ON THE IMPORTANCE OF TRADITIONAL LENDING ACTIVITY FOR BANKING SYSTEMS STABILITY

In this paper, we analyzed the role of banks' traditional lending on systemic stability. Firstly, we quanti¯ed the e®ect of correlation among banks' results on systemic risk through Monte Carlo simulation. Secondly, we veri¯ed how traditional lending a®ects banks' results correlation. Finally, combining the two e®ects, we assessed the importance of bank traditional lending on ¯nancial stability. Our results suggest that banks devoting a higher share of their assets to traditional lending show a lower correlation of their comprehensive income, thus having a mitigation e®ect on systemic stability.


Introduction
Bank traditional lending is typically considered as fundamental for sustaining the real economy.What is less evident is that it also provides a signi¯cant contribution to systemic stability.
After the Great Financial Crisis, the Basel Committee on Banking Supervision (2005) introduced several proposals to reduce both the banks' probability of default and its possible impact on the ¯nancial system.The resilience of the EU banking sector has been strengthened following the Basel III agreement, which contributed to enhance banks' loss-absorbing capacity through the introduction of potential capital bu®ers in addition to the minimum capital requirements, i.e. the capital conservation bu®er, the countercyclical bu®er, the global systemically important institution bu®er and the systemic risk bu®er.In fact, capital bu®ers are macro-prudential instruments, whose aim is to decrease bank systemic risks deriving from pro-cyclicality and excessive credit growth during an expansion phase.Furthermore, Basel III introduced new liquidity constraints and a minimum leverage ratio calculated on nonrisk-based exposures to counteract the excessive deleveraging processes.The reforms are detailed and discussed in the economic review of the ¯nancial regulation agenda (see European Commission 2014) and entered into force in January 2014 with the Capital Requirements Directive IV (CRD IV) a and the Capital Requirements Regulation (CRR).b  Benczur et al. (2017) performed a detailed quantitative assessment of the reduction in public ¯nance costs brought about by the introduction of these rules, and the analysis of Parrado-Martínez et al. (2019) reports that the European banking system shows a relative reduction of its risks from 2011 to 2016.According to their study, this reduction has been motivated to some extent by a decrease in the asset portfolio risk, but mainly by a higher banking capital.
However, in terms of macro-prudential regulation, the debate is open on how to strengthen the stability of a banking system for a given stability level of individual banks and on how to minimize the impact of possible banking crises.
For the purposes of our analysis, the term contagion refers to the risk that one ¯nancial institution's failure leads to the default of others through a domino e®ect in the interbank market, as de¯ned in Allen et al. (2012).The recent literature, starting from the seminal paper of Allen & Gale (2000), reports that two components are fundamental in determining contagion risks, namely the correlation among banks' results, and the linkages through direct (interbank) and indirect (market) exposures.
On one hand, correlation plays a fundamental role for contagion risk, because if banks tend to react in the same way to the business cycle and common external shocks, then the system is exposed to a lower number of crises, but more intense as more banks are involved at the same time.Thus, correlation mainly sets favorable conditions for contagion to start.
On the other hand, direct or indirect links among banks have the role of transmitting the crises' e®ects from one troubled bank to the others, inducing further weakening or defaults.
Correlation is often included in system modeling, as banks operating in a speci¯c system are exposed to the same business cycle, at least in part.It means that customer defaults will occur more often in some years (crises) than in others (booms), thus a®ecting banks' results.
The e®ect of this exposure to common risk sources, as to say, the exposure to possible common shocks, translates in the risk of a simultaneous weakening of a signi¯cant part of the banking system.In such a situation, even a single banking crisis can a®ect the other banks by (direct or indirect) contagion, since their loss absorbing capacity is already weakened.It is evident that the higher the number of banks involved and the deeper the impact of the common shock, the higher the risk of contagion.The role played by this parameter is, thus, of fundamental signi¯cance.
To analyze the role of bank traditional lending on ¯nancial system stability, we ¯rst veri¯ed how traditional lending a®ects banks' results correlation.Then, we quanti¯ed the e®ect of the correlation of banks' results on systemic risk, detailing its e®ects and its relations to the speci¯c structure of assets and liabilities of each bank.To this end, we used a Monte Carlo simulation-based approach that allows us to split the systemic risk in an idiosyncratic component that is mainly driven by bank capital level and asset riskiness, and a contagion component, driven by correlation and direct or indirect linkages among banks.Finally, we assessed the impact of bank traditional lending on ¯nancial stability to provide a clearer picture of the process, and to have some hints on how to limit contagion risks and its disruptive e®ects on the banking and ¯nancial system.
The remainder of the paper is structured as follows.Section 2 report a literature review.Section 3 describes the methodology and the simulation model used for testing the correlation e®ects on systems stability.Section 4 presents an empirical application to a sample of Italian banks and discusses the results of our analysis.Section 5 analyzes the economic signi¯cance and policy implications based on the results of our research, and Sec.6 concludes.

