American Research Journal of Economics, Finance and Management Volume 10 Issue 1, January-March 2022 ISSN: 2836-9416 Impact Factor: 4.85 Journal Homepage: https://americaserial.com/Journals/index.php/ARJEFM, Email: contact@americaserial.com Official Journal of America Serial Publication American Research Journal of Economics, Finance and Management https://americaserial.com/Journals/index.php/ARJEFM, Email: contact@americaserial.com 13 | P a g e BANKING LIQUIDITY PARADOX: INSIGHTS FROM AN OPTIMAL RESERVE MODEL Omer Kouakou Economics Department, Alassane Ouattara BouakΓ© University. Abstract: The banking liquidity paradox, characterized by excessively liquid banks despite the insufficient supply of business loans, is a persistent concern in Sub-Saharan Africa (SSA). This paradox stems from both involuntary and voluntary factors influencing commercial banks' excess reserve holdings. Involuntary causes include substantial foreign currency inflows resulting from exports of commodities like oil, coffee, and cocoa. These export revenues significantly boost bank liquidity, a phenomenon observed in regions like CEMAC. Additionally, factors such as accumulating foreign exchange reserves to maintain currency stability in fixed parity monetary zones, remittances from migrants, official development aid, and debt relief initiatives like the Heavily Indebted Poor Countries Initiative (HIPC) contribute to increased bank liquidity. Furthermore, the repatriation of capital after currency devaluation and the establishment of regional stock exchanges amplify capital inflows. Voluntary factors also play a role, including restrictions on central banks financing national treasuries, as well as monetary policies associated with mandatory reserves. This article delves into the intricate web of involuntary and voluntary influences driving the banking liquidity paradox in SSA, shedding light on the complexities of the region's financial landscape. Keywords: banking liquidity paradox, Sub-Saharan Africa (SSA), excess reserves, capital inflows, monetary policy, financial landscape. 1. Introduction The question of the banking liquidity paradox in the banking system concerns the insufficient supply of business loans by banks, which are nevertheless excessively liquid. This shortfall in the global supply of loanable funds has been variously interpreted. In general, the causes of excess liquidity in the countries of Sub-Saharan Africa (SSA) are grouped into two categories: involuntary causes and voluntary causes of excess reserve holding by commercial banks (AgΓ©nor, Aizenmann and Hoffmaister, 2004). The involuntary detention of excess liquidity is explained by large inflows of foreign currency generated by the exports of certain commodities such as oil, coffee, cocoa, etc. The revenues from these exports inflate the liquidity of banks as studies show it for the CEMAC zone (Beguy, 2012; Doumbia, 2011). Other sources of increased bank liquidity are: the accumulation of foreign exchange reserves to defend the parity in fixed parity monetary zones via the internal and external stability of the value of the currency (Doumbia, 2009), the influx of funds from migrants, official development aid, the cancellation of the debt of certain countries following the Heavily Indebted Poor Countries Initiative (HIPC Initiative), the repatriation of capital after the devaluation. Other factors contribute to the influx mailto:contact@americaserial.com mailto:contact@americaserial.com American Research Journal of Economics, Finance and Management Volume 10 Issue 1, January-March 2022 ISSN: 2836-9416 Impact Factor: 4.85 Journal Homepage: https://americaserial.com/Journals/index.php/ARJEFM, Email: contact@americaserial.com Official Journal of America Serial Publication American Research Journal of Economics, Finance and Management https://americaserial.com/Journals/index.php/ARJEFM, Email: contact@americaserial.com 14 | P a g e of capital: the establishment of regional stock exchanges, the prohibition of the financing of national treasuries by the central banks and the monetary policy resulting from the play of mandatory reserves. The involuntary detention of excess liquidity is explained partly by the underdeveloped nature of their financial market. For example, in a context of administered interest rates, banks are reluctant to grant loans that increase the risks of insolvency, instability and non-bankable projects (EbouΓ©, 1990, 1998b). This results in credit rationing like the one studied by Modigliani and Jaffee (1969). The excess liquidity resulting from credit rationing can also be explained by information problems between lenders and borrowers (Stiglitz and Weiss, 1981). These information problems manifest themselves in