taking regulation seriously: fire sales under …...taking regulation seriously: fire sales under...
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Introduction Model Data Results Conclusions Appendix
Taking regulation seriously: Fire salesunder solvency and liquidity constraints
Jamie Coen1,2, Caterina Lepore2 and Eric Schaanning3,4
London School of Economics1, Bank of England2, ETHZurich3, Norges Bank4
Columbia UniversityNYC, February 2018
Taking regulation seriously Coen, Lepore, Schaanning
Introduction Model Data Results Conclusions Appendix
Disclaimer
The views expressed are those of the authors only and do notnecessarily reflect those of the Bank of England or Norges Bank.
Taking regulation seriously Coen, Lepore, Schaanning
Introduction Model Data Results Conclusions Appendix
1 Introduction
2 Model
3 Data
4 ResultsAsset shock: variants of 2017 stress testFunding shockAsset and Funding shocks
5 Conclusions
6 Appendix
Taking regulation seriously Coen, Lepore, Schaanning
Introduction Model Data Results Conclusions Appendix
Motivation
“During the early ‘liquidity phase’ of the financial crisis that beganin 2007, many credit institutions, despite maintaining adequatecapital levels, experienced significant difficulties because they hadfailed to manage their liquidity risk prudently... (Such) creditinstitutions were then forced to liquidate assets in a fire-sale whichcreated a self-reinforcing downward price spiral and lack of marketconfidence triggering a solvency crisis."
(European Commission, 2015)
Taking regulation seriously Coen, Lepore, Schaanning
Introduction Model Data Results Conclusions Appendix
Motivation
• Liquidity issues during the crisis• Multiple regulatory constraints• Macroprudential stress tests
• Objectives:• Build a quantitative model of fire sales to assess the
interaction between liquidity and solvency constraints thatbanks simultaneously face.
• Which types of financial shocks and regulatory requirementscombine to produce fire sales?
• How do banks optimally liquidate their portfolios when theyare forced to do so?
Taking regulation seriously Coen, Lepore, Schaanning
Introduction Model Data Results Conclusions Appendix
Motivation
• Liquidity issues during the crisis• Multiple regulatory constraints• Macroprudential stress tests• Objectives:
• Build a quantitative model of fire sales to assess theinteraction between liquidity and solvency constraints thatbanks simultaneously face.
• Which types of financial shocks and regulatory requirementscombine to produce fire sales?
• How do banks optimally liquidate their portfolios when theyare forced to do so?
Taking regulation seriously Coen, Lepore, Schaanning
Introduction Model Data Results Conclusions Appendix
Literature review• Fire-sale models:[Greenwood et al., 2015], [Cont and Schaanning, 2017],[Duarte and Eisenbach, 2013]
• Constraints and optimal deleveraging:[Cecchetti and Kashyap, 2016],[Braouezec and Wagalath, 2016]
• Liquidity:[Hellwig, 2009], [Gorton and Metrick, 2012], [Pierret, 2015] ,[Acharya and Merrouche, 2012]
• Macro-stress tests:[Dees and Henry, 2017], [Bank of England, 2017],[Bardoscia et al., 2017], [Fique, 2017],[Puhr and Schmitz, 2014], [Calimani et al., 2017]
Taking regulation seriously Coen, Lepore, Schaanning
Introduction Model Data Results Conclusions Appendix
Model overview
Losses/outflows Deleveraging
Price impact
Regulation
Scenario
Taking regulation seriously Coen, Lepore, Schaanning
Introduction Model Data Results Conclusions Appendix
Bank balance sheets
• Marketable securities Mi ,k , k = 1...310 and i = 1...7Bonds and equity holdings that are available for sale andsuffer a price impact.
• Other assets Oi ,k , k = 1, 2: loans, intangible goods, andoff-balance sheet items, which are not available fordeleveraging.
• Cash or cash-like assets Ci ,k , k = 1, 2.
• Liabilities Li ,k , k = 1...12. These include classic retailcustomer deposits, institutional deposits, short-termwhole-sale funding, and issued debt.
• Capital Ei .
Taking regulation seriously Coen, Lepore, Schaanning
Introduction Model Data Results Conclusions Appendix
Bank balance sheets
• Marketable securities Mi ,k , k = 1...310 and i = 1...7Bonds and equity holdings that are available for sale andsuffer a price impact.
