# A Forward-Looking IFRS 9 Methodology, Focussing on the Incorporation of Macroeconomic and Macroprudential Information into Expected Credit Loss Calculation

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## Abstract

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## 1. Introduction

## 2. Literature Review

## 3. Methodology

- Perform PCA on the explanatory variables ${\mathit{X}}_{n\times p}={\left({\mathit{x}}_{1},\dots ,{\mathit{x}}_{\mathit{n}}\right)}^{T}$ to obtain the principal components ${\mathit{W}}_{n\times p}={\left({\mathit{w}}_{1},\dots ,{\mathit{w}}_{n}\right)}^{T}$, where $\mathit{W}=\mathit{V}\mathit{X}$ and ${\mathit{V}}_{p\times p}$ the orthonormal set of eigenvectors. Then, select a subset ${\mathit{W}}_{\kappa}=\mathit{X}{\mathit{V}}_{\kappa}$, with ${\mathit{V}}_{\kappa}=\left({\mathit{v}}_{1},\dots ,{\mathit{v}}_{\kappa}\right)$, where $\kappa =\mathrm{min}\left\{\kappa :{{\displaystyle \sum}}_{j=1}^{\kappa}{\lambda}_{j}/{{\displaystyle \sum}}_{j=1}^{p}{\lambda}_{j}\ge \delta \right\};\delta \approx 1$ and ${\lambda}_{j}$ the $j$th eigenvalue of ${\mathit{X}}^{T}\mathit{X}$.
- Regress the observed vector ${\mathit{Y}}_{n\times 1}={\left({y}_{1},\dots ,{y}_{n}\right)}^{T}$ of outcomes on the selected principal components as covariates, $\mathit{Y}={\mathit{W}}_{\kappa}{\mathit{\gamma}}_{\kappa}+\mathit{\u03f5}$, using ordinary least squares regression to obtain a vector of estimated regression coefficients, ${\widehat{\mathit{\gamma}}}_{\kappa}$, with dimension equal to the number of selected principal components $\kappa .$
- Transform the vector ${\widehat{\mathit{\gamma}}}_{\kappa}$ back to the scale of the actual covariates ${\widehat{\mathit{\beta}}}_{\mathit{\kappa}}={\mathit{V}}_{\kappa}{\widehat{\mathit{\gamma}}}_{\kappa}$, using the selected PCA loadings (the eigenvectors corresponding to the selected principal components) to obtain the final PCR estimator ${\widehat{\mathit{\beta}}}_{\kappa}$ (with dimension equal to the total number of covariates) for estimating the regression coefficients characterising the original model.

#### 3.1. Credit Risk Index

- Limiting the CRI to the observation that was observed in the last 12 months ensures having the same “horizons” for all observation months. If it is not limited to the last 12 months, some months will have a different number of observation months, and the denominator will not be equal over time.
- Using 12 months ensures that the changes in macroeconomic conditions are reflected in more recent populations and not confused with the behaviour far in the past (i.e., more than 12 months ago).
- The CRIs included in the development data are based only on up-to-date accounts. This is due to the assumption that an increase in credit risk has already impacted accounts that have missed at least one payment, and the behaviour of these accounts is thus more likely to be driven by a deteriorated probability of default than a deteriorated economic outlook. In addition, these up-to-date accounts have an expected lifetime of 12 months according to IFRS 9 principles (i.e., Stage 1), which serve as further motivation for specifically using a 12-month outcome period in the CRI calculation.

#### 3.2. Principal Component Regression

- The estimated sign for the regression coefficients ${\widehat{\mathit{\beta}}}_{\kappa}^{c}$ of the macroeconomic variables should be in line with economic expectations. For example, the estimated sign for the GDP coefficient should be negative since we expect default rates to decrease when GDP increases (see Durović 2019).
- All estimated coefficients of ${\widehat{\mathit{\gamma}}}_{\kappa}^{c}$ are statistically significant at $\alpha \%$ significance level, for example, $\alpha =0.05$ (see Durović 2019).

#### 3.3. Derivation of the Macroeconomic Scalar

## 4. Case Study

#### 4.1. Data

- Real gross domestic product (GDP);
- Nominal gross domestic product (NGDP);
- Consumer price index (CPI);
- House price index (HPI);
- Prime rate (PR);
- Total disposable household income (DHI);
- Household debt to disposable income (HDDI);
- Debt Service Ratio (DSR);
- New vehicle sales (NVS);
- Credit extended to households (CEH);
- Monetary credit extended (MCE);
- Instalment debtors (ID);
- Overdrafts and loans (OL).

#### 4.2. PCR

#### 4.3. Macroeconomic Scalar

## 5. Conclusions & Future Recommendations

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**PCR model against macroeconomic variables and $CR{I}^{\u2033}$. (

**a**) PR; (

**b**) CEH; (

**c**) ID; (

**d**) NVS; (

**e**) GDP_L6.

**Figure 4.**Forecasted $CR{I}^{\u2033}$ for PCR, GLM-PCR, REG and GLM with baseline, upside, and downside macroeconomic scenarios. (

**a**) PCR; (

**b**) GLM-PCR; (

**c**) REG; (

**d**) GLM-REG.

**Figure 5.**Macroeconomic scalar for PCR, GLM-PCR, REG, and GLM with baseline, upside, and downside macroeconomic scenarios. (

**a**) PCR; (

**b**) GLM-PCR; (

**c**) REG; (

**d**) GLM-REG.

Observation Date $\mathbf{\left(}{\mathit{O}}_{\mathit{n}}\mathbf{\right)}$ | Performing Accounts $\mathbf{\left(}{\mathit{a}}_{\mathit{n}}\mathbf{\right)}$ | Months after Observation (t) | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | ||

201509 | 1167 | 4 | 7 | 12 | 41 | 45 | 40 | 34 | 41 | 32 | 36 | 35 | 35 |

201510 | 1180 | 4 | 7 | 10 | 46 | 42 | 35 | 44 | 36 | 40 | 38 | 37 | 40 |

201511 | 1208 | 4 | 7 | 20 | 45 | 38 | 45 | 38 | 43 | 40 | 42 | 42 | 40 |

201512 | 1221 | 3 | 13 | 18 | 40 | 48 | 38 | 43 | 44 | 43 | 44 | 43 | 34 |

201601 | 1220 | 7 | 10 | 13 | 49 | 39 | 41 | 42 | 43 | 44 | 44 | 34 | 36 |

201602 | 1251 | 5 | 8 | 19 | 40 | 44 | 42 | 45 | 47 | 48 | 38 | 38 | 51 |

201603 | 1295 | 4 | 13 | 14 | 47 | 48 | 48 | 52 | 53 | 43 | 44 | 58 | 49 |

201604 | 1311 | 7 | 10 | 15 | 49 | 49 | 48 | 53 | 44 | 46 | 59 | 51 | 60 |

201605 | 1329 | 6 | 11 | 13 | 52 | 54 | 51 | 45 | 49 | 63 | 54 | 63 | 69 |

201606 | 1367 | 6 | 9 | 9 | 56 | 55 | 46 | 52 | 66 | 57 | 67 | 74 | 59 |

201607 | 1421 | 6 | 7 | 9 | 58 | 54 | 59 | 76 | 65 | 76 | 85 | 69 | 67 |

201608 | 1461 | 4 | 6 | 8 | 57 | 64 | 79 | 69 | 81 | 93 | 73 | 74 | 64 |

$\left({Z}_{n,1},{Z}_{n,2}{Z}_{n,3}\right)$ | $\left({Z}_{n,1},{Z}_{n,2}{Z}_{n-3,3}\right)$ | $\left({Z}_{n,1},{Z}_{n,2}{Z}_{n-6,3}\right)$ |

$\left({Z}_{n-3,1},{Z}_{n,2}{Z}_{n,3}\right)$ | $\left({Z}_{n-3,1},{Z}_{n,2}{Z}_{n-3,3}\right)$ | $\left({Z}_{n-3,1},{Z}_{n,2}{Z}_{n-6,3}\right)$ |

$\left({Z}_{n-6,1},{Z}_{n,2}{Z}_{n,3}\right)$ | $\left({Z}_{n-6,1},{Z}_{n,2}{Z}_{n-3,3}\right)$ | $\left({Z}_{n-6,1},{Z}_{n,2}{Z}_{n-6,3}\right)$ |

$\left({Z}_{n,1},{Z}_{n-3,2}{Z}_{n,3}\right)$ | $\left({Z}_{n,1},{Z}_{n-3,2}{Z}_{n-3,3}\right)$ | $\left({Z}_{n,1},{Z}_{n-3,2}{Z}_{n-6,3}\right)$ |

$\left({Z}_{n-3,1},{Z}_{n-3,2}{Z}_{n,3}\right)$ | $\left({Z}_{n-3,1},{Z}_{n-3,2}{Z}_{n-3,3}\right)$ | $\left({Z}_{n-3,1},{Z}_{n-3,2}{Z}_{n-6,3}\right)$ |

$\left({Z}_{n-6,1},{Z}_{n-3,2}{Z}_{n,3}\right)$ | $\left({Z}_{n-6,1},{Z}_{n-3,2}{Z}_{n-3,3}\right)$ | $\left({Z}_{n-6,1},{Z}_{n-3,2}{Z}_{n-6,3}\right)$ |

$\left({Z}_{n,1},{Z}_{n-6,2}{Z}_{n,3}\right)$ | $\left({Z}_{n,1},{Z}_{n-6,2}{Z}_{n-3,3}\right)$ | $\left({Z}_{n,1},{Z}_{n-6,2}{Z}_{n-6,3}\right)$ |

$\left({Z}_{n-3,1},{Z}_{n-6,2}{Z}_{n,3}\right)$ | $\left({Z}_{n-3,1},{Z}_{n-6,2}{Z}_{n-3,3}\right)$ | $\left({Z}_{n-3,1},{Z}_{n-6,2}{Z}_{n-6,3}\right)$ |

$\left({Z}_{n-6,1},{Z}_{n-6,2}{Z}_{n,3}\right)$ | $\left({Z}_{n-6,1},{Z}_{n-6,2}{Z}_{n-3,3}\right)$ | $\left({Z}_{n-6,1},{Z}_{n-6,2}{Z}_{n-6,3}\right)$ |

Variable Name | Expected Sign |
---|---|

Real gross domestic product (GDP) | Negative |

New vehicle sales (NVS) | Negative |

Total disposable household income (DHI) | Negative |

Consumer price index (CPI) | Positive |

Debt Service Ratio (DSR) | Positive |

Prime rate (PR) | Positive |

Instalment debtors (ID) | Negative |

House price index (HPI) | Negative |

Credit extended to households (CEH) | Negative |

Description | Model 1 | Model 2 | Model 3 |
---|---|---|---|

Combination number | 32680 | 3819 | 32483 |

PC used | 2 | 2 | 2 |

AIC | −1914.20 | −1910.28 | −1909.75 |

AICC | −1913.89 | −1909.98 | −1909.44 |

BIC | −1902.55 | −1898.63 | −1898.10 |

RMSE | 0.000206 | 0.000209 | 0.000210 |

Number of variables | 5 | 4 | 5 |

Variable 1 | NVS | NVS | NVS |

Variable 2 | PR | PR | PR_L3 |

Variable 3 | CEH | CEH | CEH |

Variable 4 | ID | ID_L3 | ID |

Variable 5 | GDP_L6 | GDP_L6 | |

Intercept | 0.00208 | 0.00205 | 0.00208 |

Coefficient of variable 1 | −0.00022 | −0.00028 | −0.00020 |

Coefficient of variable 2 | 0.00017 | 0.00019 | 0.00019 |

Coefficient of variable 3 | −0.00009 | −0.00021 | −0.00009 |

Coefficient of variable 4 | −0.00026 | −0.00036 | −0.00025 |

Coefficient of variable 5 | −0.00018 | −0.00017 |

Description | PCA1 | PCA2 |
---|---|---|

Coefficient of NVS | −0.24520 | 0.60779 |

Coefficient of PR | 0.41841 | −0.54217 |

Coefficient of CEH | 0.57044 | 0.03736 |

Coefficient of ID | 0.40922 | 0.50460 |

Coefficient of GDP_L6 | 0.52148 | 0.28396 |

Description | PCR | GLM_PCR | REG | GLM |
---|---|---|---|---|

Combination number | 32680 | 32680 | 3181 | 3181 |

PC used | 2 | 2 | NA | NA |

RMSE | 0.000206 | 0.000233 | 0.000188 | 0.000195 |

Number of variables | 5 | 5 | 4 | 4 |

Variable 1 | NVS | NVS | NVS | NVS |

Variable 2 | PR | PR | DSR | DSR |

Variable 3 | CEH | CEH | CEH_L3 | CEH_L3 |

Variable 4 | GDP_L6 | GDP_L6 | GDP_L3 | GDP_L3 |

Variable 5 | ID | ID | ||

Intercept | 0.00208 | −4.08182 | 0.00182 | −4.17746 |

Coefficient of variable 1 | −0.00022 | −0.07228 | −0.00015 | −0.04021 |

Coefficient of variable 2 | 0.00017 | 0.05578 | 0.00054 | 0.19122 |

Coefficient of variable 3 | −0.00009 | −0.02992 | −0.00066 | −0.23253 |

Coefficient of variable 4 | −0.00018 | −0.06145 | −0.00014 | −0.03765 |

Coefficient of variable 5 | v0.00026 | −0.08667 |

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## Share and Cite

**MDPI and ACS Style**

Breed, D.G.; Hurter, J.; Marimo, M.; Raletjene, M.; Raubenheimer, H.; Tomar, V.; Verster, T.
A Forward-Looking IFRS 9 Methodology, Focussing on the Incorporation of Macroeconomic and Macroprudential Information into Expected Credit Loss Calculation. *Risks* **2023**, *11*, 59.
https://doi.org/10.3390/risks11030059

**AMA Style**

Breed DG, Hurter J, Marimo M, Raletjene M, Raubenheimer H, Tomar V, Verster T.
A Forward-Looking IFRS 9 Methodology, Focussing on the Incorporation of Macroeconomic and Macroprudential Information into Expected Credit Loss Calculation. *Risks*. 2023; 11(3):59.
https://doi.org/10.3390/risks11030059

**Chicago/Turabian Style**

Breed, Douw Gerbrand, Jacques Hurter, Mercy Marimo, Matheba Raletjene, Helgard Raubenheimer, Vibhu Tomar, and Tanja Verster.
2023. "A Forward-Looking IFRS 9 Methodology, Focussing on the Incorporation of Macroeconomic and Macroprudential Information into Expected Credit Loss Calculation" *Risks* 11, no. 3: 59.
https://doi.org/10.3390/risks11030059