# The Governance and Disclosure of IFRS 9 Economic Scenarios

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. The Governance of Economic Forecasts

## 4. Methodology

#### 4.1. Overview of Copulas

#### 4.2. Spurious Correlation and Stationarity

#### 4.3. Copula Vine Algorithm

- Convert all the variables to standard uniform variables using the probability integral transform and empirical marginal distribution functions (Angus 1994). The uniform variables are denoted as ${U}_{1},\cdots ,{U}_{n}$ where ${U}_{j}$ corresponds to ${\eta}_{j}$.
- Calculate the correlation between each variable pair at monthly or quarterly lags out to $m$ years. Typically, lags out to one year were considered in this study.
- Look up the correlation and lag at which each variable pair displays the highest correlation with the correct sign based on the predefined expected trend (discussed in Section 5). Say, for instance, that the highest correlation is observed between (lagged) ${U}_{1}$ and ${U}_{n}$. In the next step, consider all the remaining variables, ${U}_{2},\cdots ,{U}_{n-1}$, and find which one is most correlated with the (now lagged) ${U}_{n}$. This process is repeated until all the variables have been processed or when there are no variables left exhibiting a significant correlation. This process creates lists of ordered variables based on the strength of the correlation and causal links.
- Construct the d-vine multivariate copula from the list of ordered variables, where the underlying dataset has been adjusted to incorporate the lags.

#### 4.4. Generating Scenarios Using Conditional Copulas

- Generate ${u}_{1}$ from the uniform distribution $U\left(\mathrm{0,1}\right)$.
- Generate ${u}_{2}$ from ${C}_{2}\left(\xb7|{u}_{1}\right)$.
- Generate …
- Generate ${u}_{n}$ from ${C}_{n}\left(\xb7|{u}_{1},\cdots ,{u}_{n-1}\right)$.

## 5. Economic Data and Trends

#### 5.1. Data

- GDP: SA real GDP year-on-year;
- PDI: Personal disposable income year-on-year;
- BOND: Annual moves in the long-term nominal bond yield;
- CPI: SA inflation rate calculated as the consumer price index year-on-year;
- PPI: Producer price index year-on-year;
- USDZAR: USD/ZAR year-on-year;
- GBPZAR: GBP/ZAR year-on-year;
- EURZAR: EUR/ZAR year-on-year;
- GDE: Real gross domestic expenditure year-on-year;
- HCE: Household consumption expenditure year-on-year;
- HCEG: Household consumption expenditure over GDP year-on-year;
- HHDI: Household debt to disposable income year-on-year;
- UNEMP: SA unemployment rate year-on-year;
- PCE: Private sector credit extension year-on-year;
- FIR: Residential fixed investment year-on-year.

#### 5.2. Expected Trends

- A negative relationship between real GDP growth and NPLs. Positive GDP growth is generally associated with higher household income and lower HHDI (Messai and Jouini 2013; Ghosh 2015; Kuzucu and Kuzucu 2019; Olarewaju 2020).
- A positive relationship between UNEMP and NPLs. Unemployment reduces the purchasing power of households and increases the debt burden. It leads to a decline in effective demand and lower GDE. Higher unemployment implies lower PDI (Rinaldi and Sanchis-Arellano 2006; Messai and Jouini 2013; Kuzucu and Kuzucu 2019; Syed and Aidyngul 2022).
- Increasing interest rates lead to higher NPLs (Messai and Jouini 2013; Kuzucu and Kuzucu 2019; Syed and Aidyngul 2022).
- The relationship between inflation and NPLs is not always straightforward, but in this study, a positive relationship is implemented given the negative impact of inflation on economic growth (Hodge 2006; Rinaldi and Sanchis-Arellano 2006; Nkusu 2011; Ghosh 2015; Olarewaju 2020).
- Sanusi and Meyer (2018) show a positive relationship between inflation and the exchange rate. A depreciation of the exchange rate is correlated with higher NPLs due to the impact on imports and the higher costs involved.
- Declines in real estate investment are correlated with economic downturns and implicitly higher NPLs (Żelazowski 2017; Kohlscheen et al. 2018).

