Measuring Liquidity Mismatch in the Banking Sectort;k + X k0 ;l 0 l i t;k0: ai t;k and l i t;k0 are...

Measuring Liquidity Mismatchin the Banking Sector

Jennie Bai (Georgetown)Arvind Krishnamurthy (Stanford)

Charles-Henri Weymuller (French Treasury)

IMFJune 16, 2016

Motivation

• Liquidity plays an enormous role in the financial crisis• Most dramatic episodes of crisis is due to liquidity problem rather

than due to capital problem, e.g. Bear Stern, Lehman Brothers• Liquidity support from the regulatory institutions (Fed, FHLB, FDIC,

etc) is strikingly large, Fleming (2012), He et al. (2010)

• How to measure liquidity remains a challenge without consensus.• Basel III: liquidity coverage ratio, net stable funding ratio• Federal Reserve Board: 4G flow

• In this paper we implement a liquidity measure, “Liquidity MismatchIndex (LMI),” to gauge the mismatch between the market liquidityof assets and funding liquidity of liabilities.

Jennie Bai (Georgetown) 2/37

Why do we need one more liquidity measure?

Bank Balance SheetCash Overnight debts

cash, fed fund, repo fed fund, reverse repoAssets Deposits

Treasury securities insuredAgency securities uninsuredMuni securitiesNon-agency MBS Short-term debtsStructured products Long-term debtsCorporate debt

Loans EquitiesC& I loansreal estate loansreceivables, leasing Contingent Liabilities

Fixed and other assets


Reason 1: We need a synthetical measureBalance Sheet of a Simple Bank

Cash Overnight debtscash, fed fund, repo fed fund, reverse repo

Assets DepositsTreasury securities insuredAgency securities uninsuredMuni securitiesNon-agency MBS Short-term debtsStructured products Long-term debtsCorporate debt

Loans EquitiesC& I loansreal estate loansreceivables, leasing Contingent Liabilities


• assets and liabilities need to be jointly considered

• various elements of assets (liabilities) need to be considered


Reason 2: Liquidity weights should be time-varyingak λak lk′ λlk′

Cash +100% Overnight debts -100%cash, fed fund, repo fed fund, reverse repo

Assets +60% Deposits ?Treasury securities insuredAgency securities uninsuredMuni securitiesNon-agency MBS Short-term debts -20%Structured products Long-term debts ?Corporate debt

Loans +30% EquitiesC& I loansreal estate loansreceivables, leasing Contingent Liabilities ?


• Constant weights cannot capture market conditions, hence lead toimprecise even wrong measure.


What if not? - Macro evidence

Aggregate Liquidity Mismatch in the US Banking Sector (Figure 8)

• Using constant weight in good times leads to euphoria liquidity illusion

• Using constant weight in stressed times leads to overestimate liquidity stress


What if not? - Micro evidence

Bank Borrowing Decision based on ex ante Liquidity Condition (Table 5)

Pr [Y = 1borrow,t |LIQi,s ] = α + βLIQi,s + Controlsi,s + εi,t

Scaled LMI Scaled BB LCR NSFR

s = 2006Q1 -4.59*** -1.37 -0.00 0.59**(0.00) (0.20) (0.82) (0.05)

s = 2007Q1 -4.41*** -0.71 -0.00 -0.00(0.00) (0.50) (0.70) (0.98)

s = 2008Q1 -1.98*** -1.72 0.00 0.38(0.00) (0.10) (0.75) (0.17)

Control for Tier1 cap ratio, Tier1 lev ratio, and return on asset

N 1003 985 975 1002 984 975 897 882 875 897 882 875

Adj R2 0.10 0.09 0.07 0.05 0.04 0.03 0.05 0.04 0.05 0.06 0.04 0.05

• Y = 1borrow,t if a bank decides to borrow from Fed loans during the crisis, basedon the ex ante liquidity condition at time s.

• Banks with more liquidity mismatch are more likely to borrow in the crisis,whereas other liquidity measures cannot predict bank borrowing decision.


This Paper

We propose a novel measurement framework to gauge bank liquidity:LMI, the liquidity mismatch between the market liquidity of assets andthe funding liquidity of liabilities,

LMI it =∑k

λt,akait,k +

∑k′

λt,lk′ lit,k′ .

