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 to demand shocks. We find that, when demand is moderate, fees are largely insensitive to demand shocks. However, at high demand levels, further increases in demand lead to significantly higher fees and the extent to which demand shocks impact fees is also related to search frictions in the loan market. Moreover, consistent with search models, we find significant dispersion in loan fees, with this dispersion increasing in loan scarcity and search frictions. Our findings imply that search frictions significantly impact short selling costs.

S HORT SALE CONSTRAINTS MOTIVATE a large body of theoretical research in asset pricing. In addition, a growing body of empirical work confirms that these

constraints have an economically meaningful impact. 1 Although this research suggests that short sale constraints are important, relatively few empirical studies 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 market because transactions are usually only visible to the two parties directly

involved. 2 Furthermore, the equity loan databases employed in the existing

∗ University of Washington, University of North Carolina, and Washington University in St. Louis, respectively. The authors thank Robert Battalio, Darrell Duffie, Nicolae G ˆarleanu,

Jennifer Huang, David Musto, Lasse Pedersen, an anonymous referee, the Editors, and semi- nar participants at the American Finance Association Conference, Barclays Global Investors, the Consortium for Financial Economics and Accounting Conference, the European Finance Associa- tion Conference, the IIROC-DeGroote Conference on Market Structure, Texas A&M, the University of Oregon’s 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 provider made 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) , and Hong and Stein (1999) , and empirical work demonstrating the significant economic

impact of short sale constraints includes Geczy, Musto, and Reed (2002) , Ofek and Richardson (2003) , Asquith, Pathak, and Ritter (2005) , and Cao 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% of

volume).

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literature are provided by individual equity lenders, so researchers have not had an opportunity to draw conclusions about market-wide characteristics. As

a result, a number of important questions remain unanswered: How much short selling can take place before borrowing shares becomes expensive? What causes borrowing to become expensive? What are the characteristics of the share lending supply curve? And, finally, how much variation in fees could a borrower expect to see across multiple lenders? We find that the answers to these questions are related to the presence of search frictions in the equity lending market.

The general dearth of empirical research on the equity lending market is inherently linked to its opacity, and one of the primary goals of this paper is to analyze the effects of this opacity. In one of the few theoretical models of the equity loan market, Duffie, G ˆarleanu, 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 this model empirically in a number of ways. First, we find significant dispersion in loan fees, which is consistent with the existence of search frictions in the share loan market. In addition, using stock characteristics that DGP suggest as proxies for search frictions, we show that search frictions are related to loan fee dispersion. Finally, we find that loan fee dispersion sharply increases as the average loan fee moves from moderate to high levels, consistent with DGP’s hypothesis that search frictions are related to the costs of short selling. However, the relation between the average fee and the dispersion in fees is not 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 find that lending fees are unresponsive to increases in quantity (e.g., Christoffersen et al. (2007) ), whereas others find that large positive shifts in the demand for share loans can be manifested in increased lending fees (e.g., Cohen, Diether, and Malloy (2007) ). We resolve this apparent paradox by using a nonlinear two-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 the average stock a movement from the 10th quantity percentile to the 90th results in a loan fee change of only five basis points. However, the slope of the supply schedule becomes positive and steep when demand shocks drive quantity to ab-

normally high levels, consistent with Cohen, Diether, and Malloy (2007) . 3 For example, a one standard deviation increase from the third to fourth standard

3 Cohen, Diether, and Malloy’s (2007) results connect the demand for share loans to underlying stock prices, and their study identifies changes in demand based on measured changes in prices

and quantities in the stock loan market. One of the goals of this study is to understand exactly how changes in demand for share loans affect prices for those loans. In effect, we’re estimating the underlying relation that gives rise to loan price changes and asking how that relation is affected by the presence of search costs and market structure.

561 deviation of quantity is associated with a movement in abnormal loan fees from

Supply and Search in the Equity Lending Market

3.2 basis points to 21.7 basis points. To further investigate the relation between the supply curve and search frictions, 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 is steeper at high quantity levels when search costs are higher. In addition, we examine whether factors unrelated to search costs can explain the patterns in the data that we attribute to search costs. First, we find that variation in the types of lenders active in a particular stock’s loan market can explain some of the cross-lender dispersion in specialness. It is therefore likely that differences in lender desirability are at least partly responsible for the dispersion we observe. However, our proxies for search costs continue to have a significant effect on dispersion even after controlling for variation in lender type. Second, we examine whether concentration in lender capacity, which could result in increased market power when quantity demanded is high, can explain our finding that 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 statistically different between low and high levels of lender capacity concentration.

