




































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 Bouaké 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 (Agénor, 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 (Eboué, 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. Agénor, 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 (𝑦𝑖𝑡) and liquidity  in order to maximize its profit (𝛱𝑖𝑡). 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 (𝑟𝑐𝑖𝑡) and security assets 
(𝑟𝑠𝑖𝑡),  the two types of assets that compose the bank portfolio, are:  
𝑖, ∀𝑡,        𝑟𝑠𝑖𝑡 = 𝑟𝑓                        (1)  
∀𝑖, ∀𝑡,        𝑟𝑐𝑖𝑡 = 𝑟𝑓 + 𝜌 + 𝜀𝑖𝑡      (2) 
Where 𝑟𝑓 : risk free interest rate;  : market risk premium ;  is an idiosyncratic shock that 

affects the bank  at period .   
Noting 𝑥𝑖𝑡 the proportion of the portfolio invested in loans by bank  in period  and (1 − 𝑥𝑖𝑡) the 
proportion of the portfolio invested in securities, the return of the bank portfolio is determined as 
follows:   ∀𝑖, ∀𝑡,   𝑅𝑖𝑡 = 𝑥𝑖𝑡𝑟𝑐𝑖𝑡 + (1 − 𝑥𝑖𝑡)𝑠𝑖𝑡. This expression comes down to:  

  

The bank, supposedly risk neutral, optimizes its profit. We notice 𝐶𝑖 : the volume of bank loans granted 
by the bank  at ; 𝐴𝑖𝑡: the volume of security assets; 𝑖𝐶 : the cost of the bank loan (interest rate); 𝑖𝑀𝑀 : the 
cost of refinancing on the money market; 𝑅𝐸𝐹𝑖𝑡 : 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:  
• Total revenue: revenues from bank loans (𝑖𝐶𝐶𝑖𝑡) and capital gains reported by the investment of 
security assets (𝑟𝑓𝐴𝑖𝑡);  
• The total cost is the sum of the total refinancing cost (𝑖𝑀𝑀𝑅𝐸𝐹𝑖𝑡) and the total cost of holding the 
liquidity (𝐶𝑇𝐿).  
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 = 𝑓𝐶𝐶𝑖𝑡 + 𝑓𝐴𝐴𝑖𝑡, where 𝑓𝐶 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 𝑅𝑖𝑡 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 (𝐶𝑇𝐿) 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 (𝐵𝑖𝑡), the reserve requirements of bank  (𝑅𝑂𝑖𝑡) and, on the other hand, the sum 
of the value of the gold and currencies of the bank  (𝑂𝐷𝑖𝑡) and the net loans of the bank  to the treasury 
(𝑇𝑖𝑡). So: 𝑅𝐸𝐹𝑖𝑡 = 𝐵𝑖𝑡 + 𝑅𝑂𝑖𝑡 − 𝑂𝐷𝑖𝑡 − 𝑇𝑖 . In addition, it is assumed that the deposits of bank  with the 
central bank consist only of reserve requirements 𝑅𝑂𝑖𝑡 whose rate is   such that  𝑅𝑂𝑖𝑡 = 𝑟𝐷𝑖𝑡. 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 = 𝐹𝑀𝐸𝑖𝑡 − 𝐶𝐶𝑃𝑖𝑡 with 𝐶𝐶𝑃: total postal check 
accounts, hence 𝑅𝐸𝐹𝑖𝑡 = 𝐵𝑖𝑡 + 𝑟𝐷𝑖𝑡 − 𝑂𝐷𝑖𝑡 − 𝐹𝑀𝐸𝑖𝑡 + 𝐶𝐶𝑃𝑖𝑡. Finally, knowing that the money supply created 
by the bank  in  (𝑀𝑖𝑡) is the sum of bank loans 𝐶𝑖𝑡, the monetary financing of the treasury 𝐹𝑀𝐸𝑖𝑡 and 
the value of gold and currencies 𝑂𝐷𝑖𝑡; we obtain 𝑀𝑖𝑡 = 𝐶𝑖𝑡 + 𝐹𝑀𝐸𝑖𝑡 + 𝑂𝐷𝑖𝑡  ⇒ −𝑂𝐷𝑖𝑡 − 𝐹𝑀𝐸𝑖𝑡 = 𝐶𝑖𝑡 − 𝑀𝑖𝑡. 
Because of this, 𝑅𝐸𝐹𝑖𝑡 = 𝐵𝑖𝑡 + 𝑟𝐷𝑖𝑡 + 𝐶𝑖𝑡 − 𝑀𝑖𝑡 + 𝐶𝐶𝑃𝑖𝑡. 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): 𝐶𝑉𝑖𝑡 = 𝑔𝐶𝑖𝑡2. Let us define 
the following ratios:  and . We can write: 𝐵𝑖𝑡 + 𝑟𝐷𝑖𝑡 + 𝐶𝑖𝑡 − 𝑀𝑖𝑡 + 𝐶𝐶𝑃𝑖𝑡 = 