## 6. Results

#### 6.1. Handling Non-Stationarity and Serial Correlation

#### 6.2. Leading and Lagging Relationships

#### 6.3. Multivariate Dependence Structures

- Vine Structure 1: {USDZAR, GBPZAR, EURZAR, HHDI, PDI, HCEG, BOND, UNEMP};
- Vine Structure 2: {CPI, PPI, HCE, GDP}.

#### 6.4. Benchmarking the IFRS 9 Economic Scenarios

#### 6.5. Benchmarking the IFRS 9 Economic Scenario Narrative

#### 6.6. Benchmarking the Scenario Probability

#### 6.7. Discussion of Findings

## 7. IFRS Disclosure

## 8. Concluding Remarks

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A. Historical Time Series

Category | Variable | Variable Name and Description | Source | Data Frequency |
---|---|---|---|---|

Economic Activity | Real GDP | Gross domestic product at market prices. Constant 2010 prices. Seasonally adjusted. | South African Reserve Bank, Code: KBP6006D | Quarterly |

Economic Activity | Real Gross Domestic Expenditure | Gross domestic expenditure. Constant 2010 prices. Seasonally adjusted. | South African Reserve Bank, Code: KBP6019D | Quarterly |

Economic Activity | SA Unemployment Rate | Official unemployment rate. Seasonally adjusted. | South African Reserve Bank, Code: KBP7019L | Quarterly |

Economic Activity | Household Debt to Disposable Income | Household debt to disposable income of households. Current prices. Seasonally adjusted. | South African Reserve Bank, Code: KBP6525L | Quarterly |

Compensation | Personal Disposable Income | Disposable income of households. Current prices. Seasonally adjusted. | South African Reserve Bank, Code: KBP6246L | Quarterly |

Credit Extension | Private Sector Credit Extension | All monetary institutions: total credit extended to the private sector. | South African Reserve Bank, Code: KBP1347M | Monthly |

Consumption | Consumption Expenditure by Households | Constant 2010 prices. Seasonally adjusted. | South African Reserve Bank, Code: KBP6007D | Quarterly |

Consumption | Consumption expenditure by households to GDP | Current prices. Seasonally adjusted. | South African Reserve Bank, Code: KBP6280L | Quarterly |

Interest Rates | Long-term SA Bond Yield | Yield on loan stock traded on the stock exchange for government bonds 10 years and over. | South African Reserve Bank, Code: KBP2003M | Monthly |

Inflation | Consumer Price Index | Headline CPI Year-on-Year Rates | Stats SA, Code: P0141 | Monthly |

Inflation | Producer Price Index | PPI: Final manufactured goods. December 2016 = 100. | Stats SA, Code: P0142.1 | Monthly |

Exchange Rate | USD/ZAR | Rand per US Dollar. Weighted average of the banks’ daily rates at approximately 10:30 a.m. | South African Reserve Bank | Daily |

Exchange Rate | GBP/ZAR | Rand per British Pound. Weighted average of the banks’ daily rates at approximately 10:30 a.m. | South African Reserve Bank | Daily |

Exchange Rate | EUR/ZAR | Rand per Euro. Weighted average of the banks’ daily rates at approximately 10:30 a.m. | South African Reserve Bank | Daily |

Real Estate | Residential Fixed Investment | National Accounts, Real Gross Fixed Capital Formation, Residential Buildings. Constant 2010 prices. Seasonally adjusted. | South African Reserve Bank, Code: KBP6110D | Quarterly |

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**Figure 2.**Cross-correlation graphs between selected variable pairs based on quarterly historical data from March 2010 to December 2018.

**Figure 3.**D-vine copula fitted to the economic variables {USDZAR, GBPZAR, EURZAR, HHDI, PDI, HCEG, BOND, UNEMP} with quarterly data from 2010 to 2018.

**Figure 4.**Bivariate Gumbel copula fitted to the {U: USDZAR, V: GBPZAR} variable pair and an example of the histograms of the conditional distributions.

**Figure 5.**D-vine copula fitted to the economic variables {CPI, PPI, HCE, GDP} using quarterly data from 2010 to 2018.

**Figure 6.**Bivariate Frank copula fitted to the {U: CPI, V:PPI} variable pair and an example of the histograms of the conditional distributions.

**Figure 7.**Illustrating the benchmark approach for the baseline scenarios as published in the annual financial statements of the South African banks for FYE 2019.