Literature Review
Our analysis is directly linked with the research stream focused on the e®ect of the business models' evolution on banks' results correlation.
Within the literature studying the (increasing) interconnection of banks over time, Nijskens & Wagner (2011) have veri¯ed that the introduction of credit risk transfer activities has increased their correlation, while reducing the single bank risk.Patro et al. (2013) analyzed the correlations of equity returns between 1988 and 2008 reporting that correlations are an important indicator of systemic risk.Kreis et al. (2018) perform a thorough analysis of the correlations over an extensive period, from 1980 to 2016, which reports that systemic risk was not signi¯cant until 2007, but, since then, it has become highly signi¯cant as a result of both the increase in the estimated weight of the common factors (correlation) and of their nonlinear impact on systemic risk.
Our analysis is in line with this research stream, aimed at verifying if the traditional lending activity can mitigate the impact of common risk factors, and linked with the theoretical network analysis that modeled contagion risks in banking systems.
In theoretical terms, Elsinger et al. (2006) have already acknowledged that the correlation between banks' results and common risk variables a®ects the probability of simultaneous crises with signi¯cant systemic e®ects, reporting that \between the two leading sources of systemic risk, the correlation is much more important than ¯nancial exposures."A more detailed description of this e®ect is in Co-Pierre (2013), whose analysis reports that in the case of \pure" interbank contagion the shock concentrated on a single bank impacts on the other banks through interbank losses, while in the case of a common shock all banks are hit by the simultaneous loss of a fraction of their capital.Furthermore, even when the shock only brings to default a small number of banks, a large number of banks become more vulnerable, and if contagion is triggered, it typically induces a large number of defaults and high system losses.Similar e®ects are found when considering simultaneous direct and indirect linkages by Cifuentes et al. (2005).
With regard to the common variables in°uencing the results of banking activities, Allen et al. (2012), in their paper focused on asset commonality, show that the composition of banks' asset structures interacts with the funding maturity in determining systemic risk.Acharya & Yorulmazer (2008) model the correlation among bank returns based on the characteristics of loans that compose the banks' portfolios showing that correlation can be considered the ex-ante aspect of systemic risk as it a®ects the likelihood of joint failure of banks.
Regarding indirect contagion, Siedlarek & Fritsch (2019) report that institutions holding broadly similar portfolios can be simultaneously a®ected by a drop in prices for one asset class.Frey & Hledik (2014) argue that similar asset positions across banks can determine a higher correlation between bank asset returns and ¯nancial stability.
About the common risk sources, some papers, such as Karimzadeh et al. (2013) veri¯ed that the yearly changes in GDP are strictly related to bank yields, risk and loan losses.Similarly, the analyses of Demirguc-Kunt & Huizinga (2000) and Bikker & Hu (2002) suggest that bank pro¯tability is related to the business cycle.Athanasoglou et al. (2008) veri¯ed the role of some important variables that in°uence bank results, con¯rming that the economic cycle signi¯cantly in°uences bank pro¯ts.Albertazzi & Gambacorta (2009) specify that the pro-cyclicality of bank pro¯ts is due to two di®erent e®ects, the ¯rst related to the pro¯tability of lending, which in particular has a positive e®ect on the interest margin, while the second e®ect is linked to the quality of the assets, which a®ects the losses on receivables and consequently on the related provisions.

