This article explains basic concepts and methodologies of credit risk modelling and how it is important for financial institutions.
In credit risk domain, statistics and machine learning play an important role in solving problems related to credit risk. Hence role of predictive modelers and data scientists have become so important.
What is Credit Risk?
In simple words, it is the risk of borrower not repaying loan, credit card or any other type of loan. Sometimes customers pay some installments of loan but don't repay the full amount which includes principal amount plus interest.
For example, you took a personal loan of USD 100,000 for 10 years at 9% interest rate. You paid a few initial installments of loan to the bank but stopped paying afterwards. Remaining unpaid installments are worth USD 30,000. It's a loss to the bank.
Do you remember or aware of 2008 global recession? In US, low-creditworthy customers were given home loans which were risky due to their high likelihood of default. To compensate risk, banks used to charge high interest rate. Banks further sold these loans to investors as Collateralized Debt Obligations (CDOs), considered low-risk from 2004-2007. As defaults increased, banks seized (foreclosed) properties. It caused a real estate bubble burst and a sharp decline in home prices. This led to a global recession as many financial institutions had invested in these funds.
What is Credit Risk Modelling?
Credit risk modeling refers to data driven risk models which calculates the chances of a borrower defaults on loan (or credit card). If a borrower fails to repay loan, how much amount he/she owes at the time of default and how much lender would lose from the outstanding amount. In other words, we need to build probability of default, loss given default and exposure at default models as per regulatory basel norms.
Basel Regulations
A committee was set up in year 1974 by central bank governors of G10 countries. It is to ensure that banks have minimum enough capital to give back depositors’ funds. They meet regularly to discuss banking supervisory matters at the Bank for International Settlements (BIS) in Basel, Switzerland. The committee was expanded in 2009 to 27 countries.
Basel I
Basel I
accord is the first official pact introduced in year 1988. It focused on credit risk and introduced the idea of the capital adequacy ratio which is also known as Capital to Risk Assets Ratio. It is the ratio of a bank's capital to its risk. Banks needed to maintain ratio of at least 8%. It means capital should be more than 8 percent of the risk-weighted assets. Capital is an aggregation of Tier 1 and Tier 2 capital.
Tier 1 capital
: Primary funding source of the bank. It includes shareholders' equity and retained earningsTier 2 capital
: Subordinated loans, revaluation reserves, undisclosed reserves and general provisions
In Basel I, fixed risk weights were set based on the level of exposure. It was 50% for mortgages and 100% for non-mortgage exposures (like credit card, overdraft, auto loans, personal finance etc). See the example shown below -
Mortgage $5,000 Risk Weight 50% Risk Weighted Assets $2500 (Mortage * Risk Weight) Minimum Capital Required $200 (8% * Risk Weighted Assets)
Basel II
Basel II
accord was introduced in June 2004 to eliminate the limitations of Basel I. For example, Basel I focused only on credit risk whereas Basel II focused not only credit risk but also includes operational and market risk. Operational Risk includes fraud and system failures. Market risk includes equity, currency and commodity risk.
In Basel II, there are following three ways to estimate credit risk.
- Standardized Approach
- Foundation Internal Rating Based (IRB) approach
- Advanced Internal Rating Based (IRB) Approach
For corporate, the banks relies on ratings from certified credit rating agencies (CRAs) like S&P, Moody etc. to quantify required capital for credit risk. Risk weight is 20% for high rated exposures and goes up to 150 percent for low rated exposures. For retail, risk weight is 35% for mortgage exposures and 75% for non-mortgage exposures (no rating by credit rating agencies required for retail).
Corporate Exposure $5,00,000 Credit Assessment AAA Risk Weights 20% Risk Weighted Assets $1,00,000 Minimum Capital Required $8,000
- Probability of Default (PD)
- Exposure at Default (EAD)
- Loss given Default (LGD)
- Effective Maturity (M)
Probability of default means the likelihood that a borrower will default on debt (credit card, mortgage or non-mortgage loan) over a one-year period. In simple words, it returns the expected probability of customers fail to repay the loan. Probability is expressed in the form of percentage, lies between 0% and 100%. Higher the probability, higher the chance of default.
It means how much should we expect the amount outstanding to be in the case of default. It is the amount that the borrower has to pay the bank at the time of default.
It means how much of the amount outstanding we expect to lose. It is a proportion of the total exposure when borrower defaults. It is calculated by (1 - Recovery Rate).