• ait,k and l it,k′ are bank i ’s assets and liabilities at time t

• Asset liquidity weight, λt,ak ∈ [0, 1], is determined by asset haircut,

λt,ak = 1−mt,k

• Liability liquidity weight, λt,lk′ ∈ [−1, 0), is determined by liabilitymaturity, Tk′ , and funding market condition µt ,

λt,lk′ = −e−µtTk′


Roadmap

• Part I: Propose a theoretical foundation for LMI

• Part II: Design an empirical framework for LMI

• Part III: Demonstrate the informativeness of LMI• macroprudential tool, stress test• measure a bank’s liquidity risk in differentiating the cross section of

bank’s credit crunch and borrowing decisions in the crisis


Part II: LMI - Empirical Design


Calculating LMI

LMI it =∑k

λt,akait,k +

∑k′


Asset liquidity weight:

λt,ak = 1−mt,k = exp (−(mk + δ · βkmPC1,t))

• m̄k is the average haircut for asset k over the sample

• mPC1 is the first principal component from a panel of haircuts

• βk is the loading of asset class k to mPC1

• δ bridges the gap b/w bilateral and triparty repo haircuts

Liability liquidity weight:

λt,lk′ = − exp(−κ · µtTk′).

• µt is the (negative) log of 3-month OIS-TBill spread

• Tk′ is the time-to-maturity of liability k ′

• κ scales the impact of funding liquidity condition


Data

1 Balance Sheet Information, (ait,k , lit,k′)

• Y-9C Regulatory Report during 2002:Q2 - 2014:Q3• 2882 BHCs, among them 754 BHCs are public

2 Haircuts, mt,k

• repo transaction data based on the Money Market Mutual Funds(MMMF) and their filings in SEC Edgar

• transactions in the secondary bank loan market

3 Market price of liquidity premium, µt

• the term structure of OIS-TBill spread

4 Based on our sample, replicate Basel III’s LCR, NSFR, andBerger-Bouwman liquidity creation measure


Liability-side Liquidity Weights: λlk′ = − exp(κ · µtTk ′)

µt = − ln(OIS − Tbill), Tk′ ∈ [0, 1] yr, , κ = 0.5


Haircuts by Collateral (Table 2)

Collateral Mean SD P5 P25 P50 P75 P95

A: Triparty repo market

Treasury bonds 0.018 0.003 0.012 0.016 0.020 0.020 0.020Agency bonds 0.017 0.002 0.016 0.016 0.016 0.017 0.020Municipal bonds 0.033 0.020 0.016 0.016 0.016 0.050 0.062Commercial paper 0.034 0.009 0.027 0.027 0.035 0.039 0.044Corporate debt 0.049 0.018 0.031 0.031 0.042 0.066 0.073Structured product 0.059 0.013 0.039 0.045 0.068 0.068 0.068Equity 0.073 0.023 0.052 0.052 0.066 0.090 0.114

B: Secondary loan market

Bank loan 0.061 0.083 0.010 0.020 0.020 0.060 0.255

Average 0.043 0.022 0.025 0.028 0.035 0.051 0.082

PC1 0.054 0.032 0.030 0.034 0.077 0.106 0.141


Asset Liquidity Weight (Table A.1)

λt,ak = exp (−(mk + δ · βkmPC1,t)) , δ = 5

Category(Schedule) Asset ak βk Source (Y-9C Report)

Cash cash and balances due from depository institutions - 1a, 1b(HC) federal funds sold - 3a

securities purchased under agreements to resell - 3b

Trading Assets Treasury securities 0.059 1(HC-D Col A) agency securities 0.059 2, 4a, 4b, 4d

securities issued by states and U.S. Pol. subdivisions 0.558 3structured product including non-agency MBS 0.303 4c, 4e, 5acorporate debt 0.508 5b

Available for Sale Treasury securities 0.059 1(HC-B Col D) agency securities 0.059 2, 4a(1)-(2), 4b(1)-(2), 4c(1)(a), 4c(2)(a)

securities issued by states and U.S. Pol. subdivisions 0.558 3, 4a(3), 4b(3), 4c(1)(b), 4c(2)(b)structured product including non-agency MBS 0.303 5a, 5bcorporate debt 0.508 6equity securities 0.652 7

