Rehypothecation of Securities and Bank
Liquidity and Efficiency
–
The Liquidity-Rehypothecation-Efficiency
Nexus
M. Pham // 1898264 //
Thesis Supervisor: A. Meester
Abstract
Using a panel dataset of bank level data gathered from annual reports and the Bankscope database from 2000-2011, I examine the dynamic relationship between rehypothecation of collateral and bank liquidity by applying the system GMM methodology to the Granger causality framework. I then estimate profit and cost efficiency levels via the stochastic frontier analysis methodology and test whether rehypothecation and liquidity affect efficiency. Moreover, I use the Cox Proportional Hazard Model to investigate the role of rehypothecation and liquidity in changes in profit and cost efficiency after the financial crisis of 2007.
JEL Classification: G2, G21, D2, C33
1. INTRODUCTION
Rehypothecation occurs when the client of a prime brokerage (e.g. a hedge fund) posts collateral in a financial transaction, for instance, to obtain a loan in an overnight repurchase agreement (also termed ‘repo’), and that collateral is reused by the prime broker for its own purposes, which includes being posted as collateral again. The Customer Account Agreement or Prime Brokerage Agreement with a prime brokerage client frequently includes a blanket consent allowing this type of practice (Singh & Aitken, 2009). The reuse of the collateral in lieu of other measures acts as a quid pro quo for the leverage non-banks receive from their dealers (usually large banks). Obtained collateral with the right to be rehypothecated can be re-pledged or resold as collateral against margin loans, securities borrowing, reverse repo transactions, and OTC derivatives (Singh, 2011).
Figure 1. The sources and uses of collateral (Singh, 2011).
The main providers of collateral are asset managers, which can be categorized into two types of accounts: levered accounts and unlevered (or real money) accounts. In a broad sense, levered accounts refer to hedge funds, while real money or unlevered accounts pertain to EFTs (exchange traded funds), sovereign wealth funds, central banks, pension funds, insurance companies and mutual funds. However, in practice, the demarcation line between levered and real money accounts is frequently blurred, as many real money accounts also incur leverage, deal in derivatives and have the ability to go short. One reason is that the real money accounts, such as defined benefit pension funds, increasingly take higher risks to cover their underfunded statuses (Pozsar & Singh 2011).
Central Collateral Desk Commercial Banks (de minimus) Commercial Banks (de minimus) Money Funds (Prime Government only,
etc.)
Hedge Funds
Custodians representing sovereign/official accounts, pension funds, insurers, asset managers,
The principal recipients of collateral are money market funds that supply funds to the market in exchange for collateral (frequently via commercial banks by swapping commercial paper with commercial banks for other types of collateral). The supply of collateral is managed by the central collateral desk of dealers, depicted in figure 1, which acts as an intermediary between suppliers and demanders. The major participants in the collateral industry include Goldman Sachs, Morgan Stanley, JP Morgan Chase, Bank of America, Citibank, Deutsche Bank, UBS, Barclays, Credit Suisse, Société Générale, BNP Paribas, HSBC, RBS, and Nomura. The continuous arrows in figure 1 symbolize the collateral users, while the dashed arrows represent the collateral providers. Pozsar and Singh (2011) estimate the total volume of collateral ‘mined’ (or obtained) from asset managers at $3.3 trillion and $2.4 trillion at year-end 2007 and 2010 respectively. These sums include $1.6 and $1.3 trillion in hedge fund assets, and $1.7 and $ 1.1 trillion in real money assets at end-2007 and 2010, respectively. Figure 2 reveals that the total amount of assets available for rehypothecation exceeded $10 trillion in 2008 but receded in the wake of the financial crisis. The amount of assets rehypothecated reached its apex in year of the financial crisis with $7,618 trillion dollars then declined afterwards.
Figure 2. Total volume of assets for rehypothecation (no fill) and assets rehypothecated (dark fill) for all 139 banks in the sample from 2000 to 2011 in billions USD (Source: banks’ annual reports).
Dealers generally discriminate between the tri-party type of collateral that is unrehypothecable and client collateral with unlimited re-pledging rights (Singh, 2011). The prime brokerage fee with client type of collateral ranges from zero to LIBOR + 50 basis points, while the fee in tri-party type of transactions, where the collateral remains with the custodians, can amount to LIBOR + 250 basis points. Rehypothecation of client type of collateral can reduce traders' funding liquidity needs. The ability of using rehypothecation allows the trader to repledge obtained collateral to borrow cash. The same collateral can thus be used to facilitate more than one transaction, rendering it liquid. Rehypothecation allows the recipient to fund his activity more easily rather than having to use his own cash or mobilize assets on the balance sheet (Monnet, 2011).
To date, no study has examined the exact effect of rehypothecation on liquidity and efficiency. In this paper, I investigate the relationship between rehypothecation and bank funding liquidity and bank efficiency. For this purpose, I use a sample of 139 commercial banks operating in the worldwide collateral industry from 2000 to 2011 and examine how the practice of rehypothecation impacts their funding liquidity, and vice-versa, how rehypothecation impacts bank profit (and cost) efficiency. This research contributes to the existing literature on bank liquidity and as well as bank efficiency. My research reveals that rehypothecation and liquidity are inextricably entangled and that there is bi-directional Granger causality (feedback) between the two. Moreover, rehypothecation and liquidity significantly impact profit and cost efficiency, suggesting the existence of liquidity-rehypothecation-efficiency nexus. However, rehypothecation does not account for the decrease in efficiency of certain banks after the financial crisis of 2007.
The remainder of this paper is organized as follows: section 2 provides a literature overview and theoretical framework for the interaction between bank liquidity and rehypothecation. Section 3 presents the variables and the data, section 4 describes the econometric methodology and section 5 presents the empirical results and analysis. A summary and brief discussion of the findings concludes this paper.
2. LITERATURE OVERVIEW AND THEORETICAL BACKGROUND
The Rehypothecation-Liquidity Nexus
tight, traders grow reluctant to take ‘capital intense’ positions. This lowers market liquidity and exacerbates volatility. Conversely, under certain conditions, low market liquidity can worsen the risk of financing a trade, thus increasing margins and negatively affecting funding liquidity. In this paper the focus is primarily on funding liquidity and its relationship with rehypothecation of collateral posted in securities transactions.