**Figure 8.**Illustrating the benchmark approach for the downside scenarios as published in the annual financial statements of the South African banks for FYE 2019.

**Table 1.**Economic outlook over a 1-year period for select economic variables as disclosed by six South African banks in their annual financial statements.

FYE 2019 | FYE 2020 | FYE 2021 | FYE 2019 | FYE 2020 | FYE 2021 | ||||

Bank | FYE | Scenario | Scenario Probability Range | SA Real GDP YoY | SA Real GDP YoY | SA Real GDP YoY | SA Repo Rate | SA Repo Rate | SA Repo Rate |

Bank 1 | 31-Dec | Upside | 20% to 21% | 1.40% | 3.85% | 3.08% | 5.90% | 3.50% | 4.00% |

Baseline | 50% | 0.70% | 3.04% | 1.75% | 6.30% | 3.50% | 4.75% | ||

Downside | 10% to 21% | 0.30% | 2.84% | −0.09% | 6.80% | 3.75% | 5.00% | ||

Severe Stress | 8% to 20% | n.a. | 2.14% | −1.41% | n.a. | 3.92% | 5.25% | ||

Weighted Average | n.a. | 3.10% | 1.39% | n.a. | 3.59% | 4.69% | |||

Bank 2 | 31-Dec | Upside | 16% to 25% | 1.96% | 6.52% | 2.87% | 6.00% | 3.25% | 4.25% |

Baseline | 55% | 1.33% | 4.79% | 2.05% | 6.25% | 3.75% | 4.50% | ||

Downside | 20% to 28% | 0.18% | 5.87% | 1.36% | 7.19% | 4.75% | 5.25% | ||

Weighted Average | 1.26% | 5.38% | 2.00% | 6.38% | 3.96% | 4.67% | |||

Bank 3 | 31-Dec | Upside | 30% | 2.90% | 3.20% | 2.20% | 4.60% | 2.90% | 4.30% |

Baseline | 40% | 1.50% | 3.20% | 1.70% | 6.50% | 3.30% | 3.90% | ||

Downside | 30% | −1.40% | 3.00% | 0.80% | 9.00% | 3.90% | 4.10% | ||

Weighted Average | 1.05% | 3.14% | 1.58% | 6.68% | 3.36% | 4.08% | |||

Bank 4 | 30-Jun | Upside | 12% to 23% | 2.83% | −0.60% | 4.20% | 6.19% | 2.75% | 3.25% |

Baseline | 56% to 59% | 1.05% | −0.60% | 3.10% | 6.75% | 3.25% | 3.50% | ||

Downside | 18% to 32% | 0.31% | −2.00% | −1.90% | 8.19% | 6.00% | 6.35% | ||

Weighted Average | 1.33% | −1.05% | 1.79% | 6.88% | 4.07% | 4.29% | |||

Bank 5 | 31-Mar | Positive Outcome | 1% | n.a. | n.a. | n.a. | n.a. | n.a. | n.a. |

Upside | 2% to 10% | n.a. | n.a. | n.a. | n.a. | n.a. | n.a. | ||

Baseline | 42% to 48% | n.a. | −4.40% | 4.50% | n.a. | 4.80% | 3.60% | ||

Downside | 37% to 44% | n.a. | n.a. | n.a. | n.a. | n.a. | n.a. | ||

Severe Stress | 5% to 10% | n.a. | n.a. | n.a. | n.a. | n.a. | n.a. | ||

Weighted Average | n.a. | n.a. | n.a. | n.a. | n.a. | n.a. | |||

Bank 6 | 28-Feb | Upside | 5% | n.a. | n.a. | n.a. | n.a. | n.a. | n.a. |

Baseline | 60% | n.a. | n.a. | n.a. | n.a. | n.a. | n.a. | ||

Downside | 35% | n.a. | n.a. | n.a. | n.a. | n.a. | n.a. | ||

Weighted Average | n.a. | n.a. | n.a. | n.a. | n.a. | n.a. | |||

FYE 2019 | FYE 2020 | FYE 2021 | FYE 2019 | FYE 2020 | FYE 2021 | ||||

Bank | FYE | Scenario | Scenario Probability Range | SA Inflation Rate | SA Inflation Rate | SA Inflation Rate | Exchange Rate USD/ZAR | Exchange Rate USD/ZAR | Exchange Rate USD/ZAR |

