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Modelling liquidity management in Islamic banks from a microeconomic perspective
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Modelling liquidity management in Islamic banks from a microeconomic perspective Mouldi DJELASSI , Jamel BOUKHATEM PII: DOI: Reference:
S1544-6123(19)30488-X https://doi.org/10.1016/j.frl.2019.101341 FRL 101341
To appear in:
Finance Research Letters
Received date: Revised date: Accepted date:
5 February 2019 14 October 2019 23 October 2019
Please cite this article as: Mouldi DJELASSI , Jamel BOUKHATEM , Modelling liquidity management in Islamic banks from a microeconomic perspective, Finance Research Letters (2019), doi: https://doi.org/10.1016/j.frl.2019.101341
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Highlights
We integrate Islamic financial intermediation into a standard microeconomic model to examine the determinants of banking liquidity. We show the existence of three important determinants of banking liquidity: deposit revenue sharing ratio, financing return rate and Islamic money market rate. Excess reserves in Islamic banking sector are due to high level of deposits and low level of funds supply in financing and interbank markets. These results contribute to design guidelines for empirical determinants of liquidity in Islamic banks.
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Modelling liquidity management microeconomic perspective
in
Islamic
banks
from
a
Mouldi DJELASSI Department of Banking and Financial Markets, College of Islamic Economics and Finance, Umm al Qura University – Saudi Arabia Department of Economics, High school of Economic and Business Sciences ESSECT – University of Tunis, Tunisia [email protected] [email protected]
Jamel BOUKHATEM Department of Banking and Financial Markets, College of Islamic Economics and Finance, Umm al Qura University – Saudi Arabia Department of Economics, Faculty of Economic sciences and Management FSEGT, University of Tunis el Manar– Tunisia [email protected] [email protected]
Abstract. The main objective of this paper is to examine the determinants of banking liquidity by explicitly integrating Islamic financial intermediation into a standard microeconomic model. Our model includes the banks’ liquidity reserves in line with profit-maximization motives and provides an analytical framework for interpreting the excess liquidity behavior commonly seen in the Islamic banking sector. Excess reserves result from an increase in a bank’s deposits base combined with Islamic banks’ limited opportunities for financing and placement. The monetary policy rate appears to be a key instrument that central banks can use to resolve the problem of excess reserves. Keywords: liquidity management; Islamic banking; modelling JEL classification: C6, G21
Funding acknowledgement: This study was supported by the Deanship of Scientific Research at Umm Al-Qura University- Saudi Arabia, under the Grant number 17-ADM-1-010004.
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1. Introduction Despite the development of Islamic banking as both a major financial intermediary and an important element of Islamic economic practice, little theoretical research has focused on Islamic banks. A satisfactory theory for Islamic banking behavior would therefore seem an indispensable prerequisite for gaining a clear understanding of how the Islamic banking sector functions. In this paper, we attempt to model and explain the behavior of Islamic banking firms. Any model for Islamic banking must be relatively abstract due to its inherent complexity, with the nature and the degree of this abstraction being determined by an author’s conception of what is important in Islamic banking. In general, Islamic banks are a kind of financial intermediary, but they cannot borrow through the interbank market through the usual mechanisms or rediscount at a given rate. In addition, as such institutions collect deposits and provide financing, they are not immune to liquidity and default risks.1 The purpose of this paper is therefore to understand the general functioning of Islamic banks and their liquidity management by explicitly integrating Islamic financial intermediation into a standard microeconomic model. The simplest way to look at liquidity management is to study the determinants for the volume of funds collected or distributed by the bank in line with the profit-maximization motive. The role of Islamic banks is thus considered according to two fundamental characteristics of their activity: the management of payment means (collecting deposits under the revenue-sharing rule) and financial intermediation (providing sharia-compliant financing). This model has significant implications in a variety of areas. Theoretically, the development of a simple microeconomic model for Islamic banking is an important step in discerning the determinants of liquidity in later applied research, as well as in suggesting plausible and testable hypotheses connected with them. In policy areas, such a model would provide a framework for understanding the phenomena of excess liquidity in many Islamic banks and the effects of monetary policy on their reserves. The remainder of this paper is organized as follows. Section 2 presents the basic model, and then Section 3 analyzes the liquidity behavior of individual Islamic banks in a competitive banking sector. Finally, Section 4 concludes the paper. 2. The basic model Various studies have empirically investigated the liquidity management risk in Islamic banks. However, no studies have investigated liquidity risk management in Islamic banks from a theoretical perspective, compared with an abundance of academic literature devoted to reserve
1
Islamic banks are pressured by the markets to pay their investors-depositors a rate of return higher than what would normally be expected (displaced commercial risk). In many countries where Islamic banks operate, there is disharmony between them and central banks due to the latter’s refusal to issue funds based on anything other than interest. Accordingly, Islamic banks lack this final resort to meet their liquidity needs. Finally, in Islamic banking, it is argued that a significant portion of deposits is often is held in liquid form due to the limited shortterm sharia-compliant instruments available to them (Iqbal and Mirakhor 2007, Greuning and Iqbal 2008).
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management modeling in conventional banks.1 Among the economic literature, the banking behavior models developed by Freixas and Rochet (1999) are the most convenient for the purposes of this research. The authors adopt the industrial organization approach to model banking activity as the provision of services to depositors and borrowers. Although simplistic, this approach will provide a rich set of models for tackling different issues, such as monetary policy, market failures, and some aspects of market regulation. Referring to Freixas and Rochet’s model for bank behavior, the adjusted model is adapted for the case of Islamic banks to investigate the flow of liquidity on the assets and liability side. The novelty of this model lies in incorporating the specificities of Islamic banking activities and liquidity risk management into the classical bank theory, as well as considering some forms of market structure. Despite its simplicity, this approach will support a rich analysis for tackling different issues, such as monetary policy, the determinants for optimum liquidity reserves, liquidity management in a low-depth interbank market, and the phenomena of excess liquidity in Islamic banks. We assume that the economy includes three types of agents – namely firms, banks, and depositors – with them all adopting sharia principles.2 2.1. The real sector There is a continuum for firms. All have access to the same instruments, and for the sake of simplicity, we assume they all start with no capital. Each firm has a project with costs equal to I. We further assume that firms can only obtain financing from banks on an equityparticipation basis. A project generates a financial return, which is shared between the firm (the entrepreneur) and the bank in pre-agreed proportions. As such, is the return-sharing ratio for the bank and is the return-sharing ratio for the firm. The return-sharing ratio is assumed to be fixed for the duration of the contract, and we further assume that it is the same for all firms. 2.2. The financial sector The financial sector is composed of different banks indexed by . They are defined as financial intermediaries that buy certain types of securities (e.g., financing contracts like murabaha, mudharaba, etc.) and sell different types of securities (e.g., mudharaba deposits). In our model, the bank is a mudharib profit-maximizing, risk-neutral institution that operates in an environment with three assets: financing, money market assets, and cash. Financing ( ) is a long-term instrument with a return rate equal to , while the 1
The literature concerning reserve management modeling in conventional banks goes back a long way. Early and more contemporary pioneers include Orr and Mellon (1961), Poole (1968), Frost (1971), Baltensperger (1972a, 1972b, 1974, 1980), Knobel (1977), Diamond and Dybvig (1983), Freixas and Rochet (1999), Diamond and Dybvig (2000), Diamond (2007), to name but a few. 2 This condition must be respected to make the model sharia-compliant. Under sharia-principles, economic agents do not deal in transactions with interest but rather use the principle of profit and loss sharing for a business. Islamic financing and refinancing therefore takes the form of trade and investment rather than loans. Likewise, Islamic savings accounts take the form of a profit-sharing investment account rather than an interestyielding deposit account.
