Modelling the trident SME-bank relationship

Abstract

Relationship banking (RB) with SMEs has been approached as a one-size-fits-all where no differences exist between micro, small, and medium businesses. Nevertheless, recent research has clearly identified three distinct levels of RB depending on variables such as the size and complexity of the business and the amount of borrowing. In this study, we create an original model of this fundamental trident, presented as a system of postulates and inferences in mathematical terms, to capture the structure and dynamics of the three RB levels from the supply/bank side. The model systematically shows the existence of and describes the three RB levels. Further, it highlights how each of these levels is dependent on the determinant variables and how a comparison between the three levels is possible based on the per-capita contribution of each of the determinant variables, in turn, to the per-capita RB service production. Our model provides an analytical framework that can assist banks and researchers to rigorously assess and study each level separately or in comparison to the others. It is also beneficial as it can be used to calculate the optimal allocation of the bank's limited resources among the three levels of RB and to achieve maximum value creation for all stakeholders.

1. Introduction

For many years, researchers from a variety of academic backgrounds, including finance [[1], [2], [3], [4], [5], [6]]; economics [[7], [8], [9]] and marketing [[10], [11], [12]], have studied the SME-bank relationship. In all these studies, however, relationship banking (RB) is approached as though it were an undifferentiated monolith, where no differences exist between relationships with micro, small, and medium enterprises. An example of this is the oft-quoted definitions of RB, such as that of [1], which defines it as the practice of providing financial services through a financial intermediary, which makes an investment in gathering client-specific information that is frequently of a confidential nature and assesses the viability of these investments over repeated interactions with the same client across different products.

However, a recent study has clearly identified three, rather than just one, distinct levels of RB depending on a certain number of variables, such as the size of the relationship-managed business, the amount of borrowings by the business, and the level of complexity [13]. In this study, we develop a mathematical model of the newly identified SME-bank relationship taxonomy, systematically describe it, and show the existence of the three RB levels with micro, small, and medium-sized enterprises. Furthermore, through our detailed analysis, we show how each of the three RB levels is dependent on the determinant variables and how a comparison between the three levels of RB is possible based on the per-capita contribution of each of the determinant variables, in turn, to the per-capita RB service production. Overall, our mathematical model is a conceptual contribution to improving the SME-bank relationship literature by distinguishing among the RB segments in terms of inputs and outputs.

Through this study, we contribute further to the SME-bank relationship scholarship in multiple ways. We contribute to the ongoing modelling endeavours and conversation around the different aspects of the SME-bank relationship in the same way as [7,8] have, in that we model a specific aspect for the first time. The importance of our model becomes even clearer considering the repetitive calls to develop analytical models specific to the realities and peculiarities of the SMEs sector, made in the hope of advancing the SME sector rather than continuing to use models developed for the corporate sector and adapting them–a practice undertaken with little success, as small businesses (SBs) aren't little big businesses [[14], [15], [16], [17]].

Furthermore, in the absence of an analytical framework that assists in guiding SME-bank relationship studies, analysis takes several and scattered paths, which consequently affect the quality of the outputs of these studies. An analytical framework would assist in gathering up concepts and other aspects of RB analysis with the aim of moving forward (and developing) the analysis as it has, for example, with the lending technologies framework introduced by Ref. [18]. The analytical model we develop in this study would contribute to guiding different studies on SME-bank relationships. This is so because our model will benefit all those interested in the SME-bank relationship from across the academic spectrum, as the model; s levels would be useful to rigorously study each level apart from, or in comparison to, the other level(s). For example, in an input-output optimisation objective study in finance or investment, one area of interest would be to examine how to optimally allocate the limited resources the bank has amongst the three levels in pursuit of maximum value generation for the bank's different stakeholders. In a marketing setting, the benefit would be for the marketing management scholar to investigate a marketing strategy that best served each level. This kind of analysis helps in the optimisation of input-output combinations by treating the productive units according to the level of RB they are located at within the fundamental trident, and not only according to the level of each variable on its own. This is so because the analysis required at the variable levels differs from the RB levels, which have their own variables.