LGD = (EAD – PV(recovery) – PV(cost)) / EAD PV (recovery)= Present value of recovery discounted till time of default. PV (cost) = Present value of cost discounted till time of default.
Someone takes $100,000 home loan from bank for purchase of flat. At the time of default, loan has an outstanding balance of $70,000. Bank foreclosed flat and sold it for $60,000. EAD is $70,000. LGD is calculated by dividing ($70,000 - $60,000)/$70,000 i.e. 14.3%.
Expected Loss is calculated by (PD * LGD * EAD).
Probability of Default 2% Exposure at Default $20,000 Loss Given Default 20% Expected Loss $80
There are two types of Internal Rating Based (IRB) approaches which are Foundation IRB and Advanced IRB.
PD is estimated internally by the bank while LGD and EAD are prescribed by regulator.
PD, LGD, and EAD can be estimated internally by the bank itself.
It is a duration that reflects standard bank practice is used. For Foundation IRB, the effective maturity is 2.5 years (exception is repo style transactions where it is 6 months). For Advanced IRB, M is the greater of 1 year or the effective maturity of the specific instrument.
Basel III
Basel III accord was scheduled to be implemented effective March 2019. In view of the coronavirus pandemic, the implementation had been postponed to January 1, 2023.
Basel III has incorporated several risk measures to counter issues which were identified and highlighted in 2008 financial crisis. It emphasis on revised capital standards (such as leverage ratios), stress testing and tangible equity capital which is the component with the greatest loss-absorbing capacity.
The concept of building internal models and external ratings for estimating PD, LGD and EAD remains same as it was in Basel II. However there are some changes introduced in Basel III. It is shown in the table below.
Basel II | Basel III | |
---|---|---|
Common Tier 1 capital ratio(shareholders’ equity + retained earnings) | 2% * RWA | 4.5% * RWA |
Tier 1 capital ratio | 4% * RWA | 6% * RWA |
Tier 2 capital ratio | 4% * RWA | 2% * RWA |
Capital conservation buffer(common equity) | - | 2.5% * RWA |
Does Basel IV exist?
The Basel Committee introduced "Basel III: Finalizing post-crisis reforms" in 2017, an extension of Basel III. In the US, it's termed Basel III Endgame. In the UK, it is called Basel 3.1 and some refer to it as Basel IV. But officially there are only 3 Basel Accords and it is being considered as a part of Basel III only.
The EU regulatory authority has set January 2025 as the implementation date, while both the UK and US regulatory authorities aim to implement the changes by July 2025.
IFRS 9
IFRS 9 is an International Financial Reporting Standard dealing with accounting for financial instruments. It replaces IAS 39 Financial Instruments which was based on the incurred loss model whereas IFRS 9 focuses on the expected loss model that covers also future losses.
In IFRS 9, the idea is to recognize 12-month loss allowance at initial recognition and lifetime loss allowance on significant increase in credit riskIFRS 9 vs Basel III
Probability of Default Modeling
In this section, we covered various steps and methods related to PD modeling.
Define Dependent Variable
Binary variable having values 1 and 0. 1 refers to bad customers and 0 refers to good customers.
Bad Customers
: Customers who defaulted in payment. By 'default', it means if either or all of the following scenarios have taken place.
- Payment due more than 90 days. In some countries, it is 120 or 180 days.
- Borrower has filed for bankruptcy
- Loan is partially or fully written off
Indeterminates or rollovers
: These customers fall into these 2 categories :
- Payment due 30 or max 60 days but paid after that. They are regular late payers.
- Inactive accounts
All the other customers are good customers
. Indeterminates should not be included as it would reduce the discrimination ability to distinguish between good and bad. It is important to note that we include these customers at the time of scoring.
Methodologies for Estimating PD
There are two main methodologies for estimating Probability of Default.
- Judgmental Method
- Statistical Method
It relies on the knowledge of experienced credit professionals. It is generally based on five Cs of the applicant and loan.
Character
: Check credit history of borrower. If no credit history, bank can ask for referees who bank can contact to know about the reputation of borrower.Capital
: Calculate difference between the borrower’s assets (e.g., car, house, etc.) and liabilities (e.g., renting expenses, etc.)Collateral
: Value of the collateral (security) provided in case borrower fails to repayCapacity
: Assess borrower’s ability to pay principal plus interest amount by checking job status, income etc.Conditions
includes internal and external factors (e.g. economic recession, war, natural calamities etc.)