Held for Maturity Treasury securities 0.059 1(HC-B Col B) agency securities 0.059 2, 4a(1)-(2), 4b(1)-(2), 4c(1)(a), 4c(2)(a)

securities issued by states and U.S. Pol. subdivisions 0.558 3, 4a(3), 4b(3), 4c(1)(b), 4c(2)(b)structured product including non-agency MBS 0.303 5a, 5bcorporate debt 0.508 6

Loans loans secured by real estates 1.004 1a(HC-C Col A) commercial & industry loans 1.004 4a, 4b

other loans 1.004lease financing receivables 1.004 10

Fixed Assets premises and fixed assets - 6(HC) other real estate owned - 7

investment in unconsolidated subsidiaries - 8, 9Intangible Assets goodwill and other intangible assets - 10Other Assets - 11


Liability Liquidity Weight (Table A.2)

λt,l′k

= − exp(−κ · µtTk′), κ = 0.5

Category (Schedule) Liability lk′ Tk′ Source (Y-9C Report)

Overnight Debt overnight federal funds purchased 0 14a(HC) securities sold under repo 0 14b

Deposits1 insured 10 1a, 1b

(RC-O Memo) uninsured 1

Trading Liabilities2 trading liabilities - 13a(HC-D)

Other Borrowed Money commercial paper 1/12 14a

(HC-M) with maturity <= 1 year 1 14b

with maturity > 1 year 5 14c

Other Liabilities subordinated notes and debenture 10 19a, 19b

(HC) other liabilities 10 20

Total Equity Capital equity 30 28(HC)

Contingent Liabilities3 unused commitments 5 1a,1b,1c,3a,3b,1e(HC-L) Credit Lines 10 2,3,4

Securities Lent 5 6, 8, 9

(HC-D) Collateral Values5 10 11, 14


Part III: Informativeness of LMI


What Makes a Good Liquidity Measure?

• From macro-prudential purpose:• It should quantitatively measure liquidity imbalances in the financial

system, offering an early indicator of financial crises.• It should provide an anchor for the amount of liquidity the Fed may

be called upon to provide in a financial crisis.

• From micro purpose:• It should capture liquidity risk in the cross-section of banks,

identifying which banks carry the most liquidity risk

• We show that banks with more liquidity mismatch• have a higher crash risk during the crisis;• have a higher probability to borrow from the government (Fed loans

and TARP) during the crisis


LMI as a Macro-Prudential BarometerAggregate Liquidity Mismatch in the Banking Sector

• LMI can be added up across banks, providing an anchor for fed liquidity injection.


LMI as a Macro-Prudential BarometerAggregate Liquidity Mismatch On- and Off-Balance Sheet

• Off-balance-sheet liquidity pressure (-$5trillion!) dominates during the crisis.


Contribution of Changing Liquidity Weights to LMI

• It is important to adopt market-implied time-varying weights


LMI under 1σ, 2σ Stress Scenarios

• LMI setup can be used to evaluate liquidity risk of banking sector.


Liquidity Stress Test

A. T=2007Q2 B. T=2007Q3 C. T=2012Q4

LMI [LMI ]− LMI [LMI ]− LMI [LMI ]−

Benchmark Benchmark Benchmark

T 1.72 -0.59 T -0.45 -1.72 T 8.03 -0.00[0,T ] 3.37 -0.07 [0,T ] 3.19 -0.15 [0,T ] 4.02 -0.30

Stress Scenarios Stress Scenarios Stress Scenarios

1-σ 0.29 -0.07 1-σ -3.37 -3.80 1-σ 5.95 -0.002-σ -1.68 -2.45 2-σ -7.80 -7.95 2-σ 3.56 -0.013-σ -4.44 -4.71 3-σ -14.5 -14.6 3-σ 0.16 -0.88


LMI Decomposition: Asset vs Liability

• Both asset-side and liability-side liquidty contribute to themovement in the LMI, yet the liability side plays a larger role.


Relation between Asset Liquidity and Liability Liquidity

Asset LMIit = α + β|Liab LMIit |+ εit .

