1. Introduction

Asset, liability, and income diversification is a management required skill, directly related to the business´s results and the strategic and financial development of companies (^{Campa, and Kedia, 2002}; ^{Denis, et al., 1997}), for over three decades.

Furthermore, due to a greater degree of financial liberalization throughout the world and access to the internet telecommunication tools, the banking industry has experienced significant changes throughout the world (^{Ghosn, 2019}; ^{Muñoz, et al., 2020}). This financial liberalization and the internet telecommunications tools have had a significant impact on its performance (^{Shim, 2019}; ^{Verlekar, 2019}); therefore, the interest to revisit the topic, now from the Mexican perspective, to evaluate their effect over profitability, and/or its risk.

In an effort to understand the magnitude of such effects, we analyzed the worldwide banking diversification experiences and research in relation to a) bank profitability (^{Trujillo Ponce, 2013}; ^{Sanya, and Wolfe, 2011}; ^{Chavarín Rodríguez, 2015}) and (^{Jara, et al., 2011}); and b) bank risk (^{Stiroh, 2004}; ^{Stiroh, 2006}; ^{Lepetit, et al., 2008}; ^{Sanya, and Wolfe, 2011}; ^{Kim, et al., 2020}), and (^{Marinho, and de Araújo, 2016}). The mentioned above authors agree that the income diversification is beneficial for banks. As examples of income diversification, we can mention, in addition to the interest-bearing securities, collecting non-interest income: such as fee income, trading revenue, and other types of non-interest income (^{Stiroh, 2004}).

This research paper´s objective is to increase the level of analysis of the Mexican banking industry and to empirically test if diversity, related to their assets, liabilities, and income, affects or benefits Mexican banks in relation to its profitability and /or risk. Some of the questions that we would like this paper to answer: Are the effects of income, assets, and liabilities diversification permanent on the banks’ performance? Are the effects of income, assets, and liabilities diversification permanent on the banks´ risk? And / or, on the other hand, is there a turning point where diversification is no longer convenient, for the banks’ performance and / or risk? And is it necessary to think more about banks’ specialization?

The Mexican banking system is an interesting case study, especially because of the high presence of foreign affiliates (65% of the total banking assets held in Mexico). Forty years ago, the Mexican banking sector was made up mainly of specialized local intermediaries and limited foreign competition. After the 1982 bank expropriation, the industry became wholly state-owned for less than two decades. The structural changes in the banking sector were catalyzed by the post-crisis reforms in 1995 and the North American Free Trade Agreement (NAFTA). These reforms accelerated the local expansion of international banking intermediaries, which led to the consolidation of the local banking system. Today, this industry is populated by both foreign and domestic financial institutions.

We will structure the article with the following sections: 1. Introduction, 2. Theoretical framework, 3. Study´s hypothesis, 4. Methodology, 5. Empirical results, and 6. Conclusions and discussions.

2. Theoretical framework

The banking diversification literature in the developed countries is extensive; however, in the case of Latin America the literature is uncommon, and in the Mexican case of we only identified two articles.

The first author that studied the diversification effects on the banking sector was Xu (¹⁹⁹⁶), who analyzed five Canadian banks, between 1978 and 1985. His main result suggests that the Canadian banks benefited from an international diversification strategy, generating an increased performance stability because it was linked to the systematic risk reduction of the national market. A second related article was that of Allen, and Jagtiani (²⁰⁰⁰), who analyzed 729 American banks, between 1986 and 1994. For these authors, bank diversification was accomplished by linking "security trading," a non-banking activity, to the traditional banking activities. This diversification linkage and its relationship to the banks’ profitability, suggests that non-banking operations increase the systematic market risk, which reduces the capacity of the company for additional, traditional business. In other words, banks that financed their assets with traditional deposits were less exposed to the interbank environment and were, to a lesser extent, affected by financial crises. A third related article was Archaya, et al. (²⁰⁰²), who analyzed 105 Italian banks, between 1993 and 1999. The authors´ findings suggest that the optimal bank strategy would be the specialization into few banking products.