Bank 1 | 31-Dec | Upside | 20% to 21% | 4.20% | n.a. | n.a. | n.a. | n.a. | n.a. |

Baseline | 50% | 4.30% | n.a. | n.a. | n.a. | n.a. | n.a. | ||

Downside | 10% to 21% | 5.20% | n.a. | n.a. | n.a. | n.a. | n.a. | ||

Severe Stress | 8% to 20% | n.a. | n.a. | n.a. | n.a. | n.a. | n.a. | ||

Weighted Average | n.a. | n.a. | n.a. | n.a. | n.a. | n.a. | |||

Bank 2 | 31-Dec | Upside | 16% to 25% | 4.38% | 3.68% | 4.30% | 13.70 | 14.50 | 14.43 |

Baseline | 55% | 4.60% | 4.06% | 4.72% | 14.83 | 15.46 | 15.03 | ||

Downside | 20% to 28% | 6.03% | 5.42% | 5.18% | 16.44 | 17.50 | 15.58 | ||

Weighted Average | 4.83% | 4.39% | 4.78% | 12.67 | 15.90 | 15.08 | |||

Bank 3 | 31-Dec | Upside | 30% | 3.50% | 4.10% | 4.40% | n.a. | n.a. | n.a. |

Baseline | 40% | 5.20% | 3.90% | 4.40% | n.a. | n.a. | n.a. | ||

Downside | 30% | 8.20% | 3.60% | 5.20% | n.a. | n.a. | n.a. | ||

Weighted Average | 5.59% | 3.87% | 4.64% | n.a. | n.a. | n.a. | |||

Bank 4 | 30-Jun | Upside | 12% to 23% | 3.99% | 3.30% | 3.10% | 12.60 | 12.30 | 12.00 |

Baseline | 56% to 59% | 4.89% | 3% | 4.10% | 14.50 | 15.40 | 15.20 | ||

Downside | 18% to 32% | 6.89% | 4.70% | 7.20% | 16.45 | 17.30 | 19.70 | ||

Weighted Average | 5.04% | 3.58% | 4.87% | 14.41 | 15.64 | 16.09 | |||

Bank 5 | 31-Mar | Positive Outcome | 1% | n.a. | n.a. | n.a. | n.a. | n.a. | n.a. |

Upside | 2% to 10% | n.a. | n.a. | n.a. | n.a. | n.a. | n.a. | ||

Baseline | 42% to 48% | n.a. | n.a. | n.a. | n.a. | 16.60 | 15.40 | ||

Downside | 37% to 44% | n.a. | n.a. | n.a. | n.a. | n.a. | n.a. | ||

Severe Stress | 5% to 10% | n.a. | n.a. | n.a. | n.a. | n.a. | n.a. | ||

Weighted Average | n.a. | n.a. | n.a. | n.a. | n.a. | n.a. | |||

Bank 6 | 28-Feb | Upside | 5% | n.a. | 4.10% | 2.60% | n.a. | n.a. | n.a. |

Baseline | 60% | n.a. | 4.60% | 2.90% | n.a. | n.a. | n.a. | ||

Downside | 35% | n.a. | 5.20% | 3.10% | n.a. | n.a. | n.a. | ||

Weighted Average | n.a. | 4.79% | 2.96% | n.a. | n.a. | n.a. |

**Table 2.**Summary of the Archimedean copulas and their generating functions considered in constructing the d-vine.

No. | Copula Name | Generator Function ${\mathit{\phi}}_{\mathit{\alpha}}\left(\mathit{t}\right)$ | Copula Parameter Range |
---|---|---|---|

1 | Clayton | $\frac{1}{\alpha}\left({t}^{-\alpha}-1\right)$ | $[-1,\infty )\backslash \left\{0\right\}$ |

2 | N2 | ${\left(1-t\right)}^{\alpha}$ | $[-1,\infty )$ |

3 | Ali-Mikhail-Haq | $\mathrm{ln}\frac{1-\alpha \left(1-t\right)}{t}$ | $[-\mathrm{1,1})$ |

4 | Gumbel | ${\left(-\mathrm{ln}t\right)}^{\alpha}$ | $[1,\infty )$ |

5 | Frank | $\mathrm{ln}\frac{{e}^{-\alpha t}-1}{{e}^{-\alpha}-1}$ | $(-\infty ,\infty )\backslash \left\{0\right\}$ |