Funding liquidity and rehypothecation are intimately linked. Rehypothecation of (client) collateral can meet traders’ need for funding liquidity. When a trader (e.g. a hedge fund or investment bank) buys a security, he can use this security as collateral and borrow against it, usually with a ‘haircut’ (i.e. difference between the security’s price and collateral value), which the trader must finance from his own capital. The prime broker in turn can repost the obtained collateral to fund its own positions. Botazzi et al (2012) illustrate, in a theoretical model on repo transactions, the entanglement between funding, trading and rehypothecation in the broad sense. The authors introduce a basic ‘box model’ with two representative agents, Mrs A and Mr B, who trade with each other in a securities and repo market. Initially Mr B owns the security and Mrs A holds an amount of cash equivalent to the value of the security. Mr B then sells his security to Mrs A in exchange for the cash – this is a regular securities sale. Ms A, who is now possession of the security, lends the entirety of the security to Mr B and uses this to collateralize a loan from Mr B in a repurchase agreement. Mrs A borrows a haircuted (the haircut being the difference between the cash borrowed and the value of the collateral) amount from Mr B. The two agents replicate the procedure. Mrs A uses her borrowed cash to buy a haircuted amount the security she lent to Mr B previously. Botazzi et al (2012) show that these steps can be replicated ad infinitum without ever being resolved, ultimately yielding the cash leverage multiplier !!!! . The authors extend the box model to a theoretical model on securities rehypothecation within a General Equilibrium framework. They build on the collateral model of Geanakoplos and Zame (2007, 2009) who use the term ‘pyramiding’ for rehypothecation, and the repo markets model by Duffie (1996). In Botazzi et al’s model, the loan associated with the repo, πjzj, is the product of the hairtcuted price of the
collateralized loan, where j denotes the security involved in the transaction. One of the salient findings by Botazzi et al (2012) with regards to liquidity is that dealers have an incentive to engage in both sides of the repo market of the same security. This generates liquidity for them as they benefit from the haircut advantage, i.e. the difference between the lending repo rate and the borrowing rate.
The hedge funds post collateral in the form of securities in return that it allows the primer broker to rehypothecate. The latter in turn posts the obtained collateral as collateral in an overnight repo in the money market. The interbank market lender in turn can use the obtained collateral and post it as collateral in another transaction (stylized by dashed arrow), a process, that can theoretically, be repeated an infinite amount of times to form a continuous collateral chain, provided the legal framework allows it1. In that manner, the same collateral can facilitate more than one financial transaction. Note, that in this example the ‘haircut’ is zero since the value of the collateral matches that of the loan – the haircut corresponds to the difference between the value of the cash and the value of the collateral. The level of haircut typically reflects the quality of the collateral or the creditworthiness of the pledgor.
Assets Liabilities
$10 Treasuries $10 Equity
$90 Loan to Hedge Fund $90 Repo Debt
Figure 3. Illustration of collateralized loan and rehypothecation process in an overnight repo loan; adapted from Brunnermeier et al (2012).
Pozsar and Singh (2011) present an analytical framework that outlines the dynamics between banks and non-banks (illustrated by figure 4) and highlight the crucial role that rehypothecation of collateral plays in the provision of non-M2 type of bank funding. Modern banks straddle both the traditional and shadow banking systems and employ both traditional, M2, and market-based, non-M2, liabilities for their funding. M2-type of monies encompass currency in circulation, checking accounts, certificates of deposit, savings accounts, time deposits and retail class money market funds, but are ill-suited to meet institutional investors’ cash pool money demands. Rather than M2-type of money, asset managers prefer alternatives such as short-term publicly guaranteed debt (e.g. Treasury bills and agency discount notes)
1 In the United Kingdom, an unlimited amount of the customer’s assets can be rehypothecated, while in the United States, a broker-dealer may only rehypothecate a client’s collateral up to 140%. However, US banks may be able to circumvent these limitations by running their transaction through their overseas subsidiaries in the UK. $90 Collateral (securities) $90 Collateral (securities) $90 Collateral (securities) Securities received as collateral in
overnight repo
Posted as collateral to money market in overnight repo
and privately guaranteed wholesale funding instruments (e.g. repurchase agreements, asset-backed commercial paper and other asset-asset-backed paper) issued by the shadow banking system. Those alternative sources of funding are referred to as public and private non-M2 types of money. The provision of these non-M2 types of monies involves the heavy use of collateral, which renders the shadow banking system collateral intensive. Collateral from asset managers is primarily mined by dealers, who mine the levered, or hedge fund, accounts and, in return, provide repo loans or margin loans against collateral. From the unlevered, or real money accounts, dealers mine collateral directly from the custodians.
Figure 4. Comprehensive Financial Framework (Pozsar and Singh, 2011).
Collateral mining is associated with the phenomenon of reverse maturity transformation. The traditional process of maturity transformation involves the conversion of short-term liabilities, e.g. in the form of household deposits, into long-term assets, i.e. illiquid loans. This process has been explored in a theoretical framework by Bryant (1980) and by Diamond and Dybvig (1983), who show that banks provide households with an insurance against idiosyncratic consumption shocks through investments in illiquid loans funded with demand deposits. In contrast, the process of reverse maturity transformation involves the conversion of long-term savings into short-term assets and caters mostly to the needs of institutional investors. According to Pozsar and Singh (2011) reverse maturity transformation arises from at least three type of activities: First, asset managers employ short-term instruments in reserve to cope with withdrawals or hold them out of tactical considerations,
Loans Deposits (M2) Real Assets Loans Bonds Equities
Loans WholesaleFunding
Ultimate Borrowers
(Households, etc.) (Intermediate short-term saving Shadow Banking System Ultimate Creditors(Households)
Asset Managers (Intermediate long-term savings)
Reverse Maturity Transformation
Assets (short) Assets (long) Shares Savings (short) Savings (long) “Equity”
Large Complex Modern Banks Traditional Banks
(Intermediate short-term savings)
Equity
for instance, as a source of return in active in market timing. Second, funds with derivatives-based investment strategies tend to invest their client’s funds in short-term instruments combined with derivatives (i.e. futures and swaps) to gain their desired exposure to duration, foreign exchange or credit risk. Third, reverse maturity transformation may arise from collateral mining via securities lending. In the U.S. this occurs chiefly against cash collateral, as opposed to securities collateral: securities borrowers post collateral cash to securities, which is then transferred into a cash collateral reinvestment account and invested in short-term instruments.
Pozsar and Singh (2011) propose an identity that expresses bank credit to ultimate borrowers in terms of leverage, equity and source of funding. In the traditional banking system, total bank lending is funded by the equity of the banking system or by the debt that non-banks (i.e., households, pension funds and insurers) provide to banks. This views, however, ignores the significant proportion of funding banks receive from the asset management complex through collateral and the non-M2 money demands of institutional cash pools. Therefore they propose the following measure of total bank lending that incorporates non-M2 funding banks receive from non-banks:
yi i=1 n
∑
= eizi(λi−1) + ei i=1 n∑
i=1 n∑
= ei(zh+ zk)⋅(λi−1) + ei i=1 n∑
i=1 n∑
(1)Where yi is the total claims on ultimate borrowers by bank i, ei is the equity of bank i, λi is the
leverage of bank i, zi, the fraction of non-bank funding bank i obtains, where zi can be
decomposed into zh, the fraction of M2 funding bank i receives – mainly from households,
and zk, the fraction of non-M2 bank i receives from non-banks. Rehypothecation of collateral
enters equations (1) via the zk term, which reflects the amount of non-M2 type of funding,
which is collateral intensive and therefore also rehypothecation intensive. When leverage in the financial system goes up, there is a growing concatenation of rehypothecation procedures, which results in longer collateral chains.
loans from the detrimental funding shocks. In Tian’s (2010) benchmark case, autarky, the bank can improve its margin by reallocating some funds to short-term loans. Hence, the bank’s safety net relies on holdings of liquid (i.e. short-term) assets that can be liquidated to absorb current and future deposit shocks.
