Dynamics of Securities Lending and Stock Price Interaction

 
Preliminary; Do not Quote

         Dynamics of
         Securities Lending
         and Stock Price
         Interaction

          Gangadhar Darbha, Ph.D*
          Executive Director & Head,
          Algorithmic Trading Strategies,
          Nomura Structured Finance, India.
          gangdhar.darbha@nomura.com

* I thank my colleagues Naveen Naidu, Ashish Kyal, Sukhwant Matharoo and Ben Challice
for helpful discussions. The views expressed in this paper, however, are personal.
Dynamics of Securities Lending and Stock Price Interaction - Gangadhar Darbha

                             Dynamics of Securities Lending
                               and Stock Price Interaction
                                             Abstract
The literature on securities borrowing and lending suggests that if the main objective of
securities borrowing and lending is to facilitate shorting motivated by some information
about the underlying stock, the impulses to loan quantity and fees should have uni-directional
permanent impact on stock prices; if, on the other hand, the motive is to facilitate cross-
security arbitrage or spread trades, then one would expect the impact on stock prices would
be significant but non-permanent and the variations in stock prices would also have an effect
on stock lending activity; if, as is popularly believed, the motive is only to undertake some
predatory trading strategies to build an artificial downward pressure on a stock, one would
expect the stock price impact be only transitory and the effects are uni-directional from
securities lending market to stock prices. The objective of this study is to analyze the
dynamic interactions between activities and prices in security lending and that of underlying
stock with a view to test the above hypotheses. Using the daily time series data on stock
prices, loan fees and quantities on FTSE-100, S&P-100, IBEX-35 and TOPIX-100 stocks, we
compute the Impulse Response Functions (IRFs) using a VAR model, estimated by the
method of Local Projections, on loan quantity, lending fees, stock prices and trading volume
for each stock in our database. Our findings include: (i) shocks to stock lending activity have
significant effects on stock prices; these effects are non-permanent on an average, but not
transitory, in the sense that they survive for almost a month before reverting to their original
levels; (ii) shocks to stock prices also have significant impact on stock lending activity
highlighting a bi-directional relation; and (iii) while there is significant cross-sectional
variation in these results, the average effects are similar across different geographic regions
across the globe. These findings suggest that security lending market is being used not just
for the purpose of speculative shorting but also for market efficiency enhancing cross-
security arbitrage trades.

JEL classification: G11; G12; G14
Keywords: Securities lending; Stock lending; Short-selling; Predatory trading
1. Introduction
        Securities lending is the market practice whereby securities are transferred
temporarily from one party (the lender) to another (the borrower) for a fee. The borrower
must return the securities to the lender either at the end of an agreed term, or on demand. In
law, securities lending is an absolute transfer of title (or sale) against an undertaking to return
equivalent securities. Most securities loans are collateralised with cash or other securities.
The process is facilitated by intermediaries such as custodians, investment banks or
stockbrokers. Lending of securities is primarily motivated by the fee income received from
the loan.     D‘Avolio (2002) studies a US stock lending database from April 2000 to
September 2001 and shows that the value-weighted fee obtained for lending US equities is 25
b.p. per annum, but that only 7% of loan supply is borrowed. Although generally at a thin
rate, lending improves the asset‘s total performance and can offset custodial fees and
administrative expenses. Lenders can also be motivated by the desire to borrow short-term
money, and can do this by arranging transactions such as repurchase agreements or cash-
collateralised securities lending. Securities lenders include long-term investors such as
pension funds, insurance companies and mutual funds, but also banks and broker-dealers.
In addition to facilitating short-selling, reasons for borrowing stock include market makers
borrowing securities to fill customer buy orders, exchange specialists borrowing to maintain
price stability, and stockbrokers borrowing to cover a short position after failed settlement.
Securities borrowing can also be related to hedging by the counter-parties to contracts for
differences, spread bets and swaps. The temporary transfer of ownership can also motivate
securities borrowing. This includes dividend capture strategies such as ‗scrip dividend
arbitrage‘ and ‗dividend withholding tax arbitrage‘1.

1
    In this latter case, for example, the holder of securities is subject to withholding tax on
interest or dividends, but the borrower would be free of withholding tax. Some of the benefits
the borrower obtains from receiving the dividend free of withholding tax are shared with the
lender.
Dynamics of Securities Lending and Stock Price Interaction - Gangadhar Darbha

        Short-selling is the sale of securities that the seller does not own, or that the seller
owns but chooses not to deliver. The short-seller must borrow securities in order to fulfil
delivery obligations to the purchaser. ‗Naked short-selling‘ occurs when the short-seller does
not borrow, and so does not deliver, stock to the purchaser. In the United States securities
markets, for example, Regulation SHO 2004 requires short-sellers to locate stock for
borrowing, prior to selling a stock short, with the intention of prohibiting naked short-selling.
Short-selling is particularly associated with the activities of arbitrageurs and hedge funds.
Although some funds exclusively sell short, seeking to benefit from a decline in the value of
a security, most short-selling is part of a broader trading strategy, designed to exploit
perceived pricing anomalies between two or more securities. Examples of such trading
strategies include capital structure arbitrage (see Yu, 2006), merger arbitrage (see Mitchell
and Pulvino, 2001) and pairs trading (see Jacobs and Levy, 1993). Not all short-sales are
driven by expectations of a price change; some sales are meant to stabilise prices. For
instance, underwriters often sell short to reduce volatility in the price of public offering and
buyback programs.
        If the main objective of securities borrowing and lending is to facilitate shorting
motivated by some information about the underlying stock, the impulses to loan quantity and
fees should have uni-directional permanent impact on stock prices; if, on the other hand, the
motive is to facilitate cross-security arbitrage or spread trades, then one would expect the
impact on stock prices would be significant but non-permanent and the variations in stock
prices would also have an effect on stock lending activity; if, as is popularly believed, the
motive is only to undertake some predatory trading strategies to build an artificial downward
pressure on a stock, one would expect the stock price impact be only transitory and the
effects are uni-directional from securities lending market to stock prices.
        The objective of this study is to analyze the dynamic interactions between activities
and prices in security lending and that of underlying stock with a view to test the above
hypotheses. Using the daily time series data on stock prices, loan fees and quantities on
FTSE-100, S&P-100, IBEX-35 and TOPIX-100 stocks from a global security market data
depository DataExplorers, we compute the Impulse Response Functions (IRFs) using a
Vector Auto-regression model, estimated by the method of Local Projections, on loan
quantity, lending fees, stock prices and trading volume for each stock. Our findings include:
(i) shocks to stock lending activity have significant effects on stock prices; these effects are
non-permanent on an average, but not transitory, in the sense that they survive for almost a
month before reverting to their original levels; (ii) shocks to stock prices also have significant
impact on stock lending activity highlighting a bi-directional relation; and (iii) while there is
significant cross-sectional variation in these results, the average effects are similar across
different geographic regions across the globe. These findings suggest that security lending
market is being used not just for the purpose of ―speculative‖ shorting but also for market
efficiency enhancing cross-security arbitrage trades.
The remainder of this paper is organised as follows. Section 2 contains a literature review.
Section 3 discusses the model specification, econometric methodology and data details.
Section 4 presents the results and Section 5 concludes highlighting the preliminary findings
and directions for future research.

