# How to Rate the Financial Performance of Private Companies? A Tailored Integrated Rating Methodology Applied to North-Eastern Italian Districts

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Basel Agreements and the Efficiency of Debt-Capital Markets: A Literature Review

## 3. IRM: Our Alternative Model for Assessing the Return-to-Risk Performance of Firms

#### 3.1. Understanding the Methodological Limits to Bypass Standard Practices

_{i}stands for the achieved utility; ${R}_{i}$ is the expected return rate; ${\sigma}_{i}^{2}$ its volatility (i.e., variance); $A$ is a measure of the investor’s marginal risk aversion.

_{F}); in fact, such a gap (i.e., ${R}_{F}^{*}-{R}_{F})$ incentivizes the investor to switch to risky assets, according to her/his specific degree of risk tolerance. The higher the risk aversion, the wider the gap must be, while the larger the gap between the certainty equivalent and R

_{F}, the greater the asset value is for a given risk aversion.

_{s}) and the latter to the asset-specific risk (A

_{ε}). Accordingly, the investor’s utility/certainty equivalent can be split, as in Equation (4):

_{s}and A

_{ε}, when the stochastic independence of the two sources of risk (systematic and firm specific) is assumed. However, no theories provide definitive conclusions about the relations between A, A

_{s}, and A

_{ε}(Mantovani 1998). In fact, if the investor can really diversify their portfolio, the diversifiable risk becomes irrelevant, along with A

_{ε}. An alternative explanation can also be considered: in large markets with massive volumes of transactions, the A

_{ε}of the different agents may clear each other. In other words, each transaction contributes (to a different extent) to a zero-utility game for the market as a whole.

#### 3.2. The Intuition: Substitute the Certainty Equivalent with the Confident Equivalent

_{ε}diverts from zero and the total risk aversion (A) must be considered. The risk-free rate is no longer the cornerstone that can be referred to in order to extract the utility as provided by the certainty equivalent.

**A**”. To deal with (i), one could use a CAPM-compliant approach, such as the zero-beta model by Black (1972). This allows the impact of the firm-specific risk to be embedded as well, if a short-fall approach is used to identify the investor’s risk aversion. To deal with (ii) and (iii), we propose considering a

**confident**

**equivalent**return (i.e., a minimum return threshold that must be achieved according to a certain confidence level) instead of finding the certainty equivalent. At a methodological level, this approach simplifies the estimations, since the confidence level can be exploited ex ante (as in the Basel agreement).

- (a)
- $E\left({R}_{i}\right)\ge {R}_{f}+S({\beta}_{i}{\sigma}_{m})$ i.e., the standard CAPM one (S = Sharpe ratio =$\text{}\frac{{R}_{m}-{R}_{f}}{{\sigma}_{m}}$).
- (b)
- $E\left({R}_{i}\right)\ge {R}_{f}{}^{*}+A{\sigma}_{i}{}^{2}$ i.e., the standard Lintner approach.
- (c)
- $E\left({R}_{i}\right)\ge {R}_{CE}+Z{\sigma}_{i}$ i.e., the shortfall/zero-beta compliant approach proposed here.

#### 3.3. From the Theoretical Framework towards a Methodological Implementation

_{CE}being computed for the overall market. In fact, the market clears the contribution of any (non-zero) ${A}_{\epsilon}$ and makes it possible to apply the (c) case even for incomplete markets, as in the case of unlisted and private companies. This also means that any investor may use this approach given its specific Z grade (e.g., the one fixed in the Basel agreement for the case of banks). Finally, by utilizing (c), one does not need to employ peer-group benchmarking and may focus mainly on accounting data; in fact, the only condition is to infer about the (whole) market-shortfall (Mantovani 2014).

_{m}and standard deviation of ROI for the i-th firm. This approach seems more similar to that of the cost of capital, as Equation (8) depicts.

## 4. How to Assess Creditworthiness through the IRM: An Empirical Investigation

- NFP = Net financial position = total debts − cash and cash equivalents.
- OPRE = Operating revenue.
- GFP = Gross financial position = loans + long-term debt.

_{i}

_{,t}), while the independent variables (the vectors X

_{i}

_{,t}) are ratios typically used to profile the corporate risk. Autoregressive components are also considered.

- EBIT = Earnings before interest and taxes.
- FIAS = Fixed assets.
- WKCA = Working capital.

