Corporate Finance:
Asymmetric information and capital
structure – signaling
Yossi Spiegel
Recanati School of Business
Ross, BJE 1977
“The Determination of Financial
Structure: The Incentive-Signalling
Approach”
The model
The timing:
Stage 1
Stage 0
The firm issues
debt with face
value D
The capital market
observes D and
updates the belief
about the firm’s type
Stage 2
Cash flow is realized
Cash flow is x ~ U[0,T], where T ∈ {L,H}, L < H
T is private info. to the firm
The capital market believes that T = H with prob. γ
In case of bankruptcy, the manager bears a personal loss C
The manager’s utility: U = V – C x Prob. of bankruptcy
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The full information case
The value of the firm when T is common knowledge:
T
D
 T
VT =  ∫ xdF ( x) + ∫ DdF ( x) + ∫ ( x − D )dF ( x) = xˆT
D
0
 D
With uniform dist.: xˆT = T / 2
The manager’s utility:
D
U = xˆT − C × F ( D) = xˆT − C
T
The manager will not issue debt
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Asymmetric information
DT* is the debt level of type T
B* is the prob. that the capital market
assigns to the firm being of type T
Perfect Bayesian Equilibrium (PBE),
(DH*,DL*,B*):
DH* and DL* are optimal given B*
B* is consistent with the Bayes rule
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5
Bayes rule
P(B | A)P( A)
(
)
P A| B =
P(B )
In our case, two levels of D are chosen. Suppose the probability that each type
plays them is as follows:
D1
D2
Type H (γ)
h1
h2
Type L (1−γ)
l1
l2
Having observed D1 the capital market believes that the firm is type H with
prob.:
P(H | D1 ) =
P(D1 | H )P( H )
h1γ
=
P(D1 )
h1γ + l1 (1 − γ )
In a sep. equil., h1 = 1 and l1 = 0. In a pooling equil., h1 = l1 = 1
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Separating equilibria: DH* ≠ DL*
The belief function:
1

B* =  0
γ '

D = DH *
D = DL *
o/w
In a separating equil., DL* = 0 because
type L cannot boost V by issuing debt
DL* = 0 ⇒ B*(0) = 0 ⇒ V(0) = L/2
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Separating equilibrium
The IC of H:
D
V −C× ≥
H
14243
Payoff of H
when it issues D
L
2
{
Payoff of H
when D = 0
The IC of L:
L
2
{
Payoff of L
when D = 0
D
≥V −C×
L
1424
3
Payoff of L
when it issues D
Indifference of type T between V and D:
L
D
= V −C×
2
T
{
1424
3
Payoff
if D = 0
⇒ V=
L
D
+C×
2
T
Payoff when issuing D
if it induces value V
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The set of separating equilibria
V
V=
L
D
+C
2
L
sep. equil.
V=
L
D
+C
2
H
V=
H
2
D* is defined by
L/2+CxD/L = H/2
⇒ D* = (H-L)L/2C
V=
D*
D**
Corporate Finance
L
2
D
9
The DOM criterion
D ≥ D* is a dominated strategy for type L: D = 0 always guarantees L a higher
payoff no matter what the capital market believes
The DOM criterion:
1
0

B* = 
1
γ '
D = DH *
D = DL *
D ≥ D*
o/w
The idea: type L will never play D ≥ D* while type H might. Hence, if D ≥ D*,
then the firm’s type must be H
The DOM criterion still does not determine the beliefs for D < D* and D ≠ 0
Under the DOM criterion: DL* = 0, DH*=D*
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Separating equilibria under the
DOM criterion
V
V=
L
D
+C
2
L
V=
L
D
+C
2
H
V=
H
2
DL* = 0, DH*=D*
V=
D*
D**
Corporate Finance
L
2
D
11
Pooling equilibria: DH* = DL* = Dp*
The belief function:
γ
B* = 
γ '
D = Dp *
o/w
In a pooling equil., the choice of Dp*
is uninformative; hence
H
L
ˆ
V = γ × + (1 − γ )×
2
2
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The set of pooling equilibria
V
V=
L
D
+C
2
L
V=
L
D
+C
2
H
V=
H
2
V = Vˆ
pooling
equil.
V=
D*
D**
Corporate Finance
L
2
D
13
The DOM criterion
The DOM criterion:
γ

B* =  1
γ '

D = Dp *
D ≥ D*
o/w
The DOM criterion eliminates some
pooling equilibria but not all
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The set of pooling equilibria
V
V=
L
D
+C
2
L
V=
L
D
+C
2
H
V=
H
2
V = Vˆ
pooling
equil.
V=
D*
D**
Corporate Finance
L
2
D
15
The intuitive criterion
Due to Cho and Kreps, QJE 1987
Fix a equilibrium (DL*, DH*) and consider a deviation from this
equilibrium to D’. If the deviation never benefits type x (even if it
induces the most favorable beliefs by the capital market) but can
benefit type y, then the deviation was played by type y
The intuitive criterion:
γ