The rest of the paper is organised as follows: In the next section, we start off with the literature review1 aimed at providing the necessary background to, and firmly positioning our research within, the ongoing conversation on banking theory in general, and on the SME-bank relationship specifically. We do that, initially, by providing a very concise historical development of the theory of banking and the place of relationship banking within the overall recent analytical framework. Subsequently, we then provide the background to the newly identified trident of relationship banking. After that, in Sections 4 and 5, the main building blocks of our model will be introduced, followed by the model itself. Finally, we conclude the paper, offer implications, and suggest future studies.

2. Literature review

As stated by Ref. [19], commercial underwriting and banking theory evolved across four phases of development. Traditional finance theory was initially built on a collection of presumptions that collectively made “the perfect capital market assumptions” [20]. One of these presumptions was the frictionlessness of the capital markets, with no application or brokerage fees in the supply and acquisition of funds. As a result, commercial banks, as financial intermediaries, had no particular role to play in finance theory. In the 1980s, however, financial economists started looking into the existence of commercial banks in the actual world of finance, which is marked by things like incomplete information. These commercial banks (along with other financial intermediaries) subsequently began to receive a theoretical justification for their presence, which was inspired by their dynamic, constructive, and diverse duties [21,22], which included reputation-building [23] and monitoring duties [24,25].

The result was a contemporary banking theory that did a better job of describing banking in practice and, therefore, brought the theory somewhat loser to the everyday particularities of the imperfect capital market, including free-rider problems and information asymmetry. It nevertheless continued to suffer from what has been called a simplified and dualistic viewpoint. This is due to the fact that it divided lending between loans from commercial banks, which were designated as informed lenders, and arm's-length loans, which were designated as non-informed lenders [23,26]. This had the significant result that “the primary focus in the literature on banking through the 1990s was on how bank commercial lending differed from corporate bond underwriting, while substantially ignoring the differences in loan underwriting within the commercial bank loan market” [19]. The contemporary banking theory has been further improved as a result of this recognition, along with others, leading to a more sophisticated understanding that has led to the documentation of two distinct forms of loan underwriting: relationship-based lending and transactions-based lending. The second was more appropriate for transparent sorts of firms, whereas the first was more appropriate for and targeted at informationally opaque enterprises like small businesses [[27], [28], [29]].

Lastly, a new paradigm for commercial loan underwriting was born as an outcome of the criticism of the idea that all transactions-based lending methods are directed at transparent firm borrowers, along with further advancements in the financial economics discipline. The novel paradigm was made possible by Berger and Udell [18], who offered a “unified framework” for the various transaction-based lending modes, which had previously been discussed in earlier work by different scholars, e.g., Refs. [[29], [30], [31], [32]]. Despite the fact that all of these transaction-based lending modes, with the exception of financial statement-based lending, were based on hard data, it was also argued that they were suitable for lending to informationally opaque organizations. Furthermore, ‘lending technologies’ was the term used to describe the ‘unified framework’ [18], which defined a ‘lending technique’ as “a unique combination of primary information source, screening and underwriting policies/procedures, loan contract structure, and monitoring strategies/mechanisms.”

Using the above description, there are a total of nine lending technologies. Each technology may be classified as transaction-based, where the primary information used is hard, or relationship-based, when the primary information used is soft. Additionally, these technologies can be divided into three clusters based on whether the borrower is informationally transparent or opaque.

Over the past ten or so years, the finance literature on RB has expanded quickly. The perception that a greater grasp of the nature of RB can lead to a deeper comprehension of the core of commercial banking [19] has itself generated further scholarly research. All of these, in turn, would help further develop banking theory. One such development is the identification of the SME-bank relationship taxonomy [13]. Next, we give a summary of the background of this taxonomy.