_{i}

_{,}

_{t}of risk factors, we consider three types of business risks and their operating, financial, and taxation indicators.

_{ce}, as computed for the subsample in Table 6.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

Index | Unit | Formula Derived from Orbis | Definition |
---|---|---|---|

Technology features | |||

$\mathrm{CA}/{\mathrm{FIAS}}_{\mathrm{t}}$ | % | ${\mathrm{CUAS}}_{\mathrm{t}}/{\mathrm{FIAS}}_{\mathrm{t}}$ | Current rate of assets |

$\mathrm{CA}/{\mathrm{CL}}_{\mathrm{t}}$ | % | ${\mathrm{CUAS}}_{\mathrm{t}}/{\mathrm{CULI}}_{\mathrm{t}}$ | Current equilibrium |

$\mathrm{WKCA}/{\mathrm{FIAS}}_{\mathrm{t}}$ | % | ${\mathrm{WKCA}}_{\mathrm{t}}/{\mathrm{FIAS}}_{\mathrm{t}}$ | Relative intensity of working capital |

$\mathrm{FIAS}/{\mathrm{OPRE}}_{\mathrm{t}}$ | % | $\frac{\left[\left({\mathrm{FIAS}}_{\mathrm{t}\text{}}+{\text{}\mathrm{FIAS}}_{\mathrm{t}-1}\right)/2\right]\text{}}{{\mathrm{OPRE}}_{\mathrm{t}}}$ | Absolute intensity of fixed assets |

${\mathrm{RLFA}}_{\mathrm{t}}$ | -- | $\frac{\left[\left({\mathrm{FIAS}}_{\mathrm{t}\text{}}+{\text{}\mathrm{FIAS}}_{\mathrm{t}-1}\right)/2\right]\text{}}{{\mathrm{DEPR}}_{\mathrm{t}}}$ | Residual life of fixed assets |

Financial strategy | |||

$\mathrm{DEB}/{\mathrm{EBITDA}}_{\mathrm{t}}$ | -- | $\frac{\left[\left({\mathrm{NFP}}_{\mathrm{t}}^{*}+{\mathrm{NFP}}_{\mathrm{t}-1}^{*}\right)/2\right]\text{}}{{\mathrm{EBTA}}_{\mathrm{t}}}$ | Years for debt re-financing |

${\mathrm{DEBLT}}_{\mathrm{t}}$ | % | ${\mathrm{CUAS}}_{\mathrm{t}}/{\mathrm{NFP}}_{\mathrm{t}}^{*}$ | Long-term debt rate |

$\mathrm{DEB}/{\mathrm{EQUITY}}_{\mathrm{t}}$ | -- | ${\mathrm{NFP}}_{\mathrm{t}}^{*}/{\mathrm{SHFD}}_{\mathrm{t}}$ | Debt-to-equity ratio |

$\mathrm{GDEB}/{\mathrm{EQUITY}}_{\mathrm{t}}$ | ${\mathrm{GFP}}_{\mathrm{t}}^{**}/{\mathrm{SHFD}}_{\mathrm{t}}$ | Gross debt-to-equity ratio | |

$\mathrm{DEB}/{\mathrm{OPRE}}_{\mathrm{t}}$ | -- | $\frac{\left[\left({\mathrm{NFP}}_{\mathrm{t}}^{*}+{\mathrm{NFP}}_{\mathrm{t}-1}^{*}\right)/2\right]\text{}}{{\mathrm{OPRE}}_{\mathrm{t}}}$ | Intensity of debt |

${\mathrm{LEV}}_{\mathrm{t}}$ | -- | $\frac{{\mathrm{OPPL}}_{\mathrm{t}\text{}}\text{}}{{\mathrm{OPPL}}_{\mathrm{t}}-{\mathrm{INTE}}_{\mathrm{t}}}$ | Financial leverage |

$\mathrm{INTE}/{\mathrm{DEB}}_{\mathrm{t}}$ | % | $\frac{{\mathrm{INTE}}_{\mathrm{t}}}{\left[\left({\mathrm{NFP}}_{\mathrm{t}}^{*}+{\mathrm{NFP}}_{\mathrm{t}-1}^{*}\right)/2\right]}$ | Financial interest rate |

