Diagnosing the LIBOR: Strategic Manipulation and Member

Portfolio Positions

Connan Snider∗

UCLA

Thomas Youle†

University of Minnesota

December 2009

Preliminary and Incomplete

Abstract

The London Interbank Offered Rate (Libor) is a vital benchmark interest rate to

which hundreds of trillions of dollars of financial contracts are tied. We supply new

evidence that panel banks may have acted strategically when quoting rates to the Libor

survey. This evidence stems from discontinuities involved in the Libor’s construction.

We introduce a simple model where banks’ possession of Libor indexed contracts leads

them to quote rates that are clustered at discontinuities and show that such clustering

has been severe in the 3-Month U.S. Libor throughout 2009. We then present suggestive

evidence that several banks have large exposures to the Libor through their interest

rate derivative portfolios and have recently profited from the rapid descent of the Libor.

∗Department of Economics, UCLA, snider@econ.ucla.edu, ph: (310) 794-7104.†Department of Economics, University of Minnesota, youle001@umn.edu, ph: (612) 298-4807.

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1 Introduction

The London Interbank Offered Rate (Libor) is a widely used benchmark interest rate,

intended to reflect the average rate at which banks can borrow unsecured funds from other

banks. The Libor is set daily by surveying the borrowing costs of 16 large banks. Since its

introduction in 1986, the Libor has steadily grown in importance and is now among the

most widely used indexes in financial contracts. The British Bankers Association (BBA)

estimates that $10 trillion of loans and $350 trillion of swaps are indexed by the Libor. Since

the upheaval in financial markets that began in August of 2007, the Libor has diverged

from many of its historical relationships causing market observers to question its proper

functioning. An influential article by Mollenkamp and Whitehouse (2008) argued that

the Libor was too low and suggested that banks in the panel were intentionally quoting

rates below their true borrowing costs in order to burnish the markets’ perception of their

riskiness.

In this paper we present several new types of evidence that banks have been misreport-

ing their true borrowing costs and consider an alternative source of misreporting incentives:

Bank portfolio exposure to the Libor. We present a simple model of bank quote submis-

sion in which members may or may not have financial incentives to misreport their true

borrowing costs. The model predicts that in the presence of these misreporting incentives

we should see “bunching”of quotes at particular points. This second prediction is due to

the form of the rate setting mechanism, which averages the middle eight quotes of the six-

teen. Banks with incentives to misreport will bunch around the pivotal fourth and twelfth

lowest quotes while those with no such incentives will not. Under the reputational theory

of misreporting, a bank cares about how the market perceives its own quote and not the

Libor fix itself. It therefore does not predict that banks will bunch around the pivotal

quotes. In this sense, we present evidence in favor of the portfolio hypothesis and against

the reputation hypothesis. Moreover, using more recent data, we show that evidence of

misreporting is stronger in the period since markets have calmed somewhat from their

recent upheaval. In concluding, we discuss the very different policy implications of the two

stories.

2

The Libor rates are computed daily by a survey administered by the BBA to a fixed

panel of 16 large banks. The banks are asked,

At what rate could you borrow funds, were you to do so by asking for and

then accepting inter-bank offers in a reasonable market size just prior to 11am

London time?

The four largest and smallest rates are then excluded and the average of the middle eight

responses determines that day’s Libor rate, or fix. In our model, banks have incentives to

push the Libor in one direction or the other but may face penalties for quotes that are too

different from other banks’ quotes or for quotes that are too different from actual costs.

These penalties may include the costs of being sanctioned by the BBA for manipulating the

rate or the costs of being sanctioned by the market for being an outlier. Since the top four

and bottom four quotes are excluded the expected marginal impact on the trimmed average

falls quickly as quotes increase or decrease, and thus the marginal incentives associated with

manipulating the rate also fall. In the case that banks can perfectly forecast the fourth

and twelfth highest quotes, the marginal benefits to misreporting change discontinuously

at these points, which leads to a bunching of quotes at these points.

After presenting our “bunching” evidence for the existence of strategic behavior in the

Libor panel, we go on to explore the potential magnitude of these incentives to misreport.

To do this we look at the call reports filed with the FDIC for three of the largest banks

in the panel, who also submit quotes near the lower discontinuity. We show that these

banks have recently generated large revenues from their interest rate portfolios during the

rapid descent of the Libor in 2009 and that these banks likely have a significant unhedged

exposure to the Libor. While we can not observe their exact exposures, we show that even

small unhedged exposures can generate very large payoffs for these banks, given the huge

notional value of their interest rate swap positions.

The rest of the paper proceeds as follows: In section 2 we discuss the recent history of

the Libor and the facts that have given market observers pause. In section 3 we present a

simple model of bank quote setting where banks’ payoffs depend upon the overall Libor rate.

Section 4 presents our evidence of strategic behavior suggested by the model. Section 5

presents our evidence that several panel banks have large Libor positions and have recently

profited from the Libors recent descent. Section 6 concludes.

