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Hello, and welcome to my blog series! I have always wanted to share my thoughts and insights on credit risk in the banking industry. As a Junior Writer and Data Scientist/Quant, I may not have the same level of experience as some of my peers, but I’m eager to learn and share my perspectives with others. I have a deep passion for statistics (machine learning), quantitative analytics, regulatory aspects of banking and application to credit modelling.
In this series, I’ll be exploring various topics related to credit risk & statistics, including different models and techniques used by banks, current trends and challenges in the industry, and the impact of regulations and standards such as Basel II, III, IV and IFRS9 (definitions to follow). It has to be mentioned that I will focus a lot on the banking perspectives in Europe (European Banking Authority — EBA / European Central Bank — ECB) and Africa (South African Reserve Bank — SARB) as this is where I have gained my experience. Nonetheless, the techniques and ideas that will be discussed are insights and challenges throughout the world. Join me as I dive into the complex and fascinating world of credit risk management in banking.
Recently, Machine Learning (ML) — which is basically statistics on steroids— have become a debated and hot topic in the credit risk space. The ECB has been actively exploring the use of ML in the context of banking and finance. In November 2021, the ECB published a report titled “EBA DISCUSSION PAPER ON MACHINE LEARNING FOR IRB MODELS” which provided an overview and questionnaire of the different applications of ML in Internal Rating-Based Models (IRB) — more on this later. The Bank for International Settlements (BIS) have also been exploring various topics in ML together with the ECB and the SARB.
These reports highlighted the potential benefits of using ML techniques, such as improved accuracy in forecasting, early warning signals for financial stability risks, and more efficient fraud detection. However, it also noted some of the challenges associated with using ML in central banking, such as data quality issues, model interpretability, and potential biases in the data. The use of these statistical outputs are now more important than ever (as is the data feeding into these models).
Overall, the ECB recognizes the potential benefits of using ML in banking and finance, but also emphasizes the need for careful consideration of the potential risks and challenges associated with these techniques. I’ll be exploring general statistical & ML ideas for credit modelling and validation with code & explanation — the advantages and the pitfalls I see in the industry.
What I am aiming to achieve in these posts are to share knowledge with new data scientists/credit quants entering the workspace, and perhaps to people in different industries who are interested in these applications. Credit Risk is a fascinating topic with a mixture of quantitative and qualitative ideas. It is a space where the convergence of statistics, expert opinions, and business objectives occurs — and it is rather not focused on in universities (unlike market risk with repetitive analysis of options and deriving the Black-Scholes formula).
On the quantitative side, credit risk management (on the banking book) involves statistical modelling, risk assessment, and financial analysis. Financial institutions use various tools to measure and manage credit risk, such as credit ratings, credit scoring, and Probability of Default (PD) models. These models provide a quantitative basis for assessing the likelihood of default and the potential losses associated with credit risk. These models are specifically used in Acceptance, Pricing, Expected Loss (EL), Stress Testing and Regulatory Capital (RC) calculations. We will get to each of these in the coming posts (as well as discussing the model lifecycle of each — development, validation and maintenance).
On the qualitative side, credit risk management involves factors such as industry trends, management quality, and macroeconomic conditions. Credit Quants consider these qualitative factors when assessing the creditworthiness of a borrower or a portfolio of loans. They also monitor market trends, regulatory changes, and emerging risks to anticipate potential credit risks.
The combination of quantitative and qualitative analysis makes credit risk management a challenging and dynamic field. Banks and financial institutions must continuously update their credit risk models and adapt to changing market conditions to manage their credit risk effectively.
Overall, credit risk is a fascinating topic with both quantitative and qualitative aspects that requires continuous analysis and adaptation to changing market conditions. In-depth knowledge of statistics and risk management are needed as a starter (typically at a Master’s level). Additionally, it has become much more important to be able to effectively code these large calculations that were mentioned earlier. Being familiar with two or more coding languages (such as Python, R, SAS, SQL, or C) can be a great asset for a young quant from university entering the job market.
In my discussion, I will aim to indicate the route I took and what university and online courses I would recommend for young quants to get started in these coding languages and to obtain the necessary statistical basics needed for credit modelling with traditional and ML models.
The BASEL Accords are a set of international regulations for the banking industry. These accords were developed by the BASEL Committee on Banking Supervision (BCBS), which is made up of central banks and regulatory authorities from around the world. The importance of the BASEL Accords lies in their ability to promote financial stability by ensuring that banks have sufficient capital to withstand economic downturns and financial crises. Major banks around the globe follow these accords, which serve as the fundamental basis for most credit models in banks.