We started using "diversification" and "banking" as keywords in specialized search engines, in both English and Spanish. We obtained 29 articles and performed an in-depth literature review, on the banking diversification effects. In various countries and regions of the world. The analyzed articles, spanned their analysis from 1978 to 2019 (Annex A shows the details of the 29 studies identified and related to banking diversification.)

Our first bibliographic finding was the identification of five different diversification strategies, or independent variables, used to improve performance and reduce risk: 20 articles (69.0%) used Income as an independent variable; six (20.7%) used Market; four (13.8%) used Portfolio; one (3.4%) used Assets as a variable, and one (3.4%) used Geographic diversification. (It is important to notice that the summation percentage is larger than 100%, since there are three articles that each presented two diversification strategies.)

As a second finding, the results of diversification, or the dependent variables, we identified five outcomes that affected the banks´ outcomes: the effect of the independent variables resulted in impacting the Yield in 17 articles (58.6%); the Risk in 14 articles (48.3%); the Costs in one article (3.4%); the Management in one article (3.4%); and the Revenue in one article (3.4%) %. (Again, as explained in the previous paragraph, it is important to notice that the percentage summation is larger than 100%, since there are five articles that analyzed both risk and return).

When we talk about bank income diversification options, we mean, in addition to the traditional interest income securities, non-interest income: such as fee income, trading revenue, and other types of non-interest income (^{Stiroh, 2004}). The same author points out that the income diversification strategy means a structural change of the bank´s operation, where the income increases are not related to credit operations increases. However, studies confirm that income diversification, produces both positive and negative results (^{Astrid Martínez, 2016}).

Income diversification studies with positive results: Smith, et al. (²⁰⁰³) in Western European found that, there is a positive relationship related to income diversification. In Italy, Chiorazzo, et al. (²⁰⁰⁸), identified that increases in non-banking income positively influences profitability, adjusted for risk. However, this benefit decreases as banks grow. Similarly, Elsas, et al. (²⁰⁰⁶), explored the banking systems in nine developed countries, and confirmed that income diversification, either by via organic growth or via a merger, increases profitability and that such profitability is associated with a higher market valuation. Sanya, and Wolfe (²⁰¹¹) analyzed the banking system of 11 emerging countries and found that diversification from both interest income and interest-free income delivers positive results. Likewise, Jara, et al. (²⁰¹¹) compared banks from six Latin American countries against the American banking, and found that diversification through non-traditional banking activities, which is a predominant factor in Latin American banking system, has positive effects on the banks´ performance. Carrera (²⁰¹⁹) in Ecuador, identified that when income diversification increases the risk of insolvency tends to decrease. Furthermore, Chavarín Rodríguez (²⁰¹⁵), looking for the main profitability determinants of the Mexican commercial banks, found that the main explanatory factors are the collection of commissions and fees, regardless of the nationality of the capital ownership.

Studies that describe negative results when income diversification is applied: Stiroh (²⁰⁰⁴) suggests that there is little benefit from using an income diversification strategy, basically shifting towards interest-free income. This research, conducted on more than 14,000 American banks. Additionally, Palomino (²⁰¹⁵) reviewed the diversification path of the Spanish banks and corroborated that there is an inverse relationship between income diversification and profitability, risk adjusted. Moreover, Marinho, and de Araújo (²⁰¹⁶) performed their research in Brazil, identified that the income diversification strategy did not influence the insolvency risk. In addition, Abuzayed, et al. (²⁰¹⁸) found a negative relationship between income diversification and Islamic bank stability. Allen and Jagtiani (²⁰⁰⁰) suggested that the diversification benefits, when considered in isolation from the traditional bank operations, is not large enough to justify its diversification expansion. Lepetit, et al. (²⁰⁰⁶) found that European banks when diversify their income, from new business lines, must anticipate and prepare for the upcoming operational challenges. This is particularly the case for income diversification strategies since they represent a greater risk than for those banks that concentrate on interest-bearing securities, and / or participate on the small banks segment. Furthermore, Mercieca, et al. (²⁰⁰⁷), analyzed the European banking system and did not find a direct benefit for their new business lines, from an income diversification strategy; they did find though an inverse association between non-interest income and bank performance. In this sense, Lepetit, et al. (²⁰⁰⁸), in a detailed investigation showed that there is a positive relationship between risk and product diversification; such relationship is stronger for small banks and that in all cases, risk is mostly positively correlated with the participation in commission-based activities, but not with trading activities. Finally, Lastre-Valdés (²⁰¹⁵) points out that the entities that divert from their main objectives, to increase profits and generate value, show a higher risk associated with insolvency.

