Liquidity Policies and Systemic Risk...Financial Sector. Unpublished working paper, Princeton University, 2012. Charles Calomiris and Florian Heider. A Theory of Liquidity Regulation

Liquidity Policies and Systemic Risk Tobias Adrian and Nina Boyarchenko

The views presented here are the authors’ and are not representative of the views of the Federal Reserve Bank of New York or of the Federal Reserve System

Introduction

Motivation for Liquidity Regulation

Liquidity shortages are key characteristics of the financial crises

Liquidity stress is caused by:

Short-term wholesale funding of non-traditional, illiquid assetsMismanagement of contingent liquidity riskUncertainty about counterparties and collateral disruptions

Basel III regulation promotes resilience to liquidity shocks byaddressing two objectives:

Enhance resilience to short-term funding shocks by requiring FIs tohold a minimum pool of liquid assets (LCR)Improve longer term liquidity management by requiring activity fundedwith core or stable funding (NSFR) [not finalized]

T. Adrian, N. Boyarchenko Liquidity Regulation 2

Introduction

Ratio of Unstable Liabilities to Liquid Assets

March 10, 2013 Internal FR Page 16 of 30

Liquidity Stress Ratio This report presents the Liquidity Stress Ratio (LSR) for the 50 largest banks as of 2013Q4. It also provides decompositions of the assets, liabilities, and off balance sheet components of LSR, as well as the relationship between LSR and capital ratios, profitability, risk taking, and CLASS model capital projections.

Liquidity Stress Ratio The LSR measures the potential mismatch between liability-side (plus off balance sheet) liquidity outflows and asset-side liquidity inflows.

• At 0.47, aggregate LSR has decreased slightly compared to the last quarter. • Aggregate LSR has been decreasing steadily since the crisis, suggesting that the big banks are currently much

less vulnerable to liquidity risk than they were during the pre-crisis period. The current level of aggregate LSR is almost three standard deviations below the 2007:Q3 peak of 0.77.

Fraction of liabilities that runs at a 30 day horizon under stress

Liquid assets haircutted to account for illiquidity

Haircuts are from the LCR, plot from Dong and Zhou (2014)


Introduction

Our Approach

We use a standard macro model with a financial sector

We add two key assumptions:

Financial intermediaries have to hold liquidity against liabilitiesCapital regulation is risk based as in Adrian and Boyarchenko (2012)

Framework allows us to study the equilibrium implications of liquidityrequirements on the quantity and price of credit

Framework also features systemic financial crises


Introduction

Preview of Results

Within the context of our model, liquidity requirements are apreferable prudential policy tool relative to capital requirements

Tightening liquidity requirements lowers the likelihood of systemicdistress, without impairing consumption growth

Capital requirements trade off consumption growth and distress risk


The Model

Economic Structure

Producersrandom dividend stream,At , per unit of projectfinanced by directborrowing from interme-diaries and households

Intermediariesfinanced by householdsagainst capital invest-ments

Householdssolve portfolio choiceproblem between hold-ing intermediary debt,physical capital and risk-free borrowing/lending

Atkht

it

Atkt

Cbtbht


The Model

Intermediaries’ Balance Sheet

Assets Liabilities

Productive capital (Atpktkt) Risky debt (Atpbtbt)

Risk-free debt (AtTt) Inside equity (wt)


The Model

Production

Total output evolves as

Yt = AtKt

Stochastic productivity of capital {At = eat}t≥0

dat = adt + σadZat

pktAt denotes the price of one unit of capital in terms of theconsumption good

Aggregate amount of capital Kt evolves as

dKt = (It − λk)Ktdt


The Model

Intermediaries

Financial intermediaries create new capital

dkt = (Φ(it)− λk) ktdt

Investment carries quadratic adjustment costs (Brunnermeier andSannikov (2012))

Φ (it) = φ0

(√1 + φ1it − 1

)Intermediaries finance investment projects through inside equity andoutside risky debt giving the budget constraint

TtAt + pktAtkt = pbtAtbt + wt


The Model

Intermediaries’ Risk Based Capital Constraint

Risk based capital constraint (Danielsson, Shin, and Zigrand (2011))

α

√1

dt〈ktd (pktAt)〉2 ≤ wt

Implies a time-varying leverage constraint

θkt =pktAtkt

wt≤ 1

α

√1dt

⟨d(pktAt)pktAt

⟩2Equity is proportional to the Value-at-Risk of assets implying timevarying default probabilities


The Model

Risk-based Capital Constraints

VaR is the potential loss in value of inventory positions due toadverse market movements over a defined time horizon with aspecified confidence level. We typically employ a one-day timehorizon with a 95% confidence level.

