On the Design of Contingent Capital · 2018-04-03 · Basic idea of contingent capital (CC) The...

On the Design of Contingent Capitalwith a Market Trigger

Suresh Sundaresan Zhenyu Wang

Columbia University Indiana University

The Journal of Finance

SW (CU,IU) Contingent Capital JF 1 / 23

Basic idea of contingent capital (CC)

The capital functions as a debt in a good state/bank

It has a par value, which is the initial investmentIt pays interests regularly

The capital functions as equity in a bad state/bank

It stops paying interestsIt converts to certain shares of common equity

When and why to convert

Convert when the capital is lowRecapitalize the bank to avoid distress/bankruptcy

Why are banks interested in CC

Substitute equity in regulatory capital requirementsRaise funds without earnings dilutionDeduct interest payments from taxable income

It has a par value, which is the initial investment

It pays interests regularly

It stops paying interests

It converts to certain shares of common equity

Convert when the capital is low

Recapitalize the bank to avoid distress/bankruptcy

Substitute equity in regulatory capital requirements

Raise funds without earnings dilutionDeduct interest payments from taxable income

Substitute equity in regulatory capital requirementsRaise funds without earnings dilution

Deduct interest payments from taxable income

Regulators’ objectives

Policy decisions after the financial crisis

Dodd-Frank Act: does CC enhance financial stability?Basel: allow banks to use CC as substitutes of equity?

Arguments for using CC to substitute equity

Overcome the reluctance of raising equity early

Avoid earning dilution in profitable banksLess costly for banks with debt overhung problem

Provides capital to absorb losses to avoid distress

Conversion should be mandatory and timelyRecapitalize the bank as going concern

Curtail the incentives of excessive risk-taking

Conversion must transfer value from equity to CCPunish managers for risking CC conversion

Dodd-Frank Act: does CC enhance financial stability?

Basel: allow banks to use CC as substitutes of equity?

Avoid earning dilution in profitable banks

Less costly for banks with debt overhung problem

Conversion should be mandatory and timely

Recapitalize the bank as going concern

Conversion must transfer value from equity to CC

Punish managers for risking CC conversion

Some contingent capitals issued so far

02/25/09, TARP (CAP or MCP)

Option for a bank to convert

11/05/09, Lloyds’s Enhanced Capital Notes

Accounting trigger: T1/RWA 5%

03/12/10, Rabobank’s Senior Contingent Notes

02/14/11, Credit Suisse’s Bu↵er Capital Notes

Dual triggers: E/RWA 7% or SNB decision

02/15/12 & 08/10/12, UBS Tier 2 Subordinated Notes

Dual triggers: CT1/RWA 5% or SNB decision

11/13/12 & 04/04/13, Barclays Bank Plc CC Notes

Accounting trigger: CT1/RWA 7%

01/18/13, KBC Contingent Capital Securities

02/25/09, TARP (CAP or MCP)

Option for a bank to convert

02/25/09, TARP (CAP or MCP)Option for a bank to convert

11/05/09, Lloyds’s Enhanced Capital NotesAccounting trigger: T1/RWA 5%

03/12/10, Rabobank’s Senior Contingent NotesAccounting trigger: T1/RWA 7%

02/14/11, Credit Suisse’s Bu↵er Capital NotesDual triggers: E/RWA 7% or SNB decision

02/15/12 & 08/10/12, UBS Tier 2 Subordinated NotesDual triggers: CT1/RWA 5% or SNB decision

11/13/12 & 04/04/13, Barclays Bank Plc CC NotesAccounting trigger: CT1/RWA 7%

01/18/13, KBC Contingent Capital SecuritiesAccounting trigger: CT1/RWA 7%

Advocates for market triggers

Concerns with bank option

reluctance to convert; hoping for the best or bailout

Concerns with accounting triggers

management manipulation, backward lookingrecent crisis: troubled banks had high accounting ratios

Concerns with regulatory triggers

regulator’s information & monitoring are limitedpolitical pressure: worry about false alarms; late action

Potential advantages of market triggers

force banks to convert (no management or TBTF mentality)aggregate market info (not limited, di�cult to manipulate)timely information and action (not obsolete, no delay)objective rules (market view, no politics)

management manipulation, backward looking

recent crisis: troubled banks had high accounting ratios

regulator’s information & monitoring are limited

political pressure: worry about false alarms; late action

force banks to convert (no management or TBTF mentality)

aggregate market info (not limited, di�cult to manipulate)timely information and action (not obsolete, no delay)objective rules (market view, no politics)

force banks to convert (no management or TBTF mentality)aggregate market info (not limited, di�cult to manipulate)

timely information and action (not obsolete, no delay)objective rules (market view, no politics)

force banks to convert (no management or TBTF mentality)aggregate market info (not limited, di�cult to manipulate)timely information and action (not obsolete, no delay)

objective rules (market view, no politics)

Proposals of market triggers

Triggers

Flannery (2009): convert if E/RWA x%Hart and Zingales (2010): convert if CDS spread � x bpsPennacchi (2011): convert if CC+E/deposit x%McDonald (2011): convert if ��E � x% and ��(Index) � y%

Where to place a market trigger?