Operating risks | |||

$\mathrm{WKCA}/{\mathrm{OPRE}}_{\mathrm{t}}$ | % | $\frac{\left[\left({\mathrm{WKCA}}_{\mathrm{t}\text{}}+{\text{}\mathrm{WKCA}}_{\mathrm{t}-1}\right)/2\right]\text{}}{{\mathrm{OPRE}}_{\mathrm{t}}}$ | Absolute intensity of working capital |

$\mathrm{DOL}-{\mathrm{volume}}_{\mathrm{t}}$ | -- | ${\mathrm{AV}}_{\mathrm{t}}/{\mathrm{OPPL}}_{\mathrm{t}}$ | Degree of operative leverage on volume changes |

$\mathrm{DOL}-{\mathrm{price}}_{\mathrm{t}}$ | -- | $\left[\frac{{\mathrm{MDCU}}_{\mathrm{t}}^{***}}{\left({\mathrm{MDCU}}_{\mathrm{t}}^{***}\u2013\text{}\mathrm{x}\right)}-1\right]\ast 100$ | Degree of op. lev. on price changes of x (x = 1%) |

$\mathrm{CRED}-{\mathrm{DEBT}}_{\mathrm{t}}$ | dd | $\frac{\left({\mathrm{CRED}}_{\mathrm{t}}+{\mathrm{CRED}}_{\mathrm{t}-1}\right)/2}{{\mathrm{MATE}}_{\mathrm{t}}/365}-\frac{\left({\mathrm{DEBT}}_{\mathrm{t}}+{\mathrm{DEBT}}_{\mathrm{t}-1}\right)/2}{{\mathrm{OPRE}}_{\mathrm{t}}/365}$ | Difference between delays on payments to creditors and payments from debtors |

Rate of return | |||

${\mathrm{ROI}}_{\mathrm{t}}$ | % | $\frac{{\mathrm{OPPL}}_{\mathrm{t}}}{\left[\left({\mathrm{CIN}}_{\mathrm{t}}^{***}+{\mathrm{CIN}}_{\mathrm{t}-1}^{***}\right)/2\right]}$ | Return on investment |

${\mathrm{Adjusted}\text{}\mathrm{ROI}}_{\mathrm{t}}$ | % | $\frac{{\mathrm{EBTA}}_{\mathrm{t}}-STO{K}_{t}+STO{K}_{t-1}}{\left[\left({\mathrm{CIN}}_{\mathrm{t}}^{****}+{\mathrm{CIN}}_{\mathrm{t}-1}^{****}\right)/2\right]}$ | Alternative return on investment |

${\mathrm{ROE}}_{\mathrm{t}}$ | % | $\frac{{\mathrm{PL}}_{\mathrm{t}}}{\left[\left({\mathrm{SHFD}}_{\mathrm{t}}+{\mathrm{SHFD}}_{\mathrm{t}-1}\right)/2\right]}$ | Return on equity |

${\mathrm{ROS}}_{\mathrm{t}}$ | % | ${\mathrm{OPPL}}_{\mathrm{t}}/{\mathrm{OPRE}}_{\mathrm{t}}$ | Return on sales |

$\mathrm{AV}/{\mathrm{STAF}}_{\mathrm{t}}$ | % | ${\mathrm{AV}}_{\mathrm{t}}/{\mathrm{STAF}}_{\mathrm{t}}$ | Work productivity (cost of employees) |

$\mathrm{AV}/{\mathrm{EMPL}}_{\mathrm{t}}$ | % | $\mathrm{AV}/{\mathrm{EMPL}}_{\mathrm{t}}$ | Work productivity (number of employees) |

$\mathrm{EBIT}/{\mathrm{INT}}_{\mathrm{t}}$ | -- | ${\mathrm{OPPL}}_{\mathrm{t}}/{\mathrm{INTE}}_{\mathrm{t}}$ | Interest coverage |

$\mathrm{FCFC}/{\mathrm{OPRE}}_{\mathrm{t}}$ | % | $\frac{EBT{A}_{t}+WKC{A}_{t-1}-WKC{A}_{t}}{OPR{E}_{t}}$ | Margin of free cash flow characteristic |

