M acroModel with Financial Sector - PowerPoint Presentation

Slide1

MacroModel with Financial Sector with Yuliy Sannikov Markus K. Brunnermeier

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1

CoVaR

with Tobias Adrian

Slide2

Traditional BankingRole of banks2

Originate & distributeSecuritization

Pooling

Tranching

Insuring

(CDS)

Dual purpose

Tradable assetCollateral feeds repo market for levering

Channel fundsLong-run repaymentProspect of selling offMaturity transformationRetail fundingWholesale funding (money market funds, repo partners, conduits, SIVs, …)Info-insensitive securitiesDemand depositsABCP, MTN, overnight repos, securities lending

Demand

deposits

A

L

Loans

(long-term)

Equity

ABCP/MTN

AAA

Loans

(long-term)

Equity

BBB

…

SIV/Conduit

s

Shadow banking system

Slide3

Changing banking landscapeTraditional BankingRole of banks3

Originate & distributeSecuritization

Pooling

Tranching

Insuring

(CDS)

Dual purpose

Tradable assetCollateral feeds repo market for levering

Channel fundsLong-run repaymentProspect of selling offMaturity transformationRetail fundingWholesale funding (money market funds, repo partners, conduits, SIVs, …)Info-insensitive securitiesDemand depositsABCP, MTN, overnight repos, securities lending

Demand

deposits

A

L

Loans

(long-term)

Equity

ABCP/MTN

AAA

Loans

(long-term)

Equity

BBB

…

SIV/Conduit

Slide4

Two questionsWhy is reaction so sharp?Liquidity spirals(non-linear dynamics due to adverse feedback loop)Real economic effectsmacro model with financial sector (w/ Sannikov)Too much leverage and maturity mismatch?Identify and measure externalities(risk spillovers rather risk of a bank in isolation)CoVaR (w/ Adrian)

4ABS issuance

Source: JPMorgan

Slide5

OverviewTheory (with Sannikov)Spirals: Non-linear adverse feedback loops + volatility effectsExternalitiesImplementation (with Adrian)CoVaR: measuring systemic risk contribution/externalitiesOne method: Quantile regressionsAddressing procyclicalites due to spirals5

Slide6

Brunnermeier-Sannikov (new)

Entrepreneurs

Needs financing

Start projects (trees with

payoff

a

t

K

t)dat/at=gdt +σdZt capital depreciatesinvestment6 Financial Experts

Monitoring (growth of at)Securitizes “trees”

to expand investment

Households

Provide financing

D

E

B

T

EQU

ITY

A

L

outside

inside

Optimal

dynamic

contract

direct financing

a

t

grows slower

Slide7

Role of financial experts in the economy: Entrepreneurs

7

Financial Experts

Households

Securitize investments

and sell products to

households

Direct financing

Provide funding moreefficiently than direct lending Both entrepreneurs and households benefit from the financial sector

Slide8

Model setup - overview

Entrepreneurs

Needs financing

Start projects (trees with

payoff

a

t

K

t)dat/at=gdt +σdZt capital depreciatesinvestment8 Financial Experts

Monitoring (growth of at)Securitizes “trees”

to expand investment

Households

Provide financing

D

E

B

T

EQU

ITY

A

L

outside

inside

Optimal

dynamic

contract

p

σ

p

Slide9

Model setup - overview

Entrepreneurs

Needs financing

Start projects (trees with

payoff

a

t

K

t)dat/at=gdt +σdZt capital depreciatesinvestment9 Financial Experts

Monitoring (growth of at)Securitizes “trees”

to expand investment

Households

Provide financing

D

E

B

T

EQU

ITY

A

L

outside

inside

Optimal

dynamic

contract

direct financing

a

t

grows slower

Slide10

Model setup: production of output and capitalProduction of output (numeraire) (apples): Yt = at Kt, where dat = a

tdZt Note everything will be scale invariant w.r.t. YtProduction of capital Kt

(trees):

dKt = (Φ

(I

t

/

Y

t

) - ) Kt dt,Investment-ratio It/Yt depends on ytνt price of capital (value of asset/tree)i.e. νt = price-earnings ratio dνt= tνdt+tνdZt(price of a tree in terms of apples divided by yt) max i {νtatKt