If the bank is expected to experience large losses

the value of financial claims of a bank drops

A CC protects all claims that are senior to it, not junior

junior claims signal the stress more than senior claims

Triggers should be placed on claims junior to CC

the only claim junior to CC is common equity

Triggers

Flannery (2009): convert if E/RWA x%

Hart and Zingales (2010): convert if CDS spread � x bpsPennacchi (2011): convert if CC+E/deposit x%McDonald (2011): convert if ��E � x% and ��(Index) � y%

Triggers

Flannery (2009): convert if E/RWA x%Hart and Zingales (2010): convert if CDS spread � x bps

Pennacchi (2011): convert if CC+E/deposit x%McDonald (2011): convert if ��E � x% and ��(Index) � y%

Triggers

Flannery (2009): convert if E/RWA x%Hart and Zingales (2010): convert if CDS spread � x bpsPennacchi (2011): convert if CC+E/deposit x%

McDonald (2011): convert if ��E � x% and ��(Index) � y%

Triggers

A simplified term sheet

Issuer: systemically-important financial institutions (SIFI)

Security: preferred equity or debt convertible to common equity

Maturity: [10] years, bullet fixed rate

Trigger: market value of equity falls to [4%] of RWA or lower

trigger price: k = 4% ⇥ RWA / shares outstanding

Conversion: full principal converts to equity at price [P]

conversion ratio: m = principal/P

Transferability: no restriction

Regulatory treatment: may not qualify tier 1

but counts towards the supervisory bu↵er

Coupon: [?%] (need to price CC at its par value.)

Secondary market: fair price of CC for given coupon rate

Example: a simple firm with CC

Risky asset

can have value A (e.g., 106, 104, or 80)

Senior bond

par value: B = 90 about to mature now

Contingent capital

par value: C = 10 about to mature nowmandatory conversion trigger: K = 5conversion ratio: m =? (will try various numbers)

Common equity, n shares: (n = 1)

If not converted: S = (A� B � C )/nIf converted: S = (A� B)/(n +m)If bankrupt: S = 0

Risky asset

Senior bond

Contingent capital

Risky asset

Senior bond

Contingent capital

Risky asset

Senior bond

Contingent capital

Risky asset

Senior bond

Contingent capital

Risky asset

Senior bond

Contingent capital

Risky asset

Senior bond

Contingent capital

par value: C = 10 about to mature now

mandatory conversion trigger: K = 5conversion ratio: m =? (will try various numbers)

Risky asset

Senior bond

Contingent capital

par value: C = 10 about to mature nowmandatory conversion trigger: K = 5

conversion ratio: m =? (will try various numbers)

Risky asset

Senior bond

Contingent capital

Risky asset

Senior bond

Contingent capital

Risky asset

Senior bond

Contingent capital

If not converted: S = (A� B � C )/n

If converted: S = (A� B)/(n +m)If bankrupt: S = 0

Risky asset

Senior bond

Contingent capital

If not converted: S = (A� B � C )/nIf converted: S = (A� B)/(n +m)