Judgmental methods have become past as Statistical methods are more popular these days. But it is still widely used when historical data is not available (especially new credit products).
In today's world, nobody has time to wait for 1-2 months to know about the status of loan. Also many borrowers apply for loan through bank's website. Hence real-time credit decisions by bank is required to remain competitive in the digital world. The advantage of using statistical method is that it produces mathematical equation which is an automated and faster solution for making credit decisions.
This method is unbiased and free from dishonest or fraudulent conduct by loan approval officer or manager.
This method also comes with higher accuracy as statistical and machine learning models considers hundreds of data points to identify defaulters.
Data Sources for PD Modeling
Demographic Data
: Applicant's age, income, employment status, marital status, no. of years at current address, no. of years at job, postal codeExisting Relationship
: Tenure, number of products, payment performance, previous claimsCredit Bureau Variables
: Default or Delinquency history, Bureau score, Amount of credits, Inquiries etc.
Steps of PD Modeling
- Data Preparation
- Variable Selection
- Model Development
- Model Validation
- Calibration
- Independent Validation
- Supervisory Approval
- Model Implementation : Roll out to users
- Periodic Monitoring
- Post Implementation Validation : Backtesting and Benchmarking
- Model Refinement (if any issue)
Statistical Techniques used for Model Development
- Logistic Regression is most widely used technique for estimation of PD
- Survival Analysis is generally used to compute lifetime PD (required for IFRS 9)
- Random Forest
- Gradient Boosting
- Markov chain Modeling
- Neural Network
Model Performance in PD Model
There are main 2 levels of performance testing -
- Discrimination : Ability to differentiate between good (non-defaulters) and bad (defaulters) customers
- Calibration : Check whether the actual default rate is close to predicted PD values
Discrimination : Area under Curve, Gini coefficient, KS Statistics Calibration : Hosmer and Lemeshow Test, Binomial TestCheck out this link for detailed explanation : Model Performance Simplified
Rating Philosophy
It refers to the time horizon for which ratings measure credit risk and how much they are influenced by cyclic effects.Point in time (PIT) PD
- It evaluates the chances of default at that point in time. It considers both current macro-economic factors and risk attributes of borrower.
- Since it captures current macro-economic factors so PIT PD moves up as macro-economic conditions deteriorate and moves down as macro-economic conditions improve.
- It focuses on reporting date
- IFRS 9 requires PDs to be Point in time
Through the cycle (TTC) PD
- It predicts average default rate over an economic cycle and ignores short run changes to a customer's PD and closely resembles long-term average default rate.
- Grade assigned is not dependent on current macro-economic factors
- It focuses on long-run average PD
- Basel III requires PDs to be Through the cycle
In general, hybrid model (considering both PIT and TTC) is used.
Credit Scoring and Scorecard
Probability of Default model is used to score each customer to assess his/her likelihood of default. When you go to Bank for loan, they check your credit score. This credit score can be built internally by bank or Bank can use score of credit bureaus.
Credit Bureaus collect individuals' credit information from various banks and sell it in the form of a credit report. They also release credit scores. In US, FICO score is very popular credit score ranging between 300 and 850. In India, CIBIL score is used for the same and lie between 300 and 900.
1. Application Scorecard
: It applies to new (first time) customers applying for loan or credit card. It estimate probability of default at time applicant applies for loan. See the example below how it works.
Suppose cutoff for granting loan = 350 Profile of a New Customer Age 30 Gender Male Salary 15000 Total Points = (100 + 85 + 120) = 305 Decision : Refuse Loan
We use customer's application or demographic data along with credit bureau data. There is no observation window for historical data as these are new customers. Definition of Bad is same which is 90+ days past due. Performance window is generally 12 to 24 months from opening account.
Application scorecard is used majorly for the following tasks:
- To determine whether or not to approve a customer for a loan.
- To assist in 'due diligence'. Suppose an applicant scoring very high or very low can be declined or approved outright without asking for further information.
2.Behavior Scorecard
: It applies to existing customers to assess whether customer will default in loan payment. Performance window is generally 6 to 18 months.
Behavior scorecard is used majorly for the following tasks:
- To set credit limit i.e. increase or decrease credit limit
- Debt provisioning and profit scoring.