2.1. Descriptive background into the three levels of relationship banking

[13] argued for a clear demarcation between the three levels of RB and called it a taxonomy of SME-bank relationships. Further, he named these three levels as the micro-business or many-to-many relationship model, the SB relationship model, and the medium-business or one-to-one relationship model.

This taxonomy assigns each business to a bank relationship manager (RM), who oversees the relationship on the bank's end. Businesses move up the relationship management hierarchy to the next level as their banking needs expand, and a new or different manager is assigned to manage them. Additionally, it was discovered that the resources available to RMs, such as levels of discretion, cars to visit customers, and levels of assistance, varied just as much as the skills needed by RMs to manage firms from one level of the hierarchy to the next. The next part of this section elaborates on the details of the RB at each level.

2.1.1. Micro-business (many-to-many) relationship model

At this level, businesses are handled online or over the phone, either from a call center or a nearby bank office. These small enterprises' information is housed on a centralized computer. When a business operator phones the call center for a banking product, any online business manager who is available would deal with the caller. So, using a team of online bank managers to jointly oversee a group of online firms, hence the term “many-to-many relationship management model”. At this level, none of the online business managers appear to have much discretion beyond small loans made using a business credit card or a personal loan. Another key criterion at this level of RB is the number of businesses per business manager, which tends to be extremely high. Other notable aspects include resources available to the bank manager, which are minimal.

2.1.2. Small business relationship model

Because businesses' levels of activity and complexity increase as they expand, to keep up with this expansion, banks adapt their volume, variety of products, and degree of management. It is worth noting that business complexity refers to the condition of having several interdependent and interconnected stakeholders, IT systems, and business structures. Stakeholders include suppliers, customers, regulators, employees, investors, and competitors, while business structures include units and divisions. Three elements characterize complexity, and these are level, control, and managerial [33].

The complexity level depends on the number of interconnections and their effects on a business. For example, a small supermarket is a simple business, in which the number of interconnected stakeholders may be limited to the owner, a few employees and suppliers, and a small and mostly local customer base. However, as the business grows, the number of interconnections also grows. A medium-sized business becomes a relatively more complex organization as it grows to have hundreds of product offerings, dozens or more of employees, suppliers, and investors, as well as hundreds of customers. The second characteristic is control, where, for instance, a small-business owner usually controls every aspect of his business, from ordering supplies to managing staff and setting product prices. However, the manager of a medium-business will not usually be able to control operational decisions at the store level, or even at the division level if the business opens more stores. Finally, as business grows, it becomes more complex because decisions involve more stakeholders, and here comes the third characteristic of complexity, which is managerial, that increases with business complexity. Decisions in medium-sized, complex business take longer because the consequences of mistakes are greater. This involves delegating operational responsibilities to capable people and managing resource allocation, coordinating deliveries, managing supply chains, etc.

Overall, banks offer a ‘one-to-one business relationship banking model’ in response to these changes. Every SB at this level is allocated to a designated bank manager. Every SB at this level is allocated to a specific bank manager who is physically based in one of the bank locations across the nation, is the principal contact point from the bank side, and is in charge of managing this SB's relationship with the bank. Despite the fact that it appears to vary from bank to bank, the average number of SBs per manager is substantially lower than there are for online business managers. This is a logical result of the nature of RB at this level because it takes a business manager more time and experience to adequately service these kinds of companies, which includes visiting their offices.

With reference to the discretion granted to various bank managers, these business managers benefit from larger degrees of discretion than their online counterparts, including discretion regarding dollar-lending. Furthermore, they have access to additional resources and banking assistance. At this level, a one-to-many assistance approach is employed, where, for instance, many bank business managers share the services of a credit analyst.

2.1.3. Medium-sized business (one-to-one) relationship model

The managers of medium-sized businesses—henceforth referred to as RMs—are at the top of the business banking ladder. Typically, these RMs oversee a portfolio of enterprises that is less than half that of a business manager. Additionally, RMs enjoy much higher levels of discretion than do their counterparts at the previous level, with significantly higher maximum bounds.