Φ(it/yt) – it} supply of capital: κ(νt)Kt 10

Slide11

Financing of capitalAll agentsrisk neutral (for now) common discount rate of Direct financing through households (fraction 1-ψt)

Growth of a is zeroνt ≥ 1/(+)Break even for HH

1-(+

)νt +



t

ν

+



tν = 0 (HH)Indirect financing through financial experts (fraction ψ)Growth of a is g at cost b per y dat = gatdt+atdZt Reduced form for better resource allocation(monitor, service mortgage, channel continuation funding)νt ≤ (1-b)/(+-g)

11Capital appreciationearningsfinancing cost

Slide12

Financing friction – optimal contractingExpert’s incentive problemeffort choice, yt are non-contractable, but asset value νtyt

is Incentive (“skin in the game”) constraint: tgνt - b  0

 

t = b/(gνt

)

Evolution of experts balance sheet

Asset side –

long maturity

d(

νtyt) = yt (tν+(g - )νt+ tν)dt + yt (νt + tν)dZtLiability sideDebt – overnight maturity

Outside equity: 1-tInside equitydnt = nt + yt [(1-b-(+-g)νt + 

tν+ tν

)dt + 

t (νt

+tν) dZ

t]

12

Slide13

Competitive equilibriumState variable: t = Nt/Yt dt = …. (from Ito)Nt is aggregate wealth (net-worth) of financial expertsYt is aggregate output (scale-invariant)

Solve in terms ofP/E ratio: νt = ν(t)Expert i’s

value function: ftn

t = f(

t

)

n

t

Fraction of indirect investment:

ψ(t) ≤ 1Expert i’s Bellman equationntft dt = maxy E[d(ntft)] = maxy {(nt+y[1-b-(+-g)νt+

tν +tν]) ft+nt μtf+tfy

t(ν

t+tν

)} dt FOC: [1-b-(

+-g)ν

t+ tν +

tν] + t

f 

t (

νt + t

ν) = 0 (FS)Household

FOC: 1-(+)ν

t + tν+

tν =(<) 0 (HH)

13

precautionary motive

=

μ

t

n

=

σ

t

n

Slide14

Competitive equilibriumState variable: t = Nt/Yt dt = …. (from Ito)Nt is aggregate wealth (net-worth) of financial expertsYt is aggregate output (scale-invariant)

Solve in terms ofP/E ratio: νt = ν(t)Expert i’s

value function: ftn

t= f(t

)

n

t

Fraction of indirect investment:

ψ

≤ 1Expert i’s Bellman equationntft dt = maxy E[d(ntft)] = maxy {(nt+y[1-b-(+-g)νt+tν +

tν]) ft+nt μtf+tfyt(ν

t+t

ν)} dt

FOC: [1-b-(+-g)νt

+ tν + 

tν] +

tf

t (

νt +

tν) = 0 (FS

)Household FOC: 1-(+

)νt + t

ν+ tν = 0 (HH

)

14

precautionary motive

=

μ

t

n

=

σ

t

n

1

2

3

Slide15

Competitive equilibriumState variable: t = Nt/Yt dt = …. (from Ito)Nt is aggregate wealth (net-worth) of financial expertsYt is aggregate output (scale-invariant)

Solve in terms ofP/E ratio: νt = ν(t)Expert i’s

value function: ftn

t= f(t

)

n

t

Fraction of indirect investment:

ψ

≤ 1Expert i’s Bellman equationntft dt = maxy E[d(ntft)] = maxy {(nt+y[1-b-(+-g)νt+tν +

tν]) ft+nt μtf+tfyt(ν

t+t

ν)} dt

FOC: [1-b-(+-g)νt

+ tν + 

tν] +

tf

t (

νt +

tν) = 0 (FS

)Household FOC: 1-(+

)νt + t

ν+ tν = 0 (HH

)