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2 Recent History of the Libor

The financial turmoil of 2007 - 2009 witnessed abrupt changes in the behavior of several

financial and money market indicators. There has been significant debate about the causes

of this behavior and even about the facts (see e.g. Chari, Christiano and Kehoe (2008),

Cole-Cohen (2008), and Christiano (2008)). In this section we give some relevant recent

history, focusing on the aspect of Libor behavior that has most troubled market observers:

Its unusual relationship to other measures of bank borrowing costs.

Mollenkamp and Whitehouse were the first to point out the anomalous behavior of bank

Libor quotes with respect to credit default swap (CDS) spreads, an important measure of

bank risk.1 Figure 1 illustrates an example of this odd behavior. The figure plots one

year Libor quotes and one year senior CDS spreads for Citigroup and Bank of Tokyo-

Mitsubishi. Despite Citi’s much higher CDS spread, it actually quotes below Bank of

Tokyo in the Libor. Citi’s quotes are, in fact, often considerably lower than its own CDS

spreads. This implies that there are market participants willing to offer loans at rates

at which, after purchasing credit protection, would earn a substantially negative return.2

Figure 2 shows a lower bound on the Libor based on the rule for pricing loans as the risk

free rate plus the CDS spread.3 What is notable about the picture is it highlights bank

behavior after the crisis had receded, the only time the lower bound rate actually spikes

above the actual rate, even as other indicators had returned to their normal ranges.

The Mollenkamp and Whitehouse analysis is somewhat at odds with the findings of

Taylor and Williams (2008a, 2008b) who find evidence that, at the level of the Libor fix,

increasing bank risk does explain much the behavior of the rate. Taylor and Williams look

1Credit default swaps are insurance contracts purchased on securities that payout in the event of theirdefault. The amount paid is the difference between the post-default market value of the securities and theirpar value. The rate on a CDS can be thought of as measuring the market’s perception of the default riskof the firm.

2A standard method of pricing debt sets rates as the sum of the risk free rate and the CDS spread. Theoption pricing textbook Hull (2009 p528) shows how to use CDS spreads to compute bond yields. Whilethe Libor rates refer to loans instead of bonds it is unlikely that recovery rates for uncollateralized loanswould exceed that of senior bonds. Furthermore, as loans are relatively illiquid, loan rates could presumablyinclude a liquidity or other premia. If so, the sum of the CDS spread and the risk free rate would constitutea lower bound on what the loan rate should be.

3Not all of the banks in the Libor panel have a publicy traded 1 year CDS spread, although in oursample we always have at least 12 such spreads. We assume the 4 unobserved spreads are lower than all ofthese we observe, so that if banks quoted their CDS spreads plus the riskfree rate, those quotes would bein the excluded lower four. If, instead, these 4 unobserved spreads are typical then the lower bound wouldbe considerably higher. We use one year treasury bonds as the risk free rate.

4

at the spread between the Libor and the current market rate for Overnight Index Swaps

(OIS), an important measure of stress in money markets. OIS’s are agreements where one

party pays a fixed rate of interest over the period in return for the average of the overnight

Fed Funds rate for that period. Since OIS’s do not involve the exchange of a principal

they are considerably safer than loans - the most that could be lost is a spread of interest

payments accruing over a short period. As they are low risk, we consider OIS rates as being

determined primarily by interest rate expectations. The difference between the Libor and

the OIS rate is then a measure of risk and liquidity frictions in money markets. Figure

3 shows that the Libor-OIS spread has spiked during the crisis periods after August 2007

but recently has fallen to their previous levels. Figure 3 also shows that CDS spread also

spiked during the crisis period, but unlike the Libor-OIS spread have not come down.

Table 1 displays the results of regressions similar to those performed in Taylor and

Williams, now including more recent data up to October 2009. Regressing the overall

Libor fix on the Median CDS spread delivers a coefficient of 0.621 which is within the

range of coefficients found by Taylor and Williams in their earlier period.4 We then regress

the individual Libor rates submitted by panel banks on their corresponding individual

CDS spreads and find a smaller effect. Controlling for bank-level heterogeneity in the

spreads reduces the coefficient further and it becomes negligible once we control for serial

correlation in the error terms. The estimated serial correlation is reported as ρ and is very

large, as might be expected when working with daily frequency data of this type. Note

that the standard practice of pricing bonds suggests a regression of bond rates on CDS

spreads of identical maturities should yield a coefficent near 1.

Comparing the within and between R2 of these estimators is suggestive of why the

relationship between Libor-OIS and CDS spreads breaks down at the bank-level. CDS

spreads seem to do a better job of explaining the quote changes within a single bank than

explaining the differences in quotes between banks. This is immediate given the differences

in rank ordering as shown in figure 1 where banks with comparatively high CDS spreads

submit comparatively low quotes. Furthermore, once we introduce bank-level fixed effects

and control for a serial correlation, CDS no longer seem able to explain even the within

variation in bank-level Libor-OIS spreads.

More suggestive evidence can be found by looking at bank behavior in other markets.

4We also note that we do not attempt to model the impact of Federal Reserve actions on Libor-OISspreads, as in Taylor and Williams. They find these impacts have little economic or statistical signifancewe ignore them here, as our focus is on banks decisions in submitting Libor quotes.

