haircuts and repo rates: evidence from money market mutual

Aggregate Patterns of Repo FundingTheory

Empirical Results

Haircuts and Repo Rates:Evidence from Money Market Mutual Fund Filings

Arvind Krishnamurthy1 Stefan Nagel2 Dmitry Orlov2

1Northwestern University

2Stanford University

November 2010

Arvind Krishnamurthy, Stefan Nagel, Dmitry Orlov Repo


Empirical Results

Funding of Shadow banks

MMMFBroker/Dealer

HedgeFunds

SPV(agency/non‐

agency)

Repo

Repo

ABCP

ABS

Treasuries

CorporatesecuriAes

ABCPconduit

Mortgages

Loans

ABS

“deposits”($1NAV)



Empirical Results

Tri-Party Repurchase Agreements

MMMF

Tri‐partyClearingAgent

$95m

Collateralworth$100m

$95m

Collateralworth$100m

Broker/Dealer

Haircut: 5% in this example

Repo rate: Interest paid by borrower on loan amount ($95m)

Daily unwind: Irrespective of repo term, each morning cashreturned to lender and security to borrower. Thus, intra-daycounterparty risk shifted to tri-party agent.



Empirical Results

Objectives

Which role did repo market play in financial crisis?

How big is repo funding? Often used federal Reserve data onprimary dealer repos includes inter-dealer repos(double-counting issue)“Run on repo” an in important part of the breakdown of“securitized banking” (Gorton and Metrick 2009)? Evaluatesize of repo funding with private-label ABS/MBS as collateral

How are repos structured and risks priced?

Participation constraints, haircuts, repo ratesEvaluate role of counterparty risk, collateral risk, ...View through lens of theories of collateralized lending andsecurity design

We obtain data on repo agreements of MMF from quarterlySEC filings (N-CSR, N-CSRS, N-Q) 2006Q4-2010Q2



Empirical Results

Example: Reserve Fund – Primary Fund

February 29, 2008 Repurchase Agreements

Notional Counterparty Rate Init. Rep. Collateral Coll. mkt.val.

1,000,000,000 Bear Stearns 3.28%, 2/29/08, 3/3/08 ABS, CMO, TRR, TR3 1,048,922,871450,000,000 Bear Stearns 3.33% 2/29/08 3/3/08 ABS, CMO 472,500,201500,000,000 Citigroup 3.23% 2/29/08 3/3/08 MNI, TRR 556,131,379140,000,000 Merrill Lynch 3.43% 2/29/08 3/3/08 WLR 146,599,1931,000,000,000 Morgan Stanley 3.29% 2/29/08 3/3/08 WLR 1,020,794,540...



Empirical Results

Data collection

Concentrated market: Biggest 10 MMF families control about60% of MMF assets under management

Aim: Collect data for 20 biggest MMF families

Completed so far:

BlackrockFidelityJPMorganReserve FundsMorgan StanleyVanguardDreyfusGoldman SachsFederated Funds



Empirical Results

Outline

1 Aggregate Patterns in Repo Funding

“Run on Repo” quantitatively important?

2 Theory: repo market participation, collateral choice, maturity,haircuts, repo rates

3 Empirical results



Empirical Results

Coverage of MMF Filings Sample

Quarter MMF Repo MMF Repo MMF Primarycollected Total Assets Dealer Repo($bn.) (FoF, $bn.) (FoF, $bn.) (NY Fed, $bn.)

2006Q4 (133)1 395 2312 34422007Q1 202 387 2372 36192007Q2 205 426 2466 38892007Q3 258 528 2780 38862007Q4 283 606 3033 41062008Q1 307 592 3383 42782008Q2 273 518 3318 42222008Q3 261 592 3355 39892008Q4 276 542 3757 32082009Q1 367 562 3739 27432009Q2 339 488 3585 25822009Q3 325 495 3363 24992009Q4 338 480 3259 24692010Q1 296 440 2931 24772010Q2 (66)1

1Incomplete coverage in 2006Q4 and 2010Q2Arvind Krishnamurthy, Stefan Nagel, Dmitry Orlov Repo


Empirical Results

Share of Collateral by Type (by value)

.4.6

.81

Sh

are

2007q1 2008q1 2009q1 2010q1Quarter

U.S. Treasury Agency Priv. ABS

Corporate Other



Empirical Results

Comparison with ABCP Issuance

0.0

5.1

.15

Priv. A

BS

Share

50

100

150

200

250

Issuance (

)

2007q1 2008q1 2009q1 2010q1Quarter

ABCP Issuance Priv. ABS Share

Issuance of 80day+ ABCP net of amount funded through FedCPFF programTotal contraction of ABCP outstanding ≈ $700bn. comparedwith pre-crisis repo with priv. ABS/MBS collateral ≈ $60bn.