When banks have access to ABCPs, they possess an additional instrument to deal with deposit shocks. ABCPs represent external funds that can absorb those deposit shocks. At the height of the financial crisis of 2007, ABCP was the largest short-term debt instrument with more than $1.2 trillion outstanding according to Acharya and Viswananthan (2010). ABCP reduce the impact of deposit shocks on banks’ long-term loans by allowing banks to cut down on liquid assets holdings (held for the event of deposit shocks under autarky) and increase issuance of long-term loans. This helps banks generate greater revenue, since long-term assets achieve higher returns than their short-term counterparts. Banks can rollover their long-term loans by selling the same amount of ABCP. When banks have access to MBS, banks do not need to invest in liquid assets at all, but invest all their deposits in illiquid assets directly or indirectly for higher margin, yet at the same time have a buffer of external funds from the MBS market at their disposition that shields their long-term assets from undesirable shocks.
Tian (2010) also compares ABCP and MBS to Arrow-Debreu securities, also known as state contingent claims, in a separate model. Arrow-Debreu securities are primitive binary securities with a fixed payoff if a specified state occurs and no payoff otherwise. In the model, there are two banks, A and B, that serve the inhabitants of an island. All residents put their money in either two of the banks and borrow from either of them. The initial deposits each bank receives amounts to $1 billion each (depicted in table 1). Originally, there is no equity, since the banks have not earned anything on their loans yet.
Table 1. Balance Sheets of Bank A and B at Time t = 0 (Amount in Billions Dollars).
Bank A Bank B
Assets Liabilities Assets Liabilities
$0.9 Loans $0.1 Reserves
$1.0 Deposits $0.9 Loans
$0.1 Reserves
$1.0 Deposits
million is transferred from B to A (see table 2). Loans yield a constant margin r, and the cost of recalling a loan is $c > 2r. In the absence of an interbank market or shadow banking system, both banks hold $100 million cash as buffer for deposit shocks, thus the amount of loans outstanding per bank is $0.9 billion. Banks are not revenue efficient and total profit per bank is $r·0.9 billion.
Table 2. Balance Sheets of Bank A and B at Time t = 1 in State 1 and State 2 (Amount in Billions Dollars).
Bank A State 1 (P = 0.5) Bank B State 1 (P = 0.5)
Assets Liabilities Assets Liabilities
$0.9 Loans $0.1 Cash Reserves $0.9 Deposits $0.9 Loans $0.1 Cash Reserves $0.1 Additional Loans $1.0 Deposits $0.1 Deposits from A
Bank A State 2 (P = 0.5) Bank B State 2 (P = 0.5)
Assets Liabilities Assets Liabilities
$0.9 Loans $0.1 Cash Reserves $0.1 Additional Loans $1.0 Deposits $0.1 Deposits from B $0.9 Loans $0.1 Cash Reserves $0.9 Deposits
When Arrow-Debreu securities are available, banks no longer need to hold cash buffers to mitigate deposit shocks. Let security I has a payoff of $1 in state 1 and security II a payoff in state 2 and with respective prices PI = PII = $0.50. Now bank A lends out $1 billion and
hedges deposit risk by going long in r·100 million shares of security I. Under state 1, bank A obtains r·$100 million from security I and can offer the interest to borrow $100 million from bank B. With ABCP and MBS the same improvements as with the Arrow-Debreu securities can be achieved. Both banks lend out $1 billion at the onset. In state 1, bank A experiences a deposit shock of $100 million that is withdrawn and transferred to bank B. Bank A can sell $100 million in ABCP which bank B buys with the deposit surplus of the same amount (see table 3). The converse happens in state 2. Bank B experiences a deposit shock and can sell $100 million in ABCP to bank A. Total loan outstanding per bank is $1 billion and expected revenue r·$1 billion.
-0.1 +0.1
Table 3. Balance Sheets of Bank A and B at Time t = 1 in State 1 and State 2 (Amount in Billions Dollars).
Bank A State 1 (P = 0.5) Bank B State 1 (P = 0.5)
Assets Liabilities Assets Liabilities
$0.9 Loans $0.9 Deposits $1.0 Loans
$0.1 ABCP from A
$1.0 Deposits $0.1 Deposits from A
Bank A State 2 (P = 0.5) Bank B State 2 (P = 0.5)
Assets Liabilities Assets Liabilities
$1.0 Loans $0.1 ABCP from B
$1 Deposits
$0.1 Deposits from B
$0.9 Loans $0.9 Deposits
Tian’s (2010) model does not account for repurchase agreements (repos) and rehypothecation, but can easily altered to accommodate this phenomenon. It can be shown that repos achieve superior efficiency compared to plain vanilla securities transactions with ABCPs and MBS or Arrow-Debreu securities. Both banks lend out $1 billion each initially. Come state 1, rather than having to sell $100 million of ABCP or MBS to bank B, bank A can enter into a repurchase agreement with bank B. In other words it can fund the shortage on the liability side of its balance sheet by borrowing $100 in a securitized loan from bank B. If the haircut, the difference between the value of the loan and the collateral posted, is zero, bank A can pledge the entirety of $100 worth of MBS to cover the $100 million in shortage of funding (see table 4). Bank A’s outstanding amount of loans remains $1 billion and it pays
r·$100 million interest expense on the repo loan to B (assume for simplicity, that this is the
same interest that banks receive on loans). The converse is the case for state 2, where bank B can take on a repo debt from bank A worth $100 million to cover its funding gap. With repos, total loan outstanding per bank is $1.05 billion instead of $1.0 billion with securities alone, and expected revenue is r·$1.1 billion, which is an improvement of $0.5 billion over the securities only scenario. Thus, the main difference compared to selling and buying securities only, is that bank A does not need to sell the $100m in MBS to make up for the funding shortage, but instead, is able to pledge it as collateral in the repo.
Bank B could, theoretically, re-use this collateral to create additional credit worth $100 million. It must, however, borrow from bank A to fund this additional loan – or get an additional $100 million in deposits (which is not the case in the model). Bank A can extend a loan to bank B and add $100 million worth of assets on its own balance sheet (now $1.1b), but must in turn enter a repo with bank B to fund the reverse repo it entered with bank B. Still
-0.1 +0.1
assuming the haircut is 0, the process could go on infinitely if banks also rehypothecate their repo and reverse repo loans, without a possibility for the process to be resolved, as seen in the Botazzi et al (2012) model. But enter bank C, a new entrant in the island’s banking industry. Suppose bank C initially has no deposits, but in both state 1 and state 2 it receives $200 million in deposits (with 100% certainty) due to a positive shock in the island’s population. It can then extend $100 million of long-term loans to the new inhabitants and offer $100 million as repo loan to bank B. Bank B repledges the $100 million in MBS it received from A as collateral and then uses the funding it receives from bank C (i.e. repo debt) to create new loans for the remaining 100 million new inhabitants. If a fourth bank, D, were to establish itself on the island and were to receive $100 million in new deposits, it could enter into a reverse repo with C, in the process receiving the $100m MBS from C that C received in a reverse repo from B (which B receive from A). This lengthens the collateral chain. Note that the $100m MBS remain on bank A’s balance sheet and appears neither on B’s, C’s nor D’s balance sheet (but the overall amount of assets obtained available for rehypothecation may appear as a note in their annual report).
Table 4. Balance Sheets of Bank A and B at Time t = 1 in State 1 and State 2 (Amount in Billions Dollars).