Methodology
As a ¯rst analysis, we evaluated the e®ects of correlation among banks' results on ¯nancial systems stability.
According to the literature presented in the previous paragraph, the results of the banks can be represented as the weighted sum of two components, an idiosyncratic factor, and a common factor.To this end, we denote bank i results for year s, L is , as follows: d is are mutually independent variables, and that i represents the correlation between L is and com s as in Drehman & Tarashev (2013) and in Frey & Hledik (2014).
The estimation of i can be based on the correlation of assets returns, which, in turn, can be estimated either on market values, as in Hull & White (2004), or on balance sheet values, and more speci¯cally on the pro¯ts, as in Meiselman et al. (2018), and as we do in this paper.
For testing the e®ects of di®erent correlation levels of banks' results on the system stability, as it is not possible to rely on actual data, we developed a Monte Carlo based simulation exercise, carried out through the Leave-One-Out methodology proposed in Zedda & Cannas (2020).
The basic idea under the Leave-One-Out method is the comparison between the performance of the whole banking system, and that of the same system when excluding one bank.In this way, it is possible not only to assess which is the contribution to systemic risk of each bank, but also to specify the bank's risk contribution due to the risk of idiosyncratic defaults (stand-alone contribution), and the contribution due to its role in the crises transmission (contagion risk contribution), which is useful for this study.In fact, we have to consider two interconnected e®ects in°uencing the contagion risk contribution of each bank.The ¯rst is due to the correlation between the considered bank results and the common factor, the second is due to the easing of contagion, as a consequence of the (average) correlation level of the other banks in the system.To analyze these e®ects, we developed two sets of simulations.In the ¯rst one, we tested for the e®ect of a change in each bank correlation with the common risk sources changing it uniformly for all banks in the system.In particular, we set correlation respectively to 40%, 50%, 60%, 70%, 80% and 90%, considering both its impact on the whole system and on each of the considered banks.
The systemic risk contribution of each bank h can be represented as: where: Sys i is the systemic risk contribution of bank i; i is the constant term for bank i; corr is the correlation (of all banks) to the common factor, and i is the i bank coe±cient (sensitivity) to it, which is estimated through an OLS regression.
In the second simulation set, we tested for the in°uence of the correlation level when it is di®erent for each bank while keeping it in a prede¯ned range.
In this case, the systemic risk contribution of each bank h can be represented as: where: i is the constant term; corr i is the correlation between bank i and the common factor, and i represents its coe±cient (sensitivity); corr avg is the average correlation of all banks in the system to the common factor, and i represents the i bank coe±cient (sensitivity) to it.
Based on these simulations results, we veri¯ed which of the two correlation components, corr i or corr avg , in°uences more the system's stability.
The second step of the analysis consists in testing for the relationship between the loans' incidence on total assets and the banks' results correlation, proxied employing the comprehensive income correlation.
To do that, we computed the year-on-year variation of comprehensive income V is for each bank i and each year s, proxying the banks' results L is by means of the comprehensive income R is as follows: where R is is the comprehensive income of bank i for year s.Then, we estimated the average annual values of V is , namely V s , for the whole sample, and computed the correlation between the V s values and the V is values, obtaining for each bank a proxy of its correlation with the banking system ongoing over time.

The sample
The analysis was carried out on a balanced panel of 233 Italian banks and banking groups, selecting from the whole Italian banking system the ones for which all the needed data were available for the years from 2011 to 2017 on Orbis Bank Focus, and with an incidence of loans from 40% to 90%.c,d  The summary data are shown in Tables 1 and 2. The values in Table 1 show that the system experienced a progressive reduction in the riskiness of the assets from 2011 to 2017, as estimated by its average probability to default (Assets PD), and, starting from 2013, a progressive recapitalization.
Table 2 reports some details on the distribution of the same variables for 2017, showing a rather wide dimensional range, a high number of small banks and a signi¯cant diversi¯cation of both capitalization level and interbank exposures, which c Missing values is the main reason for exclusion.The average incidence of gross loans on total assets was around 60%.Just 38 banks reported an incidence of gross loans on total assets lower than 40%, mainly referring to entities classi¯ed as banks, even if their main activity is not the typical commercial banking.So, for avoiding a subjective selection, we excluded all banks with an incidence of gross loans on total assets lower than 40%.d The variables extracted from Orbis Bank Focus are Total transitional capital, Total assets, Bank deposits, Net loans and advances to banks.The assets PD is computed as in de Lisa et al. (2011), based on Total assets and Total risk-weighted assets À À À transitional or on some estimation of the latter based on CET1 value and ratio or on Tier1 value and ratio.are variously asymmetric.Overall, the sample is su±ciently diversi¯ed to validate the correlation e®ect and to show its impact on di®erent banking structures.

Uniform variation of correlation across all banks
As a ¯rst step, we analyzed the e®ect of correlation of banks' results on systemic risk.
In doing so, we ¯rstly veri¯ed the e®ects of correlation on the selected banking system and then detailed its e®ect on single banks.

System e®ects
The ¯rst part of this analysis aims to verify the e®ect of di®erent correlation levels on the whole system riskiness.
The Leave-One-Out simulation exercise is performed by uniformly setting the correlation to the common risk sources for all banks respectively to 40%, 50%, 60%, 70%, 80% and 90%.Theoretical statistics and literature report that more correlated shocks are expected to induce a lower number of crises, but more intense, and involving several banks at the same time.As previous literature (Zedda & Cannas 2020) reports that results are di®erent for distinct crises dimension, we focused our analysis on cases when the ¯nancial stability is signi¯cantly threatened; therefore, we selected for the crises with a total loss of more than 10 bn.euro.
Our results, reported in Fig. 1, con¯rm that while the stand-alone risk contributions due to the risk of idiosyncratic defaults are not signi¯cantly a®ected by correlation, contagion risks are highly and progressively enhanced by correlation, con¯rming its role of catalyst to contagion.
Table 3 reports the same results in table form.

E®ects on single banks
The stand-alone risk contributions, obtained without taking into account contagion e®ects, generate rather stable results as expected and already recorded for the entire system, with small variations, almost partially attributable to the uncertainty margin always present in Monte Carlo simulations.
It is instead interesting to analyze the e®ect of correlation on banks' risk contributions to contagion, which show very di®erent results (see Appendix A for details), partially due to the di®erent banks' dimensions, but also to other e®ects, as in the example presented in Table 4.
In this case, bank 62 reports the highest contagion risk contribution when the correlation level is set to 40%.However, as correlation increases, the di®erence from bank 133 lowers, and for a correlation of 90% is bank 133 the one reporting the higher contagion risk contribution.Fig. 1.Expected excess losses in case of crisis.Note that a higher correlation induces higher contagion risks.
Table 3. Leave-One-Out systemic risk contributions, by correlation level, th.€.This e®ect can be explained by the di®erent bank sensitivity to correlation, which brings bank 62 contributions to grow from 9.9 to 34, so around 3.5 times higher.In contrast, bank 133 sensitivity to correlation is substantially higher, bringing its contributions from 3.7 to 35.2, so 9.5 times higher.
What is less evident is why di®erent banks are characterized by di®erent sensitivity to correlation, and if these di®erent e®ects mainly depend on the considered bank correlation to the common factor or on the (average) whole system correlation to it.

Regression analysis
To understand which variable in°uences the bank sensitivity to correlation, we performed the other 10 sets of simulations, setting di®erent correlation levels for each bank.Furthermore, we computed a standard OLS regression on the simulated results (contagion risk contributions for each bank) in which the risk contribution of the i bank on simulation j, Sys ij , is set as a dependent variable, and explained by the same bank correlation coe±cient, corr ij , multiplied by its sensitivity coe±cient, i , and the average correlation of all the banks in the system corr avgj , multiplied by its sensitivity coe±cient, i .
Thus, the regression is based on the following equation: Results, as reported in Table 5, show that the average system correlation mainly in°uences each bank's risk contribution.The i coe±cients are signi¯cant in just a small number of cases, and its average t-ratio is of 0.31.In contrast, the i coe±cients are almost always highly signi¯cant, reporting an average t-ratio of 4.37, evidencing that average correlation is more important than direct correlation in determining contagion risk contributions for the considered sample.
The subsequent analysis is devoted to test the relationship between the loans' incidence on total assets and the comprehensive income correlation.For doing this, we performed an OLS regression for testing the explanatory power of loans incidence on the di®erent correlation levels of banks' comprehensive income (as detailed at the end of Sec. 3).
Results show that the comprehensive income correlation is signi¯cantly explained by the average loans share (Loans/TA, see Table 6), with a negative coe±cient, meaning that the higher the loans incidence on total assets in the system, the lower the correlation.e The same results are shown in Fig. 2, where the banks reporting a lower incidence of loans on total assets show a higher correlation coe±cient, and vice versa, banks with a higher incidence of loans show lower, and even negative, correlation.e The regression values only show that correlation on banks' results and their loans share are correlated among them.However, it is essential to remind that the banks' assets often include long-term loans, so the previous years' investment choices signi¯cantly in°uence banks' results.Consequently, it can be reasonable to consider that correlation on results is more likely to be the e®ect of portfolio choices than vice versa.In order to consider the possible e®ect of dimension and assets riskiness on the previous outcome, we computed a robustness check including as control variables the average assets riskiness (in terms of its average Probability to Default, PD) and the logarithm of the average total assets value (from 2011 to 2017).Table 7 presents the results, which con¯rm the role of loan incidence as the main driver of the comprehensive income correlation, with a negative e®ect.Dimension just shows a sig-ni¯cance at the lower level, while the riskiness of the assets is never signi¯cant.As a further test, we also included the income correlation squared values for testing for its nonlinear incidence.
Results presented in Table 8 and Fig. 3 show that the inclusion of the squared value of the loans incidence enhances the determination coe±cient, incidentally lowering the signi¯cance of dimension.

