# Credit Scoring in SME Asset-Backed Securities: An Italian Case Study

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{+}™ model proposed by Credit Suisse First Boston (CSFB 1997).

## 2. Literature Review

## 3. Empirical Analysis

**Kolmogorov-Smirnov (KS)**The KS coefficient according to Mays and Lynas (2004) is the most widely used statistic within the United States for measuring the predictive power of rating systems. The Kolmogorov-Smirnov curve plots the cumulative distribution of non-defaulted and defaulted against the score, showing the percentage of non-defaulted and defaulted below a given score threshold, identifying it as the point of greatest divergence. According to Mays and Lynas (2004), KS values should be in the range 20%–70%. The goodness of the model should be highly questioned when values are below the lower bound. Value above the upper bound should be also considered with caution because they are ‘probably too good to be true’. The Kolmogorov-Smirnov statistic for a given cumulative distribution function $F\left(x\right)$ is:

**Lorenz curve and Gini coefficient**In credit scoring, the Lorenz curve is used to analyze the model’s ability to distinguish between “good” (non-defaulted) and “bad” (defaulted), showing the cumulative percentage of defaulted and non-defaulted on the axes of the graph (Müller and Rönz 2000). When a model has no predictive capacity, there is perfect equality. The Gini Coefficient is widely used in Europe (Řezáč and Řezáč 2011), is derived from the Lorenz curve and calculates the area between the curve and diagonal in the Lorenz curve.

**Gini coefficient**The Gini coefficient is computed as:

**Receiver Operating Characteristic (ROC)**As reported by Satchel and Xia (2008), among the methodologies for assessing discriminatory power described in the literature the most popular one is the ROC curve and its summary index known as the area under the ROC (AUROC) curve. The ROC curve is created by plotting the true positive rate (TPR) against the false positive rate (FPR) at various threshold settings. The true-positive rate is also known as sensitivity and the false-positive rate is also known as the specificity. Specificity represents the ability to identify true negatives and can be calculated as 1 minus the specificity. The ROC therefore results from:

^{+}™ model on a representative sample of approximately 20,000 counterparties, of which 10,000 refer to loans terminated (repaid or defaulted) before the first pool cut-off date while the remaining 10,000 are active at the latest pool cut-off dates and are used to provide a forecast of the future loss profile of the portfolio.

^{+}™ can be applied to different types of credit exposure including corporate and retail loans, derivatives and traded bonds. In our analysis we implement it on a portfolio of SMEs credit exposures. It is based on a portfolio approach to modelling credit risk that makes no assumption about the causes of default, this approach is similar to the one used in market risk, where no assumptions are made about causes of market price movements. CREDITRISK

^{+}™ considers default rates as continuous random variables and incorporates the volatility of default rates to capture default rates level uncertainty. The data used in the model are: (i) credit exposures; (ii) borrower default rates; (iii) borrower default rate volatilities and (iv) recovery rates. In order to reduce the computational difficulties, the exposures are adjusted by anticipated recovery rates in order to calculate the loss in case of default event. We consider recovery rates provided by ED and include them in the database. The exposures, net of recovery rates, are divided into bands with similar exposures. The model assumes that each exposure has a definite known default probability over a specific time horizon. Thus

^{+}™ assumes that default events are independent, hence, the probability generating function for the whole portfolio is the product of the individual PGF, as shown in Equation (17)

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Figure A1.**The figure illustrates the relationship between Score (x-axis) and default probability (y-axis) for 2014H1 (Panel (

**a**)), 2014H2 (Panel (

**b**)), 2015H1 (Panel (

**c**)), 2015H2 (Panel (

**d**)), 2016H1 (Panel (

**e**)).

**Figure A2.**Master scale for the sample. We illustrate 2014H1 (Panel (

**a**)), 2014H2 (Panel (

**b**)), 2015H1 (Panel (

**c**)), 2015H2 (Panel (

**d**)), 2016H1 (Panel (

**e**)).

**Figure A3.**Master scale and borrower distribution for 2014H1(Panel (

**a**,

**b**)), 2014H2 (Panel (

**c**,

**d**)), 2015H1 (Panel (

**e**,

**f**)), 2015H2 (Panel (

**g**,

**h**)), 2016H1 (Panel (

**i**,

**j**)).

**Table A1.**The table shows the portfolio composition per rating across the pool cut-off dates. The distribution of counterparties is mainly concentrated in the intermediate rating classes.