$\mathrm{FCFO}/{\mathrm{OPRE}}_{\mathrm{t}}$ | % | $\frac{{\mathrm{FCFC}}_{\mathrm{t}}-\left({\mathrm{DEPR}}_{\mathrm{t}}+{\mathrm{FIAS}}_{\mathrm{t}}-{\mathrm{FIAS}}_{\mathrm{t}-1}\right)}{{\mathrm{OPRE}}_{\mathrm{t}}}$ | Margin of free cash flow operative |

${\mathrm{TAX}}_{\mathrm{t}}$ | % | ${\mathrm{TAXA}}_{\mathrm{t}}/{\mathrm{OPPL}}_{\mathrm{t}}$ | Tax rate |

Self-elaborated account values *^{,}**^{,}*** | |||

${\mathrm{NFP}}_{\mathrm{t}}$ | € | ${\mathrm{LOAN}}_{\mathrm{t}}+{\mathrm{LTDB}}_{\mathrm{t}}-{\mathrm{CASH}}_{\mathrm{t}}$ | Net financial position |

GFP_{t} | € | ${\mathrm{LOAN}}_{\mathrm{t}}+{\mathrm{LTDB}}_{\mathrm{t}}$ | Gross financial position |

${\mathrm{MDCU}}_{\mathrm{t}}$ | % | ${\mathrm{AV}}_{\mathrm{t}}/{\mathrm{OPRE}}_{\mathrm{t}}$ | Contribution margin |

${\mathrm{CIN}}_{\mathrm{t}}$ | € | ${\mathrm{FIAS}}_{\mathrm{t}}+{\mathrm{WKCA}}_{\mathrm{t}}$ | Total net investments |

## Notes

1 | According to Cannari et al. (2011), these companies produce one fourth of the private gross domestic product, while one fifth of the national population resides and one third of total national exports originate in the area. |

2 | (Basel Committee on Banking Supervision 2014), Bank for International Settlements 2014. |

3 | (Basel Committee on Banking Supervision 2010), Bank for International Settlements 2010. |

4 | Bureau van Dijk provides complete balance sheet data in the global standard format for global companies. |

5 | See the Appendix A, Table A1, for a complete view of the indicators. |

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**Figure 1.**Dynamics of NPLs as % of total credit allowance in north-east Italy. The figures in the chart are the authors’ computations on original data as sourced from the official public database of the Bank of Italy.

Section A: $\mathrm{P}\left(\mathrm{ROI}\right)-\mathrm{T}\left(\mathrm{ROI}\right)$ and $\mathrm{DEB}/\mathrm{OPRE}$ classification | |||

P(ROI) − T(ROI) | |||

Positive | Negative | ||

DEB/OPRE_{t} | Higher | I. Firms with positive rating that raise more financial resources than sample average | II. Firms with negative rating that raise more financial resources than sample average |

Lower | III. Firms with positive rating that raise less financial resources than sample average | IV. Firms with negative rating that raise less financial resources than sample average | |

Section B:$\mathrm{P}\left(\mathrm{ROI}\right)-\mathrm{T}\left(\mathrm{ROI}\right)$ and $\mathrm{INTE}/\mathrm{DEB}$ classification | |||

P(ROI) − T(ROI) | |||

Positive | Negative | ||

INT/DEB_{t} | Lower | I. Firms with positive rating that pay less for their raised financial resources | II. Firms with negative rating that pay less for their raised financial resources |

Higher | III. Firms with positive rating that pay more for their raised financial resources | IV. Firms with negative rating that pay more for their raised financial resources |

Sectors-Definition | NACE Code Rev. 2 | Number | Total Assets | Operating Revenue | |||
---|---|---|---|---|---|---|---|

Absolute | % | Absolute | % | Absolute | % | ||

MANUFACTURING | 7740 | 61.21% | 519,996,368.85 | 67.20% | 579,216,823.03 | 73.59% | |

Manufacture of food products, beverages and tobacco products | 10; 11; 12 | 560 | 4.43% | 57,198,114.00 | 7.39% | 85,086,997.22 | 10.81% |

Manufacture of textiles, apparel, leather and related products | 13; 14; 15 | 791 | 6.26% | 42,195,142.52 | 5.45% | 54,621,447.17 | 6.94% |

Manufacture of wood and paper products and printing | 16; 17; 18 | 715 | 5.65% | 46,152,081.19 | 5.96% | 45,177,459.90 | 5.74% |