Our research has important policy implications. Because search frictions have a significant impact on lending fees, it follows that a reduction in these frictions would loosen short sale constraints. One way to reduce search frictions is to introduce a central clearinghouse for share loans, such as the NYSE lending post that was abandoned in the 1930s. Furthermore, there is evidence that short sale constraints reduce market efficiency (e.g., Asquith, Pathak, and Ritter (2005) , Nagel (2005) , Reed (2007) , and Cao et al. (2008) ). Although some regulators and journalists accused short sellers of disrupting markets and reducing efficiency during the financial crisis of 2008, a large body of recent research suggests that market quality decreased after short sales were restricted in response to the crisis (e.g., Bris (2009) , Boehmer, Jones, and Zhang (2009) , Boulton and Braga-Alves (2010) , Kolasinski, Reed, and Thornock (2013) ). Taken together, these results suggest that centralizing the share loan market could potentially improve stock market efficiency. However, as Jones and Lamont (2002) document, some stocks became expensive to borrow even with a lending post. Further, we find other factors, in addition to search frictions, that can make borrowing expensive. Thus, although it is unlikely that a central clearinghouse would eliminate all borrowing difficulty in the share loan market, our evidence suggests that search frictions are a significant contributor to borrowing costs.

Finally, our findings also have broader implications for opaque financial markets. The theoretical models we use to motivate our empirical tests need not

be limited to the equity lending market. Insofar as their underlying assump- tions of agent heterogeneity, search frictions, and the lack of centralized price quoting are consistent with the institutional details of other over-the-counter markets, our results can be generalized to those contexts.

The remainder of this paper proceeds as follows. Section I examines the search 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 search frictions to generate short sale constraints, and the resulting empirical implications. Section II describes the databases used in this study and Section III characterizes our findings. Section IV presents 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 at

which 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 short sellers that is equal to some fraction of the surplus short sellers believe they can 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 their surplus. Over time, this lending fee declines to zero as short sellers drive down prices to their long-run equilibrium values. The magnitude of the lending fee, often termed specialness, is increasing in lenders’ bargaining power, in frictions in the share lending market, and in demand for share loans.

In our investigation, we also draw on the industrial organization literature on search costs and price dispersion. When there is heterogeneity in seller costs, models in which buyers must search sequentially for a seller generally yield 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 across lenders because it assumes no heterogeneity in lenders’ costs of providing share loans (DGP assume lenders’ costs are zero). However, in practice it is likely that some heterogeneity in lenders’ costs does exist, so if search frictions drive specialness, we would expect an increased average level of specialness to be associated with increased dispersion in specialness across lenders. Using data from multiple lenders, we compute dispersion in specialness across lenders for

a given stock at a given point in time. 4 We then examine the relation of this dispersion to the average specialness in a given day, as well as investigate other proxies for search costs. In Section III.C, we explore the role played by alternative nonsearch explanations.

B. The Share Loan Supply Curve Although search frictions are constant in the DGP model, they are not likely

to 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 costs is to think in terms of local monopolies. Search frictions give each lender a local monopoly because

borrowers 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 expect more price dispersion.

Supply and Search in the Equity Lending Market

Lender 1 Fund 1

Hedge Lender 2 Fund 2

Prime Broker

2 Lender 3 Fund 3

Hedge

Prime

Lender 4 Fund 4

Hedge

Broker

Prime Broker N 2

Hedge Lender N 3 Fund N 1

Figure 1. Structure of the equity lending market. Figure 1 presents an example of the structure of the equity lending market. Hedge funds, shown as Hedge Fund 1 through Hedge Fund