15

precautionary motive

=

μ

t

n

=

σ

t

n

1

2

3

1

2

3

Slide16

Function of experts’ networth/GDP16

Marginal value of a $

Leverage

P/E ratio

GDP growth

Slide17

Results 1: Non-linear dynamics - spiralsFact 1: financial sectorincreases growth but may also increase volatilityFact 2: Loss spiralprice is more volatile, as experts approach regime when they fire-sale assetsFact 3: “Outside-equity spiral” t = b/(gνt)for low νt , fraction of outside equity shrinks (difficult to raise because agency problem gets worse)Fact 4: Leverage spiralLeverage: [v(

t)ψt – t]/[v(t)ψt

]Internal: Own risk management for ψt

<1External: Margin/haircuts

spiral (see Brunnermeier-Pedersen, 09)

17

Slide18

Introducing margin/haircut constraintLevel of debt is limited byIncentive constraint (in aggregate)+ haircut/margin constraint Spirit: asset can only be sold with a delayHaircut is multiple of price volatility h( νt + tν)/ ν

t Main changesprice-earning ratios go down price volatility goes up as long as haircuts don't binding (especially near the point where haircuts start binding)goes down when haircuts bindExperts value function rises (externalities – later)Internal risk management is enforced

Fear of haircut constraint becomes binding

18

Slide19

Vol. and leverage with haircut constraints19

Slide20

Graphs with haircut constraints (red)20

Slide21

Graphs with haircut constraints (red)21

Slide22

Graphs with haircut constraints (red)22

Slide23

Results 2: Externalities – welfare“Too much” leverage/maturity-mismatch due to externalities?Financial regulation should focus on externalitiesWithin the financial sectorBetween financial sector and real economy (entrepreneurs)Two forms of inefficiencies:Inefficient (pecuniary) externalities– regulatory correction for an instantDynamic externality - commitment problem within an institution23

Slide24

Result 2: Externalities – welfareFocus within financial sectorEffect of one expert’s choice of y on value function of everybody: f() (1-b+( + -g)

νt+tν+

tν) + f’(

)

σ

t

η



t(pt+tν)- f’()2 g + (f’() + f()) ψt (dtν/dψt

+  dtν/dψt) + f’() [1-b+(+-g)

νt+

tν+t

ν] +

[f’’()

+ f’()]

t

t(ν

t + 

tp) + [f’’()

 + 2f’(

)]t

ψtt

dtν

/dψt

.

24

Slide25

Results 2: Externalities – welfareFocus within financial sectorEffect of one expert’s choice of y on value function of everybody: f() (1-b+( + -g

)νt+tν+

tν) + f’(

)

σ

t

η



t(pt+tν)- f’()2 g + (f’() + f()) ψt (dtν/dψt

+  dtν/dψt) + f’() [1-b+(+-g

)νt+

tν+

tν] +

[f’’()

 + f’()]

t

t(

νt +

tp) + [f’’(

) + 2f’(

)]t

ψt

t dtν

/dψt

.

25

Affects the drift of

η

, and impacts other experts

Affects the volatility of

η

, and impacts other experts

Affects economic growth, and impacts other experts

Zero in individual expert’s FOC

Slide26

On externalities – welfare analysisFocus within financial sectorEffect of one expert’s choice of y on value function of everybody: f() (1-b+( + -g)

νt+tν+

tν) + f’(

)

σ

t

η



t(pt+tν)- f’()2 g + (f’() + f()) ψt (dtν/dψt

+  dtν/dψt) + f’() [1-b+(+-g

)νt+

tν+

tν] +

[f’’()

 + f’(

)]t

t(

νt +

tp) + [f’’(

) + 2f’(

)]t

ψt

t dt

ν /dψt

.

26

(+) economic growth good for experts

Zero in individual expert’s FOC

Effect on value of other expert’s assets, through prices

(-) profit causes

η

to grow, which hurts other experts

(+) effect on expected value of cash

(-) effect on expected value of assets

Fire-sale externality

Slide27

Externalities27

Slide28

Related LiteratureEnd borrowers’ financing frictionsBernanke-Gertler-(Gilchrist), …, MishkinKiyotaki-Moore Financial sector’s frictions – liquidity spiralsBrunnermeier-PedersenDiamond-Dybvig, Allen-Gale, …He-KrishnamurthyDynamic contractingDeMarzo-Fishman-Sannikov, …

28

Slide29

Differences to Bernanke-Gertler-GilchristBGG“small” aggregate shocks around steady stateidiosyncratic shocks are essentialDefault and associated costly state verification is more likelyAsset prices are driven by default (verification cost) due to idiosyncratic riskExpert’s rent is always zero (?)No incentive to keep “dry powder” (liquidity) … (No Bellman equ.)