Empirical Results

Maturity percentiles (vw.)

05

01

00

15

02

00

25

0M

atu

rity

(b

usin

ess d

ays)

2006q3 2007q3 2008q3 2009q3 2010q3Quarter

99th 98th 95th 90th



Empirical Results

Maturity percentiles (ew.)

05

01

00

15

02

00

25

0M

atu

rity

(b

usin

ess d

ays)

2006q3 2007q3 2008q3 2009q3 2010q3Quarter

90th 80th 70th 60th



Empirical Results

Haircuts by Collateral Type (vw.)

24

68

Pe

rce

nt

2007q1 2008q1 2009q1 2010q1Quarter


Corporate Other



Empirical Results

Average Repo Rate (vw.) and Fed Funds Rate/OIS

02

46

Pe

rce

nt

2006q3 2007q3 2008q3 2009q3 2010q3Quarter

Fed Funds Rate/OIS Average Repo Rate (vw.)



Empirical Results

Excess Repo Rate by Collateral Type (vw.)

−1

−.5

0.5

1P

erc

en

t

2007q1 2008q1 2009q1 2010q1Quarter


Corporate Other



Empirical Results

LiteratureModelResults

Haircuts and Repo Rates: Theory

Modigliani-Miller: Haircut and repo rate indeterminate

Haircut = leverageRepo rate = cost of debt

Theories of equilibrium haircuts with frictions

Geanakoplos (2009): Differences in beliefs between borrowerand lender about payoffs from collateral. Equilibrium haircutcreates default-free debtDuffie and DeMarzo (1999); Dang, Gorton, Holmstrom(2010): Asymmetric information about collateral payoffsbetween borrower and lender. Equilibrium haircut createsinformation-insensitive security (if sufficient concern aboutadverse selection).



Empirical Results


Theory of Haircuts and Repo Rates

Common predictions of belief divergence and asy. informationstories

Haircuts should vary with risk of collateral, but repo ratesshould (mostly) notCounterparty risk should have little effect on haircuts and reporates

Theories miss some aspects that seem important in practice

Repo is not no-recourse: Repo lenders have recourse toborrowers balance sheet in event of defaultDifferences in beliefs and asy. information can not explainexclusion of high-risk counterparties and low-quality collateralfrom repo market



Empirical Results


Model

Two dates, t0 and t1.

Single risky asset with t0 price P0 = 1 (partial equilibrium)

Borrower (trading desk in a bank) considers purchase of oneunit of risky asset with funding

1− h from repo lender (MMF), collateralized by risky asset,i.e., with haircut hh from bank (“equity”)

Four states of nature: At time t−1 just before date t1, thebank defaults with probability πd . Then, at t1, independent ofwhether the bank defaulted or not, the risky asset can betraded at price of R > 1 in the good state and L < 1 in thebad state.

Lenders are competitive. Lender, bank, and borrower arerisk-neutral.



Empirical Results


Key assumptions

Belief divergence: Borrower and bank perceive the probabilityof the bad state to be pb, while lenders have a morepessimistic belief pl > pb, as in Geanakoplos (2009)

Equity financing friction: Bank discounts expected paymentfrom “trading desk” by by 0 ≤ α ≤ 1

Liquidation cost: Lender pays cost δ per $1 of face value ifshe has to take possession of the collateral in the event thebank defaults

Recourse: In the event of default on repo loan, lender hasrecourse to bank balance sheet, so unless bank defaults, thebank bears the losses on the risky asset in the bad state



Empirical Results


Valuation and Objective

Repo: Lender has to offer face value (repurchase value) F (h)that satisfies

(1− h) =(1− πd)F (h) + πd [(1− pl)F (h) + pl min(L,F (h))]

− πdδF (h)

Equity: Borrower pays bank payment of E (h) in good state,which must satisfy

h =α[(1− pb)E (h) + (1− πd)pb(L− F (h))+

πdpb max(L− F (h), 0)]

The borrower’s objective is given by

maxh

(1− πd)(1− pb)(R − E (h)− F (h))



Empirical Results


Results

Borrowers objective is piecewise linear: Borrower (weakly)prefers either zero leverage, risk-free repo with high haircut, orrisky zero-haircut repo

Non-participation: Zero leverage is preferred over risk-freerepo if

1− πdδ

α< 1

Haircut: Risk-free repo preferred over risky zero-haircut repo if

1− πdpl

1− πdpl − δπd

(1− πdpb

1− πdpl+

(α− 1)(1− pb)

1− πdpl

)> 1



Empirical Results


Illustration of Non-Participation: Borrower Objective

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.031

0.032

0.033

0.034

0.035

0.036

0.037

Haircut

Base

Higher default prob.