• Other assets Oi ,k , k = 1, 2: loans, intangible goods, andoff-balance sheet items, which are not available fordeleveraging.
• Cash or cash-like assets Ci ,k , k = 1, 2.• Liabilities Li ,k , k = 1...12. These include classic retailcustomer deposits, institutional deposits, short-termwhole-sale funding, and issued debt.
• Capital Ei .
Taking regulation seriously Coen, Lepore, Schaanning
Introduction Model Data Results Conclusions Appendix
Regulatory constraints• Risk-weighted Capital Ratio:
CAP i(A,E ) := E i
ρ>Ai ≥ REGCAP .
• Leverage Ratio:
LEV i(A,C ,E ) := E i
1>Ai + 1>C i ≥ REGLEV ,
• Liquidity Coverage Ratio:
LCR i(A,C , L) := λ>M i + 1>C i
ω>outLi − ω>inAi ≥ REGLCR .
Taking regulation seriously Coen, Lepore, Schaanning
Introduction Model Data Results Conclusions Appendix
Regulatory constraints• Risk-weighted Capital Ratio:
CAP i(A,E ) := E i
ρ>Ai ≥ REGCAP .
• Leverage Ratio:
LEV i(A,C ,E ) := E i
1>Ai + 1>C i ≥ REGLEV ,
• Liquidity Coverage Ratio:
LCR i(A,C , L) := λ>M i + 1>C i
ω>outLi − ω>inAi ≥ REGLCR .
Taking regulation seriously Coen, Lepore, Schaanning
Introduction Model Data Results Conclusions Appendix
Regulatory constraints• Risk-weighted Capital Ratio:
CAP i(A,E ) := E i
ρ>Ai ≥ REGCAP .
• Leverage Ratio:
LEV i(A,C ,E ) := E i
1>Ai + 1>C i ≥ REGLEV ,
• Liquidity Coverage Ratio:
LCR i(A,C , L) := λ>M i + 1>C i
ω>outLi − ω>inAi ≥ REGLCR .
Taking regulation seriously Coen, Lepore, Schaanning
Introduction Model Data Results Conclusions Appendix
Shocks
We consider three type of shocks:1 Asset shock (εA): Ai ,k
0 = Ai ,k(1 − εkA). (k = 1...314)2 Funding shock (εL): Li ,k
0 = Li ,k(1 − εkL). (k = 1..12)3 Combined asset and funding shock.
E i0 = (E i − ε>AAi)+.
C i0 = (C i − ε>L Li)+.
Taking regulation seriously Coen, Lepore, Schaanning
Introduction Model Data Results Conclusions Appendix
Shocks
We consider three type of shocks:1 Asset shock (εA): Ai ,k
0 = Ai ,k(1 − εkA). (k = 1...314)2 Funding shock (εL): Li ,k
0 = Li ,k(1 − εkL). (k = 1..12)3 Combined asset and funding shock.
E i0 = (E i − ε>AAi)+.
C i0 = (C i − ε>L Li)+.
Taking regulation seriously Coen, Lepore, Schaanning
Introduction Model Data Results Conclusions Appendix
Bank deleveraging
Figure: Shrinking a bank’s balance sheet
Taking regulation seriously Coen, Lepore, Schaanning
Introduction Model Data Results Conclusions Appendix
Fire-sale lossesPrice evolution under fire sales
Pkt+1 = Pk
t
(1 − δ−1
k
N∑i=1
S i ,kt
),
Two forms of loss:• Mark-to-market losses
K∑k=1
(M i ,kt − S i ,k
t )︸ ︷︷ ︸Remaining holdings
× δ−1k
N∑i=1
S i ,kt︸ ︷︷ ︸
Price impact (above)
.
• Implementation shortfall
12
K∑k=1
S i ,kt
N∑j=1
δ−1k S j,k
t .
Taking regulation seriously Coen, Lepore, Schaanning
Introduction Model Data Results Conclusions Appendix
Fire-sale lossesPrice evolution under fire sales
Pkt+1 = Pk
t
(1 − δ−1
k
N∑i=1
S i ,kt
),
Two forms of loss:• Mark-to-market losses
K∑k=1
(M i ,kt − S i ,k
t )︸ ︷︷ ︸Remaining holdings
× δ−1k
N∑i=1
S i ,kt︸ ︷︷ ︸
Price impact (above)
.