Policy Implications
Macro-prudential regulation aims to reduce the systemic risk and its negative impact on the real economy in case of crises through instruments that mitigate the losses transmission role of the banks.Academic studies have already signaled the tendency towards the progressively increasing importance of the common risk sources in determining banking systems riskiness.
Consequently, the theme is very signi¯cant, raising the question of how it is possible to reduce systemic risks when interventions have to be taken at single bank level, that is to say, how to drive macro e®ects just intervening at the micro level.In this sense, the empirical analysis reported above can provide useful information to policy-makers to address macro-prudential regulation.On one hand, regarding simulation exercise results, we can notice that systemic risk increases signi¯cantly as banks' correlation with the common risk sources rises.On the other hand, the regression results suggest that the traditional lending activity, by decreasing the correlation of the results over banks, also reduces contagion risks.
In fact, our empirical research adds new information on the systemic risk evaluation and suggests a way to reduce it, which can be achieved by pushing banks to raise their share of loans on total assets.To this end, one signi¯cant possibility within the regulation tuning relies on the correction of capital requirements for credit risk, taking into account the negative e®ects of correlation on systemic risk.
Brie°y, a reduction of risk weighting for loans, possibly balanced by symmetrical rising in the risk weighting of other and more correlated asset categories, can induce banks to devote a higher share of their assets to traditional lending.It goes in the same direction as the SME support factor f introduced by the European Commission in the recent update of the Basel regulatory framework.g

Conclusions
In the current macro-prudential regulation framework, policy-makers mainly focus on the role of interconnectedness in the stability of banking systems.
In this paper, we analyzed the role of traditional bank lending in terms of its e®ect on systemic risk, passing by its e®ect on banks' results correlation with common risk sources.Results show that systemic risk grows signi¯cantly as the correlation f It consists of a reduction factor for loans to small and medium enterprises of 0.7619.It aims to reduce capital requirements on exposures to ¯rms with a turnover of below EUR 50 million.between banks' results and common risk sources increases, and that banks devoting higher shares of their assets to traditional lending present a lower correlation with the common risk sources.
Regression results suggest that the e®ect of correlation is substantially neutral for each bank's stability as a single; they only show its e®ects on the contagion risk contributions, i.e. the risk for each bank to turn out a contagion vehicle within the system.
Interestingly, our empirical ¯ndings suggest that a higher loans' share on banks' total assets mitigates the crises propagation within the banking network and reduces, as a consequence, the systemic risk.This means that limiting the supervision of each bank stability as a single, as in the Basel II approach, or just considering systemic risk through the banks' interlinkages, as in Basel III, determines a signi¯cant lack of information and excludes one fundamental component of systemic risk.
Concerning policy implications, our empirical results imply that a banking regulation framework aimed to incentive the traditional lending activity can reduce systemic risk without a further increase of capitalization requirements, while contributing to an e®ective sustainment of the real economy.
Appendix A. Leave-One-Out contagion risk contributions, by correlation intensity, by bank.
:1Þ where i represents the weight of the common factor com s , and ffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 1 À 2 i p represents the weight of the idiosyncratic factor d is .The above formula evidences that com s and S. Zedda, M. Patan e & L. Miggiano 2050005-4 J. Fin.Mngt.Mar.Inst.2020.08.Downloaded from www.worldscientific.comby UNIVERSITY OF SIENA on 01/18/21.Re-use and distribution is strictly not permitted, except for Open Access articles.

Fig. 2 .
Fig. 2. Year-on-year correlation of comprehensive income and incidence of gross loans on total assets for a sample of 233 Italian banks.

Fig. 3 .
Fig. 3. Year-on-year correlation of comprehensive income and incidence of gross loans on total assets for a sample of 233 Italian banks with quadratic ¯t.

Fig
Fig. A.1.Evolution of systemic risk contributions over time from 2011 to 2017.

Table 5 .
Results of OLS regression of contagion risk contributions on correlation coe±cients.J. Fin.Mngt.Mar.Inst.2020.08.Downloaded from www.worldscientific.comby UNIVERSITY OF SIENA on 01/18/21.Re-use and distribution is strictly not permitted, except for Open Access articles.

Table 6 .
Regression of correlation of comprehensive income on the average loans share of total assets.

Table 7 .
Regression of income correlation to banks input variables.

Table 8 .
Regression of income correlation to banks' input variables.