the form of asymmetric information: the bank does not know the real quality of the projects (Stiglitz and Weiss, 1981) or in the form of symmetrical ignorance (Stiglitz and Emran, 2007): the borrowers themselves even ignore the quality of their projects. This behavior of the banks is all the more marked as the lending rates (cost of credit) are very high. This increases the borrower's probability of default, the default rate and the reserve rate (Vo Thi, 2005, Prao, 2012). Banks are therefore becoming very cautious about loans granted. Other factors that increase credit rationing are the weak legal, judicial and regulatory framework (Sacerdoti, 2005), the lack of bankable projects, gaps in accounting standards, and the existence of a poorly developed justice system (Doumbia, 2011). The reduction of these uncertainties involves the production of reliable accounting documents, the development of the clientagent relationship via proximity and trust, an update of accounting and auditing standards. Excess liquidity, linked to the holding of voluntary liquidity, is also justified by the high level of deposits by governments in some countries and by deficient loans (Saxegaard, 2006). The voluntary holding of liquidity meets the desire of secondary banks facing growing uncertainty to avoid potential risks. This precautionary banking behavior resulting in excess liquidity has various consequences, particularly with regard to the effectiveness of monetary policy. Nissanke and Aryeetey (1998) show that bank excess liquidity weakens the transmission mechanism of monetary policy. More specifically, it becomes difficult, in the presence of excess liquidity, to regulate the money supply via the reserve requirement ratio and the monetary multiplier. Saxegaard (2006) tests this result for a sample of SSA countries. His study suggests that liquidity weakens the ability of monetary authorities to influence the conditions of demand in these countries. AgΓ©nor, Aizenmann and Hoffmaister (2004) obtain similar results. Ideas are proposed to absorb the excess bank liquidity by minimizing the uncertainties that cause the precautionary behavior of banks. Beguy (2012) proposes the establishment by the State of a guarantee fund allowing banks to recover part of their debts in the event of default. In doing so, this guarantee fund absorbs the banks' excess liquidity. For some, this entails a good restructuring of the judicial system in terms of efficiency to encourage banks to increase business loans (Pagano and Bianco, 2005). Another measure according to Beguy (2012) is the tax bonus. Indeed, for him the State can encourage the Banks to grant the credits by the implementation of a fiscal bonus, to those who will commit the most to the financing of the private sector. Thus, works that address the issue of voluntary excess liquidity have explained it essentially by the risky environment faced by risk averse banks. These uncertainties are due to financial markets imperfections, information asymmetries, weak judicial and regulatory framework, etc. Our objective, in this paper, is to show that, whatever the degree of uncertainty (low uncertainty or high uncertainty), excess liquidity mailto:contact@americaserial.com mailto:contact@americaserial.com American Research Journal of Economics, Finance and Management Volume 10 Issue 1, January-March 2022 ISSN: 2836-9416 Impact Factor: 4.85 Journal Homepage: https://americaserial.com/Journals/index.php/ARJEFM, Email: contact@americaserial.com Official Journal of America Serial Publication American Research Journal of Economics, Finance and Management https://americaserial.com/Journals/index.php/ARJEFM, Email: contact@americaserial.com 15 | P a g e may appear. This is the case when expected portfolio return of the risk neutral bank is sufficiently low. To address this issue, we take over a theoretical analysis, unlike most of the studies about excess liquidity that use empirical analysis. More precisely, we develop a model of optimal behavior of the bank. This model is an adaptation of Baumol's (1952) optimal cash model. The rest of the article is structured as follows: Section 2 models the optimal behavior of a risk-neutral bank. Then, in section 3, the hypothesis of a risk-averse bank makes it possible to highlight the main role of uncertainties in absorbing the excess banking liquidity. Section 4 concludes the paper. 2. The optimal behavior of the risk neutral bank 2.1. The assomptions A risk-neutral bank realigns its portfolio once a period and is assumed to invest its total fund 𝑇 in two types of assets (loans and risk-free securities). The bank decides how much of its portfolio to allocate to loans risk-free securities (𝑦𝑖𝑑) and liquidity in order to maximize its profit (𝛱𝑖𝑑). Loans, if they generate a higher expected return than that of risk-free securities, also induce more risk. Loans have two types of risk: market risk and default risk (credit risk). Loan yields (π‘Ÿπ‘π‘–π‘‘) and security assets (π‘Ÿπ‘ π‘–π‘‘), the two types of assets that compose the bank portfolio, are: 𝑖, βˆ€π‘‘, π‘Ÿπ‘ π‘–π‘‘ = π‘Ÿπ‘“ (1) βˆ€π‘–, βˆ€π‘‘, π‘Ÿπ‘π‘–π‘‘ = π‘Ÿπ‘“ + 𝜌 + πœ€π‘–π‘‘ (2) Where π‘Ÿπ‘“ : risk free interest rate; : market risk premium ; is an idiosyncratic shock that affects the bank at period . Noting π‘₯𝑖𝑑 the proportion of the portfolio invested in loans by bank in period and (1 βˆ’ π‘₯𝑖𝑑) the proportion of the portfolio invested in securities, the return of the bank portfolio is determined as follows: βˆ€π‘–, βˆ€π‘‘, 𝑅𝑖𝑑 = π‘₯π‘–π‘‘π‘Ÿπ‘π‘–π‘‘ + (1 βˆ’ π‘₯𝑖𝑑)𝑠𝑖𝑑. This expression comes down to: The bank, supposedly risk neutral, optimizes its profit. We notice 𝐢𝑖 : the volume of bank loans granted by the bank at ; 𝐴𝑖𝑑: the volume of security assets; 𝑖𝐢 : the cost of the bank loan (interest rate); 𝑖𝑀𝑀 : the cost of refinancing on the money market; 𝑅𝐸𝐹𝑖𝑑 : the refinancing of bank with the central bank in . The profit of the bank is the difference between its total revenue and its total cost: β€’ Total revenue: revenues from bank loans (𝑖𝐢𝐢𝑖𝑑) and capital gains reported by the investment of security assets (π‘Ÿπ‘“π΄π‘–π‘‘); β€’ The total cost is the sum of the total refinancing cost (𝑖𝑀𝑀𝑅𝐸𝐹𝑖𝑑) and the total cost of holding the liquidity (𝐢𝑇𝐿). The profit of the bank at period is written: To determine the total cost of holding liquidity, we draw on Baumol's optimal cash management model (1952), which we adapt to banking behavior. A bank must therefore hold at all times a level of liquidity such that it is not short of cash. Indeed, it must at all times satisfy the withdrawals of funds from its customers either at the counters or automated teller machines (ATMs). Insufficient liquidity can lead to insolvency of the bank. At the same time, however, this amount of liquidity should not be too large, because there is an option cost to holding it: the rate of return on the investments in which it could be mailto:contact@americaserial.com mailto:contact@americaserial.com American Research Journal of Economics, Finance and Management Volume 10 Issue 1, January-March 2022 ISSN: 2836-9416 Impact Factor: 4.85 Journal Homepage: https://americaserial.com/Journals/index.php/ARJEFM, Email: contact@americaserial.com Official Journal of America Serial Publication American Research Journal of Economics, Finance and Management https://americaserial.com/Journals/index.php/ARJEFM, Email: contact@americaserial.com 16 | P a g e invested. It is assumed that the cash flows of the bank are certain, liquidity outflows are at a constant rate. The average liquidity held by the bank is 𝐿/2 (With : bank liquidity at the beginning of the period). The bank's assets portfolio (loans, security assets) can be used to regenerate bank liquidity when needed. When liquidity becomes insufficient, the bank sells part of its portfolio at the beginning of the period to bring liquidity back to the desired level. In doing so, it regenerates its liquidity in the next period. The rate of decline in liquidity is constant over a period. Each conversion of securities into cash corresponds to transaction costs (commission paid by the bank to its broker for the sale of securities, time spent by the bank on such transactions). Therefore, the lower the bank liquidity, the higher the number of conversions and the higher the transaction costs of the bank. Let be the fixed costs that the bank incurs each time it converts securities into money. We have: 𝐹 = 𝑓𝐢𝐢𝑖𝑑 + 𝑓𝐴𝐴𝑖𝑑, where 𝑓𝐢 are the fixed costs related to the conversion of risky securities into money and 𝑓𝐴 are the fixed costs related to the conversion of safe securities into money. During a period, the total transaction costs of a bank related to the management of its liquidity are the product of the number of conversions that multiplies the fixed costs per conversion. With the additional assumption that the total fund the bank must have at period is a multiple of deposits it has in its reserves, . Thus, we have: In addition, the holding of liquidity also includes an option cost. Cash does not pay any interest. The option cost related to the holding of cash therefore corresponds to the interest income sacrificed as a result of the conversion of securities into cash. If 𝑅𝑖𝑑 is the rate of return on the bank portfolio from which the cash is generated, and since the average annual cash position of the bank is (𝐿/2), the option cost of holding the liquidity is as follows: The total cost of holding the liquidity (𝐢𝑇𝐿) is the sum of the transaction