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money market assets ( ) are short-term investments in Islamic money markets with rate of return . Finally, cash is a storage mechanism that gives no return. The bank collects deposits ( ) from rabb al mel (depositors) based on mudharaba partnerships at a rate of return and essentially finance the investment needs of firms.1 We assume that banks have access to money markets and/or the interbank market. The interbank market allows banks to meet their liquidity needs by borrowing from, or lending to, their peers. Unlike in the traditional banking system, however, Islamic banks cannot borrow through the interbank market using the usual mechanisms or rediscount at a given discount rate. Any financing between banks must instead be based on profit and loss sharing or markup principles. We assume here that banks can finance their needs through the interbank market only on murabaha basis.2 A murabaha commodity provides certain returns because it is based on a pre-agreed “margin” or “markup” from the sale and purchase of the underlying assets. We note that is the rate of return through the Islamic interbank market (i.e., the rate of profit on a murabaha commodity).3 A bank uses labor and physical capital as inputs for producing different financial services for depositors and firms. This intermediation activity is costly, so bank will pay amount to generate of deposits and of financing. This is represented by the cost function . To simplify the analysis, we assume that the cost is the same for all banks . We further assume that projects financed by a bank are imperfectly correlated, because banks are then motivated to choose them to diversify their financing portfolios and ensure a stable return for their depositors. The typical balance sheet of bank would look as follows: Assets (cash reserves)
Liabilities (Customers’ deposits)
(interbank operations, net) (financing and investment) 1
Islamic banks typically raise deposits through profit-sharing investment accounts (PSIAs). These accounts, in their unrestricted form, are reported on the balance sheet of an Islamic bank. They can be regarded as discretionary wealth-management accounts being offered by private banks or as a sharia-compliant substitute for conventional deposit accounts. The PSIAs have two characteristics: (a) they can capture liquidity risks in Islamic banks because their holders have the right of withdrawal, and (b) secondly, they can be considered a capital account because the bank is assumed to pay investment account holders their contractual shares of any profit resulting from the investment of their funds. For further analysis, see Archer and Karim (2009) and Archer, Karim, and Sundararajan (2009). 2 Liquidity management is not just managing cash reserves. There are secondary liquidity reserve instruments such as commodity murabaha, wakala, Islamic certificates of deposit, and Sukuk (Islamic bonds). However, for Islamic banks, the murabaha commodity and similar instruments dominate the current landscape for liquidity management because substitute instruments like Sukuk often cannot be traded on secondary markets under sharia rules (Thomson Reuters, 2017). 3 We assume that the sale and repurchase of a commodity is the only way a bank can augment or reduce its resources. This operation is equivalent to using the rediscounting mechanism, where r is the quasi-discount rate.
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The Islamic bank issues mudharaba deposits , purchases mudharaba financing , and transfers cash through its account at the central bank, which generates no interest.1 We suppose that a bank maintains cash reserves at a proportion of deposits. Thus, for any bank :
(1) If the bank has excess reserves, it can loan it through the interbank market. Conversely, if it has a deficit, it can borrow through the same market. We consider to be the net amount 2 due from/to other banks and financial institutions (positive or negative). 2.3. The investors Individual investors are small, and we assume that each only invests his or her savings in an investment account offered by a bank on an equity-participation basis. Bank is assumed to pay investors (its depositors) a rate of return based on the profit from its operations. This profit is shared between the depositors and the bank in some mutually agreed proportion ( ) (i.e., return- or revenue-sharing ratio). We sometimes assume that is fixed for the duration of the contract. 3. Microeconomic analysis of liquidity: The behavior of individual Islamic banks in a competitive banking sector We consider a problem where bank wants to determine the amount of cash reserves to hold. The simplest way to introduce liquidity management is to study the determinants for the volume of funds collected or distributed by bank in line with the profit-maximization motive. Assuming the bank has access to two sources of funding (i.e., deposits and the interbank market), the amount of cash reserves can be defined as: (2) Where represents the net source of funds from the interbank market, which can be positive or negative. Now, suppose for simplicity’s sake that cash reserves are costless for the bank (i.e., no return received but no management cost) and that the bank is a price taker. It therefore takes as given 1
In accordance with article 7 of the Banking Control Law and regulations issued by the Saudi Arabian Monetary Agency (SAMA), a bank is required to maintain a statutory deposit with SAMA at a stipulated percentage of its demand, time, and other deposits, calculated at the end of each Gregorian month. The statutory deposit with SAMA is not available to finance the bank’s day-to-day operations and therefore not part of the cash and cash equivalents. Banks therefore maintain a statutory deposit with SAMA comprising 7% of total demand deposits plus 4% of savings and time deposits. In addition to this statutory deposit, banks must also maintain liquid reserves no less than 20% of its deposit liabilities, either in the form of cash or assets that can be converted into cash within 30 days (SAMA, 2017). 2 Money due from other banks and financial institutions are financial assets with fixed or determinable payments and set maturities that are not quoted in an active market. These money market placements represent funds loaned on a sharia-compliant (i.e., not interest based) murabaha basis.
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the rate of financing , the return-sharing ratio , and the interbank market rate . 1 Considering the management costs, the profit of bank is formulated as: (3) Bank profit is defined as the difference between the revenue a bank receives and the costs it incurs. P is the total profit earned from the n businesses financed by bank after sharing it between the bank and the businesses on a PLS basis . P is positive, because we assumed earlier that all projects financed by a bank are imperfectly correlated.2 represents the margin for the sale and purchase of commodities on the interbank market. represents the cost of deposits collected by bank and costs for deposits and financing.
is the total management
rf and rd are, respectively, the rates of return from financing and depository investment, so, we have:
(4) (
Therefore,
)
(5)
can be rewritten as: (6)
Both the revenues and costs of bank i depend upon the actions taken by the bank. In the case of financial intermediation, these actions may take three important forms: financing activities, collecting deposits, and making interbank transactions. The bank, which is assumed to be a profit-oriented, risk-neutral financial intermediary, then decides how to maximize its profit subject to the constraints:
1
Each bank is assumed to take prices as given, so these are exogenous variables for the profit-maximization problem. Thus, a bank is concerned only with maximizing profit levels for financing and deposits. Such a pricetaking bank is referred to as a competitive bank. We have chosen this market structure because we consider Islamic financial products to be homogeneous and available from many banks. For example, the profit-sharing investment account (PSIA) is a homogeneous product offered by many banks at the same sharing ratio. Any bank that provides anything lower than the going sharing ratio will immediately lose all its depositors. In the same way, the murabaha contract is a financing form provided by many Islamic banks, and any bank charging above the going market price for its product will lose all its customers. Hence, each bank must adopt the market rates for profit-sharing ratio and financing as given when determining optimal choices for deposits and financing. 2 Because of the domination of trade financing modes, we can assume that Islamic banks have predetermined short-term revenues with a minimum probability of bearing loss.