Source: Goldman Sachs 2011 Annual Report


The Model

Commercial Bank Tightening Standards

Q2−91 Q2−93 Q2−95 Q2−97 Q2−99 Q2−01 Q2−03 Q2−05 Q2−07 Q2−09 Q2−110

20

40

60V

IX

−50

0

50

100

Cre

dit T

ight

enin

g

ρ=0.68013


The Model

Procyclicality induced by Risk based Capital Constraint−4 −2 0 2 4−1

−0.5

0

0.5

Total Credit Growth

Inte

rmed

iate

d C

redi

t Gro

wth

−5 0 5

−5

0

5

Equity Growth

Leve

rage

Gro

wth

−1 −0.5 0 0.5 1−5

0

5

Debt Growth

Leve

rage

Gro

wth

−0.05 0 0.05 0.1 0.15 0.2−0.2

−0.1

0

0.1

0.2

Total Credit Growth

Inte

rmed

iate

d C

redi

t Gro

wth

−1 −0.5 0 0.5 1−1

−0.5

0

0.5

1

Equity Growth

Leve

rage

Gro

wth

−1 −0.5 0 0.5 1−1

−0.5

0

0.5

1

Debt Growth

Leve

rage

Gro

wth

y = 0.0086 + 0.56xR2 = 0.056

y = −0.071 + 0.76xR2 = 0.46

Source: Adrian and Boyarchenko (2012)


The Model

Systemic Risk Return Tradeoff

2 4 6 8 10α

Wel

fare

2 4 6 8 10

0.2

0.4

0.6

0.8

1

α

Dis

tres

s pr

obab

ility

6 month1 year5 year



The Model

Intermediaries’ Liquidity Constraint

Liquidity constraint (similar to Basel III’s liquidity coverage ratio)

Requires intermediaries to hold cash in proportion to outstanding debt

1 + θbt − θkt︸︷︷︸cash/equity

≥ Λ θbt︸︷︷︸debt/equity

where

θbt =pbtAtbt

wt

The constraint can be rewritten as

θbt ≥1

1− Λ(θkt − 1) = Λ(θkt − 1)

Intermediaries are required to hold cash to buffer potential short termfunding needs


The Model

Intermediaries’ Optimization

Intermediary are myopic mean-variance optimizers solving

maxθt ,θbt ,it

Et

[dwt

wt

]− γ

2Vt

[dwt

wt

],

subject to the dynamic intermediary budget constraint

dwt

wt= θt (drkt − rftdt)− θbt (drbt − rftdt) + rftdt,

the risk-based capital constraint constraint

θ−1t ≥ α

√1

dt

⟨d (pktAt)

pktAt

⟩2

,

and the liquidity constraint

θbt ≥ Λ(θkt − 1)


The Model

Systemic Distress

Distress occurs when

τD = inft≥0{wt ≤ ωpktAtKt}

Term structure of systemic distress

δt (T ) = P (τD ≤ T | (wt , θt))

In distress

Management changes

Intermediary leverage reduced to θ ≈ 1 by defaulting on debt

Intermediary instantaneously restarts with wealth

wτ+D=θτDθ

wτD


The Model

Systemic Distress and Capital Regulation

2 4 6 8 10α

Wel

fare

2 4 6 8 10

0.2

0.4

0.6

0.8

1

α

Dis

tres

s pr

obab

ility

6 month1 year5 year



The Model

Households

Household preferences are:

E[∫ +∞

0e−(ξt+ρht) log ctdt

]Liquidity preference shocks (as in Allen and Gale (1994) and Diamondand Dybvig (1983)) are exp (−ξt)

dξt = σξdZξt

Households do not have access to the investment technology

dkht = −λkkhtdt


Solution

Market Structure

Market Intermediaries Households Total

Capital kt kht Kt

Consumption itktAt ct AtKt

Risky Debt −bt bht 0

Risk-Free Debt TtAt ThtAt BAt


Solution

Equilibrium

An equilibrium in this economy is:

A set of price processes {pkt , pbt , rft}t≥0A set of household decisions {kht , bht , ct}t≥0A set of intermediary decisions {kt , ρt , it , θt , θbt}t≥0

Such that:

1 Household’s optimize

2 Intermediary’s optimize

3 The capital market clears

4 The risky bond market clears

5 The risk-free debt market clears

6 The goods market clears


Solution

Solution Strategy

Equilibrium is characterized by two state variables, leverage θt andrelative intermediary net worth ωt

ωt =wt

wt + wht=

wt

pktAtKt

Represent state dynamics as

dωt

ωt= µωtdt + σωa,tdZat + σωξ,tdZξt

dθktθkt

= µθtdt + σθa,tdZat + σθξ,tdZξt

Numerical solution


Solution

Roadmap

Examine the trade-off between

Liquidity requirements and capital requirements

Liquidity requirements and supply of risk-free debt

Varying the tightness of liquidity and capital regulation affects

the risk-taking behavior of intermediariesthe intermediaries’ leverage cycleendogenous volatility amplificationendogenous systemic risk