Countercyclical leverageEntrepreneur take on same position after drop in networthLeverage increases after drop in net-worthDebt vs. Equity No fire-sale externality

29

BruSan

Focus on (large) aggregate shocks

(idiosyncratic shocks not essential)

(no restriction to steady state)

Asset

price drops

due to fire salesExpert’s rent depends on state

tIncentive to keep “dry powder” (liquidity) …Procyclical leverage

Experts reduce position after drop in networth

Liquidity spirals

Securitization

(

debt, inside +

outside equity)

Fire-sale externality

(rationale for regulation)

Slide30

Differences to Kiyotaki-MooreKM – (Kiyotaki version)Zero-prob. temporary shockPersistent (dynamic loss spiral)Amplified through collateral valueNon- vs. productive (leveraged) sectorDual role of durable assetProductionCollateral

Exogenous contractOne period contractDebt is limited by collateral valueDurable asset doesn’t depreciates (capital, fully)30

BruSan

Permanent

TFP shocks

Margin/haircut spiral (leverage)

Loss

spiral

Investment

through leveraged financial sector

Dual role of durable assetProductionSecuritizationOptimal contract

Dynamic contract

Debt is limited

due idiosyncratic risk and costly state verification

δ

-depreciation rate

Slide31

Differences to He-KrishnamurthyHe-Krishnamurthy Endowment economyGDP growth is exogenously fixedNo physical investmentNo direct investment in risky asset by householdsLimited participation modelContractingOnly short-run relationship (t to t+dt

) Fraction of return, fee Asset composition (risky vs. risk-free) is not contractableNon-effort lowers return by xdtx is

exogenous,not linked to fundamental Private benefit from shirking

No benchmarkingPricing Implications

When experts wealth declines, their market power increases, and so does their fee

Price impact depends on assumption that household have larger discount rate than experts

Procyclical

Leverage

In H-K calibration paper

No fee, households are rationed in their investmentAs expert wealth approaches 0, interest rate can go to –∞ Heterogeneous labor income for newborns of lDtNon-log utility function31BruSanProduction economy

GDP growth depends on net-wealthPhysical investmentDirect investments by all householdsContracting

(Potential) long-run relationship

Fraction of return, fee, size of asset pool

Effort increases

fundamental

growth to

gdt

Monetary

benefit from shirking

No benchmarking

Pricing

Implication

Price drop with state variable

Countercyclcial

Leverage

Entrepreneur take on same position after drop in

networth

Leverage increases after drop in net-worth

Slide32

ConclusionIncorporate financial sector in macromodelHigher growthHigher volatilityMain insights:Adverse feedback loopsExternalities (rationale for financial regulation)Within financial sectorToward the real economy32

Slide33

Macro-prudential regulationExternalities – “stability is a public good”Fire-sale externality Fire-sales depress prices also for othersVolatility: Precautionary hoarding uncertainty about future funding…Network externality: Hiding owns’ commitmentUncertainty for counterparties (of counterparties …)Countercyclical regulation – counteract spiralsRegulation strict during boomsLean against credit bubblesIncorporate funding structure

33

Slide34

OverviewTheory (with Sannikov)Spirals: Non-linear adverse feedback loopsExternalitiesImplementation (with Adrian)CoVaR: measuring systemic risk contribution/externalitiesOne method: Quantile regressionsAddressing procyclicalites due to spirals34

Slide35

“CoVaR” with Tobias AdrianSystemic risk measureCapture externalities and contribution to systemic risk“Clone property”Splitting one institution to 10 identical clones (which perfectly comove with each other) does not reduce systemic riskContrast to current regulation focus on risk in isolation, VaRincentive to hang on to others, become big, interconnectedprocyclicalAmplify non-linearities even further

35

VaR

1%

Slide36

Who should be regulated?“Clone Property”Split individually systemic institution i in 10 identical clones c: CoVaRi= 10 CoVaRc