(1) (2) (3) (4)|Liab LMI| 1.54*** 1.60*** 0.34*** 0.35***

(0.02) (0.02) (0.03) (0.03)Constant 66.06 62.26 137.60 52.99

(3.55) (3.35) (2.45) (12.67)

Time FE N Y N YBank FE N N Y YN 2500 2500 2500 2500R-squared 0.67 0.71 0.89 0.91

Note: ∗p < 0.10, ∗ ∗ p < 0.05, ∗ ∗ ∗p < 0.01

• Banks with more negative liability-side liquidity are likely, for liquiditymanagement reasons, to hold more liquid assets

• We verify the prediction of the model by Hanson, Shleifer, Stein, andVishny (2014), with refined measure and larger sample


Fed Liquidity Injection

Federal Reserve liquidity facilities during December 2007 to June 2010:559 financial institutions receive liquidity from the Fed, among which are87 BHCs.

Facility Announcement Expiration Participants Term

TAF Dec12, 2007 Mar08, 2010 Depository Inst. 28 or 84 days

TSLF Mar11, 2008 Feb01, 2010 Primary dealers 28 days

PDFF Mar16, 2008 Feb01, 2010 Primary dealers overnight

AMLF Sep19, 2008 Feb01, 2010 BHCs and branches < 120 days for D∗

of foreign banks < 270 days for non-D

CPFF Oct07, 2008 Feb01, 2010 U.S. CP issuers 3 months

MMIFF Oct21, 2008 Oct30, 2009 Money Mkt Funds 90 days or less

TALF Nov25, 2008 Jun30, 2010 U.S. eligible banks <5 years

*: D denotes depository institutions; non-D is non-depository institutions.


LMI and Bank Borrowing

∆LMI (post minus crisis) ∆LMI(crisis minus pre-crisis)

• Fed loans improve bank liquidity


Bank ex ante Liquidity (Risk) and Borrowing Decision-Tab5

Pr [Y = 1borrow |LIQi,t ] = α + βLIQi,s + Controlsi,s + εi,t

Scaled LMI Scaled (LMI – LMI1σ)

In 2006Q1 -4.59*** 14.19***(0.00) (0.00)

In 2007Q1 -4.41*** 11.07***(0.00) (0.01)

In 2008Q1 -1.98*** 2.94***(0.00) (0.00)


N 1003 985 975 1003 985 975Adj R2 0.10 0.09 0.07 0.06 0.05 0.05

• Results are robust for borrowing decision on both fed loans and TARP.

• Results are robust if LHS=log(Borrow Amt).


Bank ex ante Liquidity (Risk) and Borrowing Decision-Tab5

Pr [Y = 1borrow |LIQi,t ] = α + βLIQi,s + Controlsi,s + εi,t

Scaled BB LCR NSFR

In 2006Q1 -1.37 -0.00 0.59**(0.20) (0.82) (0.05)

In 2007Q1 -0.71 -0.00 -0.00(0.50) (0.70) (0.98)

In 2008Q1 -1.72 0.00 0.38(0.10) (0.75) (0.17)


N 1002 984 975 897 882 875 897 882 875Adj R2 0.05 0.04 0.03 0.05 0.04 0.05 0.06 0.04 0.05

• Results are robust for borrowing decision on both fed loans and TARP.

• Results are robust if LHS=log(Borrow Amt).


Bank Liquidity and Crash Probability (Table 6)

Pr(Crash = 1|Xi,s) = α + βLIQi,s + Controlsi,s + εi,t

Scaled LMI Scaled BB

In 2006Q1 -5.28*** 0.43(0.00) (0.67)

In 2007Q1 -4.95*** -1.07(0.00) (0.40)

In 2008Q1 -2.42** 0.06(0.02) (0.96)


N 339 345 349 339 345 349Adj R2 0.05 0.07 0.06 0.02 0.05 0.05

• Crash = 1 if the return of a bank’s stock is lower than -25% in onequarter or -35% in two quarters during the peak of financial crisis.

• Results are robust for alternative definitions in Xiong and Baron (2015)[-20% in one quarter, -30% in two quarters].


