# A Comprehensive Stability Indicator for Banks

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## Abstract

**:**

## 1. Introduction

## 2. Existing Stability or Soundness Indicators

## 3. Key Principles of the Model

## 4. Model Methodology and Motivation for Factor Choice

#### 4.1. The 3C Factors

_{E}), market asset values of the firm (A), debt (F) and market asset value volatility (σ

_{A}) (Conditions). The firm defaults when liabilities exceed assets. This equals the payoff of a call option on the firm’s value with strike price F. If, at time T, loans exceed assets, then the option will expire unexercised and the owners will default. The call option is in the money where A

_{T}− F > 0, and out the money where A

_{T}− F < 0. As A − F is a measure of the firm’s capital, in our model A = F is where the lender has run out of capital. An increase in Conditions risk indicates capital erosion, which needs to be restored, as noted by the BOE and IMF (see Section 1). In calculating the Conditions, we follow the (Merton 1974) approach, as outlined in (Bharath and Shumway 2008). An initial asset value and its volatility (σ

_{A}) is estimated in Equation (1):

#### 4.2. The Comprehensive Stability Indicator

Conditions | = market asset value volatility, per Equation (1) |

Creditworthiness | = nonperforming loans to total gross loans |

Leverage | = total capital to total assets ratio |

KM | = market value of capital (per Equation (2), which measures Leverage based on the impact of a change in Conditions) |

CSI | = Comprehensive stability indicator (Equation (3), which is Leverage to Creditworthiness, modified by changes in Conditions) |

t | = time period (year), and thus Conditions_{t} is Conditions for historical period t |

tc | = current time period (i.e., if the most recent period in the sample is 2017, then Conditions_{tc} is Conditions_{2017}) |

DF | = distress factor, which is the predetermined shock applied to a variable in a particular scenario. In our scenario in Section 6 we apply distress to current factors up to the 90% threshold (α = 0.90) level of historical experiences (e.g., the 90th percentile worst year in our sample). Our example analysis of the US banks that is undertaken in Section 6 shows that for Conditions this is 2.0 × the current Conditions level and that the associated Creditworthiness at that distressed Conditions level is 2.5 × the current Creditworthiness level. Thus, DF_{Conditions0.90} = 2.0 and DF_{Creditworthinesss}_{0.90} = 2.5. Therefore, Conditions_{distressed} = Conditions_{tc} × 2.0 and Creditworthiness_{distressed} = Creditworthiness_{tc} × 2.5. |

Zone | = red, orange, or green, as determined by Section 6.1.4. |

Note: The above factors are developed using figures for the total US market to determine a uniform Distress Factor (DF). This DF is then applied to the 3Cs specific to each bank in the sample. |

_{2008}will be lower than CSI for other years in our sample, showing a deterioration in financial soundness, and a need to restore the Leverage of the firm. CSI is linked to colour bands red (danger), orange (caution) and green (pass).

## 5. Data and Testing the Appropriateness of the Model

_{0}+ β

_{1}Creditworthiness

_{t}+ β

_{2}Conditions

_{t}+ β

_{3}Leverage

_{t-3}+ ε

^{2}, which measures the extent to which the factors can explain BF was found to be a high 91.2% for the multiple regression, with high (99%) significance for Creditworthiness and Conditions (lag ¾ year), and relatively lower (95%) significance for Leverage. To test the additional value of each variable, we commence with our highest factor (Creditworthiness at R

^{2}= 86.5%), then add the other variables. Adding Conditions (lag ¾ year) (which on its own has an R

^{2}of 43.9%), increases the R

^{2}obtained by Creditworthiness by a further 4.0% to 90.5% but Leverage adds very little value to the explanation as seen by the very small increase in total R

^{2}of 0.7%. If we add the Credit to GDP variable recommended by Drehmann et al. in Section 2 as a good indicator of capital buffers, (which on its own has an R

^{2}of 29.5%) we improve the R

^{2}of our multiple regression model only marginally to 92.1%. These figures re-enforce Creditworthiness and Conditions as important causal factors, and Leverage as a non-causal factor, but as discussed, a safety net factor.