5

Table 1: Bank-level 3 Month LIBOR-OIS Spreads

LIBOR Bank-level LIBOR quotes

Pooled Random Fixed Random FixedOLS Effects Effects Effects, Effects,

AR(1) AR(1)

Median 0.621CDS (0.035)

CDS 0.474 0.373 0.377 0.039 0.038(0.102) (0.098) (0.098) (0.009) (0.009)

Constant 0.173 0.112 0.333 0.334 0.505 0.921(0.020) (0.036) (0.067) (0.090) (0.085) (0.001)

N 581 19235 7839 7839 7839 7824R2 0.296 0.372Within R2 0.199 0.199 0.199 0.002Between R2 0.001 0.001 0.001 0.005ρ 0.995 0.995

6

The BBA publishes benchmark Libor rates in 10 different currencies, each with their own

fixed panel of banks. Figure 4 shows the fix for five such Libor benchmarks. Several

features of the series stand out. First the dollar Libor and, to a lesser extent, the pound

Libor sharply decline in the fall of 2007. Second the dollar Libor experiences a sharp

increase in the fall of 2008 and then declines, as do all the rates.

Many banks participate in multiple Libor panels and presumably there is some rela-

tionship between their borrowing costs in these different currencies. In the period starting

around August 2007, it has become common for a bank included in multiple currency Li-

bor panels to simultaneously quote a higher rate than another bank in one currency panel

and lower rate in another currency. Figure 5 shows the differences in bank quotes in two

currencies for four pairs of banks. The figure displays this rank reveral phenomenon. For

example it is common for Bank of America to quote a lower rate than the Bank of Tokyo-

Mitsubishi in the yen-Libor while submitting a lower quote in the US-Libor. Since we are

dealing with the same bank in both currencies, the probability of default and the expected

loss in the event of default is the same for loans issued in either currency.5 This suggests

that differences in banks’ Libor quotes are not primarily due to differences in credit risk,

something we would expect of their true borrowing costs. The figure also shows that these

differences are more pronounced in the most recent period of relative market calm.

3 A Simple Model of Quote Setting in the Libor

In this section we introduce a simple model of how member banks submit their quotes.

Let i = 1, . . . , 16 be the banks in the Libor panel for a given currency and tenor. Let

t = 1, . . . , T denote the days where the Libor was administered. We let qit ∈ [0, q] denote

the quote of bank i at date t. The Libor fix, Lt = L(qit, q−it), is then the average of the

middle 8 quotes. The true borrowing costs of each bank is denoted cit ∈ R+ and the profile

of costs ct is distributed according to the joint distribution Ft.

We write the net “profit”accruing to bank i in period t as:

Πit(qit, q−it, cit) = vitL(qit, q−it) + πit(qit, q−it, cit)

where vit is the bank’s portfolio exposure to the Libor and πit captures the reputational

5While bankruptcy laws vary across countries they do not vary across the currency denomination ofthe obligations.

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motives of the bank. We allow the reputational concerns reflected in πit to depend on the

quotes of other panel banks and its true borrowing cost, cit. This is consistent with our

favored interpretation that bank portfolio positions give them an incentive to manipulate

the Libor, but they face reputational or other costs for being too far away from other

banks and, potentially, for setting quotes too far from their actual costs of borrowing.

Note that they are subscripted by bank and time, so we allow for incentives to vary due

to, for example, changing bank portfolios.

We choose to model a bank’s payoffs as linear in the Libor as the majority of contracts

have linear payouts. Adjustable rate mortgages, futures, forwards, swaps and corporate

loans all have linear payouts in their underlying reference index, often the Libor. A portfolio

composed entirely of these contracts would itself have a payout linear in the Libor, and

although these banks likely do possess a small amount of nonlinear contracts, we consider

linearity to be a good approximation. We also assume that πit is continuously differentiable,

strictly concave in qit and ∂2πit∂cit∂qit

> 0. These latter assumptions reflect our view that banks

suffer reputational penalties for submitting increasingly ‘extreme’ quotes and for quotes

that are far away from their true costs. We also assume that Ft is absolutely continuous

and has full support on R16+ .

We assume that each bank is able to perfectly forecast the quotes of the others when

choosing their period quotes, which are chosen to maximize their current period profits.

We view this assumption as reasonable whenever banks change their daily quotes in a

slow and predictable manner, such as during much of 2009. Our regressions of quotes

on their lag, for example, typically have a root mean squared errors under 2 basis points

and, presumably, the banks are able to formulate better forecasts. The previous day’s

quotes serve as a natural coordination mechanism. In situations where banks’ quotes are

less predictable, such as during the spike of Libor in the fall of 2008, then the assumption

of perfect information is less appropriate. We discuss this further in section 4, when we

analyze the quote bunching in 2009 and its relative absence in 2008.

With perfect information, we can characterize interior quotes by the following first

order condition:

(1) −vit∂L

∂qit= −vit

81(`(q−it) < qit < r(q−it)) =

∂πit∂qit

where `(q−it) is the fourth lowest quote of q−it and r(q−it) is the twelth lowest. The first

equality uses the fact that the derivative of the Libor L with respect to qit is 18 if i is strictly

8

included in the middle eight and zero if strictly excluded.6 We interpret the leftmost term

as the marginal benefit stemming from a bank’s possession of Libor indexed contracts and

the rightmost term as the marginal cost associated with misreporting.