2014H1 | 2014H2 | 2015H1 | 2015H2 | 2016H1 | |||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Rating | Freq. | Perc. | Cum. | Rating | Freq. | Perc. | Cum. | Rating | Freq. | Perc. | Cum. | Rating | Freq. | Perc. | Cum. | Rating | Freq. | Perc. | Cum. |

A | 4 | 0.01 | 0.01 | A | 31 | 0.11 | 0.11 | A | 57 | 0.25 | 0.25 | A | 106 | 0.81 | 0.81 | A | 42 | 0.41 | 0.41 |

B | 30 | 0.09 | 0.10 | B | 1250 | 4.52 | 4.63 | B | 1919 | 8.57 | 8.82 | B | 1306 | 10.03 | 10.84 | B | 95 | 0.92 | 1.33 |

C | 301 | 0.92 | 1.02 | C | 2519 | 9.11 | 13.74 | C | 8002 | 35.72 | 44.54 | C | 1506 | 11.56 | 22.41 | C | 523 | 5.06 | 6.39 |

D | 716 | 2.18 | 3.20 | D | 1288 | 4.66 | 18.39 | D | 7610 | 33.97 | 78.51 | D | 502 | 3.85 | 26.26 | D | 1562 | 15.12 | 21.50 |

E | 3498 | 10.65 | 13.85 | E | 7355 | 26.59 | 44.98 | E | 1775 | 7.92 | 86.43 | E | 1413 | 10.85 | 37.11 | E | 1149 | 11.12 | 32.62 |

F | 7272 | 22.15 | 36.00 | F | 12165 | 43.97 | 88.95 | F | 2060 | 9.20 | 95.63 | F | 6877 | 52.81 | 89.92 | F | 2988 | 28.92 | 61.54 |

G | 15679 | 47.75 | 83.75 | G | 2660 | 9.62 | 98.57 | G | 751 | 3.35 | 98.98 | G | 1163 | 8.93 | 98.85 | G | 3148 | 30.47 | 92.01 |

H | 4984 | 15.18 | 98.93 | H | 150 | 0.54 | 99.11 | H | 72 | 0.32 | 99.30 | H | 30 | 0.23 | 99.08 | H | 711 | 6.88 | 98.89 |

I | 153 | 0.47 | 99.40 | I | 82 | 0.30 | 99.41 | I | 115 | 0.51 | 99.81 | I | 39 | 0.30 | 99.38 | I | 32 | 0.31 | 99.20 |

L | 197 | 0.60 | 100.00 | L | 164 | 0.59 | 100.00 | L | 42 | 0.19 | 100.00 | L | 81 | 0.62 | 100.00 | L | 83 | 0.80 | 100.00 |

**Table A2.**The table shows rating (column 1), amount of non-defaulted loans (column 2), amount of defaulted (column 3), default frequency (column 4) and total number of loans included in the sample per rating class (column 5). We report the statistics for the different pool cut-off dates.

2014H1 | Non-Defaulted | Defaulted | pd_actual (%) | Total | 2014H2 | Non-Defaulted | Defaulted | pd_actual (%) | Total | |
---|---|---|---|---|---|---|---|---|---|---|

A | 4 | 0 | 0.00 | 4 | 31 | 0 | 0.00 | 31 | ||

B | 30 | 0 | 0.00 | 30 | 1229 | 21 | 1.68 | 1250 | ||

C | 298 | 3 | 1.00 | 301 | 2482 | 37 | 1.47 | 2519 | ||

D | 707 | 9 | 1.26 | 716 | 1267 | 21 | 1.63 | 1288 | ||

E | 3452 | 46 | 1.32 | 3498 | 7186 | 169 | 2.30 | 7355 | ||

F | 7169 | 103 | 1.42 | 7272 | 11819 | 346 | 2.84 | 12165 | ||

G | 15264 | 415 | 2.65 | 15679 | 2587 | 73 | 2.74 | 2660 | ||

H | 4810 | 174 | 3.49 | 4984 | 146 | 4 | 2.67 | 150 | ||

I | 134 | 19 | 12.42 | 153 | 58 | 24 | 29.27 | 82 | ||

L | 62 | 135 | 68.53 | 197 | 46 | 118 | 71.95 | 164 | ||

2015H1 | Non-Defaulted | Defaulted | pd_actual(%) | Total | 2015H2 | Non-Defaulted | Defaulted | pd_actual(%) | Total | |