N 1 , can be clients of multiple prime brokers, Prime Broker 1 through Prime Broker N 2 . These prime brokers can have relationships with multiple securities lenders, Lender 1 through Lender N 3 . The relationships 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 borrowers among their clients, so matching is nearly costless. In addition, brokers have the ability to contact different lenders for information about availability and pricing, and most of the time the lenders with whom they have an existing relationship have an ample supply of most stocks. However, conversations with industry participants indicate that certain stocks may not be available from all lenders, and in these cases we would expect brokers to search for shares. The existence of third-party lenders, or “finders” as in Fabozzi (1997) , supports this view. Figure 1 shows 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, searching for shares will become more difficult and costly. Accordingly, just as search frictions lead to increases in specialness, we expect the share loan supply curve to have a positive slope when demand is high. On the other hand, if a loan program for a particular stock involves certain fixed costs, then the marginal cost of share loans is likely decreasing at very low levels of quantity, inducing

a 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 lenders when demand is low, potentially giving these lenders some monopoly power. As share loan demand increases from very low to moderate levels, we expect the number of lenders to increase, thereby reducing monopoly power and yielding

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

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

In 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 empirically in Section III.C.

C.1. Differences in Lender Desirability Because borrowers are able to borrow from multiple lenders, and because

each lender draws from portfolios with different characteristics, it is reasonable to hypothesize that borrowers may prefer some lenders to others. Differences in lender desirability would lead to differences in the average fees charged by lenders. Similarly, differences in lender desirability could lead to price dispersion, as borrowers pay more to borrow from certain lenders and less to borrow from 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 dominant lender 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 share loans is low, the lender of last resort must compete with other lenders. However, because the competing lenders have a limited inventory, a sufficiently large demand shock could plausibly deplete this inventory, giving the lender of last resort a monopoly. As a result, we would expect a supply curve that is flat at low levels of quantity, where lenders compete, and then upward sloping once

5 For example, Kaplan, Moskowitz, and Sensoy (2013) conduct an experiment in which they examine the impact of shifting the supply of shares in the equity lending market by randomly

making available for lending the shares of some of the stocks in an anonymous money manager’s portfolio. However, they note that the manager restricted the experiment to only include firms that were likely to be “in high demand at the time the lending program began.”

565 quantity reaches the point at which the lender of last resort has monopoly

Supply and Search in the Equity Lending Market

power. If the lender of last resort hypothesis is true, the upward sloping supply curve is driven more by inventory concentration than by search costs.

C.3. Lender Cost Differences

In Duffie (1996) , the supply curve of treasuries available for loan becomes steep and upward sloping not because of search costs, but because of differences in the cost of lending among potential lenders. Duffie refers to these costs as transactions costs, but they could just as easily be interpreted as costs that are constant for each lender and varying across lenders. Lenders with low costs provide loans in most scenarios, but lenders with high costs are only willing to lend when demand shocks drive loan fees to sufficiently high levels. In other words, 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 several different sources. Our principal analyses use two databases containing loan quantities and lending fees from 12 different equity lenders: the first contains transaction-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 September

26, 2003 to December 31, 2007. In a supplemental analysis, we also examine the quantity of shares available to be borrowed in the market over the period January 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 loan

market and a data aggregator for major equity lenders. In its role as a market maker, the firm intermediates loans by borrowing from one party and lending to another. As such, our data provider also contributes its own transactions to the database. More importantly for the purposes of this paper, in its role as a data aggregator our data provider collects information about equity loan market conditions from several equity lenders. In particular, the firm provides current and historical stock loan market rates based on live data feeds from equity lenders. These lenders contribute current and historical data about their own loan portfolios in exchange for access to this market-wide information.

Our database consists of historical loan portfolios from 12 lenders. As shown in Table I , the lenders providing data are direct lenders, agent lenders, retail brokers, 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 specific 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 given by the data provider.

Table I

Equity Lending Database Statistics

Table I presents summary statistics for the transaction-level equity lending database, which covers September 26, 2003 to May 9, 2007 (for certain lenders coverage is a subset of this period). Percent of Obs. is the percentage of observations that each lender accounts for in the database. Rebate Rate is the rebate rate on cash collateral for securities on loan. Number of Relationships is the number of loans made in each stock on a daily basis for a given lender. The database is discussed in detail in Section II of the text.

Number of Relationships Lender

Rebate Rate

(stock/day) ID Lender Type

Percent

(in percent)

Median Max 1 Broker-dealer

Description

of Obs.