Figure 4 shows the discontinuous marginal benefit curve and a schedule of marginal cost

curves for a bank where vit < 0. Each marginal cost curve is associated with a different

underlying true borrowing cost, due to the monoticity of the marginal cost curve in cit.

For each of the curves which pass through the discontinuity, the optimal quote is equal to

`(q−it). This is the important idea that delivers the bunching on the discontinuities - that

there is a range of true borrowing costs in which the bank wishes to push the Libor as low

as it possibly can, but once it has achieved this, it has no incentive to set its quote lower.

We now state a proposition that forms the basis of our prediction we should see bunching

around the pivotal quotes `(q−it) and r(q−it).

Proposition 1 Let q−it be such that `(q−it) < r(q−it). Then if vit < 0 (> 0) there is an

interval of costs where i’s best response is to quote qit = `(q−it) (= r(q−it)). Moreover, the

width of this interval is increasing in |vit|.

This proposition, combined with the absolute continuity and full support of Ft, will

deliver a point mass at r(q−it) or `(q−it) in the distribution of qit conditional on q−it.

While we don’t formally model the quote submission process as a game, this logic extends

to a perfect information game as well.

Proposition 2 Let vit < 0 for some bank i and let ct = (c1t, ..., c16t) be a given profile

of borrowing costs. If there is a Nash equilibrium q∗t where q∗it = `(q∗−it) < r(q∗−it) then

there is an interval (cl, cu) of costs for i such that for any cit ∈ (cl, cu), q∗t remains a Nash

equilibrium for the new cost profile ct = (c1t, .., cit, ..., c16t).

So, in this situation, there will be mass points on equilibria where banks are tying

for the fourth lowest quote. While we have been focusing on the discontinuity in which

bunching occurs, there are similarly ‘gaps’ on the other discontinuity, as is common in

these discontinuity problems. These gaps imply that the best response functions are not

necessarily continuous in the quotes of the other banks, which precludes standard proofs

for the existence of equilibria in pure strategies. While the theoretical investigation of

6If qit ties with `(q−it) or r(q−it) then the Libor is not differentiable and i’s optimal quote is notcharacterized by this first order condition.

9

the existence of such equilibria is outside of the scope of our paper, we now turn to the

equilibria we observe in the data and see if there is bunching on the fourth and twelth

ranked quotes as predicted by the model.

4 Empirical Evidence

In this section we present empirical evidence of bunching behavior in light of the above

model and then try to measure the magnitude of skewing. To this latter end we consider

the counterfactual Libor that would arise if banks continued to behave as they did prior to

August 2007. We argue that in the pre-August 2007 period, Libor panel banks coordinated

by choosing quotes according to the previous day’s Eurodollar Bid Rate, a market rate,

plus a fixed number of basis points. We show that this historical relationship broke down

in the turmoil period.

4.1 Quote Bunching

Figure 7 shows the distribution of 3 Month US Libor quotes relative to the lower pivotal

quote for four time periods. As banks nearly always round their quotes to a basis point,

and the bin width in these histograms is a single basis point, there are often many banks

that submit quotes at exactly the lower pivot. In the figure we omit the fourth lowest

quote from each day to avoid misleading clustering at zero resulting from the fact that

there is always a fourth lowest quote. In the period July - October 2009 there are nearly

200 quotes exactly equal to lower pivotal quote. The second most common quote is a

single basis point above the pivotal quote. The 1st and 2nd quarters of 2009 also contain

pronounced bunching. In the fourth quarter of 2008 the Libor unprecedently spiked in

the wake of the collapse of Lehman Brothers and then fell sharply. In this period banks

were often adjusting their quotes in increments of 5 basis points, which is clear from the

repeated pattern in the first histogram in figure 7. From the model we would expect the

high level of uncertainty over this period would translate into less precise beliefs about the

location of the lower pivotal quote, and thus less bunching.

For comparison, figure 8 shows a similarly constructed histogram for CDS spreads, now

with the fourth lowest CDS spread subtracted from each. In contrast to the Libor quotes

the distribution of CDS spreads is quite smooth, consistent with our assumptions on the

cost distribution.

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4.2 Euro-Libor and Euribor

There are several other indexes with a similar structure to the Libor. The most popular

index for Euro-interest rate contracts is the Euribor, which distinct from the Euro-Libor.

The Euribor is computed each day by a survey of 44 mostly European banks. The top

15% and bottom 15% of rates are excluded and the average of the middle 70% determines

the fix. The question is also slightly different, the Euribor asking ‘What is the rate at

which euro interbank term deposits are being offered by one prime bank to another within

the EMU zone?’ adding that it is meant to be ‘the best price between the best banks’.

Prior to 1998, this was the question asked of the Libor panel banks.7 The question was

changed after the BBA decided no universal definition of a prime bank could be given.