• Implementation shortfall
12
K∑k=1
S i ,kt
N∑j=1
δ−1k S j,k
t .
Taking regulation seriously Coen, Lepore, Schaanning
Introduction Model Data Results Conclusions Appendix
Fire-sale lossesPrice evolution under fire sales
Pkt+1 = Pk
t
(1 − δ−1
k
N∑i=1
S i ,kt
),
Two forms of loss:• Mark-to-market losses
K∑k=1
(M i ,kt − S i ,k
t )︸ ︷︷ ︸Remaining holdings
× δ−1k
N∑i=1
S i ,kt︸ ︷︷ ︸
Price impact (above)
.
• Implementation shortfall
12
K∑k=1
S i ,kt
N∑j=1
δ−1k S j,k
t .
Taking regulation seriously Coen, Lepore, Schaanning
Introduction Model Data Results Conclusions Appendix
Bank optimisation problem: Minimize liquidation losses
minSi,Ri
(M i − 12S
i)>(S i
δ),
subject to the constraints
CAP i(A,E ;S) ≥ REGCAP
LEV i(A,C ,E ;S,R) ≥ REGLEV
LCR i(A,C , L;S,R) ≥ REGLCR
CASH i(A,C ;S,R) ≥ 0.
Note: banks only internalise the effects of their own sales, and notthe spillover effects of sales by other banks.
Taking regulation seriously Coen, Lepore, Schaanning
Introduction Model Data Results Conclusions Appendix
Bank optimisation problem: Minimize liquidation losses
minSi,Ri
(M i − 12S
i)>(S i
δ),
subject to the constraints
CAP i(A,E ;S) ≥ REGCAP
LEV i(A,C ,E ;S,R) ≥ REGLEV
LCR i(A,C , L;S,R) ≥ REGLCR
CASH i(A,C ;S,R) ≥ 0.
Note: banks only internalise the effects of their own sales, and notthe spillover effects of sales by other banks.
Taking regulation seriously Coen, Lepore, Schaanning
Introduction Model Data Results Conclusions Appendix
Bank optimisation problem: Minimize liquidation losses
minSi,Ri
(M i − 12S
i)>(S i
δ),
subject to the constraints
CAP i(A,E ;S) ≥ REGCAP
LEV i(A,C ,E ;S,R) ≥ REGLEV
LCR i(A,C , L;S,R) ≥ REGLCR
CASH i(A,C ;S,R) ≥ 0.
Note: banks only internalise the effects of their own sales, and notthe spillover effects of sales by other banks.
Taking regulation seriously Coen, Lepore, Schaanning
Introduction Model Data Results Conclusions Appendix
Calibration
• Balance sheet data taken from regulatory returns (COREPand FINREP) and Bank of England stress test data.
• Regulatory weights based on Basel guidance, Europeanlegislation and firms’ annual statements.
• Regulatory ratios & constraints taken from regulatoryreturns.
• Market depths based on national authorities’ publishedstatistics on average trading volumes and S&P price indicesfor government bonds, and BoAML prices and oustandingvolumes for corporate bonds.
Taking regulation seriously Coen, Lepore, Schaanning
Introduction Model Data Results Conclusions Appendix
Stress scenarios
We consider three scenarios:1 Asset shock (εA): Bank of England 2017 Stress scenario and
shocks of increased intensity.2 Funding shock (εL): Depositor run (20%, 40% and 60%
deposit outflows).3 Combined asset and funding shock: Bank of England 2017
Stress scenario and 20% deposits outflows.
Taking regulation seriously Coen, Lepore, Schaanning
Introduction Model Data Results Conclusions Appendix
Asset shock: variants of 2017 stress test
Asset shock
• Risk-weighted capital requirements tend to be more tightlybinding than leverage constraints.
• Banks constrained by risk-weighted capital constraints sell onaverage more illiquid assets, and in larger amounts, than whenconstrained by the leverage ratio.
• The size of unexpected losses, which are not internalized bybanks, can be as important as the size of expected losses.
