# Loss Given Default (LGD) Calculation Implementation

Loss Given Default (LGD) is a key in the field of credit risk management and financial analysis. It represents the amount of loss a lender or creditor faces when a borrower defaults on a loan, expressed as a percentage of the total exposure at the time of default. LGD is an essential component in calculating the expected loss, which also includes the probability of default (PD) and the exposure at default (EAD).

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LGD is measured through a combination of historical data analysis, recovery rates, and market conditions, among other factors. The process involves several steps:

• Exposure at Default (EAD): This is the total value that is at risk when a default occurs. It includes the outstanding balance of the loan plus any committed but undrawn amounts.
We use the following histogram or density plot showing the distribution of LGD rates observed in the past. This can help in understanding the variability of LGD and setting appropriate LGD estimates for different types of exposures.

• Recovery Rate (RR): This is the proportion of the EAD that is recovered after the default has occurred. Recoveries can come from collateral, selling of the defaulted loans, or other methods of recuperation.
• Calculating LGD: LGD is calculated as 1 minus the recovery rate, often expressed as a percentage. If the recovery rate is 40%, then LGD would be 60%. LGD is 1 - Recovery rate or 1 - Recovered Amount / EAD.
This chart will show the distribution of LGD on defaulted exposures with year wise recovery.

• Historical Data and Statistical Models: Financial institutions use historical default and recovery data to model and predict LGD. This can involve statistical techniques, regression analysis, or machine learning models to estimate LGD based on various risk factors such as loan characteristics, borrower creditworthiness, and economic conditions.
• Collateral Value: The value and type of collateral securing a loan significantly affect LGD. Loans secured by tangible assets like real estate typically have lower LGDs due to the potential to recover losses through the sale of the collateral.
Then we show how the value of collateral held against loans affects the LGD. It is useful for secured loans where the recovery process involves selling the collateral.

We will also show a scatter plot showing the relationship between the time taken to recover from a default and the resulting LGD. Longer recovery times can be associated with higher LGD due to the costs and depreciation of collateral value over time.

• Market Conditions: Economic and market conditions at the time of default affect the recoverable value of collateral and, subsequently, the LGD. For instance, real estate values in a market downturn can lead to higher LGDs for mortgages.
• Workouts and Recovery Processes: The effectiveness of a lender’s processes for managing defaulted loans, including negotiations, restructuring, and legal actions, can also impact recovery rates and LGD.

LGD is a dynamic measure that can vary significantly across different loan types, industries, and economic cycles. Financial institutions continually refine their LGD models to better predict potential losses and manage their risk exposure.

The following approaches can be used to calculate LGD based on the loan portfolio:

 Approach Description Example Suitable for Historical Loss Ratio (HLR) Simplest method: Takes the average of historical losses divided by defaulted loan amounts. Doesn't consider risk factors. HLR = Total Loss on Defaulted Loans / Total Amount Defaulted Retail loans, small portfolios Vintage Analysis Groups loans by origination date (vintage) and calculates LGD for each vintage separately. Provides more granularity but relies on sufficient historical data. Calculate LGD for each vintage year based on defaults and recoveries within that year. Mortgage loans, corporate loans Benchmarking Uses industry averages or data from similar institutions. Easy to implement, but may not reflect specific portfolio characteristics. Use published LGD benchmarks for a specific loan type and region. Credit cards, consumer loans Regression Analysis Develops a statistical model that predicts LGD based on borrower characteristics and loan terms. Requires advanced analytics skills and good quality data. Model predicts LGD based on factors like credit score, loan-to-value ratio, delinquency history. Complex loan products, large portfolios Loss Forecasting Models Sophisticated models that incorporate economic scenarios, borrower behavior, and recovery strategies. Requires significant expertise and resources. Model forecasts LGD under different economic conditions and considers recovery actions. Large commercial loans, structured finance

From an IFRS Perspective:

• IFRS 9 Financial Instruments: This standard requires entities to measure and report credit losses using the Expected Credit Loss (ECL) model, which includes LGD as a crucial component. The calculation of LGD under IFRS 9 involves forward-looking information, considering economic conditions and forecasts.
• Lifetime ECL for Significant Increases in Credit Risk: When a financial instrument shows a significant increase in credit risk, entities must measure ECL over the instrument's entire lifetime. LGD estimations should incorporate the likelihood of default and potential recovery rates over this period.
• Incorporation of Forward-looking Information: LGD models must consider forward-looking macroeconomic data and scenarios to estimate future losses more accurately. This includes changes in unemployment rates, GDP growth, real estate prices, etc.
• Disclosure Requirements: IFRS 9 requires detailed disclosures about the assumptions used in calculating LGD, the model's methodologies, and the impact of changes in economic scenarios.

From a Basel Framework Perspective:

• Credit risk management, including the calculation of LGD for different types of exposures. Banks using the Internal Ratings-Based (IRB) approach must estimate LGD based on historical data and adjust for downturn conditions.
• Downturn LGD: Institutions must estimate LGD under stressed conditions or downturn periods. This ensures that the LGD reflects worse-than-average conditions, particularly for unsecured exposures where recoveries can significantly fluctuate.
• Collateral and Guarantees: The Basel framework emphasizes the treatment of collateral and guarantees in LGD calculations. The valuation and management of collateral, including the frequency of revaluation and the consideration of legal and operational constraints on using collateral, are critical.
• Minimum LGD Values: The Basel framework sets minimum LGD values for different types of exposures. For example, secured and unsecured parts of claims have different LGD floors, ensuring a baseline level of risk coverage.
• Validation and Back-testing: Banks are required to validate their LGD models regularly, including back-testing against actual outcomes and stress testing to evaluate the model's performance under extreme but plausible scenarios.

Common Considerations for Both IFRS and Basel:

• Data Quality and Availability: High-quality, relevant, and sufficient data are essential for accurate LGD estimation. This includes detailed information on defaults, recoveries, and time to recovery.
• Model Governance: Robust governance frameworks are necessary to oversee the development, implementation, and ongoing management of LGD models. This includes model documentation, approval processes, and periodic reviews.
• Regulatory Compliance: Institutions must ensure that their LGD calculations comply with local and international regulatory requirements, which may vary depending on the jurisdiction.

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