𝑝′𝑀𝑖𝑡 + 𝑟𝑝𝑀𝑖𝑡 + 𝐶𝑖𝑡 − 𝑀𝑖𝑡 + 
 1 − 𝑝 − 𝑝′ ′ . Remembering that 𝐹 = 𝑓𝐶𝐶𝑖𝑡 + 𝑓𝐴𝐴𝑖𝑡 ,   , and  

𝑇𝑖𝑡 = 𝑥𝑖𝑡𝐶𝑖𝑡 + 𝑦𝑖𝑡𝐴𝑖𝑡+(1 − 𝑥𝑖𝑡 − 𝑦𝑖𝑡)𝐿𝑖𝑡, 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 𝑦𝑖𝑡/𝑥𝑖𝑡 contains the monetary variables 𝑖𝐶, 𝑖𝑀𝑀, 𝑟, 𝑝, 𝑖𝐷 through , so that 
the following proposition holds:  
Proposition 1: The liquidity ratio depends on financial parameters, namely 𝑥𝑖𝑡, 𝑦𝑖𝑡, 𝑓𝐶,𝐴,𝑟𝑓, 𝜌. It 
depends also on the monetary variables 𝑖𝐶, 𝑖𝑀𝑀, 𝑟, 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:  
• 𝑅𝑖𝑡 increases, that is, when the risk-free rate 𝑟𝑓 and/or the market risk premium  (here, the yield 
on loans) increases, ceteris paribus; cf. equation (3):  ;  

• 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, 𝑓𝐶, 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 𝜀𝑖𝑡 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  𝑈(𝛱𝑖𝑡). 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 𝜀𝑖𝑡 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 𝑆𝑖𝑡  allowing it to predict 
the value that will take the variable 𝜀𝑖𝑡 at the end of the period. This observed signal, different for each 
bank, is composed of a heterogeneous noise 𝜀𝑖𝑡 and a homogeneous noise 𝜐𝑡 whose intensity  varies 

from one period to another. The homogeneous noise 𝜐𝑡, unlike 𝜀𝑖𝑡, is an aggregate shock. It is  
assumed to be uncorrelated with 𝜀𝑖𝑡. 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 𝜐𝑡 increases, the bank observes that 𝑆𝑖𝑡 increases, which causes 
an increase of the uncertainty on 𝜀𝑖𝑡 and therefore on the yield of the portfolio 𝑅𝑖𝑡. 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 𝜀𝑖𝑡 as well as the optimal rate of return of the 
loans. But the bank has no other choice: to forecast  𝑙𝑖𝑡, it needs information about 𝜀𝑖𝑡. The best 
prediction of 𝜀𝑖𝑡 is its expected unconditional value (𝜀𝑖𝑡), which is equal to . But observation of the signal 
𝑆𝑖𝑡 can allow the bank to improve this prediction by using the expected value of 𝜀𝑖𝑡 conditional on the 
received signal (𝜀𝑖𝑡/𝑆𝑖𝑡).   
The informative nature of this signal implies that (𝜀𝑖𝑡/𝑆𝑖𝑡) ≠ 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 Calmès and Salazar (2006). It will be noted 𝐸(𝛱𝑖𝑡/𝑆𝑖𝑡). 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:  

  

𝜆𝑡𝑆𝑖𝑡)        (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 𝜎𝜐2𝑡 increases, the proportion 𝑥𝑖𝑡 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 𝜀𝑖𝑡 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; 
Calmès, 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 𝑥𝑖𝑡 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, « The Credit Crunch in East Asia: What Can Bank 
Excess Liquid Assets Tell Us ? », Journal of International Money and Finance, vol. 23, pp. 27–
49.  

Aryeetey E., 1998, « Informal Finance for Private Sector Development in Africa », Economic Research 
Papers 41, BAD.  

Baum, C.F., M. Caglayanet N. Ozhan (2002), “The Impact of Macroeconomic Uncertainty on Bank 
lending behavior”, Document de travail.  

Baumol, W.J. (1952), « The Transactions Demand for Cash: An Inventory Theoretic Approach», 
Quarterly Journal of Economics, LXVI, (nov), pp. 545-556.  

Beguy, O. (2012), « Trois essais sur la surliquidité bancaire dans la communauté économique et 
monétaire d'Afrique Centrale (CEMAC) ». Thèse de doctorat unique de sciences économiques 
soutenue à l’université d'Auvergne - Clermont-Ferrand I.  