Broker-dealers box to other broker-dealers,

some lending to hedge funds

2 Broker-dealer

Retail brokerage accounts lent to

Broker-dealer box to other broker-dealers,

conduit trades

4 Direct lender

Hedge fund assets lent directly to

Broker-dealers box to other broker-dealers,

conduit trades

6 Broker-dealer

Broker-dealers box to other broker-dealers,

some lending to hedge funds

7 Broker-dealer

Broker-dealers box to other broker-dealers,

some lending to hedge funds

8 Direct lender

3.19 3.15 1.87 1 102 9 Broker-dealer

Mutual fund assets direct to broker-dealers

Hedge fund, pension plans assets lent

directly to other hedge funds or broker-dealers, some conduit trades

10 Direct lender

Hedge fund assets lent directly to

11 Agent lender

Endowments, pension plan assets lent to

12 Agent lender

Institutional assets lent to broker-dealers

567 that are lent (both directly and through agents) are retail brokerages, pension

Supply and Search in the Equity Lending Market

plans, insurance companies, and mutual funds. These market participants represent 36% of the securities lenders by number. 7 In most of the analyses that follow, including the estimation of the supply schedule, we use the sum of outstanding share loans by all lenders normalized by total shares outstanding as our measure of market loan quantity.

We use two separate equity lending databases: the first database comprises 5,042,056 observations of individual loan transactions from September 26, 2003 to May 9, 2007 and includes the number of shares, the daily loan rate, and several identification variables. The loan rate is the interest paid on the borrower’s collateral, also known as the rebate rate. The relative scarcity of a particular stock is measured in terms of its specialness, or the difference between its loan rate and the market’s prevailing, or benchmark, loan rate. Our data provider computes specialness at the firm-day level and this variable is contained in the second database we use, which contains data that has been aggregated to the firm-day level. In addition to daily specialness, the aggregate database contains a measure of the daily quantity and several identification variables. It comprises 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 this aggregate data in our analysis of the share loan supply curve ( Tables IV–VI below).

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

a different benchmark rate. Based on D’Avolio (2002) and Geczy, Musto, and Reed (2002) , we calculate specialness by taking the benchmark rate to be the federal funds rate minus a 10 to 20 basis point spread for each lender. We use the mode of the distribution of loan fees above the federal funds rate to identify each lender’s spread (the difference between the loan rate and the benchmark)

by loan size category. 8 The median spread is 16 basis points, and the spread has a relatively large range: the 25th percentile is one basis point and the 75th percentile is 50 basis points. Among loans above $100,000, the interquartile range 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 transactions made by a given lender. Because borrowers consolidate orders to take advantage of volume discounts and thereby minimize transaction costs, each

7 State Street’s publicly available white paper, “Securities Lending, Liquidity, and Capital Market-Based Finance,” indicates that there were 33 dealers in the equity lending market as

of 2001. 8 As in D’Avolio (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 borrower. The number of transactions for each lender therefore serves as a proxy for the number of unique borrowers, or “relationships,” that a lender has on a given day.

In Table I , we report descriptive statistics on the time series of each lender’s relationships. Interestingly, we find significant variation across lenders in the mean number of relationships, with the average number of relationships per day ranging between one and 10. Furthermore, there is a dynamic aspect to the number of relationships: the mean and median are well below the maximum for most firms. To take one example, for lender #7 the maximum number of relationships is 232, but the mean number of relationships is only 5.06 and the median is 2. The disparity we find between the maximum versus the means and medians indicates that the number of relationships is not constant, which is 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 from whom they borrow the majority of their shares, but for scarce stocks borrowers search across a large number of potential lenders. We also note that the cross-sectional variation in the number of relationships documented here is consistent 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 quantities. To this data set we add the daily stock price, ask price, bid price, and shares outstanding for each firm using data from the Center for Research in Security Prices (CRSP). We also add Federal Funds Rate, which is the effective federal funds rate from the H.15 statistical release provided by the Federal Reserve; S&P Price/Earnings, which is defined as the monthly price to earnings ratio for the S&P500 from Compustat; and VIX, which is calculated as the rolling mean value of the CBOE volatility index for the S&P500 over the preceding 22 trading days.