There are three main BASEL accords:
- BASEL I:
This accord was issued in 1988. The accord focused on three pillars. The BCBS established a set of regulations to ensure that banks maintain sufficient capital to fulfill their financial commitments and withstand financial and economic pressures. Minimum Capital Requirements: The first pillar requires banks to maintain a minimum amount of capital, based on a percentage of their Risk-Weighted Assets (RWAs), to absorb Unexpected Losses (UL). The higher the risk of a bank’s assets, the more capital it must hold. This was the main objective of BASEL I. Banks were required to maintain a minimum Capital Adequacy Ratio (CAR) of 8%, calculated as a percentage of their RWAs. The CAR is the ratio of a bank’s capital to its RWAs, where RWAs are calculated by assigning different risk weights to different categories of assets based on their perceived riskiness. The risk weights under BASEL 1 were divided into five categories, ranging from zero for government securities to 100% for certain types of loans and other risky assets. The minimum capital requirement of 8% meant that for every €100 of RWAs, banks had to hold at least €8 of capital.
Regulatory Capital ≥ 8%× Risk-Weights × Asset Values
The risk weight categories included:
- 0% risk weight for fully secured home loans, government bonds and cash.
- 20% risk weight for claims on OECD banks and certain multilateral development banks (loans to other banks & public sector companies in these OECD — Organization for Economic Co-operation and Development countries).
- 50% risk weight for claims on non-OECD banks, securities firms and certain other financial institutions (home loans that are not fully secured — not covered 100% by collateral).
- 100% risk weight for most corporate loans, mortgages, and claims on non-financial institutions.
- 200% risk weight for certain exposures like derivatives, bridge loans, and non-traded assets.
BASEL 1 also introduced the concept of Tier 1 and Tier 2 capital, with Tier 1 capital consisting of the highest quality capital it can hold namely equity capital (ordinary shares) and disclosed reserves, and Tier 2 capital consisting of subordinated debt (a type of debt that ranks below other debts in the event of bankruptcy or liquidation), loan-loss reserves, and certain types of hybrid capital. Banks were now monitored on their CAR (which represents a bank’s ability to meet all of its financial obligations, not just absorb losses) as well as their Common Equity Tier 1 (CET1) ratios (a measure of a bank’s core capital compared to its RWAs — which represents a bank’s ability to absorb losses and continue operating without needing external funding).
CAR = (Tier 1 + Tier 2) / Risk-Weighted Assets
CET1 = Tier 1 / Risk-Weighted Assets
Supervisory Review: The second pillar requires banks to have a process for assessing their overall risk profile and determining whether their capital levels are adequate. Regulators (such as the ECB or SARB) are responsible for supervising this process and ensuring that banks have sufficient capital to cover their risks. All quantitative models built under Pillar 1 needs to be reviewed by overseeing supervisors. Market Discipline: The third pillar aims to promote market discipline by requiring banks to disclose information about their risk profile, capital adequacy, and risk management practices to the public. The idea is that market participants will use this information to make more informed investment decisions and put pressure on banks to manage their risks effectively.
Overall, the BASEL 1 framework laid the foundation for modern RC (not to be mistaken for economic capital which is the best estimate of required capital that financial institutions use internally to manage their own risk and to allocate the cost of maintaining RC among different units within the organization) requirements and helped improve the stability of the global banking system. However, it was criticized for its simplicity and for not taking into account the varying degrees of risk within different asset classes (and collateral). Operational Risk & Market Risk was also not taken into account. As a result, the Basel Committee continued to refine the framework, leading to the introduction of Basel 2 and Basel 3.
2. BASEL II:
This accord was issued in 2004 and introduced a more risk-sensitive approach to capital requirements. BASEL II used a set of formulas to determine the amount of capital banks needed to hold based on the risks they were taking on (formulas below). The same rule for 8% of minimum capital requirement hold, however a minimum of 4% of CET1 capital was now imposed. It also introduced a new framework for assessing credit risk, operational risk, and market risk. Under BASEL II, banks are required to use internal models to calculate their capital requirements for credit risk, subject to supervisory approval. Smaller banks were provided with simpler formulas to compute the minimum amount of capital they must hold to safeguard against risk, known as the “Standardized Approach (SA).” Meanwhile, larger banks were offered the option of using the “Advanced Internal Ratings-Based (AIRB)” approach (with the Vasicek distribution as the fundamental description of credit losses and the measurement of credit risk) which enabled them to devise their own models to determine their risk capital. This is where PD, Loss Given Default (LGD) and Exposure at Default (EAD) calculations/models became mandatory under this approach. Banks used these models to calculate how much the it stands to lose when borrowers default (Loss = PD x LGD x EAD). An additional approach was also introduced as the the “Foundation Internal Ratings-Based (FIRB)” approach, where the bank uses its own internal ratings to determine risk weights for different types of assets. However, some of the model parameters are still determined by the regulators, and it is considered less sophisticated than the AIRB Approach. Once the PD, LGD, and EAD are known, risk-weight functions provided in the BASEL accord can be used to calculate the RC. We will discuss these approaches in-depth later.