2.     Literature Review
       Various studies examine the relationship between short-interest in a security (the
value of shares shorted relative to market capitalization , or relative to average daily turnover)
and stock price variation. These studies attempt to test the theory that short-sellers are, on
average, well informed traders. Figlewski (1981), Brent et al. (1990), Figlewski and Webb
(1993) and Woolridge and Dickinson (1994) find no evidence of a strong relation between
short-interest and abnormal return. By contrast, Senchack and Starks (1993) investigate the
market reaction to monthly short-sale announcements from both the New York and the
American Stock Exchanges. They examine the wealth effects of short-interest
announcements, and the relation between wealth effects and the degree of unexpected
increases in short-interest. Using monthly common-stock short-interest figures from 1980 to
1986, they identify companies showing ‗unusually large‘ increases in short interest. They
find evidence that some significant negative price reaction occurs in an extended period
around the announcement of a substantial increase in short-interest.
       By focusing on firms with large short-interest only, Asquith and Muelbroek (1996)
argue that the power of such tests can be improved. They find a strong and consistent relation
between short-interest and excess returns. Shares with high levels of short interests perform
significantly worse than comparable shares without high levels of short interest.
Only limited, monthly information on short interest has been publicly available in the USA
prior to 2005, and this has limited the scope of research into this topic. Aitken et al. (1998)
analyse information provided by the Australian Stock Exchange (ASX), covering intra-day
information on short positions in listed ASX equities. Short trades were reported to the
market soon after execution. The authors investigate the immediate market reaction to short
Dynamics of Securities Lending and Stock Price Interaction - Gangadhar Darbha

sales and find a significantly negative abnormal return following short-sales. Abnormal
returns are calculated by comparing short-sales to matched non-short sale trades. Ackert and
Athanassakos (2004) study Canadian monthly data from 1991-1994 and from 1998-1999. For
different levels of short interest (defined in their study as the ratio of the number of shares
shorted to trading volume) they study subsequent abnormal returns and find that after high
levels of short interest, poor performance persists into the future. In a study of NYSE
proprietary system order data from 2000 – 2004, Boehmer et al. (2006) measure 20 day
abnormal returns following from high levels of short-selling. They find that ―As a group, []
short sellers are extremely well informed‖ and that ―institutional, non-program short sales are
the most informative.‖ However, the authors caution that the full information upon which
their study was based, is not publically available, and that trading strategies based on their
findings could not be formed in practice.
        Dechow et al. (2001) examine the extent of short selling during the period 1976-1993,
using public US data. The authors identify a strong relation between the trading strategies of
short sellers and ratios of fundamentals to market prices, such as book to market ratios. They
show that short-sellers target equities that have low fundamental to price ratios, and then
unwind their positions as these ratios revert to the mean. They also show that short sellers
refine their trading strategies in three ways: by avoiding equities where short-selling is
expensive; by using information other than fundamental to price ratios that has predictive
ability with respect to future returns; and by avoiding equities with low fundamental to price
ratios where the low ratios are due to temporarily low fundamentals (as opposed to
temporarily high prices). Their evidence suggests that ―short sellers are sophisticated
investors who play an important role in keeping the price of stocks in line with
fundamentals.‖
Jones and Lamont (2002) study the centralised stock loan market on the floor of the New
York Stock Exchange (known as the ‗loan crowd‘) from 1926-1933. They show that as
stocks ‗enter the loan crowd‘, they generally have high valuations and low subsequent
returns. Size-adjusted returns are 1-2% lower for stocks that enter the loan crowd for the first
time, and despite the high costs of borrowing and shorting these securities, it is profitable to
short them.
Angel et al. (2003) study 3 months of short trades reported to NASDAQ during 2000.
They assess the frequency of short selling for their sample of NASDAQ trades. They find
that 2.36% of trades are short trades, and that 2.88% of shares traded were shorted, with the
median less than the mean in both cases, suggesting that short sales tend to be concentrated in
certain shares on a subset of days. Where the degree of short-selling is greater than average,
significantly negative market-adjusted returns follow in the next three days. Short-selling is
more common in actively traded companies and in shares with higher price volatility. The
authors also find that short-selling is focused on shares that had exhibited greater than
average prior price performance.
          D‘Avolio (2002) examines stock lending fees and shows that ‗growth‘ and ‗low-
momentum‘ stocks are relatively more likely to be ‗special‘ (i.e. have higher than average
lending fees), leading to practical difficulties and costs in creating the long/ short factor
portfolios found in the finance literature. Geczy et al. (2002) analyse a private database of US
securities lending. They examine if investors can actually realize the returns of such long-
short factor portfolios, including the book-to market strategy from DeBondt and Thaler
(1987) and Fama and French (1993), and the price momentum strategy from Jegadeesh and
Titman (1993). The authors find that the expected-return difference between unconstrained
factor portfolios found in the literature and portfolios that investors could actually hold is
significantly smaller than the unconstrained factor portfolios‘ documented profitability. They
argue that if short-selling problems explain the availability of factor portfolio returns to
unskilled managers, then these short selling problems are not borrowing costs, but perhaps
prohibitions on short-selling, or liquidity constraints, such as those cited in Shleifer and
Vishny (1997).
          Cohen, Deither and Malloy (2007), using the data on loan quantities and fees from a
large institutional investor, find that shorting demand is an important predictor of future stock
returns and their results are stronger in environments with less public information. They
interpret their finding to indicate that shorting market is an important mechanism for private
information revelation.
          The literature thus reveals a growing body of evidence that short-sellers are well
informed, and that highly-shorted stocks subsequently perform poorly. As shorts are, on
average, well-informed, the potential importance of information about short positions has
become clear. However, an awareness of the borrowing costs, constraints and risks of
shorting are also highlighted, and these diminish any trading opportunities that might arise.
While the stock lending and borrowing activity is being used as a proxy for shorting, the
literature highlights that the former may also be used for hedging and cross-security arbitrage
trades.
Dynamics of Securities Lending and Stock Price Interaction - Gangadhar Darbha