We investigate the submitted rates of 4 banks that are included in both the Euro-Libor

and Euribor panels. Figure 9 shows their 3-month Euro-Libor and Euribor rates along

with the lower discontinuities in the respective panels. Deutsche Bank, Societe Generale

and Barclays bank submit identical or very nearly identical quotes in both panels in the

period following Lehman’s bankruptcy. HSBC, however, submits very different rates in

the two respect panels. Moreover, the submitted quotes largely track the respective lower

discontinuities in both panels. This behavior is suggested by our model if HSBC has

financial incentives to lower one or both of these indexes due to their interest rate contracts.

HSBC reported in July 2008 that if Euro interest rates were to fall by 1% over the next 12

months they would make $357 million in net interest revenue.8 Euro rates fell by 5% over

this period of July 2008 - July 2009, which also contains the period of HSBC’s unusual

cross-panel quote behavior documented in figure 9.

4.3 Constructing the Correct Libor: Eurodollar Bid Rate

The Eurodollar Bid Rate is a market rate for eurodollar deposits. Eurodollars are dollars

held by banks outside of the united states, and have historically been an important source

of funding for large American banks. We also show that the Eurodollar Bid Rate has had

a historically tight relationship with the Libor. Prior to August 2007, indeed for the whole

7The exact question was ‘At what rate do you think interbank term deposits will be offered by oneprime bank to another prime bank for a reasonable market size today at 11am?’

8This figure is reported in their 2008 interim report, which can be found at http://www.hsbc.com/1/PA_1_1_S5/content/assets/investor_relations/hsbc2008ir0.pdf on page 189. Note that HSBC reportsthis estimate requires many assumptions. Irrespective of the exact value, every HSBC financial reportexamined so far has shown they make large net gains from declining Euro interest rates.

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Table 2: Structural Break Test

U.S. LiborLevels Differences

Eurodollar Bid Rate 0.608 0.696(0.033) (0.031)

U.S. Libor 0.392 -0.123(0.033) (0.032)

Eurodollar Bid Rate -0.605 -0.589* 1(After August 2007) (0.034) (0.034)

U.S. Libor 0.600 0.586* 1(After August 2007) (0.034) (0.034)

N 1911 1392R2 1.000 0.423Chow Test Statistic 175.07 148.5

All explanatory variables are lagged.

history of the Libor prior to then, the banks submitted quotes between 6 to 12 basis points

above the Eurodollar Bid Rate. Banks were treating the Libor, the London Interbank

Offered Rate, as their perception of the ask rate corresponding to the listed bid rate for

Eurodollars. The Eurodollar Bid Rate-Libor spread of 6-12 basis points was then simply

something like a bid-ask spread. Since 2007, for the first time the Libor descended below

the Eurodollar Bid Rate and at times quite dramatically. Figure 10 shows the Eurodollar-

Libor spread which is slightly negative prior to August 2007 and then spikes significantly

once the Libor dramatically drops below the Eurodollar rate.

In table 2 we perform a structural break test to show the collapse of this historic

relationship. We can see that, both in levels and in differences, the previous days Eurodollar

Bid Rate was more important for determining the following days Libor than the previous

Libor rate. This suggests that, prior to the crisis, banks simply observed the preceding days

Eurodollar Bid Rate and added a fixed spread. After the crisis, however, the Eurodollar

Bid Rate has much less predictive power on the following days Libor. The lagged Libor

rate instead becomes much more important as it drops below the Eurodollar rate.

12

In their recent study, Abrates-Metz et. al. (2008) investigate the possibility of collusion

among Libor panel banks in the post August 2007 period. A commonly used screen for

collusion tests for whether cross sectional prices-or quotes in this case-have lower variance

during the suspected collusion relative to a benchmark period. They find that the variance

is substantially lower in the benchmark pre-August 2007 period. Our results suggest the

answer for this is that in the benchmark period, banks are coordinating on the previous days

Eurodollar rate. Though, the cross sectional variance in costs presumably also increased

dramatically in the period after August 2007. It is worth noting, our model does not rule

out this type of coordination.

The above results suggest an obvious counterfactual to construct: What would Libor

quotes have been had banks continued to follow their pre August 2007 rule? We first

calculate this rule by running the regression in Table 2, bank by bank. Figure 11 show plots

of the counterfactual quotes for Bank of America, whose portfolio exposure we examine in

the next section along with JP Morgan and Citigroup. To give a sense of the magnitudes

of skewing generated by this model, Table 3 shows the average and standard deviation of

bank quote “skewing”, assuming the pre-August 2007 rule gives the correct quotes. Again,

it is evident that measures of manipulation are stronger in the period when market turmoil

had partially subsided. Manipulation is not the only explanation for the break between

the Eurodollar rate and Libor quotes. Cassola, Hortacsu, and Kastl (2009) point out that,

because of the lack of actual transactions in the interbank market during the crisis period,

Libor quotes were uninformative as the banks themselves had little information. However,

it is unclear, from this theory why quotes would be biased downward, or why banks would

abandon the Eurodollar Bid Rate as a coordination mechanism. An alternative explanation

is that the lack of market data lowered the cost of misreporting as market observers had

fewer, accurate benchmarks with which to compare Libor quotes. We also note that the

break is broadly consistent with the reputational explanation for misreporting but, again,

it is puzzling that quote behavior has not started to revert to past behavior despite the

calming of markets.

5 Derivative Positions and Manipulation

Having established evidence for strategic misreporting, we now turn our attention to the

sources of misreporting incentives. We argue bank portfolio exposure to the Libor is a

good candidate for generating these incentives. In general, the exact portfolio positions13

Table 3: Average Magnitude of Quote Skewing: Eurodollar Bid Rate - Libor Quote

Pre Aug. 07 Aug. 07 - Aug. 08 Post Jan. 09Bank mean sd. mean sd. mean sd.

Barclays .02 .01 - .081 .10 -.37 .13Bank of America .02 .02 -.11 .10 -.393 .14

Bank of Tokyo-Mitsubishi .029 .01 -.095 .10 -.320 .14Citigroup .022 .01 -.118 .10 -.400 .13

Credit Suisse .022 .01 -.097 .10 -.370 .13Deutsche Bank .02 .01 -.106 .10 -.412 .14

HBOS .023 .01 -.111 .10 -.382 .13HSBC .022 .01 -.11 .10 -.51 .13

JP Morgan .023 .01 -.111 .11 -.434 .13Lloyd’s .022 .01 -.108 .11 -.381 .13Norin .03 .02 -.090 .10 -.31 .14

Rabo Bank .022 .01 -.111 .10 -.403 .13RBOS .019 .01 -.097 .10 -.301 .12

Royal Bank of Canada .015 .01 -.119 .10 -.345 .10UBS .022 .01 -.111 .10 -.361 .11

WestLB .022 .01 -.098 .10 - .333 .17

14

are unobservable and for this reason we focus our analysis on the three American bank

holding companies in the U.S. Libor panel: Citigroup, Bank of America, and JP Morgan.

These banks are required to provide information about their interest rate derivatives and

net interest revenue in the quarterly ‘Reports and Conditions and Income’ (call reports)

to the FDIC. This allows us to observe both the market and notional value of a variety

different types of interest rate derivatives held, as well as the trading revenue generated

by interest rate derivatives as a whole. Generally speaking, these banks have very large

interest rate derivative positions and these have been recently very profitable.

Many interest rate derivatives held by banks are held for the purpose of hedging other

items on the balance sheet, so notional portfolio sizes can be misleading. Perhaps the best

picture of aggregate exposure is given by aggregate revenue that banks earn from their

derivative portfolios. Table 4 shows the net interest revenue banks have made over the last

2 years, including the contribution of trading revenue on interest rate derivatives. Notably

each of the three banks experience large net revenue increases in the first quarter of 2009,

when the Libor fell dramatically, though we cannot see how much of this revenue is derived

from contracts referencing the Libor. It is important to keep in mind, however, that the

Libor is the preeminent index used in interest rate contracts and futures in the U.S.

Table 5 shows the notional value of the interest rate swaps9 held by these banks. As

the most common swap agreement is the ‘vanilla’ swap of a fixed rate in return for the

3-Month Libor, it is likely that a sizable proportion of their total swap positions are such

contracts. Given the large notional values, if their portfolio had just a net exposure of 1%

to the Libor this could contribute significantly to their net interest income. J.P.Morgan,

for example, possessed a notional value of over $54 trillion in interest rate swaps in the

fourth quarter of 2008. If their swap position had just a 1% net exposure to the Libor, then

their costs on their contracts would be proportional to $540 billion. It then follows if they

were to succeed in modifying the Libor by 25 basis points in a quarter they would make

1/4 ∗ 540 ∗ .025 = 0.337 or $337 million in that quarter. If they had a 10% net exposure

they could make $3.37 billion.10

The bunching on the lower discontinuity shown earlier in figure 7 suggests that some

9An interest rate swap is an agreement where one party pays a fixed rate of interest in return for afloating rate. The ‘notional value’ of such a contract is the value used to compute the interest payments.While similar to a principal, the notional value is never exchanged and exists solely for computing payments.

10Note we are focusing solely on swaps whose payouts are linear in the Libor. These banks also participateheavily in other more complex derivatives, such as ‘swaptions’ - options to purchase swaps, whose payoffsmay be substantially nonlinear in the Libor.

15

Table 4: Net Interest Revenues ($m)

Citigroup Bank of JPMorganQuarter America Chase

2007.1 12,129 9,182 6,8872007.2 13,032 8,683 7,4552007.3 13,774 7,026 8,9612007.4 14,046 3,803 6,5612008.1 12,366 10,394 7,5672008.2 13,664 11,725 8,7602008.3 11,527 11,832 6,0842008.4 7,728 12,888 11,2712009.1 18,248 14,034 15,2142009.2 12,355 15,078 14,0812009.3 13,741 11,042 14,189

Source: Bank Holding Company FR Y-9C Reports. The shown values are the sum ofreported Net Interest Revenue and Trading Revenue on Interest Rate Derivatives.