36groupexamples

macro-prudentialmicro-prudential

“individually systemic”

International banks

(national champions)

Yes

Yes

“systemic as part

of a herd”Leveraged hedge fundsYesNonon-systemic largePension fundsN0Yes“tinies”unleveredN0No

Slide37

CoVaR – systemic risk measureVaRqi is implicitly defined as quantileCoVaRqj|i is the VaR conditional on

institute i (index) is in distress (at it’s VaR level)ΔCoVaR

qj|i =

CoVaRqj|i –

VaR

q

j

Various conditionings? (direction matters!)

Contribution

ΔCoVaRQ1: Which institutions contribute (in a non-causal sense)VaRsystem| institution i in distress Exposure ΔCoVaRQ2: Which institutions are most exposed if there is a systemic crisis?VaRi | system in distressNetwork ΔCoVaRVaR of institution j conditional on i

in non-causal sense!

q-prob. event

Slide38

Network CoVaRconditional onorigin of arrow38

270

70

118

247

57

108

116

50

357

133116 726772122 495076

564 68

Slide39

OverviewTheory (with Sannikov)Spirals: Non-linear adverse feedback loopsExternalitiesImplementation – CoVaR (with Adrian)CoVaR: measuring systemic risk contribution/externalitiesOne method: Quantile regressionsAddressing procyclicalites due to spirals39

Slide40

Quantile Regressions: A RefresherOLS Regression: min sum of squared residualsPredicted value:Quantile Regression: min weighted absolute valuesPredicted value:

40

Note out (non-traditional) sign convention!

Slide41

Quantile Regression: A Refresher41

Slide42

Financial Intermediary DataPublicly traded financial intermediaries 1986-2008Commercial bank, security broker-dealers, insurance companies, real estate companies, etc.Weekly market equity data from CRSPQuarterly balance sheet data from COMPUSTATCDS and option data of top 10 US banks, daily 2004-200842

Slide43

Change in total asset value XitChange in total asset value (detrended) where At+ = market equity * leverage ratios “detrend factor”43

Slide44

44   

  

 

 

Variable

Mean

Std. Dev.

Min

Max

Observations

Returns

overall

0.27

55.92

-2430.04

2420.38

N = 47895

between

1.07

-4.40

2.98

n = 44

within

55.91

-2431.34

2419.08

T-bar = 1088

Portfolio VaR

overall

-105.59

128.35

-1547.03

237.35

N = 47895

between

110.07

-366.58

-3.45

n = 44

within

71.16

-1433.60

493.51

T-bar = 1088

Delta CoVaR

overall

-500.76

523.62

-4956.01

2285.65

N = 47895

between

361.39

-1262.44

278.14

n = 44

within

383.75

-4488.66

2533.57

T-bar = 1088

 

 

 

 

 

 

 

Summary Statistics of Risk Measures OLD

Slide45

ΔCoVaR vs. VaRVaR and ¢ CoVaR relationship is very weakData up to 12/0645

Slide46

OverviewTheory (with Sannikov)Spirals: Non-linear adverse feedback loopsExternalitiesImplementation – CoVaR (with Adrian)CoVaR: measuring systemic risk contribution/externalitiesOne method: Quantile regressionsAddressing procyclicalites due to spiralsStep 1: Time-varying CoVaRs

Step 2: Predict CoVaR using institution characteristicsBalance sheet variables (leverage, maturity mismatch, + interdependence, …)Market variables (CDS, implied vol.,…)

46

Slide47

OverviewMeasuring Systemic Risk ContributionOne Method: Quantile RegressionsCoVaR vs. VaRAddressing ProcyclicalityStep 1: Time-varying CoVaRsStep 2: Predict CoVaR using institution characteristicsBalance sheet variables

(leverage, maturity mismatch, + interdependence, …)Market variables (CDS, implied vol.,…)47

Slide48

Step 1: Time-varying CoVaRControl for macro factors, Mt interpretationVIX Level “Volatility”3 month yieldRepo – 3 month Treasury “Flight to Liquidity”Moody’s BAA – 10 year Treasury “Credit indicator”10Year – 3 month Treasury “Business Cycle”Real estate index “Housing”Equity market riskObtain Panel data of CoVaR