         A limitation of most of the empirical studies in this context is that is to pose the
problem in a uni-variate regression setting correlating the changes in stock prices with stock
lending activity and loan fees. However, to get better understanding of the dynamic inter-
relations between activity and prices in stock and stock lending markets, one should
formulate the analysis in multi-variate dynamic regression framework and compute the
responses of stock prices to demand and supply shocks in security lending market and vice-
versa over different time horizons. We propose to undertake such an analysis in this paper.

    3. Model Specification, Econometric Methodology and Data details
    3.1. Model Specification
         The primary objective of the empirical exercise under taken in this paper is to
compute by how much the stock prices (and volume) react to ―demand and supply shocks‖ in
stock lending and borrowing activity and what impact shocks to stock prices have on the
stock lending and borrowing activity. While we do not explicitly postulate and test any
hypotheses based on a structural model (Duffie, Garleanu and Pedersen (2001)), our
objective is to characterize the empirical regularities, if any, in the data using a consistent and
flexible econometric framework. Towards that purpose, we estimate the dynamic multi-
variate regression model via the method of Local Projections involving (log of) stock price,
trading volume, loan quantity (percent of lendable securities on loan, to be precise) and loan
fee for each of the stocks in FTSE-100 and S&P-100 indices.
         More precisely, the empirical questions that we are seeking to answer are:
   (i)       Do increases in loan ―Demand‖ have significant negative impact on stock prices?
   and How ―persistent‖ are these effects?
   (ii) Do increases in loan Fee and ―costs of lending‖ generate upward bias in stock price
   variation over short-run and long-run?
   (iii) Do prices and activity in security lending market respond to changes in stock prices as
   well?
         By specifying an econometric model which allows for dynamic lead-lag relations
among price and activity variables in stock and stock lending markets, we are able to control
for potential endogeneity in the time series evolution of these variables, an aspect not taken
into account in most of the previous studies. Our model readily allows for estimating the bi-
directional response coefficients of stock prices and stock lending activity at different time-
horizons taking into account the lead-lag relations among the variables under study.
        In analysing the impulse-response coefficients, we must note that the shocks to loan
quantity and loan fee, however, may not unambiguously indicate the whether the shocks are
to the loan demand or supply. Following Cohen et al. (2007), we decompose the competing
effects of shocks to shorting demand and shorting supply by exploiting the ―price-quantity
pairs‖ to identify which theoretical channel drives the relation between securities lending
market and stock prices. For example, an increase in the loan Fee (a measure of price in
security lending market) coupled with an increase in the percent of loan quantity out of the
lendable pool would correspond to a positive demand shock in security lending market.
Similarly, a decrease in loan quantity coupled with an increase in loan fee corresponds to a
negative supply shock in the security lending market.
        Differentiating the loan demand and supply shock effects on stock prices is crucial for
the channel through which the later respond to activity in security lending market (Cohen et
al. (2007)). If shorting2 demand is the dominant channel, then coupling of increased price and
increased quantity are important. Increased quantity, for instance, could be informative for
future stock returns if it proxies for additional market frictions or risks of shorting, or if it
signals higher probability of informed trading. Alternatively, as in Diamond and Verrecchia
(1987), high unexpected short interest may signal large quantity of negative private
information, since few liquidity traders and or hedgers are likely to short in the face of high
shorting costs. If shorting demand is important empirically, then private information or other
indirect costs of shorting are key factors in the link between shorting market and stock prices.
The factors driving changes in shorting supply are different. Supply shifts are driven by
changes in institutions marginal cost of lending. For example, because many lending
institutions also operate mutual funds, they have other incentives to holding stocks.