cost and the option cost: 2.2. The optimization program of the risk-neutral bank The profit of the bank becomes: We can refine this expression of the bank profit. To do this, we start from the fact that the refinancing of bank 𝑖 with the central bank is the difference between, on the one hand, the sum of banknotes in circulation of the bank (𝐡𝑖𝑑), the reserve requirements of bank (𝑅𝑂𝑖𝑑) and, on the other hand, the sum of the value of the gold and currencies of the bank (𝑂𝐷𝑖𝑑) and the net loans of the bank to the treasury (𝑇𝑖𝑑). So: 𝑅𝐸𝐹𝑖𝑑 = 𝐡𝑖𝑑 + 𝑅𝑂𝑖𝑑 βˆ’ 𝑂𝐷𝑖𝑑 βˆ’ 𝑇𝑖 . In addition, it is assumed that the deposits of bank with the central bank consist only of reserve requirements 𝑅𝑂𝑖𝑑 whose rate is such that 𝑅𝑂𝑖𝑑 = π‘Ÿπ·π‘–π‘‘. The net mailto:contact@americaserial.com mailto:contact@americaserial.com American Research Journal of Economics, Finance and Management Volume 10 Issue 1, January-March 2022 ISSN: 2836-9416 Impact Factor: 4.85 Journal Homepage: https://americaserial.com/Journals/index.php/ARJEFM, Email: contact@americaserial.com Official Journal of America Serial Publication American Research Journal of Economics, Finance and Management https://americaserial.com/Journals/index.php/ARJEFM, Email: contact@americaserial.com 17 | P a g e contribution of the bank to the treasure at period t is: 𝑇 = 𝐹𝑀𝐸𝑖𝑑 βˆ’ 𝐢𝐢𝑃𝑖𝑑 with 𝐢𝐢𝑃: total postal check accounts, hence 𝑅𝐸𝐹𝑖𝑑 = 𝐡𝑖𝑑 + π‘Ÿπ·π‘–π‘‘ βˆ’ 𝑂𝐷𝑖𝑑 βˆ’ 𝐹𝑀𝐸𝑖𝑑 + 𝐢𝐢𝑃𝑖𝑑. Finally, knowing that the money supply created by the bank in (𝑀𝑖𝑑) is the sum of bank loans 𝐢𝑖𝑑, the monetary financing of the treasury 𝐹𝑀𝐸𝑖𝑑 and the value of gold and currencies 𝑂𝐷𝑖𝑑; we obtain 𝑀𝑖𝑑 = 𝐢𝑖𝑑 + 𝐹𝑀𝐸𝑖𝑑 + 𝑂𝐷𝑖𝑑 β‡’ βˆ’π‘‚π·π‘–π‘‘ βˆ’ 𝐹𝑀𝐸𝑖𝑑 = 𝐢𝑖𝑑 βˆ’ 𝑀𝑖𝑑. Because of this, 𝑅𝐸𝐹𝑖𝑑 = 𝐡𝑖𝑑 + π‘Ÿπ·π‘–π‘‘ + 𝐢𝑖𝑑 βˆ’ 𝑀𝑖𝑑 + 𝐢𝐢𝑃𝑖𝑑. It is assumed, moreover, that the bank bears interest on deposits with 𝑖𝐷 the interest rate on deposits, and some variable costs whose growth rate increases with the activity of banks (here measured by the distributed credit): 𝐢𝑉𝑖𝑑 = 𝑔𝐢𝑖𝑑2. Let us define the following ratios: and . We can write: 𝐡𝑖𝑑 + π‘Ÿπ·π‘–π‘‘ + 𝐢𝑖𝑑 βˆ’ 𝑀𝑖𝑑 + 𝐢𝐢𝑃𝑖𝑑 = 𝑝′𝑀𝑖𝑑 + π‘Ÿπ‘π‘€π‘–π‘‘ + 𝐢𝑖𝑑 βˆ’ 𝑀𝑖𝑑 + 1 βˆ’ 𝑝 βˆ’ 𝑝′ β€² . Remembering that 𝐹 = 𝑓𝐢𝐢𝑖𝑑 + 𝑓𝐴𝐴𝑖𝑑 , , and 𝑇𝑖𝑑 = π‘₯𝑖𝑑𝐢𝑖𝑑 + 𝑦𝑖𝑑𝐴𝑖𝑑+(1 βˆ’ π‘₯𝑖𝑑 βˆ’ 𝑦𝑖𝑑)𝐿𝑖𝑑, the bank profit is written: Finally, after some refittings, the expression of the bank profit is refined as follows: The bank chooses the triplet so as to maximize the profit . The first order conditions give the following results: The resolution of the system formed by the three equations , and leads to the optimal level of credit supply , the optimal liquidity holding and the optimal demand for security assets . We determine the liquidity ratio defined here as the ratio of the optimal liquidity to the optimal credit. From the equation (12), we obtain: mailto:contact@americaserial.com mailto:contact@americaserial.com American Research Journal of Economics, Finance and Management Volume 10 Issue 1, January-March 2022 ISSN: 2836-9416 Impact Factor: 4.85 Journal Homepage: https://americaserial.com/Journals/index.php/ARJEFM, Email: contact@americaserial.com Official Journal of America Serial Publication American Research Journal of Economics, Finance and Management https://americaserial.com/Journals/index.php/ARJEFM, Email: contact@americaserial.com 18 | P a g e Knowing that , it follows: In this expression, the term 𝑦𝑖𝑑/π‘₯𝑖𝑑 contains the monetary variables 𝑖𝐢, 𝑖𝑀𝑀, π‘Ÿ, 𝑝, 𝑖𝐷 through , so that the following proposition holds: Proposition 1: The liquidity ratio depends on financial parameters, namely π‘₯𝑖𝑑, 𝑦𝑖𝑑, 𝑓𝐢,𝐴,π‘Ÿπ‘“, 𝜌. It depends also on the monetary variables 𝑖𝐢, 𝑖𝑀𝑀, π‘Ÿ, 𝑝, 𝑖𝐷. Formally: Now let's introduce the liquidity ratio threshold . This is the liquidity ratio defined normatively as the threshold beyond which there is bank excess liquidity. Formally, there is bank excess liquidity, that is, , when: where , the return of the banking portfolio of loans and securities. can be interpreted as the cost of converting into liquidity a portfolio consisting of a credit unit and the corresponding number of security assets. can be interpreted as the number of securities held in the portfolio (proportion of credits and corresponding proportion of security securities). The product of these two terms is then nothing other than the total cost of converting the bank's portfolio into liquidity. is the average conversion cost and is the average return over the period. When this cost is too high, which is higher than the average yield of the banking portfolio, the bank prefers to keep a lot of liquidity. Otherwise, when the average yield of the banking portfolio over the period is higher than the average cost of conversion, the bank is encouraged to invest its funds