A | 57 | 0 | 0.00 | 57 | 105 | 1 | 0.94 | 106 | ||

B | 1890 | 29 | 1.51 | 1919 | 1286 | 20 | 1.53 | 1306 | ||

C | 7825 | 177 | 2.21 | 8002 | 1478 | 28 | 1.86 | 1506 | ||

D | 7366 | 244 | 3.21 | 7610 | 491 | 11 | 2.19 | 502 | ||

E | 1742 | 33 | 1.86 | 1775 | 1377 | 36 | 2.55 | 1413 | ||

F | 2015 | 45 | 2.18 | 2060 | 6681 | 196 | 2.85 | 6877 | ||

G | 715 | 36 | 4.79 | 751 | 1142 | 21 | 1.81 | 1163 | ||

H | 69 | 3 | 4.17 | 72 | 30 | 0 | 0.00 | 30 | ||

I | 37 | 78 | 67.83 | 115 | 36 | 3 | 7.69 | 39 | ||

L | 8 | 34 | 80.95 | 42 | 25 | 56 | 69.14 | 81 | ||

2016H1 | Non-Defaulted | Defaulted | pd_actual% | Total | ||||||

A | 42 | 0 | 0.00 | 42 | ||||||

B | 95 | 0 | 0.00 | 95 | ||||||

C | 517 | 6 | 1.15 | 523 | ||||||

D | 1547 | 15 | 0.96 | 1562 | ||||||

E | 1136 | 13 | 1.13 | 1149 | ||||||

F | 2929 | 59 | 1.97 | 2988 | ||||||

G | 3050 | 98 | 3.11 | 3148 | ||||||

H | 695 | 16 | 2.25 | 711 | ||||||

I | 27 | 5 | 15.63 | 32 | ||||||

L | 38 | 45 | 54.22 | 83 |

**Table A3.**The table compares default probabilities estimated by the regression model (pd_model) and default frequencies (pd_actual) across the pool cut-off dates. The values of the two statistics are close, especially for the intermediate rating classes.

2014H1 | 2014H2 | 2015H1 | 2015H2 | 2016H1 | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

pd_model | pd_actual | pd_model | pd_actual | pd_model | pd_actual | pd_model | pd_actual | pd_model | pd_actual | |||||

A | 0.02 | 0.00 | 0.23 | 0.00 | 0.69 | 0.00 | 0.31 | 0.94 | 0.08 | 0.00 | ||||

B | 0.04 | 0.00 | 0.38 | 1.68 | 1.05 | 1.51 | 0.55 | 1.53 | 0.11 | 0.00 | ||||

C | 0.11 | 1.00 | 0.63 | 1.47 | 1.72 | 2.21 | 0.95 | 1.86 | 0.27 | 1.15 | ||||

D | 0.23 | 1.26 | 1.00 | 1.63 | 2.54 | 3.21 | 1.53 | 2.19 | 0.46 | 0.96 | ||||

E | 0.52 | 1.32 | 2.11 | 2.30 | 4.31 | 1.86 | 2.51 | 2.55 | 0.86 | 1.13 | ||||

F | 1.23 | 1.42 | 2.95 | 2.84 | 6.37 | 2.18 | 3.02 | 2.85 | 2.15 | 1.97 | ||||

G | 2.78 | 2.65 | 6.55 | 2.74 | 8.90 | 4.79 | 5.74 | 1.81 | 3.19 | 3.11 | ||||

H | 5.34 | 3.49 | 9.09 | 2.67 | 13.12 | 4.17 | 9.92 | 0.00 | 6.02 | 2.25 | ||||

I | 13.77 | 12.42 | 17.85 | 29.27 | 24.81 | 67.83 | 16.26 | 7.69 | 14.54 | 15.63 | ||||

L | 35.87 | 68.53 | 38.72 | 71.95 | 35.17 | 80.95 | 28.42 | 69.14 | 31.45 | 54.22 |

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1. | The list of the ECB templates is available at https://www.ecb.europa.eu/paym/coll/loanlevel/transmission/html/index.en.html. |