Next step: Relate to institution specific (panel) data48

Slide49

Step 1: Time-varying ΔCoVaRDerive time-varying VaRtFor institution i:For financial system:Derive time-varying CoVaRtΔCoVaRt = CoVaRt - VaR

t49

Slide50

Table 2: Average Exposures to Risk Factors50  

  

INSTITUTIONS

COEFFICIENT

VaR

system

VaR

i

CoVaR

system|i

Repo spread (lag)

-

1163***

-0.60

-877.94***

Credit spread (lag)

-107.75

-0.47

-226.75**

Term spread (lag)

128.71

0.64

18.80

VIX (lag)

-68.97***

-

0.16***

-

43.35***

3 Month Yield (lag)

118.73

0.42

15.95*

Market Return (lag)

242.74***

0.50***

196.00***

Housing (lag)

5.63

0.03

5.17

*** p< 0.01

** p<

0.05

* p< 0.1

 

 

 

 

Slide51

Table 1: Summary Statistic51 

  

 

Variable

Mean

Std. Dev.

Obs

X

i

overall

0.20

10.18

N = 316697

between

0.43

n

= 430

within

10.17

T-bar = 737

VaR

i

overall

-8.58

24.67

N = 316697

between

19.69

n

= 430

within

12.38

T-bar = 737

Δ

CoVaR

i

overall

-578.41

572.54

N = 316697

between

347.36

n

= 430

within

462.40

T-bar = 737

 

 

 

 

Slide52

Time-varying VaR 52

Slide53

Time-varying VaR and ΔCoVaR53

Slide54

Step 2a: Portfolios Sorted on CharacteristicsInstitutional characteristics matter… but individual financial institutions have changed the nature of their business over timeForm decile portfolios, each quarter, according to previous quarter’s data:LeverageMaturity mismatchSizeBook-to-MarketAdd 4 industry portfoliosBanksSecurity broker-dealers

Insurance companiesReal estate companies 54

Slide55

Table 3A: ΔCoVaR Forecasts by Characteristics Cross-section, Portfolios, 1%55 

 

 

 

COEFFICIENT

2 Years

1 Year

1 Quarter

Δ

CoVaR

(lagged)

0.71***

0.80***

0.94***

VaR

(lagged)

-1.99***

-2.27***

-0.47***

Leverage (lagged)

-9.43***

-10.73***

-2.53**

Maturity mismatch

(lagged)

-0.89***

-0.30

-0.14

Relative

Size (lagged)

-170.84***

-161.99***

-38.58***

Book-to-Market

(lagged)

85.24***

87.65***

31.03**

Constant

-40.92**

-50.04**

-19.93*

Observations

3627

3805

3939

R

2

0.62

0.69

0.89

 

 

 

 

Slide56

Discussion of Table 3AAt 2-year horizon, all characteristics are significantLeverage, maturity mismatch, size are positive related to systemic risk contributionHigher book-to-market indicates less systemic riskTwo effectsCloseness to default boundaryRiskiness of assetsLatter effect seems to dominate56

Slide57

Table 3B: ΔCoVaR Forecasts by Characteristics Cross-section, 2 years 57 

 

 

 

COEFFICIENT

1%

5%

10%

Δ

CoVaR

(lagged)

0.71***

0.63***

0.70***

VaR

(lagged)

-1.99***

-1.86***

-1.38***

Leverage (lagged)

-9.43***

-5.08***

-4.23**

Maturity mismatch

(lagged)

-0.89***

-0.51***

0.10

Relative

Size (lagged)

-170.84***

-105.62***

-86.84***

Book-to-Market

(lagged)

85.24***

26.95***

-14.77**

Constant

-40.92**

-14.70*

36.88***

Observations

3627

3627

3627

R

2

0.62

0.62

0.70

 

 

 

 

Slide58

Discussion of Table 3BCoefficients get larger further out in the tail, indicating more $-value of assets at risk in the tailCoefficients appear significant, as beforeIn addition to including time effects as in Tables 3, we are adding fixed effects in Table 4Shows the extent to which changes to future systemic risk can be forecasted over time58