If bankrupt: S = 0

Risky asset

Senior bond

Contingent capital

If conversion ratio is too high or too low

Suppose m = 3. When the asset value turns out to be 106

If investors believe CC will not convert

S = (106� 90� 10)/1 = 6 > K , C = par value = 10

If investors believe CC will convert

S = (106� 90)/(1 + 3) = 4 < K , C = 3⇥ 4 = 12

Two pairs of rational stock price and CC value

S = (104� 90� 10)/1 = 4 < K , C = 10

S = (104� 90)/(1 + 1) = 7 > K , C = 1⇥ 7 = 7

No pair of stock price and CC value is rational

S = (106� 90� 10)/1 = 6 > K , C = par value = 10

S = (106� 90)/(1 + 3) = 4 < K , C = 3⇥ 4 = 12

S = (104� 90� 10)/1 = 4 < K , C = 10

S = (104� 90)/(1 + 1) = 7 > K , C = 1⇥ 7 = 7

S = (106� 90� 10)/1 = 6 > K , C = par value = 10

S = (106� 90)/(1 + 3) = 4 < K , C = 3⇥ 4 = 12

S = (104� 90� 10)/1 = 4 < K , C = 10

S = (104� 90)/(1 + 1) = 7 > K , C = 1⇥ 7 = 7

S = (106� 90� 10)/1 = 6 > K , C = par value = 10

S = (106� 90)/(1 + 3) = 4 < K , C = 3⇥ 4 = 12

S = (104� 90� 10)/1 = 4 < K , C = 10

S = (104� 90)/(1 + 1) = 7 > K , C = 1⇥ 7 = 7

S = (106� 90� 10)/1 = 6 > K , C = par value = 10

S = (106� 90)/(1 + 3) = 4 < K , C = 3⇥ 4 = 12

S = (104� 90� 10)/1 = 4 < K , C = 10

S = (104� 90)/(1 + 1) = 7 > K , C = 1⇥ 7 = 7

S = (106� 90� 10)/1 = 6 > K , C = par value = 10

S = (106� 90)/(1 + 3) = 4 < K , C = 3⇥ 4 = 12

S = (104� 90� 10)/1 = 4 < K , C = 10

S = (104� 90)/(1 + 1) = 7 > K , C = 1⇥ 7 = 7

S = (106� 90� 10)/1 = 6 > K , C = par value = 10

S = (106� 90)/(1 + 3) = 4 < K , C = 3⇥ 4 = 12

S = (104� 90� 10)/1 = 4 < K , C = 10

S = (104� 90)/(1 + 1) = 7 > K , C = 1⇥ 7 = 7

S = (106� 90� 10)/1 = 6 > K , C = par value = 10

S = (106� 90)/(1 + 3) = 4 < K , C = 3⇥ 4 = 12

S = (104� 90� 10)/1 = 4 < K , C = 10

S = (104� 90)/(1 + 1) = 7 > K , C = 1⇥ 7 = 7

S = (106� 90� 10)/1 = 6 > K , C = par value = 10

S = (106� 90)/(1 + 3) = 4 < K , C = 3⇥ 4 = 12

S = (104� 90� 10)/1 = 4 < K , C = 10

S = (104� 90)/(1 + 1) = 7 > K , C = 1⇥ 7 = 7

S = (106� 90� 10)/1 = 6 > K , C = par value = 10

S = (106� 90)/(1 + 3) = 4 < K , C = 3⇥ 4 = 12

S = (104� 90� 10)/1 = 4 < K , C = 10

S = (104� 90)/(1 + 1) = 7 > K , C = 1⇥ 7 = 7

S = (106� 90� 10)/1 = 6 > K , C = par value = 10

S = (106� 90)/(1 + 3) = 4 < K , C = 3⇥ 4 = 12

S = (104� 90� 10)/1 = 4 < K , C = 10

S = (104� 90)/(1 + 1) = 7 > K , C = 1⇥ 7 = 7

S = (106� 90� 10)/1 = 6 > K , C = par value = 10

S = (106� 90)/(1 + 3) = 4 < K , C = 3⇥ 4 = 12

S = (104� 90� 10)/1 = 4 < K , C = 10

S = (104� 90)/(1 + 1) = 7 > K , C = 1⇥ 7 = 7

S = (106� 90� 10)/1 = 6 > K , C = par value = 10

S = (106� 90)/(1 + 3) = 4 < K , C = 3⇥ 4 = 12

S = (104� 90� 10)/1 = 4 < K , C = 10

S = (104� 90)/(1 + 1) = 7 > K , C = 1⇥ 7 = 7

If conversion ratio is just right: m = 2

In case asset value = 104

No conversion: S = (104� 90� 10)/1 = 4 < K

Conversion: S = (104� 90)/(1 + 2) = 4.66 < K

CC is expected to convert; stock price is 4.66

No conversion: S = (106� 90� 10)/1 = 6 > K

Conversion: S = (106� 90)/(1 + 2) = 5.33 > K

CC is expected not to convert; stock price is 6

m = 2 guarantees a unique equilibrium

no ambiguity about conversion for all Amarket settles to a unique equilibrium

Only m = 2 guarantees a unique equilibrium

m = 2 = C/(K/n) = 10/(5/1) = 2Otherwise, payo↵ function is not well-defined or measurable