to grant more loans and acquire more securities. This results in a decrease in liquidity: From these results follows the proposition 2: Proposition 2: The bank has excess liquidity when the financial market is underperforming with respect to investments in securities and/or loans: mailto:contact@americaserial.com mailto:contact@americaserial.com American Research Journal of Economics, Finance and Management Volume 10 Issue 1, January-March 2022 ISSN: 2836-9416 Impact Factor: 4.85 Journal Homepage: https://americaserial.com/Journals/index.php/ARJEFM, Email: contact@americaserial.com Official Journal of America Serial Publication American Research Journal of Economics, Finance and Management https://americaserial.com/Journals/index.php/ARJEFM, Email: contact@americaserial.com 19 | P a g e This excess liquidity is absorbed in two cases: β€’ 𝑅𝑖𝑑 increases, that is, when the risk-free rate π‘Ÿπ‘“ and/or the market risk premium (here, the yield on loans) increases, ceteris paribus; cf. equation (3): ; β€’ The fixed costs related to the conversion of safe securities into liquidity, 𝑓𝐴, and the fixed costs related to the conversion of debt securities into liquidity, 𝑓𝐢, fall, ceteris paribus. In the model of the risk-neutral bank developed above, bank excess liquidity results from the optimal behavior of the bank which optimizes its profits. Excess liquidity is a sign that the financial market is not providing the right incentives for investment in securities or loan financing. Whatever the degree of economic uncertainty (low uncertainty or high uncertainty), there is excess liquidity when the total cost of conversion in liquidity of securities per unit of credit granted is greater than the expected return of the bank portfolio. So the ultimate determinant of the optimal excess liquidity here is not the uncertainty but the low expected return of the bank portfolio. The level of economic uncertainty explains indirectly the bank’s optimal excess liquidity, through the idiosyncratic shock πœ€π‘–π‘‘ contained in the bank’s portfolio return The main role played by the economic uncertainty appears in a context of high expected return of the bank portfolio. In this case, the excess liquidity is absorbed by the economy. More precisely, the bank reallocates the excess liquidity by reassigning the proportion of credit and safe securities in its portfolio. Either the bank increases the proportion of loans deemed to be riskier or it increases the proportion of safe securities. Such a reassignment requires lifting the hypothesis of a risk-neutral bank. Hence, it is assumed that the bank is risk averse, and we show how the uncertainty affects the proportions of loans and safe securities in the bank’s portfolio. 3. The optimal behavior of the risk averse bank 3.1. The assumptions The objective-function of the risk averse bank is the expected utility of its profit π‘ˆ(𝛱𝑖𝑑). As the degree of uncertainty in the economy grows, it becomes increasingly difficult to determine the optimal rate of return on loans. This pushes the bank to use an informative signal to try to predict this optimal rate of return on loans. In other words, in times of great economic uncertainty (experience of crisis, restructuring of the banking system, instability of deposits, informational asymmetry, symmetrical ignorance, weak legal, judicial and regulatory framework, etc.), signals coming from the market are ambiguous. Hence the banks use the expectation of loan return conditional on the perceived signal, to predict this optimal return. We know that the return of the portfolio of bank in period depends largely on πœ€π‘–π‘‘ which is realized only at the end of the period. However, it is at the beginning of the period t that each bank determines the composition of its portfolio. It does so according to the imperfect information available to it. At period , the bank observes an imperfect signal 𝑆𝑖𝑑 allowing it to predict the value that will take the variable πœ€π‘–π‘‘ at the end of the period. This observed signal, different for each bank, is composed of a heterogeneous noise πœ€π‘–π‘‘ and a homogeneous noise πœπ‘‘ whose intensity varies from one period to another. The homogeneous noise πœπ‘‘, unlike πœ€π‘–π‘‘, is an aggregate shock. It is assumed to be uncorrelated with πœ€π‘–π‘‘. Formally, we have: mailto:contact@americaserial.com mailto:contact@americaserial.com American Research Journal of Economics, Finance and Management Volume 10 Issue 1, January-March 2022 ISSN: 2836-9416 Impact Factor: 4.85 Journal Homepage: https://americaserial.com/Journals/index.php/ARJEFM, Email: contact@americaserial.com Official Journal of America Serial Publication American Research Journal of Economics, Finance and Management