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(7) and equation (1): Therefore, the bank’s profit can be rewritten as follows: [
]
–
(8)
The profit of an Islamic bank is based on a combination of its funds-providing activity (the financing market), its activity in raising funds from depositors (the deposits market), and its total net management costs. The bank’s problem is therefore to maximize profit by choosing the right amount of financing and deposits to generate. The financing and deposits markets are modeled as being perfectly competitive, and banks are price takers for the financing rate , deposits-sharing rate , and interbank rate . Each individual bank must select amounts of financing and deposits that are suitable for its various characteristics. Thus, profit maximization, given the assumptions on the cost function (decreasing returns to scale and convexity), is: –
(9)
–
(10)
–
(11)
( – )
(12)
The intuition behind these conditions should be clear: If the marginal revenue of an activity (i.e., financing or deposits) is greater than the marginal cost, it would cost the bank money to expand this activity. These fundamental conditions have several concrete interpretations. Therefore, a bank must choose the right level of financing. Equation (11), which concerns the fundamental condition of profit maximization, shows that a level of financing should be chosen such that the supply of one unit of financing should produce a marginal revenue equal to the corresponding marginal cost. The bank must also determine the amount of deposits to collect. The fundamental condition of profit maximization (Eq. 12) asserts that it should collect deposits such that the marginal revenue from employing one additional unit of these resources should be equal to its marginal cost. Next, a competitive bank sets intermediation margins equal to the marginal management costs. Equations (11) and (12) implicitly determine the credit supply function and the deposit demand function, respectively (see Equations 13 and 14):
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(
–
)
(13)
(
–
)
(14)
a. Optimal financing supply:
(
)
Result 1 -
An increase in will cause increased income from financing, so the bank is encouraged to increase its supply of financing:
-
A decrease in causes a decreased marginal return from funds in the money market, so the bank is encouraged to increase its supply of financing:
-
An increase in causes increased marginal costs for funding from deposits, so the bank is motivated to reduce its supply of financing:
-
An increase in management costs causes an increase in the marginal costs of banks, so the bank reduces its supply of financing:
(
), where (+) or (–) indicates the postulated signs of partial
derivatives. b. An optimal bank’s demand for deposits:
(
)
Result 2 -
An increase in causes an increase in bank costs and consequently a decrease in the optimal level of the bank’s demand for deposits ( ).
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-
An increase in leads to an increased return from the interbank market, so the bank is encouraged to increase its demand for deposits:
-
The coefficient is considered a tax on deposits, so an increase in this coefficient will cause an increase in the opportunity costs for the bank and a decrease in its demand for deposits:
-
An increase in management costs leads to an increase in the marginal cost of bank resources, so the bank reduces its demand for deposits:
(
) , where (+) or (–) indicates the postulated signs of partial
derivatives. c. Optimal refinancing supply (or demand) in the interbank market The optimal decision for the interbank market can be deduced from the balance sheet constraint. On the assets side, the allocation of loanable funds by banks results from their profit-maximization behavior. The balance sheet constraint can be rewritten as follows: ( (15)
)
(
)
The position of bank on the interbank market is then expressed as follows: (
)
(
)
(
–
) (16)
Here, the decision of the bank is to determine how much funds to supply (or demand) to (or from) the interbank market. The fundamental condition of profit maximization says the bank should provide (or collect) enough refinancing such that the marginal revenue from providing (employing) one more unit is equal to its marginal cost. Result 3 If the net position of bank on the interbank market is positive, an increase in its refinancing supply can occur due to one of the following conditions:
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-
A decrease in the return rate for financing causes a decrease in the supply of F and encourages the bank to increase its refinancing supply through the interbank market.
-
An increase in the refinancing return encourages the bank to increase its financing supply and its demand for deposits. The decrease in the amounts of financing and deposits leads to an increase in .
-
An increase in causes an increase in the marginal cost of funding from deposits, so the bank reduces its demand for deposits. The decreased volume of deposits leads to a decrease in Mi.
-
An increase in diminishes the volume of the refinancing supply due to a reduction in the bank’s demand for deposits, which in turn leads to a decrease in Mi.
( ), where (+) or (–) indicates the postulated signs of the partial derivatives. If the net position in the interbank market is negative (i.e., the bank is a net borrower), we get the reverse sign. d. The optimal bank’s demand for reserves We can present the optimal demand for reserves in two different ways: In the first way, we consider the reserves to be proportional to deposits. In our model, the amount of banking deposits depends on the profit-sharing ratio , which is itself determined by the deposit market equilibrium condition (eq.14). The expression for the reserve quantity when banks are explicitly modeled as profit maximizers is then: (
)
(17) 11
This expression demonstrates that the amount of cash reserves needed by bank depends upon the deposit market equilibrium condition (endogenous liquidity). Alternatively, we can present the optimal bank’s demand for cash reserves as: ((
)
)
–
–
(18)
This expression demonstrates that the demand for cash reserves is determined by equilibrium conditions in three markets (i.e., deposits, financing, and interbank). In this general case, we obtain: Result 4 -
(
) : An increase in
or
will lead to a decrease in the optimal level
for the bank’s demand for deposits and consequently a decrease in its demand for reserves. In fact, the rise in increases the opportunity cost for deposits compared to the refinancing cost for a given value of ̅ . Likewise, an increase in will lead to an increase in banking costs. The bank is therefore encouraged to prefer interbank market financing over deposits to obtain more funds. In this way, the bank’s profit is higher at greater return rates for financing or lower interbank rates . Thus, the bank can improve its situation by allowing to provide more financing and holding less cash , provided that is high. -
-
( ) : If we assume a negative net position on the interbank market, the bank holds more cash following a hike in the interbank financing rate . Accordingly, an increase in causes an increase in the marginal cost of funds from the money market, so the bank reduces its financing demand from the interbank market, reduces its supply of financing to firms, and increases its demand for deposits. Finally, the bank )1 holds more cash ( If we assume a positive net position on the interbank market, the increase in leaves the bank investing in interbank market assets and holding less cash, because the ). In this case, the bank trades the cost of opportunity cost of cash is very high ( holding cash against the return on investment that assets may provide. (
): The amount of cash
financing return rate
held by the bank decreases with an increase in the
. This is explained by considering the objective of profit
1
Equations 11 and 12 demonstrate that the movements in all return rates are proportional to those of the interbank market, so if the interbank market rate increases, the rates and also increase. Consequently, the volume of financing Fi decreases and the volume of deposits Di increases. Finally, the bank holds more cash.
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maximization. The bank only focuses on financing while cash is always unprofitable investment.1 -
(
because it will provide a return,
): The management costs have a contradictory effect. An increase
in the management cost of deposits leads to a decrease in the optimal level for the bank’s demand for deposits, so there is corresponding drop in its demand for reserves. However, an increase in the management cost of financing causes a decrease in the optimal level for the bank’s supply of financing, which in turn increases the volume of reserves. (
), where (+) or (–) indicates the postulated
signs of partial derivatives.
e. Application and interpretation of the model According to Result 4, in a competitive environment, an increase in the deposit-sharing ratio or financing rate reduces the amount of reserves held by banks. The effect of the interbank rate, meanwhile, on reserves depends upon the net position of the bank. In the case of a negative net position on the interbank market, the bank holds more cash following an increase in the interbank financing rate. However, if we assume a positive net position, an increase in leads to the bank investing more in interbank market assets and holding less cash. Meanwhile, an increase in the management costs of financing discourages a bank from providing financing, which in turn means it holds more cash reserves. The preceding model has several implications, and it is important here to make a preliminary attempt at providing a framework for understanding the phenomenon of excess liquidity that is experienced by the Islamic banks of many countries. 2 Understanding this phenomenon requires some reformulation of the model, however. First, we define excess liquidity as the amount of reserves over and above that required for precautionary purposes. We define as the compulsory reserves for bank , so:
(19) with
being the excess reserves held by bank .
(20) The balance sheet constraints can be rewritten as:
1
if , an increase of pushes the bank into obtaining greater profits by investing more in interbank market assets and reducing its holdings of cash and bank financing . 2
For more details about this phenomenon, see (Hassoun 2003, Islamic Financial Services Board, 2008, Standard & Poor's 2010, Ernst & Young 2011, 2012 and Thomson Reuters Report (2017).
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(21) And we can present the optimal excess reserves as: [ [ (22)
–
]
[
–
]
]
According to this model, the excess reserves in the Islamic banking sector can be explained by a low-level supply of funds to the financing and interbank markets. This situation is brought about by a low level of return rates and high management costs for financing.1 Thus, an increase in financing rates would increase the supply of financing and help decrease excess reserves. If Islamic banks are unable finance projects because of their high management costs and low return rates, one would still expect them to invest their unremunerated cash in the money market, at least if one exists, and offer attractive investment opportunities. A bank continues to invest in the money market if the spread between the return on such placements and the return on reserves is positive. 2 In this case, one would expect interbank placements to be negatively correlated with excess liquidity. If the return rate dropped to zero, the economy would be in a liquidity trap and only involuntary excess reserves would arise. Thus, the interbank return rate appears to present a key instrument for central banks to influence the amount of reserves held by Islamic banks. The optimal monetary policy in our model involves providing liquidity to Islamic banks at a high return rate. One of the defining characteristics of cash reserves is their reliance on deposit inflows. In the context of Islamic banks, it has been argued that a significant portion of deposits is often held in liquid form because banks are unable to fully absorb these flows. Hence, the model demonstrates that banks where deposits inflows are important will tend to have greater excess liquidity. However, if an Islamic bank is unable to fully absorb these deposit inflows, why don’t they limit them? Firstly, if a depositor is the national government (as is the case in GCC countries), then it may be difficult for an Islamic bank to refuse to accept such deposits. Secondly, many individual depositors in Islamic banks are not motivated by profit but rather by their belief in sharia principles and values and a desire to promote Islamic projects.3 They therefore use moral persuasion to make Islamic banks accept their deposits, even when it will lead to excess liquidity. 4. Conclusion 1
Stiglitz and Weiss (1981) suggest that asymmetric information may make banks reluctant to supply loans because of adverse selection and the resulting increase in the riskiness of the bank’s portfolio. If an adverse selection increases the costs of financing (agency costs), the bank will prefer to hold none-remunerated reserves. Agenor et al. (2004) confirm the role of increased default risk uncertainty as a rationale for commercial banks’ voluntary buildup of holdings of non-remunerated liquid assets during the East Asian crisis. 2 For simplicity, we suppose in this model that cash reserves are costless for the bank (i.e., no return received or management cost). 3 According to Rifki (2010), an empirical survey of Indonesian Islamic banks revealed that 82% of depositors open time deposit accounts to support Islamic projects (Ummah) and will close their accounts if an Islamic bank is found not to be sharia compliant (71%).
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This study has theoretically investigated the liquidity management behavior of Islamic banks under specific assumptions about the competitive environment in which they operate. We have demonstrated that the development of a simple microeconomic model for an Islamic bank is an important first step in discerning the determinants of liquidity in subsequent applied research, as well as suggesting plausible and testable hypotheses. The quantity of cash reserves needed by a bank depends on its level of involvement in the deposit, financing, and refinancing markets. Therefore, depositors’ liquidity behavior and banking financing strategies are essential elements in liquidity risk management. Based on banks’ profit-maximizing motives, this research considers three important determinants of banking liquidity: the deposit revenue-sharing ratio, the financing return rate, and the Islamic money market rate of return. A bank’s decision to demand more funds from depositors (and therefore increase liquidity inflow) is based on the return-sharing ratio level. On the other side, a bank’s ability to give more funds back to investors (and increase its liquidity outflow) is based on the returns it receives from financing and refinancing activities. According to this model, excess reserves in the Islamic banking sector are caused by a high level of deposits combined with a low level of investment in financing and interbank markets. This situation is brought about by low rates of return in these markets and high management costs for financing. References Agenor, P.R., Aizenman, J. Hoffmaister A.W., 2004. The credit crunch in East Asia: what can bank excess liquid assets tell us? Journal of International Money and Finance. 23 (1), 27-49. Alexander, D. and Archer, S., 2009. Financial instruments. Accounting/Financial Reporting Standards Guide. Chicago, IL: CCH.
International
Archer, S., and Karim, R.A.A., 2009. Profit-sharing investment accounts in Islamic banks: Regulatory problems and possible solutions. Journal of Banking Regulation.10, 300–306. Archer, S., Karim, R.A.A. and Sundararajan, V., 2009. Are profit sharing investment accounts (PSIA) deposits or investments? Supervisory and capital adequacy implications of PSIA in Islamic finance. Kuala Lumpur: IFSB (Islamic Financial Services Board), Working Paper Baltensperger, E., 1972a. Economies of scale, firm size and concentration in banking. Journal of Money, Credit and Banking. 4 (3), 467-488. Baltensperger, E., 1972b. Costs of banking activities: Interactions between risk and operating costs. Journal of Money, Credit and Banking. 4 (3), 595-561. Baltensperger, E., 1974. The precautionary demand for reserves. American Economic Review 64 (1), 205-210. Baltensperger, E., 1980. Alternative approach to the theory of the banking firm. Journal of Monetary Economics. 6 (1), 1-37. Diamond, D.W., 2007. Banks and liquidity creation: A simple exposition of the DiamondDybvig model. Economic Quarterly. 93 (2), 189-200. Diamond, D.W., Dybvig Ph. H., 1983. Bank runs, deposit insurance, and liquidity. Journal of Political Economy. 91 (3), 401-419. 15
Diamond, D.W., Dybvig Ph. H., 2000. “Bank Runs, Deposit Insurance, and Liquidity.” Federal Reserve Bank of Minneapolis Quarterly Review 24 (Winter): 14–23. Diamond, D.W., Rajan, R.G., 2001. Banks and liquidity. American Economic Review. 91 (2), 422-425. Ernst & Young, 2011. World Islamic Banking Competitiveness Report 2011-12. Ernst & Young, 2012. World Islamic Banking Competitiveness Report 2012-13. Freixas, X., Rochet, J-Ch., 1999. Microeconomics of Banking. Second Edition, the MIT Press. Frost, P.A., 1971. Bank’s demand for excess reserves. Journal of Political Economy. 79 (4), 802-825. Greuning, V., and Iqbal, Z., 2008. Risk Analysis for Islamic Banks, The World Bank Documents and Reports, N 42481, Washington, D.C. Islamic Financial Services Board, 2008. Technical note on issues in strengthening liquidity management of institutions offering Islamic financial services: the development of Islamic money markets. Islamic Financial Services Board Keister, T., McAndrews, J.J., 2009. Why are banks holding so many excess reserves? Current Issues in Economics and Finance. 15 (8), 1-10. Khaled, S. and Khandker, A. 2017, Determination of Mark-Up Rate under Zero-Interest Financial System: A Microeconomic Approach. Islamic Economic Studies. 25 (2), 15-34. Knobel, A., 1977. The demand for reserves by commercial banks. Journal of Money, Credit and Banking. 9 (1), 32-47. Mirakhor, A. and Iqbal, Z., 2007. Profit-and-loss Sharing Contracts in Islamic Finance, in Handbook of Islamic Banking, edited by Kabir Hassan and Mervyn Lewis, Edward Elgar Publishing. Modigliani, F., Rasche, R., Cooper, J. Ph., 1970. Central bank policy, the money supply, and the short-term rate of interest. Journal of Money, Credit and Banking. 2 (2), 166-218. Orr, D., Mellon, W.G., 1961. Stochastic reserves losses and expansion of bank credit. American Economic Review. LI (4), 614-623. Poole, W., 1968. Commercial bank reserve management in an uncertain world: implications for monetary policy. Journal of Finance. 23 (5), 769-791 Rifki, I., 2010. How do Islamic banks manage liquidity risk? An empirical survey on the Indonesian Islamic banking industry. Kyoto Bulletin of Islamic Area Studies. 3 (2), 54-81. SAMA, 2017. Fifty Third Annual Report, http://www.sama.gov.sa Standard & Poor’s, 2010. Islamic Finance Outlook. S&P Global Ratings. Stiglitz, J.E., Weiss, A., 1981. Credit rationing with imperfect information. American Economic Review. 71 (3), 393-410. Thomson Reuters (2017). Liquidity management through sukuk: innovative solutions, Report.
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Modelling liquidity management in Islamic banks from a microeconomic perspective Mouldi DJELASSI , Jamel BOUKHATEM PII: DOI: Reference:
S1544-6123(19)30488-X https://doi.org/10.1016/j.frl.2019.101341 FRL 101341
To appear in:
Finance Research Letters
Received date: Revised date: Accepted date:
5 February 2019 14 October 2019 23 October 2019
Please cite this article as: Mouldi DJELASSI , Jamel BOUKHATEM , Modelling liquidity management in Islamic banks from a microeconomic perspective, Finance Research Letters (2019), doi: https://doi.org/10.1016/j.frl.2019.101341
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Highlights
We integrate Islamic financial intermediation into a standard microeconomic model to examine the determinants of banking liquidity. We show the existence of three important determinants of banking liquidity: deposit revenue sharing ratio, financing return rate and Islamic money market rate. Excess reserves in Islamic banking sector are due to high level of deposits and low level of funds supply in financing and interbank markets. These results contribute to design guidelines for empirical determinants of liquidity in Islamic banks.
1
Modelling liquidity management microeconomic perspective
in
Islamic
banks
from
a
Mouldi DJELASSI Department of Banking and Financial Markets, College of Islamic Economics and Finance, Umm al Qura University – Saudi Arabia Department of Economics, High school of Economic and Business Sciences ESSECT – University of Tunis, Tunisia [email protected] [email protected]
Jamel BOUKHATEM Department of Banking and Financial Markets, College of Islamic Economics and Finance, Umm al Qura University – Saudi Arabia Department of Economics, Faculty of Economic sciences and Management FSEGT, University of Tunis el Manar– Tunisia [email protected] [email protected]
Abstract. The main objective of this paper is to examine the determinants of banking liquidity by explicitly integrating Islamic financial intermediation into a standard microeconomic model. Our model includes the banks’ liquidity reserves in line with profit-maximization motives and provides an analytical framework for interpreting the excess liquidity behavior commonly seen in the Islamic banking sector. Excess reserves result from an increase in a bank’s deposits base combined with Islamic banks’ limited opportunities for financing and placement. The monetary policy rate appears to be a key instrument that central banks can use to resolve the problem of excess reserves. Keywords: liquidity management; Islamic banking; modelling JEL classification: C6, G21
Funding acknowledgement: This study was supported by the Deanship of Scientific Research at Umm Al-Qura University- Saudi Arabia, under the Grant number 17-ADM-1-010004.
2
1. Introduction Despite the development of Islamic banking as both a major financial intermediary and an important element of Islamic economic practice, little theoretical research has focused on Islamic banks. A satisfactory theory for Islamic banking behavior would therefore seem an indispensable prerequisite for gaining a clear understanding of how the Islamic banking sector functions. In this paper, we attempt to model and explain the behavior of Islamic banking firms. Any model for Islamic banking must be relatively abstract due to its inherent complexity, with the nature and the degree of this abstraction being determined by an author’s conception of what is important in Islamic banking. In general, Islamic banks are a kind of financial intermediary, but they cannot borrow through the interbank market through the usual mechanisms or rediscount at a given rate. In addition, as such institutions collect deposits and provide financing, they are not immune to liquidity and default risks.1 The purpose of this paper is therefore to understand the general functioning of Islamic banks and their liquidity management by explicitly integrating Islamic financial intermediation into a standard microeconomic model. The simplest way to look at liquidity management is to study the determinants for the volume of funds collected or distributed by the bank in line with the profit-maximization motive. The role of Islamic banks is thus considered according to two fundamental characteristics of their activity: the management of payment means (collecting deposits under the revenue-sharing rule) and financial intermediation (providing sharia-compliant financing). This model has significant implications in a variety of areas. Theoretically, the development of a simple microeconomic model for Islamic banking is an important step in discerning the determinants of liquidity in later applied research, as well as in suggesting plausible and testable hypotheses connected with them. In policy areas, such a model would provide a framework for understanding the phenomena of excess liquidity in many Islamic banks and the effects of monetary policy on their reserves. The remainder of this paper is organized as follows. Section 2 presents the basic model, and then Section 3 analyzes the liquidity behavior of individual Islamic banks in a competitive banking sector. Finally, Section 4 concludes the paper. 2. The basic model Various studies have empirically investigated the liquidity management risk in Islamic banks. However, no studies have investigated liquidity risk management in Islamic banks from a theoretical perspective, compared with an abundance of academic literature devoted to reserve
1
Islamic banks are pressured by the markets to pay their investors-depositors a rate of return higher than what would normally be expected (displaced commercial risk). In many countries where Islamic banks operate, there is disharmony between them and central banks due to the latter’s refusal to issue funds based on anything other than interest. Accordingly, Islamic banks lack this final resort to meet their liquidity needs. Finally, in Islamic banking, it is argued that a significant portion of deposits is often is held in liquid form due to the limited shortterm sharia-compliant instruments available to them (Iqbal and Mirakhor 2007, Greuning and Iqbal 2008).
3
management modeling in conventional banks.1 Among the economic literature, the banking behavior models developed by Freixas and Rochet (1999) are the most convenient for the purposes of this research. The authors adopt the industrial organization approach to model banking activity as the provision of services to depositors and borrowers. Although simplistic, this approach will provide a rich set of models for tackling different issues, such as monetary policy, market failures, and some aspects of market regulation. Referring to Freixas and Rochet’s model for bank behavior, the adjusted model is adapted for the case of Islamic banks to investigate the flow of liquidity on the assets and liability side. The novelty of this model lies in incorporating the specificities of Islamic banking activities and liquidity risk management into the classical bank theory, as well as considering some forms of market structure. Despite its simplicity, this approach will support a rich analysis for tackling different issues, such as monetary policy, the determinants for optimum liquidity reserves, liquidity management in a low-depth interbank market, and the phenomena of excess liquidity in Islamic banks. We assume that the economy includes three types of agents – namely firms, banks, and depositors – with them all adopting sharia principles.2 2.1. The real sector There is a continuum for firms. All have access to the same instruments, and for the sake of simplicity, we assume they all start with no capital. Each firm has a project with costs equal to I. We further assume that firms can only obtain financing from banks on an equityparticipation basis. A project generates a financial return, which is shared between the firm (the entrepreneur) and the bank in pre-agreed proportions. As such, is the return-sharing ratio for the bank and is the return-sharing ratio for the firm. The return-sharing ratio is assumed to be fixed for the duration of the contract, and we further assume that it is the same for all firms. 2.2. The financial sector The financial sector is composed of different banks indexed by . They are defined as financial intermediaries that buy certain types of securities (e.g., financing contracts like murabaha, mudharaba, etc.) and sell different types of securities (e.g., mudharaba deposits). In our model, the bank is a mudharib profit-maximizing, risk-neutral institution that operates in an environment with three assets: financing, money market assets, and cash. Financing ( ) is a long-term instrument with a return rate equal to , while the 1
The literature concerning reserve management modeling in conventional banks goes back a long way. Early and more contemporary pioneers include Orr and Mellon (1961), Poole (1968), Frost (1971), Baltensperger (1972a, 1972b, 1974, 1980), Knobel (1977), Diamond and Dybvig (1983), Freixas and Rochet (1999), Diamond and Dybvig (2000), Diamond (2007), to name but a few. 2 This condition must be respected to make the model sharia-compliant. Under sharia-principles, economic agents do not deal in transactions with interest but rather use the principle of profit and loss sharing for a business. Islamic financing and refinancing therefore takes the form of trade and investment rather than loans. Likewise, Islamic savings accounts take the form of a profit-sharing investment account rather than an interestyielding deposit account.