Income diversification recent studies: Escobar (²⁰¹⁹) analyzed the effects of income diversification. This research showed an improved bank performance, via higher returns in a multiproduct industry. However, the results also indicate that the income diversification benefit is reversed in periods of economic or financial crises. Kim, et al. (²⁰²⁰) found a significantly non-linear effect (inverted U-shaped) between the applied income diversification strategy and the bank´s financial stability. This research suggest that a moderate degree of bank diversification increases bank stability, but excessive diversification has an adverse effect. On a continuing analysis, considering periods with and without crisis, the authors suggest that it is better for banks to concentrate on traditional intermediation functions (deposits and loans), instead of diversifying their activities and investments. Paltrinieri, et al. (²⁰²¹) not found some relationship between income diversification and stability for both conventional and Islamic banks. Finally, Muñoz, et al. (²⁰²⁰) showed that income diversification had a positive and non-linear effect on the banks´ performance. The non-linear link suggests that the positive effect is reversed if the banking industry is highly diversified. Furthermore, on a continuing analysis, considering periods with and without crisis, the authors suggest that, during crisis periods, the banking industry must reduce its degree of diversification to obtain a higher performance.

Studies related to the effects of asset, portfolio, and other diversification strategies: Archaya, et al. (²⁰⁰²), using data from Italian banks, compared the specialization effect, portfolio diversification, geographical operations, and sectorial terms against the banks´ level of performance and risk. They found that for banks with low levels of risk and geographical diversification resulted in an improved risk-return ratio. Whereas, banks with high risk levels, no type of diversification - regardless of the considered factor such as industry, sector, or geographic location - produced an adequate level of compensation. Moreover, in the Peruvian study of Cortez (²⁰¹⁴), the author found that the asset-based portfolio diversification strategy, by credit type (such as direct, consumer, and mortgage), has a positive effect on the banks´ performance. However, also in Peru, expanding the scope of the previous study, Serpa (²⁰²⁰) found that diversification by economic sector and / or geographical area, does not have any performance effect. Regarding the liability diversification literature review, we did not detect any relevant article.

3. Study hypothesis

To stablish if the assets, liabilities, and / or income diversification distresses or benefits Mexican banks on its profitability and /or risk, we partially replicated the methodological footsteps of Muñoz, et al. (²⁰²⁰). Their mentioned research analysis showed that diversification has a positive and non-linear effect on bank performance. We also partially replicated the Kim, et al. (²⁰²⁰) study, which suggested that a moderate degree of bank diversification increases banking stability, but excessive diversification has an adverse effect. Taken into consideration the mentioned above studies, we came up with the following hypotheses, proposed for the segment of larger Mexican banks, those that hoard approximately 80% of the Mexican banking market.

H1. Asset diversification increases will have a non-linear relation (inverted u-form) that translates into increases on its profitability (risk adjusted).

H2. Liability diversification increases will have a non-linear relation (inverted u-form) that translates into increases on its profitability (risk adjusted).

H3. Income diversification increases will have a non-linear relation (inverted u-form) that translates into increases on its profitability (risk adjusted).

These hypotheses suggests that a moderate degree of diversification, on the larger banks operating on the Mexican sector, would increase their profitability, but excessive diversification would have an adverse effect.

We followed too the methodological footsteps of Kim, et al. (²⁰²⁰), who found a significantly nonlinear (U-shaped) effect between income diversification and financial stability. Additionally, we did too partially replicate the Archaya, et al. (²⁰⁰²) study, whose authors proposed that asset portfolio diversification by credit type, (such as direct, consumer, and mortgages), improved the risk-return banks´ ratio. Based on these latter studies, we proposed the following three hypotheses for the same market segment.

H4. Asset diversification increases will have a non-linear relation (U-shaped) that translates into increases on its level of risk.

H5. Liability diversification increases will have a non-linear relation (U-shaped) that translates into increases on its level of risk.