## 6. Results of the CSI Modelling

#### 6.1. Results for the US as a Whole

#### 6.1.1. Factor 1: Creditworthiness

_{2017}risk is at relatively low historical levels (Figure 2), the US had low Creditworthiness risk (below 1%) just prior to the GFC, which spiked during the GFC (almost 5%), after which, financial sector reforms such as the Dodd–Frank Act were introduced, and Creditworthiness showed a reducing trend to 1.13% in 2017. The lines in Figure 2 plot the annual figure for Creditworthiness, which as defined in Section 4 is NPL to Gross Loans for U.S. banks as provided by the World Bank at an aggregated country level.

#### 6.1.2. Factor 2: Conditions

#### 6.1.3. Factor 3: Capital

#### 6.1.4. Combined Factors: The Comprehensive Stability Indicator (CSI)

#### 6.2. Results for Individual Banks Compared to Federal Reserve Tests

_{2014}and Creditworthiness

_{2014}for each of the 20 banks in the sample, how well each individual bank could withstand a future shock that reflects realistic and plausible extreme changes to Conditions, guided by the past volatility of the US market. The distressed scenario thus applied a uniform shock to each of the banks in the sample, and ascertained changes to their colour zone. For the overall US banking market, calculated from figures in Table 2, Conditions

_{0.90}was approximately 2.0× higher than Conditions

_{2014}and Creditworthiness at the Conditions

_{0.90}level exceeded Creditworthiness

_{2014}by approximately 2.5×. So, to illustrate our model, we used these as our distress factors (DF

_{Conditions}= 2.0; DF

_{Creditworthiness}= 2.5) to apply to the 20 individual banks. Thus, Conditions

_{distressed}= Conditions

_{2014}× 2.0, and Creditworthiness

_{distressed}= Creditworthiness

_{2014}× 2.5. Again, banks or regulators can determine their own distress factors. We then used these Creditworthiness

_{distressed}and Conditions

_{distressed}values to calculate KM

_{distressed}(=Leverage

_{2014}× Conditions

_{2014}/Conditions

_{distressed}), CSI

_{distressed}, (=KM

_{distressed}/Creditworthiness

_{distressed}) and Zone

_{distressed}for each bank. As shown in Table 3, applying these factors to our model achieved a 99% level of confidence similarity to the Federal Reserve tests in the rankings of banks (best to worst), using a Spearman ranking correlation test which compares the relative ordinal risk of observations across datasets (Powell et al. 2018).

^{2014}per Equation (3)) for our model, for the same set of banks as contained in column 1 for each quartile. What is evident is that, as the risk increases for each quartile on the US Federal Reserve tests, our model also shows a corresponding increase in risk. The lower section of Table 4 shows the percentage of banks that achieved orange on our model out of the 15 banks in the lower risk quartiles Q1–3, as compared to the highest risk Q4 quartiles. 80% of our oranges align with the banks in the highest risk quartile of U.S. Federal Reserve tests. Overall, therefore, our model ranks banks very similar (at a 99% confidence level per Table 3) to the U.S. Federal reserve tests, but it has the advantage of the orange ‘warning’ indicator.

## 7. Conclusions and Implications

## Author Contributions

## Funding

## Conflicts of Interest

## References

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Factor | Significance | Factor | R^{2} | Adjusted R^{2} |
---|---|---|---|---|

Creditworthiness | *** | Creditworthiness | 86.5% | 86.2% |

Conditions_{(lag3/4)} | *** | Creditworthiness + Conditions_{(lag3/4)} | 90.5% | 90.2% |

Leverage | ** | All factors | 91.2% | 90.9% |

Year (t) | Creditworthiness | β | Leverage | Β | Conditions | β | KM | β | CSI | Zone |
---|---|---|---|---|---|---|---|---|---|---|

2005 | 0.70% | 0.25 | 10.30% | 0.88 | 0.013 | 0.21 | 21.96% | 2.83 | 31.37 | Green |

2006 | 0.80% | 0.29 | 10.50% | 0.90 | 0.015 | 0.25 | 19.03% | 2.45 | 23.79 | Green |

