a multiple lender approach to understanding supply and search in the equity lending market

8/11/2019 A Multiple Lender Approach to Understanding Supply and Search in the Equity Lending Market

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THE JOURNAL OF FINANCE VOL. LXVIII, NO. 2 APRIL 2013

A Multiple Lender Approach to Understanding

Supply and Search in the Equity Lending Market

ADAM C. KOLASINSKI, ADAM V. REED, and MATTHEW C. RINGGENBERG

ABSTRACT

Using unique data from 12 lenders, we examine how equity lending fees respond todemand shocks. We find that, when demand is moderate, fees are largely insensitiveto demand shocks. However, at high demand levels, further increases in demand leadto significantly higher fees and the extent to which demand shocks impact fees is alsorelated to search frictions in the loan market. Moreover, consistent with search mod-

els, we find significant dispersion in loan fees, with this dispersion increasing in loanscarcity and search frictions. Our findings imply that search frictions significantlyimpact short selling costs.

SHORT SALE CONSTRAINTS MOTIVATEa large body of theoretical research in assetpricing. In addition, a growing body of empirical work confirms that theseconstraints have an economically meaningful impact.1 Although this researchsuggests that short sale constraints are important, relatively few empiricalstudies attempt to explain the variation of short sale constraints across stocks,

and even fewer seek to provide a motivation for the origin of these constraints.Short sale constraints can take many forms, but one of the most important

is the fee that short sellers pay to borrow shares in the equity lending market.Despite its one trillion dollar size, relatively little is known about this mar-ket because transactions are usually only visible to the two parties directlyinvolved.2 Furthermore, the equity loan databases employed in the existing

University of Washington, University of North Carolina, and Washington University inSt. Louis, respectively. The authors thank Robert Battalio, Darrell Duffie, Nicolae Garleanu,Jennifer Huang, David Musto, Lasse Pedersen, an anonymous referee, the Editors, and semi-

nar participants at the American Finance Association Conference, Barclays Global Investors, theConsortium for Financial Economics and Accounting Conference, the European Finance Associa-tion Conference, the IIROC-DeGroote Conference on Market Structure, Texas A&M, the Universityof Oregons Institutional Asset Management Conference, the University of Virginia, and the Uni-versity of Washington. We are grateful for financial support from the Q Group. Our data providermade this work possible and provided invaluable advice over the course of numerous discussions.Finally, we thank William Frohnhoefer for providing institutional details.

1 The theoretical literature on short selling includes Miller (1977), Diamond and Verrecchia(1987), andHong and Stein (1999),and empirical work demonstrating the significant economicimpact of short sale constraints includes Geczy, Musto, and Reed (2002), Ofek and Richardson(2003),Asquith, Pathak, and Ritter (2005), andCao et al. (2008).

2 Conversations with industry participants indicate that this is slowly changing. A central

counterparty exchange is slowly gaining volume (the exchange currently handles less than 1% ofvolume).

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560 The Journal of Finance R

literature are provided by individual equity lenders, so researchers have nothad an opportunity to draw conclusions about market-wide characteristics. Asa result, a number of important questions remain unanswered: How muchshort selling can take place before borrowing shares becomes expensive? What

causes borrowing to become expensive? What are the characteristics of theshare lending supply curve? And, finally, how much variation in fees could aborrower expect to see across multiple lenders? We find that the answers tothese questions are related to the presence of search frictions in the equitylending market.

The general dearth of empirical research on the equity lending market isinherently linked to its opacity, and one of the primary goals of this paper isto analyze the effects of this opacity. In one of the few theoretical models ofthe equity loan market,Duffie, Garleanu, and Pedersen (2002,hereafter DGP)suggest that search frictions, which result from opacity, give share lenders

market power, allowing them to charge fees to short sellers. We examine thismodel empirically in a number of ways. First, we find significant dispersionin loan fees, which is consistent with the existence of search frictions in theshare loan market. In addition, using stock characteristics that DGP suggestas proxies for search frictions, we show that search frictions are related toloan fee dispersion. Finally, we find that loan fee dispersion sharply increasesas the average loan fee moves from moderate to high levels, consistent withDGPs hypothesis that search frictions are related to the costs of short selling.However, the relation between the average fee and the dispersion in fees isnot monotonic: dispersion is also high when the average fee is abnormally low,

resulting in a U-shaped pattern.We also examine how search frictions allow lenders to change their prices in

response to exogenous shifts in demand. In the existing literature, some con-troversy exists regarding the way demand affects prices; some researchers findthat lending fees are unresponsive to increases in quantity (e.g.,Christoffersenet al. (2007)), whereas others find that large positive shifts in the demand forshare loans can be manifested in increased lending fees (e.g.,Cohen, Diether,and Malloy (2007)). We resolve this apparent paradox by using a nonlineartwo-stage least squares method to estimate the share loan supply schedule.We find that the loan supply schedule is essentially flat, and that specialness

is invariant to quantity demand shocks most of the time. For example, for theaverage stock a movement from the 10th quantity percentile to the 90th resultsin a loan fee change of only five basis points. However, the slope of the supplyschedule becomes positive and steep when demand shocks drive quantity to ab-normally high levels, consistent withCohen, Diether, and Malloy (2007).3 Forexample, a one standard deviation increase from the third to fourth standard

3 Cohen, Diether, and Malloys (2007)results connect the demand for share loans to underlyingstock prices, and their study identifies changes in demand based on measured changes in pricesand quantities in the stock loan market. One of the goals of this study is to understand exactlyhow changes in demand for share loans affect prices for those loans. In effect, were estimating the

underlying relation that gives rise to loan price changes and asking how that relation is affectedby the presence of search costs and market structure.


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Supply and Search in the Equity Lending Market 561

deviation of quantity is associated with a movement in abnormal loan fees from3.2 basis points to 21.7 basis points.

To further investigate the relation between the supply curve and search fric-tions, we examine how the shape of the supply curve relates to several proxies

for search frictions. We find evidence that the share loan supply schedule issteeper at high quantity levels when search costs are higher. In addition, weexamine whether factors unrelated to search costs can explain the patterns inthe data that we attribute to search costs. First, we find that variation in thetypes of lenders active in a particular stocks loan market can explain someof the cross-lender dispersion in specialness. It is therefore likely that differ-ences in lender desirability are at least partly responsible for the dispersion weobserve. However, our proxies for search costs continue to have a significanteffect on dispersion even after controlling for variation in lender type. Second,we examine whether concentration in lender capacity, which could result in in-

creased market power when quantity demanded is high, can explain our findingthat supply curves tend to become steep at high quantity levels. However, con-trary to this hypothesis, we find that the loan supply curve is not statisticallydifferent between low and high levels of lender capacity concentration.

Our research has important policy implications. Because search frictionshave a significant impact on lending fees, it follows that a reduction in thesefrictions would loosen short sale constraints. One way to reduce search fric-tions is to introduce a central clearinghouse for share loans, such as the NYSElending post that was abandoned in the 1930s. Furthermore, there is evidencethat short sale constraints reduce market efficiency (e.g., Asquith, Pathak,

and Ritter (2005),Nagel (2005),Reed (2007), andCao et al. (2008)). Althoughsome regulators and journalists accused short sellers of disrupting marketsand reducing efficiency during the financial crisis of 2008, a large body of re-cent research suggests that market quality decreased after short sales wererestricted in response to the crisis (e.g., Bris (2009), Boehmer, Jones, andZhang (2009), Boulton and Braga-Alves (2010), Kolasinski, Reed, and Thornock(2013)). Taken together, these results suggest that centralizing the share loanmarket could potentially improve stock market efficiency. However, asJonesand Lamont (2002)document, some stocks became expensive to borrow evenwith a lending post. Further, we find other factors, in addition to search fric-

tions, that can make borrowing expensive. Thus, although it is unlikely that acentral clearinghouse would eliminate all borrowing difficulty in the share loanmarket, our evidence suggests that search frictions are a significant contributorto borrowing costs.

Finally, our findings also have broader implications for opaque financial mar-kets. The theoretical models we use to motivate our empirical tests need notbe limited to the equity lending market. Insofar as their underlying assump-tions of agent heterogeneity, search frictions, and the lack of centralized pricequoting are consistent with the institutional details of other over-the-countermarkets, our results can be generalized to those contexts.

The remainder of this paper proceeds as follows. Section I examines thesearch cost literature and explores the applicability of search cost models to
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the equity lending market with a particular focus on the ability of searchfrictions to generate short sale constraints, and the resulting empirical impli-cations.Section IIdescribes the databases used in this study andSection IIIcharacterizes our findings.Section IVpresents our summary and conclusion.