H6. Income diversification increases in will have a non-linear relation (U-shaped) that translates into increases on its level of risk.

These last three hypotheses suggest that a moderate degree of diversification, on the larger banks Mexican sector, would increase their risk profile - but excessive diversification would also impact the risk profile.

There are other kind of bank diversifications, such as market and / or geographical segmentation, higher levels of corporate governance, and / or the host country´s economic level of development (^{Hsieh, et al., 2013}). However, for the purpose of this paper, we will be exclusively focusing on asset, liability, and income diversification strategies and their effects.

4. Methodology

For each of the six mentioned above hypotheses (H1. to H6.), two regression analyzes will be applied; we used both linear and second-degree polynomial equations. Furthermore, we will validate too which of them generates a significant relationship and which presents a greater variance explanation. For example, for the first 3 hypotheses on profitability or performance, the following models will be compared with the following lineal equation (1) and polynomial (2):

Where: diversification j=1 refers to assets´ diversification, diversification j=2 to liabilities´ diversification, and diversification j=3 to income´s diversification; and t is the year of measurement of the variables. For the risk related hypotheses, the models will be evaluated with the following lineal equation (3) and polynomial (4):

For this research paper, we collected for each considered bank: diversification, profitability, and risk data, for a total observation period of 11 years, and grouped the data within a cross-sectional regression. The operational definition of variables is presented later in this section.

5. Empirical results

As the reader is aware, as the diversification values approach 0.00, there is greater diversification; on the other hand, the closer the diversification value is to 1.00, it means a higher level of concentration - or business specialization. This rule applies to all diversification variables considered (Asset, Liability, and Income), in the present paper.

Regarding the Asset diversification strategy followed by the large Mexican banks, we observed diametrically different strategies. Santander presents the highest asset diversification value, with an HHIA index of 0.175; while Compartamos presents the highest specialization, with an HHIA index of 0.743 (85.9% of all Compartamos´ assets were concentrated on consumer loans, during 2013).

In terms of Liability diversification, HSBC presents the highest liability diversification with an HHIL of 0.161; while BanCoppel presents the highest HHIL concentration with an of 0.901 (94.9% of all BanCoppel's liabilities, in 2021, where placed in the interest-bearing deposit account).

Regarding Income diversification, Banorte presents the greatest income diversification, with an HHII index of 0.172; while Compartamos concentrates its income, with an HHII index of 0.921 (96.0% of Compartamos´ income, during 2011, where placed in its interest-bearing consumer loan portfolio).

In relation to the ROA of the large Mexican banks, during our 11-year study, there were only five entry cases recording accounting losses: In 2020, the year of the world pandemic beginning, Compartamos presented a ROA ratio of -4.0%, Banco Azteca of -2.7%, and HSBC of -0.1%. In 2016, Bank of America recorded a ROA ratio of -0.4%, and in 2015 HSBC recorded a ROA ratio of -0.1%. These five data entries represent only 3% of the sample; all other cases or entries, of the 11-year collected sample, including 2021 a complete pandemic year, presented positive rations, representing 97% of the sample. During the study period, Compartamos presented an exceptional profitability, between 2011 and 2016; its ROA ratios were between 11.9% and 15.6% annually.

Now switching gears, to the banks´ risk, some of them recorded practically no provisions, preventive estimates for the value of the credit risks. For instance, Banco del Bajío in 2019; Bank of America in 2011, 2019 and 2021; and Banregio in 2012 and 2013. For this reason, during these years, their LLP risk ratio was zero. On the other hand, BanCoppel, in 2011 and 2014, provisioned more than 40% of its entire loan portfolio. The variables statistics, of the sample, are depicted in the following Table 6.

An index HHI value = 1 describes a maximum concentration and a HHI value = 0 describes a maximum diversification. This convention fact applies regardless of the variable type considered: Asset, Liability, and Income. Therefore, the observed reductions in the HHI values seem to indicate a long-term reduction of the diversification strategies.

The above table highlights the risk´s volatility values of the banks considered in the sample, in the sense that the standard deviation of the LLP risk variable (7.8%) is significantly higher than its mean (5.5%); which means that some banks in Mexico lend to risky endeavors and / or sectors, while others are extremely conservative.