Higher liq. cost

Base case: R = 1.1, L = 0.8, pb = 0.2, pl = 0.5, α = 0.996,πd = 0.02, and δ = 0.1.

Alternative cases with πd = 0.04 or δ = 0.2.



Empirical Results

Participation, Collateral Choice, MaturityHaircutsRepo Rates

Counterparty Participation

Model

Model: Non-participation (zero leverage) is preferred overrisk-free repo if

1− πdδ

α< 1

Holding δ and α fixed, this implies participation constraintbased on πd

Empirically

Counterparty risk measure x (5yr Sr. CDS rate) as empiricalcounterpart to πd

We only observe participants, so not possible to estimateparticipation condition



Empirical Results


Distribution of Counterparty CDS Rates

0.0

5.1

.15

.2F

ractio

n

0 200 400 600 800 1000Counterparty 5−yr. Senior CDS rate (bps)



Empirical Results


Collateral Choice

Model

Non-participation (zero leverage) is preferred over risk-freerepo if

1− πdδ

α< 1

Holding α fixed, participation with high-δ collateral only if πd

low

δ likely higher with higher collateral risk



Empirical Results


Collateral Choice

Empirically

Collateral category q ∈ {0, 1, 2} ordered by collateral risk(Treasuries, Agencies, Others)

Choice of q modeled as function of latent variable q∗,

q∗ = a′0z + a1x + a2g + η, η|z , x , g ∼ N (0, 1)

where q = 0 if q∗ ≤ θ1, q = 1 if θ1 < q∗ ≤ θ2, q = 3 ifq∗ < θ3.

Macro variables z may help capture time-variation in δ

Government MMF dummy g , can be viewed as proxy forfunds that face extremely high δ for riskier collateral

Estimation of P(q = 0|x , z), ..., P(q = 3|x , z) with orderedprobit



Empirical Results


Collateral by Counterparty CDS Rate

0.2

.4.6

.81

Fra

ctio

n (

by v

alu

e)

< 50bps 50bps − 100bps 100bps − 250bps > 250bps

U.S. Treasury Agency Other



Empirical Results


Collateral Choice: Ordered Probit

Marginal effects on collateral-category probabilities

3mLIBOR-OIS spread and CDS rates in percentVIX in percent divided by

√250

(1) (2) (3)U.S. Treasury Agency Other

3mLIBOR-OIS -0.053 0.009 0.045(0.065) (0.010) (0.055)

VIX 0.137 -0.022 -0.115(0.035) (0.005) (0.032)

Govt. MMF dummy 0.570 -0.128 -0.442(0.023) (0.019) (0.022)

Counterparty CDS Rate -0.009 0.001 0.008(0.013) (0.002) (0.010)

Observations 7968 7968 7968



Empirical Results


Maturity Choice

Higher counterparty risk also likely implies increasedprobability of a future substantial revision of counterparty risk:With shorter maturity lender retains option to terminate,which reduces expected liquidiation costs

Shortening of maturity may be first response before reachingnon-participation status

Regressionlog(m) = b′0z + b1x + ν



Empirical Results


Maturity by Counterparty CDS Rate

05

10

15

Ave

rag

e I

nitia

l M

atu

rity

(d

ays,

va

lue

−w

eig

hte

d)

< 50bps 50bps − 100bps 100bps − 250bps > 250bps



Empirical Results


Maturity Choice: OLS

Dependent variable: Log of initial maturity

3mLIBOR-OIS 0.236(0.183)

VIX -0.161(0.138)

Custodian CDS Rate -0.147(0.223)

Counterparty CDS Rate -0.304(0.052)

Observations 7967Adjusted R2 0.024



Empirical Results


Maturity Choice: Probit

Marginal effects on probability that repo is overnight

3mLIBOR-OIS 0.012(0.044)

VIX -0.003(0.028)

Custodian CDS Rate -0.057(0.047)

Counterparty CDS Rate 0.092(0.019)

Observations 7968



Empirical Results


Haircuts

Model

Haircut set so that repo is riskless

Generalizing to more realistic setting where haircut makesrepo almost, but not entirely riskless: Collateral risk should beprimary influence, as higher haircut does alter πd and δ