2. | The ECB and the national central banks of the Eurosystem have been lending unlimited amounts of capital to the bank system as a response to the financial crisis. For more information see: https://www.ecb.europa.eu/explainers/tell-me-more/html/excess_liquidity.en.html. |

3. | A default shall be considered to have occurred with regard to a particular obligor when either or both of the following have taken place: (a) the institution considers that the obligor is unlikely to pay its credit obligations to the institution, the parent undertaking or any of its subsidiaries in full, without recourse by the institution to actions such as realising security; (b) the obligor is past due more than 90 days on any material credit obligation to the institution, the parent undertaking or any of its subsidiaries. Relevant authorities may replace the 90 days with 180 days for exposures secured by residential or SME commercial real estate in the retail exposure class (as well as exposures to public sector entities). |

4. | CRIF Ratings is an Italian credit rating agency authorized to assign ratings to non-financial companies based in the European Union. The agency is subject to supervision by the ESMA (European Securities and Markets Authority) and has been recognized as an ECAI (External Credit Assessment Institution). |

5. | The complete list of fields definitions and criteria can be found at https://www.ecb.europa.eu/paym/coll/loanlevel/shared/files/RMBS_Taxonomy.zip?bc2bf6081ec990e724c34c634cf36f20. |

6. | The Credit Risk Plus model assumes independence between default events. Therefore, the probability generating function for the whole portfolio corresponds to the product of the individual probability generating functions. |

7. | The approximation ignores terms of degree 2 and higher in the default probabilities. The expression derived from this approximation is exact in the limit as the PD tends to zero, and five good approximations in practice. |

8. |

**Figure 1.**Panel (

**a**) illustrates the relationship between score and PD. For each company we compute a score based on the logistic regression output that is an indication of individual PD. Panel (

**b**) shows the master scale. This is an indicator of the counterparty’s riskiness level. For its creation, we follow the approach presented by Siddiqi (2017). The default probability is linearized through the calculation of the natural logarithm, then the vector of the logarithms of the PD is divided into 10 equal-sized classes and the logarithms of the cut-offs of each class is converted to identify the cut-offs to be associated with each scoring class with an exponential function.

**Figure 2.**Panel (

**a**) illustrates the Kolmogorov-Smirnov curve and the associated statistics for the first pool cut-off date. We show that the KS statistic associated to a score of $623.21$ is $23.8\%$. Panel (

**b**) reports the ROC curve and the AUROC value for the first report date. Table 6 reports AUROC, KS statistic and KS score for the entire sample.

**Figure 3.**Panel (

**a**) reports the final master scale obtained for the first pool cut-off date. To create the master scale we linearize the PD vector through the calculation of the natural logarithm, then this is divided into 10 equal classes and we convert the log of the cut-off of each class in order to identify the cut-off to be associated with each score with the exponential function. Panel (

**b**) confirms the frequency of borrowers for each class. In the right y-axis we indicate the default probability associated for each class and in the left y-axis is indicated the frequency of the loans.

**Figure 4.**Considering the variable Seniority (field AS26 in the ECB template) we divide secured from unsecured loans. Panel (

**a**) reports the box plot for the secured loans included in the total sample (taking into account all the pool cut-off dates), Panel (

**b**) shows the box plot for unsecured loans. It is clear that banks expect to recover more from secured loans compared to unsecured ones.

**Figure 5.**The Figure shows the box plot of the recovery rates computed by the banks divided into the rating classes. We note that the RR decreases from A to L, even though not monotonously.

**Figure 6.**The figure illustrates the loss distribution for unactive loans at the pool cut-off date 2014H1 (Panel (

**a**)) and for active loans at the report date 2016H1 (Panel (

**b**)). We indicate in the figure loss distribution (black solid line), real loss portfolio loss (black dash-dot line), EL −$\sigma $ (blue dotted line), EL (blue dash-dot line), EL + $\sigma $ (thick blue dash-dot line), 99th percentile (red solid line) and 95th percentile (red dotted line). It is possible to calculate the real portfolio loss only on inactive loans, therefore this threshold is present only in Panel (

**a**).

**Table 1.**The table shows the amount of non-defaulted and defaulted exposures for each pool cut-off date. We observe that the average default rate per each reference date remains constant and is equal to $2.84\%$ over the entire sample. We account only for the loans that are active in the pool cut-off date and include the loans that defaulted between two pool cut-off dates. In the case of the first report date, we consider the defaults that occurred from 2011, the date of securitization of the pool, until the first half of 2014, due to missing information on the performance of the securitized pool prior to this date. We analyze in total 106,257 loans granted to SMEs.