- Renewals
Application scorecard is applied on new customers (generally lower than 1 year) whereas Behavior scorecard is applied on existing customers (greater than 1 year). For application scorecard, we don't require well-calibrated default probabilities. But calibrated default probabilities are required for behavior scorecard as per Basel norms. These two scorecards are also different in terms of usage. See the explanation above in their respective section how they are generally used.
It predicts probability that a loan already late for a given number of days will be late for another given number of days. They are typically built for performance windows of one month.
It predicts the probability a borrower will apply for a new loan once the current loan is paid off.
Important Terminologies related to Credit Risk
Stressed PD: A stressed PD depends on the risk attributes of borrower but is not highly affected by macroeconomic factors as adverse economic conditions are already factored into it.
Unstressed PD: An unstressed PD depends on both current macroeconomic and risk attributes of borrower. It moves up or down depending on the economic conditions.
Under Basel II and III, financial institutions need to estimate downturn LGD and EAD. By 'downturn', it means adverse economic conditions. We need to select the month with highest default rate and then take two consecutive quarters (6-month) window on both sides of this point and consider it as downturn period and then take maximum of EAD and LGD which provides the downturn estimates. It is required because LGD and EAD can be affected by downturn economic conditions.
It is the probability of default during the second year given that it does not default during the first year. To calculate conditional PD, we need probability of not defaulting by the end of year 1 (P0) and unconditional probability of defaulting during the second year (P1).
If P0=0.5 and P1=0.1 so Conditional PD i.e. Prob(default | Survival) would be 0.1/0.5 = 20%
Lifetime PD vs 12 month PD
As per IFRS 9, we require two types of PDs for calculating expected credit losses (ECL).
- 12-month PDs for stage 1 assets - Chances of default within the next 12 months
- Lifetime PDs for stage 2 and 3 assets - Chances of default over the remaining life of the financial instrument.
Suppose 12-month PD is 3% which means survival rate is 97% (1 - PD). 2nd and 3rd year conditional PD is 4% and 5%.
- 1st year cumulative survival rate (CSR) is same as first year survival rate (SR).
- 2nd year cumulative survival rate = 1st year CSR * SR of 2nd year = 97% * 96% = 93%
- 3rd year cumulative survival rate = 2nd year CSR * SR of 3rd year = 93% * 95% = 88%. Lifetime PD = 1 - 88% = 12%
Macroeconomic factors to consider to estimate ECL
Estimating Expected Credit Loss (ECL) is crucial for banks and other financial institutions to manage the risk of lending money. To do this well, they must think about different macroeconomic factors that can affect how likely people are to repay their loans. Here are some important macroeconomic factors to consider when estimating ECL:
- GDP: The overall economic growth of a country affects borrowers' ability to repay loans and influences credit risk.
- Unemployment Rate: High unemployment rates can lead to reduced income and higher credit default rates, impacting credit quality.
- Index of Industrial Production: The performance of industries can impact the creditworthiness of borrowers in specific sectors.
- Import and Export: Global economic conditions and trade trends influence businesses' performance, affecting credit risk.
- Interest Rate: Changes in interest rates can affect borrowers' ability to service their debt, impacting credit losses.
- Inflation Rate: High inflation rates can weaken borrowers' purchasing power and lead to higher credit risk.
- House Price Index: Real estate market conditions can affect the credit quality of loans related to property.
- Exchange Rate: For institutions dealing with multiple currencies, exchange rate fluctuations can influence credit risk.
Stress Testing
In simple terms, stress testing is like giving a financial institution (such as a bank) a really tough test to see if it can handle difficult situations. Instead of just looking at regular situations, stress tests make them imagine extreme and rare problems, like a big economic crisis or unexpected disasters. By doing this, we can figure out how strong and prepared the institution is to handle these tough times and make sure it can stay stable even in the worst-case scenarios. For example, how a 5% increase in the unemployment rate affects the performance of a bank.
There are three types of stress testing.
- Scenario Analysis : Banks use scenario analysis to imagine different future situations and see how they might affect their financial health. It helps them prepare for risks and make better decisions.
- Reverse Stress Testing : In reverse stress testing, banks start with a negative outcome and figure out what could cause it. It helps them identify vulnerabilities and improve risk management.
- Sensitivity Analysis : Sensitivity analysis involves testing different factors to see how they impact the bank's performance. It helps banks understand their exposure to risks and adjust their strategies accordingly.