Bank Liquidity and Crash Probability (Table 6)

Pr(Crash = 1|Xi,s) = α + βLIQi,s + Controlsi,s + εi,t

LCR NSFR

In 2006Q1 0.10 0.16(0.15) (0.54)

In 2007Q1 0.07 1.01(0.57) (0.19)

In 2008Q1 -0.02 1.17(0.82) (0.15)


N 311 319 325 311 319 325Adj R2 0.03 0.06 0.04 0.03 0.07 0.05

• Crash = 1 if the return of a bank’s stock is lower than -25% in onequarter or -35% in two quarters during the peak of financial crisis.

• Results are robust for alternative definitions in Xiong and Baron (2015)[-20% in one quarter, -30% in two quarters].


LMI Performance under Various Sets of Parameters {δ, κ}

Fed Loan TARP CrashRow Scenario ¯λAk

¯λL′k

MIN SLMI DLMI SLMI DLMI SLMI DLMI

δ κ t1 t3 t1 t3 t1 t3 t1 t3 t1 t3 t1 t3

(1) 5.0 0.50 0.78 -0.45 -6.41 - - + + - - + + - - / /(2) Real 0.50 0.75 -0.45 -6.43 - - + + - - + + - - / /(3) 3.5 0.50 0.80 -0.45 -6.18 - - + + - - + + - - / /(4) 7.9 0.50 0.73 -0.45 -6.82 - - + + - - + + - - / /

(5) 5.0 1.00 0.78 -0.38 -2.72 - - + + - - / + - - / /(6) 3.5 1.00 0.80 -0.38 -2.29 - - + + - - / + - - / /(7) 7.9 1.00 0.73 -0.38 -3.04 - - + + - - / + - - / /

(8) 5.0 1.50 0.78 -0.34 -0.30 - - + + - - / + - - / /(9) 3.5 1.50 0.80 -0.34 -0.07 - - + + - - / + - - / /

(10) 7.9 1.50 0.73 -0.34 -0.72 - - + + - - / + - - / /

(11) 5.0 0.25 0.78 -0.53 -9.47 - - + + - - + + - - / /(12) 3.5 0.25 0.80 -0.53 -9.24 - - + + - - + + - - / /(13) 7.9 0.25 0.73 -0.53 -9.88 - - + + - - + + - - / /

(14) 5.0 2.00 0.78 -0.32 1.06 - - + + - - / + - - / /(15) 3.5 2.00 0.80 -0.32 1.29 - - + + - - / + - - / /(16) 7.9 2.00 0.73 -0.32 0.64 - - + + - - / + - - / /

• LMIs under various sets of parameters overall generate robust results

• LMI performance using the real bilateral data is similar to that using δ = 5

• LMI minimum value become unreasonable when κ is too small (0.25) or too large (>1.50)


LMI Performance under Various Sets of Parameters {δ, κ}

Fed Loan TARP CrashRow Scenario ¯λAk

¯λL′k

MIN SLMI DLMI SLMI DLMI SLMI DLMI

δ κ t1 t3 t1 t3 t1 t3 t1 t3 t1 t3 t1 t3

(1) 5.0 0.50 0.78 -0.45 -6.41 - - + + - - + + - - / /(2) Real 0.50 0.75 -0.45 -6.43 - - + + - - + + - - / /(3) 3.5 0.50 0.80 -0.45 -6.18 - - + + - - + + - - / /(4) 7.9 0.50 0.73 -0.45 -6.82 - - + + - - + + - - / /

(5) 5.0 1.00 0.78 -0.38 -2.72 - - + + - - / + - - / /(6) 3.5 1.00 0.80 -0.38 -2.29 - - + + - - / + - - / /(7) 7.9 1.00 0.73 -0.38 -3.04 - - + + - - / + - - / /

(8) 5.0 1.50 0.78 -0.34 -0.30 - - + + - - / + - - / /(9) 3.5 1.50 0.80 -0.34 -0.07 - - + + - - / + - - / /

(10) 7.9 1.50 0.73 -0.34 -0.72 - - + + - - / + - - / /

(11) 5.0 0.25 0.78 -0.53 -9.47 - - + + - - + + - - / /(12) 3.5 0.25 0.80 -0.53 -9.24 - - + + - - + + - - / /(13) 7.9 0.25 0.73 -0.53 -9.88 - - + + - - + + - - / /

(14) 5.0 2.00 0.78 -0.32 1.06 - - + + - - / + - - / /(15) 3.5 2.00 0.80 -0.32 1.29 - - + + - - / + - - / /(16) 7.9 2.00 0.73 -0.32 0.64 - - + + - - / + - - / /

• δ = 5, κ = 0.5 is the reasonable choice.