B* =  1
γ '

D = Dp *
D is dominated by D p *
o/w
The intuitive criterion still does not determine the beliefs everywhere
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The set of pooling equilibria under
the intuitive criterion
V
V=
L
D
+C
2
L
V=
L
D
+C
2
H
V=
H
2
V = Vˆ
pooling
equil.
V=
D*
D**
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L
2
The intuitive
criterion
eliminates all
pooling equil.
D
17
Conclusions
The only equilibrium which survives the intuitive
criterion is DL* = 0 and DH* = D*
This equilibrium is the Pareto undominated separating
equilibrium and it is called the “Riley outcome”
Debt can be used as a signal of high cash flow
The debt of type H:
L
D H
+C =
2
L 2
⇒
(
H − L )L
D* =
2C
D*↑ when L↑, H-L↑, and C↓, D* is independent of γ!
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Leland and Pyle, JF 1977
“Informational asymmetries, financial
structure, and financial intermediation”
The model
The timing:
Stage 1
Stage 0
An entrepreneur
sell a fraction 1-α of
the firm to outside
equityholders
The capital market
observes 1-α and
updates the belief
about the firm’s type
Stage 2
Cash flow is realized
Cash flow is x ~ [0,∞), with Ex = xT and Var(x)=σ2, where T ∈ {L,H}, xL < xH
T is private info. to the firm
The capital market believes that T = H with prob. γ
The entrepreneur’s expected utility:
b
EU (WT ) = EWT − × Var (WT )
2
Corporate Finance
WT = αx + (1 − α )V
20
The full information case
The variance of WT:
Var (WT ) = E (αx + (1 − α )V − EWT )
2
= E (α ( x − xT )) = α 2σ 2
2
The entrepreneur’s expected utility:
b
2 2
EU (WT ) = αxT + (1 − α )V − × α
σ
14
4244
3 2 123
Under full info., V = xT:
EWT
Var ( x )
b
EU (WT ) = xT − × α 2σ 2
2
⇒
α* = 0 ⇒ The entrepreneur will sell the entire firm
Why? Because the entrepreneur is risk-averse and the capital
market is risk-neutral
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Asymmetric information
αT* is the equity participation of type T
B* is the prob. that the capital market
assigns to the firm being of type T
Perfect Bayesian Equilibrium (PBE),
(αH*, αL*,B*):
αH* and αL* are optimal given B*
B* is consistent with the Bayes rule
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Separating equilibria: αH* ≠ αL*
The belief function:
1

B* =  0
γ '

α = αH *
α = αL *
o/w
In a separating equil., αL* = 0 because
type L cannot boost V by keeping equity
αL* = 0 ⇒ B*(0) = 0 ⇒ V(0) = xL
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Separating equilibrium
The IC of H:
b 2 2
αxH + (1 − α )V − α σ
2 44
14444244
3
Payoff of H when he keeps a fraction α of the firm
≥
xL
{
Payoff of H
when α = 0
The IC of L:
xL
{
Payoff of L
when α = 0
≥
b
2 44
1444
4244
3
αxL + (1 − α )V − α 2σ 2
Payoff of L when he keeps a fraction α of the firm
Indifference of type T between V and α:
b 2 2
xL − αxT bσ 2 α 2
xL = αxT + (1 − α )V − α σ
⇒ V=
+
×
{
2 44
1−α
2 1−α
1444
4244
3
Payoff
if α = 0
Payoff when keeping a fraction α
of the firm if it induces a value V
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The set of separating equilibria
V
xL − αxH bσ 2 α 2
bσ 2 α 2
V=
+
×
V = xL +
×
1−α
2 1−α
2 1−α
sep.
equil.
V = xH
V = xL
α*
α * = − Z + Z (Z + 2 )
α**
Z≡
Corporate Finance
xH − xL
bσ 2
α
25
The Riley outcome
Using L’s IC, the ownership share of type H is:
Payoff of L
when α = 0
Payoff of L when he keeps a fraction α of the firm
and the market believes that his type is H
xH − xL
bσ 2
increases with the extent of asymmetric info., xH-xL
decreases with risk aversion, b
decreases with the variance of cash flows, σ2
Using H’s IC:
xL
{
Payoff of H
when α = 0
⇒ α* = − Z
{ + Z (Z + 2 )
α* increases with Z which
b
14444244244
3
αxL + (1 − α )xH − α 2σ 2
=
xL
{
=
b 2 2
αxH + (1 − α )xH − α σ
144442442443
2(xH − xL )
⇒ α ** =
bσ 2
Payoff of H when he keeps a fraction α of the firm
and the market believes that his type is H
α** < 1 iff 2(xH–xL)< bσ2; otherwise, type H prefers every α > 0 over α = 0
provided that he convinces outsiders that the firm’s type is H
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