2
 In what follows we are using shorting demand and demand for security borrowing interchangeably with full
awareness that motives for shorting need not be just a negative view on stock prices.
Dynamics of Securities Lending and Stock Price Interaction - Gangadhar Darbha

Following a sale of shares of certain stock in its funds, a lending institution experiences an
inward shift of supply curve for its stock. However, any movement in marginal cost will shift
the curve. The interpretation and implications of shifts driven by contractions of shorting
supply are therefore quite different from those of shifts driven by increases in shorting
demand. Supply shifts inward (outward) indicate tightening (loosening) of short-sale
constraints, while demand shifts capture either informed trading or additional market frictions
and risks associated with shorting. Thus, isolating the relative effects of supply and demand
empirically is crucial for developing a better understanding of the impact of the shorting
market on stock prices.
        In this study, we first postulate four unanticipated impulses to loan quantity and prices
and analyse their impact on stock prices over different time horizons. These are: (i) a
percentage point increase in quantity on loan (as a proportion of outstanding lendable
securities) and a one standard deviation increase in loan fee implying a demand shock and (ii)
one standard deviation increase in loan fee coupled with a percentage point increase in loan
quantity implying a negative supply shock. In terms of testable implications, the impact of (i)
is expected to be negative on stock prices while that of (ii) is expected to be positive. We also
study (iii) the response of stock lending and loan fee variables to shocks in stock prices; as
discussed above, if the stock borrowing and lending market is being used to facilitate cross-
asset arbitrage trades, one would expect a strong feedback impact from stock prices to stock
lending and borrowing activity.
The size and the duration of these impacts cannot be derived from theoretical arguments
alone, and will have to be inferred from empirical impulse response functions. Towards that
end, after labelling these shocks, we estimate the response functions by estimating the
dynamic regression model over multiple time horizons using the method of Local
Projections, the details of which are explained in the next section.

3.2. Impulse Response Functions by the Method of Local Projections3
          Vector-Autoregressions (VARs) have been the main workhorse of empirical macro
economics for last 20 years or so in modelling the dynamic inter-relations between various
macro economic variables and in computing the impulse-response functions (IRFs) of the
variables of interest.       Impulse responses (and variance decompositions) are important
statistics in their own right in in the sense that they provide the empirical regularities that
substantiate theoretical models of the economy and are therefore a natural empirical
objective.
          While the estimation of a (linear) VAR readily permits one to compute the IRFs,
computation of the later can be achieved through more flexible regression framework such as
the method of Local Projections that do not require specification and estimation of the
unknown true multivariate dynamic system itself (Jorda (2005)). The advantages of local
projections are numerous: they can be estimated by simple least squares; they provide
appropriate inference (individual or joint) that does not require of asymptotic delta-method
approximations nor of numerical techniques for its calculation; they are robust to
misspecification of the DGP; and they easily accommodate experimentation with highly
nonlinear specifications that are often impractical or infeasible in a multivariate context.
Since local projections can be estimated by uni-variate equation methods, they can be easily
calculated with available standard regression packages and thus become a natural alternative
to estimating impulse responses from VARs.

3
    This section is based on Jorda (2005).
Dynamics of Securities Lending and Stock Price Interaction - Gangadhar Darbha

        The key insight is that estimation of a model based on the sample, such as a VAR,
represents a linear global approximation to the DGP ideal and is optimally designed for one-
period ahead forecasting. Even when the model is misspecified, it may still produce
reasonable one-period ahead forecasts (see Stock and Watson, 1999). However, an impulse
response is a function of forecasts at increasingly distant horizons, and therefore
misspecification errors are compounded with the forecast horizon. This paper suggests that it
is preferable to use a collection of projections local to each forecast horizon instead, thus
matching design and evaluation.
        Local projections are based on sequential regressions of the endogenous variable
shifted several steps ahead and therefore have many points of commonality with direct multi-
step forecasting. The ideas behind direct forecasting (sometimes also called adaptive
forecasting or dynamic estimation) go back to at least Cox (1961). Weiss (1991) establishes
consistency and asymptotic normality of the direct forecasts under general conditions. The
accuracy of direct forecasting has been evaluated in several papers. Tsay (1993) and Lin and
Tsay (1996) show that direct forecasting performs very well even relative to models where
cointegrating restrictions are properly incorporated. Bhansali (1996, 1997) and Ing (2003)
show that direct forecasts outperform iterated forecasts for autoregressive models whose lag
length is too short - a typical scenario when a VAR is used to approximate a VARMA model,
for example. Bhansali (2002) provides a nice review on this recent literature. Direct
forecasting seeks an optimal multi-step forecast whereas the local projections proposed here
seek a consistent estimate of the corresponding impulse response coefficients. Obviously,
these objectives are not disjoint in much the same way that they are not when estimating a
VAR.

3.2.1 Estimation
        Impulse responses are almost universally estimated from the Wold decomposition of a
linear multivariate Markov model such as a VAR. However, this two-step procedure
consisting on first estimating the model and then inverting its estimates to find the impulse
responses is only justified if the model coincides with the DGP. Furthermore, deriving correct
impulse responses from cointegrated VARs can be extremely complicated (see Hansen,
2003). Instead, impulse responses can be defined without reference to the unknown DGP,
even when its Wold decomposition does not exist (see Koop et al., 1996; and Potter, 2000).
Specifically, an impulse response can be defined as the difference between two forecasts (see
Hamilton, 1994; and Koop et al., 1996):

Where the operator E (.|.) denotes the best, mean squared error predictor;                   is an n × 1

random vector;                                   0 is of dimension n × 1;           is the n × 1 vector of

reduced-form disturbances; and D is an n × n matrix, whose columns                    contain the relevant
experimental shocks.
          Time provides a natural arrangement of the dynamic causal linkages among the

variables in      , but does not identify its contemporaneous causal relations. The VAR

literature has often relied on assuming a Wold-causal order for the elements of                to organize
the   triangular     factorization     of     the     reduced-form,      residual     variance-covariance

matrix,            . Such an identification mechanism, for example, is equivalent to defining

the experimental matrix as                  so that its       column,   , then represents the ―structural

shock‖ to the       element in       (in the usual parlance of the VAR literature).
          Expression (1) shows that the statistical objective in calculating impulse responses is
to obtain the best, mean-squared, multi-step predictions. These can be calculated by
recursively iterating on an estimated model optimized to characterize the dependence
structure of successive observations, of which a VAR is an example. While this approach is
optimal if indeed the postulated model correctly represents the DGP, better multi-step
predictions can often be found with direct forecasting models that are re-estimated for each

forecast horizon. Therefore, consider projecting                   onto the linear space generated by