Pool Cut-Off Date | Non-Defaulted | Defaulted | % Default | Tot. |
---|---|---|---|---|

2014H1 | 31930 | 904 | 2.75 | 32834 |

2014H2 | 26851 | 813 | 2.94 | 27664 |

2015H1 | 21724 | 679 | 3.03 | 22403 |

2015H2 | 12651 | 372 | 2.86 | 13023 |

2016H1 | 10076 | 257 | 2.49 | 10333 |

Tot. | 103232 | 3025 | 2.84 | 106257 |

**Table 2.**The table shows the amount of collaterals, loans and borrowers included in the sample for each pool cut-off date. The dataset links together borrower, loan and collateral. In total 159,641 collaterals are associated with 117326 loans belonging to 106,257 companies.

Pool Cut-Off Date | Collateral Database | Loan Database | Borrower Database |
---|---|---|---|

2014H1 | 53,418 | 36,812 | 32,834 |

2014H2 | 45,694 | 30,774 | 27,664 |

2015H1 | 34,583 | 24,640 | 22,403 |

2015H2 | 14,472 | 14,000 | 13,023 |

2016H1 | 11,474 | 11,100 | 10,333 |

Tot. | 159,641 | 117,326 | 106,257 |

**Table 3.**The table shows the information value computed for each variable included in the sample. We report the statistic associated to the variable for each pool cut-off date. Since not all the variables inserted in the regression can be considered strong predictors of borrower’s default we decide to insert in the regression those variables that have a IV superior to 0.01, in the lack of other, better information.

Variable | 2014H1 | 2014H2 | 2015H1 | 2015H2 | 2016H1 |
---|---|---|---|---|---|

Interest Rate Index | 0.04 | 0.08 | 0.01 | 0.00 | 0.00 |

Business Type | 0.02 | 0.05 | 0.02 | 0.03 | 0.02 |

Basel Segment | 0.00 | 0.01 | 0.00 | 0.00 | 0.01 |

Seniority | 0.09 | 0.08 | 0.02 | 0.12 | 0.29 |

Interest Rate Type | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |

Nace Code | 0.05 | 0.01 | 0.01 | 0.01 | 0.07 |

Number of Collateral | 0.00 | 0.00 | 0.03 | 0.00 | 0.00 |

Weighted Average Life | 0.26 | 0.27 | 0.22 | 0.16 | 0.37 |

Maturity | 0.00 | 0.08 | 0.00 | 0.08 | 0.00 |

Payment ratio | 0.11 | 0.08 | 0.14 | 0.09 | 0.10 |

Loan To Value | 0.10 | 0.08 | 0.07 | 0.06 | 0.11 |

Geographic Region | 0.01 | 0.00 | 0.02 | 0.01 | 0.03 |

**Table 4.**The table shows per each LTV class (column 1) the amount of non-defaulted loans (column 2), defaulted loans (column 3); probability, computed as the ratio between non-defaulted and defaulted (column 4) and Weight of Evidence (column 5). As we can see the application of the MAPA algorithm allows to cut the variable into classes with a monotone WOE. The table confirms the relation between LTV and WOE. We show that as the LTV increases the WOE decreases as well as the probability (odds ratio) meaning that the borrower is riskier. For each computed class we associate a score, meaning that a borrower with a lower LTV, i.e., in the third class (0.333–0.608) is associated with a score higher (less risky) compared to a borrower in the fourth class. For sake of space we report the results only for the third pool cut-off date but the same considerations could also be carried out for the other report dates.

LoanToValue 2015H1 | Non-Defaulted | Defaulted | Probability | WOE |
---|---|---|---|---|

0–0.285 | 3383 | 67 | 50.49 | 0.35 |

0.285–0.333 | 1523 | 31 | 49.12 | 0.33 |

0.333–0.608 | 3531 | 89 | 39.67 | 0.11 |

0.608–0.769 | 3357 | 95 | 35.33 | 0.002 |

0.769–1 | 2074 | 77 | 26.93 | −0.26 |

1–inf | 2904 | 117 | 24.82 | −0.35 |

Tot. | 16772 | 476 | 35.23 |

**Table 5.**We illustrate in the table the coefficient and the significance of the variables included in the regression. We denote by *** the significance level of 1%, with ** the level of 5%. The table reports the number of observations, Chi

^{2}-statistic vs. constant model and p-value.