Overall, BASEL II was designed to be more flexible and risk-sensitive than its predecessor, BASEL I. However, it has also been criticized for being too complex and allowing banks to use internal models to manipulate their capital ratios. As a result, the BCBS has continued to refine and update the BASEL framework over time.
3. BASEL III:
This accord was issued in 2010 in response to the global financial crisis of 2008. BASEL III focused on strengthening bank capital requirements and introducing new liquidity and leverage ratios to reduce the risk of bank failures. It also placed a greater emphasis on stress testing.
Some of the key differences between the BASEL accords include the risk weights assigned to different types of assets, the methods used to calculate capital requirements (Tier 1 capital increased from 4% to 6%), and the emphasis on liquidity and leverage ratios. Additionally, each subsequent accord has built on the previous one to provide a more comprehensive framework for regulating the banking industry.
4. BASEL IV:
This accord further strengthen the regulation, supervision, and risk management practices of the banking industry. The reforms aim to address issues and weaknesses identified in the previous BASEL frameworks, particularly with regards to the calculation of RWAs and the use of internal models.
Some of the key features of BASEL IV include:
- Output Floor: The introduction of an output floor for RWA, which means that banks using internal models will be required to hold a minimum level of capital regardless of the risk weightings produced by their models. Banks capital requirements will be floored to a certain percentage of the standardized requirement, i.e. from 50% to 72.5%.
- Credit Risk: Changes to the calculation of credit risk RWA, including the removal of certain IRB approaches and the introduction of more granular risk weightings for exposures to small and medium-sized enterprises (SMEs).
The implementation of BASEL IV is ongoing, with various jurisdictions expected to adopt the reforms at different times. The reforms are expected to significantly impact the banking industry and require banks to hold higher levels of capital. This will continue to improve comparability among capital levels of banks.
The Credit Loss Distribution is a statistical representation of the potential losses that a financial institution may incur due to credit risk. It is used to estimate the EL and UL of a credit portfolio.
The credit loss distribution is based on the probability distribution of credit losses, which can be modelled using various techniques, such as the Normal distribution, Poisson distribution or binomial distribution, depending on the nature of the credit risk.
The EL is the average amount of loss (that are incurred when obligors fail to pay or default) that is expected to be incurred over a certain time period based on historical data and probability distributions. It is calculated as the product of the PD, LGD and EAD. This is the average/mean loss that should be provisioned for. Banks and corporations set aside provisions for such losses. However, these values interrelate and merge in intricate manners, leading to unforeseen ULs. The CAR does not account for ELs on bank runs. Bank runs occur when a large number of depositors withdraw their money from a bank due to concerns about the bank’s solvency or liquidity. Bank runs can lead to liquidity shortages and can potentially cause a bank to fail. This suggests that a bank may need to hold additional capital to mitigate the risk of losses from bank runs.
The UL, on the other hand, is the potential loss that can occur beyond the expected loss. It is based on extreme scenarios and is calculated as the difference between the EL and the worst-case loss that can occur in the tail of the distribution. Here the difference is between the Credit Value at Risk (CVaR) and the ELs = dispersion of ELs (it is the capital of a bank should cover losses that exceed provisions — and can be regarded as part of economic capital). EL and UL changes continuously due to macroeconomic factors and portfolio sizes. This is where the BASEL equations play a vital role in capital management for banks. According to Basel II, the credit risk capital charge should aim to cover ULs and account for rare events, specifically at the 99.9th percentile. The RC is used to cover the UL. The sum of the provisions and the RC should equal the 99.9% loss. If banks do not insure themselves, they may be vulnerable to losses beyond this percentile.
By analyzing the credit loss distribution, banks can determine the capital required to cover potential losses from credit risk, as well as the overall risk of the credit portfolio. It is an important tool for risk management and regulatory compliance, particularly under Basel II, III and IFRS 9.