Manufacture of coke and refined petroleum products | 19 | 13 | 0.10% | 781,687.40 | 0.10% | 1,016,381.95 | 0.13% |

Manufacture of chemicals and chemical products | 20 | 207 | 1.64% | 16,280,064.67 | 2.10% | 19,285,752.88 | 2.45% |

Manufacture of pharmaceuticals, medicinal chemical and botanical products | 21 | 14 | 0.11% | 3,299,509.57 | 0.43% | 3,400,539.27 | 0.43% |

Manufacture of rubber and plastics products and other non-metallic mineral products | 22;23 | 887 | 7.02% | 61,207,649.54 | 7.91% | 57,556,877.22 | 7.31% |

Manufacture of basic metals and fabricated metal products, except machinery and equipment | 24;25 | 1790 | 14.16% | 101,220,759.76 | 13.08% | 110,234,214.18 | 14.01% |

Manufacture of computer, electronic and optical products | 26 | 200 | 1.58% | 10,323,986.84 | 1.33% | 11,307,819.33 | 1.44% |

Manufacture of electrical equipment | 27 | 392 | 3.10% | 38,293,899.72 | 4.95% | 42,395,887.43 | 5.39% |

Manufacture of machinery and equipment n.e.c. | 28 | 1066 | 8.43% | 78,689,218.42 | 10.17% | 82,224,883.47 | 10.45% |

Manufacture of transport equipment | 29; 30 | 133 | 1.05% | 10,791,531.71 | 1.39% | 11,057,239.61 | 1.40% |

Other manufacturing and repair and installation of machinery and equipment | 31; 32; 33 | 972 | 7.69% | 53,562,723.52 | 6.92% | 55,851,323.42 | 7.10% |

SERVICE | 4904 | 38.79% | 253,799,100.59 | 32.80% | 207,865,504.72 | 26.41% | |

Agriculture, forestry and fishing | 01; 02; 03 | 341 | 2.70% | 28,219,668.48 | 3.65% | 28,939,922.01 | 3.68% |

Mining and quarrying | 05; 06; 07; 08; 09 | 79 | 0.62% | 5,420,448.67 | 0.70% | 3,185,615.17 | 0.40% |

Electricity, gas, steam and air-conditioning supply | 35 | 75 | 0.59% | 16,053,148.42 | 2.07% | 17,070,451.49 | 2.17% |

Water supply, sewerage, waste management and remediation | 36; 37; 38; 39 | 202 | 1.60% | 16,663,958.39 | 2.15% | 13,183,644.09 | 1.68% |

Transportation and storage | 49; 50; 51; 52; 53 | 936 | 7.40% | 46,420,204.99 | 6.00% | 50,042,648.69 | 6.36% |

Accomodation and food service activities | 55; 56 | 676 | 5.35% | 30,467,807.26 | 3.94% | 14,774,800.39 | 1.88% |

Publishing, audiovisual, broadcasting activities, telecommunications, IT and other information services | 58; 59; 60; 61; 62; 63 | 456 | 3.61% | 14,071,321.09 | 1.82% | 13,236,518.29 | 1.68% |

Real estate activities | 68 | 362 | 2.86% | 31,027,385.17 | 4.01% | 11,586,698.44 | 1.47% |

Legal, accounting, management, architecture, engineering, technical testing; analysis activities; scientific research and development; other professional, scientific and technical activities | 69; 70; 71; 72; 73; 74; 75 | 559 | 4.42% | 19,952,499.38 | 2.58% | 15,913,189.48 | 2.02% |

Administrative support service activities | 77; 78; 79; 80; 81; 82 | 504 | 3.99% | 17,431,731.32 | 2.25% | 18,547,760.66 | 2.36% |

Public administration and defence, compulsory social security | 84 | 0 | 0.00% | - | 0.00% | - | 0.00% |

Education | 85 | 69 | 0.55% | 1,247,680.51 | 0.16% | 1,161,479.24 | 0.15% |

Human health services, residential care and social work activities | 86; 87; 88 | 341 | 2.70% | 10,506,674.89 | 1.36% | 10,368,701.96 | 1.32% |

Arts, entertainment and recreation | 90; 91; 92; 93 | 206 | 1.63% | 12,648,369.32 | 1.63% | 6,995,970.01 | 0.89% |