Calmès, C., 2004, « Regulatory Changes and Financial Structure: the case of Canada », Swiss Journal 
of Economics and Statistics (SJES), vol. 140 (I), pp. 1-35, March.   

Calmès, C. et Salazar, J. (2006),  « Variance macroéconomique conditionnelle et mesure de dispersion 
des actifs dans les portefeuilles bancaires » pp. 688-700, in F.-É. Racicot et R. Théoret, « Finance 
computationnelle et gestion des risques », Presses de l’Université du Québec.  

Doumbia, S., 2011, « Surliquidité bancaire et « sous-financement de l'économie ». Une analyse du 
paradoxe de l'UEMOA », 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-économiques de la répression financière dans les Pays en 
développement" Economie Appliquée, tome LXIII, n° 4, pp. 93-117.  

Eboue C. (1998) : " La libéralisation financière dans les pays en développement – une évaluation 
préliminaire du cas africain", Gestion macro-économique, nouvelles approches et enjeux de 
politique économique, Abidjan, octobre 1998.  

Emran, M.S. et Stiglitz, J.E. (2007), “Financial liberalization, financial restraint, and entrepreneurial 
development », http://cid.harvard.edu/neudc07docs/neudc07_s5_p02_emran.pdf.  

Jaffee, D.M., Modigliani, F. (1969), “ A Theory and Test of Credit Rationing”, American Economic 
Review, vol. 59, issue 5, 850-72.  

Jappelli, T., Pagano, M. and Bianco, M., 2005, « 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), “ 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), “Portfolio selection”, Journal of Finance, March, p.77-91.  

Markowitz, H.M. (1959), “Portfolio selection: Efficient Diversification of Investment”, New York, 
Wiley.  

Nissanke, M. and E. Aryeetey 1998. “Financial Integration and Development, Liberalization and 
Reform in Sub-Saharan Africa”, ODI and Routledge, London.   

Sacerdoti, E. (2005), « Access to Bank Credit in Sub-Saharan Africa: Key Issues and Reform Strategies”, 
IMF Working Paper WP/05/166, 38 p.   

Saxegaard M., 2006, « Excess Liquidity and Effectiveness of Monetary Policy : Evidence from Sub-
Saharan Africa », IMF Working Paper, WP/06/115, Washington D.C., FMI.  

Sigouin, C. (2003), «Investment Decisions, Financial Flows, and   Self-enforcing  Contracts», 
International Economic Review, vol . 44, n° 4, p .1359-1382.  

Stiglitz, J.E., Weiss, A., 1981, “Credit Rationing in Markets with Imperfect Information”, American 
Economic Review, Vol. 71, No. 3 (June), pp. 393-410.  

Tobin, J. (1958), “Liquidity 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), “ 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), “The 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, « Conséquences de Bâle II sur la tarification et la distribution des crédits 
», Banque et Marchés, n° 78, p. 46- 51.   

Appendix A1   
Let’s prove that .   

The return of the banking portfolio is  so that the conditional variance of 𝜀𝑖𝑡 is :  

 

  

  
We have 𝑉𝑎(𝑟𝑓/𝑆𝑖𝑡) = 0 since 𝑟𝑓 is certain and  𝑉𝑎𝑟(𝜌/𝑆𝑖𝑡) = 0 since  is constant, so that :  
            ∀𝑖, ∀𝑡,   𝑉𝑎(𝑅𝑖𝑡/𝑆𝑖𝑡) = 𝑥𝑖𝑡2𝑉𝑎𝑟 (𝜀𝑖𝑡/𝑆𝑖𝑡)                                            (𝐴1 .   
As the conditional expectation of 𝜀𝑖𝑡 is a proportion 𝜆𝑡 of the signal 𝑆𝑖𝑡, namely (𝜀𝑖𝑡/𝑆𝑖𝑡) = 𝜆𝑡𝑆𝑖𝑡, the 
conditional variance of  𝜀𝑖𝑡 is a proportion 𝜆𝑡 of its unconditional variance:  
𝑉𝑎𝑟 𝜀𝑖𝑡/𝑆𝑖𝑡) = 𝜆𝑡𝑉𝑎𝑟 (𝜀𝑖𝑡) = 𝜆𝑡𝜎𝜀2𝑡                                                      (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 𝑥𝑖𝑡, the first order condition gives:  
  

  

From equation A2.1, we obtain:  

We have  since 𝜀𝑖𝑡 ⊥ 𝜐𝑡.  
Thus:  
  

  

Finally :  
  

  

  
  

mailto:contact@americaserial.com