2007 | 1.40% | 0.51 | 10.30% | 0.88 | 0.050 | 0.83 | 5.71% | 0.74 | 4.08 | Green |

2008 | 3.00% | 1.08 | 9.30% | 0.79 | 0.279 | 4.61 | 1.02% | 0.13 | 0.34 | Red |

2009 | 4.96% | 1.79 | 12.37% | 1.06 | 0.052 | 0.87 | 5.41% | 0.70 | 1.09 | Red |

2010 | 4.39% | 1.59 | 12.74% | 1.09 | 0.044 | 0.73 | 6.43% | 0.83 | 1.47 | Orange |

2011 | 3.78% | 1.37 | 12.23% | 1.05 | 0.052 | 0.86 | 5.46% | 0.70 | 1.44 | Orange |

2012 | 3.32% | 1.20 | 11.96% | 1.02 | 0.031 | 0.51 | 9.17% | 1.18 | 2.76 | Green |

2013 | 2.45% | 0.89 | 11.78% | 1.01 | 0.026 | 0.43 | 11.00% | 1.42 | 4.49 | Green |

2014 | 1.85% | 0.67 | 11.66% | 1.00 | 0.027 | 0.45 | 10.47% | 1.35 | 5.66 | Green |

2015 | 1.47% | 0.53 | 11.71% | 1.00 | 0.039 | 0.64 | 7.40% | 0.95 | 5.02 | Green |

2016 | 1.32% | 0.48 | 11.59% | 0.99 | 0.030 | 0.49 | 9.57% | 1.23 | 7.25 | Green |

2017 | 1.13% | 0.41 | 11.65% | 1.00 | 0.024 | 0.40 | 11.65% | 1.50 | 10.34 | Green |

Average | 2.35% | 11.39% | 0.052 | 9.56% | 7.62 | |||||

90th percentile | 0.052 |

_{2017}/Conditions

_{t}) and CSI (comprehensive stability indicator) is per Equation (3), where CSI

_{t}= KM

_{t}/Creditworthiness

_{t}, and t represents the year for which the statistic is being calculated. Zones have been set according to the CSI level as: red < 1.2, orange < 2, green ≥ 2. β (Beta)is the relevant statistic for year t as shown in the prior column, relative to the long-term average for that variable (as shown in the final row of that column). The 90th percentile (α = 0.90) is the 90th percentile ranking for an indicator (e.g., 9th best or second worst in a 10 year sample, which lies slightly below the 12th ranked observation in a 13 year sample).

Zone (Our Model) | Count | % | Association b/w Our Model and Fed Tier 1 Model | |
---|---|---|---|---|

Green | 15 | 75.0% | n | 20 |

Orange | 5 | 25.0% | r | 0.662 |

Red | 0 | 0.0% | t | 3.751 |

Critical value 95% | 2.101 | |||

Critical value 99% | 2.878 | |||

Significance | *** |

Quartile | Fed Model—Stressed Tier 1 Ratio (%) | Our Model—Distressed CSI | |||

Q1 average | 12.7 | 5.0 | |||

Q2 average | 10.1 | 3.4 | |||

Q3 average | 9.1 | 3.1 | |||

Q4 average | 7.3 | 1.8 | |||

Quartile | No. Green | % Green | No Orange | % Orange | |

Q1–3 (15 banks) | 14 | 93.3% | 1 | 6.7% | |

Q4 (five banks) | 1 | 20.0% | 4 | 80.0% |

© 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/).

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**MDPI and ACS Style**

J. Powell, R.; H. Vo, D.
A Comprehensive Stability Indicator for Banks. *Risks* **2020**, *8*, 13.
https://doi.org/10.3390/risks8010013

**AMA Style**

J. Powell R, H. Vo D.
A Comprehensive Stability Indicator for Banks. *Risks*. 2020; 8(1):13.
https://doi.org/10.3390/risks8010013

**Chicago/Turabian Style**

J. Powell, Robert, and Duc H. Vo.
2020. "A Comprehensive Stability Indicator for Banks" *Risks* 8, no. 1: 13.
https://doi.org/10.3390/risks8010013