Variable | 2014H1 | 2014H2 | 2015H1 | 2015H2 | 2016H1 |
---|---|---|---|---|---|

Coefficient | Coefficient | Coefficient | Coefficient | Coefficient | |

(int.) | 3.550 *** | 3.481 *** | 3.456 *** | 3.523 *** | 3.652 *** |

InterestRateIndex | 0.698 *** | ||||

Seniority | 1.489 *** | 1.493 *** | 0.598 | 1.325 *** | 0.944 *** |

Code_Nace | 1.048 *** | 0.952 *** | 0.798 ** | 0.927 ** | 0.947 *** |

WeightedAverageLife | 1.007 *** | 0.953 *** | 1.168 *** | 0.912 *** | 0.798 *** |

Payment_Ratio | 2.456 *** | 2.296 *** | 1.482 *** | 2.300 *** | 2.253 *** |

Geographic_Region | 1.675 *** | 1.405 *** | 1.432 *** | 0.903 *** | |

Observations | 32834 | 27664 | 22403 | 13023 | 10333 |

Chi^{2}-statistic vs. constant model | 670 | 541 | 373 | 190 | 222 |

p-value | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |

**Table 6.**The table reports Kolmogorov-Smirnov statistic, KS score and the area under the ROC curve for the analyzed pool cut-off dates. We can observe that the statistics differs over the sample, due to the different loans included in the pool that changed over the period.

Statistics | 2014H1 | 2014H2 | 2015H1 | 2015H2 | 2016H1 |
---|---|---|---|---|---|

Area under ROC curve | 0.66 | 0.62 | 0.62 | 0.60 | 0.68 |

KS statistic | 0.23 | 0.18 | 0.18 | 0.15 | 0.27 |

KS score | 623.21 | 621.4 | 636.43 | 545.84 | 632.18 |

**Table 7.**The table reports Kolmogorov-Smirnov statistic, KS score and the area under the ROC curve for the out-of-sample. We can observe that the statistics differs over the sample, due to the different loans included in the pool that changed over the period.

Statistics | 2014H1 | 2014H2 | 2015H1 | 2015H2 | 2016H1 |
---|---|---|---|---|---|

Area under ROC curve | 0.68 | 0.62 | 0.62 | 0.63 | 0.68 |

KS statistic | 0.27 | 0.17 | 0.17 | 0.18 | 0.27 |

KS score | 610.76 | 654.45 | 662.80 | 673.09 | 628.56 |

**Table 8.**The table indicates rating (column 1 and 6), amount of non-defaulted exposures (column 2), amount of defaulted loans (column 3), sample default frequency (column 4) and total loan amount in the first pool cut-off date. Column 7 reports the default probability derived from the logistic regression and column 8 reports the actual frequency of default and is equal to column 4. What we can observe is that the model is able to compute the cut-offs in a way that the default frequencies are monotone increasing from A-rated to L-rated. We report the statistics for the entire sample in Appendix A.

Rating 2014H1 | Non-Defaulted | Defaulted | pd_actual (%) | Total | pd_estimate | pd_actual | |
---|---|---|---|---|---|---|---|

A | 4 | 0 | 0.00 | 4 | A | 0.02 | 0.00 |

B | 30 | 0 | 0.00 | 30 | B | 0.04 | 0.00 |

C | 298 | 3 | 1.00 | 301 | C | 0.11 | 1.00 |

D | 707 | 9 | 1.26 | 716 | D | 0.23 | 1.26 |

E | 3452 | 46 | 1.32 | 3498 | E | 0.52 | 1.32 |

F | 7169 | 103 | 1.42 | 7272 | F | 1.23 | 1.42 |

G | 15264 | 415 | 2.65 | 15679 | G | 2.78 | 2.65 |

H | 4810 | 174 | 3.49 | 4984 | H | 5.34 | 3.49 |

I | 134 | 19 | 12.42 | 153 | I | 13.77 | 12.42 |

L | 62 | 135 | 68.53 | 197 | L | 35.87 | 68.53 |

**Table 9.**The table shows the average recovery rate derived from the field AS37 of the ECB template. We can see that the RR are decreasing from A-rated to L-rated companies, even though not monotonously.