Varying the supply of risk-free debt affects the equilibrium risk-freerate and thus the equilibrium cost of issuing risky debt


Welfare

Trading off Liquidity and Capital Regulation


Conclusion

Conclusion

Impact of liquidity and capital requirements in general equilibrium

The model features

Procyclical financial intermediary leverage cycleEndogenous volatilityEndogenous systemic risk

Within the context of our model, liquidity requirements are apreferable prudential policy tool relative to capital requirements

Tightening liquidity requirements lowers the likelihood of systemicdistress, without impairing consumption growthIn contrast, capital requirements trade off consumption growth anddistress probabilities


Conclusion

Related Literature

Liquidity Regulation: Goodhart, Kashyap, Tsomocos, andVardoulakis (2012), Perotti and Suarez (2011), Calomiris and Heider(2013)

Leverage Cycles: Geanakoplos (2003), Fostel and Geanakoplos(2008), Brunnermeier and Pedersen (2009)

Amplification in Macroeconomy: Bernanke and Gertler (1989),Kiyotaki and Moore (1997)

Financial Intermediaries and the Macroeconomy: Gertler andKiyotaki (2012), Gertler, Kiyotaki, and Queralto (2011), He andKrishnamurthy (2012, 2013), Brunnermeier and Sannikov (2011,2012)


Conclusion

Tobias Adrian and Nina Boyarchenko. Intermediary Leverage Cycles and FinancialStability. Federal Reserve Bank of New York Staff Report No. 567, 2012.

Franklin Allen and Douglas Gale. Limited market participation and volatility ofasset prices. American Economic Review, 84:933–955, 1994.

Ben Bernanke and Mark Gertler. Agency Costs, Net Worth, and BusinessFluctuations. American Economic Review, 79(1):14–31, 1989.

Markus K. Brunnermeier and Lasse Heje Pedersen. Market Liquidity and FundingLiquidity. Review of Financial Studies, 22(6):2201–2238, 2009.

Markus K. Brunnermeier and Yuliy Sannikov. The I Theory of Money.Unpublished working paper, Princeton University, 2011.

Markus K. Brunnermeier and Yuliy Sannikov. A Macroeconomic Model with aFinancial Sector. Unpublished working paper, Princeton University, 2012.

Charles Calomiris and Florian Heider. A Theory of Liquidity Regulation.Unpublished working paper, 2013.

Jon Danielsson, Hyun Song Shin, and Jean-Pierre Zigrand. Balance sheetcapacity and endogenous risk. Working Paper, 2011.


Conclusion

Douglas W. Diamond and Philip H. Dybvig. Bank runs, deposit insurance andliquidity. Journal of Political Economy, 93(1):401–419, 1983.

Ana Fostel and John Geanakoplos. Leverage Cycles and the Anxious Economy.American Economic Review, 98(4):1211–1244, 2008.

John Geanakoplos. Liquidity, Default, and Crashes: Endogenous Contracts inGeneral Equilibrium. In M. Dewatripont, L.P. Hansen, and S.J. Turnovsky,editors, Advances in Economics and Econometrics II, pages 107–205.Econometric Society, 2003.

Mark Gertler and Nobuhiro Kiyotaki. Banking, Liquidity, and Bank Runs in anInfinite Horizon Economy. Unpublished working papers, Princeton University,2012.

Mark Gertler, Nobuhiro Kiyotaki, and Albert Queralto. Financial Crises, BankRisk Exposure, and Government Financial Policy. Unpublished working papers,Princeton University, 2011.

Charles A.E. Goodhart, Anil K. Kashyap, Dimitrios P. Tsomocos, andAlexandros P. Vardoulakis. Financial Regulation in General Equilibrium. NBERWorking Paper No. 17909, 2012.


Conclusion

Zhiguo He and Arvind Krishnamurthy. A Model of Capital and Crises. Review ofEconomic Studies, 79(2):735–777, 2012.

Zhiguo He and Arvind Krishnamurthy. Intermediary Asset Pricing. AmericanEconomic Review, 103(2):732–770, 2013.

Nobuhiro Kiyotaki and John Moore. Credit Cycles. Journal of Political Economy,105(2):211–248, 1997.

Enrico Perotti and Javier Suarez. A Pigovian Approach to Liquidity Regulation.International Journal of Central Banking, 7(4):3–41, 2011.