Other services | 94; 95; 96 | 98 | 0.78% | 3,668,202.70 | 0.47% | 2,858,104.78 | 0.36% |

Predictive Regression | |||||
---|---|---|---|---|---|

const | 0.0995 | *** | DEB/EBlTDA_{t-1} | −0.0002 | * |

(0.0000) | (0.0649) | ||||

CA/FlAS_{t-1} | 0.0002 | *** | DEB/EQUlTY_{t-1} | −0.0014 | *** |

(0.0000) | (0.0000) | ||||

CA/CL_{t} | 0.0131 | *** | ROE_{t} | 0.0210 | *** |

(0.0000) | (0.0000) | ||||

FCFO/OPRE_{t} | 0.0108 | *** | ROE_{t-1} | 0.0142 | *** |

(0.0000) | (0.0000) | ||||

DOL_{t} (volume) | −0.0001 | * | EBIT/lNT_{t} | 0.0000 | *** |

(0.0509) | (0.0000) | ||||

DOL_{t} (price) | −0.0008 | *** | EBIT/lNT_{t-1} | 0.0000 | *** |

(0.0022) | (0.0000) | ||||

DOI_{t-l} (price) | −0.0005 | * | ROS_{t} | 0.4515 | *** |

(0.0831) | (0.0000) | ||||

FIAS/OPRE_{t} | −0.0172 | *** | ROS_{t-1} | 0.0652 | *** |

(0.0000) | (0.0005) | ||||

FIAS/OPRE_{t-1} | −0.0130 | *** | TAX_{t} | 0.0051 | *** |

(0.0000) | (0.0129) | ||||

INT/DEB_{t} | 0.0005 | * | TAX_{t-1} | 0.0023 | * |

(0.0832) | (0.0887) | ||||

DEB/OPRE_{t} | 0.0180 | *** | RLFA_{t} | −0.0001 | * |

(0.0002) | (0.0605) | ||||

DEB/OPRE_{t-1} | −0.0315 | *** | RFLA_{t-1} | −0.0002 | ** |

(0.0000) | (0.0430) | ||||

DEB/EBlTDA_{t} | −0.0002 | ** | |||

(0.0389) | |||||

R-squared | 0.0256 | ||||

Adjusted R-squared | 0.0256 | ||||

F-Stat (p-value) | 0.0000 |

IRM | Ranking | IRM | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Positive | Negative | # Firms | Clusters | % Firms | Positive | Negative | ||||||

Intensity of debt | higher | 3138 | 3689 | 6827 | 725 | 1 | 5.34% | Price of financing | lower | 4371 | 2391 | 6762 |

lower | 4947 | 1809 | 6756 | 479 | 2 | 3.53% | higher | 3714 | 3107 | 6821 | ||

8085 | 5498 | 13,583 | 2413 | 3 | 17.76% | 8085 | 5498 | 13,583 | ||||

1330 | 4 | 9.79% | ||||||||||

IRM | 3646 | 5 | 26.84% | IRM | ||||||||

positive | negative | 2628 | 6 | 19.35% | positive | negative | ||||||

Intensity of debt | higher | 23.10% | 27.16% | 50.26% | 1301 | 7 | 9.58% | Price of financing | lower | 32.18% | 17.60% | 49.78% |

lower | 36.42% | 13.32% | 49.74% | 1061 | 8 | 7.81% | higher | 27.34% | 22.87% | 50.22% | ||

59.52% | 40.48% | 100.00% | 13,583 | 100.00% | 59.52% | 40.48% | 100.00% |

**Note**. The red and orange colours in the ranking clusters can be summed to obtain similar coloured cross matches for quantity and pricing. In fact, by summing up cluster #8 with the left-hand, red-highlighted #6, one obtains the left-hand, red-coloured match, while summing it up with the right-hand, red-highlighted #4 provides the right-hand, red-coloured match. Similarly, one may sum cluster #7 with #5 to obtain the left figures or with #3 for those on the right. Green clusters (#1 and #2) represent those with the highest possible efficiency: indeed, they are subsets of the green areas on the left and right matches.