https://americaserial.com/Journals/index.php/ARJEFM, Email: contact@americaserial.com 20 | P a g e In the absence of perfect information, if πœπ‘‘ increases, the bank observes that 𝑆𝑖𝑑 increases, which causes an increase of the uncertainty on πœ€π‘–π‘‘ and therefore on the yield of the portfolio 𝑅𝑖𝑑. In other words, when the degree of uncertainty in the economy increases, the noise in the signal also increases and it becomes more and more difficult to determine the true value of πœ€π‘–π‘‘ as well as the optimal rate of return of the loans. But the bank has no other choice: to forecast 𝑙𝑖𝑑, it needs information about πœ€π‘–π‘‘. The best prediction of πœ€π‘–π‘‘ is its expected unconditional value (πœ€π‘–π‘‘), which is equal to . But observation of the signal 𝑆𝑖𝑑 can allow the bank to improve this prediction by using the expected value of πœ€π‘–π‘‘ conditional on the received signal (πœ€π‘–π‘‘/𝑆𝑖𝑑). The informative nature of this signal implies that (πœ€π‘–π‘‘/𝑆𝑖𝑑) β‰  0. Suppose, like Baum and al (2002), that this conditional expectation is a proportion 3.2. The optimization program of the risk averse bank With this justification of the choice of conditional expectation in the bank's program, it follows that the objective-function of the bank is the expected utility of the conditional profit to the perceived informative signal, as in CalmΓ¨s and Salazar (2006). It will be noted 𝐸(𝛱𝑖𝑑/𝑆𝑖𝑑). Some restrictions on the utility function or on the prior distribution of random yields make it possible to write the objective- function above as a mean-variance function (Tobin, 1958; Markowitz, 1959; Levy-Markowitz, 1979). Thus, by noting , the degree of bank aversion to risk, we can write the expected utility of the conditional profit of bank at period , as follows: The expected return of the portfolio of the bank at period conditional on the received signal is thus written: πœ†π‘‘π‘†π‘–π‘‘) (22) It is shown that the conditional variance of the return of this banking portfolio is (proof in appendix A1): The objective function of the bank is then written: Maximizing with respect to , the first order conditions are (proof in appendix A2): mailto:contact@americaserial.com mailto:contact@americaserial.com American Research Journal of Economics, Finance and Management Volume 10 Issue 1, January-March 2022 ISSN: 2836-9416 Impact Factor: 4.85 Journal Homepage: https://americaserial.com/Journals/index.php/ARJEFM, Email: contact@americaserial.com Official Journal of America Serial Publication American Research Journal of Economics, Finance and Management https://americaserial.com/Journals/index.php/ARJEFM, Email: contact@americaserial.com 21 | P a g e 3.3. Absorption of excess liquidity in a context of uncertainty Let us now show that economic uncertainty is also reflected in a decrease in the supply of funds of the bank. For this, we determine the direction of the relationship between the homogeneous aggregate shock and the proportion of loans in the bank's portfolio: When the degree of uncertainty in the economy 𝜎𝜐2𝑑 increases, the proportion π‘₯𝑖𝑑 of funds invested in loans decreases in favor of safe securities. Indeed, with the increase of the noise in the signal, it becomes more and more difficult to determine the true value of πœ€π‘–π‘‘ as well as the optimal rate of return of the loans. In this case, when the risk perceived by the bank exceeds a signal that it considers acceptable, it is encouraged to lower the proportion of funds invested in loans and to increase that invested in safe securities. It is also possible to evaluate the impact of uncertainty on the variance of the ratio of loans to banks' assets: As the level of uncertainty in the economy increases, so does the variance in the ratio of loans to total assets. In this case, the bank reallocates the excess liquidity by reassigning the proportion of credit and safe securities in its portfolio. More precisely, the bank decreases the proportion of loans deemed to be riskier and increases the proportion of safe securities. These theoretical results are consistent with the results of various empirical studies (Sigouin, 2003; CalmΓ¨s, 2004; Beguy, 2012). The excess liquidity does not systematically go to the financing of the economy. It can be mainly invested in safe securities. We summarize theses results in the following proposition. Proposition 3: In a context of high expected return of the bank portfolio, when the degree of uncertainty in the economy increases, the proportion π‘₯𝑖𝑑 of funds invested in loans decreases in favor of securities security. As the level of uncertainty in the economy increases, so does the variance in the ratio of loans to total assets. This means that banks tend to choose portfolios that are similar in terms of asset allocation. This leads to a decrease in the overall supply of funds on the market. 