Transforming the Credit Risk Management Process - Calibrating Risk Drivers

Part 2: Calibrating Risk Drivers

Since credit risk cannot be measured directly, there is no single indicator of credit risk. It is measured in an indirect way, by measuring, controlling and managing the credit risk drivers.

The Basel II Accord (the Accord) has identified four risk drivers:

• Exposure
• Probability of Default (PD)
• Loss Given Default (LGD)
• Maturity

Exposure is the amount lent to the borrower and is the simplest and most direct measure of credit risk. Special measurement techniques are needed for exposure, which vary and are difficult to measure. Such exposure includes commitments, un-drawn lines and derivatives, where exposure fluctuates over a period. Credit risk is driven by the probability of default. Once at default, credit losses accentuate from the inability to recover. It is obvious that the credit risk is higher for the exposure of higher maturity. Basel has correctly identified each of these factors as credit risk drivers.

Traditionally, exposure and credit quality or Probability of Default (PD) has been used as a measure of credit risk. The risk weights and type of the counterparty used in the Basel Accord I is nothing but an exercise to calibrate exposures to the risk (and therefore the capital required). Since it is very difficult to measure Loss Given Default (LGD), maturity and correlation, PD is the only other estimate of credit risk. If one looks at the Accord II, LGD is either taken as constant or is estimated from credit loss and PD. The Accord estimates maturity and correlation in terms of PD. In a nutshell, PD is heavily loaded to measure the credit risk, or it can be said that it is the sole measure of credit risk for the time being, since it represents other risk drivers. In reality, each of the credit drivers is a poor substitute/representative for other credit drivers since each of them measure different aspects of risk. Therefore, each credit driver has to be measured independently.

The primary driver for the substitution is, of course, the ease of measurability. Therefore, a calibration process faces a three-fold challenge:

• Identification of Risk Indicators representing each of the risk drivers (especially LGD and Maturity).
• There is not much past data for drivers other than PD
• Contaminated PD data – since it is used to represent other drivers also.

Take Note – Next-level Risk Practices: There is a purpose for dividing the Basel Accord into three pillars. While pillar I prescribes the methodology and benchmarks for risk measurement, pillar II and III:

• Encourage banks to develop and use better risk management techniques in monitoring and managing their risks.
• Develop treatment for
• Risk drivers not fully captured
• Risk drivers not considered

Credit Risk Measurement Techniques are Essentially Calibrating Techniques

1. Linking risk indicators such as macroeconomic factors, and idiosyncratic factors including the market information for credit spread and equity prices to risk drivers. The risk indicators are of use only when they are calibrated to the risk drivers. Risk drivers are the factors developed to convert the risk indicators into risk measurements.
2. Quantum of each risk driver indicates the quantum of credit risk on a cardinal scale; although, we need to calibrate the same to credit losses to measure the risk in absolute terms. For sure, we can say that higher quantum of risk drivers means a higher risk. This is the theme of this paper.

Take Note- Risk Measurement Templates: According to Basel Committee, credit rating (Probability of Default) is a summary indicator of the risk inherent in individual credit. Ratings typically embody an assessment of risks of loss due to failure by a given borrower to pay as promised, based on considerations of relevant obligors, facility characteristics and industry or macro economic factors.

Calibrating Credit Risk Drivers

Calibration is a three-fold problem comprising:

• Calibrating idiosyncratic and systemic factors to credit risk dimensions
• Calibrating credit risk dimensions to the credit risk or loss
• Ability to measure expected losses from unexpected losses

The problem is that the credit risk drivers themselves cannot be measured directly, with the exception of exposure. Therefore, credit risk drivers are determined by measuring macroeconomic factors and idiosyncratic factors including credit spread and market prices; credit losses and credit risk mitigants; and, measuring default/loss events and linking them together. This phenomenon of measuring obligor attributes and macroeconomic factors to measure the credit risk drivers by linking them to credit losses has brought two-fold problems: calibration and measuring correlation. We shall dwell on linkages of correlation with credit risk/credit loss separately in the next sections.

Take Note – Architecture and best practices: Measuring risk drivers is a question of cost benefits. Risk drivers are measured either at individual exposure levels or at the portfolio level (taking portfolio as a single exposure i.e. mortgage loans). The choice of measuring risk drivers at the individual level or at the portfolio level is a question of cost benefits, data availability to measure factors such as the ability, and the willingness to pay. Generally, individual exposures are measured at a portfolio level. Since the exposure is very small, it is very difficult to measure the ability and willingness to pay.

Calibration Process

In a very simple way Credit Loss is defined as follows:

Credit Loss = EAD (Exposure at Default) x PD x LGD

Therefore, for an exposure of a single USD, the credit loss is a multiple of PD and LGD proving that PD and LGD calibration are a closely linked process.

Quantification of Loss: Calibrating to PD and LGD

• Defining default
• This is the most important step in calibration. Default definition can seriously affect the value of historical loss and default information, whether internally in the bank or from external sources.
• Banks need to demonstrate that PD and LGD data are calibrated as closely as possible to the same definition of what comprises a default event.
• While mapping/calibrating loss to an external source, definition of defaults need to be exercised with great care. For different default definitions, data will need to be appropriately modified. Use of rating agency results to quantify the probability of default implicitly means that the bank is applying the agencies’ definition of a default event.
• Time horizon: Four types of time horizons
• Multiple time horizons driven by the maturity of facility
• Multiple time horizons leading to a different set of PDs. Time horizon is driven by the business cycle
• Averaging PDs over a complete business cycle to estimate a one-year default. This method is generally adopted by rating agencies
• One-time horizon/one-year horizon for all the exposures
• Factors impacting time horizon
• Time required to take loss mitigation action
• Publication of default data
• New information from the obligor
• Time horizon for the model, which is being calibrated and requires data reconciliation.