RMs are required to be initiators when dealing with their clients, calling and emailing them, visiting their places of work, and offering them new products and services. SB managers, on the other hand, follow the "set and forget" guidance and are more reactive than initiative takers with regard to their clients. In addition, RMs are required to interact directly with clients and get to know them better than SB managers do. This clearly shows that managers at this level spend more time on individual customers than those working at the previous level.

Furthermore, RMs have an assistant manager, who could be called an account manager (AM). This AM manages the day-to-day affairs of the relationship-managed client account and handles matters like inquiries and term deposits. This is due to the fact that customers want banking to be simple after, say, a loan has been contracted, and the AM is in charge of achieving that from the bank side. Only when something significant is happening, like a new loan application, is the RM called in. In that case, the RM becomes involved until the application is approved, sends everything to the solicitor for documentation, and then the AM takes it over and completes the remaining tasks. As seen from the bank's perspective, this frees up the EM to handle greater and more lucrative responsibilities.

3. Components of modelling the RB levels

3.1. Representation of the three levels of relationship banking

The relationships that exist between the three levels of RB and the different criteria can be depicted as follows:

• (i)The levels of RB noted $Y$ and the levels of discretion per bank manager and resources at the bank manager's disposition noted $X_1$ are positively correlated, i.e. $\frac{dY}{d{X}_1}>0$. These resources, which include a car and a phone, increase with the RB type, moving from micro-RB (where the micro-business manager has little, if any, discretion or resources) to small RB and finally to a medium relationship, where the RM is given the maximum discretion in SME banking.
• (ii)The amount of borrowing noted $X_2$, business size, and complexity all have a positive relationship with levels of RB noted $Y$, i.e., $\frac{dY}{d{X}_2}>0$. The RB model employed will advance from that of the micro-business to the SB and finally to the medium business, when size of the business managed grows (from micro, small, to medium), paired with the business's complexity, and increased borrowing.
• (iii)The levels of RB noted $Y$ are negatively correlated to the number of businesses to manage per relationship banking manager noted $X_3$, i.e., $\frac{dY}{d{X}_3}<0$.

According to this relationship, the number of businesses managed per RM has an inverse relationship with the relationship model. The number of businesses to be managed significantly decreases as the relationship moves up the ladder from micro to medium.

The rest of this section will first summarise the main determinants of the explanatory variables (like business size and amount of borrowings per business) in their relationship with the dependent variable, which is the RB level. Then, in mathematical terms, modelling of the three RB levels will be presented.

3.2. Determinants of the model

In mathematical notation format, Table 1 (below) boils down the main variables that will be used in the model. Explanations of each variable follow the table, and then the model follows that.

• •S_i: size of the business managed at the RB level $i$. Size can be measured via one of the standard proxy measures such as sales, assets, or the number of employees. As the size of a business increases, we suppose the business will move up through the levels of relationship from L₁ to L₂, and then L₃.
• •C_i: refers to complexity, as explained above, at level $i$ of the RB. An example of this is a business with foreign suppliers and foreign customers. This business would require bank services such as foreign exchange due to changes in exchange rates, commodity prices, and payment in foreign currencies. As $i$ increases, the business's complexity increases.
• •B_i refers to the amount of borrowing by the business being managed at the RB level L_i. As $i$ increases, the amount of borrowing per business also increases.2 More borrowing means more involvement by the bank or its RM, particularly with medium-sized businesses.
• •K_i denotes skills that the bank manager should have to manage an RB with businesses at level $i$. For the bank manager to acquire these skills, there must be investment, either by the bank manager or the bank itself in things like obtaining a degree, training, and experience.
• •R_i resources available to the bank manager to do his/her work, such as a computer, a car, and (in)direct access to an assistant manager's help. As mentioned above, the level of resources at the bank manager's disposal, like a car to visit the place of work of the relationship-managed client, varies between levels. At the small level of RB, the bank manager would be expected to have resources such as a computer, a phone, and direct access to the services of a shared assistant manager (with other bank managers at the same RB level), but not a car. At the next level up in the relationship, the manager would have a car and direct access to a full-time assistant manager.
• •D_i represents the level of discretion given to the bank manager at level $i$. As we move up the levels, more discretion is given to the bank manager.
• •N_i represents the number of businesses managed by an individual RB manager, i.e., the number of businesses in each bank manager's portfolio to manage. Moving up the levels of RB, L₁ through L₃, the number of businesses per bank manager decreases substantially. This means that we have $N_1>N_2>N_3$.