Taking regulation seriously Coen, Lepore, Schaanning
Introduction Model Data Results Conclusions Appendix
Asset shock: variants of 2017 stress test
Asset sales: leverage ratio only
60
0
10
20
30
40
50
60
Mar
ket
dep
th (
£tn
)
Leverage only All constraints Risk-weighted only
Mean market depth of initial holdings
2017BoE 2017BoEx1.1 2017BoEx1.25
Taking regulation seriously Coen, Lepore, Schaanning
Introduction Model Data Results Conclusions Appendix
Asset shock: variants of 2017 stress test
Asset sales: capital ratio only
0
10
20
30
40
50
60
Mar
ket
dep
th (
£tn
)
Leverage only All constraints Risk-weighted only
Mean market depth of initial holdings
2017BoE 2017BoEx1.1 2017BoEx1.25
Leverage only All constraints Risk-weighted only
Taking regulation seriously Coen, Lepore, Schaanning
Introduction Model Data Results Conclusions Appendix
Asset shock: variants of 2017 stress test
Asset sales: all constraints
0
10
20
30
40
50
60
Mar
ket
dep
th (
£tn
)
Leverage only All constraints Risk-weighted only
Mean market depth of initial holdings
2017BoE 2017BoEx1.1 2017BoEx1.25
Taking regulation seriously Coen, Lepore, Schaanning
Introduction Model Data Results Conclusions Appendix
Asset shock: variants of 2017 stress test
Fire-sale losses
0
5
10
15
20
25
30
2017BoE 2017BoEx1.1 2017BoEx1.25
Fire
-sal
e lo
sses
(£
bn
)
Initial shock (multiples of 2017 stress test)
All constraints Risk-weighted only Leverage only
Taking regulation seriously Coen, Lepore, Schaanning
Introduction Model Data Results Conclusions Appendix
Asset shock: variants of 2017 stress test
Fire-sale losses: decomposition
0
5
10
15
20
25
30
2017BoE 2017BoEx1.1 2017BoEx1.25
Fire
-sal
e lo
sses
(£
bn
)
Initial shock (multiples of 2017 stress test)
Expected losses Unexpected losses
Taking regulation seriously Coen, Lepore, Schaanning
Introduction Model Data Results Conclusions Appendix
Funding shock
Funding shock: deposit outflows
• Banks prefer to use cash and sell highly liquid assets first tominimise losses.
• However, as the shock becomes larger, banks are forced to sellless liquid assets.
• When banks defend their LCRs to keep them above 100%,they need to sell less liquid assets in larger amounts.
• Hence fire-sale losses are significantly larger relative to thecase when banks do not defend their LCRs.
Taking regulation seriously Coen, Lepore, Schaanning
Introduction Model Data Results Conclusions Appendix
Funding shock
Asset sales
10
15
20
25
30
35
40
0% 20% 40% 60% 80%
Mar
ket
dep
th (
£tn
)
Initial deposit outflows (% total deposits)
Don't defend LCR Defend LCR
Mean market depth of initial holdings
Taking regulation seriously Coen, Lepore, Schaanning
Introduction Model Data Results Conclusions Appendix
Funding shock
Fire-sale losses
0
2
4
6
8
10
12
14
20% 40% 60%
Fire
-sal
e lo
sses
(£
bn
)
Initial deposit outflows (% total deposits)
Defend LCR Don't defend LCR
Taking regulation seriously Coen, Lepore, Schaanning
Introduction Model Data Results Conclusions Appendix
Funding shock
Fire-sale losses: decomposition
0
2
4
6
8
10
12
14
20% 40% 60%
Fire
-sal
e lo
sses
(£
bn
)
Initial deposit outflows (% total depsosits)
Expected losses Unexpected loses
Taking regulation seriously Coen, Lepore, Schaanning
Introduction Model Data Results Conclusions Appendix
Asset and Funding shocks
Asset and Funding shocks
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Leverageonly
Risk-weightedonly
LCRonly
Allconstraints
Fire
-sal
e lo
sses
(£
bn
)
Taking regulation seriously Coen, Lepore, Schaanning
Introduction Model Data Results Conclusions Appendix
Conclusions
• Both risk-weighted capital and liquidity constraints canbecome binding and generate significant fire sales losses, byincentivising sales of larger amounts of less liquid assets.
• Models that only account for a leverage constraint might thenunder-estimate fire sale losses.
• Unexpected fire sales losses, e.g. losses due to deleveraging byother banks, can be larger than banks’ expected losses fromtheir own sales.