Bank A State 1 (P = 0.5) Bank B State 1 (P = 0.5)
Assets Liabilities Assets Liabilities
$0.9 Loans $0.1 MBS $0.9 Deposits $0.1 Repo Debt $1.0 Loans $0.1 Reverse Repo $1 Deposits $0.1 Deposits from A
Bank A State 2 (P = 0.5) Bank B State 2 (P = 0.5)
Assets Liabilities Assets Liabilities
$0.9 Loans $0.1 Reverse Repo $1 Deposits $0.1 Deposits from B $0.9 Loans $0.1 MBS $0.9 Deposits $0.1 Repo Debt
Bank Efficiency and Rehypothecation
The extension of Tian’s (2010) model illustrates that banks can become more profit efficient on condition that they make use of the money market to insure themselves against deposit shocks (and provided that costs of using the interbank do not escalate relative to the benefits). In order to study the influence of rehypothecation of collateral on cost and profit efficiencies
-0.1 +0.1
+0.1 -0.1
MBS Collateral
of banks and provide some economic intuition, the models from Hughes et al (2000) and Estrada and Osorio (2004) are adapted to accommodate the concept of rehypothecation (by augmenting them with securitized loans, wholesale funding and off-balance sheet activities). The optimization problem of a bank endowed with financial technology represented by function F(x, y, z) ≤ 0 can be described in the following setup:
Let y be the vector of outputs (assets), such that y = yl + yf + yo + ys, where yl denotes
information-intensive loans (not including repos), yf financial interbank services, yo other
investments and ys securitized loans, (i.e. repo loans), made chiefly by dealer-brokers to their
clients (i.e. asset managers) and only de minimis to other banks, as pointed out by Pozsar and Singh (2011). Using the repo loan definition by Botazzi et al (2012), the vector of securitized loans can be defined as ys = j=1pj⋅ζj
n
∑
= p⋅ζ , where ζj is the amount of the security jengaged in the repo, pj is the haircuted price of the collateralized loans. The associated repo
rate, or the interest rate on the secured loan, is ρjy.
Let x = xd + xw + xp, represents the level of inputs where xd denotes the level of deposits,
xw the level of wholesale funds and xp denoting labour and physical capital. Wholesale funds
include money market funds and secured funding (i.e. reverse repos). For simplicity reason and illustration purposes, let us assume wholesale funding only involves secured funding. Then the vector of repo debts or reverse repos (used to finance the asset side of the balance sheet) can be written as xw = j=1pj⋅ζj
n
∑
= p⋅ζ , where ζj is the amount of the security jengaged in the reverse repo, pj is the hairtcuted price of the collateralized loans and p·ζ the
vector of prices of haircuted loans times the vector of collateral. The repo rate, that is the interest rate on the debt, is denoted by ρj
x. Note, that the interest rate paid by the bank on the
reverse repo is usually lower than the interest rate paid by the non-bank debtor on the repo, ρj
x < ρ j
y – this allows the bank to make a profit on the loan. The input prices corresponding
to the inputs are denoted by the vector w, with w = wd + ww + wp + wz1 + wz2, where z1 and z2
are fixed netputs with z1 representing equity capital and z2 off-balance sheet activities, such as
loan commitments, certain letters of credit or revolving underwriting facilities. Input prices for wholesale funding can be defined as the totality of interest expenses: ww = ρj
x = j=1 n
∑
ρj,where ρj
x is the repo rate associated with the secured debt on asset j and ρx the vector of repo
One can distinguish three alternative cost functions (Estrada & Osorio, 2004): the operating cost function, cash flow cost function and economic cost function. The operating cost function considers capital structure by conditioning cost on levels of financial capital but excludes the associated expenses from the cost function. Deposits (and wholesale funds) and financial capital are taken as given and not included in the specification. The cash-flow measure of cost includes the cost of deposits (and wholesale funds) but excludes the cost of equity capital. Finally, the minimum economic cost function is conditioned on the price of financial capital, rather than level of equity, and the price of deposits (and wholesale funds). For the minimum economic cost function C(y, w), the bank’s optimization problem becomes:
Min
xd,xw,xp
C( p, w, z)= w'd xd + w'wxw+ w'pxp+ w'z1xz1+ w'z 2xz 2
s.t. F(x, y, z) ≤ 0 (2) Solving this optimization problem yields the conditional factor demand equations, or, in terms of Hughes and Mester (1993), the restricted input requirement set:
x* = x*(y, w, z) (3)
Hence, the conditional demand for inputs depends on y, the amount of output sold at prevailing prices, w, the given factor prices in input markets, and z the level fixed netputs, i.e. the level of capital and of off-balance sheet activities in the production period. The minimum cost is then obtained by substituting the x* into the cost function:
C*= w' xi * (y, w, z)= c(y, w, z) = c (y
{
l, yf, yo, ys), (wd, ww, wp), (z1, z2)}
= c (yl, yf, yo, p⋅ζ ),(wd,ρ x , wp), (z1, z2){
}
(4)Thus with rehypothecation, the minimum cost level depends directly on the hairtcuted amount of collateral obtained from debtors in the repo, p·ζ, and on the reverse repo rate involving the same security, ρx.
Max
p,x Π (p, w, z) = p' y − w' x s.t. F(x, y) = 0 and G(y, p, w, z) = 0 (5)
Where F(y, x) is the transformation function of the factor vector x to output vector y and G(y,
p, w, z) represents the bank’s pricing opportunity set for transforming given values of y, w and z into output prices. The function reflects the bank’s assessment of the willingness of
customers to pay the prices the bank wishes to charge as well as any conjectural variations incorporated in pricing rules that the bank may follow, such as differentiability marking up the cost of funds, therefore the inclusion of input prices in the function (Estrada & Osorio, 2004). The solution for the optimal level of output prices p* = p*(y, w, z) and input quantities
x* = x* (y, w) is:
x* = x*
( p, w, z) p* = p*
( p, w, z) (6)
Substituting these expressions into the alternative profit function yields the optimal profit:
Π = p* (y, w, z)' y− w' x* (y, w, z) = Π (y
{
l, yf, yo, ys), (wd, ww, wp), (z1, z2)}
= Π (yl, yf, yo, p⋅ζ ),(wd,ρ x , wp), (z1, z2){
}
(7)The optimal level of the alternative profit function can also be expressed in terms of a vector of repo loans p·ζ where the engaged collateral is rehypothecated to obtain funding in the form of reverse repos in the money market, which incurs ρx, the vector of reverse repo rate
associated with the vector of collateral ζ that has been rehypothecated.
Figures 5a and 5b illustrate the concept of profit and cost efficiency respectively. Profit or cost efficiency is the product of technical efficiency and allocative efficiency. Technical efficiency is the bank's ability to produce on the frontier isoquant, while allocative efficiency refers to the ability to produce at a given level of output using the profit maximizing output ratios or cost minimizing input ratios. Or put differently, technical inefficiency refers to deviations from the frontier isoquant, and allocative inefficiency reflects the deviations from the maximum output ratios or the minimum cost input ratios. Banks that are profit efficient or cost efficient are both technically and allocatively efficient.