4
money market assets ( ) are short-term investments in Islamic money markets with rate of return . Finally, cash is a storage mechanism that gives no return. The bank collects deposits ( ) from rabb al mel (depositors) based on mudharaba partnerships at a rate of return and essentially finance the investment needs of firms.1 We assume that banks have access to money markets and/or the interbank market. The interbank market allows banks to meet their liquidity needs by borrowing from, or lending to, their peers. Unlike in the traditional banking system, however, Islamic banks cannot borrow through the interbank market using the usual mechanisms or rediscount at a given discount rate. Any financing between banks must instead be based on profit and loss sharing or markup principles. We assume here that banks can finance their needs through the interbank market only on murabaha basis.2 A murabaha commodity provides certain returns because it is based on a pre-agreed “margin” or “markup” from the sale and purchase of the underlying assets. We note that is the rate of return through the Islamic interbank market (i.e., the rate of profit on a murabaha commodity).3 A bank uses labor and physical capital as inputs for producing different financial services for depositors and firms. This intermediation activity is costly, so bank will pay amount to generate of deposits and of financing. This is represented by the cost function . To simplify the analysis, we assume that the cost is the same for all banks . We further assume that projects financed by a bank are imperfectly correlated, because banks are then motivated to choose them to diversify their financing portfolios and ensure a stable return for their depositors. The typical balance sheet of bank would look as follows: Assets (cash reserves)
Liabilities (Customers’ deposits)
(interbank operations, net) (financing and investment) 1
Islamic banks typically raise deposits through profit-sharing investment accounts (PSIAs). These accounts, in their unrestricted form, are reported on the balance sheet of an Islamic bank. They can be regarded as discretionary wealth-management accounts being offered by private banks or as a sharia-compliant substitute for conventional deposit accounts. The PSIAs have two characteristics: (a) they can capture liquidity risks in Islamic banks because their holders have the right of withdrawal, and (b) secondly, they can be considered a capital account because the bank is assumed to pay investment account holders their contractual shares of any profit resulting from the investment of their funds. For further analysis, see Archer and Karim (2009) and Archer, Karim, and Sundararajan (2009). 2 Liquidity management is not just managing cash reserves. There are secondary liquidity reserve instruments such as commodity murabaha, wakala, Islamic certificates of deposit, and Sukuk (Islamic bonds). However, for Islamic banks, the murabaha commodity and similar instruments dominate the current landscape for liquidity management because substitute instruments like Sukuk often cannot be traded on secondary markets under sharia rules (Thomson Reuters, 2017). 3 We assume that the sale and repurchase of a commodity is the only way a bank can augment or reduce its resources. This operation is equivalent to using the rediscounting mechanism, where r is the quasi-discount rate.
5
The Islamic bank issues mudharaba deposits , purchases mudharaba financing , and transfers cash through its account at the central bank, which generates no interest.1 We suppose that a bank maintains cash reserves at a proportion of deposits. Thus, for any bank :
(1) If the bank has excess reserves, it can loan it through the interbank market. Conversely, if it has a deficit, it can borrow through the same market. We consider to be the net amount 2 due from/to other banks and financial institutions (positive or negative). 2.3. The investors Individual investors are small, and we assume that each only invests his or her savings in an investment account offered by a bank on an equity-participation basis. Bank is assumed to pay investors (its depositors) a rate of return based on the profit from its operations. This profit is shared between the depositors and the bank in some mutually agreed proportion ( ) (i.e., return- or revenue-sharing ratio). We sometimes assume that is fixed for the duration of the contract. 3. Microeconomic analysis of liquidity: The behavior of individual Islamic banks in a competitive banking sector We consider a problem where bank wants to determine the amount of cash reserves to hold. The simplest way to introduce liquidity management is to study the determinants for the volume of funds collected or distributed by bank in line with the profit-maximization motive. Assuming the bank has access to two sources of funding (i.e., deposits and the interbank market), the amount of cash reserves can be defined as: (2) Where represents the net source of funds from the interbank market, which can be positive or negative. Now, suppose for simplicity’s sake that cash reserves are costless for the bank (i.e., no return received but no management cost) and that the bank is a price taker. It therefore takes as given 1
In accordance with article 7 of the Banking Control Law and regulations issued by the Saudi Arabian Monetary Agency (SAMA), a bank is required to maintain a statutory deposit with SAMA at a stipulated percentage of its demand, time, and other deposits, calculated at the end of each Gregorian month. The statutory deposit with SAMA is not available to finance the bank’s day-to-day operations and therefore not part of the cash and cash equivalents. Banks therefore maintain a statutory deposit with SAMA comprising 7% of total demand deposits plus 4% of savings and time deposits. In addition to this statutory deposit, banks must also maintain liquid reserves no less than 20% of its deposit liabilities, either in the form of cash or assets that can be converted into cash within 30 days (SAMA, 2017). 2 Money due from other banks and financial institutions are financial assets with fixed or determinable payments and set maturities that are not quoted in an active market. These money market placements represent funds loaned on a sharia-compliant (i.e., not interest based) murabaha basis.
6
the rate of financing , the return-sharing ratio , and the interbank market rate . 1 Considering the management costs, the profit of bank is formulated as: (3) Bank profit is defined as the difference between the revenue a bank receives and the costs it incurs. P is the total profit earned from the n businesses financed by bank after sharing it between the bank and the businesses on a PLS basis . P is positive, because we assumed earlier that all projects financed by a bank are imperfectly correlated.2 represents the margin for the sale and purchase of commodities on the interbank market. represents the cost of deposits collected by bank and costs for deposits and financing.
is the total management
rf and rd are, respectively, the rates of return from financing and depository investment, so, we have:
(4) (
Therefore,
)
(5)
can be rewritten as: (6)
Both the revenues and costs of bank i depend upon the actions taken by the bank. In the case of financial intermediation, these actions may take three important forms: financing activities, collecting deposits, and making interbank transactions. The bank, which is assumed to be a profit-oriented, risk-neutral financial intermediary, then decides how to maximize its profit subject to the constraints:
1
Each bank is assumed to take prices as given, so these are exogenous variables for the profit-maximization problem. Thus, a bank is concerned only with maximizing profit levels for financing and deposits. Such a pricetaking bank is referred to as a competitive bank. We have chosen this market structure because we consider Islamic financial products to be homogeneous and available from many banks. For example, the profit-sharing investment account (PSIA) is a homogeneous product offered by many banks at the same sharing ratio. Any bank that provides anything lower than the going sharing ratio will immediately lose all its depositors. In the same way, the murabaha contract is a financing form provided by many Islamic banks, and any bank charging above the going market price for its product will lose all its customers. Hence, each bank must adopt the market rates for profit-sharing ratio and financing as given when determining optimal choices for deposits and financing. 2 Because of the domination of trade financing modes, we can assume that Islamic banks have predetermined short-term revenues with a minimum probability of bearing loss.