No conversion: S = (104� 90� 10)/1 = 4 < K

Conversion: S = (104� 90)/(1 + 2) = 4.66 < K

No conversion: S = (106� 90� 10)/1 = 6 > K

Conversion: S = (106� 90)/(1 + 2) = 5.33 > K

No conversion: S = (104� 90� 10)/1 = 4 < K

Conversion: S = (104� 90)/(1 + 2) = 4.66 < K

No conversion: S = (106� 90� 10)/1 = 6 > K

Conversion: S = (106� 90)/(1 + 2) = 5.33 > K

No conversion: S = (104� 90� 10)/1 = 4 < K

Conversion: S = (104� 90)/(1 + 2) = 4.66 < K

No conversion: S = (106� 90� 10)/1 = 6 > K

Conversion: S = (106� 90)/(1 + 2) = 5.33 > K

No conversion: S = (104� 90� 10)/1 = 4 < K

Conversion: S = (104� 90)/(1 + 2) = 4.66 < K

No conversion: S = (106� 90� 10)/1 = 6 > K

Conversion: S = (106� 90)/(1 + 2) = 5.33 > K

No conversion: S = (104� 90� 10)/1 = 4 < K

Conversion: S = (104� 90)/(1 + 2) = 4.66 < K

No conversion: S = (106� 90� 10)/1 = 6 > K

Conversion: S = (106� 90)/(1 + 2) = 5.33 > K

No conversion: S = (104� 90� 10)/1 = 4 < K

Conversion: S = (104� 90)/(1 + 2) = 4.66 < K

No conversion: S = (106� 90� 10)/1 = 6 > K

Conversion: S = (106� 90)/(1 + 2) = 5.33 > K

No conversion: S = (104� 90� 10)/1 = 4 < K

Conversion: S = (104� 90)/(1 + 2) = 4.66 < K

No conversion: S = (106� 90� 10)/1 = 6 > K

Conversion: S = (106� 90)/(1 + 2) = 5.33 > K

No conversion: S = (104� 90� 10)/1 = 4 < K

Conversion: S = (104� 90)/(1 + 2) = 4.66 < K

No conversion: S = (106� 90� 10)/1 = 6 > K

Conversion: S = (106� 90)/(1 + 2) = 5.33 > K

No conversion: S = (104� 90� 10)/1 = 4 < K

Conversion: S = (104� 90)/(1 + 2) = 4.66 < K

No conversion: S = (106� 90� 10)/1 = 6 > K

Conversion: S = (106� 90)/(1 + 2) = 5.33 > K

No conversion: S = (104� 90� 10)/1 = 4 < K

Conversion: S = (104� 90)/(1 + 2) = 4.66 < K

No conversion: S = (106� 90� 10)/1 = 6 > K

Conversion: S = (106� 90)/(1 + 2) = 5.33 > K

no ambiguity about conversion for all A

market settles to a unique equilibrium

No conversion: S = (104� 90� 10)/1 = 4 < K

Conversion: S = (104� 90)/(1 + 2) = 4.66 < K

No conversion: S = (106� 90� 10)/1 = 6 > K

Conversion: S = (106� 90)/(1 + 2) = 5.33 > K

No conversion: S = (104� 90� 10)/1 = 4 < K

Conversion: S = (104� 90)/(1 + 2) = 4.66 < K

No conversion: S = (106� 90� 10)/1 = 6 > K

Conversion: S = (106� 90)/(1 + 2) = 5.33 > K

No conversion: S = (104� 90� 10)/1 = 4 < K

Conversion: S = (104� 90)/(1 + 2) = 4.66 < K

No conversion: S = (106� 90� 10)/1 = 6 > K

Conversion: S = (106� 90)/(1 + 2) = 5.33 > K

m = 2 = C/(K/n) = 10/(5/1) = 2

Otherwise, payo↵ function is not well-defined or measurable

No conversion: S = (104� 90� 10)/1 = 4 < K

Conversion: S = (104� 90)/(1 + 2) = 4.66 < K

No conversion: S = (106� 90� 10)/1 = 6 > K

Conversion: S = (106� 90)/(1 + 2) = 5.33 > K

Pricing before maturity — asset and bond

• m = 2 guarantees a unique equilibrium at maturity

• but it does not guarantee this before maturity

asset t100.00 ⇠⇠⇠⇠⇠⇠⇠⇠⇠⇠⇠t120.00 prob = 0.25

t100.00 prob = 0.50XXXXXXXXXXXt 80.00 prob = 0.25

bond r⇠⇠⇠⇠⇠⇠⇠⇠⇠⇠⇠t 90.00 no default

t 90.00 no defaultXXXXXXXXXXXt 80.00 default

asset t100.00 ⇠⇠⇠⇠⇠⇠⇠⇠⇠⇠⇠t120.00 prob = 0.25

asset t100.00

⇠⇠⇠⇠⇠⇠⇠⇠⇠⇠⇠t120.00 prob = 0.25

asset t100.00 ⇠⇠⇠⇠⇠⇠⇠⇠⇠⇠⇠t120.00 prob = 0.25

t100.00 prob = 0.50

XXXXXXXXXXXt 80.00 prob = 0.25

asset t100.00 ⇠⇠⇠⇠⇠⇠⇠⇠⇠⇠⇠t120.00 prob = 0.25

bond r

⇠⇠⇠⇠⇠⇠⇠⇠⇠⇠⇠t 90.00 no default

asset t100.00 ⇠⇠⇠⇠⇠⇠⇠⇠⇠⇠⇠t120.00 prob = 0.25

t 90.00 no default

XXXXXXXXXXXt 80.00 default

asset t100.00 ⇠⇠⇠⇠⇠⇠⇠⇠⇠⇠⇠t120.00 prob = 0.25

Pricing before maturity — CC and equity

Equilibrium 1: late conversion

tCoCo:

tEquity:

⇠⇠⇠⇠⇠⇠⇠⇠⇠⇠⇠t10.00 no conversion

⇠⇠⇠⇠⇠⇠⇠⇠⇠⇠⇠t20.00 = (120� 90� 10)/1

t 6.67 convert to 2 shares

t 3.33 = (100� 90)/(1 + 2)

XXXXXXXXXXXt 0.00 firm defaults

C = 5.83

S = 6.67

Equilibrium 2: early conversiontCoCo: tEquity:

= 2(100� 87.50)/(1 + 2)

= 1(100� 87.50)/(1 + 2)C = 8.33

S = 4.17

Pricing before maturity — CC and equityEquilibrium 1: late conversion

tCoCo:

tEquity:

⇠⇠⇠⇠⇠⇠⇠⇠⇠⇠⇠t20.00 = (120� 90� 10)/1

t 3.33 = (100� 90)/(1 + 2)

C = 5.83

S = 6.67

= 2(100� 87.50)/(1 + 2)

= 1(100� 87.50)/(1 + 2)C = 8.33

S = 4.17

tCoCo:

tEquity:

⇠⇠⇠⇠⇠⇠⇠⇠⇠⇠⇠t20.00 = (120� 90� 10)/1

t 3.33 = (100� 90)/(1 + 2)

C = 5.83

S = 6.67

= 2(100� 87.50)/(1 + 2)

= 1(100� 87.50)/(1 + 2)C = 8.33

S = 4.17

tCoCo:

tEquity:

⇠⇠⇠⇠⇠⇠⇠⇠⇠⇠⇠t20.00 = (120� 90� 10)/1

t 3.33 = (100� 90)/(1 + 2)

C = 5.83

S = 6.67

= 2(100� 87.50)/(1 + 2)

= 1(100� 87.50)/(1 + 2)C = 8.33

S = 4.17

tCoCo:

tEquity:

⇠⇠⇠⇠⇠⇠⇠⇠⇠⇠⇠t20.00 = (120� 90� 10)/1

t 3.33 = (100� 90)/(1 + 2)

C = 5.83

S = 6.67

= 2(100� 87.50)/(1 + 2)

= 1(100� 87.50)/(1 + 2)C = 8.33

S = 4.17

tCoCo:

tEquity:

⇠⇠⇠⇠⇠⇠⇠⇠⇠⇠⇠t20.00 = (120� 90� 10)/1

t 3.33 = (100� 90)/(1 + 2)

C = 5.83

S = 6.67

= 2(100� 87.50)/(1 + 2)

= 1(100� 87.50)/(1 + 2)C = 8.33

S = 4.17

tCoCo:

tEquity:

⇠⇠⇠⇠⇠⇠⇠⇠⇠⇠⇠t20.00 = (120� 90� 10)/1

t 3.33 = (100� 90)/(1 + 2)

C = 5.83

S = 6.67

= 2(100� 87.50)/(1 + 2)

= 1(100� 87.50)/(1 + 2)C = 8.33

S = 4.17

tCoCo:

tEquity:

⇠⇠⇠⇠⇠⇠⇠⇠⇠⇠⇠t20.00 = (120� 90� 10)/1

t 3.33 = (100� 90)/(1 + 2)

C = 5.83

S = 6.67

Equilibrium 2: early conversion

tCoCo: tEquity:

= 2(100� 87.50)/(1 + 2)

= 1(100� 87.50)/(1 + 2)C = 8.33

S = 4.17

tCoCo:

tEquity:

⇠⇠⇠⇠⇠⇠⇠⇠⇠⇠⇠t20.00 = (120� 90� 10)/1

t 3.33 = (100� 90)/(1 + 2)

C = 5.83

S = 6.67

= 2(100� 87.50)/(1 + 2)

= 1(100� 87.50)/(1 + 2)C = 8.33

S = 4.17

tCoCo:

tEquity:

⇠⇠⇠⇠⇠⇠⇠⇠⇠⇠⇠t20.00 = (120� 90� 10)/1

t 3.33 = (100� 90)/(1 + 2)