                   , specifically

                                                    (2)

where       is an n × 1 vector of constants, the              are matrices of coefficients for each lag i
and horizon s + 1. I denote the collection of h regressions in (2) as local projections, a term
aptly evocative of non-parametric considerations.
          According to definition (1), the impulse responses from the local-linear projections in

(2) areWith the obvious normalization                     .
Dynamics of Securities Lending and Stock Price Interaction - Gangadhar Darbha

                                                                            (3)
An extensive literature (see Bhansali, 2002 and references therein) on the direct, multi-step
forecasts implied by (2) establishes their consistency and asymptotic normality properties

(see Weiss, 1991). The consistency and distributional properties of the estimates       — the
impulse response coefficients are discussed in Jorda (2005).
        A few final practical comments conclude this section. First, the maximum lag p
(which can be determined by information criteria, for example) need not be common to each
horizon s (to see this consider a VMA(q) DGP, for example). Second, the lag length, and the

dimension of the vector           will impose degree-of-freedom constraints on the maximum
practical horizon h for very small samples. Third, consistency does not require that the
sequence of h system regressions in (2) be estimated jointly — the impulse response for the

jth variable in    can be estimated by univariate regression of           onto              .
Finally, local projections are also useful in computing the forecast-error variance
decomposition.
3.2.2 Relation to VARs and Inference

        A VAR specifies that the n×1 vector              depends linearly on                ,
through the expression

                                                                                  (5)
where    is an       vector of disturbances and                         . The VAR(1) companion
form to this VAR can be expressed by defining4

                       ;                                   ;                  (6)
and then realizing that according to (5) and (6),

                                                                              (7)
from which s-step ahead forecasts can be easily computed since

and therefore

                                                                                     (8)

where    is the    upper, n × n block of the matrix        (i.e., F raised to the power s).

        Assuming           is covariance-stationary (or in other words, that the eigen values of F
lie inside the unit circle) the infinite vector moving-average representation of the original
VAR in expression (5) is

                                                                                     (9)
and the impulse response function is given by

Expression (8) establishes the relationship between the impulse responses calculated by local
projection and with a VAR. Specifically, comparing expression (2), repeated here for
convenience,

4
 For a more detailed derivation of some of the expressions that follow the reader should
consult Hamilton (1994), chapter 10.
Dynamics of Securities Lending and Stock Price Interaction - Gangadhar Darbha

                                                                                         (10)
with expression (8) rearranged,

                                                                                  (11)
It is obvious that,

                                                                                         (12)
Hence, when the DGP is the VAR in (5), expressions (10) and (11) establish the equivalence
between impulse responses calculated by local projections and with this VAR. Expression

(12) shows that the error terms of the local projection,               , are a moving average of the
forecast errors from time t to t + s, which knowledge can be used to improve efficiency.

          Define:                         ,                           and                            , so
that we can stack the h local projections in expression (10) and take advantage of the
structure of the residuals implied by the VAR assumption and estimate the following system
jointly

                                                                                                (13)where
(ignoring the constant terms) the parameter matrices are constrained as follows

                                                       ;

Defining                       then                                         .   Maximum         likelihood
estimation of this system can then be accomplished by standard GLS formulas according to,

                                                                                           (14).
The usual impulse responses would then be given by rows 1 through n and columns 1

through             of   and standard errors are provided directly from the regression output.
Further simplification is available due to the special structure of the variance-covariance

matrix , which allows GLS estimation of the system block by block.
          In fact, ML estimation of (13) delivers asymptotically exact formulas for single and
joint inference on the impulse response coefficients of the implied VAR rather than the usual
point-wise, analytic, delta-method approximations (see Hamilton, 1994; Chapter 11), or
simulation based estimates based on Monte Carlo or bootstrap replications5 In general the
true DGP is unknown and so is the specific structure of Φ, hence the GLS restrictions
described above are unavailable. This poses no difficulty, however, as the error terms us t+s
in expression (2) will follow some form of moving-average structure whose order is a
function of the horizon s. Thus, impulse responses can be calculated by univariate regression
methods with a heteroskedasticity and autocorrelation (HAC) robust estimator with little loss
of efficiency. In principle, the efficiency of these estimators can be improved upon by
recursively including the residuals of the stage s − 1 local projection as regressors in the stage
s local projection.
          In practice the DGP is unknown and it is preferable to make as few assumptions as
possible on its specification. Thus valid inference for local projection impulse responses can

be obtained with HAC robust standard errors. For example, let            be the estimated HAC,

variance-covariance matrix of the coefficients       in expression (2), then a 95% confidence
interval for each element of the impulse response at time s can be constructed approximately

as                     Monte Carlo experiments in Jorda (2005) suggest that even when the
true underlying model is a VAR, unrestricted local projections experience small efficiency
losses.

5
  Sims and Zha (1999) provide methods for joint inference in impulse responses but they
involve complicated and rather computationally intensive Bayesian methods that most
practitioners have not yet adopted.
Dynamics of Securities Lending and Stock Price Interaction - Gangadhar Darbha