7
(7) and equation (1): Therefore, the bank’s profit can be rewritten as follows: [
]
–
(8)
The profit of an Islamic bank is based on a combination of its funds-providing activity (the financing market), its activity in raising funds from depositors (the deposits market), and its total net management costs. The bank’s problem is therefore to maximize profit by choosing the right amount of financing and deposits to generate. The financing and deposits markets are modeled as being perfectly competitive, and banks are price takers for the financing rate , deposits-sharing rate , and interbank rate . Each individual bank must select amounts of financing and deposits that are suitable for its various characteristics. Thus, profit maximization, given the assumptions on the cost function (decreasing returns to scale and convexity), is: –
(9)
–
(10)
–
(11)
( – )
(12)
The intuition behind these conditions should be clear: If the marginal revenue of an activity (i.e., financing or deposits) is greater than the marginal cost, it would cost the bank money to expand this activity. These fundamental conditions have several concrete interpretations. Therefore, a bank must choose the right level of financing. Equation (11), which concerns the fundamental condition of profit maximization, shows that a level of financing should be chosen such that the supply of one unit of financing should produce a marginal revenue equal to the corresponding marginal cost. The bank must also determine the amount of deposits to collect. The fundamental condition of profit maximization (Eq. 12) asserts that it should collect deposits such that the marginal revenue from employing one additional unit of these resources should be equal to its marginal cost. Next, a competitive bank sets intermediation margins equal to the marginal management costs. Equations (11) and (12) implicitly determine the credit supply function and the deposit demand function, respectively (see Equations 13 and 14):
8
(
–
)
(13)
(
–
)
(14)
a. Optimal financing supply:
(
)
Result 1 -
An increase in will cause increased income from financing, so the bank is encouraged to increase its supply of financing:
-
A decrease in causes a decreased marginal return from funds in the money market, so the bank is encouraged to increase its supply of financing:
-
An increase in causes increased marginal costs for funding from deposits, so the bank is motivated to reduce its supply of financing:
-
An increase in management costs causes an increase in the marginal costs of banks, so the bank reduces its supply of financing:
(
), where (+) or (–) indicates the postulated signs of partial
derivatives. b. An optimal bank’s demand for deposits:
(
)
Result 2 -
An increase in causes an increase in bank costs and consequently a decrease in the optimal level of the bank’s demand for deposits ( ).
9
-
An increase in leads to an increased return from the interbank market, so the bank is encouraged to increase its demand for deposits:
-
The coefficient is considered a tax on deposits, so an increase in this coefficient will cause an increase in the opportunity costs for the bank and a decrease in its demand for deposits:
-
An increase in management costs leads to an increase in the marginal cost of bank resources, so the bank reduces its demand for deposits:
(
) , where (+) or (–) indicates the postulated signs of partial
derivatives. c. Optimal refinancing supply (or demand) in the interbank market The optimal decision for the interbank market can be deduced from the balance sheet constraint. On the assets side, the allocation of loanable funds by banks results from their profit-maximization behavior. The balance sheet constraint can be rewritten as follows: ( (15)
)
(
)
The position of bank on the interbank market is then expressed as follows: (
)
(
)
(
–
) (16)
Here, the decision of the bank is to determine how much funds to supply (or demand) to (or from) the interbank market. The fundamental condition of profit maximization says the bank should provide (or collect) enough refinancing such that the marginal revenue from providing (employing) one more unit is equal to its marginal cost. Result 3 If the net position of bank on the interbank market is positive, an increase in its refinancing supply can occur due to one of the following conditions:
10
-
A decrease in the return rate for financing causes a decrease in the supply of F and encourages the bank to increase its refinancing supply through the interbank market.
-
An increase in the refinancing return encourages the bank to increase its financing supply and its demand for deposits. The decrease in the amounts of financing and deposits leads to an increase in .
-
An increase in causes an increase in the marginal cost of funding from deposits, so the bank reduces its demand for deposits. The decreased volume of deposits leads to a decrease in Mi.
-
An increase in diminishes the volume of the refinancing supply due to a reduction in the bank’s demand for deposits, which in turn leads to a decrease in Mi.
( ), where (+) or (–) indicates the postulated signs of the partial derivatives. If the net position in the interbank market is negative (i.e., the bank is a net borrower), we get the reverse sign. d. The optimal bank’s demand for reserves We can present the optimal demand for reserves in two different ways: In the first way, we consider the reserves to be proportional to deposits. In our model, the amount of banking deposits depends on the profit-sharing ratio , which is itself determined by the deposit market equilibrium condition (eq.14). The expression for the reserve quantity when banks are explicitly modeled as profit maximizers is then: (
)
(17) 11
This expression demonstrates that the amount of cash reserves needed by bank depends upon the deposit market equilibrium condition (endogenous liquidity). Alternatively, we can present the optimal bank’s demand for cash reserves as: ((
)
)
–
–
(18)
This expression demonstrates that the demand for cash reserves is determined by equilibrium conditions in three markets (i.e., deposits, financing, and interbank). In this general case, we obtain: Result 4 -
(
) : An increase in
or
will lead to a decrease in the optimal level
for the bank’s demand for deposits and consequently a decrease in its demand for reserves. In fact, the rise in increases the opportunity cost for deposits compared to the refinancing cost for a given value of ̅ . Likewise, an increase in will lead to an increase in banking costs. The bank is therefore encouraged to prefer interbank market financing over deposits to obtain more funds. In this way, the bank’s profit is higher at greater return rates for financing or lower interbank rates . Thus, the bank can improve its situation by allowing to provide more financing and holding less cash , provided that is high. -
-
( ) : If we assume a negative net position on the interbank market, the bank holds more cash following a hike in the interbank financing rate . Accordingly, an increase in causes an increase in the marginal cost of funds from the money market, so the bank reduces its financing demand from the interbank market, reduces its supply of financing to firms, and increases its demand for deposits. Finally, the bank )1 holds more cash ( If we assume a positive net position on the interbank market, the increase in leaves the bank investing in interbank market assets and holding less cash, because the ). In this case, the bank trades the cost of opportunity cost of cash is very high ( holding cash against the return on investment that assets may provide. (
): The amount of cash
financing return rate
held by the bank decreases with an increase in the
. This is explained by considering the objective of profit
1
Equations 11 and 12 demonstrate that the movements in all return rates are proportional to those of the interbank market, so if the interbank market rate increases, the rates and also increase. Consequently, the volume of financing Fi decreases and the volume of deposits Di increases. Finally, the bank holds more cash.
12
maximization. The bank only focuses on financing while cash is always unprofitable investment.1 -
(
because it will provide a return,
): The management costs have a contradictory effect. An increase
in the management cost of deposits leads to a decrease in the optimal level for the bank’s demand for deposits, so there is corresponding drop in its demand for reserves. However, an increase in the management cost of financing causes a decrease in the optimal level for the bank’s supply of financing, which in turn increases the volume of reserves. (
), where (+) or (–) indicates the postulated
signs of partial derivatives.
e. Application and interpretation of the model According to Result 4, in a competitive environment, an increase in the deposit-sharing ratio or financing rate reduces the amount of reserves held by banks. The effect of the interbank rate, meanwhile, on reserves depends upon the net position of the bank. In the case of a negative net position on the interbank market, the bank holds more cash following an increase in the interbank financing rate. However, if we assume a positive net position, an increase in leads to the bank investing more in interbank market assets and holding less cash. Meanwhile, an increase in the management costs of financing discourages a bank from providing financing, which in turn means it holds more cash reserves. The preceding model has several implications, and it is important here to make a preliminary attempt at providing a framework for understanding the phenomenon of excess liquidity that is experienced by the Islamic banks of many countries. 2 Understanding this phenomenon requires some reformulation of the model, however. First, we define excess liquidity as the amount of reserves over and above that required for precautionary purposes. We define as the compulsory reserves for bank , so:
(19) with
being the excess reserves held by bank .
(20) The balance sheet constraints can be rewritten as:
1
if , an increase of pushes the bank into obtaining greater profits by investing more in interbank market assets and reducing its holdings of cash and bank financing . 2
For more details about this phenomenon, see (Hassoun 2003, Islamic Financial Services Board, 2008, Standard & Poor's 2010, Ernst & Young 2011, 2012 and Thomson Reuters Report (2017).