C = 5.83

S = 6.67

= 2(100� 87.50)/(1 + 2)

= 1(100� 87.50)/(1 + 2)

C = 8.33

S = 4.17

tCoCo:

tEquity:

⇠⇠⇠⇠⇠⇠⇠⇠⇠⇠⇠t20.00 = (120� 90� 10)/1

t 3.33 = (100� 90)/(1 + 2)

C = 5.83

S = 6.67

= 2(100� 87.50)/(1 + 2)

= 1(100� 87.50)/(1 + 2)C = 8.33

S = 4.17

An example in dynamic continuous-time model

Asset: dAt = r Atdt + �Atdzt

Risk: zt = Brownian

current asset value A

100asset volatility � 4%

risk-free rate r 3%shares outstanding n 1

par value of bond B 87coupon rate of bond b 3.34%maturity of bond T 5 yearsbankruptcy cost ! 10%

par value of CC C 5coupon rate of CC c 0%maturity of CC T 5 yeartrigger on equity K 1conversion ratio m 5trigger verification ⇤ daily

firm value F

98.35bond value B

88.03stock price S

[5.86, 6.46]CC value C

[3.86, 4.46]

Risk: zt = Brownian

firm value F

98.35bond value B

88.03stock price S

[5.86, 6.46]CC value C

[3.86, 4.46]

Risk: zt = Brownian

firm value F

98.35bond value B

88.03stock price S

[5.86, 6.46]CC value C

[3.86, 4.46]

Risk: zt = Brownian

firm value F

98.35bond value B

88.03stock price S

[5.86, 6.46]CC value C

[3.86, 4.46]

Risk: zt = Brownian

firm value F

98.35bond value B

88.03stock price S

[5.86, 6.46]CC value C

[3.86, 4.46]

Risk: zt = Brownian

firm value F

98.35bond value B

88.03stock price S

[5.86, 6.46]CC value C

[3.86, 4.46]

Risk: zt = Brownian

firm value F

98.35bond value B

88.03stock price S

[5.86, 6.46]CC value C

[3.86, 4.46]

Risk: zt = Brownian

firm value F

98.35bond value B

88.03stock price S

[5.86, 6.46]CC value C

[3.86, 4.46]

Risk: zt = Brownian

firm value F

98.35bond value B

88.03stock price S

[5.86, 6.46]CC value C

[3.86, 4.46]

Risk: zt = Brownian

firm value F

98.35bond value B

88.03stock price S

[5.86, 6.46]CC value C

[3.86, 4.46]

An example in jump di↵usion process

Asset: dAt = (r � �E[y � 1])Atdt + �Atdzt + (y � 1)Atdq

Risk: zt = Brownian, qt = Poisson(�), ln(y) ⇠ N(µy , �2

100asset volatility � 4%arrival rate of jumps � 4mean of log-jump size µy �1%volatility of jump size �y 3%risk-free rate r 3%shares outstanding n 1

firm value F

94.74bond value B

87.00stock price S

[3.84, 5.44]CC value C

[2.30, 3.90]

firm value F

94.74bond value B

87.00stock price S

[3.84, 5.44]CC value C

[2.30, 3.90]

firm value F

94.74bond value B

87.00stock price S

[3.84, 5.44]CC value C

[2.30, 3.90]

firm value F

94.74bond value B

87.00stock price S

[3.84, 5.44]CC value C

[2.30, 3.90]

firm value F

94.74bond value B

87.00stock price S

[3.84, 5.44]CC value C

[2.30, 3.90]

firm value F

94.74bond value B

87.00stock price S

[3.84, 5.44]CC value C

[2.30, 3.90]

firm value F

94.74bond value B

87.00stock price S

[3.84, 5.44]CC value C

[2.30, 3.90]

firm value F

94.74bond value B

87.00stock price S

[3.84, 5.44]CC value C

[2.30, 3.90]

firm value F

94.74bond value B

87.00stock price S

[3.84, 5.44]CC value C

[2.30, 3.90]

firm value F

94.74bond value B

87.00stock price S

[3.84, 5.44]CC value C

[2.30, 3.90]

If conversion transfers value from equity to CC

0 20 40 60 80 100 120 140 160 180 200

Equity value if not converted

Number of Weeks

Trigger = 40

Transfer 10 out from equity Equity value if converted

Value Value

If conversion transfers value from CC to equity

0 20 40 60 80 100 120 140 160 180 200

Equity value if not converted

Number of Weeks

Trigger = 40

Transfer 10 into equity.

Equity value if converted

A sudden large loss causes equity value to jump below trigger.