I. Search Frictions and the Share Lending Market

A. Specialness, Search Frictions, and Price Dispersion

DGP present a dynamic model in which search frictions limit the frequency atwhich share lenders and borrowers are able to find one another. Thus, lenders,if they have some bargaining power, are able to charge a lending fee to shortsellers that is equal to some fraction of the surplus short sellers believe theycan gain. Short sellers are willing to pay the fee because, if they refuse, they

might not be able to find another lender and thus would have to forgo theirsurplus. Over time, this lending fee declines to zero as short sellers drive downprices to their long-run equilibrium values. The magnitude of the lending fee,often termed specialness, is increasing in lenders bargaining power, in frictionsin the share lending market, and in demand for share loans.

In our investigation, we also draw on the industrial organization literatureon search costs and price dispersion. When there is heterogeneity in sellercosts, models in which buyers must search sequentially for a seller generallyyield a positive relation between average prices, price dispersion across sellers,and search costs(Reinganum (1979),Sirri and Tufano (1998),Baye, Morgan,and Scholten (2006)). The DGP model does not predict dispersion in fees acrosslenders because it assumes no heterogeneity in lenders costs of providing shareloans (DGP assume lenders costs are zero). However, in practice it is likelythat some heterogeneity in lenders costs does exist, so if search frictions drivespecialness, we would expect an increased average level of specialness to beassociated with increased dispersion in specialness across lenders. Using datafrom multiple lenders, we compute dispersion in specialness across lenders fora given stock at a given point in time.4 We then examine the relation of thisdispersion to the average specialness in a given day, as well as investigateother proxies for search costs. InSection III.C,we explore the role played byalternative nonsearch explanations.

B. The Share Loan Supply Curve

Although search frictions are constant in the DGP model, they are not likelyto be so in practice. As DGP point out, these frictions are likely to be close to zero

4 One natural way to understand the DGP model in the context of heterogeneous search costsis to think in terms of local monopolies. Search frictions give each lender a local monopoly becauseborrowers have greater difficulty finding lenders competitors. When share loan demand is high,search frictions increase the monopoly power of lenders. Furthermore, if there is heterogeneity

among lenders, each will have a different monopoly price, so as search frictions increase, we expectmore price dispersion.


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Hedge

Fund 1

Prime

Broker

1

Lender 1

Hedge

Fund 2

Hedge

Fund 3

Hedge

Fund 4

Hedge

Fund N1

Lender 2

Lender 3

Lender 4

Lender N3

Prime

Broker

2

Prime

Broker

3

Prime

Broker

N2

Figure 1. Structure of the equity lending market. Figure 1 presents an example of thestructure of the equity lending market. Hedge funds, shown asHedge Fund 1throughHedge Fund

N1, can be clients of multiple prime brokers,Prime Broker 1 throughPrime Broker N2. These primebrokers can have relationships with multiple securities lenders, Lender 1throughLender N3. Therelationships with these lenders can be regular (bold line), occasional (solid line), or infrequent(dashed line).

when demand for loans is low. In this case, brokers have more lenders than bor-rowers among their clients, so matching is nearly costless. In addition, brokershave the ability to contact different lenders for information about availabilityand pricing, and most of the time the lenders with whom they have an existingrelationship have an ample supply of most stocks. However, conversations with

industry participants indicate that certain stocks may not be available from alllenders, and in these cases we would expect brokers to search for shares. Theexistence of third-party lenders, or finders as inFabozzi (1997), supports this

view.Figure 1shows the structure of these relationships.The supply of easily obtainable loans is thus more likely to be exhausted if

there is a large shock to the demand for share loans; in such a case, searchingfor shares will become more difficult and costly. Accordingly, just as searchfrictions lead to increases in specialness, we expect the share loan supply curveto have a positive slope when demand is high. On the other hand, if a loanprogram for a particular stock involves certain fixed costs, then the marginal

cost of share loans is likely decreasing at very low levels of quantity, inducinga downward slope in the left-hand portion of the share loan supply schedule.


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The presence of fixed costs also likely lowers the number of willing lenderswhen demand is low, potentially giving these lenders some monopoly power. Asshare loan demand increases from very low to moderate levels, we expect thenumber of lenders to increase, thereby reducing monopoly power and yielding

a downward slope in the left-hand portion of the share loan supply schedule.5Moreover, the existing literature finds that loan rates tend to be lower for largeloans than for small loans (DAvolio (2002),Geczy, Musto, and Reed (2002)). Inother words, the evidence suggests that volume discounting is prevalent in theequity lending market. Thus, we expect the share loan supply schedule to benonmonotonic, with a downward slope at low quantity levels, a relatively flatslope for moderate quantities, and an upward slope at high quantity levels.

C. Alternative Explanations for an Upward Sloping Supply Curve and Loan

Fee DispersionIn addition to search costs, other economic factors could plausibly explain

both dispersion in loan fees and an upward sloping share loan supply curve.We describe these alternative hypotheses below and analyze them empiricallyinSection III.C.

C.1. Differences in Lender Desirability

Because borrowers are able to borrow from multiple lenders, and becauseeach lender draws from portfolios with different characteristics, it is reasonable

to hypothesize that borrowers may prefer some lenders to others. Differencesin lender desirability would lead to differences in the average fees charged bylenders. Similarly, differences in lender desirability could lead to price disper-sion, as borrowers pay more to borrow from certain lenders and less to borrowfrom others. We refer to this hypothesis as the lender desirability hypothesis.

C.2. Lender of Last Resort

Another possible explanation is that, for a given stock, there is a dominantlender who has a large proportion, but perhaps not all, of the lendable shares.

Such a lender could act as the lender of last resort. When demand for shareloans is low, the lender of last resort must compete with other lenders. However,because the competing lenders have a limited inventory, a sufficiently largedemand shock could plausibly deplete this inventory, giving the lender of lastresort a monopoly. As a result, we would expect a supply curve that is flat atlow levels of quantity, where lenders compete, and then upward sloping once

5 For example, Kaplan, Moskowitz, and Sensoy (2013) conduct an experiment in which theyexamine the impact of shifting the supply of shares in the equity lending market by randomlymaking available for lending the shares of some of the stocks in an anonymous money managers

portfolio. However, they note that the manager restricted the experiment to only include firms thatwere likely to be in high demand at the time the lending program began.


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quantity reaches the point at which the lender of last resort has monopolypower. If the lender of last resort hypothesis is true, the upward sloping supplycurve is driven more by inventory concentration than by search costs.

C.3. Lender Cost Differences

InDuffie (1996), the supply curve of treasuries available for loan becomessteep and upward sloping not because of search costs, but because of differencesin the cost of lending among potential lenders. Duffie refers to these costs astransactions costs, but they could just as easily be interpreted as costs that areconstant for each lender and varying across lenders. Lenders with low costsprovide loans in most scenarios, but lenders with high costs are only willing tolend when demand shocks drive loan fees to sufficiently high levels. In otherwords, the fact that we see an increase in the slope of the supply curve may be

a result of differences in lenders costs, not search costs.

II. Data

To test the hypotheses developed above, we use databases from severaldifferent sources. Our principal analyses use two databases containing loanquantities and lending fees from 12 different equity lenders: the first containstransaction-level data over the period September 26, 2003 to May 9, 2007,and the second contains data at the stock-day level over the period September26, 2003 to December 31, 2007. In a supplemental analysis, we also examinethe quantity of shares available to be borrowed in the market over the periodJanuary 1, 2007 to December 31, 2009.

A. Loan Quantity and Lending Fees

The data provider for our study is both a market maker in the equity loanmarket and a data aggregator for major equity lenders. In its role as a marketmaker, the firm intermediates loans by borrowing from one party and lendingto another. As such, our data provider also contributes its own transactionsto the database. More importantly for the purposes of this paper, in its roleas a data aggregator our data provider collects information about equity loan

market conditions from several equity lenders. In particular, the firm providescurrent and historical stock loan market rates based on live data feeds fromequity lenders. These lenders contribute current and historical data about theirown loan portfolios in exchange for access to this market-wide information.

Our database consists of historical loan portfolios from 12 lenders. As showninTable I,the lenders providing data are direct lenders, agent lenders, retailbrokers, broker-dealers, and hedge funds.6 The principal owners of the shares

6 Despite the apparent distinction between lender types, our data provider has not provided spe-cific definitions of these categories. Table I presents the extent of our information on the description

of lenders; any further description of lender types in the paper is not based on information givenby the data provider.


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TableI

EquityLendin

gDatabaseStatistics

Tab

leIpresentssummarystatistics

forthetransaction-levelequityl

endingdatabase,whichcoversSeptember26,2003toMay9,2007(forcertain

lenderscoverageisasubsetofthisperiod).PercentofObs.isthepercentageofobservationsthateac

hlenderaccountsforinthedata

base.

Rebate

Rat

eistherebaterateoncashcollateralforsecuritiesonloan.

NumberofRelationshipsisthenumbe

rofloansmadeineachstockon

adailybasis

for

agivenlender.ThedatabaseisdiscussedindetailinSectionIIof

thetext.