6 | Joe | $-\mathrm{ln}\left({1-\left(1-t\right)}^{\alpha}\right)$ | $[1,\infty )$ |

7 | N7 | $-\mathrm{ln}\left(\alpha t+\left(1-\alpha \right)\right)$ | $\left(\mathrm{0,1}\right]$ |

8 | N8 | $\frac{1-t}{1+\left(\alpha -1\right)t}$ | $[1,\infty )$ |

9 | Gumbel–Barnett | $\mathrm{ln}\left(1-\alpha \mathrm{ln}t\right)$ | $\left(\mathrm{0,1}\right]$ |

10 | N10 | $\mathrm{ln}\left(2{t}^{-\alpha}-1\right)$ | $\left(\mathrm{0,1}\right]$ |

11 | N11 | $\mathrm{ln}\left(2-{t}^{\alpha}\right)$ | $(0,\frac{1}{2}]$ |

12 | N12 | ${\left(\frac{1}{t}-1\right)}^{\alpha}$ | $[1,\infty )$ |

13 | N13 | ${\left(1-\mathrm{ln}t\right)}^{\alpha}-1$ | $(0,\infty )$ |

14 | N14 | ${\left({t}^{\raisebox{1ex}{$-1$}\!\left/ \!\raisebox{-1ex}{$\alpha $}\right.}-1\right)}^{\alpha}$ | $[1,\infty )$ |

15 | Genest–Ghoudi | ${\left(1-{t}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\alpha $}\right.}\right)}^{\alpha}$ | $[1,\infty )$ |

16 | N16 | $\left(\frac{\alpha}{t}+1\right)\left(1-t\right)$ | $[0,\infty )$ |

17 | N17 | $-\mathrm{ln}\frac{{\left(1+t\right)}^{-\alpha}-1}{{2}^{-\alpha}-1}$ | $(-\infty ,\infty )\backslash \left\{0\right\}$ |

18 | N18 | ${e}^{\raisebox{1ex}{$\alpha $}\!\left/ \!\raisebox{-1ex}{$\left(t-1\right)$}\right.}$ | $[2,\infty )$ |

19 | N19 | ${e}^{\raisebox{1ex}{$\alpha $}\!\left/ \!\raisebox{-1ex}{$t$}\right.}-{e}^{\alpha}$ | $(0,\infty )$ |

20 | N20 | $exp\left({t}^{-\alpha}\right)-e$ | $(0,\infty )$ |

21 | N21 | $1-{\left[1-{\left(1-t\right)}^{\alpha}\right]}^{1/\alpha}$ | $[1,\infty )$ |

22 | N22 | $arcsin\left(1-{t}^{\alpha}\right)$ | $\left(\mathrm{0,1}\right]$ |

**Table 3.**Summary of the estimated coefficients of the ARIMA(${p}_{A},d,{q}_{A}$)${\left({p}_{S},{d}_{S},{q}_{S}\right)}_{S}$–GARCH($p$,$q$) models.

Variable | ${\mathit{\lambda}}_{0}$ | ${\mathit{\lambda}}_{1}$ | ${\mathit{\lambda}}_{2}$ | ${\mathit{\lambda}}_{3}$ | ${\mathbf{\Lambda}}_{4}$ | ${\mathbf{\Lambda}}_{8}$ | ${\mathit{\sigma}}^{2}$ | $\mathit{\omega}$ | ${\mathit{\gamma}}_{1}$ | ${\mathit{\beta}}_{1}$ |
---|---|---|---|---|---|---|---|---|---|---|