We winsorize all variables in the aggregate database at the 1st and 99th percentiles and we filter our database to include only those firms with at least 250 observations. After this filter is applied, 586,435 observations remain in the database. In Table II we report summary statistics for the final sample. Although the average value of Specialness is only 37 basis points, it has a standard deviation of 1.36 and it is highly right-skewed, with a skewness of

5.86. In addition, Loan Quantity as a percentage of shares outstanding is also highly right skewed.

III. Results

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

Supply and Search in the Equity Lending Market

Table II

Summary Statistics of Instruments and Short Sale Variables

Table II contains summary statistics for the aggregate-level database, which contains 586,435 observations 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. Discretionary Accruals is calculated quarterly as in Sloan (1996) . Short (Long) Bollinger is an indicator variable that takes the value one if a stock’s price is more than two standard deviations above (below) the 20-day moving average price and zero otherwise. Market Capitalization, in billions, is from CRSP. News Sentiment is a numerical score based on textual analysis of publicly released firm-specific news articles, where low (high) scores indicate negative (positive) news. Short-Term Momentum is the raw buy-and-hold return of a stock over the previous five trading days and Long-Term Momen- tum is the one-year momentum factor as in Carhart (1997) . Loan Quantity / Shares Outstanding is the quantity of shares borrowed divided by the number of shares outstanding each day for each firm. 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 market rebate rate. Federal Funds Rate is 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. VIX is the rolling mean value of the CBOE volatility index for the S&P500 over the preceding 22 trading days. All variables are winsorized at the 1st and 99th percentiles.

Standard Variable

Mean

Median Deviation Skewness

Panel A: Firm

Discretionary accruals

0.849 20.076 Short Bollinger

0.295 2.731 Long Bollinger

0.256 3.347 Market capitalization

30.749 6.544 (in $ Billions) News sentiment

0.042 −0.440 Short-term momentum

0.055 −0.003 Long-term momentum

Panel B: Short Sale Transactions

Aggregate specialness

1.366 5.860 (in percent) Loan quantity/shares

Panel C: Macro

Federal funds rate (in percent)

1.647 −0.359 S&P price/earnings

by search cost models. First, we estimate the share loan supply curve and show that search costs are closely connected to its shape. Next, we empirically verify that the generic predictions of sequential search cost models hold for the equity loan market—that is, that search costs are positively correlated with price dispersion and the level of prices. Finally, we explore other possible explanations for the empirical patterns we find.

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lnes a

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 by outstanding shares to account for persistent differences in loan quantities across securities. For each firm, these relative quantities are then assigned to a decile based on their position relative to other trade quantities for that firm and year. The figure plots the mean specialness across all firms 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 market rebate rate. The rebate rate for an equity loan is the rate at which interest on collateral is rebated back to the borrower.

A. Modeling the Share Loan Supply Curve Presumably, short sale constraints arise as short sellers’ demand for share

loans increases. 9 However, not all increases in share loan demand lead to increases 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 of D’Avolio (2002) , in which we plot specialness (or excess loan fee) as a function of quantity loaned. To account for persistent differences in loan quantity across securities, we calculate relative quantity loaned. In other words, quantity is measured as the rank of normalized loan quantity, defined as the number of shares lent divided by total shares outstanding. We find that specialness declines mildly in loan quantity at low levels of loan quantity, but when loan quantity is above the 70th percentile, specialness increases sharply in loan quantity. The changing sensitivity of specialness to quantity has prac- tical importance for borrowers: upward shifts in the quantity demanded do not necessarily increase loan prices and may even decrease them in some cases.

9 D’Avolio (2002) shows a positive correlation between short interest and loan fees.

571 This initial approach is inherently limited, however. The supply schedule

Supply and Search in the Equity Lending Market

cannot be mapped out correctly using prices and quantities unless the supply curve does not shift during the measurement period. To trace out the supply curve more carefully, we turn to a two-stage regression approach, similar to that of Angrist, Graddy, and Imbens (2000) . Specifically, we use exogenous shifts 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 supply curve may not be linear. To allow for this possibility, we employ a nonlinear technique that builds on the linear approach of Angrist, Graddy, and Imbens (2000) .

In Subsection A.1 below, we use economic theory to propose several instruments for share loan demand and then conduct an empirical falsification test of their validity. In Subsection A.2 we describe our technique for estimating the share 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 different search cost characteristics.