Part I: LMI - Theoretical Foundation


Liabilities-side Liquidity LMI{l it,T}

Dynamic optimization problem

V S({l it,T}, t) =

flow of profits︷︸︸︷(∫ ∞t

l it,Tπt,TdT

)dt +

cost of liquidity︷︸︸︷(−θi l it,t

)dt

+µdt V NS({l it,T}, t + dt

)+ (1− µdt)V S

({l it,T}, t + dt

)• V S({l it,T}, t) is the bank’s value in stress episodes, and V NS is the

bank’s value in non-stressed episodes

• {lt,T} is a stream of liabilities maturing at time T

• πt,T is premium by issuing debt lt,T (πt,S > πt,T for S < T )

• θi is cost per dollar of liquidity needed to cover the stress

• µdt is the probability that at date t + dt the stress episode ends


Liabilities-side Liquidity LMI{l it,T}

We define

V ({l it,T}, t) ≡ Π({l it,T}, t) + θiLMI ({l it,T}, t)

The profit function is recursive:

Π({l it,T}, t) =

(∫ ∞t

l it,Tπt,TdT

)dt + Π

({l it+dt,T}, t + dt

)Then the liquidity need at time t, LMI ({l it,T}, t) can be expressed as:

LMI ({l it,T}, t) = −l it,tdt + (1− µdt)LMI ({l it+dt,T}, t + dt) (1)


Liability-side Liquidity Weights λT−t

Look for an LMI function that is maturity invariant:

LMI ({l it,T}, t) =

∫ ∞t

l it,TλT−tdT ,

where λT−t is a liquidity weight at time t for a liability that matures attime T .

Substitute the candidate function into the recursion equation and solve,

λT−t = −e−µ(T−t).


Measuring µ

Bank’s problem:

max{l it,T}

Π({l it,T}, t) + ψiθiLMI ({l it,T}, t)

with FOC: ∫ T

t

πs,Tds = ψiθie−µt(T−t)

We measure π using OIS-TBill as a proxy for a liquidity premium π:

−µt = κ ln(OIS-Tbill).

• Intuition: liquidity weights should be based on market prices of liquidity

• Small OIS-TBill means high µ (shorter duration of stress event)

• κ is a free parameter which scales the relation between OIS-Tbill and µt


Assets-side Liquidity LMI{ait,k}

Define cash that can be sourced from assets:

wt =∑k

(1−mt,k)ait,k

Bank problem in a stress event:

LMI ({l it,T},wt , t) = max∆t≥0

(−max(l it,t −∆t , 0)dt

+(1− µdt)LMI ({l it+dt,T},wt + dwt , t + dt))

where,dwt = −∆t .

Solution: Set ∆t = lt,t .


LMI Summary

LMI it =∑k

λt,akait,k +

∑k′


Asset-side liquidity weight

λt,ak = 1−mt,k

and Liability-side liquidity weight:

λt,lk′ = −e−µtTk′ .


Conclusion

• We propose and implement a liquidity measurement system.

• The LMI is useful for macro-prudential purposes

1 It can be aggregated2 It can be “stressed”

• LMI is also informative in the cross-section that predict bank’s crashrisk, bank’s borrowing decision from Fed loans and TARP.

1 It contains additional information beyond Tier1 Leverage ratio,Capital ratio, Risk-adj Asset Ratio, bank profitability, etc

2 It contains more accurate information than other liquidity measures,such as Basel III LCR, NSFR, and liquidity creation in Berger andBouwman (2009).


Measuring Liquidity Mismatch in the Banking Sectort;k + X k0 ;l 0 l i t;k0: ai t;k and l i t;k0 are...

Documents

Transcript of Measuring Liquidity Mismatch in the Banking Sectort;k + X k0 ;l 0 l i t;k0: ai t;k and l i t;k0 are...