4. Data, Data Transformation and Estimation Details
        The data used in this study covering the price and activity variables in stock
borrowing and lending for each stock in FTSE-100, S&P-100, IBEX-35 and TOPIX-100
indices are compiled Data Explorers Ltd. Their database provides: date, name of company,
number and value of shares traded for each company for each day, daily end of day share
price and market capitalisation for each company, number and value of shares on loan for
each company for each day, and dividend record dates. We make use of the Data Explorers.
        Data Explorers collect data throughout the day from all securities finance
practitioners: Agent Lenders, Sell Side and Buy Side. Their data set contains more than 9
million daily position updates from over 20,000 securities lending programs around the world
sourced directly from global securities lending desks at leading financial institutions. It
encompasses more than 85% of global transactions. Stock Price and Average volumes data
was taken from internal data dump which gets data from Bloomberg. The sample period
considered for FTSE-100 is from 1st March 2007 till June 2011, for S&P-100 is from 1st
March 2005 till June 2011, for IBEX-35 is from 1st March 2006 till June 2011 and for
TOPIX-100 is from 1st October 2005 till June 2011.
      We aggregate the transaction level data for each stock to obtain the average daily
averages of the variables under study as follows:
      (i)        % Utilization = 100*(Total quantity of the security on loan / Total quantity of
   the security available for lending). An increase in % utilization is likely to indicate
   ―increase in loan demand‖ compared to an increase in loan quantity alone. However, as
   discussed above, to define demand and supply shocks more precisely, we use the data on
   ―% utilization - loan fee pairs‖.
      (ii)       Average Fee = Weighted average of the transaction level fee with weights
   being quantities of transaction.
      (iii)      Stock Price = daily closes from Bloomberg
      (iv)       Average Volume = 20-day Average traded volume computed from
   Bloomberg.
   We estimate the local projections model in (2) on the vector of four variables: percent
utilization, average loan fee, log price and log of average daily volume. The dynamic
regression model for each horizon and each stock are estimated using OLS, with the optimal
lag-length selected by AIC. Since the presentation of all results for all stocks will be too
cumbersome, in what follows we focus on the market-cap weighted average and cross-
sectional distribution of the Impulse Response coefficients for stock prices, loan quantity and
loan fee at different time horizons.

5. Results
5.1 Stock Price Response to Demand and Supply Shifts in Stock Lending
5.1.1 Market-Cap Weighted Average IRFs
       While we estimate the VAR model for each stock within each Index, we report the
cross-sectional moments of those response functions weighted by each stock‘s median market
capitalization. In Figures 1, 5, 9 and 13, we present the cross-sectional market-cap weighted
average of the IRF coefficients for horizons up to 40days for FTSE-100, S&P-100, IBEX-35
and TOPIX-100 respectively. Upper panel in each of these figure indicate the response of
stock price and volume to a demand shock as defined above, while the lower panel indicates
the response of the same w.r.t a supply shock.
       The patterns in the upper-left panels in each of these figures clearly indicate that on an
average, a positive demand shock, defined as 1 standard deviation shock to proportion of
quantity lent and the loan fee, in security lending market would have a significant negative
impact on stock prices with the impact ranging in the short run from -0.4% (FTSE) to -0.05%
(TOPIX); however over a horizon of two months the impact ranges from -0.6% (TOPIX) to -
0.16% (S&P). Across the geographical regions the negative response of stock prices, both in
short- and long-run, to demand shocks in security lending market clearly indicate that
participants in the security lending market are well informed about the future stock prices. It
is to be noted that excepting the case of TOPIX stocks, in all other markets the impact seem
to die out in the long-run even though it remains significant over the horizons we analysed.
The patterns in the upper right panel in these figures indicate that the traded volume is
significantly and positively responding to demand shocks both in the short and long run
across geographical regions. These findings reinforce the results of Boehmer et al. (2006) and
Cohen, Deither and Malloy (2007), that short-sellers are extremely informative and activities
in security lending market have significant information for the future path of stock prices.
       The patterns in the lower-left panels of figures -1, -5, -9, -13 indicate, that on an
average, a positive supply shock to security lending market, defined as -1 standard deviation
of shock to proportion of quantity lent and 1 standard deviation of shock to loan fee, would
have a positive impact on stock prices; unlike in response to a demand shock, responses to
supply shocks seem to be less and varied across time and regions. While the effects are
Dynamics of Securities Lending and Stock Price Interaction - Gangadhar Darbha

positive for FTSE, S&P and IBEX in the medium to long run, for TOPIX they are negative
both in the short and long run.
In sum, the market-cap weighted IRF coefficients indicate that positive demand shocks to
security lending market seem to have a negative impact on stock prices, while the positive
supply shocks seem to have less information for the rise in stock prices. The later finding
would require further analysis in terms of the identification of shocks as well geographical
variation in the results.
5.1.2 Market-Cap Weighted cross-sectional densities of IRF Coefficients
        In the previous section, we looked at the market-cap weighted averages of the IRFs
wrt to demand and supply shocks in stock lending markets. While informative about dynamic
inter-relationships, weighted averages could mask significant variation in IRFs across stocks
within each geographical region. To understand the later, we estimate cross-sectional
densities (kernel density estimates weighted by market-cap weights) and plot them for each
horizon and for each geographical region. Figures 2, 6, 10, 14 plot the cross-sectional
densities for IRFs wrt demand shocks while figures 3, 7, 11, 15 for plot the cross-sectional
densities for IRFs wrt supply shocks for FTSE, S&P, IBEX and TOPIX respectively. The
patterns in these graphs clearly indicate that there is substantial variation in the IRFs across
stocks even within each geographical region even though the cross-sectional weighted
averages indicate a clearer dynamic inter-relation. As noted previously, the results are
relatively clearer for IRFs wrt demand shocks than those of supply shocks in security lending
market. For example, the (weighted) cross-sectional densities have greater mass left of 0
indicating that for more stocks, prices respond negatively with respect to ―demand‖ shocks;
IRFs with respect to positive supply shocks, on the other hand, display positively skewed
densities although there is substantially more cross-sectional variation in these. Comparing
across geographic regions, one can notice that cross-sectional variation in relatively more for
TOPIX compared to FTSE, S&P and IBEX. The results also point out more cross-sectional
dispersion of IRF coefficients over longer time horizons indicating that responses are more
varied as the time horizon increases. This could imply that while on an average the activity in
security lending market anticipates the stock price variation, at an individual stock level there
may be different objectives for stock borrowing and lending leading to cross-sectionally more
disperse patterns. As pointed out in the previous section, the cross-sectional variation in
results would require further analysis in terms of explaining them in terms of stock specific
characteristics.
5.2 Response of Stock Lending Activity to shocks to stock prices
        So far we have analysed the impact of demand and supply shocks in security lending
market on the stock prices. However, as explained earlier, the causal relation between these
security lending and stock prices could be bi-directional if the former is being used to execute
cross-security arbitrage trades and not just speculative shorting. To empirically measure the
importance of this channel, we now analyse the IRF coefficients of proportion of quantity
lent out of the total stock available for lending and loan fee wrt the shocks to stock prices.
Figures 4, 8, 12, 16 present the market-cap weighted IRFs for loan Quantity and loan Fee for
FTSE, S&P, IBEX and TOPIX respectively.            The results clearly indicate that there is
significant bi-directional causality between stock prices and security lending market; a
negative shock to stock prices is found to have significant positive impact on loan utilization
proportion and loan fee across horizons and across geographic regions. The result is strong
for the TOPIX stocks and relatively weak for FTSE stocks. The cross-sectional density
functions plotted in figures 17 – 20 also point out that while there is some cross-sectional
variation in results, the patterns are broadly consistent with the above finding that there is a
significant causal impact from stocks price to security lending market activity. This result, in
conjunction with the results of the previous section, would, prima facie, points us to the
possibility that security lending market is not only being used for for the purpose of
speculative shorting but also for market efficiency enhancing cross-security arbitrage trades.