A.1. Instruments for Share Loan Demand To identify the share loan supply schedule, we must use variables that affect

the demand for loans but not the supply. Prior research suggests that most of the supply of shares available for loan comes from institutions with stable, low-turnover portfolios (e.g., D’Avolio (2002) ). On the other hand, the literature

has shown that many short sellers have relatively short time horizons. 10 Thus, one category of potentially valid instruments includes variables that are related to short-term trading strategies but not long-term trading strategies. It stands to reason that low-turnover institutions are, by definition, not concerned with the shorter term components of price movements. Accordingly, variables that isolate the short-term components of price fluctuations are likely to make valid instruments, consistent with Boehmer, Jones, and Zhang’s (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 instruments 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 not the strategies of low-turnover institutions is daily News Sentiment, which is a measure of the amount of positive or negative information contained in publicly released firm-specific news articles. Low-turnover institutions (i.e., equity lenders) are unlikely to trade every time there is a news article about one of the stocks in their portfolio. On the other hand, Engelberg, Reed, and Ringgen- berg (2012) and Fox, Glosten, and Tetlock (2010) show that short sellers do respond 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 trading days, and Diether (2008) finds the median short position is held for 11 trading days.

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a potential instrument for share lending demand, where News Sentiment is defined for each firm and day as a numerical score between −1 and 1; low scores indicate negative news and high scores indicate positive news. The news data 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 press releases 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 Jones newswire, which includes, among other sources, the Wall Street Journal and Barron’s.

We also consider variables that capture the short-term component of price fluctuations. Specifically, we consider several variables related to technical analysis. Survey evidence suggests that institutional portfolio managers use technical 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 of

a stock over the previous five trading days. Diether, Lee, and Werner (2010) show that short sellers do respond to short-term momentum; however, it is unlikely that low-turnover institutions, which provide the bulk of lendable shares, respond to it. To make sure our short-term measures of returns are isolating the high-frequency component of price movement, we also include Long-Term Momentum as a control variable, where Long-Term Momentum is defined as the traditional one-year momentum factor as in Carhart (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 stock price is respectively above or below its 20-day moving average by more than two

standard deviations. 11 We use the rule to define the indicator variables Short Bollinger and Long Bollinger, where Short Bollinger and Long Bollinger equal one when a stock is respectively above or below its 20-day moving average by more than two standard deviations and zero otherwise.

Finally, we consider Discretionary Accruals, as computed in Sloan (1996) , as

a potential instrument. Discretionary accruals constitute a decision by management to shift earnings from one period to another. Thus, high or low discretionary accruals cannot persist and must, by construction, be followed by

a reversal. Recent accounting studies suggest that this reversal occurs in less than a year, and all the negative (positive) abnormal returns associated with high (low) discretionary accruals are realized by the time of the accrual reversal (e.g., Allen, Larson, and Sloan (2010) , Fedyk, Singer, and Sougiannis (2011) ). Discretionary accruals are therefore unlikely to be related to trading by low-turnover institutions and hence the quantity of lendable shares. On the other hand, prior literature finds that short selling is related to discretionary accruals (e.g., Cao et al. (2008) ).

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

573 Having made an a priori case for our instruments based on economic theory,

Supply and Search in the Equity Lending Market

we next conduct a formal empirical falsification test of their validity. For this test, we use a data set that contains the aggregate number of shares that equity lenders have available for loan over the period January 1, 2007 to December

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

The data we use for this test comes from Data Explorers, a leading provider of data in the equity loan market. Data Explorers aggregates and distributes information regarding the equity lending market at the daily frequency. The data are sourced directly from a wide variety of contributing customers including beneficial owners, hedge funds, investment banks, lending agents, and prime brokers. The database contains information on the aggregate quantity lenders actually lend out as well as the aggregate quantity of shares lenders have available for loan, including those not lent. Our falsification test uses the quantity available normalized by shares outstanding. We henceforth refer to this variable as lendable shares.

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

Lendable Shares it =β 1 Accruals it +β 2 ShortB it +β 3 LongB it +β 4 News it (1) +β 5 STMom it + Controls it + FE i +ε it ,

where Accruals are discretionary accruals, ShortB and LongB are the short and long Bollinger indicator variables, News is news sentiment, and STMom is short-term momentum. We include stock fixed effects, and we cluster the standard errors by stock and day to ensure robustness to heteroskedasticity as well as serial and cross-sectional correlation. If the candidate instruments meet the exclusion restriction, they should have no explanatory power in this regression. The results, presented in Table III , are consistent with our a priori 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 from zero.