Table 1.

Main determinants of the model.

Relationship banking levels $i\text{:}$	Dependent variables:
$L_i$	$S_i,C_i,B_i,K_i,R_i,D_i,and{N}_i$

Note: $\mathit{i}=\mathbf{1,2,3}$ indicates the RB level with micro-business, SB, and medium business, respectively.

3.3. The model details

The RB service production $Y$ is related to the RB level $L_{i}withi=1,2,3$. The production function $Y_{L_i}$ depends on the variables $S_i,C_i,B_i,N_i,K_i,R_i,and{D}_i$ detailed above and is related to $L_i$ such that each level would have its own behaviour and function $F_{L_i}$. Thus, we can write with $i=1,2,3$:

$$Y_{L_i}=F_{Li}\left(S_i,C_i,B_i,N_i,K_i,R_i,D_i,Z_i\right)+{\epsilon }_i$$ (1)

with ${\epsilon }_i$ stands for a stochastic error term, and $Z_i$ represents exogenous variables such as monetary policy and economic growth. It is worth noting that as micro-businesses tend to be noncomplex, we assume complexity to be absent for $i=1$, in other words $C_1$ takes zero value.

3.4. Working out the per-capita variables of the model

In light of the details about the determinants of the model discussed above, we can show that per capita borrowing at ${\mathit{L}}_{\mathbf{1}}$ would be smaller than per capita borrowing at ${\mathit{L}}_{\mathbf{2}}$, which is in turn smaller than per capita borrowing at ${\mathit{L}}_{\mathbf{3}}$. At the relationship level ${\mathit{L}}_{\mathit{i}}$, we have ${\mathit{B}}_{\mathit{i}}$ the amount of total borrowing and the number of businesses served ${\mathit{N}}_{\mathit{i}}$. The per capita borrowing at level ${\mathit{L}}_{\mathit{i}}$ is

$${\mathit{b}}_{\mathit{i}}=\frac{{\mathit{B}}_{\mathit{i}}}{{\mathit{N}}_{\mathit{i}}}.\mathrm{A}\mathrm{s}{\mathit{B}}_{\mathbf{1}}<{\mathit{B}}_{\mathbf{2}}<{\mathit{B}}_{\mathbf{3}}\mathbf{a}\mathbf{n}\mathbf{d}\mathbf{0}<{\mathit{N}}_{\mathbf{3}}<{\mathit{N}}_{\mathbf{2}}<{\mathit{N}}_{\mathbf{1}}\mathbf{t}\mathbf{h}\mathbf{e}\mathbf{n}{\mathit{b}}_{\mathit{i}}<{\mathit{b}}_{\mathit{i}+\mathbf{1}}\text{.}$$

Following the same steps with all other variables in Table 1 (above), we get Table 2 (below).

Table 2.

Per capita variables and per capita relationship banking service production.