Softwares used in risk analytics
Let's split this section into two parts -1. Data Extraction
Most of the data is stored in relational databases (SQL Server, Teradata). Analyst need to have expert level knowledge of SQL to extract or manipulate data. Data is not saved in a single SQL table or database. In order to extract relevant data fields from database, you need to select multiple tables and join them based on matching key(s). During this process, you need to apply some business rules (excluding some type of customers or accounts). Transaction table is generally in mainframe environment so basic knowledge of mainframe and UNIX would be key. Mainframe and UNIX are not primary skill sets banks generally look for in risk analyst (It's good to have!). Developers are generally hired for this work.
2. Model Building
SAS is the most widely used software in risk analytics. Despite huge popularity of R and Python these days, more than 90% of banks and other financial institutions still use SAS. Banks also started exploring R and Python. They are building (or already built) syntax library (repository) in R and Python language for credit risk projects.
SAS can be easily integrated with relational databases and mainframe. Many companies execute both data extraction and model building steps in SAS environment only.
Hope you have got a fair idea of how predictive modeling is used in credit risk domain and what are the key credit risk parameters. In risk analytics, domain knowledge is more important than technical or statistical knowledge. Hope this article helped you in filling that gap. Please provide your feedback in the comment box below.
Hi Deepanshu really very informative for beginner's like me....
ReplyDeleteCan you please example of how behavior score card can be used to set credit Limit
Behaviour score generated based on customer history(Transaction, Delinquent,overlimit or past due or loan defaulter or credit card credit limit utilization. So in that case if BEH score is good that means, He/she is a good customer. So bank can use this beh score range and can increase credit limit
DeleteHi Deepanshu
ReplyDeletecould you explain the risk weight and how will they set the threshold
Amazing ! Im working in credit risk reporting and I haven't yet come across such a concise and clear theoretical background
ReplyDeleteGlad you found it useful. Cheers!
DeleteWe need an example. Or clear credit risk for portfolio in excel file.
DeleteVery useful content..I have been working in banking sector last 5 years, but still it clarified few concept for me..kudos to you for enlighten people.
ReplyDeleteIn credit risk we "snapshot" and "vintage" are commonly used. Is there any difference between snapshot and vintage or are these used interchangeably?
ReplyDeleteGood article, can you please provide pd, lgd models procedure end to end
ReplyDeleteThanks! The info is very well organized, informative and easy to follow!
ReplyDeleteThank you so much! Very informative!
ReplyDeleteInformative and easy to understand
ReplyDeleteCould you reflect on how to convert a facility level TTC PD to PIT PD?
ReplyDeleteLet's say facility is of 5 year maturity. From a given TTC PD, X % how do we arrive at yearly break of PIT PD?
It's truly a guide. Thanks so much.
ReplyDeletePls. When was this article published?
ReplyDeleteI need to reference in my work. Thank you.
August, 2019. Thanks!
DeleteGood article but the title is misleading - a better title would be "Very Preliminary Introduction to Credit Risk Modelling".
ReplyDeleteThnkyou for sharingg!! its really helpful
ReplyDeleteCan you please write something on how to build Low Default Portfolio Model?
ReplyDeleteSure. Drop me a line.
DeleteUpdated. Thanks for pointing it out.
ReplyDeleteBrilliant summation, it is well broken down for beginners and intermediate analyst consumption. Thank you
ReplyDeleteIt was best article on credit risk.brilliantly explained
ReplyDeleteIt is a great article specially for the beginerrs like me. I would like to dig deeper into this and need help with the reading and practical material. Not able to find it.
ReplyDeleteOne must say, this has to be the best introduction to credit risk modeling. Just one thing that I would like to highlight, the place where the article makes transition from explaining the regulatory modeling to business decision scorecard development, it could be made more explicit. Rest, it is superb.
ReplyDeleteWell written and nicely explained the concepts.
ReplyDeleteExcellent article.You have done good service to credit risk professionals for giving clarity on the subject.
ReplyDeleteThis article was everything I needed and more.Thank you!
ReplyDeleteconcise, easy understading and very useful content thanks for sharing
ReplyDeleteExcellent Job!
ReplyDeleteThis is so detailed. Thank you so much.
ReplyDeleteAmazing content! Thanks and please consider writing a book that demystifies all credit risk management concepts :)
ReplyDeleteI loved it
ReplyDeleteGreat article. I am a computer engineer and I am new to the Credit risk concepts. This was v helpful. Thank you so much :)
ReplyDeleteGreat Content, can you also made a blog on how to select the target indicator of default.
ReplyDeleteThankyou !!