In the case of profit efficiency, a bank maximizes its profits by choosing the optimal level of inputs. Assume there are two outputs Y1 and Y2 (see figure 5a) with prices p1 and p2
maximizes profit when the isoprofit line is tangent to the production frontier – point Q’. At this point the bank is both technically and allocatively efficient. In contrast, if the bank produces at point Q, which still lies on the frontier, but not on the maximum isoprofit line, the bank is still technically efficient, but is allocatively inefficient. Technical efficiency is measured by the ratio of OP to OQ and takes values between 0 and 1 (0 if P equals O and 1 if P lies on the frontier and equals Q). Allocative efficiency is measured by the ratio OQ to OR and takes a value between 0 and 1, where 1 represents full allocative efficiency. If the bank produces at point P instead of Q, hence, no longer on the frontier, then profit efficiency is measured as the ratio of OP to OR. Profit efficiency can also be obtained by multiplying allocative efficiency (OQ/OR) by technical efficiency (OP/OQ).
In the case of cost efficiency (figure 5b), the bank minimizes costs with respect to inputs X1 and X2 and that have respective input prices p1 and p2. The ratio of these input
prices is represented by the slope of the line AA’. If the bank produces at point Q, which is on the frontier, allocative efficiency is given by the ratio OQ to OR, while technical efficiency is measured by OQ to OP. The bank’s cost efficiency is then computed by multiplying both ratios so that cost efficiency equals OP over OR. The bank is fully efficient if this ratio is equal to 1.
Figure 5a. Profit Efficiency. Figure 5b. Cost Efficiency.
To illustrate how repos and rehypothecation affect efficiency, take two inputs, deposits and wholesale funding (in case of cost efficiency). In the absence of an interbank market (as illustrated in the model by Tian, 2010), wholesale funding is not available, but the second input is a fixed amount of reserves instead. Cash reserves against negative deposit shocks do
not generate profits because they cannot be used to create loans. The associated input price is the opportunity cost of holding these reserves, in other words, the foregone interest income on the loans that have not been created. Hence, without interbank market, the frontier (in the cost efficiency case) is much higher, since the opportunity costs of holding reserves exceeds input prices of wholesale funding (e.g. repo rate on the collateralized repo debt). This, however, does not necessarily affect cost efficiency since no bank can trade in securitized loans when there is no money market (because cost efficiency is measured relative to the frontier). When banks do have access to the interbank market, but banks’ use of money market funding and use of repos and rehypothecation differs, then disparities in cost efficiency can arise2. As seen in Tian’s (2010) model, rather than having to sell their securities to cover funding shortages, banks can hypothecate their securities to take out repo loans to fund their activities on the asset side of the balance sheet (i.e. outputs). Without rehypothecation, banks can only hypothecate the amount of securities that are featured on their balance sheet. With rehypothecation, banks are able to take on additional repo debts by repledging the assets they obtained as collateral from their clients. In this manner, the output of loans is amplified and by re-allowing their collateral to be rehypothecated, banks can decrease input prices, as they receive a more favourable repo rate as quid-pro-quo. One the one hand, collateral management may incur additional costs, which can have a negative effect on banks’ costs and cost efficiency. On the other hand, additional loans may have a positive impact of profits and profit efficiency. Since to date, no study has investigated the effect of rehypothecation on bank efficiency, one of the aims of this paper will be to measure this effect.
The first objective of this paper is to examine the relationship between liquidity and rehypothecation since the two are closely linked. The second objective is to assess the effect of rehypothecation and liquidity on bank efficiency. And the third objective is to examine what role rehypothecation (and liquidity) may play in decreases of profit and cost efficiency after the crisis of 2007.
The following research questions are addressed:
1. Does rehypothecation cause liquidity? Or does liquidity cause rehypothecation? 2. How do the two influence each other?
3. Is there a rehypothecation-liquidity nexus?
4. What is the effect of rehypothecation and liquidity on bank cost and profit efficiency?
5. What role do rehypothecation and liquidity play in in the decrease of bank efficiency after the financial crisis of 2007?
3. DESCRIPTION OF DATA
The data used for the analysis is a balanced panel of 139 banks and financial institutions that report rehypothecation of collateral or possession of collateral with re-pledging rights in their annual report or SEC filings (10-K, 20-F, or 40-F) over the years 2000-2011.
The bank specific and industry specific data were obtained from the Bureau van Dijk Bankscope database. When possible, only consolidated statements were employed (to match the rehypothecation data which pertains chiefly to group entities). Data on collateral available for rehypothecation and collateral rehypothecated was collated from the banks’ annual reports. The macroeconomic determinants, the inflation rate and the GDP were retrieved from the World Development Indicator database from the World Bank and the IMF International Financial Statistics database.
difference between loans and deposits to total assets and is on average -25%, a negative gap. In other words, deposit liabilities exceed loans by on average 25% relative to total assets. However, this is only the average and a number of banks in the sample exhibit a positive financing gap over the whole sample period. Liquidity creation (LC) is a measured devised by Berger and Bouwman (2009), which aims to capture how banks create liquidity rather than transform it and can also be regarded as an attempt to measure market liquidity (Tian, 2010). The LC measure assigns weights to both assets and liabilities depending on their liquidity:
LC = {½ · illiquid assets + 0 · semi-liquid assets – ½ · liquid assets} +
{½· illiquid liabilities + 0 · semi-liquid liabilities – ½ · liquid liabilities} (8)
The measure of liquidity creation was computed according to the maturity classification of Berger and Bouwman (2009) without off-balance sheet items (due to data availability)3. The average liquidity creation in the sample amounts to $29.8 billion per year in absolute terms (or in relative terms with respect to total assets, 4.82%). This suggests that the average bank generated substantial liquidity per year over the period 2000 to 2011, which is consistent with the high, positive, interbank ratio and the fact that the sample includes almost all bank in the top 100 list of banks of the world, ranked according to asset size. The average volume of collateral available for rehypothecation is $90.4 billion. The maximum volume was held by Mizuho Financial Group in 2008 and amounts to $1.88 trillion. The mean volume of collateral re-pledged or re-sold amounts to $70.7 billion and the maximum, $1.21 trillion – also by the Mizuho Group. The high, average annual rehypothecation volume of banks in the sample reflects the fact that many banks are also dealer/brokers. This is congruent with the fact that, on average, banks in the sample are net liquidity provider on the interbank market and net liquidity creators.
Figures 6a to 6f show the mean of the liquidity ratios used in this study compared to other liquidity indicators over the period 2000-2011. Figure 6a compares the net loans to assets (LTA) ratio to the net loans to customer and short term funding (LTDSTF) and the net loans to total deposits and borrowing (LTTDB) ratios. Both the LTA and the LTTDB ratios decline steadily over the whole period, with a slight kink in 2008. In contrast, the LTDSTF exhibits an increasing trend with large spike in the middle of 2006, indicating that customer deposits and short term funding declined by approximately 5% relative to the year 2000.