Necessary condition for a unique equilibrium

Theorem 1

CC contract specifies trigger Kt and conversion ratio mt

CC contract specifies the set of trigger verification time ⇤If a unique pair of dynamic rational expectations equilibrium ofstock price and CC value (St ,Ct) exists, then

mt = Ct/(Kt/n) for all t 2 ⇤

Underlying assumptions

asset value is risky (di↵usion process)sudden large loss is possible (jump risk)bankruptcy is costly (loss of asset value at default)

Implications

Setting mt to have unique equilibrium requires observing Ct

For constant m and K , it requires Ct = mK/nCC conversion cannot be punitive: m⌧S⌧ m⌧K⌧/n = C⌧

Theorem 1

Implications

Theorem 1

Implications

Theorem 1

CC contract specifies the set of trigger verification time ⇤

If a unique pair of dynamic rational expectations equilibrium ofstock price and CC value (St ,Ct) exists, then

Implications

Theorem 1

Implications

Theorem 1

Implications

Theorem 1

Implications

Theorem 1

asset value is risky (di↵usion process)

sudden large loss is possible (jump risk)bankruptcy is costly (loss of asset value at default)

Implications

Theorem 1

asset value is risky (di↵usion process)sudden large loss is possible (jump risk)

bankruptcy is costly (loss of asset value at default)

Implications

Theorem 1

Implications

Theorem 1

Implications

Theorem 1

Implications

Theorem 1

Implications

For constant m and K , it requires Ct = mK/n

CC conversion cannot be punitive: m⌧S⌧ m⌧K⌧/n = C⌧

Theorem 1

Implications

Other pricing models

Albul, Je↵ee & Tchistyi (’10), Tsyplakov & Himmelberg (’12)

firm value is exogenousplace trigger on firm value, not equity value

Pennacchi (’11)

firm value is exogenousshort-term deposits are always priced at par and exogenousplace trigger on (asset � deposits) / deposits

McDonald (’11)

market index and firm equity value are exogenoususe double riggers on both market index and equity value

Glasserman & Nouri (’12)

firm value is exogenous: geometric brownian motion“book equity value” is non-stochasticplace trigger on “book equity value” / firm value

Pennacchi (’11)

McDonald (’11)

firm value is exogenous

place trigger on firm value, not equity value

Pennacchi (’11)

McDonald (’11)

Pennacchi (’11)

McDonald (’11)

Pennacchi (’11)

McDonald (’11)

Pennacchi (’11)

firm value is exogenous

short-term deposits are always priced at par and exogenousplace trigger on (asset � deposits) / deposits

McDonald (’11)

Pennacchi (’11)

firm value is exogenousshort-term deposits are always priced at par and exogenous

place trigger on (asset � deposits) / deposits

McDonald (’11)

Pennacchi (’11)

McDonald (’11)

Pennacchi (’11)

McDonald (’11)

Pennacchi (’11)

McDonald (’11)

market index and firm equity value are exogenous

use double riggers on both market index and equity value

Pennacchi (’11)

McDonald (’11)

Pennacchi (’11)

McDonald (’11)

Pennacchi (’11)

McDonald (’11)

firm value is exogenous: geometric brownian motion

“book equity value” is non-stochasticplace trigger on “book equity value” / firm value

Pennacchi (’11)

McDonald (’11)

firm value is exogenous: geometric brownian motion“book equity value” is non-stochastic

place trigger on “book equity value” / firm value

Pennacchi (’11)

McDonald (’11)

The problems without a unique equilibrium

Economic theory

A unique equilibrium is often associated with

a stable market pricean e�cient asset allocation

Lack of unique equilibrium leaves price to uncertain forces

unknown how investors’ formation of expectationunknown about asset allocation e�ciency

Price manipulation and market instability

Equity holders prefer the equilibrium that avoids conversionCC holders prefer the equilibrium that forces conversion

Lab experiment [Davis, Prescott & Korenok (2011)]

stock price is highly uncertainassets are allocated ine�cientlyfrequent conversion errors

Economic theory

a stable market price

an e�cient asset allocation

Economic theory

unknown how investors’ formation of expectation

unknown about asset allocation e�ciency

Economic theory

Equity holders prefer the equilibrium that avoids conversion

CC holders prefer the equilibrium that forces conversion

Economic theory

stock price is highly uncertain

assets are allocated ine�cientlyfrequent conversion errors

Economic theory

stock price is highly uncertainassets are allocated ine�ciently

frequent conversion errors

Economic theory

The regulators’ concerns

Fed Governor Daniel Tarullo

It is unclear that CC for a going concern can be “structured soas to convert in a timely, reliable fashion.”

Financial Stability Oversight Council (FSOC)

“The loss absorption potential of a company’s capital structurecould be lower, because uncertainty may exist prior toconversion about whether instrument would actually convert tocommon equity in time to e↵ectively absorb losses.”