Rating | Average Recovery Rate (%) |
---|---|

A | 87.5 |

B | 86.6 |

C | 86.7 |

D | 83.8 |

E | 75.6 |

F | 72.5 |

G | 75.7 |

H | 77.4 |

I | 70.3 |

L | 62.5 |

**Table 10.**The table reports rating (column 1), mean and standard deviation of the estimated PD from the logistic regression (column 2 and 3), mean and st.dev. of the default frequencies in the sample (column 4 and 5). We use the estimated PD derived from the logistic regression and the Recovery Rates to calculate the loss distribution of the portfolio with the CREDITRISK

^{+}™ model.

Rating | Estimate | Frequency | ||
---|---|---|---|---|

Mean (%) | st.dev (%) | Mean (%) | st.dev (%) | |

A | 0.27 | 0.26 | 0.19 | 0.38 |

B | 0.43 | 0.41 | 0.94 | 0.77 |

C | 0.74 | 0.64 | 1.54 | 0.45 |

D | 1.15 | 0.92 | 1.85 | 0.79 |

E | 2.06 | 1.51 | 1.83 | 0.55 |

F | 3.15 | 1.94 | 2.25 | 0.55 |

G | 5.43 | 2.52 | 3.02 | 0.98 |

H | 8.70 | 3.15 | 2.51 | 1.42 |

I | 17.45 | 4.41 | 26.57 | 21.84 |

L | 33.93 | 4.02 | 68.96 | 8.61 |

**Table 11.**The table illustrated the capital exposed to risk and the thresholds for loss of the portfolio with unactive loans (either repaid or defaulted) at the pool cut-off date of 2014H1. The capital exposed to risk is calculated as the sum of all the portfolio exposures net of recovery rates computed by banks and reported by ED. The total net capital is therefore 48 million euro, with an expected loss (EL) of 2.66 million. The table reports the expected loss threshold (EL ± $\sigma $), 95th and 99th percentile loss.

Threshold | Amount (€) | Percentage (%) |
---|---|---|

Capital exposed to risk | 48922828 | 100.00 |

EL − $\sigma $ | 1991170 | 4.07 |

EL | 2661592 | 5.44 |

EL + $\sigma $ | 3332014 | 6.81 |

95th percentile | 3894574 | 7.96 |

99th percentile | 4630839 | 9.46 |

**Table 12.**The table reports the capital exposed to risk and the thresholds for loss of the portfolio with active loans at the pool cut-off date of 2016H1. The capital exposed to risk is calculated as the sum of all the portfolio exposures net of recovery rates. The total net capital is 447 million Euro, with an expected loss (EL) of 5.72 million. The table reports the expected loss threshold (EL ±$\sigma $), 95th and 99th percentile loss.

Threshold | Amount (€) | Percentage (%) |
---|---|---|

Capital exposed to risk | 247841024 | 100.00 |

EL − $\sigma $ | 4026790 | 1.62 |

EL | 5729076 | 2.31 |

EL + $\sigma $ | 7431362 | 2.99 |

95th percentile | 8828005 | 3.56 |

99th percentile | 10608768 | 4.28 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Bedin, A.; Billio, M.; Costola, M.; Pelizzon, L. Credit Scoring in SME Asset-Backed Securities: An Italian Case Study. *J. Risk Financial Manag.* **2019**, *12*, 89.
https://doi.org/10.3390/jrfm12020089

**AMA Style**

Bedin A, Billio M, Costola M, Pelizzon L. Credit Scoring in SME Asset-Backed Securities: An Italian Case Study. *Journal of Risk and Financial Management*. 2019; 12(2):89.
https://doi.org/10.3390/jrfm12020089

**Chicago/Turabian Style**

Bedin, Andrea, Monica Billio, Michele Costola, and Loriana Pelizzon. 2019. "Credit Scoring in SME Asset-Backed Securities: An Italian Case Study" *Journal of Risk and Financial Management* 12, no. 2: 89.
https://doi.org/10.3390/jrfm12020089