Rebat

eRate

NumberofRelationships

(inpe

rcent)

(stock/day)

Len

der

Percent

ID

LenderType

Description

ofObs.

Mean

Median

Mean

Median

Max

1

Broker-dealer

Broke

r-dealersboxtootherbroker-dealers,

som

elendingtohedgefunds

16

.

10%

1.63

1.

55

2.84

1

225

2

Broker-dealer

Retailbrokerageaccountslentto

broker-dealers

7.

86%

2.65

1.

50

1.27

1

26

3

Broker-dealer

Broke

r-dealerboxtootherbroker-dealers,

conduittrades

6.

85%

4.13

4.

25

2.02

1

31

4

Directlender

Hedgefundassetslentdirectlyto

broker-dealers

0.

07%

0.78

1.

08

9.92

8

204

5

Broker-dealer

Broke


conduittrades

3.

52%

2.47

2.

00

1.25

1

39

6

Broker-dealer

Broke


som


31

.

39%

4.20

4.

30

5.74

4

136

7

Broker-dealer

Broke


som


6.

63%

2.53

1.

75

5.06

2

232

8

Directlender

Mutualfundassetsdirecttobroker-dealers

17

.

92%

3.19

3.

15

1.87

1

102

9

Broker-dealer

Hedgefund,pensionplansassetslent

dire

ctlytootherhedgefundsor

broker-dealers,someconduittrades

0.

83%

4.60

5.

15

3.27

2

40

10

Directlender

Hedgefundassetslentdirectlyto

broker-dealers

0.

30%

2.58

1.

00

1.01

1

2

11

Agentlender

Endow

ments,pensionplanassetslent

to

broker-dealers

4.

95%

4.33

4.

75

1.43

1

101

12

Agentlender

Institutionalassetslenttobroker-dealers

3.

58%

2.27

1.

02

2.41

1

75


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that are lent (both directly and through agents) are retail brokerages, pensionplans, insurance companies, and mutual funds. These market participantsrepresent 36% of the securities lenders by number.7 In most of the analysesthat follow, including the estimation of the supply schedule, we use the sum of

outstanding share loans by all lenders normalized by total shares outstandingas our measure of market loan quantity.

We use two separate equity lending databases: the first database comprises5,042,056 observations of individual loan transactions from September 26, 2003to May 9, 2007 and includes the number of shares, the daily loan rate, and sev-eral identification variables. The loan rate is the interest paid on the borrowerscollateral, also known as the rebate rate. The relative scarcity of a particularstock is measured in terms of its specialness, or the difference between its loanrate and the markets prevailing, or benchmark, loan rate. Our data providercomputes specialness at the firm-day level and this variable is contained in

the second database we use, which contains data that has been aggregatedto the firm-day level. In addition to daily specialness, the aggregate databasecontains a measure of the daily quantity and several identification variables. Itcomprises 1,511,874 observations of loan transactions aggregated to the stock-day level over the period September 26, 2003 to December 31, 2007. We use thisaggregate data in our analysis of the share loan supply curve (Tables IVVIbelow).

As discussed above, the database of individual transactions contains the dailyloan rate. To calculate the dispersion in loan fees(Tables VIIandVIIIbelow),we need a loan-specific measure of specialness. However, each lender may have

a different benchmark rate. Based onDAvolio (2002)andGeczy, Musto, andReed (2002),we calculate specialness by taking the benchmark rate to be thefederal funds rate minus a 10 to 20 basis point spread for each lender. We usethe mode of the distribution of loan fees above the federal funds rate to identifyeach lenders spread (the difference between the loan rate and the benchmark)by loan size category.8 The median spread is 16 basis points, and the spreadhas a relatively large range: the 25th percentile is one basis point and the 75thpercentile is 50 basis points. Among loans above $100,000, the interquartilerange is 0 to 25 basis points.

B. Lender Relationships

We also examine the extent to which lenders have relationships with mul-tiple borrowers. For each stock on each day, we count the number of trans-actions made by a given lender. Because borrowers consolidate orders to takeadvantage of volume discounts and thereby minimize transaction costs, each

7 State Streets publicly available white paper, Securities Lending, Liquidity, and CapitalMarket-Based Finance, indicates that there were 33 dealers in the equity lending market asof 2001.

8As in DAvolio (2002) and Geczy, Musto, and Reed (2002), loans are categorized as small

(loans below $100,000), medium (loans between $100,000 and $1,000,000), and large (loans above$1,000,000).


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transaction in a given stock on a given day is likely to represent a unique bor-rower. The number of transactions for each lender therefore serves as a proxyfor the number of unique borrowers, or relationships, that a lender has on agiven day.

InTable I,we report descriptive statistics on the time series of each lendersrelationships. Interestingly, we find significant variation across lenders in themean number of relationships, with the average number of relationships perday ranging between one and 10. Furthermore, there is a dynamic aspect to thenumber of relationships: the mean and median are well below the maximumfor most firms. To take one example, for lender #7 the maximum number ofrelationships is 232, but the mean number of relationships is only 5.06 and themedian is 2. The disparity we find between the maximum versus the meansand medians indicates that the number of relationships is not constant, whichis consistent with the idea that borrowers choose to search for stocks only when

the costs of searching are exceeded by the benefits of finding loans. Intuitively,this could mean that borrowers have a few relationships with lenders fromwhom they borrow the majority of their shares, but for scarce stocks borrow-ers search across a large number of potential lenders. We also note that thecross-sectional variation in the number of relationships documented here isconsistent with heterogeneity in search costs.

C. Data Compilation

For our analysis of the share loan supply curve, we use the aggregate

database, which contains 1,511,874 daily observations on loan fees and quan-tities. To this data set we add the daily stock price, ask price, bid price, andshares outstanding for each firm using data from the Center for Research inSecurity Prices (CRSP). We also addFederal Funds Rate, which is the effectivefederal funds rate from the H.15 statistical release provided by the FederalReserve;S&P Price/Earnings,which is defined as the monthly price to earn-ings ratio for the S&P500 from Compustat; and VIX, which is calculated asthe rolling mean value of the CBOE volatility index for the S&P500 over thepreceding 22 trading days.

We winsorize all variables in the aggregate database at the 1st and 99thpercentiles and we filter our database to include only those firms with at least250 observations. After this filter is applied, 586,435 observations remain inthe database. InTable II we report summary statistics for the final sample.

Although the average value of Specialness is only 37 basis points, it has astandard deviation of 1.36 and it is highly right-skewed, with a skewness of5.86. In addition,Loan Quantityas a percentage of shares outstanding is alsohighly right skewed.

III. Results

Our primary goal is to understand empirical patterns in the equity loanmarket, and measure the extent to which these patterns can be explained


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Table II

Summary Statistics of Instruments and Short Sale Variables

Table II contains summary statistics for the aggregate-level database, which contains 586,435observations at the firm-day level for the period September 26, 2003 to December 31, 2007. The

database is filtered to include only those firms with more than 250 observations. DiscretionaryAccrualsis calculated quarterly as inSloan (1996).Short(Long)Bollingeris an indicator variablethat takes the value one if a stocks price is more than two standard deviations above (below) the20-day moving average price and zero otherwise. Market Capitalization, in billions, is from CRSP.News Sentimentis a numerical score based on textual analysis of publicly released firm-specificnews articles, where low (high) scores indicate negative (positive) news.Short-Term Momentumisthe raw buy-and-hold return of a stock over the previous five trading days andLong-Term Momen-tumis the one-year momentum factor as inCarhart (1997).Loan Quantity / Shares Outstandingis the quantity of shares borrowed divided by the number of shares outstanding each day for eachfirm.Specialness, in percent, is a measure of the cost of borrowing a stock and is calculated as thedifference between the rebate rate for a specific loan and the prevailing market rebate rate.FederalFunds Rateis the effective rate available in the H.15 statistical release from the Federal Reserve.S&P Price/Earnings is the monthly price to earnings ratio for the S&P500 from Compustat. VIXisthe rolling mean value of the CBOE volatility index for the S&P500 over the preceding 22 tradingdays. All variables are winsorized at the 1st and 99th percentiles.

StandardVariable N Mean Median Deviation Skewness

Panel A: Firm

Discretionary accruals 8,925 0.060 0.004 0.849 20.076Short Bollinger 530,363 0.097 0.000 0.295 2.731Long Bollinger 530,363 0.071 0.000 0.256 3.347Market capitalization

(in $ Billions)

578,018 12.515 3.558 30.749 6.544

News sentiment 528,379 0.004 0.000 0.042 0.440Short-term momentum 525,260 0.004 0.003 0.055 0.003Long-term momentum 529,915 0.156 0.149 0.310 0.119

Panel B: Short Sale Transactions

Aggregate specialness(in percent)

586,435 0.373 0.042 1.366 5.860

Loan quantity/sharesoutstanding

578,022 0.049% 0.011% 0.161% 7.542%

Panel C: Macro

Federal funds rate (in percent) 1,558 3.471 3.990 1.647 0.359S&P price/earnings 52 2.946 2.924 0.118 2.814

VIX 1,073 14.824 14.136 3.366 10.541

by search cost models. First, we estimate the share loan supply curve andshow that search costs are closely connected to its shape. Next, we empirically

verify that the generic predictions of sequential search cost models hold forthe equity loan marketthat is, that search costs are positively correlated

with price dispersion and the level of prices. Finally, we explore other possibleexplanations for the empirical patterns we find.