Table 5: Notional value of Interest Rate Swaps ($m)

Citigroup Bank of JPMorganQuarter America Chase

2007.1 15,712,307 19,305,479 43,357,9202007.2 16,133,587 19,873,919 49,287,8782007.3 18,371,402 22,339,658 59,919,0282007.4 16,955,132 22,472,948 52,097,8782008.1 19,585,284 25,261,266 55,188,1262008.2 18,732,046 26,162,587 59,821,0752008.3 17,360,100 26,230,767 54,907,1162008.4 15,859,923 26,577,385 54,524,0462009.1 14,177,696 49,717,209a 49,282,4652009.2 15,613,216 49,577,518 48,914,1182009.3 15,230,030 48,676,584 48,893,217

Source: Bank Holding Company FR Y-9C Reports.a. Bank of America completes merger with Merrill Lynch.

16

Table 6: Citigroup’s Counterfactual Net Interest Revenues ($m)

1% Increase 1% DecreaseInstantaneous Gradual Instananeous Gradual

2009.2 -1,767 -1,005 1,935 9362009.1 -1,654 -888 1,543 6602008.4 -801 -456 391 402008.3 -1,811 -707 893 4902008.2 -1,236 -756 1,170 6332008.1 -1,423 -781 1,162 6662007.4 -940 -527 837 5402007.3 -684 -337 738 3722007.2 -572 -309 553 3292007.1 -677 -335 470 348

Source: Citigroup’s 10-K and 10-Q reports. Instantaneous means a ‘parallel instantanenous100bp change’ while Gradual means ‘a more gradual 100bp (25bp per quarter) parallelchange in rates’

banks may profit from lowering the overall rate of the Libor. Table 6 shows Citigroup’s

reported counterfactual gains from movements in the interest rate. While it is unclear

exactly what simulations and assumptions Citigroup used to compute these numbers, the

picture painted is clear: Citigroup makes more (loses less) money when interest rates are

falling. We have seen that Citigroup owns large amounts of interest rate derivatives and

it is likely a very sizable proportion of these reference the 3-Month US Libor. In the

first quarter of 2009 Citigroup reported that they would make $936 million in net interest

revenue if interest rates would fall by 25 basis points a quarter over the next year and

$1,935 million if they were to fall 1% instantaneously. The Libor ended up falling by over

1% in the first quarter of 2009 and would fall another 1% over the next two quarters. We

also note the persistent proximity of Citigroup’s quote to the lower discontinuity in this

period.

6 Conclusion

In this paper we have presented new evidence corroborating concerns that Libor panel

banks may be understating their true borrowing costs. Previous analyses of the problem

17

have suggested the cause of this misreporting is the desire of panel banks to appear strong,

especially during the recent banking crisis. In contrast, our theory of misreporting incen-

tives points to a more fundamental source, namely that bank portfolio exposure to the

Libor give them incentives to push the rate in a direction favorable to these positions.

Our theory, then, suggests that the rate may perform badly even in times of market calm,

whereas the reputation theory suggests that we may only have to worry during periods of

severe market stress.

The nature of the Libor mechanism, which averages the middle eight quotes out of six-

teen, helps us formulate a novel strategy for testing the theory. When the location of the

“pivotal”quotes are highly predictable, as they appear to be in our sample, banks with in-

centive to manipulate the Libor fix bunch around these quotes because the marginal change

in the fix drops discontinuously there. Borrowing costs, on the other hand, presumably

have no relationship with these pivotal points and so neither should quotes from banks

with no incentives to manipulate the fix. We find evidence that actual bids do display this

bunching behavior.

The problem of trying to figure out what the Libor should have been is more thorny

than simply establishing that it may have been wrong. The primary problem is that while

our static optimization model provides tight predictions for the correlation of bank quotes

given an average level of those quotes, it allows for several possible explanations for why

quotes are at that average level. The simplest of these explanations is that the level of

quotes are driven by costs. On the other hand, since there are no explicit incentives for

accurate reporting, there is not necessarily any connection between costs and quotes and

the overall level of quotes can simply be explained by some banks skewing severely and

other banks simply not wanting to be too far away from the average. In this case the

magnitude of skewing may be large. In constructing counterfactual quotes in this paper,

we take a middle path. We show, first of all, prior to August of 2007 Libor quotes were

closely connected to the market Eurodollar Bid Rate and then assume the Eurodollar Bid

Rate provides an accurate measure of costs. Our counterfactual then asks: what would

quotes have been had banks continued to set quotes according to the Bid Rate? Under

these assumptions, we find skewing magnitudes on the order of 30 basis points or more.

Understanding the source of misreporting incentives has important policy implications.

Concerns about the proper functioning has led a large money market broker ICAP to

recently launch the ‘New York Funding Rate’ which is intended to be a rival the Libor. The

primary innovation of the New York Funding Rate is that submitted quotes are anonymous.18

This reflects the view that the primary motive for banks to submit downward or misleading

quotes is to signal their strength or soundness. If, alternatively, a major incentive for banks

to misreport their true borrowing costs is to influence the overall rate of the Libor, as we

suggest, anonymity may actually make it easier for banks to misreport. Though there may

be many other reasons for it, it is interesting to note that the New York Funding Rate has

been lower than the Libor since its inception.

