower leverage than the rest of the informed investors but
• less equity capital at τ = 2
36/42
Savings Glut
and Financial
Fragility
Patrick
Bolton, Tano
Santos, José
A.
Scheinkman
Fragility
6
Equity capital at τ = 2
5.5
5
4.5
4
3.5
3
2.5
1
1.2
1.4
1.6
K
37/42
1.8
2
2.2
Savings Glut
and Financial
Fragility
Patrick
Bolton, Tano
Santos, José
A.
Scheinkman
Mistakes by all
• Agents are sure that α = 0.
• The equilibrium that obtains is one that is consistent with
α=0
• Ex-post, if they were mistaken about α, they are
“surprised” to realize losses
• Leverage is lower than in the case α > 0 for all
institutions, but
• True capital is lower than assumed capital.
38/42
Savings Glut
and Financial
Fragility
Patrick
Bolton, Tano
Santos, José
A.
Scheinkman
Fragility
5.5
Capital under wrong beliefs
Equity capital at τ = 2
5
4.5
4
α = .2
3.5
3
α = .4
2.5
2
1
1.2
1.4
1.6
1.8
K
39/42
2
2.2
Savings Glut
and Financial
Fragility
Patrick
Bolton, Tano
Santos, José
A.
Financial
Scheinkman
Crises
Evidence of Mistakes (Willen)
José
Scheinkman
Housing
Coditional Forecasts from Lehman (Foote et al. )
Name
(1) Aggressive
(2)
(3) Base
(4) Pessimistic
(5) Meltdown
13/13
40/42
Scenario
Probability Cum Loss
11% HPA over the life of the pool
15%
1.4%
8% HPA for life
15%
3.2%
HPA slows to 5% by end-2005
50%
5.6%
0% HPA for the next 3 years 5% thereafter
15%
11.1%
-5% for the next 3 years, 5% thereafter
5%
17.1%
Table 2. Conditional Forecasts of Losses on Subprime Investments from Lehman Brothers.
This table shows that investors knew that subprime investments would turn sour if housing prices fell. The
“meltdown” scenario for housing prices above implies cumulative losses of 17.1 percent on subprime-backed
bonds; such losses would be large enough to wipe out all but the highest-rated tranches of most subprime
deals. The table also shows that investors placed small probabilities on these adverse price scenarios, a fact
that explains why they were so willing to buy these bonds.
Source: “HEL Bond Profile Across HPA Scenarios” from Lehman Brothers: “U.S. ABS Weekly Outlook,”
August 15, 2005.
Savings Glut
and Financial
Fragility
Patrick
Bolton, Tano
Santos, José
A.
Scheinkman
Originate and distribute
• Let the utility of the originator be
U e (e )
≡
+
− ψ (e − e )
h h ii
π e mp d + (1 − m)p + (1 − e ) α mp d + (1 − m)p + (1 − α)p
+
(1 − π ) exh
+
B (π )
• B (π ): Benefits of distribution, Bπ > 0 and Bππ < 0
• When α = 0, πK > 0.
41/42
Savings Glut
and Financial
Fragility
Patrick
Bolton, Tano
Santos, José
A.
Scheinkman
Conclusion
• Model where financial sector “recycles” savings into assets
of endogenous quality:
•
•
•
•
Increase in capital decreases yields
Lower quality of assets
Lower the quality of assets held by financial intermediaries
Increases levevage
• To do
• Consider change in supply of assets and endogenize
distribution decision
• Dynamics
• ...
42/42