USDZAR | 0.00 | 0.00 | 0.00 | 0.00 | −0.55 | −0.32 | 104.36 | 0.00 | 0.00 | 0.99 |

GBPZAR | −0.01 | 0.00 | 0.00 | 0.00 | −0.63 | −0.39 | 76.33 | 0.00 | 0.00 | 0.99 |

EURZAR | 0.00 | 0.00 | 0.00 | 0.26 | −0.73 | −0.44 | 81.12 | 0.00 | 0.00 | 0.99 |

BOND | 0.00 | 0.00 | −0.38 | 0.00 | −0.66 | 0.00 | 0.36 | 0.00 | 0.00 | 0.98 |

CPI | 0.00 | 0.47 | 0.00 | 0.00 | −0.49 | 0.00 | 0.94 | 0.00 | 0.00 | 0.98 |

PPI | 0.00 | 0.38 | 0.00 | 0.00 | −0.70 | −0.35 | 3.26 | 1.99 | 0.49 | 0.00 |

GDP | 0.00 | 0.45 | 0.00 | 0.00 | −0.55 | −0.40 | 0.35 | 0.11 | 0.00 | 0.71 |

GDE | 0.00 | 0.00 | 0.00 | 0.00 | −0.57 | −0.25 | 1.92 | 0.72 | 0.22 | 0.42 |

HCE | −0.0004 | 0.7117 | 0 | 0 | −0.3828 | −0.3277 | 0.3756 | 0.1154 | 0 | 0.7124 |

HCEG | 0.0005 | −0.2172 | 0 | 0 | −0.5191 | −0.3356 | 1.7211 | 0.5888 | 0.0918 | 0.5743 |

PDI | 0.00 | 0.00 | 0.00 | 0.00 | −0.56 | 0.00 | 1.66 | 0.00 | 0.00 | 0.95 |

HHDI | 0.00 | 0.33 | 0.38 | 0.00 | −0.78 | −0.41 | 2.54 | 0.00 | 0.00 | 0.97 |

UNEMP | 0.00 | 0.00 | 0.00 | 0.00 | −0.40 | −0.37 | 6.98 | 0.90 | 0.00 | 0.86 |

PCE | 0.00 | 0.00 | 0.00 | 0.37 | −0.49 | 0.00 | 1.26 | 0.00 | 0.00 | 0.96 |

FIR | 0.00 | 0.42 | 0.00 | 0.00 | −0.44 | 0.00 | 17.90 | 3.29 | 0.08 | 0.74 |

d-Vine No. | Variable Pair | Correlation | Lag in Quarters | Copula No. | Copula Parameter |
---|---|---|---|---|---|

1 | USDZAR; GBPZAR | 83% | 0 | 4 | 2.464 |

1 | GBPZAR; EURZAR | 79% | 0 | 20 | 0.515 |

1 | EURZAR; HHDI | 50% | 0 | 3 | 0.971 |

1 | HHDI; PDI | −49% | 0 | 5 | −3.426 |

1 | PDI; HCEG | 43% | 0 | 6 | 1.51 |

1 | HCEG; BOND | −42% | 0 | 3 | −1 |

1 | BOND; UNEMP | 50% | 2 | 21 | 2.33 |

2 | CPI; PPI | 65% | 0 | 5 | 5 |

2 | PPI; HCE | −46% | 0 | 5 | −3.201 |

2 | HCE; GDP | 47% | 0 | 1 | 0.887 |

IFRS Scenario: Downturn 5% | Benchmark Probability | |||||
---|---|---|---|---|---|---|

Scenario Values s_{1} | Scenario Values s_{2} | Scenario Values s_{3} | Implied Probability P(Benchmark ≤ s_{1}) | Implied Probability P(Benchmark ≤ s_{2}) | Implied Probability P(Benchmark ≤ s_{3}) | |

Economic Variable | Year 1 | Year 2 | Average | Year 1 | Year 2 | Average |

USDZAR | 28 | 5 | 16.5 | 98% | 63% | 89% |

CPI | 6.0 | 6.0 | 6.0 | 94% | 94% | 94% |

GDP | −0.72 | 0.0 | −0.36 | 46% | 58% | 52% |

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**MDPI and ACS Style**

Stander, Y.S.
The Governance and Disclosure of IFRS 9 Economic Scenarios. *J. Risk Financial Manag.* **2023**, *16*, 47.
https://doi.org/10.3390/jrfm16010047

**AMA Style**

Stander YS.
The Governance and Disclosure of IFRS 9 Economic Scenarios. *Journal of Risk and Financial Management*. 2023; 16(1):47.
https://doi.org/10.3390/jrfm16010047

**Chicago/Turabian Style**

Stander, Yolanda S.
2023. "The Governance and Disclosure of IFRS 9 Economic Scenarios" *Journal of Risk and Financial Management* 16, no. 1: 47.
https://doi.org/10.3390/jrfm16010047