Figure 6b shows the mean values of the liquid assets to total assets (LATA), the liquid assets to customer deposits and short term funding (LTCDSTF) and the liquid assets to total deposits and borrowing (LATTDB) ratios. Overall all ratios exhibit a downward propensity, with the LATA showing the most drastic decrease, from over 70% in 2000 to below 40% in 2011. This indicates that, on average, banks held less liquid assets relative to total assets. Figure 6c illustrates the average amount of collateral received with rehypothecation rights and collateral received that has been rehypothecated. The average level for both measures in 2000 is approximately $100 billion. The level of assets with rehypothecation rights peaks in 2005, whereas the level of assets rehypothecated peaks one year earlier, steadily declining afterwards. Hence, the decrease in rehypothecation after the financial crisis of 2007 observed by Aitken and Singh (2009) is, with regards to the average rehypothecation volume, the continuation of a trend that started in 2005 that was exacerbated by the increased awareness of counterparty risk following the Lehman Brothers collapse. Figure 6d shows the rehypothecation measures relative total assets. The overall picture is the same as for the absolute levels. Assets available for rehypothecation spikes in 2004; the total amount of collateral obtained that can be repledged reached almost 30% of total assets. Assets rehypothecated peaked in 2005, with almost 20% of total assets. The ratio between assets that can be rehypothecated and assets rehypothecated is illustrated in figure 6f. The ratio exhibits several peaks over the entire period, but tends to decrease over time, indicating that banks obtain collateral with rehypothecation right, but make less use of it. Figure 6e shows the ratio of interbank assets to interbank liabilities. The ratio decreased from about 220% in 2000 to about 140% in 2011. While, on average, banks in the sample remain net interbank lenders, the amount of lending they extended in the money market has dramatically decreased.
collateral when taking out a loan. The correlation between liquidity creation and rehypothecation is negligible.
Table 5. Descriptive Statistics of Liquidity and Rehypothecation Measures.
Variable N Min Max Mean Std. Dev.
1. Loans to Total Assets 1131 0 112.17 51.20 25.25
2. Liquid Assets to Deposits and Short Term Funding 1161 2.95 811.19 57.07 80.40 3. Interbank Assets to Interbank Liabilities 931 -26.40 991.94 158.04 177.45
4. Financing Gap Ratio 1002 -14,800 6,600 -25.00 1,054
5. Liquidity Creation (maturity) 519 -2.71·108 4.96·108 2.98·107 8.11·107
6. Assets Available for Rehypothecation 896 0 1,884,003 90,373 214,271
7. Assets Rehypothecated 772 0 1,214,340 70,658 166,527
Notes: a. All measures in percentage (%) except liquidity creation (in thousands USD) and assets available for rehypothecation and assets rehypothecated (in millions USD).
b. All variables sourced from the Bankscope Fitch database; rehypothecation measure collated from banks’ annual reports and SEC filings.
Table 6. Correlation Matrix For Liquidity Measures and Rehypothecation.
LTA LATCSTF IBR FGR LC AAFR AR
LTA 1.0000 LATDSTF -0.7025 1.0000 IBR 0.1418 0.0093 1.0000 FGR 0.1781 -0.1018 0.1118 1.0000 LC -0.1731 -0.1142 0.1084 -0.0563 1.0000 AFR -0.3937 0.3818 -0.1416 -0.0180 0.0100 1.0000 AR -0.3688 0.3871 -0.1197 -0.0156 -0.0460 0.9746 1.0000
Notes: a. LTA: loans to assets
b. LATDSTF: liquid assets to customer and short-term funding c. IBR: Interbank ratio
d. FGR: funding gap ratio e. LC: liquidity creation
f. AFR: assets available for rehypothecation g. AR: assets rehypothecated
equity-to-assets ratio is 7.19% in the sample. The equity-to-assets ratio is measure of solvency, that is, the bank's ability to meet its debt obligations if it converted all of its assets into cash to pay creditors. Three size indicator variables are also included. They are computed according to the classification by Berger et al (2005): small if GTA (gross total assets) is below $100 million, medium if GTA is between $100 million and $1 billion, large if GTA is between $1 billion and $10 billion and huge if GTA exceeds $10 billion. Loan loss reserves to impaired loans measures the adequacy of reserves, with higher ratios indicating greater conservatism and are on average 105.01% in the sample. The average cost-income ratio in the sample is 65.18% and measures how efficiently revenue is generated. There are two competing views of the interpretation of this ratio: in the first, a low ratio is indicative of low efficiency and low productivity. In the alternative view, a low ratio reflects high efficiency due to more fierce competition, which results in lower margins (Bikker, 1999). Off-balance sheet activities represent on average 19.2% of total bank assets. The maximum of 489% indicates that some banks’ off-balance sheet items surpass on-balance sheet assets by as much as four to fivefold and that some banks rely increasingly on non-interest income. The year 2008 and year 2009 dummies are included to capture the effect of the realization of the financial crisis. The market concentration is measured as the combined total assets of the five largest banks in the country to the country’s total bank assets. On average, in the sample, the five largest five banks in the country represent 62.63% of all assets, indicating high levels of concentration.
Figures 6a-6f. Effect of Liquidity, Profitability and Credit Risk on Rehypothecation from 2000 to 2011.
Figure 6a. Mean Net Loans to Customer Deposits and Short-Term Funding, Net Loans to Total Assets and Net Loans to Total Deposits and Borrowing.
Figure 6b. Mean Liquid Assets to Total Assets, Liquid Assets to Customer Deposits and Short-Term Funding and Liquid Assets to Total Deposits and Borrowing. 48 52 56 60 64 68 72 76 80 84 00 01 02 03 04 05 06 07 08 09 10 11 Mean Net Loans to Customer Deposits and Short Term Funding Mean Net Loans to Total Assets
Mean Net Loans to Total Deposits and Borrowing
30 40 50 60 70 80 90 00 01 02 03 04 05 06 07 08 09 10 11 Mean Liquid Assets to Total Assets
Figure 6c. Mean Assets (Collateral Obtained) Available
for Rehypothecation and Mean Assets Rehypothecated. Figure 6d.Available for Rehypothecation to Total Assets and Mean Assets (Collateral Obtained) Mean Assets Rehypothecated to Total Assets.
Figure 6e. Mean Interbank Assets to Interbank Liabilities
Ratio. Figure 6f.for Rehypothecation to Assets Rehypothecated Ratio. Mean Assets (Collateral Obtained) Available
Table 7. Descriptive Statistics of Control Variables.
Variable N Min Max Mean Std. Dev.
1. Equity to Assets (Capital) 1304 -13.71 60.33 7.186 5.665
2. Bank Size Dummy Variables (S, M, L, H)
3. Loan Loss Reserves to Impaired Loans (Credit Risk) 909 -2.582 910 105.01 108.80 4. Return on Average Equity (Profitability) 1309 -532.38 96.663 8.309 24.290
5. Cost Income (Operating Efficiency) 1318 -355.1 511.95 65.18 28.79
6. Off-Balance Sheet Activities to Total Assets 1207 0 489.3 19.2 38.5
7. Year 2008 and year 2009 dummies (Realization of the financial crisis)
8. Market Concentration (Assets of Top 5 Banks) 1511 17.90 136.82 62.63 28.38
9. Inflation 1660 -5.065 21.46 2.039 2.069
10. Total Country Bank Assets to GDP 1564 0.00 3.54 0.403 0.360
11. Money Market Rate 1248 0 23.37 2.450 2.450
Notes: All measures in percentage (%).
