Impact of Covid-19 on SME portfolios in Morocco: Evaluation of banking risk costs and the effectiveness of state support measures

This study proposed a method for constructing rating tools using logistic regression and linear discriminant analysis to determine the risk profile of SME portfolios. The objective, firstly, is to evaluate the impact of the crisis due to the Covid-19 by readjusting the profile of each company by using the expert opinion and, secondly, to evaluate the efficiency of the measures taken by the Moroccan state to support the companies during the period of the pandemic. The analysis in this paper showed that the performance of the logistic regression and linear discriminant analysis models is almost equivalent based on the ROC curve. However, it was revealed that the logistic regression model minimizes the risk cost represented in this study by the expected loss. For the support measures adopted by the Moroccan government, the study showed that the failure rate (critical situation) of the firms benefiting from the support is largely lower than that of the non-beneficiaries.


INTRODUCTION
The Covid-19 gave rise to a cessation of activity in several economic sectors, which generated a wave of company failures, increasing the rate of default. The intervention of the public power to safeguard employment and guarantee the continuity of activities helped to minimize the risk and reduce the failure of companies.
In this context, rating models designed on the basis of data from a normal economic environment give biased results because the probability of default ( ) PD calculated by the model does not correspond to the reality imposed by the crisis. This imposes the readjustment of the risk profile of the portfolio by using different techniques such as the Bayesian approach or the expert's opinion. This paper proposes a Malus system that allows readjusting the risk profile of the portfolio by taking into account the PD conditioned by the intervention of the public power.
To determine the impact of the crisis and to evaluate the effectiveness of state intervention, this paper studied the downgrading of the rating of a portfolio composed of small and medium-sized enterprises of a bank in Morroco and the variation of the provision for expected loss

LITERATURE REVIEW AND HYPOTHESES
This paper defines the approach to the construction of rating tools and the determination of the empirical probability of default by class by two techniques which are the LR and . LDA The use of linear discriminant analysis for solvency modeling goes back to the 1960s with the research of Altmane (1967). The use of this technique has later attracted the interest of several researchers such as Deakin (1972). It continues to be of interest to researchers such as Habachi et al. (2019) who combined the LDA and expert opinion, and Svabova et al. (2020) who combined LR and LDA to determine models of failure prediction for SMPs.
As far as logistic regression is concerned, the first studies were started in the 1980s. However, this is still the most common technique for modeling the default. Indeed, several recent studies have addressed this area such as Madar (2014), Benbachir and Habachi (2018), and Zizi et al. (2020).
The explanation of the failure is made by variables specific to each company. They can be quantitative, qualitative, or macroeconomic variables. The qualitative variables have been studied by Courdec and Renault (2005), Grunert  In addition, several researchers have compared modeling approaches to determine the best performing models such as Altman et al. (1994), who compared linear discriminant analysis and neural networks, Worth and Cronin (2003), who compared linear discriminant analysis and logistic regression in the health domain, and Pavlyshenko (2016), who studied learning machines and linear and the Bayesian logistic regression for failure prediction.
Credit rating has been studied by Figini  Measuring the performance of models is a major concern for researchers. This study uses the ROC curve. Indeed, the ROC curve has been studied by several researchers to evaluate the performance of prediction models such as Bradley (1997) for the evaluation of machine learning algorithms, Satchel and Xia (2008), who applied the use of the curve in the evaluation of scoring, and Engelmann et al. (2003), who used the ROC curve to evaluate the discriminative power of scoring systems.

METHODOLOGY
Credit risk is defined as the probability that a borrower will not meet its obligations in accordance with the contractual terms. This probability is determined for a one-year horizon.
A counterparty is considered to be in default if these receivables are reclassified as distressed, particularly if there is the persistence of unpaid payments for a period exceeding 90 days, three unpaid installments, a significant decrease in sales, reclassification of the case as a contentious claim, chronic overage of authorizations, expired authorizations not renewed for a period exceeding 90 days, and account freeze (account with no activity for a period exceeding 180 days). Under IFRS 9, the expected loss is covered by provisions and must be accounted for. The same orientation has been adopted by the Basel Committee (Bank for International Settlements, 2015).
In the IRB -foundation, determination of the PD is the most important component. This section presents the methodology adopted to model the PD by LR approach and LDA approach and to construct the rating tools related to them, then the approach used to readjust the portfolio by the expert opinion and finally to determine the .

EL
The variables ( ) , j X 1,..,12 j = used in this study are defined as follows:   • 4 : X ROE is defined as the ratio of net income to equity.
• 5 : X The financial costs are defined as the ratio between the financial costs and 1 . X • 6 : X The debt ratio is defined as the ratio of medium and long-term debt to equity.
The proportion of current assets financed by equity is defined as the ratio of the remaining equity after financing fixed assets divided by current assets.
• 8 : X The capital structure is defined as the ratio of equity to total liabilities. • 9 : X The turnover of fixed assets and requirement working capital (current assets -current liabilities) is defined by the ratio between 1 X and the sum of fixed assets and requirement working capital.