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0.78

0.83

0.88

0.93

0.98

1.03

1.08

1 2 3 4 5 6 7 8 9 10

Specialness

Trade Quantity / Outstanding Shares

(grouped into deciles)

Mean 95% Confidence Interval

Figure 2. Specialness as a function of trade quantity in 2006.Trade quantity is divided byoutstanding shares to account for persistent differences in loan quantities across securities. Foreach firm, these relative quantities are then assigned to a decile based on their position relativeto other trade quantities for that firm and year. The figure plots the mean specialness across allfirms for each decile. Specialness, in percent, is a measure of the cost of borrowing a stock and is

calculated as the difference between the rebate rate for a specific loan and the prevailing marketrebate rate. The rebate rate for an equity loan is the rate at which interest on collateral is rebatedback to the borrower.

A. Modeling the Share Loan Supply Curve

Presumably, short sale constraints arise as short sellers demand for shareloans increases.9 However, not all increases in share loan demand lead toincreases in loan fees (Christoffersen et al. (2007)). So the question remains,by how much does demand need to increase before loan fees increase?

As a first pass, in Figure 2 we conduct a simple experiment, modeled on

that ofDAvolio (2002),in which we plot specialness (or excess loan fee) as afunction of quantity loaned. To account for persistent differences in loan quan-tity across securities, we calculate relative quantity loaned. In other words,quantity is measured as the rank of normalized loan quantity, defined as thenumber of shares lent divided by total shares outstanding. We find that spe-cialness declines mildly in loan quantity at low levels of loan quantity, butwhen loan quantity is above the 70th percentile, specialness increases sharplyin loan quantity. The changing sensitivity of specialness to quantity has prac-tical importance for borrowers: upward shifts in the quantity demanded do notnecessarily increase loan prices and may even decrease them in some cases.

9 DAvolio (2002)shows a positive correlation between short interest and loan fees.


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This initial approach is inherently limited, however. The supply schedulecannot be mapped out correctly using prices and quantities unless the supplycurve does not shift during the measurement period. To trace out the supplycurve more carefully, we turn to a two-stage regression approach, similar to

that of Angrist, Graddy, and Imbens (2000). Specifically, we use exogenousshifts in the demand for equity loans as a means to identify the supply curve.

As discussed in Section I.B, economic theory suggests that the share loan supplycurve may not be linear. To allow for this possibility, we employ a nonlineartechnique that builds on the linear approach ofAngrist, Graddy, and Imbens(2000).

InSubsection A.1below, we use economic theory to propose several instru-ments for share loan demand and then conduct an empirical falsification testof their validity. InSubsection A.2we describe our technique for estimating theshare loan supply curve and we present our results. Finally, in Subsection A.3,

we examine how the shape of the supply curve differs for firms with differentsearch cost characteristics.

A.1. Instruments for Share Loan Demand

To identify the share loan supply schedule, we must use variables that affectthe demand for loans but not the supply. Prior research suggests that mostof the supply of shares available for loan comes from institutions with stable,low-turnover portfolios (e.g.,DAvolio (2002)). On the other hand, the literaturehas shown that many short sellers have relatively short time horizons.10 Thus,

one category of potentially valid instruments includes variables that are re-lated to short-term trading strategies but not long-term trading strategies. Itstands to reason that low-turnover institutions are, by definition, not concernedwith the shorter term components of price movements. Accordingly, variablesthat isolate the short-term components of price fluctuations are likely to make

valid instruments, consistent withBoehmer, Jones, and Zhangs (2008, p. 498)finding that . . . short selling is dominated by short-term trading strategies.

Accordingly, in what follows below we define and discuss five candidate in-struments that are likely to affect the demand for loans but not the supply:

News Sentiment,Short-Term Momentum, Short Bollinger,Long Bollinger,and

Discretionary Accruals.One variable that is likely to impact the strategies of short sellers but notthe strategies of low-turnover institutions is daily News Sentiment, which is ameasure of the amount of positive or negative information contained in pub-licly released firm-specific news articles. Low-turnover institutions (i.e., equitylenders) are unlikely to trade every time there is a news article about one ofthe stocks in their portfolio. On the other hand,Engelberg, Reed, and Ringgen-berg (2012) andFox, Glosten, and Tetlock (2010) show that short sellers dorespond to daily news events. Accordingly, we consider News Sentiment as

10

Geczy, Musto, and Reed (2002)show that the median duration of a stock loan is three tradingdays, andDiether (2008)finds the median short position is held for 11 trading days.
http://-/?-http://-/?-http://-/?-


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a potential instrument for share lending demand, where News Sentiment isdefined for each firm and day as a numerical score between 1 and 1; lowscores indicate negative news and high scores indicate positive news. The newsdata come from RavenPack, Inc., a leading provider of news analytics data for

use in quantitative and algorithmic trading. In the normal course of its busi-ness, RavenPack uses proprietary algorithms to process news articles and pressreleases into machine-readable content and the data used in this study are de-rived from all news articles and press releases that appeared in the Dow Jonesnewswire, which includes, among other sources, the Wall Street Journal and

Barrons.We also consider variables that capture the short-term component of price

fluctuations. Specifically, we consider several variables related to technicalanalysis. Survey evidence suggests that institutional portfolio managers usetechnical trading rules when their time horizons are short (weeks), but not

when their time horizons are long (e.g., Carter and Van Auken (1990), Menkhoff(2010)). Accordingly, we consider Short-Term Momentum as an instrument,where Short-Term Momentum is defined as the raw buy-and-hold return ofa stock over the previous five trading days. Diether, Lee, and Werner (2010)show that short sellers do respond to short-term momentum; however, it isunlikely that low-turnover institutions, which provide the bulk of lendableshares, respond to it. To make sure our short-term measures of returns areisolating the high-frequency component of price movement, we also include

Long-Term Momentumas a control variable, where Long-Term Momentumisdefined as the traditional one-year momentum factor as inCarhart (1997).

In addition, we use another technical trading rule, namely, Bollinger bands(Bollinger (2002)), to motivate two additional candidate instruments. Specifi-cally, the Bollinger band strategy prescribes going short and long when a stockprice is respectively above or below its 20-day moving average by more than twostandard deviations.11 We use the rule to define the indicator variables Short

BollingerandLong Bollinger, whereShort BollingerandLong Bollingerequalone when a stock is respectively above or below its 20-day moving average bymore than two standard deviations and zero otherwise.

Finally, we considerDiscretionary Accruals, as computed inSloan (1996), asa potential instrument. Discretionary accruals constitute a decision by man-

agement to shift earnings from one period to another. Thus, high or low dis-cretionary accruals cannot persist and must, by construction, be followed bya reversal. Recent accounting studies suggest that this reversal occurs in lessthan a year, and all the negative (positive) abnormal returns associated withhigh (low) discretionary accruals are realized by the time of the accrual re-

versal (e.g., Allen, Larson, and Sloan (2010), Fedyk, Singer, and Sougiannis(2011)). Discretionary accruals are therefore unlikely to be related to tradingby low-turnover institutions and hence the quantity of lendable shares. On theother hand, prior literature finds that short selling is related to discretionaryaccruals (e.g.,Cao et al. (2008)).

11 Technical traders differ on the precise parameters, so we choose a 20-day moving average andtwo standard deviation bands because Bollinger designates them as the default (Bollinger (2002)).


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Having made an a priori case for our instruments based on economic theory,we next conduct a formal empirical falsification test of their validity. For thistest, we use a data set that contains the aggregate number of shares that equitylenders have available for loan over the period January 1, 2007 to December

31, 2009. We then test whether any of our instruments are significantly relatedto this aggregate quantity of lendable shares. If they are not, we infer that ourinstruments meet the exclusion restriction and are unrelated to the quantityof lendable shares.

The data we use for this test comes from Data Explorers, a leading providerof data in the equity loan market. Data Explorers aggregates and distributesinformation regarding the equity lending market at the daily frequency. Thedata are sourced directly from a wide variety of contributing customers in-cluding beneficial owners, hedge funds, investment banks, lending agents, andprime brokers. The database contains information on the aggregate quantity

lenders actually lend out as well as the aggregate quantity of shares lendershaveavailablefor loan, including those not lent. Our falsification test uses thequantity available normalized by shares outstanding. We henceforth refer tothis variable as lendable shares.

To conduct our falsification test, we run the following panel data regressionin which the dependent variable is the log of the number of lendable sharesand the independent variables are the candidate instruments discussed above:

Lendable Sharesit = 1Accrualsit +2ShortBit +3LongBit +4Newsit

+ 5STMomit +Controlsit +FEi + it,(1)

where Accruals are discretionary accruals, ShortB and LongB are the shortand long Bollinger indicator variables, News is news sentiment, and STMomis short-term momentum. We include stock fixed effects, and we cluster thestandard errors by stock and day to ensure robustness to heteroskedasticityas well as serial and cross-sectional correlation. If the candidate instrumentsmeet the exclusion restriction, they should have no explanatory power in thisregression. The results, presented inTable III, are consistent with our a pri-ori arguments. The coefficients on our candidate instruments (Discretionary

Accruals, Short Bollinger, Long Bollinger, News Sentiment, and Short-Term

Momentum) are individually and jointly statistically indistinguishable fromzero.In addition to being statistically insignificant, our point estimates suggest

that the effect of our candidate instruments on lendable shares is also econom-ically negligible. Take, for instance, the coefficient estimate on News Sentimentof0.0129. This implies that a one standard deviation increase inNews Sen-timentof 0.042 units shifts the log of lendable shares by 0.0005 [0.0005 =0.01290.042], a negligible amount compared to the standard deviation of thelog of lendable shares of 0.6952. Other point estimates imply that a one stan-dard deviation increase inShort-Term Momentumand Discretionary Accruals

impacts lendable shares by the economically negligible amounts of 0.0007and 0.0002, respectively. Finally, the coefficients on the Bollinger indicator


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Table III

Effect of Candidate Instrumental Variables on the Quantity of

Lendable Shares

Table III displays the results of a panel data regression of Lendable Shares on five different

candidate instruments for the period January 1, 2007 to December 31, 2009 of the form

Lendable Sharesit = 1Accrualsit +2ShortBit +3LongBit +4Newsit

+5STMomit+Controls+FEi + it.

Lendable Sharesis the natural log of the number of shares available for loan each firm and day asa percentage of shares outstanding. The candidate instruments are described in detail inSectionIII.Aof the text. Federal Funds Rate is the effective federal funds rate as reported by the H.15statistical release, Long-Term Momentum is the natural log of the one-year momentum factoras in Carhart (1997), S&P Price/Earnings is the natural log of the S&P500 price to earningsratio for the preceding month, and VIX is the rolling mean value of the CBOE volatility indexfor the S&P500 over the preceding 22 trading days. Firm fixed effects are included and F-Test ofInstrumentsassesses whether the candidate instruments are jointly different from zero. Robuststandard errors clustered by firm and date are below the parameter estimates in parentheses.indicates significance at the 1% level, indicates significance at the 5% level, and indicatessignificance at the 10% level.

Explanatory Variable Dependent Variable: Lendable Shares

Discretionary accruals 0.0002(0.02)

Short Bollinger 0.0012(0.00)

Long Bollinger 0.0032(0.00)

News sentiment 0.0129(0.02)

Short-term momentum 0.0125(0.02)

Federal funds rate 0.0097(0.01)

Long-term momentum 0.0232

(0.01)S&P price/earnings 0.0387

(0.01)VIX 0.0005

(0.00)

Firm fixed effect YesN 642,134F-test of instruments 2.02P-value 0.85R2 0.02

variables imply that a stock price movement from within the Bollinger bandsto a point above or below them impacts the quantity of lendable shares by anegligible 0.0012 and 0.0032, respectively. Accordingly, because the candidate

instruments are both statistically and economically insignificant in the falsifi-cation test, we adopt Discretionary Accruals, Short Bollinger, Long Bollinger,


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News Sentiment, andShort-Term Momentumas instruments in the estimationof the supply curve.

A.2. Estimating the Share Loan Supply Schedule

Using the instruments discussed above, we estimate the share loan supplycurve, which allows us to determine the influence of short sellers demand forshare loans on specialness and the extent to which increases in loan prices arerelated to search frictions. We discuss our estimation procedure in detail below.

To ensure comparability across stocks, we standardize our loan quantity vari-able. First, we divide quantity by total shares outstanding for each stock. Thisremoves the effect of stock price on quantity, which would likely be sufficient foran estimation using market-wide quantity. However, because our lenders holdonly a segment of the quantity of lendable shares of each stock, and because

that segment may vary by stock, we need to further normalize each stocksquantity. Thus, we standardize each stocks quantity variable by subtractingthe mean and dividing by the standard deviation of each stocks loan quantityas a percentage of shares outstanding. We denote this standardized value ofshare loan quantity byQ.

Next, we need to take into consideration the highly skewed nature of bothquantity and specialness, as well as the probable nonlinearity of the supplycurve. To this end, we employ a trans-log specification in which we model thestarted natural log of specialness as a function of the started natural log ofquantity demanded and its square.12 Greene (1997) notes that this sort of

specification is highly flexible and can be interpreted as a second-order ap-proximation of virtually any smooth functional form. Using the instrumentsdiscussed above, we thus represent the share loan demand and supply sched-ules as the following limited information system, with the supply schedule (3)as the identified equation:

LN(Qit + C) = i + 1LN(Sit +D) + 2Accrualsit + 3ShortBit + 4LongBit

+ 5Newsit + 6STMomit +Controlsit + it(2)

LN(Sit +D) = i +1LN(Qit +C)+2LN(Qit +C)2+Controlsit + it, (3)

whereC and D are start constants that ensure the log is defined,13 Qis loanquantity, S is specialness, Accruals are Discretionary Accruals, ShortB and

LongB are the Short and Long Bollinger indicator variables, News is NewsSentiment,and STMom is Short-Term Momentum, all as defined above. TheControlsvector includes the federal funds rate, long-term (365 day) momentum,the level of the VIX index, and the P/E ratio of the S&P500. We also employ

12 Since our quantity variable is standardized to make it comparable across stocks, it can takenegative values. Likewise, specialness can be negative. Therefore, as Fox (1997)suggests for right-skewed variables with negative values, we use the started logtransformation of both quantity and

specialness. Our results are not sensitive to the choice of start constant.13 We use start constantsC = 10 andD = 1, but our results are not sensitive to different values.


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Table IV

First-Stage Estimation of the Share Loan Supply Curve

Table IVpresents the first-stage results from a two-stage instrumental variables panel data re-gression of daily data over the period September 26, 2003 to December 31, 2007. The excluded

instruments are discussed in Section III.Aof the text and, because there are two endogenous re-gressors (the started log quantity and its square), there are two first-stage regressions. Firm fixedeffects are included in all models. The F-statistic tests the null of weak identification. Robust stan-dard errors clustered by firm and date are shown below the parameter estimates in parentheses.indicates significance at the 1% level, indicates significance at the 5% level, and indicatessignificance at the 10% level.

Dependent Variable

Explanatory Variable LN(Quantity + C) LN(Quantity + C)2

Discretionary accruals 0.0028 0.4056(0.00) (0.32)

Short Bollinger 0.0017 0.2395(0.00) (0.19)

Long Bollinger 0.0004 0.0575(0.00) (0.05)

News sentiment 0.0101 1.4461(0.01) (1.15)

Short-term momentum 0.0216 3.0968(0.01) (2.46)

(Quantity+C)2 32.2487(24.78)

Federal funds rate 0.0024 0.3487(0.00) (0.28)

Long-term momentum 0.0018 0.2544(0.00) (0.20)

S&P price/earnings 0.0140 2.0318(0.01) (1.62)

VIX 0.0030 0.4298(0.00) (0.34)

Firm fixed effect Yes YesN 508,744 508,744F-test of excluded instruments 5.50 5.52

P-value 0.0000 0.0000

stock fixed effects. We estimate equation (3) for a panel of stock-days over theperiod September 26, 2003 to December 31, 2007 using the nonlinear two-stageleast squares procedure suggested byWooldridge (2002).14 For robustness, wealso estimate the equation using limited-information maximum likelihood andFuller-kmethods. The results from the first-stage regression, including a testof weak identification, are reported inTable IV.Our results from estimatingequation (3), the supply curve, along with additional specification tests, arepresented inTable V.

14

We stress that we are not running whatWooldridge (2002, p. 236237) calls the forbiddenregression, but rather the more involved, unbiased procedure he describes.


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Table V

Second-Stage Estimation of the Share Loan Supply Curve.

Table Vpresents the second-stage results from a panel data regression of the started natural log ofloan fee (Specialness + D), on the started natural log of quantity (Q + C), according to the model:

LN(Specialnessi,t +D) = 1 LN(Qi,t +C) +2 LN(Qi,t +C)2 +4

n=1

n+2Controln,i,t +FEi + it ,

where LN(Q+C) and LN(Q+ C)2 are the fitted values from the first-stage regressions shown inTable IV. Results below useC = 10 andD = 1, but are unchanged if we use other start constants.Federal Funds Rateis the effective federal funds rate as reported by the H.15 statistical release,Long-Term Momentumis the natural log of the one-year momentum factor as in Carhart (1997),S&P Price/Earnings is the natural log of the S&P500 price to earnings ratio for the precedingmonth, andVIXis the rolling mean value of the CBOE volatility index for the S&P500 over thepreceding 22 trading days. All variables are measured over the period September 26, 2003 toDecember 31, 2007. Firm fixed effects are included in all models and estimation is done usingthree different estimators (2SLS, Fuller, and LIML). Robust standard errors clustered by firm anddate are shown below the parameter estimates in parentheses. indicates significance at the 1%level, indicates significance at the 5% level, and indicates significance at the 10% level.

Estimation Method

Explanatory Variable (1) 2SLS (2) Fuller (3) LIML

LN(Quantity + C) 295.6990 403.3024 411.4129

(58.93) (110.30) (114.98)LN(Quantity + C)2 61.1657 83.8573 85.5697

(12.33) (23.23) (24.22)Federal funds rate 0.0889 0.1091 0.1107

(0.02) (0.03) (0.03)

Long-term momentum 0.1358

0.1736

0.1764

(0.04) (0.05) (0.05)S&P price/earnings 0.2588 0.4758 0.4923

(0.21) (0.33) (0.35)VIX 0.0162 0.0185 0.0186

(0.01) (0.01) (0.01)Firm fixed effect Yes Yes YesN 508,744 508,744 508,744Kleibergen-Paap rK LM statistic 25.263 25.263 25.263P-value 0.0001 0.0001 0.0001Cragg-Donald WaldF-statistic 10.394 10.394 10.394Sargan-Hansen statistic 5.885 3.721 3.606P-value 0.2079 0.4451 0.4619

As can be seen inTable V,the log of quantity and its square are stronglysignificant in all specifications, implying that exogenous shifts in quantity de-manded impact specialness. Note that the parameters are qualitatively simi-lar across the three different estimation methods. Moreover, the specificationstests shown inTables IVandVindicate that our instruments satisfy the ex-clusion restrictions and that weak instrument bias is not a concern.

To examine the economic significance of these results, Figure 3 plots the

supply curve for the average stock as implied by our two-stage least squaresparameter estimates. Consistent with the finding in Christoffersen et al. (2007)


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A.3. Cross-Sectional Patterns in Supply Curves

Given our findings above about the shape of the share loan supply curve, wenext examine the importance of search costs in determining the supply curves

shape. Specifically, we compare the shape of the supply curve for subsamplesof stocks likely to have different search costs. DGP suggest that search costsare likely to be higher for small firms and illiquid firms, so we use Market Cap-italizationand Bid-Ask Spread, both calculated using daily data from CRSP,as two of the measures on which we create subsamples. Interestingly, firm sizeand liquidity may also affect the shape of the supply curve under alternativeexplanations, so these two variables do not provide sharp distinctions betweenpossible explanations.

We also use two search cost proxies related to the structure of the equitylending market that take advantage of the richness of our multiple lenderdata set. If finding lenders is costly, and smaller lenders are more difficultto find than large lenders, we expect search costs to be higher in equity loanmarkets that tend to be fragmented among many small lenders. Unlike sizeand liquidity, these proxies give us more traction in distinguishing variouspossible explanations, which we more fully discuss inSection III.C.

The first of our market structurerelated search cost proxies is based on loanvolume concentration. In the DGP model, agents are randomly matched withsearch intensity and, all else equal, a lower search intensity leads to higherloan fees because it is more costly for agents to match. In practice, if the loanmarket is highly fragmented and no lender holds a significant amount of shares,it is likely that matching will be costlier. Accordingly, for each stock and eachweek, we compute the total loan volume for each lender as a fraction of sharesoutstanding and we use this measure to compute a Herfindahl index.15 Nextwe compute the time-series average of this index for a given stock and referto it as Lender Volume Concentration. Small values of this variable indicatethat, for a typical week, lending in a given stock tends to be disbursed amongmany lenders with low volume, suggesting the market tends to be fragmentedamong many lenders with low levels of volume. If search costs are important inthis market, and search costs play a role in shaping the supply curve, then weexpect low values ofLender Volume Concentrationto be associated with highersupply curve slope coefficients.

Our second market structurerelated search cost proxy is based on the num-ber of lenders active in a stock on a typical week as well as a proxy for lendersize. To construct this measure, for each stock we compute the time-seriesaverage loan size of each lender (as a percentage of shares outstanding) andcompare it to the average loan size across all lenders in the stock. If a lendersaverage loan size is smaller than the average for all lenders in the stock, werefer to that lender as small. Otherwise the lender is large. Next, for eachstock week, we count the number of small and large lenders and take thetime-series averages for the stock and label these averages as Number Small

15

We compute the index by week instead of by day because some stocks have many days forwhich there is very little trading activity.


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LendersandNumber Large Lenders,respectively. The number of small lendersthus measures the extent to which a stocks share loan market tends to befragmented among many lenders with smaller-than-average volume. If searchcosts play an important role in shaping the supply curve, we expect the slope

of the curve to be larger when Number Small Lenders is higher. On the otherhand, if large lenders are easier to find, we expect search costs to be lower when

Number Large Lendersis high.To test whether the shape of the supply curve is different for firms with dif-

ferent search cost characteristics, we compute the sample medians ofMarketCapitalization,Bid-Ask Spread, Lender Volume Concentration,Number Small

Lenders, andNumber Large Lenders. For each of these characteristics, we thencreate two subsamples of stocks: low and high, where the low (high) subsampleincludes all firms with values below (above) the median of the relevant charac-teristic. We then reestimate the supply curve, allowing its parameters to differ

across subsamples, and then conduct Wald tests of the null hypothesis thatthey do not differ.

The results are reported inTable VI . We find that the parameters of thesupply curve are statistically different for all measures of search costs, includ-ingMarket Capitalization, Bid-Ask Spread, Lender Volume Concentration, aswell as Number Small Lenders, and Number Large Lenders. Consistent withthe search cost hypothesis, we find that the coefficient on the quantity squaredterm is larger, and hence the supply curve is more steeply upward sloping,when firms are smaller, when firms are less liquid, and when firms loan vol-ume is dispersed among many lenders. Interestingly, whereas the results in

Panels A, B, and C strongly support the search cost hypothesis, the resultsin Panels C and D are generally weaker. For both Number Small Lendersand

Number Large Lenders, the curves are economically similar across subsamples.Thus, the results in Table VI generally support the search cost hypothesis,though not all search cost proxies appear to influence the shape of the supplycurve.

B. Industrial Organization, Search Costs, and the Equity Loan Market

DGP describe the prevalence of search frictions in the opaque equity lend-ing market, and in the previous section we present evidence that search fric-tions influence the shape of the equity loan supply curve. In this section, wefurther examine the role of search costs in the equity loan market by ex-amining them in light of the industrial organization literature on sequen-tial search costs. First, in Subsection B.1 we use panel data regressions toconfirm that loan fee dispersion is associated with various proxies for searchfrictions as well as the average level of fees. This result confirms the predic-tion of sequential search models that price dispersion is positively associatedwith search frictions. Then, in Subsection B.2, we explore in greater depth

how the loan fee level, or specialness, is a function of the dispersion in loanfees.


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Table VI

Sensitivity of Share Loan Supply Curve to Firm Characteristics and

Search Cost Proxies

Table VIpresents second stage results from six different panel data regressions that estimate the

share loan supply curve. In each panel, we examine the impact that a firm characteristic has on thesupply curve by creating two subsamples of stocks, low and high, where the low (high) subsamplesinclude all firms with values below (above) the median value of the relevant firm characteristic. Wethen jointly estimate the supply curve for the low and high subsamples, allowing the parametersto differ across subsamples, and conduct a Wald test of the null that the subsamples do not differ.The table displays the results for the LN(Quantity + C) and LN(Quantity+ C)2 parameters for thelow and high firm characteristic subsamples. Market Capis the average market capitalization foreach firm from CRSP. Bid-Ask Spreadis the average bid-ask spread for each stock calculated usingthe closing mid-price on each day. Volume Concentrationis a Herfindahl index using each lendersdaily volume in a stock. # Small(Large)Lendersis the mean number of small (large) lenders thatdealt in a particular stock each week. Capacity Concentration is a Herfindahl index using eachlenders maximum possible loan volume in a stock. Robust standard errors clustered by firm and

date are shown below the parameter estimates in parentheses.

indicates significance at the 1%level, indicates significance at the 5% level, and indicates significance at the 10% level.

Subsample LN LN Test Low Firm FixedDefinition (Qty + C) (Qty + C)2 versus High Effect N

Panel A: Market Capitalization

Low market cap 232.5745 48.8247 27.60

(70.76) (15.05) (0.00) Yes 508,744High market cap 186.8668 38.2192

(33.49) (7.23)

Panel B: Bid-Ask Spread

Low bid-ask spread 156.1564 30.6390 18.97

(38.77) (8.16) (0.00) Yes 508,744High bid-ask spread 235.3641 49.4966

(72.94) (15.48)

Panel C: Lender Volume Concentration

Low volume conc. 211.6295 44.2605 19.61

(37.42) (7.97) (0.00) Yes 507,492High volume conc. 138.3305 29.0247

(30.28) (6.45)

Panel D: Number Small Lenders

Low # small 249.2926 51.4099 12.29

lenders (64.57) (13.87) (0.06) Yes 507,492High # small 196.0426 40.6479

lenders (56.33) (11.65)

Panel E: Number Large Lenders

Low # large 139.2103 29.1954 26.11

lenders (27.76) (5.82) (0.00) Yes 507,492High # large 173.3962 35.9402

lenders (43.34) (9.45)

(continued)


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Table VIContinued

Subsample LN LN Test Low Firm FixedDefinition (Qty + C) (Qty + C)2 versus High Effect N

Panel F: Lender Capacity Concentration

Low capacity 299.2151 62.2386 5.58conc. (119.48) (25.28) (0.47) Yes 507,492

High capacity 328.9796 66.4139

conc. (84.27) (17.19)

B.1. Dispersion and Search Costs

One of the most relevant empirical predictions of sequential search cost

models is that increases in search costs will be associated with increases inboth price dispersion and the average price level. In this section, using searchcosts proxies identified inSection III.A.3, we test whether these predictionshold in the equity lending market.

Our first task is to compute measures of loan fee dispersion. For each stock-day we calculate each lenders average specialness. We then define Cross-

Lender Dispersion as the standard deviation of average lender specialnessacross lenders for each stock-day. Because many stocks have a large num-ber of days with little to no equity lending volume, we compute the weeklyaverage of Cross-Lender Dispersion, giving us a stock-week panel of obser-

vations. The stock-week is our unit of observation for all tests within thissection.As search cost proxies, we use the same proxies as inSection III.A.3.Specif-

ically, we use the average Market Capitalization and Bid-Ask Spread for theweek, as well as our weekly measures ofLender Volume Concentration, Num-ber Small Lenders, andNumber Large Lenders. In addition, we use the aver-age loan fee charged by all lenders in a given week as the level of the loanfee.

Next, we test the extent to which loan fee dispersion is related to search costsand the loan fee level by running the following panel data regressions for eachfirmi and weekt:

Dispersionit = +1log(MktCapit) + 2Bid Ask Spreadit + 3Loan Feeit

+4(LoanFeeit)2+ 5NumberSmallLendersit

+ 6NumberLarge Lendersit + it (4)

Dispersionit = +1log(MktCapit) + 2Bid Ask Spreadit +3Loan Feeit

+ 4(Loan Feeit )2+5V olume Concentrationit + it. (5)


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We estimate both equations using OLS and include time fixed effects withstandard errors clustered by firm.16 The results, presented in Models 1 and2 ofTable VII, are largely consistent with the prediction that increases insearch costs are associated with increases in price dispersion. We find that

market capitalization does play a role. The statistically negative coefficient onlog(MktCap)in both model specifications indicates that larger firms have lessprice dispersion, which is consistent withDAvolio (2002) andGeczy, Musto,and Reed (2002), who find that larger firms are more widely held and heldin larger quantities by equity lenders, and as a result, their stock is easierto borrow. In other words, loans in large, and presumably widely held, stocksare associated with lower search costs and lower price dispersion. Further evi-dence for this comes from the coefficients on our two market structure proxiesfor search costs,Number Small Lendersand Lender Volume Concentration.InModels 1 and 2, the two variables have significant positive and negative coef-

ficients, respectively, indicating that fee dispersion is higher when the equityloan market is fragmented among many small lenders.

We further note that the coefficient on loan fee is positive and significant inboth model specifications, indicating that dispersion increases in the averagefee level, consistent with the predictions of sequential search models in theindustrial organization literature. Because lending fees are highly skewed andpossibly have a larger effect as they reach extreme levels, we also run thefollowing specification:

Dispersionit = +1log(MktCapit )+ 2Bid Ask Spreadit +3Loan Feeit

+ 4(Loan Feeit )

2

+5V olume Concentrationit+ 6Special Dummyit +7(Special DummyitV olume Concentrationit )+ it,

(6)

where SpecialDummy is an indicator variable that equals one when the loanfee exceeds 25 basis points and equals zero otherwise.17 Note that the coeffi-cient onSpecialDummyis strongly significant, which supports the predictionsof the sequential search cost models that, in the presence of search costs, ex-treme scarcity will be associated with more price dispersion. Note further thatthe coefficient on the interaction term between SpecialDummy and LenderVolume Concentration is strongly negative, which indicates that the effect of

extreme loan fees on dispersion is enhanced when the market for share loansin a particular stock is fragmented among many small lenders and search costs

16 To ensure that cross-sectional correlation in the error terms is not confounding our inferences,we also compute standard errors clustered by both firm and time as suggested byPetersen (2009).As can be seen in the Internet Appendix (available in the online version of this article), the double-clustered standard errors are not materially different from those we obtain with a single firmcluster. Hence, we conclude cross-sectional correlation is not important in this context and presentour main results using standard errors clustered by firm.

17 DAvolio (2002)finds that the value-weighted average cost to borrow is 25 basis points perannum and notes that any stock with a rebate rate below the general collateral rate could be

considered special. Our cutoff of 25 basis points is intended to identify stocks that are generallymore costly to borrow than the typical stock.


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Table VII

Determinants of Price Dispersion

The dependent variable is the standard deviation of the loan fee (specialness). Log(Market Cap-italization) is the log of market capitalization for each firm from CRSP. Bid-Ask Spread is the

difference between the bid and ask price from CRSP measured as a percentage of the closingmid-price. Number of Small (Large) Lenders is the number of small (large) lenders that dealtin a particular stock each week. Volume Concentration is a Herfindahl index using each lendersdaily volume in a stock. Special Dummy =1 if the mean weekly specialness for a stock is 0.25,and Agent & Brokers Dummy, Agent & Direct Lenders Dummy, and Broker & Direct LendersDummy=1 if the stock has transactions by lenders of both relevant types during a given week.All Three Lender Types Dummy = 1 if a stock has transactions by all three lenders types. All dataare weekly; to obtain weekly data from daily observations we use the time-series mean over theweek. Standard errors are reported in parentheses and are clustered by firm with weekly fixed ef-fects.Interceptis the mean of the fixed effects. indicates significance at the 1% level, indicatessignificance at the 5% level, and indicates significance at the 10% level.

Model

Explanatory Variable (1) (2) (3) (4) (5)

Intercept 0.8845 1.2514 0.3550 0.2875 0.8873

(0.15) (0.16) (0.08) (0.08) (0.15)Log(market capitalization) 0.0391 0.0293 0.0033 0.0046 0.0392

(0.01) (0.01) (0.00) (0.00) (0.01)Bid-ask spread 3.0114 3.3303 3.5745 3.9085 3.0260

(4.07) (4.21) (4.40) (4.41) (4.05)Mean loan fee 0.1954 0.2007 0.0649 0.0645 0.1936

(0.05) (0.04) (0.06) (0.06) (0.05)Mean loan fee squared 0.0020 0.0022 0.0019 0.0020 0.0020

(0.00) (0.00) (0.00) (0.00) (0.00)Number of small lenders 0.0340 0.0312

(0.00) (0.00)Number of large lenders 0.0326 0.0309

(0.00) (0.00)Volume concentration 0.4526 0.1791 0.0931

(0.05) (0.02) (0.03)Special dummy 1.7948 1.7957

(0.23) (0.23)Vol. conc. special dummy 1.1997 1.2063

(0.23) (0.23)Agent andbrokers dummy 0.0812 0.0927

(0.01) (0.01)

Agent and direct lendersdummy

0.0446 0.0630

(0.02) (0.02)Broker and direct lenders

dummy0.0233 0.0073

(0.01) (0.01)All three lender types

dummy0.0489 0.0229

(0.01) (0.02)Time fixed effect Yes Yes Yes Yes YesN 118,280 118,280 118,280 118,280 118,280Adj.R2 0.23 0.22 0.31 0.31 0.23


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are higher. A clear picture now emerges: as stocks scarcity increases, borrow-ers are forced to search beyond large lenders, and, because it can be costlyfor borrowers to find smaller lenders, the scarce stocks exhibit increased pricedispersion.

B.2. Specialness and Dispersion

Building on the search cost literatures prediction that price dispersion isdriven by search frictions, we would like to further investigate the functionalrelation between specialness and dispersion. A connection between the level ofprice dispersion and the cost of borrowing supports the hypothesis that searchfrictions drive short sale constraints.