Calibrating Probability of Default: PD is calibrated to idiosyncratic information such as financial ratios and market prices along with impact of macroeconomic factors by measuring industry, management and other impacts, also called credit rating. Some form of credit rating is always in practice in every bank. A major problem is to calibrate ratings to losses. Credit rating is also measured as a two-step process of quantitative and judgmental measurement. As a thumb rule, idiosyncratic attributes are measured quantitatively and macroeconomic impacts are measured judgmentally. It should be noted that what needs to be measured can vary across firms, industries, banks, geography and country. Judgmental factors are also converted into some quantitative factors ultimately.

Take Note – Transformation Process: The difference between Credit Administration and Credit Risk Management is in the calibration of risk drivers to the credit losses. If risk drivers are calibrated and the calibration is back-tested, it is risk management; or else it is termed credit administration. 

Steps in Calibrating PD to Credit Loss: Correlation plays an important role in calibrations. It should be noted that actual or historical data have both impacts captured – default and correlations. Here are the following steps for PD calibration:

• Identify variables with better explanatory power
• The purpose of the credit risk model is to measure, estimate or predict the probability distribution of future credit losses on a bank’s portfolio. With the assumption that the past pattern will continue, model scores are mapped to an empirical probability of default using historical data.
• Adjusting the difference between the historical default rates and actual default rates. If actual default rates can be found out (which are different from historical default rates), mapping of scores can be adjusted to the actual default rates.

Take Note – Transformation Process: Basel has prescribed standards for the usage of historical data and it encourages calibrating historical data. Calibration to historical data as a mandatory requirement, is due to the fact that it is not a risk measurement framework, but a capital calculation framework and, therefore, discourages banks to miss capital requirements. Ideally, going forward models should be calibrated to the future estimation of the risk (ex-post) rather than to the past historical data (ex-ante).

Prediction Capabilities of Risk Driver Models: are to be tested on two dimensions – predication and calibration. (Calibration layers are either absent or very thin for market risk models). The predication capability of a model enables it to discriminate between two credits in a finer way and in category I- and category II-type errors. Ideally, instead of historical data, models should be calibrated to the data which represents actual conditions. As the data sharing and understanding about risk measurement will improve, it is likely that banks will start calibrating their models to the data having predictive capabilities.

Take Note – Architecture and Best Practices: ex-post (predicted) estimates must be supported by ex-ante and any reasons for the change.

Calibrating credit grades to credit losses

Benchmarking – this is a part of a calibration exercise. It is a set of activities that uses alternative tools to draw inferences about the correctness of risk measurements ratings before outcomes are actually known. This is generally done by getting the rating done by another rating agency or model. Benchmarking is not same as back-testing.

Basel recommends two-dimensional rating systems – separately for Obligor and Facility. Obligor rating must be calibrated to PD and facility rating must be calibrated to LGD. Both ratings must consider the impact of economic weaknesses.

Importance of Model Inputs or Data: Credit rating models must take account of shortcomings in the data, notably the lack of mark-to-market price data on loan books. The different models tackle this by devising proxies for market prices using other information about the obligor. For example, some employ bond ratings or a bank’s own internal counterparty ratings, while others use the equity market capitalization of obligors. All credit risk models inevitably depend heavily on the quality of data inputs. For example, it is essential for ratings-based models that ratings are accurate and consistent indications of credit standing. While a rating provides information on the current credit standing of an obligor, rating migration patterns indicate how credit standings may change over the modelling horizon.

Calibration Standards:

Regulators encourage conservative estimates (over estimates of risk) than otherwise. For calibration to be effective, back-testing needs to be performed on a regular basis. Calibration and back-testing of such calibration is the differentiating factor from traditional credit administration to risk management. It is the path of moving from a relative risk measurement to absolute risk measurement. Validation/back-testing is the backbone of calibration. Yet the Accord has not prescribed validation methods or standards.

Take Note – Transformation Process: Measuring each of the credit drivers has not yet been developed fully. Basel Accord has prescribed a limited calibration standard only for PD, LGD (other drivers are linked to PD) and collaterals (explained in other sections). Calibration standards are likely to emerge and be strengthened going forward.

Issues in Measurement of Risk Drivers: The following table shows calibration issues:

Present Status of Calibration

All said and done, credit risk cannot be measured due to the problem of data availability (data is not available from external source) and data frequency (data is not available from internal source). Efforts are being made to solve the data problem in two ways:

1. By developing and using models which can derive the credit risk measurements from market prices. Merton models, KMV models and credit spreads models are an example.
2. Self-regulating organizations, industry associations and supervisors are making efforts to pool data. However, both these efforts have limited impact on the credit risk measurement since all these data are obligor-, portfolio- and geography-specific.

Basel is making efforts by conducting various studies including QIS studies and publication of various weights and formulas and variables in formulas. With all the debate and comments on the Basel, these numbers fairly represent the economic capital or the credit risk. These numbers can be utilized for reverse engineering, calibration and broad measurements. Under pillar II of the Accord, these numbers are going to be further refined by supervisors for their regulated institutions, which will augment risk measurement.