Logistic regression
The correlation between a firm's default and each variable i The estimation of the parameters is made by the maximum likelihood method available by software such as SPSS and XL-STAT.

S inv χ >
The model adopted can predict the classification of companies. However, two situations must be distinguished: 1. The firms are classified by the model in their current class. Healthy firms are considered to be "true healthy" and firms in default are considered to be "true default". N is the number of good classified companies.
2. The firms that are not classified by the model in their current class. For healthy firms classified as defaults, they are considered "false default", while those in default classified as healthy are considered "false healthy".
The classification matrix A is defined by: .  The explanatory variables to be retained are determined by univariate analysis between the default and each variable. In fact, only the variables whose ROC curve is greater than 0.60 are retained.

True healty false healthy
The validate the multivariate model is made by the following tests, whose hypothesis formulation, statistical tests, and decision rules (the Wald test, the likelihood ratio test, and the Hosmer-Lemeshow test) are presented in Appendix A.

Linear discriminant analysis (LDA)
The firms must be classified by the discriminate function into two classes "healthy" and "default". In 1936, Fisher (1936) proposed a score function that predicts the classification in the two classes. This function, also called score function, is defined as:  The univariate analysis allows determining the discriminating variables. Indeed, a variable is discriminant if the means of the group is equal. The null hypothesis H 0 says that "equality of group means.". The statistical test is defined by the Fisher's Ratio. The decision rule is to reject H 0 if p-value is less than 5%. The functions at group centroids allow calculating the mean of scores of each group:

The rating models
Based on the score function, this study defines two rating tools consisting of the following classes: • Class 1: class of companies with an excellent financial position and very low default risk. The score is high and exceeds 86.
• Class 2: class of companies with a very good financial situation and very good quality characters. The score is high and exceeds 76.
• Class 3: class of companies with a good financial situation and good quality characters. The score is high and exceeds 65.
• Class 4: class of companies with a relatively good financial situation and good quality characters. The score is high and exceeds 55. 1 High commissioner of planning, Kingdom of Morocco.
• Class 5: class of companies with a medium financial situation and relatively good quality characters. The score is high and exceeds 46.
• Class 6: class of companies with a medium financial situation and medium quality characters. The score is high and exceeds 40.
• Class 7: class of companies with a critical financial situation. The score is high and exceeds 30.
• Class 8: class of companies with a very critical financial situation. The score is lower than 30.
The rating score of the company ( ) where i S is the score assigned to the company ( ) i by the classification function.
For each class , C , the PD of the firms in that The probability of default per class is defined as the ratio of the number of defaulting firms in the class to the total number of firms in that class.

Impact of Covid-19 adjustment of the portfolio risk profile
The impact of the Covid-19 crisis has far exceeded the recession generated by the 2008 financial crisis. Indeed, the consequences of this crisis are very important for the real and financial economy, whose first effects have affected the secondary and tertiary sectors and the financial markets.
In Morocco, the crisis is particularly penalizing the activities of very small and medium enterprises. According to a first survey carried out by the HCP 1 in April 2020 among enterprises, the production units temporarily or permanently out of the business of VSE and SME represent respectively 72% and 26% of enterprises in each category.
In this context, the Moroccan state has focused its policy on two pillars, namely solidarity and the dynamism of the banking sector. For the first pillar, the crisis plan is based on the establishment of the Covid-19 fund, which has made it possible to mobilize the necessary funds to finance containment, economic recovery, the vaccination campaign, etc. For the second pillar, the policy adopted is based on the establishment of a guarantee fund managed by the CGC 2 with the objective of maintaining jobs and activity through the distribution of "Oxygen" credit, followed by an action aimed at the relaunching of the economy through the distribution of "Relaunch" credit. The banking action within this framework had an objective of approximately 80 million MAD destined to finance 140,000 eligible companies.
The use of statistical data for the construction of the rating tool is made on the basis of data concerning the 2019 financial year because the data concerning 2020 are impacted by the crisis. This situation leads to a gap between the rating assigned by the rating tool and the real profile of the rated companies.
To correct this gap, this study readjusted the rating model using expert opinion to define a malus system that takes into account the state support and the classification of companies into two classes: "healthy" and "critical" conditional on the state support. Therefore, in the function of the recourse to state support and the company's situation, the rating of the company will be readjusted using the following malus: • Healthy situation without state support: Maintaining the class.

• Healthy situation with state support:
Degradation of a single class.
• Critical situation without state support: Degradation of two classes.
• Critical situation with state support: Degradation of three classes or default. 2 Central guarantee fund, Kingdom of Morocco.