We describe our empirical approach as follows. First we compute Cross-Lender Dispersion for each stock every day by computing the standard deviation

of average loan fees across lenders. Next, we assign each stock-day observationto market-wide specialness deciles, where we use each stocks time series ofmarket-wide specialness to define deciles. Finally, we compute, and graph inTable VIII, the average daily Cross-Lender Dispersion for each specialnessdecile. We also computeIn-Lender Dispersion, which we define as follows. First,for each day and each stock, we compute the standard deviation of the fees thateach lender charges on that day. Next, for each stock-day, we take the averagelender fee standard deviation. Finally, we assign stock-day observations tomarket-wide specialness deciles in the same manner as above, and we graph theaverage ofIn-Lender Dispersionfor each decile. In short, In-Lender Dispersion

captures the extent to which lenders charge different prices to different clients.Interestingly, for Cross-Lender Dispersion the results are not monotonic:

there is a pattern of decreasing dispersion for very low specialness decilesand then increasing dispersion as specialness goes from moderate to high(Table VIII, Panel A). However, in the higher deciles, higher levels of pricedispersion are correlated with higher loan fees. Therefore, search frictionsappear to influence the ability of lenders to charge high lending fees. Theseresults are statistically significant in a regression framework. Specifically, asconfirmed by the significantly positive coefficient on Market Specialness Decilein Model 1 of Panel B and the significantly positive coefficient on Market Spe-

cialness Decile Squared in Model 2. The result that dispersion is increasingin specialness is consistent with search models, validating the importance ofsearch costs in this opaque market. Taken together, the patterns in price dis-persion across lenders inSubsection B.1,and in this section, provide evidencethat costly search contributes to specialness.

The results forIn-Lender Dispersion as a function of specialness also are non-monotonic(Table VIII, Panel A). There is a pattern of decreasing dispersionfrom low to moderate specialness deciles, and a pattern of increasing dispersionfrom moderate to high specialness deciles. Regression results support this pat-tern: the square of the market-wide specialness decile is a statistically strong

predictor of In-Lender Dispersion. This pattern is consistent with the notionthat lenders have monopoly power both when scarcity is high and when it is low,


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Table VIII

Price Dispersion

Variations in lending fees (specialness) are calculated as the standard deviation of each lendersprice for a given security and day. Cross-Lender Dispersion is the mean standard deviation of

lenders average prices. Specifically, for each stock and day we calculate each lenders mean special-ness and take the standard deviation of the sample of lenders averages. The standard deviationsare then organized by market-wide specialness deciles and averaged. In-Lender Dispersionis thestandard deviation of a particular lenders loans in each stock every day and we take the aver-age of these in-lender standard deviations by specialness deciles. For each stock, Lender VolumeConcentration is defined as the sum of squared lender volume as a percentage of total volume.Panel A shows a graph of cross-lender and in-lender price dispersion as a function of scarcity(market specialness), while Panel B shows the regression results from models of price dispersionon market-wide specialness (in deciles). Each regression is run on a firm-by-firm basis and wepresent the cross-sectional mean of the resulting estimates as inCoval and Shumway (2005)andSkoulakis (2006)with the standard errors shown below the parameter estimates in parentheses.Adj.R2 is the mean of the adjustedR2 across all firm-level results. indicates significance at the1% level, indicates significance at the 5% level, and indicates significance at the 10% level.

Panel A: Cross-Lender and In-Lender Price Dispersion as a Function of Specialness

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1 2 3 4 5 6 7 8 9 10

Market Specialness Decile

Cross-Lender Dispersion In-Lender Dispersion

Panel B: Price Dispersion Regressions

Dependent variable

Cross-lender dispersion In-lender dispersionExplanatoryVariable (1) (2) (3) (4)

Intercept 0.4529 2.6990 0.0552 0.0402(3.07) (1.60) (0.20) (0.37)

Lender volumeconcentration

0.5288 3.1551 0.2203 0.2711

(2.93) (1.31) (0.20) (0.37)Market specialness decile 0.1713 0.0177 0.0217 0.0535

(0.10) (0.10) (0.00) (0.02)Market specialness decile 0.0183 0.0071

squared (0.00) (0.00)Adj.R2 0.24 0.35 0.16 0.25


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and thus under these conditions lenders are better able to price-discriminate.When scarcity is low, borrowers are not searching for securities and thus are notcomparing prices, so lenders have more pricing power. On the other hand, whenscarcity is high, borrowers face search costs. As the difficulty of finding shares

increases, lenders who do make loans have more pricing power. Finally, if mildscarcity drives borrowers to search around for shares but these borrowers caneasily find alternatives, the pricing power of the lenders is diminished.

C. Alternative Hypotheses

Although our results on price dispersion and the nonlinear supply curve areconsistent with a search cost explanation, it is plausible that they might beconsistent with the alternative hypotheses described in Section I.C. In thissection we examine the following alternative hypotheses: (1) differences in

lender desirability, (2) lender of last resort, and (3) variation in lending costs.We find evidence that the first of these factors contributes to some of theempirical patterns we uncover. It cannot, however, explain all of them. Asa result, on balance the evidence suggests that search costs are an impor-tant factor, but not the only factor, driving empirical patterns in the lendingmarket.

C.1. Differences in Lender Desirability

Recall from Section I.C that variation in lender desirability, from a bor-

rowers point of view, could plausibly induce dispersion in the fees borrowersare willing to pay to different lenders. We begin our investigation of this alter-native explanation for loan fee dispersion by looking at average specialness bylender type. We group lenders into the categories defined by our data provider:lenders, broker-dealers, and direct lenders. An overview of the lenders in eachcategory is presented inTable I, whereas the results broken out by lender cat-egory are reported inTable IX. We find that there are significant differencesamong lender categories with direct lenders charging the lowest average spe-cialness (0.16), and broker-dealers charging the highest (0.65). Although thedescriptions inTable Igive an intuitive impression that the direct lenders and

the agent lenders may have more stable loan portfolios than broker-dealers, ourdata descriptions provide no direct evidence for this view. It is definitely possi-ble that other characteristics make broker-dealers more desirable lenders. Inother words, the difference in mean loan fees across lender types is consistentwith the differences in lender desirability hypothesis.

We next investigate the sources of price dispersion while noting the pres-ence of multiple types of lenders. Specifically, Table VIIpresents results froma regression of price dispersion on measures of search costs and variablesindicating the participation of multiple lender types for a given stock-day. Thestatistically significant estimate of 0.0489 on the variable All Three Lender

Types Dummy in Model 4 shows that price dispersion is indeed higher whenlenders in different categories are participating simultaneously. Moreover,
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Table IX

Loan Fees by Lender Type

The table examines loan fees (specialness) and lender type. Panel A displays summary statisticsfor the level of loan fees and trade quantity for each lender type. For the level of the loan fee and

quantity, the mean is first calculated at the stock-day level for each lender, and then summarystatistics are calculated across lender types. For the mean, the statistical significance of the differ-ence between lenders is assessed using a t-test. For the median, the statistical significance is not atest of the difference of medians, but rather a Wilcoxon-MannWhitney test of whether or not thetwo samples come from the same distribution. Panel B examines the dispersion of loan fees brokenout by the type of lender(s) participating in the market. Price Dispersionis the time-series averageof the standard deviations of lenders average prices. Specifically, for each stock and day, we cal-culate the lenders average specialness and then take the standard deviation across the sample oflenders.Dispersionis then calculated as the time-series mean of the standard deviations for eachlender category shown below. indicates significance at the 1% level, indicates significance atthe 5% level, and indicates significance at the 10% level.

Panel A: Level of Loan Fee and Quantity

Loan fee Trade quantity

Lender Type Median Mean Median Mean

Agent lender (1) 0.0000 0.4462 47,000 2,892,561Broker-dealer (2) 0.0061 0.6522 25,000 613,316Direct lender (3) 0.0090 0.1608 1,000,000 3,691,838Difference: 1 versus 2 0.0061 0.2060 22,000 2,279,245

Difference: 1 versus 3 0.0090 0.2854 953,000 799,278

Difference: 2 versus 3 0.0029 0.4914 975,000 3,078,523

Panel B: Dispersion of Loan Fees

Lenders Types Participating inMarket Price dispersion Percent of observations

Agent lender only 0.4471 5.35%Broker-dealer only 0.7240 65.27%Direct lender only 0.4510 13.58%Agent lender and broker-dealer 0.4967 5.33%Agent lender and direct lender 0.2765 0.63%Broker-dealer and direct lender 0.2041 8.63%Agent lender, broker-dealer, and

direct lender0.3587 1.20%

price dispersion is significantly higher when the specific combination ofAgentLenders andBroker-Dealers is in the market and also whenBroker-Dealers andDirect Lenders are both active. Interestingly, price dispersion is

a multiple lender approach to understanding supply and search in the equity lending market

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