In addition to being statistically insignificant, our point estimates suggest that the effect of our candidate instruments on lendable shares is also economically negligible. Take, for instance, the coefficient estimate on News Sentiment of −0.0129. This implies that a one standard deviation increase in News Sen- timent of 0.042 units shifts the log of lendable shares by −0.0005 [−0.0005 = −0.0129×0.042], a negligible amount compared to the standard deviation of the log of lendable shares of 0.6952. Other point estimates imply that a one standard deviation increase in Short-Term Momentum and Discretionary Accruals impacts lendable shares by the economically negligible amounts of –0.0007 and 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 Shares it =β 1 Accruals it +β 2 ShortB it +β 3 LongB it +β 4 News it +β 5 STMom it +Controls+FE i +ε it .

Lendable Shares is the natural log of the number of shares available for loan each firm and day as a percentage of shares outstanding. The candidate instruments are described in detail in Section III.A of the text. Federal Funds Rate is the effective federal funds rate as reported by the H.15 statistical release, Long-Term Momentum is 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 preceding month, and VIX is the rolling mean value of the CBOE volatility index for the S&P500 over the preceding 22 trading days. Firm fixed effects are included and F-Test of

Instruments assesses whether the candidate instruments are jointly different from zero. Robust standard 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 ∗ indicates

significance 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

Yes N

642,134 F-test of instruments

variables imply that a stock price movement from within the Bollinger bands to a point above or below them impacts the quantity of lendable shares by a negligible –0.0012 and 0.0032, respectively. Accordingly, because the candidate instruments are both statistically and economically insignificant in the falsification test, we adopt Discretionary Accruals, Short Bollinger, Long Bollinger,

575 News Sentiment, and Short-Term Momentum as instruments in the estimation

Supply and Search in the Equity Lending Market

of the supply curve.

A.2. Estimating the Share Loan Supply Schedule Using the instruments discussed above, we estimate the share loan supply

curve, which allows us to determine the influence of short sellers’ demand for share loans on specialness and the extent to which increases in loan prices are related to search frictions. We discuss our estimation procedure in detail below.

To ensure comparability across stocks, we standardize our loan quantity variable. First, we divide quantity by total shares outstanding for each stock. This removes the effect of stock price on quantity, which would likely be sufficient for an estimation using market-wide quantity. However, because our lenders hold only 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 stock’s quantity. Thus, we standardize each stock’s quantity variable by subtracting the mean and dividing by the standard deviation of each stock’s loan quantity as a percentage of shares outstanding. We denote this standardized value of share loan quantity by Q.

Next, we need to take into consideration the highly skewed nature of both quantity and specialness, as well as the probable nonlinearity of the supply curve. To this end, we employ a trans-log specification in which we model the started natural log of specialness as a function of the started natural log of

quantity 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 instruments discussed 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(Q it + C) = δ i +γ 1 LN(S it + D) + γ 2 Accruals it +γ 3 ShortB it +γ 4 LongB it (2) +γ 5 News it +γ 6 STMom it + Controls it +η it

LN(S

it + D) = α i +β 1 LN(Q it + C) + β 2 LN(Q it + C) + Controls it +ε it , (3) where C and D are “start” constants that ensure the log is defined, 13 Q is loan

quantity, S is specialness, Accruals are Discretionary Accruals, ShortB and LongB are the Short and Long Bollinger indicator variables, News is News Sentiment, and STMom is Short-Term Momentum, all as defined above. The Controls vector 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 take negative values. Likewise, specialness can be negative. Therefore, as Fox (1997) suggests for right-

skewed variables with negative values, we use the started log transformation of both quantity and specialness. Our results are not sensitive to the choice of start constant.

13 We use start constants C = 10 and D = 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 IV presents the first-stage results from a two-stage instrumental variables panel data regression of daily data over the period September 26, 2003 to December 31, 2007. The excluded instruments are discussed in Section III.A of the text and, because there are two endogenous re- gressors (the started log quantity and its square), there are two first-stage regressions. Firm fixed effects are included in all models. The F-statistic tests the null of weak identification. 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.

A Multiple Lender Approach to Understanding Supply and Search in the Equity Lending Market