As in the reputation enhancement story of misreporting, the primary problem our

theory points to is that in the Libor, and similar indexes derived from surveys, participants

face little in the way of costs for submitting false or misleading quotes. Creating a system

that properly incentivizes truthful reporting would require major changes and possible

unintended consequences would have to be carefully weighed. On the other hand, our

theory suggests a simple approach based on diminishing the incentives for misreporting

by adding more banks to the panel. Just as adding firms to a market (usually) makes

a market more competitive by reducing the impact any one firm has on price, adding

banks to the panel would lower the marginal impact any one bank would have on the rate.

Another alternative would be to encourage contracts that reference market rates, such as

the Eurodollar bid rate.

Appendix

Proof of Proposition 1:

Suppose that vit < 0. Whenever costs are such that

−vit8>∂πit(qit, q−it, cit)

∂qit|qit=`(q−it)(2)

0 <∂πit(qit, q−it, cit)

∂qit|qit=`(q−it)(3)

then `(q−it) is a local optimum. If, further

(4) 0 >∂πit(qit, q−it, cit)

∂qit|qit=r(q−it)

then `(q−it) is a global optimum. This follows from the concavity of πit in qit which

ensures ∂πit/∂qit is decreasing in qit. If (2) is satisfied for `(q−it) then it is satisfied for any

qit ∈ [`(q−it), r(q−it)]. Similarly if (3) is satisfied for ` then it is satisfied for any qit < `.

19

Finally, if (4) is satisfied for r then it is satisfied for any qit > r. So no other interior

solution is optimal. The other discontinuity, r, is not a local equilibrium.

Our assumption on the cross derivatives ensures that ∂πit/∂qit is strictly increasing

in cit and is thereby invertible in cit. Denote its inverse conditional on qit and q−it as

g(·, qit, q−it). The above conditions, in terms of g then become,

g(−vit/8, `(q−it), q−it) > cit(5)

g(0, `(q−it), q−it) < cit(6)

g(0, r(q−it), q−it) > cit(7)

which defines an open interval of costs which is weakly increasing in −vit.A symmetric argument follows for the case when vit > 0. �

Proof of Proposition 2 If q∗it = `(q−it) is optimal, it is necessarily a local equilibrium,

so equations (5) and (6) must hold for q∗it. The only possible other optimal solution is

qit > r(qit) that satisfies the first order condition ∂πit/∂qit = 0. As q∗it is optimal, it must

be Π(q∗it, q−it, cit) ≥ Π(qit, q−it, cit) or equivalently,

(8) −vit[r(q−it)− `(q−it)] ≥∫ qit

`(q−it)

∂πit∂qit

dqit

As ∂πit/∂qit is increasing in cit for each qit, the right hand side of (8) is increasing in cit.

So for any cit < cit, (8) is satisfied, and if cit satisfies (5) and (6) as well then it remains

optimal for i to quote q∗it for costs in this interval. As i quotes the same, and no other cost

has changed, it remains a best response for every other bank to quote q−it and q∗t remains

an equilibirium for the new cost profile containing cit.

References

[1] M. Kraten A. Metz Abrantes-Metz, R. and G. Seow. Libor manipulation? Mimeo,

August 2008.

[2] P. Bajari and L. Ye. Deciding between competition and collusion. Review of Economics

and Statistics, 84(4):971–989, 2002.

20

[3] B. Duygan Bump E. Cohen-Cole and Jose Fillat. Looking behind aggregates: A reply

to ”facts and myths about the financial crisis of 2008”. Federal Reserve Bank of

Boston Working Paper QAU08-5, November 2008.

[4] C. Mollenkamp and J. Whitehouse. Bankers cast doubt on key rate amid crisis. The

Wall Street Journal, April 15 2008.

[5] A. Hortacsu N. Cassola and J. Kastl. The 2007 subprime market crisis through the

lens of european central bank auctions for short term funds. University of Chicago

Working Paper, July 2009.

[6] R. Porter and D. Zona. Detection of bid rigging in procurement auctions. Journal of

Political Economy, 101:518–538, 1993.

[7] R. Porter and D. Zona. Ohio school milk markets: An analysis of bidding. The RAND

Journal of Economics, 30(2):263–288, 1999.

[8] J. Taylor and J. Williams. Further results on a black swan in the money market.

Stanford Institute for Economic Policy Research Working Paper 07-046, May 2008.

[9] J. Taylor and J. Williams. A black swan in the money market. American Economic

Journals: Macroeconomics, 1(1), January 2009.

[10] L. Christiano V.V. Chari and P. Kehoe. Facts and myths about the financial crisis of

2008. Federal Reserve Bank of Minneapolis Working Paper No. 666, October 2008.

21

Figure 1: One Year LIBOR Quotes and CDS Spreads

22

Figure 2: A Conservative Lower Bound: CDS plus Riskfree

23

Figure 3: Libor-OIS and CDS spreads

24

Figure 4: Cross Currency Libor Fixes

25

Fig

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26

Figure 6: Quote Skewing in the Perfect Information Case

27

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29

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30

Figure 10: 3 Month Eurodollar - U.S. Libor Spread

31

Figure 11: Cross Currency Libor Fixes

32