• Relaxing banks’ regulatory constraints during stress may be apossible mitigating action to avoid fire sales. For example,allowing banks to draw down their LCR.
Taking regulation seriously Coen, Lepore, Schaanning
Introduction Model Data Results Conclusions Appendix
Conclusions
• Both risk-weighted capital and liquidity constraints canbecome binding and generate significant fire sales losses, byincentivising sales of larger amounts of less liquid assets.
• Models that only account for a leverage constraint might thenunder-estimate fire sale losses.
• Unexpected fire sales losses, e.g. losses due to deleveraging byother banks, can be larger than banks’ expected losses fromtheir own sales.
• Relaxing banks’ regulatory constraints during stress may be apossible mitigating action to avoid fire sales. For example,allowing banks to draw down their LCR.
Taking regulation seriously Coen, Lepore, Schaanning
Introduction Model Data Results Conclusions Appendix
Next steps
• Run more rounds of fire sales.• Explore solvency-liquidity nexus by running asset and fundingshocks (both at the same time and sequentially).
• Sensitivity analysis: market depths, price function, targetingvs threshold.
• Constraints: UK leverage framework, LCR with limits toreserves usability.
Taking regulation seriously Coen, Lepore, Schaanning
Introduction Model Data Results Conclusions Appendix
Thank you
Taking regulation seriously Coen, Lepore, Schaanning
Introduction Model Data Results Conclusions Appendix
Acharya, V. V. and Merrouche, O. (2012).Precautionary hoarding of liquidity and interbank markets:Evidence from the subprime crisis*.Review of Finance, pages 107–160.
Bank of England (2017).Stress testing the uk banking system:2017 results.
Bardoscia, M., Barucca, P., Brinley-Codd, A., and Hill, J.(2017).The decline of solvency contagion risk.Bank of England Staff Working Paper No.662.
Taking regulation seriously Coen, Lepore, Schaanning
Introduction Model Data Results Conclusions Appendix
Braouezec, Y. and Wagalath, L. (2016).Risk-based capital requirements and optimal liquidation in astress scenario.Review of Finance, page rfw067.
Calimani, S., Hałaj, G., Żochowski, D., et al. (2017).Simulating fire-sales in a banking and shadow banking system.Technical report, European Systemic Risk Board.
Cecchetti, S. and Kashyap, A. (2016).What binds? interactions between bank capital and liquidityregulations.
Cont, R. and Schaanning, E. (2017).Fire sales, indirect contagion and systemic stress testing.Norges Bank Working Paper.
Taking regulation seriously Coen, Lepore, Schaanning
Introduction Model Data Results Conclusions Appendix
Dees, S. and Henry, J. (2017).Stress-test analytics for macroprudential purposes: Introducingstampe.SATELLITE MODELS, page 13.
Duarte, F. and Eisenbach, T. M. (2013).Fire sale spillovers and systemic risk.Federal Reserve Bank of New York Staff Report, 645.
Fique, J. (2017).The MacroFinancial Risk Assessment Framework (MFRAF),Version 2.0.Bank of Canada.
Taking regulation seriously Coen, Lepore, Schaanning
Introduction Model Data Results Conclusions Appendix
Gorton, G. and Metrick, A. (2012).Securitized banking and the run on repo.Journal of Financial Economics, 104(3):425 – 451.Market Institutions, Financial Market Risks and FinancialCrisis.Greenwood, R., Landier, A., and Thesmar, D. (2015).Vulnerable banks.Journal of Financial Economics, 115(3):471 – 485.
Hellwig, M. F. (2009).Systemic Risk in the Financial Sector: An Analysis of theSubprime-Mortgage Financial Crisis.De Economist, 157(2):129–207.
Taking regulation seriously Coen, Lepore, Schaanning
Introduction Model Data Results Conclusions Appendix
Obizhaeva, A. A. (2012).Liquidity estimates and selection bias.Working Paper.
Pierret, D. (2015).Systemic risk and the solvency-liquidity nexus of banks.International Journal of Central Banking, 11(3):193–227.
Puhr, C. and Schmitz, S. W. (2014).A view from the top: The interaction between solvency andliquidity stress.Journal of risk management in institutions, 7(1):38–51.
Taking regulation seriously Coen, Lepore, Schaanning