5. Summary and Conclusion
        The literature on securities borrowing and lending suggests that if the main objective
of securities borrowing and lending is to facilitate shorting motivated by some information
about the underlying stock, the impulses to loan quantity and fees should have uni-directional
permanent impact on stock prices; if, on the other hand, the motive is to facilitate cross-
security arbitrage or spread trades, then one would expect the impact on stock prices would
be significant but non-permanent and the variations in stock prices would also have an effect
on stock lending activity; if, as is popularly believed, the motive is only to undertake some
predatory trading strategies to build an artificial downward pressure on a stock, one would
expect the stock price impact be only transitory and the effects are uni-directional from
securities lending market to stock prices. The objective of this study is to analyze the
dynamic interactions between activities and prices in security lending and that of underlying
stock with a view to test the above hypotheses. Using the daily time series data on stock
prices, loan fees and quantities on FTSE100, S&P100 and TOPIX100 stocks, we estimate the
Dynamics of Securities Lending and Stock Price Interaction - Gangadhar Darbha

Impulse Response Functions (IRFs) using the method of Local Projections for stock prices,
trading volume, loan quantity and lending fees for each stock. Our findings include: (i) there
is significant bi-directional causal interaction between security lending and stock market
variables, (ii) these effects are non-permanent on an average, but not transitory, in the sense
that they survive for almost a month before reverting to their original levels, and (iii) while
there are is significant cross-sectional variation in these results, the average effects are similar
across different geographic regions across the globe. These findings suggest that security
lending market is being used not just for the purpose of speculative shorting but also for
market efficiency enhancing cross-security arbitrage trades. Given that there is substantial
variation across stocks within each geographical region, further detailed analysis relating
such variation in IRFs to stock specific factors is required in order to draw firm conclusions.
We propose to undertake such a study in future.
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Fig.1 Market-cap Weighted Average IRF for FTSE-100

                         Price to Dd-OUT shock                             volume to Dd-OUT shock
        -0.15                                                    1

                                                               0.5
         -0.2

                                                                 0

        -0.25
                                                               -0.5

                                                                -1
         -0.3

                                                               -1.5

        -0.35
                                                                -2

         -0.4                                                  -2.5
                5   10      15    20   25       30   35   40          5   10      15    20   25    30   35   40

                         Price to Su-IN shock                                  volume to Su-IN shock
        0.25                                                   1.4

                                                               1.2
         0.2
                                                                 1

                                                               0.8
        0.15

                                                               0.6

         0.1
                                                               0.4

                                                               0.2
        0.05
                                                                 0

           0                                                   -0.2
                5   10      15    20   25       30   35   40          5   10      15    20   25    30   35   40
Dynamics of Securities Lending and Stock Price Interaction - Gangadhar Darbha

Fig.2 Market-cap Weighted Cross-sectional density functions of IRF(h) for FTSE-100

           1
                          Stock Price Response to DO shock
                         h=5
                         h=10
          0.9            h=20
                         h=40

          0.8

          0.7

          0.6

          0.5

          0.4

          0.3

          0.2

          0.1

           0
           -2.5     -2          -1.5   -1    -0.5      0       0.5      1       1.5   2

Fig.3 Market-cap Weighted Cross-sectional density functions of IRF(h) for FTSE-100
0.9
                    Stock Price Response to SI shock
                  h=5
                  h=10
0.8               h=20
                  h=40

0.7

0.6

0.5

0.4

0.3

0.2

0.1

 0
      -2   -1.5          -1   -0.5   0   0.5   1   1.5   2   2.5   3
Dynamics of Securities Lending and Stock Price Interaction - Gangadhar Darbha

Fig.4 Market-cap Weighted Average IRF for FTSE-100

                      LoanQty to StkPrice shock                              fee to StkPrice shock
          0.05                                              0.05

          0.04                                                 0

          0.03                                              -0.05

          0.02                                               -0.1

          0.01                                              -0.15
                 5   10   15    20     25    30   35   40           5   10      15    20   25    30   35   40
Fig.5 Market-cap Weighted Average IRF for S&P-100

                    Price to Dd-OUT shock              volume to Dd-OUT shock
       -0.05                                0.4

        -0.1                                0.2

       -0.15                                  0

        -0.2                                -0.2

       -0.25                                -0.4
               5   10 15 20 25 30 35 40            5   10 15 20 25 30 35 40