Empirical Results


Haircuts

Empirically

Regression

h = c ′0z + c1x + c2m + c3w + ξ

with collateral risk measures w

Collateral volatility: Standard deviation of collateral index pricechanges in prior monthCollateral worst return: Worst daily price change of collateralindex in prior five years



Empirical Results


Haircuts: Collateral Risk and Counterparty Credit Risk

Collateral indices

Treasuries: Barclays US Treasury IndexAgency: Barclays US MBS indexPrivate-label MBS/ABS: Barclays US ABS home equityCorporate: Barclays US Corporate Investment GradeCommercial Paper: Fed St. Louis Commercial paper (priceindex constructed from yields)Certificates of Deposit: BBA 3m LIBOR (price indexconstructed from yields)Munis: Barclays Municipal BondEquity: S&P500 index



Empirical Results


Decomposing Variation in Haircuts

Nonparametric approach: Dummy variable regressions

Time dummies (year-month)Time dummies interacted with collateral, counterparty,maturity dummies

Incremental R2 DGF F p-value

Collateral×Time 0.38 219 37.51 0.00Counterparty×Time 0.02 801 1.67 0.00Maturity×Time 0.02 50 7.01 0.00Full 0.67 1114 15.05 0.00



Empirical Results


Haircuts: Regression

3mLIBOR-OIS -0.607(0.159)

VIX -0.197(0.099)

Initial maturity 0.004 0.003(0.001) (0.001)

Collateral volatility 1.546 1.657(0.255) (0.271)

Collateral worst return -0.282 -0.243(0.020) (0.022)

Counterparty CDS Rate 0.167 0.131(0.063) (0.056)

Year-month dummies N YObservations 7521 7521Adjusted R2 0.357 0.384



Empirical Results


Repo rates

Model

Haircut set so that repo is riskless, but in more general casewhere risk not entirely eliminated, risk-neutral valuationimplies repo rate

r =πd

1− πdpl − πdδ(λ(h) + δ)

where

λ(h) = pl

(1− L

1− h

)is the expected loss (to the lender) given default.



Empirical Results


Repo rates

Empirically

Empirical measurement of λ(h)

Gaussian expected loss

φ(−h/σ)

Φ(−h/σ)σ

where σ is measured by the standard deviation of collateralindex price changes in prior monthHaircut-adj. collateral worst-return: Worst daily price changeof collateral index in prior five years in excess of haircut

Regression

r = d ′0z + d1m + d2x + d3λ(h) + d4(x × λ(h)) + ξ



Empirical Results


Decomposing Variation in Excess Repo Rates

Incremental R2 DGF F p-value

Collateral×Time 0.32 219 29.49 0.00Counterparty×Time 0.06 806 1.59 0.00Maturity×Time 0.04 50 17.42 0.00Full 0.62 1119 13.14 0.00



Empirical Results


Excess Repo Rates: Regression

3mLIBOR-OIS 0.146 0.145(0.083) (0.083)

VIX -0.080 -0.075(0.064) (0.066)

Custodian CDS Rate 0.069 0.059(0.075) (0.075)

Initial maturity -0.000 0.000 -0.000 0.000(0.000) (0.000) (0.000) (0.000)

Counterparty CDS Rate -0.031 -0.041 -0.069 -0.086(0.039) (0.036) (0.073) (0.070)

Expected loss λ(h) 0.092 0.089 0.081 0.073(0.013) (0.013) (0.015) (0.014)

Haircut-adj. collateral worst return -0.012 -0.007 -0.025 -0.014(0.006) (0.006) (0.010) (0.009)

λ(h)× Counterparty CDS rate 0.010 0.013(0.013) (0.013)

Haircut-adj. coll. worst return × Counterparty CDS rate 0.013 0.009(0.010) (0.009)

Year-month dummies N Y N YObservations 7065 7065 7065 7065

Adjusted R2 0.131 0.222 0.133 0.224



Empirical Results


Conclusion

Aggregate amounts of repo funding provided by MMF

Private-label ABS/MBS completely disappear as collateral in2008/2009, but aggregate amount small relative to contractionin ABCP: “Run on repo” may be symptomatic for relatedproblems, but by itself not a major factor in breakdown ofshadow bank financing

Terms of tri-party repo agreements

Counterparty risk in repo markets affects participation,collateral choice, and maturityConditional on participation and collateral choice, counterpartyrisk has little influence on haircuts and repo ratesCollateral risk is main driver of haircuts and repo rates, and“long memory” of realized tail events seems to matter inaddition to recent volatilityElevated levels of haircuts and repo rates still persist sincecrisis


haircuts and repo rates: evidence from money market mutual

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