Per capita variable at level $L_i$	Relationship of the per-capita variable between all levels	Per-capita RB service production’ & ‘Per-capita determinant variable
$s_i=S_i/N_i$	$s_1<s_2<s_3$	$y_{L_i}/s_{L_i}$
$c_i=C_i/N_i$	$c_1<c_2$	$y_{L_i}/c_{L_i}$
$b_i=B_i/N_i$	$b_1<b_2<b_3$	$y_{L_i}/b_{L_i}$
$n_i=N_i/N_i=1$	–	–
$k_i=K_i/N_i$	$k_1<k_2<k_3$	$y_{L_i}/k_{L_i}$
$r_i=R_i/N_i$	$r_1<r_2<r_3$	$y_{L_i}/r_{L_i}$
$d_i=D_i/N_i$	$d_1<d_2<d_3$	$y_{L_i}/d_{L_i}$
$z_{L_i}=Z_{L_i}/N_i$	$z_{L_1}<z_{L_2}<z_{L_3}$
$y_{L_i}=Y_{L_i}/N_i$	$y_{L_1}<y_{L_2}<y_{L_3}$

Of particular interest is the last row, which is the per capita RB service production. The last cell in column 2 shows that per capita RB service production at $L_1$ is smaller than that of $L_2$, which is, in turn smaller than that of $L_3$. This points to our first important result, which systematically shows the existence of three RB levels.

Using the per capita variables, function (1) can be rewritten as $\mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h}i=1,2,3$:

$$y_{L_i}=f_{L_i}\left(s_i,c_i,b_i,1,k_i,r_i,d_i,z_i\right)+u_i$$ (2)

where $u_i$ is the non-observed term, named the stochastic error. Furthermore, dividing ‘per-capita RB service production’ at $L_i$ by ‘per-capita borrowing’ at level $L_i$, would result in how much ‘per-capita borrowing’ would produce ‘per-capita RB service’: $\frac{y_{L_i}}{b_{L_i}}$.

Following the same process with all other variables vis-à-vis $y_{L_i}$ we get the last column in Table 2 (above). It points to our second important result, which systematically shows how each of the three RB levels is dependent on the determinant variables. Further, it shows how it is possible to compare between $y_{L_1},y_{L_2},\mathrm{a}\mathrm{n}\mathrm{d}{y}_{L_3}$ based on the per-capita contribution of each of the determinant variables in turn to the per-capita RB service production.

4. Conclusion

This paper has developed an analytical model to conceptualize and understand the three distinct levels of relationships between micro, small, and medium firms and their bank. The model shows the existence of three distinct RB levels and how these levels are dependent on the specific determinant variables.

From one level to the next, a business manager's ability to devote time to a specific client varies. The same thing can be said about the resources offered by banks and accessible by the bank business manager. Additionally, variations are not just confined to a bank's inputs and related costs (per customer at various levels); instead, and as a bank’s expectation, variations are also present in the profits and amount of return realized per customer.

Our model's ability to distinguish between the various RB segments has numerous implications. First, we would anticipate the return function to differ from one level of RB to another because the cost function also varies from one level to another. Banks would prefer a return function that is proportionate to the cost function associated with each segment or level. Second, a distinct separation between each segment's inputs and outputs is imperative for an accurate assessment of each segment. Lastly, when making investment decisions, a bank must perform a distinct cost-benefit analysis for every segment to decide among the three levels of RB, how much of its limited resources to allocate to each level so as to make the best use of those resources, and when and how to adjust its management model when necessary. Our model facilitates all of the above.

Furthermore, with the final implication, the proposed model can be used to work out the optimal allocation of the bank's limited resources among the three levels of RB and help achieve maximum value creation for its stakeholders. To achieve that optimal allocation, further modelling is required. However, that is beyond the scope of the current research, and to keep the conversation on the trident bank-SME relationship going, we suggest modelling of the optimal allocation as future research. Another issue that is worth investigating is the need to empirically test and validate the proposed model.

Author contribution statement

Zakaria Boulanouar, Ph.D.; Hassan Ghassan, PhD: Conceived and designed the experiments; Performed the experiments; Analyzed and interpreted the data; Contributed reagents, materials, analysis tools or data; Wrote the paper.

Data availability statement

No data was used for the research described in the article.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.