**Table 5.**Subset overlaps between IRM results, intensity of debt (left) and price of financing (right).

Subset A: 7700 Manufacturing Firms | ||||||||||||

IRM | Ranking | IRM | ||||||||||

Positive | Negative | # Firms | Clusters | % Firms | Positive | Negative | ||||||

Intensity of debt | higher | 1491 | 2636 | 4127 | 381 | 1 | 4.64% | Price of financing | lower | 2529 | 1568 | 4097 |

lower | 2998 | 1092 | 4090 | 303 | 2 | 3.69% | higher | 1960 | 2160 | 4120 | ||

4489 | 3728 | 8217 | 1110 | 3 | 13.51% | 4489 | 3728 | 8217 | ||||

789 | 4 | 9.60% | ||||||||||

IRM | 2148 | 5 | 26.14% | IRM | ||||||||

positive | negative | 1857 | 6 | 22.60% | positive | negative | ||||||

Intensity of debt | higher | 18.15% | 32.08% | 50.23% | 850 | 7 | 10.34% | Price of financing | lower | 30.78% | 19.08% | 49.86% |

lower | 36.49% | 13.29% | 49.77% | 779 | 8 | 9.48% | higher | 23.85% | 26.29% | 50.14% | ||

54.63% | 45.37% | 100.00% | 8217 | 100.00% | 54.63% | 45.37% | 100.00% | |||||

Subset B: 4731 Services Firms | ||||||||||||

IRM | Ranking | IRM | ||||||||||

Positive | Negative | # Firms | Clusters | % Firms | Positive | Negative | ||||||

Intensity of debt | higher | 1647 | 1053 | 2700 | 344 | 1 | 6.41% | Price of financing | lower | 1842 | 823 | 2665 |

lower | 1949 | 717 | 2666 | 176 | 2 | 3.28% | higher | 1754 | 947 | 2701 | ||

3596 | 1770 | 5366 | 1303 | 3 | 24.28% | 3596 | 1770 | 5366 | ||||

541 | 4 | 10.08% | ||||||||||

IRM | 1498 | 5 | 27.92% | IRM | ||||||||

positive | negative | 771 | 6 | 14.37% | positive | negative | ||||||

Intensity of debt | higher | 30.69% | 19.62% | 50.32% | 451 | 7 | 8.40% | Price of financing | lower | 34.33% | 15.34% | 49.66% |

lower | 36.32% | 13.36% | 49.68% | 282 | 8 | 5.26% | higher | 32.69% | 17.65% | 50.34% | ||

67.01% | 32.99% | 100.00% | 5366 | 100.00% | 67.01% | 32.99% | 100.00% |

**Note**. Red and orange colours in ranking clusters can be summed to obtain similar coloured cross matches for quantity and pricing. In fact, by summing up cluster #8 with the left-hand, red-highlighted #6, one can obtain the left-hand, red-coloured match; while summing it up with the right-hand, red-highlighted #4, one can obtain the right-hand, red-coloured match. Similarly, one may sum cluster #7 with #5 to attain the left-hand figures or with #3 for those one on the right. Green clusters (#1 and #2) represent those with the highest possible efficiency: indeed, they are subsets of the green areas on the left and right matches.

# of Firms | 12,431 | 7700 | 4731 |

Total | Manufacturing | Service | |

sample | subset | subset | |

P(ROI) | 0.0682 | 0.0735 | 0.0588 |

σ(ROI) | 0.1322 | 0.1898 | 0.1447 |

ROI_{ce,i} (10%) | −0.1013 | −0.1699 | −0.1267 |

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## Share and Cite

**MDPI and ACS Style**

Mantovani, G.M.; Gadzinski, G.
How to Rate the Financial Performance of Private Companies? A Tailored Integrated Rating Methodology Applied to North-Eastern Italian Districts. *J. Risk Financial Manag.* **2022**, *15*, 493.
https://doi.org/10.3390/jrfm15110493

**AMA Style**

Mantovani GM, Gadzinski G.
How to Rate the Financial Performance of Private Companies? A Tailored Integrated Rating Methodology Applied to North-Eastern Italian Districts. *Journal of Risk and Financial Management*. 2022; 15(11):493.
https://doi.org/10.3390/jrfm15110493

**Chicago/Turabian Style**

Mantovani, Guido Max, and Gregory Gadzinski.
2022. "How to Rate the Financial Performance of Private Companies? A Tailored Integrated Rating Methodology Applied to North-Eastern Italian Districts" *Journal of Risk and Financial Management* 15, no. 11: 493.
https://doi.org/10.3390/jrfm15110493