Slide59

Table 4: ΔCoVaR Forecasts by Characteristics Time Series/Cross Section, Portfolios, 1%59 

 

 

 

COEFFICIENT

2 Years

1 Year

1 Quarter

Δ

CoVaR

(lagged)

0.41***

0.58***

0.86***

VaR

(lagged)

-1.30***

-1.74***

0.06

Leverage (lagged)

0.92

-8.10***

-1.64

Maturity mismatch

(lagged)

-0.31

-0.53

-0.33

Relative

Size (lagged)

-230***

-229***

-56***

Book-to-Market

(lagged)

29.25

42.69

31.03**

Constant

-332.58***

-239.05***

-96.84***

Observations

3627

3805

3939

R

2

0.69

0.73

0.89

 

 

 

 

Timing of tail risk is harder to forecast than cross-section contribution

Slide60

Step 2b: Forecasting with Market VariablesCDS spread and equity implied volatility for 10 largest US commercial and investment banks(from Bloomberg)Betas:Extract principal component from CDS spread changes/implied vol changes within each quarter from daily dataRegress each CDS spread change/ implied vol change on first principal component60

Slide61

Table 6: ΔCoVaR Forecasts by Market Variables Cross Section, Portfolios, 1%61 

 

 

 

COEFFICIENT

2 Years

1 Year

1 Quarter

Δ

CoVaR

(lagged)

0.60***

0.79***

0.94***

VaR

(lagged)

-1.84

0.05

-0.08

CDS beta (lagged)

-1.727**

787.92

95.37

CDS

(lagged)

1.320

-2.211

-40.26

Implied

Vol

beta

(lagged)

-8.30

-590.28**

-85.78

Implied

Vol

(lagged)

-144.60

111.02

234.56***

Constant

-335.30

-147.72

-114.07*

Observations

114

154

184

R

2

0.36

0.57

0.77

 

 

 

 

short data-span (2004-2008)!

Slide62

Extension to our AnalysisCo-Expected Shortfall (“Co-ES”)Advantage: coherent risk measureDisadvantage: any estimate “in” the tail is very noiseInclusion of additional informationderivative positionsoff-balance sheet exposureCrowdedness measureInterdependence measuresBank supervision information62

Slide63

Countercyclical RegulationWhen market is relaxedStrict Laddered ResponseStep 1: supervision enhancedStep 2: forbidden to pay out dividendsSee connection to debt-overhang problem)Step 3: No Bonus for CEOsStep 4: Recapitalization within two months + debt/equity swapWhen market is strict Relax regulatory requirement

63

Slide64

Causal risk spill over effectsNon-causal64Adverse feedback loop - amplification

A

B

C

Slide65

Shock Amplifier vs. Absorber OLD65INSTITUTIONS

VaR_index

VaR_index

COEFFICIENT

1 Year

1.5 Years

1 Year

1.5 Years

Fitted CoVaR_contrib (lag)

4.46**6.43***

(1.91)

(1.95)

Resid CoVaR_contrib (lag)

0.50

0.52

(0.40)

(0.41)

Fitted CoVaR_exp (lag)

0.75

0.51

(1.42)

(1.34)

Resid CoVaR_exp (lag)

2.94***

3.95***

(0.57)

(0.54)

VaR_index (lag)

0.30**

0.13

-1.25***

-1.96***

(0.12)

(0.12)

(0.33)

(0.32)

Slide66

What type of charge?Capital chargeStrictly bindingMight stifle competitionPigouvian tax + government insuranceGenerates revenueIn times of crisis it is cheap to issue government debt very salientPrivate insurance scheme (Kashap, Rajan & Stein, 2008 + NYU report)Requires lots of regulation66

Slide67

ConclusionTheoryLiquidity spirals - non-linear dynamicsExternalitiesMacro-prudential regulationFocus on externalitiesMeasure for systemic risk is needed, e.g. CoVaRCountercyclical regulationFind variables that predict average future CoVaR

Forward-looking measures, spreads, …Also,VaR measure is not sufficient – incorrect focusQuantile regressions are simple and efficient way to calculate CoVaR

67