40,000 60,000 80,000 100,000 120,000 140,000 160,000 00 01 02 03 04 05 06 07 08 09 10 11 Mean Assets Available for Rehypothecation Mean Assets Rehypothecated
.05 .10 .15 .20 .25 .30 00 01 02 03 04 05 06 07 08 09 10 11 Mean Assets for Rehypothecation to Total Assets Mean Assets Rehypothecated to Total Assets
100 120 140 160 180 200 220 240 260 00 01 02 03 04 05 06 07 08 09 10 11
Mean Interbank Assets to Interbank Liabilities
52 56 60 64 68 72 76 80 00 01 02 03 04 05 06 07 08 09 10 11
To measure the influence of the macroeconomic environment, the two variables, inflation and the country’s total bank assets to gross domestic product (GDP) are included. The latter is representative of the overall development of the banking industry relative to the country’s economy. On average, the country’ total bank assets represented 0.40% of total GDP. Lastly, the money market rate, or short-term rate, is the rate at which short-term borrowings are effected between financial institutions or at which short-term government paper is issued or traded in the market. On average it amounted to 2.45% over the period 2000 to 2011.
4. ECONOMETRIC METHODOLOY
4.1 GRANGER CAUSALITY BETWEEN REHYPOTHECATION AND
BANK RISK
To explore the dynamic relationship between the different dimension of bank funding liquidity and rehypothecation of obtained collateral the generalized method of moments system estimator by Arellano and Bond (1991) and the Blundell and Bond (1995) is applied to the Granger Causality framework. According to Granger (1969) there is Granger causality from xt to yt if past (i.e. lagged) values of xt improve the prediction of yt given the past values
of yt. More formally, Granger causality is defined as follows: let Ωt be the total information
set available at time t containing the two time series {xt}t∈Ζ and {yt}t∈Ζ and taking the form
Ωt := {xt, xt-1, …, xt−j , yt, …, yt−i, …}. Let xt be the set of all current and past values of xt and
taking the form xt:= { xt, xt-1, …, xt−k, …}, analogously, yt:= {yt, yt-1, …, yt-j, …} and let σ 2(·)
denotes the variance of the corresponding forecast error. Then xt is Granger causal for yt with
respect to Ωt if the variance of the optimal linear predictor of yt+h, based on Ωt, has smaller
variance than the optimal linear predictor of yt+h based only on lagged values of yt, for any h:
σ2
yt|Ωt
(
)
< σ2yt+h |Ωt− xt
(
)
(9)Conversely, xt is not Granger causal for yt with respect to Ωt if the variance of the optimal
linear predictor of yt+h, based on Ωt, has strictly equal variance as the optimal linear predictor
of yt+h based only on lagged values of yt, for any h. Moreover, there is feedback between xt
panel setting of banks operating globally in the collateral industry, the GMM framework that investigates the relationship between liquidity and rehypothecation can be specified as:
yit =α0+ αjyit− j j=1 m
∑
+ δjxit− j +νi+ uit j=0 n∑
(10) xit =α0+ αjxit− j j=1 m∑
+ δjyit− j +νi+ uit j=0 n∑
(11)Where xit and yit are the variables of interest of bank i at time t, with i = 1, …, N; t = 1,…, T; vi
is the unobserved bank-specific effect, uit the idiosyncratic error, while m and n are the
number of lags, of the variables xit and yit respectively, and are assumed to be finite and
smaller than T. Granger causality between rehypothecation (assets available for rehypothecation, assets rehypothecated and the ratio of assets rehypothecated to assets available for rehypothecation) is tested for the following measures: 1) Loans to Assets, 2) Liquid Assets to Customer and Short-Term Funding, 3) Interbank Assets to Interbank, 4) Financing Gap Ratio and 5) Liquidity Creation.
Hence, the basic model that examines the dynamic and inter-temporal relationship between liquidity and rehypothecation take the following form:
Liquidit =α0+ αjLiquidit− j j=1 m
∑
+ δjRehypoit− j +νi+ uit j=0 n∑
(12) Rehypoit =α0+ αjRehypoit− j j=1 m∑
+ δjLiquidit− j+νi+ uit j=0 n∑
(13)Where Liquidit denotes one of the above-mentioned measures of liquidity of bank i at time t,
and where Rehypoit is a corresponding measure of rehypothecation of obtained collateral.
Their GMM system estimator is a joint estimation of the equation in levels and in first differences (Roodman, 2006). In order to ensure the consistency of the GMM estimates, two specification tests are performed: 1) the Arellano-Bond test for zero autocorrelation AR(2), which tests the null hypothesis that the error terms are not second-order serially correlated and 2) the Hansen test of over-identification, which assesses the validity of the instruments used in the Granger causality specification. The AR(2) test on the residuals in first differences is used to detect AR(1) in the underlying levels variables. Note, that in the context of an Arellano-Bond GMM regression, which is run on first differences, first order serial correlation of error terms is to be expected, and therefore the results of the Arellano-Bond AR(1) test are usually ignored (Roodman, 2006)4.
4.2 LAG LENGTH SELECTION AND PANEL UNIT ROOT TEST
Since the results from the Granger-Causality test are highly sensitive to the lag length employed, it is salient to select the correct lag length specification, as an inappropriate lag length may lead to inconsistent estimates. For this purpose Hsiao’s (1979) proposed an approach based on Akaike’s final prediction error (FPE) or its asymptotically equivalent the Akaike Information Criterion (AIC). However, it has been pointed out that Akaike’s criteria asymptotically overestimate the true order of an auto-regressive (AR) process with a non-zero probability (Shibata, 1980; Geweke and Meese, 1981). Odaki (1987) showed that one could use either AIC, Hannan-Quinn Criterion (HQC) or Schwartz-Bayesian Criterion (SBC) since they all exhibit the desired asymptotic power for Granger causality detection. In order to select the appropriate lag length specification the SBC criterion is used in this paper. The SBC is given by:
SBC(m, n) = ˆσ2⋅(m+ n)lnT
T (14)
Where N is the number of observations, T the number of periods, m is the number of lags of variable xit, n, the number of lags of variable yit and ˆσ2 the sum of the squared residuals.
Despite the comparable asymptotic properties of AIC, HQC and SBC, it is still possible that lag length specification differ between the three criteria (Urbain, 1988).
The Granger causality concept requires that processes be (weakly) stationary.
Therefore, a Levin, Lin and Chu test (2002) panel unit root test is employed to determine stationarity of the liquidity and rehypothecation variables. Hlouskova and Wagner (2005) show that the Levin, Lin and Chu test (2002) and the Breitung (2000) test have the highest power to detect the presence of a unit root, compared to other tests. The null hypothesis of the Levin, Lin and Chu test (2002) used in this paper is:
H0: ρi = 1 for i = 1, …, N. (15)
Against the homogeneous alternative:
H1: -1 < ρi = ρ < 1 for i = 1, …, N. (16)
Under the homogeneous alternative the first order serial correlation coefficient ρ is required to be identical in all unites. The results of the panel unit root test are presented in table 1 of the appendix.
