A COMPLETE GUIDE TO CREDIT RISK MODELLING

As these home loan borrowers had high chance to default, many of the them started defaulting on their loans and banks started seizing (foreclose) their property. The real estate bubble burst and a sharp decline in home prices. Many financial institutions globally invested in these funds resulted to a recession. Banks, investors and re-insurers faced huge financial losses and bankruptcy of many financial and non-financial firms. Even non-financial firms were impacted badly because of either their investment in these funds or impacted because of a very low demand and purchasing activities in the economy. In simple words, people had a very little or no money to spend which leads to many organisations halted their production. It further leads to huge job losses. US Government bailed out many big corporate houses during recession. You may have understood now why credit risk is so important. The whole economy can be in danger if current and future credit losses are not identified or estimated properly.

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 jurisdictions, including Brazil, Canada, Germany, Australia, Argentina, China, France, India, Saudi Arabia, the Netherlands, Russia, Hong Kong, Japan, Italy, Korea, Mexico, Singapore, Spain, Luxembourg, Turkey, Switzerland, Sweden, South Africa, the United Kingdom, the United States, Indonesia and Belgium.

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.

1. Tier 1 capital : Primary funding source of the bank. It includes shareholders' equity and retained earnings
2. Tier 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

It has four credit risk components :

• 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.

Expected Loss is calculated by (PD * LGD * EAD). 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%.

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. 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 has recently become effective starting 2019. In some countries, central banks have fixed Dec'2019 as the deadline to meet capital requirements under the Basel III norm. 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

IFRS 9

IFRS 9 is 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 risk

As per IFRS 9, there are three stages of Credit Risk which are as follows -

1. Stage 1 - Credit risk has not increased significantly since initial recognition, indicates low credit risk at reporting date
2. Stage 2 - Credit risk has increased significantly since initial recognition
3. Stage 3 - Permanent reduction in the value of financial asset at the reporting date

How IFRS 9 is different from Basel III?

Yes, they are different but both requires building PD, LGD and EAD models. See the difference between them below.

Parameters	Basel III	IFRS 9
Objective	Expected + Unexpected Loss	Expected Loss
PD	One year PD	12 month PD for stage 1 assets, Lifetime PD for stage 2 and 3 assets
Rating Philosophy	TTC rating philosophy	PIT rating philosophy
LGD	Downturn LGD (both direct + indirect costs)	Best estimate LGD (only direct costs)
EAD	Downturn EAD	Best estimate EAD
Expected Loss /Expected CreditLoss (ECL)	EL=PD*LGD*EAD	EL=PD*PV of cash shortfalls

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 advanced IRB approach under Basel norms.

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.

We consider 12 months as performance window to flag defaults which means if a customer has defaulted any time in next 12 months, it would be flagged as ‘Bad’

Methodologies for Estimating PD

There are two main methodologies for estimating Probability of Default.

1. Judgmental Method
2. 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 repay
• Capacity : 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 code
• Existing Relationship : Tenure, number of products, payment performance, previous claims
• Credit 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 -

1. Discrimination : Ability to differentiate between good (non-defaulters) and bad (defaulters) customers
2. 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 Test

Check 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.

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 at least two consecutive quarters of negative growth in real GDP. 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

GDP
Unemployment rate
Index of Industrial Production
Import
Export
Interest rate
Inflation rate
House price index
Exchange rate

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.

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