It is important to realize that we identified three non-significant correlations regarding the study´s variables. First, the relationship between a liability diversification increase (HHIL) and a return increase (ROA) indicates that they are independent variables. Second, the relationship between the liability diversification (HHIL) increase and risk (LLP) increase are also practically independent variables. Third, and finally, the relationship between an income diversification increase (HHII) and a risk (LLP) increase is not relevant either. The following Table 7 contains the detail of the mentioned correlations (gray marked cells).

These results seem to indicate that an increase in the asset concentration is significantly related to a profitability increase (0.468 with p=0.000) and a risk reduction (-0.295 with p=0.000). However, a liability and income diversification policies change does not reflect a significant relationship with neither, profitability nor risk.

Now we will verify the nature of the relevant equations: if the variables’ relationships are linear and/or polynomial. In relation to the ROA profitability, the regression equations, their adjustments, and the results hypothesis tests, we summarized them all in the following Table 8.

The normality values of the Kolmogorov - Smirnov (KS) disturbances test indicate that the errors do not conform to a normal distribution (p < 0.050). However, this assumption is not essential if the objective of the investigation are the estimates. This is particularly the case when the T and F tests continue to be valid asymptotically, for large samples (^{Gujarati, 1992}). The Durbin Watson test values indicate that there is no spatial serial correlation, which occasionally occurs in cross-sectional analyses; therefore, the assumption of the classical model is not violated.

We calculated the three ROA profitability polynomial regression analyzes (HHIA, HHIL, and HHII). In relation to the Asset diversification variable equation, HHIA, presents an inverted U - shaped graph (R² adj= 0.281), presented in the Figure 1. This equation allows to calculate the turning point at which the asset diversification HHIA maximizes the ROA return. When deriving the regression function with respect to the asset diversification, a ROA maximum increase point is obtained by promoting an asset specialization allocation (HHIAt - HHIAt-1) of 11.32%.

Source: Our own.

Figure 1 The ROA return with respect to an asset diversification HHIA strategy.  

With respect to the asset HHIA and income HHII diversifications strategies, we obtained linear and curvaceous regressions that did not present meaningful values to predict the ROA.

In summary we only approved H1; H2 and H3 were discarded. We approved H1 because we found that a higher asset concentration is better for the banks´ return, up to a 11.33% inflection point, up to which the banks’ profitability begins to decrease. We were not able to approve H2 and H3; situation that implies that a higher or lower, income and / or liability concentration no it's enough to determine a better return strategy.

We presented in the Table 9 the following regression equations related to risk LLP, their adjustment, and the results of the hypothesis tests.

Like the outcome obtained for the profitability analysis, the risk related results provided by the Kolmogorov - Smirnov (KS) and Durbin Watson tests, the obtained values are adequate and, therefore, statistically valid.

With respect to the three LLP risk polynomial regression analyzes (HHIA, HHIL, and HHII), we obtained the following two adjusteded determination coefficient values. These values are related to assets HHIA (R² adj= 0.097) and income HHII (R² adj= 0.039) variable diversification; if it presents a U-shaped graph, as shown in Figures 2 and 3 , it will allow us to calculate the turning point where the assets diversification minimizes LLP risk. By deriving the regression function with respect to asset diversification (HHIA), we obtained a minimizing point related to LLP risk that promotes an asset specialization allocation at 13.02%. With respect to income diversification (HHII), a minimizing point in LLP risk is obtained by promoting an income specialization allocation at 0.93%.

Source: Our own

Figure 2 LLP risk return with respect to liability diversification HHIL strategy 

Source: Our own

Figure 3 LLP risk return with respect to income diversification HHII strategy.  

With respect to the Liability HHIL diversifications, we obtained regression curves that were U-shaped to be able to predict the risk LLP. Summarizing: We approved the H4; we found that a higher asset concentration is better for the risk´s return ratio, up to a turning point (at 13.02%), from where the risk begins to increase. We did not approve the H5, which implies that a higher or lower liability concentration no it's enough to determine a better strategy for the bank´s risk. We approved the H6. We found a U-shaped equation with an inflection point close to zero (0.94%), which implies that any strategy to modify the income participation percentage is related to a risk increase.