4. Concluding remarks In this paper, we have developed a theoretical model in which excess banking liquidity results from an optimal behavior of a risk neutral profit-maximizing bank. Whatever the degree of economic uncertainty (low uncertainty or high uncertainty), there is excess liquidity if the expected return of the banking portfolio (safe securities, loan financing, etc.) is too low. In order to overcome the excess liquidity in countries facing a subfinancing of the economy, the regulator can implement incentive measures that reinforce the return of bank portfolios. Put another way, an economic policy implication is that the absorption of excess liquidity does not only go through policies aimed at minimizing uncertainty but especially by measures to strengthen financial market incentives for bank portfolios. Examples of such measures are: setting a satisfactory level of credit cost for banks through monetary policy; setting a satisfactory level of risk free rate; reduced costs of bank deposits; reduced fixed costs related to the conversion of safe securities into liquidity; reduces fixed costs related to the conversion of debt securities into liquidity; etc. mailto:contact@americaserial.com mailto:contact@americaserial.com American Research Journal of Economics, Finance and Management Volume 10 Issue 1, January-March 2022 ISSN: 2836-9416 Impact Factor: 4.85 Journal Homepage: https://americaserial.com/Journals/index.php/ARJEFM, Email: contact@americaserial.com Official Journal of America Serial Publication American Research Journal of Economics, Finance and Management https://americaserial.com/Journals/index.php/ARJEFM, Email: contact@americaserial.com 22 | P a g e In our model, the uncertainties play an active role in a context of high expected return of the bank portfolio. In this case, the excess liquidity decreases but it is not systematically oriented towards the financing of the economy. In order to drain excess liquidity towards the financing of private sector of the economy, the regulator should enforce measures that minimize the economic uncertainties. Knowing that uncertainty increases the credit risk, the regulator can apply measures to control credit risk so that the excess liquidity is oriented more on financing the economy than on investing in safe securities. Such measures concern the development of insurance products (credit insurance, credit derivatives, etc.), the establishment of specific guarantee funds that can absorb the banks' excess liquidity by allowing them to recover a portion of their receivables in the event of default. Another measure is the tax bonus which encourages, via tax give aways, banks that are more involved in the financing of the economy. An extension of this work could be to empirically test the hypothesis that, for banks considered to hold excess liquidity, one would expect to find that the expected return on their banking portfolio is low. And for the others, the expected return on their banking portfolio is sufficiently high. Further study is expected in the future. References Agenor P.-R., Aizenman J., Hoffmaister A.W., 2004, Β« The Credit Crunch in East Asia: What Can Bank Excess Liquid Assets Tell Us ? Β», Journal of International Money and Finance, vol. 23, pp. 27– 49. Aryeetey E., 1998, Β« Informal Finance for Private Sector Development in Africa Β», Economic Research Papers 41, BAD. Baum, C.F., M. Caglayanet N. Ozhan (2002), β€œThe Impact of Macroeconomic Uncertainty on Bank lending behavior”, Document de travail. Baumol, W.J. (1952), Β« The Transactions Demand for Cash: An Inventory Theoretic ApproachΒ», Quarterly Journal of Economics, LXVI, (nov), pp. 545-556. Beguy, O. (2012), Β« Trois essais sur la surliquiditΓ© bancaire dans la communautΓ© Γ©conomique et monΓ©taire d'Afrique Centrale (CEMAC) Β». ThΓ¨se de doctorat unique de sciences Γ©conomiques soutenue Γ  l’universitΓ© d'Auvergne - Clermont-Ferrand I. CalmΓ¨s, C., 2004, Β« Regulatory Changes and Financial Structure: the case of Canada Β», Swiss Journal of Economics and Statistics (SJES), vol. 140 (I), pp. 1-35, March. CalmΓ¨s, C. et Salazar, J. (2006), Β« Variance macroΓ©conomique conditionnelle et mesure de dispersion des actifs dans les portefeuilles bancaires Β» pp. 688-700, in F.