liquidity policies and systemic risk...financial sector. unpublished working paper, princeton...
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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)
T. Adrian, N. Boyarchenko Liquidity Regulation 3
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
T. Adrian, N. Boyarchenko Liquidity Regulation 4
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
T. Adrian, N. Boyarchenko Liquidity Regulation 5
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
T. Adrian, N. Boyarchenko Liquidity Regulation 6
The Model
Intermediaries’ Balance Sheet
Assets Liabilities
Productive capital (Atpktkt) Risky debt (Atpbtbt)
Risk-free debt (AtTt) Inside equity (wt)
T. Adrian, N. Boyarchenko Liquidity Regulation 7
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
T. Adrian, N. Boyarchenko Liquidity Regulation 8
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
T. Adrian, N. Boyarchenko Liquidity Regulation 9
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
T. Adrian, N. Boyarchenko Liquidity Regulation 10
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
T. Adrian, N. Boyarchenko Liquidity Regulation 11
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
T. Adrian, N. Boyarchenko Liquidity Regulation 12
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)
T. Adrian, N. Boyarchenko Liquidity Regulation 13
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
Source: Adrian and Boyarchenko (2012)
T. Adrian, N. Boyarchenko Liquidity Regulation 14
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
T. Adrian, N. Boyarchenko Liquidity Regulation 15
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)
T. Adrian, N. Boyarchenko Liquidity Regulation 16
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
T. Adrian, N. Boyarchenko Liquidity Regulation 17
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
Source: Adrian and Boyarchenko (2012)
T. Adrian, N. Boyarchenko Liquidity Regulation 18
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
T. Adrian, N. Boyarchenko Liquidity Regulation 19
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
T. Adrian, N. Boyarchenko Liquidity Regulation 20
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
T. Adrian, N. Boyarchenko Liquidity Regulation 21
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
T. Adrian, N. Boyarchenko Liquidity Regulation 22
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
T. Adrian, N. Boyarchenko Liquidity Regulation 23
Welfare
Trading off Liquidity and Capital Regulation
T. Adrian, N. Boyarchenko Liquidity Regulation 24
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
T. Adrian, N. Boyarchenko Liquidity Regulation 25
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)
T. Adrian, N. Boyarchenko Liquidity Regulation 26
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.
T. Adrian, N. Boyarchenko Liquidity Regulation 27
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.
T. Adrian, N. Boyarchenko Liquidity Regulation 28
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.
T. Adrian, N. Boyarchenko Liquidity Regulation 29
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
T. Adrian, N. Boyarchenko Liquidity Regulation 30
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
T. Adrian, N. Boyarchenko Liquidity Regulation 31
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
T. Adrian, N. Boyarchenko Liquidity Regulation 32
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
T. Adrian, N. Boyarchenko Liquidity Regulation 33
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
T. Adrian, N. Boyarchenko Liquidity Regulation 34
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
T. Adrian, N. Boyarchenko Liquidity Regulation 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
T. Adrian, N. Boyarchenko Liquidity Regulation 36
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
T. Adrian, N. Boyarchenko Liquidity Regulation 37
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
T. Adrian, N. Boyarchenko Liquidity Regulation 38