# Bankruptcy Prediction and Stress Quantification Using Support Vector Machine: Evidence from Indian Banks

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Data Descriptions and Methodology

#### 3.1. Two-Step Feature Selection

_{i}, H]/N + diff [A, L

_{i}, M]/N

**D**CDCDCD 1

**C**CDCDCD 1

**D**CDCDCD 1

**C**CDCDCD −1

_{1}and I

_{2}, where ${\mathrm{I}}_{1}$ = ${\mathrm{L}}_{i}$ and ${\mathrm{I}}_{2}$ is either “H” or “M” when performing weight updates. The diff. function for the discrete feature is defined as

#### 3.2. Support Vector Machine

#### 3.2.1. Why Support Vector Machine?

#### 3.2.2. Support Vector Machine for Linearly Separable Data

**.**Under the stated conditions, the instance of each class will be above or below the hyperplane. Two margins can, therefore, be defined as in Figure 2.

#### 3.3. Support Vector Machine for the Non-Linear Case (Kernel Machine)

#### Kernel Trick

#### 3.4. Overfitting and Cross-Validation

## 4. Empirical Results and Discussion

#### 4.1. Empirical Results

Input Features | Coefficient |

provision_for_loan_Interest_income(t−1) | 6.056 |

Tier1CAR(t−1) | 4.37 |

Bias Term | 3.96 |

Cut-off value | 6.97 |

#### 4.2. Stress Quantification of Banks

#### Decision Linear Boundary

- (a)
- By using the SVMLK predictive model, is it possible to find quantitative information about bank features to avoid a predicted bank failure?
- (b)
- How financially strong are the banks that are predicted as survival banks by using SVMLK predictive model?

#### 4.3. Mathematical Approach for Stress Quantification Using SVMLK

#### 4.3.1. Change in Both Features

**is given by ${\mathrm{B}}^{\u2019}\left(\mathrm{a}\frac{\mathrm{a}{\mathrm{x}}_{\mathrm{p}}+\mathrm{b}{\mathrm{y}}_{\mathrm{p}}+\mathrm{c}}{\sqrt{{\mathrm{a}}^{2}+{\mathrm{b}}^{2}}},\mathrm{b}\frac{\mathrm{a}{\mathrm{x}}_{\mathrm{p}}+\mathrm{b}{\mathrm{y}}_{\mathrm{p}}+\mathrm{c}}{\sqrt{{\mathrm{a}}^{2}+{\mathrm{b}}^{2}}}\right)$.**

^{’}#### 4.3.2. Change in One Feature

#### 4.4. Comparison of Bank Financial Health

_{t}and M

_{t}as shown in Figure 9.

**,**while the minimum and maximum distances of banks forecasted as insolvent from the linear decision boundary were 4.02 and 10.86. Based on these distances, we used sensitivity analysis to quantify the amount of stress based on two important bank features: provision_for_loan_Interest_income(t−1) and Tier1CAR(t−1).

#### 4.4.1. Changing the Status of Bank “A” from Insolvent to Solvent by Changing Both Variables

#### 4.4.2. Marginal Cases: Changing the Status of Bank “A” from Insolvent to Solvent by Changing a Single Variable

**Case**

**1.**

Features | Original Values | Critical Values |

provision_for_loan_Interest_income(t−1) | 0.00123 | 0.49 |

Tier1CAR(t−1) | 0.1123 | 0.1123 |

**Case**

**2.**

Features | Original Values | Critical Values |

provision_for_loan_Interest_income(t−1) | 0.00123 | 0.00123 |

Tier1CAR(t−1) | 0.1123 | 0.54 |

## 5. Conclusions

## 6. Limitations of the Study

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

Name | Type | Definition |
---|---|---|

Financial Status (Failed or Survival) | Categorical | Binary indicator equal to 1 for failed banks and 0 for surviving banks |

Total_Assets (TA) | Quantitative | Total earning assets |

Cash_Balance_TA | Quantitative | Cash and due from depository institutions/TA |

Net_Loan_TA | Quantitative | Net loans /TA |

Deposit_TA | Quantitative | Total Deposits/TA |

Subordinated_debt_TA | Quantitative | Subordinated Debt/TA |

Average_Assets_TA | Quantitative | Average Assets till 2017/Total Assets |

Tier1CAR | Quantitative | Tier1 risk-based capital/Total Assets |

Tier2CAR | Quantitative | Tier 2 risk-based capital/Total Assets |

IntincExp_Income | Quantitative | Total interest expense/total interest income |

Provision_for_loan_Interest_income | Quantitative | Provision for loan and lease losses/total interest income |

Nonintinc_intIncome | Quantitative | Total noninterest income/total interest income |

Return_on_capital_employed | Quantitative | Salaries and employee benefits/total interest income |

Operating_income_T_Interest_income | Quantitative | net operating income/total interest income |

Cash_dividend_T_Interest_Income | Quantitative | Cash dividends/total interest income |

Operating_income_T_Interest_income | Quantitative | Net operating income/total interest income |