The cost of risk
This study evaluates the cost of risk by the expected loss (EL) defined by the multiplication of the three components of credit risk, namely , PD EAD , and .
LGD This is the average loss associated with a credit at each date of its term.

The database
The sample used is composed of 721 small and medium-sized enterprises in Morocco. Healthy enterprises represent 92.51% (667 enterprises) and failing enterprises represent 7.49% (54 enterprises).

Univariate analysis by logistic regression
The results of the Wald test and the discriminant power of each variable are presented in

Univariate analysis by linear discriminant analysis
The results of the equality means of group test are presented in Table B3 (Appendix B). The univariate analysis shows that 1 , X 3 , X 6 , X 7 , X 9 , X 12 X do not have significant discriminating power because the p-value is higher than 0.05. However, this study uses the variables that increase the discriminating power of the model.  The results of the Hosmer-Lemeshow test show the p-value equal to 0.08. Consequently, the 0 : H "the model is correct" is accepted.
In terms of discriminatory power, the model is acceptable because the ROC curve is equal to 78.9%.
The estimation of the parameters allows determining the score function. Indeed, the ( )

The rating grid
The distribution of the companies in the sample and PD per class is presented in Table 1. The portfolio adjustment is based on expert opinion. The experts associated with this study are the credit portfolio managers who manage the sample of companies used. Expert opinion determines which companies have benefited from state support and which have not by class and classifies them as healthy or critical companies which allow determining the downgrading of the companies in the different rating classes.
The classification of companies according to state support and their solvency is given in Table 2.
The number of companies benefiting from state support is equal to 565 which represents 84.7% of the portfolio. Among these companies, 503 are considered healthy, which represents 89% of the portfolio supported by the state. The latter covers several sectors such as trade which represents 50.09% (283) private educational institution which represents 11.15% (63), Buildings and public works which represents 9.56% (54) tour-ism 7.79% (44), services 11.50% (65) and others with 9.91% (56).
The rate of critical enterprises that benefited from state support is 12.32%, which is much lower than the rate of critical enterprises that did not benefit from state support, which is 75.86%. This means that the state action has cushioned the rate of defiance due to the Covid-19 crisis.
This assessment is confirmed for classes 6, 7, and 8 by the fact that the criticality rate for companies that have benefited from state support is 29.57% whereas it is 100% for companies that have not benefited from state support.
The downgrading of the companies in the different rating classes by each model is presented in Tables 3 and 4.
The portfolio adjustment resulted in 32 companies being classified as default.  The portfolio adjustment resulted in 22 companies being classified as default.

The cost of risk
The portfolio studied represents a total use of out- Knowing that the CCF is 75% , the LGD is 45% and that the PD per class is given in Table 1, the total expected loss ( ) EL by class per logistic regression model is presented in Table 5. Table 5 shows that it is necessary to make a provision for the debts of companies reclassified as defaults, i.e. 501.79 million MAD, as well as the expected loss.

Comparison of two models
The discriminating power shows a small difference of 0.7% between the two models. Indeed, the ROC curve of the logistic regression and linear discriminant analysis models are respectively 78.9% and 78.2% .
As regards the , EL the logistic regression model generates a lower expected loss (215.87 million MAD) than that generated by the linear discriminant analysis model (261.54 million MAD). The variation is 21.32%.
After readjusting the risk profile of the portfolio, the provision increased as it covers the expected loss and the defaulted debts. Indeed, it reached 756.77 million MAD for the logistic regression model against 917.32 million MAD for the linear discriminant analysis, i.e. a variation of 21.22%.
The Covid-19 crisis has led to a catastrophic increase in provisions. Indeed, they are 250.56% and 250.73% respectively for the LR and the LDA models.

DISCUSSION
The use of expert opinion showed that the risk profile of the portfolio had deteriorated significantly due to the Covid-19 crisis. Tables 4 and 5 show that the readjustment of the portfolio resulted in the reclassification of high-risk businesses to default. Table 3 shows that the use by banks of the financing possibilities guaranteed by the state for economic stimulation has made it possible to reduce the rate of company failures since the rate of companies in a critical situation that have benefited from state support is lower than that of companies that have not benefited from state support.
Before adjustment, the model based on logistic regression is relatively better than the one based on linear discriminant analysis with a small difference of about 0.7%. Despite this small difference, the two models generate a totally different expected loss since the model based on linear discriminant analysis generates a 21.32% higher expected loss.
After readjustment, the global provision increased by 250%. However, the model based on linear discriminant analysis generates an aggregate provision that is 21.22% higher than the logistic regression.

CONCLUSION
This study examines two hypotheses, namely the impact of modeling on the cost of risk under IFRS 9 and the effectiveness of the measures taken by the state for economic recovery. For both hypotheses, this study constructs two rating tools using two techniques, which are logistic regression and linear discriminant analysis.

APPENDIX A
The Likelihood ratio test The likelihood ratio test is presented as follows: