# Measuring the Performance of Bank Loans under Basel II/III and IFRS 9/CECL

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Recent Developments in Accounting and Banking Supervision

#### 3.1. Loan Loss Provisioning under IFRS 9 and CECL

**Stage 1**: Normally performing loans, banks have to reserve one-year expected loss**Stage 2**: Loan with substantially deteriorated credit quality, banks have to reserve lifetime expected loss**Stage 3**: Defaulted loans, banks have to build a specific loan loss provision

#### 3.2. Minimum Capital Requirements under Basel II/III

## 4. A Framework for Loan Performance Measurement

- Interest Rate Income
- -
- Funding Costs
- -
- Expected Loss Coverage
- -
- Operational Costs
- —
- ————————————
- ÷
- Allocated Capital Buffer
- —
- ————————————
- =
- RAROC

#### 4.1. Estimation of Credit Risk Parameters

#### 4.2. Determination of Cost Components

## 5. An Example for Residential Mortgages

## 6. Discussion

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

RAROC | risk-adjusted return on capital |

RORAC | return on risk-adjusted capital |

PD | default probability |

LGD | loss given default |

EAD | exposure at default |

CCF | credit conversion factor |

CPR | conditional prepayment rate |

## References

- Abad, Jorge, and Javier Suarez. 2018. The Procyclicality of Expected Credit Loss Provisions. Technical Report. Madrid: CEMFI. [Google Scholar]
- Aguais, Scott D., Lawrence R. Forest, Martin King, Marie C. Lennon, and Brola Lordkipanidze. 2007. Designing and implementing a Basel II compliant PIT–TTC Ratings Framework. In The Basel Handbook: A Guide for Financial Practitioners, 2nd ed. Edited by Micheal Ong. London: Risk Books, pp. 267–98. [Google Scholar]
- Altavilla, Carlo, Miguel Boucinha, and José-Luis Peydró. 2018. Monetary policy and bank profitability in a low interest rate environment. Economic Policy 33: 531–86. [Google Scholar] [CrossRef][Green Version]
- Andreeva, Galina, Jake Ansell, and Jonathan Crook. 2007. Modelling profitability using survival combination scores. European Journal of Operational Research 183: 1537–49. [Google Scholar] [CrossRef]
- Baione, Fabio, Paolo De Angelis, and Ivan Granito. 2020. Capital allocation and RORAC optimization under Solvency 2 standard formula. Annals of Operations Research, 1–17. [Google Scholar] [CrossRef]
- Banasik, John, Jonathan N. Crook, and Lyn C. Thomas. 1999. Not if but when will borrowers default. The Journal of the Operational Research Society 50: 1185–90. [Google Scholar] [CrossRef]
- BCBS. 2006. International Convergence of Capital Measurement and Capital Standards: A Revised Framework. Available online: http://www.bis.org/publ/bcbsca.htm (accessed on 12 April 2019).
- BCBS. 2011. Basel III: A Global Regulatory Framework for more Resilient Banks and Banking Systems. Available online: http://www.bis.org/publ/bcbs189.htm (accessed on 12 April 2019).
- BCBS. 2017. Basel III: Finalising Post-Crisis Reforms. Available online: https://www.bis.org/bcbs/publ/d424.pdf (accessed on 12 April 2019).
- BCBS. 2019. CRE 35-IRB Approach: Treatment of Expected Losses and Provisions. Available online: https://www.bis.org/basel_framework/chapter/CRE/35.htm?inforce=20191215&export=pdf (accessed on 4 May 2020).
- Birge, John R., and Pedro Júdice. 2013. Long-term bank balance sheet management: Estimation and simulation of risk-factors. Journal of Banking & Finance 37: 4711–20. [Google Scholar]
- Braun, Alexander, Hato Schmeiser, and Florian Schreiber. 2018. Return on risk-adjusted capital under Solvency II: Implications for the asset management of insurance companies. The Geneva Papers on Risk and Insurance-Issues and Practice 43: 456–72. [Google Scholar] [CrossRef]
- Busch, Ramona, Christian Drescher, and Christoph Memmel. 2017. Bank Stress Testing under Different Balance Sheet Assumptions. Technical Report 978-3-95729-351-0. Frankfurt am Main: Deutsche Bundesbank, Available online: http://hdl.handle.net/10419/157254 (accessed on 7 April 2020).
- Carlehed, Magnus, and Alexander Petrov. 2012. A Methodology for Point-in-Time-Through-the-Cycle Probability of Default Decomposition in Risk Classification Systems. The Journal of Risk Model Validation 6: 3–25. [Google Scholar] [CrossRef]
- Chawla, Gaurav, Lawrence R. Forest, and Scott D. Aguais. 2016a. Point-in-Time Loss Given Default Rates and Exposures at Default Models for IFRS 9/CECL and stress testing. Journal of Risk Management in Financial Institutions 9: 249–63. [Google Scholar]
- Chawla, Gaurav, Lawrence R. Forest, and Scott D. Aguais. 2016b. Some options for evaluating significant deterioration under IFRS 9. The Journal of Risk Model Validation 10: 69–89. [Google Scholar] [CrossRef]
- Crouhy, Michel, Stuart M. Turnbull, and Lee M. Wakeman. 1999. Measuring Risk-adjusted Performance. Journal of Risk 2: 5–36. [Google Scholar] [CrossRef]
- Engelmann, Bernd. 2020. Calculating Lifetime Expected Loss for IFRS 9: Which Formula Is Correct? Available online: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3238632 (accessed on 7 May 2020).
- Engelmann, Bernd, and Ha Pham. 2020. A RAROC valuation scheme for loans and its application in loan origination. Risks 8: 63. [Google Scholar] [CrossRef]
- Engelmann, Bernd, and Robert Rauhmeier. 2011. The Basel II Risk Parameters: Estimation, Validation, Stress Testing—With Applications to Loan Risk Management, 2nd ed. Berlin: Springer. [Google Scholar]
- European Systemic Risk Board. 2019. Expected Credit Loss Approaches in Europe and the United States: Differences from a Financial Stability Perspective. Available online: https://www.esrb.europa.eu/pub/pdf/reports/esrb.report190116_expectedcreditlossapproachesEuropeUS.en.pdf (accessed on 17 May 2020).
- FASB. 2016. Accounting Standards Update No. 2016-13, Financial Instruments-Credit Losses (Topic 326): Measurement of Credit Losses on Financial Instruments. Connecticut: Financial Accounting Standards Board. [Google Scholar]
- Gordy, Michael B., and Bradley Howells. 2006. Procyclicality in Basel II: Can we treat the disease without killing the patient? Journal of Financial Intermediation 15: 395–417. [Google Scholar] [CrossRef][Green Version]
- Gupton, Gred M., Christopher Clemens Finger, and Mickey Bhatia. 1997. Creditmetrics: Technical Document. New York: JP Morgan & Co. Incorporated. [Google Scholar]
- Hasan, Maher M., Christian Schmieder, and Claus Puhr. 2011. Next Generation Balance Sheet Stress Testing. IMF Working Papers 2011/083. Washington: International Monetary Fund. [Google Scholar]
- IASB. 2014. IFRS Standard 9: Financial Instruments. London: International Accounting Standards Board. [Google Scholar]
- Ita, Andreas. 2016. Capital Allocation in Large Banks—A Renewed Look at Practice. Available online: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2726165 (accessed on 12 April 2019).
- Kapinos, Pavel, and Oscar A. Mitnik. 2016. A top-down approach to stress-testing banks. Journal of Financial Services Research 49: 229–64. [Google Scholar] [CrossRef]
- Klaassen, Pieter, and Idzard Van Eeghen. 2018. Bank capital allocation and performance management under multiple capital constraints. Journal of Risk Management in Financial Institutions 11: 194–206. [Google Scholar] [CrossRef][Green Version]
- Krüger, Steffen, Daniel Rösch, and Harald Scheule. 2018. The impact of loan loss provisioning on bank capital requirements. Journal of Financial Stability 36: 114–29. [Google Scholar] [CrossRef][Green Version]
- Le Sourd, Véronique. 2007. Performance measurement for traditional investment. Financial Analysts Journal 58: 36–52. [Google Scholar]
- Loterman, Gert, Iain Brown, David Martens, Christophe Mues, and Bart Baesens. 2012. Benchmarking regression algorithms for loss given default modeling. International Journal of Forecasting 28: 161–70. [Google Scholar] [CrossRef]
- Malik, Madhur, and Lyn C. Thomas. 2010. Modelling credit risk of portfolio of consumer loans. Journal of the Operational Research Society 61: 411–20. [Google Scholar] [CrossRef]
- McGowan, Müge A., Dan Andrews, and Valentine Millot. 2018. The walking dead? Zombie firms and productivity performance in OECD countries. Economic Policy 33: 685–736. [Google Scholar] [CrossRef][Green Version]
- Merton, Robert C. 1974. On the Pricing of Corporate Debt: The Risk Structure of Interest Rates. Journal of Finance 29: 449–70. [Google Scholar]
- Miu, Peter, Bogie Ozdemir, Evren Cubukgil, and Michael Giesinger. 2016. Determining hurdle rate and capital allocation in credit portfolio management. Journal of Financial Services Research 50: 243–73. [Google Scholar] [CrossRef][Green Version]
- Montesi, Giuseppe, and Giovanni Papiro. 2018. Bank stress testing: A stochastic simulation framework to assess banks’ financial fragility. Risks 6: 82. [Google Scholar] [CrossRef][Green Version]
- Ong, Michael K. 2007. The Basel Handbook: A Guide for Financial Practitioners, 2nd ed. London: Risk Books. [Google Scholar]
- Punjabi, Sanjeev, and Oliver Dunsche. 1998. Effective risk-adjusted performance measurement for greater shareholder value. Journal of Lending and Credit Risk Management 81: 18–24. [Google Scholar]
- Repullo, Rafael, and Javier Suarez. 2004. Loan pricing under Basel capital requirements. Journal of Financial Intermediation 13: 496–521. [Google Scholar] [CrossRef][Green Version]
- Repullo, Rafael, and Javier Suarez. 2013. The Procyclical Effects of Bank Capital Regulation. The Review of Financial Studies 26: 452–90. [Google Scholar] [CrossRef][Green Version]
- Saurina, Jesús, and Carlos Trucharte. 2007. An Assessment of Basel II Procyclicality in Mortgage Portfolios. Journal of Financial Services Research 32: 81–101. [Google Scholar] [CrossRef][Green Version]
- Skoglund, Jimmy. 2017. Credit risk term-structures for lifetime impairment forecasting: A practical guide. Journal of Risk Management in Financial Institutions 10: 188–95. [Google Scholar] [CrossRef]
- Skoglund, Jimmy, and Wei Chen. 2016. The application of credit risk models to macroeconomic scenario analysis and stress testing. Journal of Credit Risk 12: 1–45. [Google Scholar] [CrossRef]
- Skoglund, Jimmy, and Wei Chen. 2020. On the Comprehensive Balance Sheet Stress Testing and Net Interest Income P/L Attribution. Available online: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3547286 (accessed on 19 May 2020).
- Stein, Roger M. 2005. The relationship between default prediction and lending profits: Integrating ROC analysis and loan pricing. Journal of Banking & Finance 29: 1213–36. [Google Scholar]
- Stoughton, Neal M., and Josef Zechner. 2007. Optimal Capital Allocation using RAROC
^{TM}and EVA^{®}. Journal of Financial Intermediation 16: 312–42. [Google Scholar] [CrossRef] - Tasche, Dirk. 2007. Capital Allocation to Business Units and Sub-Portfolios: The Euler Principle. Technical Report. arXiv arXiv:0708.2542. [Google Scholar]
- Tobback, Ellen, David Martens, Tony Van Gestel, and Bart Baesens. 2014. Forecasting Loss Given Default models: Impact of account characteristics and the macroeconomic state. Journal of the Operational Research Society 65: 376–92. [Google Scholar] [CrossRef][Green Version]
- Xu, Xin. 2016. Estimating Lifetime Expected Credit Losses under IFRS 9. Technical Report. Available online: https://dx.doi.org/10.2139/ssrn.2758513 (accessed on 12 May 2019).
- Zaik, Edward, John Walter, Gabriela Retting, and Christopher James. 1996. RAROC at Bank of America: From theory to practice. Journal of Applied Corporate Finance 9: 83–93. [Google Scholar] [CrossRef]

1 | One weakness of this article is that we did not utilize real data. Although one of the authors has done some implementation work of this framework in practice, both the results and the data could not be utilized for research purposes due to confidentiality restrictions. |

2 | Some authors call the resulting performance measure when economic capital is used RARORAC (Risk-Adjusted Return On Risk-Adjusted Capital) to avoid misunderstandings. |

3 | A good source of the latest developments is the paper archive of the bi-annual credit scoring conference in Edinburgh: https://crc.business-school.ed.ac.uk/category/conference-papers/. |

4 | Using (3) for capital calculations implicitly assumes that a bank is required to have at least 8% of RWA, which might not be true after the introduction of new capital buffers in BCBS (2011). The actual percentage, however, might differ between banks depending on the policy of its national supervisor. Therefore, we stick to 8% for the purpose of this article. |

5 | We have assumed that aside from PDs which clearly have to be stage-dependent, all other risk parameters are stage-independent. This might not be true in general. For instance, in loan segments where prepayments are possible without penalty, prepayment probabilities might depend on credit quality making ${\widehat{N}}_{i}$ stage-dependent. |

6 | Whether all these parameters are necessary and meaningful depends on the particular portfolio and the legal environment the bank is operating in. If the loans do not include credit lines, $ccf$ is not needed and if prepayment without penalty is prohibited, there might be no use for $cpr$. |

Expiry | Interest Rate |
---|---|

1 Year | 12M Libor + ${s}_{1}$ |

2 Years | 12M Libor + ${s}_{2}$ |

⋮ | ⋮ |

n Years | 12M Libor + ${s}_{n}$ |

Year | S (%) | s (%) | ${\mathit{\delta}}^{\mathit{M}}$ | $\widehat{\mathit{\lambda}}$ (%) | $\mathit{\delta}$ | ${\widehat{\mathit{f}}}_{float}$ (%) | ${\widehat{\mathit{f}}}_{fix}(\%)$ |
---|---|---|---|---|---|---|---|

1 | 1.00 | 0.100 | 0.9901 | 1.000 | 0.9891 | 1.100 | 1.100 |

2 | 1.20 | 0.100 | 0.9764 | 1.403 | 0.9745 | 1.503 | 1.300 |

3 | 1.30 | 0.110 | 0.9619 | 1.504 | 0.9588 | 1.635 | 1.410 |

4 | 1.40 | 0.120 | 0.9458 | 1.710 | 0.9413 | 1.861 | 1.520 |

5 | 1.50 | 0.135 | 0.9280 | 1.917 | 0.9218 | 2.115 | 1.634 |

6 | 1.70 | 0.150 | 0.9030 | 2.764 | 0.8950 | 2.994 | 1.849 |

7 | 1.90 | 0.165 | 0.8750 | 3.204 | 0.8650 | 3.468 | 2.063 |

8 | 2.10 | 0.180 | 0.8441 | 3.659 | 0.8321 | 3.957 | 2.276 |

9 | 2.30 | 0.200 | 0.8106 | 4.132 | 0.7961 | 4.517 | 2.494 |

10 | 2.50 | 0.220 | 0.7748 | 4.626 | 0.7578 | 5.062 | 2.712 |

Year | $UR$ (%) | $HPIgr$ (%) | $MR$ (%) |
---|---|---|---|

0 | 3.00 | 2.00 | 5.00 |

1 | 3.00 | 2.00 | 5.00 |

2 | 3.50 | 1.50 | 4.80 |

3 | 4.00 | 1.00 | 4.60 |

4 | 4.50 | 0.50 | 4.40 |

5 | 5.00 | 0.50 | 4.20 |

6 | 5.00 | 0.00 | 4.00 |

7 | 5.00 | 0.00 | 4.00 |

8 | 5.00 | 0.00 | 4.00 |

9 | 5.00 | 0.00 | 4.00 |

Year | ${\mathsf{\Phi}}^{-1}\left(\mathit{d}\right)$ | Z |
---|---|---|

1 | −2.39 | −0.60 |

2 | −2.39 | −0.60 |

3 | −2.355 | −0.40 |

4 | −2.32 | −0.20 |

5 | −2.285 | 0.00 |

6 | −2.26 | 0.14 |

7 | −2.25 | 0.20 |

8 | −2.25 | 0.20 |

9 | −2.25 | 0.20 |

10 | −2.25 | 0.20 |

**Table 5.**Projection of house price ($HP$), loan balance (N), $LTV$ (in %), $DSC$ (in %), PIT $PD$ conditional on $AD=0$ (in %) by (33), PIT $PD$ conditional on $AD=1$ (in %) by (33), $LT{V}_{dt}$ in the 25% house price decline scenario, TTC $PD$ conditional on $AD=0$ (in %), TTC $PD$ conditional on $AD=1$ (in %), PIT loss rate l (in %), downturn $LGD$ (in %) by (34), prepayment probability (in %) by (35), arrears rate (in %) by (36), cure rate (in %) by (37), Stage 2 probability (in %).

Year | $HP$ | N | $LTV$ | $DSR$ | ${\mathit{p}}_{AD=0}$ | ${\mathit{p}}_{AD=1}$ | ${PD}_{AD=0}$ | ${PD}_{AD=1}$ | ${LTV}_{dt}$ | l | $LGD$ | $cpr$ | $ar$ | $cr$ | t |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 500,000 | 500,000 | 100.0 | 27.5 | 1.30 | 20.3 | 1.84 | 23.7 | 133.3 | 11.00 | 27.7 | 0.25 | 1.23 | 58.2 | 0.00 |

2 | 510,000 | 490,000 | 96.1 | 27.5 | 1.25 | 19.6 | 1.77 | 23.0 | 128.1 | 9.04 | 25.1 | 0.29 | 1.22 | 58.2 | 1.24 |

3 | 517,650 | 479,650 | 92.7 | 27.5 | 1.23 | 18.8 | 1.60 | 21.1 | 123.5 | 7.33 | 22.8 | 0.42 | 1.24 | 57.7 | 1.53 |

4 | 522,827 | 468,938 | 89.7 | 27.5 | 1.22 | 18.1 | 1.46 | 19.4 | 119.6 | 5.85 | 20.8 | 0.55 | 1.25 | 57.2 | 1.63 |

5 | 525,441 | 457,851 | 87.1 | 27.5 | 1.21 | 17.4 | 1.33 | 17.7 | 116.2 | 4.57 | 19.1 | 0.68 | 1.26 | 56.7 | 1.68 |

6 | 528,068 | 446,375 | 84.5 | 27.5 | 1.21 | 17.0 | 1.24 | 16.8 | 112.7 | 3.26 | 17.4 | 0.80 | 1.27 | 56.2 | 1.72 |

7 | 528,068 | 434,498 | 82.3 | 27.5 | 1.18 | 16.4 | 1.18 | 16.0 | 109.7 | 2.14 | 15.9 | 0.93 | 1.27 | 56.2 | 1.74 |

8 | 528,068 | 422,206 | 80.0 | 27.5 | 1.15 | 16.1 | 1.15 | 15.6 | 106.6 | 1.00 | 14.3 | 0.95 | 1.27 | 56.2 | 1.75 |

9 | 528,068 | 409,483 | 77.5 | 27.5 | 1.13 | 15.8 | 1.13 | 15.3 | 103.4 | 1.00 | 12.7 | 0.97 | 1.27 | 56.2 | 1.76 |

10 | 528,068 | 396,315 | 75.1 | 27.5 | 1.10 | 15.5 | 1.10 | 15.0 | 100.1 | 1.00 | 11.0 | 1.00 | 1.27 | 56.2 | 1.77 |

**Table 6.**Projection of expected loan balance, expected interest income, expected funding costs, expected operational costs, ECL conditional on Stag 1, LLP conditional on Stage 1, adjusted minimum capital conditional on Stage 1, RAROC conditional on Stage 1 (in %), ECL conditional on Stage 2, LLP conditional on Stage 2, adjusted minimum capital conditional on Stage 2, RAROC conditional on Stage 2 (in %), total expected RAROC (in %).

Year | $\widehat{\mathit{N}}$ | $\mathit{z}\xb7\widehat{\mathit{N}}$ | $\widehat{\mathit{f}}\xb7\widehat{\mathit{N}}$ | $\mathit{c}\xb7\widehat{\mathit{N}}$ | ${ELC}^{1}$ | ${LLP}^{1}$ | ${\overline{\mathit{K}}}_{min}^{1}$ | ${RAROC}^{1}$ | ${ELC}^{2}$ | ${LLP}^{2}$ | ${\overline{\mathit{K}}}_{min}^{2}$ | ${RAROC}^{2}$ | $RAROC$ |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 500,000 | 17,500 | 12,592 | 2500 | 718 | 715 | 22,340 | 7.3 | 13,853 | 26,757 | 69,948 | −11.84 | 7.33 |

2 | 488,775 | 17,107 | 12,482 | 2444 | 551 | 552 | 19,368 | 8.18 | 10,640 | 20,265 | 64,309 | −10.00 | 7.26 |

3 | 477,067 | 16,697 | 12,347 | 2385 | 427 | 431 | 16,114 | 9.27 | 7922 | 14,926 | 57,374 | −8.24 | 8.19 |

4 | 464,438 | 16,255 | 12,196 | 2322 | 326 | 332 | 13,457 | 10.19 | 5807 | 10,648 | 51,226 | −6.58 | 9.09 |

5 | 450,949 | 15,783 | 12,028 | 2255 | 244 | 250 | 11,287 | 10.84 | 4171 | 7258 | 45,789 | −5.03 | 9.75 |

6 | 436,663 | 15,283 | 11,840 | 2183 | 165 | 172 | 9513 | 11.23 | 2767 | 4607 | 40,855 | −3.32 | 10.20 |

7 | 421,624 | 14,757 | 11,621 | 2108 | 99 | 107 | 8164 | 11.14 | 1633 | 2720 | 36,451 | −1.55 | 10.24 |

8 | 405,897 | 14,206 | 11,367 | 2029 | 40 | 47 | 7024 | 10.79 | 651 | 1,533 | 32,173 | 0.47 | 10.06 |

9 | 389,924 | 13,647 | 11,078 | 1950 | 39 | 44 | 5890 | 9.71 | 640 | 1085 | 27,383 | −0.07 | 9.01 |

10 | 373,707 | 13,080 | 10,749 | 1869 | 38 | 41 | 4819 | 8.66 | 622 | 577 | 22,897 | −0.68 | 7.97 |

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## Share and Cite

**MDPI and ACS Style**

Engelmann, B.; Pham, H. Measuring the Performance of Bank Loans under Basel II/III and IFRS 9/CECL. *Risks* **2020**, *8*, 93.
https://doi.org/10.3390/risks8030093

**AMA Style**

Engelmann B, Pham H. Measuring the Performance of Bank Loans under Basel II/III and IFRS 9/CECL. *Risks*. 2020; 8(3):93.
https://doi.org/10.3390/risks8030093

**Chicago/Turabian Style**

Engelmann, Bernd, and Ha Pham. 2020. "Measuring the Performance of Bank Loans under Basel II/III and IFRS 9/CECL" *Risks* 8, no. 3: 93.
https://doi.org/10.3390/risks8030093