6. Conclusions and discussions

Based on the regression equations that we obtained, from our 11-year sample of the 15 largest and most important banks in Mexico, the best diversification strategies in Mexico for banks would be of a mixed nature, as presented in Table 10.

In short, asset specialization grants greater profitability and lower risk - but up to a certain point, because a further radical transformation can be detrimental to the banks´ profitability and risk. However, with respect to the liability’s specialization or diversification strategy, it is not possible to identify an optimal strategy point, that at the same time increases profitability and reduces risk.

Our findings are consistent with the convenience of using an asset specialization strategy; fact that it is consistent with the Patrón (²⁰¹⁵) studies of Bolivia, Archaya, et al. (²⁰⁰²)´s Italian study, and Serpa (²⁰²⁰)´s Peruvian study of high-risk banks; However, Xu (¹⁹⁹⁶)´s Canadian study obtained conflicting results in relation to our results. In our opinion, the difference in results may be due to the long time span between the studies.

Regarding the convenience of whether specialize or diversify banks´ income, the only study in Mexico that addresses this phenomenon is that of Chavarín Rodríguez (²⁰¹⁵). The author found that one of the profitability determinants was fee related charges; associated with income diversification. However, our study did not find any direct and significant relationship between income diversification and profitability. In our opinion, the difference in the results lies in the fact that the database used by Chavarín Rodriguez (²⁰¹⁵) covers a period of a deep banking crisis, from 2007 to 2013, with an ROA of -0.64% on average, where the commission collection could be a relief, while ours cover a longer period (2011 - 2021) and it includes a different crisis type with a +2.0% ROA.

A contribution of our investigation is the use of non-linear regressions, which allow us to identify inflection points for the three mentioned strategies - needed for maximizing and minimizing risk and return, expanding the methodology used by Kim, et al. (²⁰²⁰).

It is difficult to answer the diversification vs. especializtion questions without limiting the circumstances surranding their effects. The proposal, identified at empirical tests, indicate that in order to increase their performance, banks have to specialize. However, to reduce risk, banks have to diversify. Higher performance and risk reduction can no be simoultaneously achieved. However, under normal circumstances, not during crises, the effects of specialization are recomended. Nevertheless, during crises, diversification will produce better results - by not assuming the concentration risk associated with a problematic product and / or guild.

From our perspective, one of the main limitations for a deeper analysis of the Mexican Banking system has to do with the way the local regulatory authority groups together information in general, including several types of income interest. For instance, consumer, mortgages, and auto loans’ interest is reported under the same interest category. This does not allow researchers to figure out whether a particular loan type is profitable and by how much more. The past due portfolio is also reported together with interest income, situation that does not allows to figure out the actual health of each individual loan portfolio.

Another potential limitation has to do with the fact that we did not analyze all the potential sources of diversification. For instance, we did not analyze market and geographic diversification.

A third potential limitation has to do with the selected time frame of the study. Even though, it was an eleven-year study, the analyzed time does not include several financial crises. 2020, the pandemic year was included in the analysis, was an extraordinary event. We would have liked to be able to analyze a period with “normal” financial crisis.

A fourth potential limitation has to do with the fact that we treated all banks similarly, when in fact they are not. For instance, the Mexican banking is integrated by several different type members; there are banks and financial groups, not all banks offer the same products, for instance. It is for this reason and the fact that their diversification achieved might come from grouping together the current business - after the 1982 national banking expropriation.

For us, a better understanding of the interest level of the different banks and loan types would provide a deeper understanding of the profitability levels of the largest banks, in relation to others, and therefore it would be something desirable. For instance, we would like to understand why BBVA has a disproportionate net income allocation, in relation to the portfolio it carries, of the whole Mexican banking system.

A first attractive alternative and complementary research line would be the use of the Capital Asset Pricing Model (CAPM), in addition to the ROA analysis, to determine the profitability of banks since it would include the effect of the local markets. Another potential research line would be linking the specialization vs. diversification analysis with the stickiness effect of costs and expenses. This is important because, even though banks´ fixed assets are a requirement for their operations, many of the brank offices are rented, making the investing in facilities riskier during crises periods.