Death spiral

The negative e↵ect on price as the speculators create excessivepressure on the issuer’s stock price toward trigger or zeroFSOC warned the Congress that “market-based triggers canexacerbate the problem of death spiral.”

Death spiral

The negative e↵ect on price as the speculators create excessivepressure on the issuer’s stock price toward trigger or zero

FSOC warned the Congress that “market-based triggers canexacerbate the problem of death spiral.”

Death spiral

Equilibrium in alternative market conditions

Di�culty in practical implementation

If there is no jump or bankruptcy costIf CC pays instantaneous risk-free rate until conversionThen Ct = mK/n = C is a unique equilibrium

Issue equity to avoid conversion?

Design CC to be always punitive (how?)If conversion is punitive, there can still be two equilibria

an equilibrium without conversion or issuancean equilibrium with issuance to avoid conversion

Practical CC contracts exclude this design

Financial distress cost makes the issue even worse

still have multiple equilibria in CC and equity valueseven multiple equilibria in firm and senior debt values

If there is no jump or bankruptcy cost

If CC pays instantaneous risk-free rate until conversionThen Ct = mK/n = C is a unique equilibrium

If there is no jump or bankruptcy costIf CC pays instantaneous risk-free rate until conversion

Then Ct = mK/n = C is a unique equilibrium

Design CC to be always punitive (how?)

If conversion is punitive, there can still be two equilibria

an equilibrium without conversion or issuance

an equilibrium with issuance to avoid conversion

still have multiple equilibria in CC and equity values

even multiple equilibria in firm and senior debt values

Regulatory decisions around the world

No CC in basic requirement (7%) or SIFI surcharge (0-2.5%)Regional regulators may allow CC for additional requirements

Trigger: � 7% for tier 1, plus regulatory triggerMaturity: perpetual for tier 1, � 5 years for tier 2Share issuance: must be capped

Switzerland’s FINMA

Requires SIFI to maintain at least 19% capital ratio10% equity, 3% “high-trigger” CC, 6% “low-trigger” CC

European Commission’s directives

4.5% equity, 1.5% “additional tier-1” CC, 2% tier 2 CCplus up to 7.5% surcharges, all common equity (no CC)

No CC in basic requirement (7%) or SIFI surcharge (0-2.5%)

Regional regulators may allow CC for additional requirements

Trigger: � 7% for tier 1, plus regulatory trigger

Maturity: perpetual for tier 1, � 5 years for tier 2Share issuance: must be capped

Trigger: � 7% for tier 1, plus regulatory triggerMaturity: perpetual for tier 1, � 5 years for tier 2

Share issuance: must be capped

Requires SIFI to maintain at least 19% capital ratio

10% equity, 3% “high-trigger” CC, 6% “low-trigger” CC

4.5% equity, 1.5% “additional tier-1” CC, 2% tier 2 CC

plus up to 7.5% surcharges, all common equity (no CC)

U.K. Independent Commission on Banking

Does not endorse CC as regulatory toolEquity is the only form of loss-absorbing capacity that worksConcerned with the destabilizing e↵ects of CC

Canada (OFSI)

Does not endorse CC with early conversion featuresSupport convertible structured for resolution of failing banks

China: 11.5% equity and liquid capital, no CC

United States:

June ’12: Fed/OCC/FDIC proposed rules to implement Basel IIIJuly ’12: FSOC reported to the Congress

to discuss “a range of potential issues” of CCto recommend that contingent capital“remain an area for continued private sector innovation”

Canada (OFSI)

United States:

Does not endorse CC as regulatory tool

Equity is the only form of loss-absorbing capacity that worksConcerned with the destabilizing e↵ects of CC

Canada (OFSI)

United States:

Does not endorse CC as regulatory toolEquity is the only form of loss-absorbing capacity that works

Concerned with the destabilizing e↵ects of CC

Canada (OFSI)

United States:

Canada (OFSI)

United States:

Canada (OFSI)

United States:

Canada (OFSI)

Does not endorse CC with early conversion features

Support convertible structured for resolution of failing banks

United States:

Canada (OFSI)

United States:

Canada (OFSI)

United States:

Canada (OFSI)

United States:

Canada (OFSI)

United States:

June ’12: Fed/OCC/FDIC proposed rules to implement Basel III

July ’12: FSOC reported to the Congress

Canada (OFSI)

United States:

Canada (OFSI)

United States:

to discuss “a range of potential issues” of CC

to recommend that contingent capital“remain an area for continued private sector innovation”

Canada (OFSI)

United States:

On the Design of Contingent Capital · 2018-04-03 · Basic idea of contingent capital (CC) The...

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