-Γ‰. Racicot et R. ThΓ©oret, Β« Finance computationnelle et gestion des risques Β», Presses de l’UniversitΓ© du QuΓ©bec. Doumbia, S., 2011, Β« SurliquiditΓ© bancaire et Β« sous-financement de l'Γ©conomie Β». Une analyse du paradoxe de l'UEMOA Β», Revue Tiers Monde, vol. 205, no. 1, pp. 151-170. mailto:contact@americaserial.com mailto:contact@americaserial.com American Research Journal of Economics, Finance and Management Volume 10 Issue 1, January-March 2022 ISSN: 2836-9416 Impact Factor: 4.85 Journal Homepage: https://americaserial.com/Journals/index.php/ARJEFM, Email: contact@americaserial.com Official Journal of America Serial Publication American Research Journal of Economics, Finance and Management https://americaserial.com/Journals/index.php/ARJEFM, Email: contact@americaserial.com 23 | P a g e Eboue C. (1990): "Les effets macro-Γ©conomiques de la rΓ©pression financiΓ¨re dans les Pays en dΓ©veloppement" Economie AppliquΓ©e, tome LXIII, nΒ° 4, pp. 93-117. Eboue C. (1998) : " La libΓ©ralisation financiΓ¨re dans les pays en dΓ©veloppement – une Γ©valuation prΓ©liminaire du cas africain", Gestion macro-Γ©conomique, nouvelles approches et enjeux de politique Γ©conomique, Abidjan, octobre 1998. Emran, M.S. et Stiglitz, J.E. (2007), β€œFinancial liberalization, financial restraint, and entrepreneurial development Β», http://cid.harvard.edu/neudc07docs/neudc07_s5_p02_emran.pdf. Jaffee, D.M., Modigliani, F. (1969), β€œ A Theory and Test of Credit Rationing”, American Economic Review, vol. 59, issue 5, 850-72. Jappelli, T., Pagano, M. and Bianco, M., 2005, Β« Courts and Banks: Effects of Judicial Enforcement on Credit Markets”, Journal of Money, Credit and Banking, vol. 37, issue 2, pp. 223-244. Levy, H., Markowitz, H.M. (1979), β€œ Approximating Expected Utility by a Function of Mean and Variance”, American Economic Review, Vol. 69, No. 3 (June), pp. 308-317. Markowitz, H.M. (1952), β€œPortfolio selection”, Journal of Finance, March, p.77-91. Markowitz, H.M. (1959), β€œPortfolio selection: Efficient Diversification of Investment”, New York, Wiley. Nissanke, M. and E. Aryeetey 1998. β€œFinancial Integration and Development, Liberalization and Reform in Sub-Saharan Africa”, ODI and Routledge, London. Sacerdoti, E. (2005), Β« Access to Bank Credit in Sub-Saharan Africa: Key Issues and Reform Strategies”, IMF Working Paper WP/05/166, 38 p. Saxegaard M., 2006, Β« Excess Liquidity and Effectiveness of Monetary Policy : Evidence from Sub- Saharan Africa Β», IMF Working Paper, WP/06/115, Washington D.C., FMI. Sigouin, C. (2003), Β«Investment Decisions, Financial Flows, and Self-enforcing ContractsΒ», International Economic Review, vol . 44, nΒ° 4, p .1359-1382. Stiglitz, J.E., Weiss, A., 1981, β€œCredit Rationing in Markets with Imperfect Information”, American Economic Review, Vol. 71, No. 3 (June), pp. 393-410. Tobin, J. (1958), β€œLiquidity Preference as Behavior Toward Risk”, Review of Economic Studies, Frebruary, 25, p. 6586. mailto:contact@americaserial.com mailto:contact@americaserial.com http://cid.harvard.edu/neudc07docs/neudc07_s5_p02_emran.pdf American Research Journal of Economics, Finance and Management Volume 10 Issue 1, January-March 2022 ISSN: 2836-9416 Impact Factor: 4.85 Journal Homepage: https://americaserial.com/Journals/index.php/ARJEFM, Email: contact@americaserial.com Official Journal of America Serial Publication American Research Journal of Economics, Finance and Management https://americaserial.com/Journals/index.php/ARJEFM, Email: contact@americaserial.com 24 | P a g e Tsiang, S.C. (1972), β€œ The Rationale of the Mean-Standard Deviation Analysis, Skewness Preference, and the Demand for Money”, American Economic Review, vol. 62, issue 3, 354-71. Tsiang, S.C. (1974), β€œThe rationale of the mean-standard deviation analysis: Reply and errata for the original article”, American Economic Review, vol. 64, 442-450. Vo Thi Phuong. Nga, 2005, Β« ConsΓ©quences de BΓ’le II sur la tarification et la distribution des crΓ©dits Β», Banque et MarchΓ©s, nΒ° 78, p. 46- 51. Appendix A1 Let’s prove that . The return of the banking portfolio is so that the conditional variance of πœ€π‘–π‘‘ is : We have π‘‰π‘Ž(π‘Ÿπ‘“/𝑆𝑖𝑑) = 0 since π‘Ÿπ‘“ is certain and π‘‰π‘Žπ‘Ÿ(𝜌/𝑆𝑖𝑑) = 0 since is constant, so that : βˆ€π‘–, βˆ€π‘‘, π‘‰π‘Ž(𝑅𝑖𝑑/𝑆𝑖𝑑) = π‘₯𝑖𝑑2π‘‰π‘Žπ‘Ÿ (πœ€π‘–π‘‘/𝑆𝑖𝑑) (𝐴1 . As the conditional expectation of πœ€π‘–π‘‘ is a proportion πœ†π‘‘ of the signal 𝑆𝑖𝑑, namely (πœ€π‘–π‘‘/𝑆𝑖𝑑) = πœ†π‘‘π‘†π‘–π‘‘, the conditional variance of πœ€π‘–π‘‘ is a proportion πœ†π‘‘ of its unconditional variance: π‘‰π‘Žπ‘Ÿ πœ€π‘–π‘‘/𝑆𝑖𝑑) = πœ†π‘‘π‘‰π‘Žπ‘Ÿ (πœ€π‘–π‘‘) = πœ†π‘‘πœŽπœ€2𝑑 (𝐴1.3) Finally: mailto:contact@americaserial.com mailto:contact@americaserial.com 25 American Research Journal of Economics, Finance and Management https://americaserial.com/Journals/index.php/ARJEFM, Email: contact@americaserial.com 25 | P a g e Journal of Finance and Bank Management, Vol. 6, No. 1, June 2018 Appendix A2 Maximizing the objective function of the bank with respect to π‘₯𝑖𝑑, the first order condition gives: From equation A2.1, we obtain: We have since πœ€π‘–π‘‘ βŠ₯ πœπ‘‘. Thus: Finally : mailto:contact@americaserial.com