4.3 CONTROL VARIABLES AND HERDING BEHAVIOR
Using the approach of Horváth et al (2012) who examine the relationship between bank liquidity and capital using a fixed 4 lag framework, additional bank control variables with 0 lags are included into the rehypothecation-liquidity specification. These variables do not affect the SBC (or the HQC/ FPE), since the number of lags is 0. In the Granger concept, the absence of lags implies that theses variables are not Granger causal. The main rationale for including these bank control variables is to counteract the possibility of spurious causality that could arise in a bivariate setting, when both variables have common causes that are absent from the regression equation. This can lead to the erroneous finding of Granger-causality even in the absence of a direct relationship between two variables. Therefore, employing a multivariate setting can help to alleviate the problem of spurious causality (Hsiao, 1982). However, as pointed out by Atukeren (2007), the ‘missing-cause problem’ is not necessarily resolved in a multivariate setting and any finding of Granger-causality remains in principle
prima facie. Furthermore, Berger and DeYoung (1997) point out: "Granger-causality yields
gross statistical associations that can only indicate consistency or inconsistency with an hypothesis, not proof of economic causation."
Liquidit =α0+ αjLiquidit− j j=1 m
∑
+ δjRehypoit− j j=0 n∑
+ϕ0PeerLiquidit+ϕ1PeerRehypoit + ßpXit p r=1 P∑
+ ßrXit r r=1 R∑
+ ßsXit s s=1 S∑
+νi+ uit (17) Rehypoit =α0+ αjRehypoit− j j=1 m∑
+ δjLiquidit− j j=0 n∑
+ϕ0PeerLiquidit+ϕ1PeerRehypoit + ßpXit p r=1 P∑
+ ßrXit r r=1 R∑
+ ßsXit s s=1 S∑
+νi+ uit (18)Where the zi,t’s are explanatory variables grouped into bank-specific, industry-level and
macro-economics determinants (denoted by sub- and superscripts p, r and s respectively); vi is
the unobserved bank-specific effect and uit the idiosyncratic error.
In addition to the bank control variables, a herding measure proposed by Bonfim and Kim (2012) is introduced into the equation. PeerLiquidit denotes the average liquidity
indicator of peer banks and is defined as Liquidjt Nit−1
j≠1
∑
, Nit – 1 being the total numbers of peersof bank i at time t for a given country5. The coefficient φo of the peer liquidity term captures
the extent to which banks’ liquidity choices reflect those of the relevant peer group. Due to potential reverse causality problem described by Manski (1993), in that it cannot be ruled out a bank's liquidity decisions affect its peer group's liquidity decisions (and vice-versa), the peer liquidity term is instrumented by the predicted average peer liquidity for a given year (and a given country). Bonfim and Kim (2012) argue that the predicted value of liquidity indicators of peer banks, based on the regressions of the determinants of liquidity indicators, is orthogonal to systematic or herding effects. Hence, the predicted value of the liquidity indicators of peer banks do not directly affect the liquidity indicator of bank i at time t, as the predicted values are based solely on observable bank characteristics.
Analogously, the term PeerRehypoit represents the level of rehypothecation of all
country’s banks at time t less the amount of bank i at time t. Peer rehypothecation is defined
as Rehypojt
Nit−1
j≠1
∑
, where Nit – 1 is the total numbers of peers of bank i at time t for a givencountry. The coefficient φo of the peer liquidity term captures the extent to which banks’
rehypothecation choices reflect those of the relevant peer group. The peer rehypothecation term is instrumented by the average peer rehypothecation for a given year (and a given country).
4.4 ANALYSIS OF BANK EFFICIENCY
In order to estimate the banks’ level of profit and cost efficiency and the effect of bank liquidity and rehypothecation of securities on bank efficiency, the so-called 1-step, parametric estimation methods hereunder are used, where either the 2nd or the 1st moment of the inefficiency terms is conditioned on the bank-specific variables of interest (liquidity, rehypothecation and capital):
1) Conditional variance model by Wang and Schmidt (2002) 2) Conditional mean model by Battese and Coelli (1995)
The main advantage of the 1-step procedure over the 2-step procedure is that, that it does not yield biased estimates like the 2-step procedure. The latter is described by Coelli and Battese (1998): estimates of the inefficiency scores from an unconditional parametric model in the first step, are regressed upon bank-specific regressors of interest in the second step – usually via Tobit regression due to the censored nature of the efficiency scores. Wang and Schmidt (2002) argue that the two-step procedure yields biased results, because the model estimated at the first step is misspecified when the bank-specific covariates are not taken into account when computing the bank inefficiency levels. Moreover, there are two potential sources of bias: first, bias can arise when the input variables and the bank-specific variables of interest (in this case liquidity and rehypothecation) are correlated. Second, when input and bank-specific variables are independent, then the non-inclusion of latter can cause the inefficiencies to be underdispersed and the estimates of the effect of the bank-specific factors on inefficiency, to be downward-biased towards zero. For this reason, the 1-step methodology is preferred in this study.
With regards to the choice of the specification, the Fourier flexible functional form profit function with 3 inputs and 2 outputs of equation (19) is used to estimate inefficiency scores. Πit(y, w, z) is the natural logarithm of normalized bank profit of bank i at time t; the xit
are the normalized and log-transformed outputs bound to the interval [0, 2п], which are windsorized to the interval [0.1, 2п·0.9], following the method of Berger et al. (1997), in order to facilitate the estimation at the extremes. γ0 and γ are unknown parameter to be
estimate cost efficiency. In order to obtain non-negative values a constant is added to total bank profit and total cost following the methodology described by Maudos et al (2001).
Πit(y, w, z)=β0+ βjln(yjit)+
1
2 k=1βjkln(yjit)⋅ln(yjit)
2
∑
j=1 2∑
j=1 3∑
+ βlln(wlit) l=1 2∑
+1 2 k=1βjkln(wjit)⋅ln(wkit) 2∑
j=1 2∑
+12 k=1βjkln(wjit)⋅ln(ykit) 2
∑
j=1 2∑
+ + κrln(zrit) r=1 2∑
+1 2 s=1κrsln(zrit)ln( 2∑
r=1 2∑
zsit) +1 2 r=1ηirln(wlit)ln( 2∑
i=1 2∑
zrit)+ 1 2 r=1ρjrln(yjit)ln( 2∑
j=1 2∑
zrit)+
[
φCos(xnit)+ϕSin(xnit)]
n=1 3
∑
+ ⎡⎣φ cos(xnit+ xqit)+ϕ sin(xnit+ xqit)⎤⎦ q=n 2∑
n=1 2∑
+ ⎡⎣φ cos(xnit+ xqit+ xwit)+ϕ sin(xnit+ xqit+ xwit)⎤⎦ w=q 2
∑
q=n 2∑
n=1 2∑
+Uit+ Vit (19)The parameters and the inefficiency terms of the Battese and Coelli (1995) model and the Wang and Schmidt (2002) model are estimated via the maximum likelihood method. The log-likelihood function is expressed in terms of the parameters σ2 =σ2 +σ2
V S , γ ≡σ2/σS2, where 2 / 1 2 2 2 ( ) V U S σ σ σ = + and 2 / 2 S U σ σ
γ = . Following Lang and Welzel (1996), the restrictions hereunder are imposed to ensure symmetry and linear homogeneity:
βjk =βkj ∀ j, k ;βik =βki ∀ i, k βj = 1 j=1 3
∑
, βjk = 0 j=1 3∑
∀ j, βjk = 0 j=1 3∑
∀ k, (20)Linear homogeneity in input prices is imposed by normalizing the dependent variable, profit (or total cost), and all factor price variables, wi’s, and then log-transforming them.