Net_Interest_margin | Quantitative | Net interest margin earned by bank |

Return_on_assets | Quantitative | Return on total assets of firm |

Equity_cap_TA | Quantitative | Equity capital to assets |

Return_on_Assets | Quantitative | Return on total assets of banks |

Noninteerst_Income | Quantitative | Noninterest Income earned by banks |

Treasury_income_T_Interest_income | Quantitative | Net income attributable to bank/total interest income |

Net_loans_Deposits | Quantitative | Net loans and leases to deposits |

Net_Interest_margin | Quantitative | Net interest income expressed as a percentage of earning assets. |

Salaries_employees_benefits_Int_income | Quantitative | Salaries and employee benefits/total interest income |

TA_employee | Quantitative | Total assets per employee of bank |

## Appendix B

Variables Name | Relief Score |
---|---|

Tier1CAR(t−1) | 0.18 |

Subordebt_TA(t−1) | 0.12 |

Tier2CAR(t−2) | 0.1 |

Provision_for_loan_Interest_income(t−4) | 0.1 |

Subordebt_TA(t−3) | 0.09 |

Provision_for_loan_Interest_income(t−1) | 0.08 |

Provision_for_loan_Interest_income(t−2) | 0.08 |

Provision_for_loan_Interest_income(t−3) | 0.07 |

TA_emplyee(t−3) | 0.07 |

TA_emplyee(t−2) | 0.06 |

Tier2CAR(t−1) | 0.06 |

TA_emplyee(t−4) | 0.05 |

TA_emplyee(t−1) | 0.05 |

Noninterest_expences_Int_income(t−3) | 0.04 |

Subordebt_TA(t−4) | 0.02 |

Salaries_and_employees_benefits_Int_income(t−3) | 0.01 |

Tier2CAR(t−3) | 0.00 |

Return_on_capital_employed_(t−2) | 0.00 |

Operating_income_T_Interest_income(t−4) | 0.00 |

Cash_TA(t−3) | 0.00 |

Noninterest_expences_Int_income(t−4) | 0.00 |

Deposits_TA(t−2) | 0.00 |

Return_on_advances_adjusted_to_cost_of_funds(t−1) | 0.00 |

Operating_income_T_Interest_income(t−3) | 0.00 |

Return_on_capital_employed(t−3) | 0.00 |

Salaries_and_employees_benefits_Int_income(t−4) | 0.00 |

Net_loans_TA(t−3) | 0.00 |

Deposits_TA(t−1) | 0.00 |

Treasury_income_T_Interest_income(t−4) | 0.00 |

Return_on_assets(t−3) | 0.00 |

Net_loans_TA(t−2) | 0.00 |

Net_loans_TA(t−1) | 0.00 |

Return_on_assets(t−1) | 0.00 |

Return_on_capital_employed(t−4) | 0.00 |

IntincExp_Income(t−2) | 0.00 |

Cash_TA(t−2) | 0.00 |

IntincExp_Income(t−4) | 0.00 |

Noninterest_expences_Int_income(t−1) | 0.00 |

Return_on_advances_adjusted_to_cost_of_funds(t−2) | 0.00 |

Nonintinc_intIncome(t−4) | 0.00 |

Nonintinc_intIncome(t−1) | 0.00 |

Deposits_TA(t−3) | 0.00 |

Equity_cap_TA(t−1) | 0.00 |

IntincExp_Income(t−3) | 0.00 |

Operating_income_T_Interest_income(t−1) | 0.00 |

Avg_Asset_TA(t−2) | 0.00 |

Total_Assets(t−3) | 0.00 |

Noninteerst_Income(t−3) | 0.00 |

Provision_for_loan(t−2) | 0.00 |

Total_Assets(t−4) | 0.00 |

Salaries_and_employees_benefits_Int_income(t−1) | 0.00 |

Noninteerst_Income(t−2) | 0.00 |

Total_Assets(t−1) | 0.00 |

Return_on_capital_employed(t−1) | 0.00 |

Noninteerst_Income(t−4) | 0.00 |

Subordebt_TA(t−2) | 0.00 |

Total_Assets(t−2) | 0.00 |

Noninterest_expences_Int_income(t−2) | 0.00 |

Equity_cap_TA(t−2) | 0.00 |

Noninteerst_Income(t−1) | 0.00 |

Salaries_and_employees_benefits_Int_income(t−2) | 0.00 |

Nonintinc_intIncome(t−3) | 0.00 |

Treasury_income_T_Interest_income(t−3) | 0.00 |

Return_on_assets(t−4) | 0.00 |

Treasury_income_T_Interest_income(t−1) | 0.00 |

Tier1CAR(t−3) | 0.00 |

Avg_Asset_TA(t−3) | 0.00 |

Tier1CAR(t−4) | 0.00 |

Equity_cap_TA(t−3) | 0.00 |

IntincExp_Income(t−1) | 0.00 |

Return_on_assets(t−2) | 0.00 |

Treasury_income_T_Interest_income(t−2) | 0.00 |