Exposure at Default (EAD)
This refers to the calculation of a bank’s potential exposure to a counterparty in the event of the counterparty’s default. It is measured in currency and is estimated for a period of one year or until maturity, whichever comes first. The EAD for loan commitments (the expected outstanding balance if the facility defaults, which is equal to the expected utilization plus a percentage of the unused commitments including unpaid fees and accrued interest) is based on BASEL Guidelines and measures the portion of the facility that is likely to be drawn in the event of a default. BASEL II requires banks to provide an estimate of the exposure amount for each transaction in their internal systems. The purpose of these estimates is to fully capture the risks associated with an underlying exposure.
Example: Let’s say a bank extends a €10000 credit line to a customer. The customer uses €5000 of the credit line and pays off €2000, leaving a current outstanding balance of €3000. The bank estimates that if the customer were to default at this point, they would likely draw down the entire remaining balance of €3000. Therefore, the EAD in this example would be €3000. This represents the amount that the bank would be exposed to if the customer were to default.
Typically, EAD is a linear formula and is calculated per loan product. There are different ways to estimate EAD (for example through conversion factors) and we will discuss these later.
Loss Given Default (LGD)
The EBA defines LGD as the proportion of an exposure that is not expected to be recovered in the event of default. It is calculated as the difference between the EAD and the amount recovered through collateral or other means, expressed as a percentage of the EAD (loss is defined as the difference between the observed exposure at default and the sum of all the discounted cashflows where loss rate = observed loss as a percentage of observed EAD).
Example: Suppose a borrower takes out a €10000 loan from a bank. If the borrower defaults on the loan, the bank will try to recover the amount owed by selling any collateral (e.g., property) put up against the loan. Suppose the collateral is sold for €8000. Then the LGD would be:
LGD = (Total amount of loan — Amount recovered) / Total amount of loan LGD = (€10000 — €8000) / €10000 LGD = 0.2 or 20%
This means that in the event of default, the bank would lose 20% of the total amount of the loan, or $2000 in this case.
Usually after default occurs a client can either cure (defaulter paying off all outstanding debt), Restructuring (loan characteristics and terms are changed and modified), Liquidation/Foreclosure (banks repossess the collateral).
Typically LGD is calculated per loan product and involves statistical estimation using either regression (Linear, Logistic, Survival Models, etc) or historical averages. As per BASEL II guidelines, it is recommended that banks and other financial institutions calculate the Downturn LGD (loss given default during a downturn in the business cycle) for regulatory purposes. This helps to reflect the potential losses that may occur during an economic downturn. We will look into different definitions of LGD, Loss Rates (implied historical loss rates and workout loss rates) and statistical estimation later.
PD & The Definition of Default
Lending money to both retail and non-retail (e.g. corporate) customers is a primary function of banks. To ensure responsible lending practices, banks must have effective systems in place to determine who is eligible for credit. Credit scoring is a critical risk assessment technique used to analyze and quantify the credit risk of a potential borrower. The objective of credit scoring is to measure the probability that a borrower will repay their debt (binary outcome of default or non-default — additionally cure models can also be built separately which is the probability that the client will cure or payoff the loan which is also binary). The result of this process is a score that reflects the creditworthiness of the borrower (Logit models are very popular in scorecard development). To ensure there are consistencies across banks on what is regarded as a default, regulation has set tight measures on this.
The EBA defines default as the occurrence of one or more of the following events:
- When a bank considers that the obligor is unlikely to pay its credit obligations in full, without recourse by the bank to actions such as realizing security (i.e., the obligor is “unlikely to pay” criterion).
- When the obligor is past due more than 90 days on any material credit obligation to the bank (i.e., the “90 days past due” criterion).
- When the bank has reason to believe that the obligor has entered into bankruptcy or other financial reorganization (i.e., the “bankruptcy” criterion).
The EBA requires banks to use the above criteria to identify and report defaulted exposures in their portfolios, and to ensure that they have adequate policies, procedures, and systems in place to accurately identify and report such exposures. We obtain (through External ratings — provided by rating agencies, but some regulators prohibit their usage, for example, S&P, Fitch or Moody’s ratings for corporations or governments), estimate or interpolate (through the use of Scorecards, Logit or Probit models) the PD of a particular rating/grade/pool as the long-run average of the one-year default rates.