Conclusion

Intermediaries’ binding Liquidity ConstraintsS

hort

−te

rm A

sset

s

Capital

2 3 4 50

0.1

0.2

0.3

0.4

0.5

0

0.2

0.4

0.6

0.8

1

Capital

Liqu

idity

2 4

0.2

0.4

0.6

0.8

0

0.2

0.4

0.6

0.8

1

Sho

rt−

term

Ass

ets

Liquidity

0.2 0.4 0.6 0.80

0.1

0.2

0.3

0.4

0.5

0

0.2

0.4

0.6

0.8

1


Conclusion

Risk Free Rate

Sho

rt−

term

Ass

ets

Capital

2 3 4 50

0.1

0.2

0.3

0.4

0.5

0.085

0.09

0.095

0.1

Capital

Liqu

idity

2 4

0.2

0.4

0.6

0.8

0.093

0.094

0.095

0.096

0.097

0.098

Sho

rt−

term

Ass

ets

Liquidity

0.2 0.4 0.6 0.80

0.1

0.2

0.3

0.4

0.5

0.085

0.09

0.095

0.1


Conclusion

Households’ Risky AssetsS

hort

−te

rm A

sset

s

Capital

2 3 4 50

0.1

0.2

0.3

0.4

0.5

0.5

1

1.5

2

2.5

3

Capital

Liqu

idity

2 4

0.2

0.4

0.6

0.8

1

2

3

4

5

Sho

rt−

term

Ass

ets

Liquidity

0.2 0.4 0.6 0.80

0.1

0.2

0.3

0.4

0.5

0.5

1

1.5

2

2.5

3

3.5

4

4.5


Conclusion

Household Welfare

Sho

rt−

term

Ass

ets

Capital

2 3 4 50

0.1

0.2

0.3

0.4

0.5

Capital

Liqu

idity

2 3 4 5

0.2

0.4

0.6

0.8

Sho

rt−

term

Ass

ets

Liquidity

0.2 0.4 0.6 0.80

0.1

0.2

0.3

0.4

0.5

Low

High

Low

High

Low

High


Conclusion

Debt-to-equity Ratios

Sho

rt−

term

Ass

ets

Capital

2 3 4 50

0.1

0.2

0.3

0.4

0.5

2

4

6

8

10

12

Capital

Liqu

idity

2 3 4 5

0.2

0.4

0.6

0.8

5

10

15

20

25

Sho

rt−

term

Ass

ets

Liquidity

0.2 0.4 0.6 0.80

0.1

0.2

0.3

0.4

0.5

5

10

15

20


Conclusion

Distress probability

Sho

rt−

term

Ass

ets

Capital

2 3 4 50

0.1

0.2

0.3

0.4

0.5

Capital

Liqu

idity

2 3 4 5

0.2

0.4

0.6

0.8

Sho

rt−

term

Ass

ets

Liquidity

0.2 0.4 0.6 0.80

0.1

0.2

0.3

0.4

0.5

0

0.1

0.2

0.3

0.4

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35


Conclusion

Local Volatility

Sho

rt−

term

Ass

ets

Capital

2 3 4 50

0.1

0.2

0.3

0.4

0.5

0.1

0.15

0.2

Capital

Liqu

idity

2 3 4 5

0.2

0.4

0.6

0.8

0.14

0.16

0.18

0.2

Sho

rt−

term

Ass

ets

Liquidity

0.2 0.4 0.6 0.80

0.1

0.2

0.3

0.4

0.5

0.1

0.12

0.14

0.16

0.18

0.2

0.22

0.24


Conclusion

Exposures of Return to Capital to Fundamental Shocks

Sho

rt−

term

Ass

ets

Capital

σka

2 3 4 50

0.2

0.4

0.020.040.060.080.10.12

Capital

Liqu

idity

σka

2 3 4 5

0.2

0.4

0.6

0.8

0.05

0.1

0.15

Sho

rt−

term

Ass

ets

Liquidity

σka

0.2 0.4 0.6 0.80

0.2

0.4

0

0.05

0.1S

hort

−te

rm A

sset

s

Capital

σkξ

2 3 4 50

0.2

0.4

−0.2

−0.15

−0.1

Capital

Liqu

idity

σkξ

2 3 4 5

0.2

0.4

0.6

0.8

−0.14

−0.12

−0.1

Sho

rt−

term

Ass

ets

Liquidity

σkξ

0.2 0.4 0.6 0.80

0.2

0.4

−0.2

−0.15

−0.1

−0.05


Conclusion

Consumption Growth

Sho

rt−

term

Ass

ets

Capital

2 3 4 50

0.1

0.2

0.3

0.4

0.5

Sho

rt−

term

Ass

ets

Liquidity

0.2 0.4 0.6 0.80

0.1

0.2

0.3

0.4

0.5

Capital

Liqu

idity

2 3 4 5

0.2

0.4

0.6

0.8

Low

High

Low

High

Low

High


Documents

Liquidity Policies and Systemic Risk...Financial Sector. Unpublished working paper, Princeton University, 2012. Charles Calomiris and Florian Heider. A Theory of Liquidity Regulation