13
(21) And we can present the optimal excess reserves as: [ [ (22)
–
]
[
–
]
]
According to this model, the excess reserves in the Islamic banking sector can be explained by a low-level supply of funds to the financing and interbank markets. This situation is brought about by a low level of return rates and high management costs for financing.1 Thus, an increase in financing rates would increase the supply of financing and help decrease excess reserves. If Islamic banks are unable finance projects because of their high management costs and low return rates, one would still expect them to invest their unremunerated cash in the money market, at least if one exists, and offer attractive investment opportunities. A bank continues to invest in the money market if the spread between the return on such placements and the return on reserves is positive. 2 In this case, one would expect interbank placements to be negatively correlated with excess liquidity. If the return rate dropped to zero, the economy would be in a liquidity trap and only involuntary excess reserves would arise. Thus, the interbank return rate appears to present a key instrument for central banks to influence the amount of reserves held by Islamic banks. The optimal monetary policy in our model involves providing liquidity to Islamic banks at a high return rate. One of the defining characteristics of cash reserves is their reliance on deposit inflows. In the context of Islamic banks, it has been argued that a significant portion of deposits is often held in liquid form because banks are unable to fully absorb these flows. Hence, the model demonstrates that banks where deposits inflows are important will tend to have greater excess liquidity. However, if an Islamic bank is unable to fully absorb these deposit inflows, why don’t they limit them? Firstly, if a depositor is the national government (as is the case in GCC countries), then it may be difficult for an Islamic bank to refuse to accept such deposits. Secondly, many individual depositors in Islamic banks are not motivated by profit but rather by their belief in sharia principles and values and a desire to promote Islamic projects.3 They therefore use moral persuasion to make Islamic banks accept their deposits, even when it will lead to excess liquidity. 4. Conclusion 1
Stiglitz and Weiss (1981) suggest that asymmetric information may make banks reluctant to supply loans because of adverse selection and the resulting increase in the riskiness of the bank’s portfolio. If an adverse selection increases the costs of financing (agency costs), the bank will prefer to hold none-remunerated reserves. Agenor et al. (2004) confirm the role of increased default risk uncertainty as a rationale for commercial banks’ voluntary buildup of holdings of non-remunerated liquid assets during the East Asian crisis. 2 For simplicity, we suppose in this model that cash reserves are costless for the bank (i.e., no return received or management cost). 3 According to Rifki (2010), an empirical survey of Indonesian Islamic banks revealed that 82% of depositors open time deposit accounts to support Islamic projects (Ummah) and will close their accounts if an Islamic bank is found not to be sharia compliant (71%).
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This study has theoretically investigated the liquidity management behavior of Islamic banks under specific assumptions about the competitive environment in which they operate. We have demonstrated that the development of a simple microeconomic model for an Islamic bank is an important first step in discerning the determinants of liquidity in subsequent applied research, as well as suggesting plausible and testable hypotheses. The quantity of cash reserves needed by a bank depends on its level of involvement in the deposit, financing, and refinancing markets. Therefore, depositors’ liquidity behavior and banking financing strategies are essential elements in liquidity risk management. Based on banks’ profit-maximizing motives, this research considers three important determinants of banking liquidity: the deposit revenue-sharing ratio, the financing return rate, and the Islamic money market rate of return. A bank’s decision to demand more funds from depositors (and therefore increase liquidity inflow) is based on the return-sharing ratio level. On the other side, a bank’s ability to give more funds back to investors (and increase its liquidity outflow) is based on the returns it receives from financing and refinancing activities. According to this model, excess reserves in the Islamic banking sector are caused by a high level of deposits combined with a low level of investment in financing and interbank markets. This situation is brought about by low rates of return in these markets and high management costs for financing. References Agenor, P.R., Aizenman, J. Hoffmaister A.W., 2004. The credit crunch in East Asia: what can bank excess liquid assets tell us? Journal of International Money and Finance. 23 (1), 27-49. Alexander, D. and Archer, S., 2009. Financial instruments. Accounting/Financial Reporting Standards Guide. Chicago, IL: CCH.
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Archer, S., and Karim, R.A.A., 2009. Profit-sharing investment accounts in Islamic banks: Regulatory problems and possible solutions. Journal of Banking Regulation.10, 300–306. Archer, S., Karim, R.A.A. and Sundararajan, V., 2009. Are profit sharing investment accounts (PSIA) deposits or investments? Supervisory and capital adequacy implications of PSIA in Islamic finance. Kuala Lumpur: IFSB (Islamic Financial Services Board), Working Paper Baltensperger, E., 1972a. Economies of scale, firm size and concentration in banking. Journal of Money, Credit and Banking. 4 (3), 467-488. Baltensperger, E., 1972b. Costs of banking activities: Interactions between risk and operating costs. Journal of Money, Credit and Banking. 4 (3), 595-561. Baltensperger, E., 1974. The precautionary demand for reserves. American Economic Review 64 (1), 205-210. Baltensperger, E., 1980. Alternative approach to the theory of the banking firm. Journal of Monetary Economics. 6 (1), 1-37. Diamond, D.W., 2007. Banks and liquidity creation: A simple exposition of the DiamondDybvig model. Economic Quarterly. 93 (2), 189-200. Diamond, D.W., Dybvig Ph. H., 1983. Bank runs, deposit insurance, and liquidity. Journal of Political Economy. 91 (3), 401-419. 15
Diamond, D.W., Dybvig Ph. H., 2000. “Bank Runs, Deposit Insurance, and Liquidity.” Federal Reserve Bank of Minneapolis Quarterly Review 24 (Winter): 14–23. Diamond, D.W., Rajan, R.G., 2001. Banks and liquidity. American Economic Review. 91 (2), 422-425. Ernst & Young, 2011. World Islamic Banking Competitiveness Report 2011-12. Ernst & Young, 2012. World Islamic Banking Competitiveness Report 2012-13. Freixas, X., Rochet, J-Ch., 1999. Microeconomics of Banking. Second Edition, the MIT Press. Frost, P.A., 1971. Bank’s demand for excess reserves. Journal of Political Economy. 79 (4), 802-825. Greuning, V., and Iqbal, Z., 2008. Risk Analysis for Islamic Banks, The World Bank Documents and Reports, N 42481, Washington, D.C. Islamic Financial Services Board, 2008. Technical note on issues in strengthening liquidity management of institutions offering Islamic financial services: the development of Islamic money markets. Islamic Financial Services Board Keister, T., McAndrews, J.J., 2009. Why are banks holding so many excess reserves? Current Issues in Economics and Finance. 15 (8), 1-10. Khaled, S. and Khandker, A. 2017, Determination of Mark-Up Rate under Zero-Interest Financial System: A Microeconomic Approach. Islamic Economic Studies. 25 (2), 15-34. Knobel, A., 1977. The demand for reserves by commercial banks. Journal of Money, Credit and Banking. 9 (1), 32-47. Mirakhor, A. and Iqbal, Z., 2007. Profit-and-loss Sharing Contracts in Islamic Finance, in Handbook of Islamic Banking, edited by Kabir Hassan and Mervyn Lewis, Edward Elgar Publishing. Modigliani, F., Rasche, R., Cooper, J. Ph., 1970. Central bank policy, the money supply, and the short-term rate of interest. Journal of Money, Credit and Banking. 2 (2), 166-218. Orr, D., Mellon, W.G., 1961. Stochastic reserves losses and expansion of bank credit. American Economic Review. LI (4), 614-623. Poole, W., 1968. Commercial bank reserve management in an uncertain world: implications for monetary policy. Journal of Finance. 23 (5), 769-791 Rifki, I., 2010. How do Islamic banks manage liquidity risk? An empirical survey on the Indonesian Islamic banking industry. Kyoto Bulletin of Islamic Area Studies. 3 (2), 54-81. SAMA, 2017. Fifty Third Annual Report, http://www.sama.gov.sa Standard & Poor’s, 2010. Islamic Finance Outlook. S&P Global Ratings. Stiglitz, J.E., Weiss, A., 1981. Credit rationing with imperfect information. American Economic Review. 71 (3), 393-410. Thomson Reuters (2017). Liquidity management through sukuk: innovative solutions, Report.
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