Net_Interest_margin(t−4) | 0.00 |

Tier1CAR(t−2) | 0.00 |

Cash_TA(t−1) | 0.00 |

Provision_for_loan(t−4) | 0.00 |

Net_Interest_margin(t−2) | 0.00 |

Net_Interest_margin(t−1) | 0.00 |

Cash_TA(t−4) | 0.00 |

Deposits_TA(t−4) | 0.00 |

Equity_cap_TA(t−4) | 0.00 |

Net_loans_TA(t−4) | 0.00 |

Return_on_advances_adjusted_to_cost_of_funds(t−4) | 0.00 |

Return_on_advances_adjusted_to_cost_of_funds(t−3) | 0.00 |

Provision_for_loan(t−3) | 0.00 |

Avg_Asset_TA(t−4) | 0.00 |

Operating_income_T_Interest_income(t−2) | 0.00 |

Net_loans_Deposits(t−3) | 0.00 |

Nonintinc_intIncome(t−2) | 0.00 |

Net_Interest_margin(t−4) | 0.00 |

Net_loans_Deposits(t−4) | 0.00 |

Avg_Asset_TA(t−1) | 0.00 |

Tier2CAR(t−4) | −0.01 |

Net_loans_Deposits(t−2) | −0.01 |

Cash_dividend_T_Interest_Income(t−2) | −0.01 |

Cash_dividend_T_Interest_Income(t−1) | −0.01 |

Cash_dividend_T_Interest_Income(t−4) | −0.01 |

Net_loans_Deposits(t−1) | −0.01 |

Cash_dividend_T_Interest_Income(t−3) | −0.02 |

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**Figure 6.**Representation of stress quantification. The x-axis denotes the provision_for_loan_Interest_income(t−1) and the y-axis represents Tier1CAR(t−1).

**Figure 9.**Quantifying and comparing the financial health of surviving banks after the environmental change.

Mathematical Kernel Equation | Name of Kernel |
---|---|

$\mathrm{K}\left({\mathrm{z}}_{\mathrm{i}},{\mathrm{z}}_{\mathrm{j}}\right)=\left({\mathrm{z}}_{\mathrm{i}}{}^{\mathrm{T}}{\mathrm{z}}_{\mathrm{j}}+\mathrm{p}\right)$ | Linear |

$\mathrm{K}\left({\mathrm{z}}_{\mathrm{i}},{\mathrm{z}}_{\mathrm{j}}\right)=\mathrm{exp}\left(-\mathsf{\alpha}\left[{\Vert {\mathrm{z}}_{\mathrm{i}}-{\mathrm{z}}_{\mathrm{j}}\Vert}^{2}\right]\right)$ | RBF (Radial Basis Function) |

Subordebt_TA (t−2) | 0.18 |

Subordebt_TA (t−1) | 0.12 |

Tier1CAR(t−2) | 0.1 |

Provision_for_loan_Interest_income (t−4) | 0.1 |

Subordebt_TA(t−3) | 0.09 |

Provision_for_loan_Interest_income(t−1) | 0.08 |

Provision_for_loan_Interest_income(t−2) | 0.08 |

Provision_for_loan_Interest_income(t−3) | 0.07 |

TA_employee(t−3) | 0.07 |

TA_employee(t−2) | 0.06 |

Tier1CAR(t−1) | 0.06 |

TA_employee(t−4) | 0.05 |

TA_employee(t−1) | 0.05 |

Noninterest_expences_Int_income(t−3) | 0.04 |

Subordebt_TA(t−4) | 0.02 |

Salaries_and_employees_benefits_Int_income(t−3) | 0.01 |

Total Accuracy | Solvent Predictive Accuracy | Insolvent Predictive Accuracy |
---|---|---|

92.86% | 100% | 75% |

Total Accuracy | Solvent Predictive Accuracy | Insolvent Predictive Accuracy |
---|---|---|

71.43% | 100% | 0% |

Features | Original Values | Critical Values |
---|---|---|

provision_for_loan_Interest_income(t−1) | 0.00123 | 2.0 |

Tier1CAR(t−1) | 0.1123 | 1.6 |

© 2020 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**

Shrivastav, S.K.; Ramudu, P.J. Bankruptcy Prediction and Stress Quantification Using Support Vector Machine: Evidence from Indian Banks. *Risks* **2020**, *8*, 52.
https://doi.org/10.3390/risks8020052

**AMA Style**

Shrivastav SK, Ramudu PJ. Bankruptcy Prediction and Stress Quantification Using Support Vector Machine: Evidence from Indian Banks. *Risks*. 2020; 8(2):52.
https://doi.org/10.3390/risks8020052

**Chicago/Turabian Style**

Shrivastav, Santosh Kumar, and P. Janaki Ramudu. 2020. "Bankruptcy Prediction and Stress Quantification Using Support Vector Machine: Evidence from Indian Banks" *Risks* 8, no. 2: 52.
https://doi.org/10.3390/risks8020052