                    Price to Su-IN shock                volume to Su-IN shock
        0.15                                  0

         0.1
                                            -0.5

        0.05

                                             -1
          0

       -0.05                                -1.5
               5   10 15 20 25 30 35 40            5   10 15 20 25 30 35 40
Dynamics of Securities Lending and Stock Price Interaction - Gangadhar Darbha

Fig.6 Market-cap Weighted Cross-sectional density functions of IRF(h) for S&P- 100

            1.8
                                 Stock Price Response to DO shock
                            h=5
                            h=10
            1.6             h=20
                            h=40

            1.4

            1.2

             1

            0.8

            0.6

            0.4

            0.2

             0
             -2.5           -2          -1.5          -1           -0.5          0   0.5   1
Fig.7 Market-cap Weighted Cross-sectional density functions of IRF(h) for S&P-100

        1.8
                      Stock Price Response to SI shock
                   h=5
                   h=10
        1.6        h=20
                   h=40

        1.4

        1.2

         1

        0.8

        0.6

        0.4

        0.2

         0
              -4     -3        -2         -1         0          1          2
Dynamics of Securities Lending and Stock Price Interaction - Gangadhar Darbha

Fig.8 Market-cap Weighted Average IRF for S&P-100

                    LoanQty to StkPrice shock                        fee        to StkPrice shock
         0.06                                         2.5

                                                       2

         0.04                                         1.5

                                                       1

         0.02                                         0.5

                                                       0

           0                                         -0.5

                                                       -1

        -0.02                                        -1.5
                                                            5   10         15      20     25    30   35   40
                   10         20          30    40
Fig.9 Market-cap Weighted Average IRF for IBEX-35

                        Price to Dd-OUT shock                          volume to Dd-OUT shock
       -0.05                                                 4

                                                           3.5
        -0.1
                                                             3

                                                           2.5
       -0.15
                                                             2
        -0.2                                               1.5

                                                             1
       -0.25
                                                           0.5

        -0.3                                                 0
               5   10      15    20   25    30   35   40          5   10      15    20   25    30   35   40

                        Price to Su-IN shock                               volume to Su-IN shock
         0.3                                               -0.5

        0.25
                                                            -1
         0.2

                                                           -1.5
        0.15

         0.1
                                                            -2

        0.05
                                                           -2.5
          0

       -0.05                                                -3
               5   10      15    20   25    30   35   40          5   10      15    20   25    30   35   40
Dynamics of Securities Lending and Stock Price Interaction - Gangadhar Darbha

Fig.10 Market-cap Weighted Cross-sectional density functions of IRF(h) for IBEX-35

                                        Stock Price Response to DO shock
           1.4
                 h=5
                 h=10
                 h=20
                 h=40
           1.2

            1

           0.8

           0.6

           0.4

           0.2

            0
            -2          -1.5      -1          -0.5             0           0.5   1   1.5
Fig.11 Market-cap Weighted Cross-sectional density functions of IRF(h) for IBEX-35

                                      Stock Price Response to SI shock
         1.4
                 h=5
                 h=10
                 h=20
                 h=40
         1.2

          1

         0.8

         0.6

         0.4

         0.2

          0
          -1.5          -1     -0.5                  0                   0.5   1   1.5
Dynamics of Securities Lending and Stock Price Interaction - Gangadhar Darbha

Fig.12 Market-cap Weighted Average IRF for IBEX-35

                      LoanQty to StkPrice shock                             fee to StkPrice shock
           0.2                                                2

                                                            1.5
          0.15
                                                              1
           0.1
                                                            0.5
          0.05
                                                              0

            0                                               -0.5

         -0.05                                               -1
                 5   10   15    20     25    30   35   40          5   10      15    20   25    30   35   40
Fig.13 Market-cap Weighted Average IRF for TOPIX-100

         Price to Dd-OUT shock volume to Dd-OUT shock
        0.1                                             0.7

          0                                             0.6

        -0.1                                            0.5

        -0.2                                            0.4

        -0.3                                            0.3

        -0.4                                            0.2

        -0.5                                            0.1

        -0.6                                              0

        -0.7                                            -0.1
                 5   10   15   20   25   30   35   40          5   10   15   20   25   30   35   40

       -0.15
               Price to Su-IN shock                       volume to Su-IN shock
                                                        0.3

        -0.2                                            0.2

       -0.25                                            0.1

        -0.3                                              0

       -0.35                                            -0.1

        -0.4                                            -0.2

       -0.45                                            -0.3

        -0.5                                            -0.4
                 5   10   15   20   25   30   35   40          5   10   15   20   25   30   35   40

Fig.14 Market-cap Weighted Cross-sectional density functions of IRF(h) for TOPIX-100
Dynamics of Securities Lending and Stock Price Interaction - Gangadhar Darbha

          2.5
                           Stock Price Response to DO shock
                          h=5
                          h=10
                          h=20
                          h=40

           2

          1.5

           1

          0.5

           0
                -5   -4          -3   -2      -1       0        1       2       3   4
Fig.15 Market-cap Weighted Cross-sectional density functions of IRF(h) for Topix-100

        2.5
                          Stock Price Response to SI shock
                        h=5
                        h=10
                        h=20
                        h=40

         2

        1.5

         1

        0.5

         0
              -5   -4          -3   -2   -1   0      1       2      3      4
Dynamics of Securities Lending and Stock Price Interaction - Gangadhar Darbha

Fig.16 Market-cap Weighted Average IRF for TOPIX-100

                          LoanQty to StkPrice shock                              fee to StkPrice shock
          0.09                                                   2.5

          0.08                                                     2

          0.07                                                   1.5

          0.06                                                     1

          0.05                                                   0.5

          0.04                                                     0

          0.03                                                   -0.5
                 5   10       15    20     25     30   35   40          5   10     15    20     25       30   35   40
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