There are many interesting discussions around PDs such as Stressed and Unstressed PDs; Through-the-cycle (TTC) and Point-in-Time (PIT); Estimation (either through traditional statistics or ML). We will look at these topics in-depth later when we discuss the model lifecycle.
The Asymptotic Single Risk Factor (ASRF) framework is a credit risk model used to calculate RC requirements for credit risk under the BASEL II framework. It assumes that the portfolio’s risk can be represented by a single systematic factor, known as the “factor model” and uses this factor to estimate the portfolio’s risk. When describing default events, it is commonly assumed that a single factor, which is the state of the world’s economy, is tied to all loan values and obligor’s default probabilities in a simple manner (by the correlation between). This approach allows for the calculation of the RC charge for credit risk to be made using a single-factor model, which is much simpler than trying to model each individual exposure in a portfolio. The ASRF approach is particularly useful for banks with large and diverse portfolios, as it allows them to estimate RC requirements with reasonable accuracy while minimizing the computational burden.
The ASFR formulas involve calculating the EL and UL of a portfolio of exposures, and then applying a capital charge based on the UL. The formulas take into account the correlation between obligor defaults and the systematic factor (usually GDP), as well as the variability of the factor over time. The ASFR approach is considered a simplified version of the more AIRB approach.
This approach is based on the asset value factor model and has its origin in Merton’s structural approach (1974). Models based on asset value propose that the probability of a firm’s default or survival is contingent on the value of its assets at a specific risk measurement horizon, typically at the end of that horizon. If the value of its assets falls below a critical threshold, its default point, the firm defaults, otherwise it survives. The origins of asset value models can be traced back to Merton’s influential paper published in 1974. Vasicek (2002) adapted Merton’s single asset model which can be used to model a credit portfolio, by creating a function that transforms unconditional default probabilities into default probabilities tied to a single systematic risk factor. The AIRB approach employs an analytical approximation of CVaR using the Vasicek distribution.
The derivation for the logic follows as:
Banks assess each outstanding loan on an individual basis to determine the associated risk, including the likelihood of default by the obligor. For retail loans such as mortgages, factors like income, age, residence, loan nature, and macroeconomic indicators like house prices and unemployment rates they all play a role in determining the risk of a loan. However, since loan defaults are correlated with one another, the BASEL capital requirements mandate that capital must be calculated for a bucket of loans with similar characteristics. To determine the input parameters for capital requirements (PD, LGD, and EAD), they must represent the entire bucket. The PD for the entire bucket is the average of all individual PDs. The methodology described above in the image can be extended to determine the default fraction distribution of a credit portfolio, which is a bucket of loans. However, this requires an important assumption that the credit portfolio is infinitely granular, meaning that it contains an infinite number of loans and no individual loan represents a significant portion of the total portfolio exposure. In such a portfolio, there is no idiosyncratic risk since all idiosyncratic risk is diversified. Now consider the following.
The final equation can be interpreted as the default fraction in the infinitely granular portfolio, conditional on y. The BASEL framework (and IFRS9 TTC PDs to PIT PDs which we will discuss later) builds upon these equations where credit losses and measurement are described using the Vasicek one-factor distribution. This model assumes the presence of a single risk factor, typically measured by GDP. Additionally, all loans are linked to this single risk factor through a single correlation value. Longer-term loans are considered riskier than short-term loans, and the correlation value varies with the PD. However, the LGD is not correlated with the PD.
For a defaulted exposure/past due exposure, that is where PD=1 or 100% in the above RWA formula, the capital requirement (K) is equal to the greater of zero and the difference between its LGD and the bank’s best estimate of expected loss (BEEL). The RWA formula remains the same.
I have focused a lot on the theoretical aspects here and I would like the reader to note that to build or validate credit models effectively, one can’t necessarily skip these basics as the banking credit model frameworks are built around these definitions & formulas. Of course, assuming the bank follows the IRB approach — for SA approach it is much more straight forward in the sense that the regulators provide the formulas to use directly. In the case of AIRB — banks estimate PDs, EADs, LGDs through the use of various statistical (and ML models).
The series will focus a lot on different modelling and validation techniques through quantitative coding perspectives but I will refer back to this post for the general basics. In the following posts we will look at rating philosophies, IFRS9, use cases of AIRB models in a bank (stress testing, etc), statistical modelling (Logistic Regression & ML models) and statistical validation techniques (discriminatory power, calibration, stability — where there will be a lot more coding involved).
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Disclaimer: The views expressed in this article are my own and do not represent a strict outlook or the view of any corporation.