Credit Risk Measurement

Three Components: PD, LGD, and EAD

Determining the cost of Credit Risk

Expected Loss (EL) = Probability of Default (PD) × Loss Given Default (LGD) × Exposure at Default (EAD)

Definition

Probability of Default (PD)

The likelihood of a borrower being unable to repay.

The chance that an event of default will occur over a given period of time.

Loss Given Default (LGD)

The fraction of exposure at default that is lost in the case of default.

The complement of the Recovery Rate (RR): LGD = 1 − RR. In other words, the degree of security of a facility and the expected percentage of the EAD that will be lost after default, representing the total economic loss.

Exposure at Default (EAD)

The exposure at risk in the case of default.

The predicted amount of money a lender could lose if a borrower defaults on a credit obligation. It is calculated by adding the already drawn portion of a loan or facility to an estimated portion of the undrawn balance, using a Credit Conversion Factor (CCF).

Credit Risk Measurement

Three Dimensions: Cash Flows, Secured, and Guaranteed
The Good Box and the Bad Box
CF (+)
CF (-)
Secured (+)
Unsecured (-)
Guaranteed (+)
Unguaranteed (-)
Options Cash Flows Secured Guaranteed Borrower
1 (right box) + + + Ideal borrower
2 + + - CRE project
3 + - - Fortune 500
4 (wrong box) - - - Special assets
5 - + - Large ABL
6 - + + Small ABL
7 - - + Rich relative
8 + - + Services firm
  • 3 dimensions: Cash Flows, Secured, Garanteed
  • Cash Flows: related to PD
  • Secured and Guaranteed: related to LGD
  • This is why we use default as the event in the formula below; need a good definition of default conceptually; not mix up PD and LGD or CF and Sec/Guar

Credit Risk Measurement

Loss Distribution and Risk

  • Time horizon: 1 year
  • Typical EL:
  • Typical UL:
  • EL = Prob(event) × E[loss|event]
  • Event: any event (e.g., default, charge‑off, etc.) could give us correct EL in the formula above. What event should we use? Default.
  • Risk is uncertainty. If there is no uncertainty, there is no risk.
  • If we are 100% sure that loss will equal EL, no matter how high it is, there is no risk.
  • Risk is unexpected loss, which is measured by EC.
  • RAROC: numerator is net profit, which has accounted for credit losses; denominator is economic capital, which measures risk.

Events of Default

Understanding Default Triggers and Implications

What does it mean to default?

Legal documents related to debt issuance, such as credit agreements and bond indentures, typically define events of default that, if not cured, result in a default on the borrower's obligations. Defaults may relate to any kind of fixed income security, including high-yield bonds, leveraged loans, and other types of debt. A default usually provides the company's creditors with enhanced access to information, higher interest rates called default interest, and opportunities to renegotiate the terms of the debt going forward. In dire situations, a default may trigger an acceleration of the maturity of the debt such that the principal amount is immediately due and payable. Default interest, which may begin upon the event of default or at the time of acceleration of the debt, may involve a premium of 2 or 3 percentage points above the rate normally in effect. There are three types of default that are relevant to distressed M&A: payment default, technical default, and cross default.

Payment default

arises when a company fails to make a scheduled payment to one or more of its creditors. Usually, creditors give companies a grace period within which to make a late payment after the scheduled due date. If a company still has not made the payment by the end of the grace period, then a payment default occurs.

Technical defaults

occur when a company's declining performance triggers one or more defaults with respect to its covenants (often called "tripping covenants"). When a company goes out a revolving line of credit or a term loan with its senior lenders or issues debt, such as bonds, with its unsecured creditors, the legal agreements between the company and its creditors specify certain covenants relating to financial, legal, administrative, and other issues. By defining minimum expectations, these covenants are a primary means for a creditor to remain a passive investor and allow the borrower to exercise its business judgment for managing day-to-day operations. When a borrower's performance falls below these minimum expectations, however, creditors understandably become concerned about the company's future performance. Therefore, when a company breaches one or more of these covenants, there is a technical default. A technical default can arise even if the company makes all of its payments on time.

Cross default

occurs when a default with one group of creditors triggers defaults with other creditors. Companies with more complicated capital structures have multiple tranches of debt, with different legal agreements for each tranche. In such situations, it is typical for each tranche of debt to have as a covenant that the company is not in default with any other tranche of debt. If one group of creditors gains rights as a result of a default, the other creditors want to level the playing field by gaining those rights as well. Also, if one group of creditors is on notice that a company's performance is declining below minimum expectations, then other groups of creditors want that same notice. When a cross default occurs, a company's distress may accelerate if it finds itself simultaneously negotiating with multiple groups of creditors, causing a major distraction for management as it tries to run the day-to-day operations of the business.

Basel Framework: Definition of Default

In the Basel framework, default generally refers to a borrower's failure to meet their financial obligations, specifically a loan or credit agreement, either due to non-payment or other indicators of unlikeliness to pay. This failure can be triggered by a borrower being past due on payments for a certain period (typically 90 days) or by the lender considering the borrower unlikely to repay, even if not yet past the due date.

Key Components of Basel's Default Definition

  • Payment Past Due: A common trigger for default is when a borrower is past due on payments for a specific period. Basel II/III typically uses 90 days as the threshold, but some exceptions exist.

  • Unlikeliness to Pay:This component allows for a broader definition of default beyond just missed payments. It includes situations where a bank, based on its internal risk management procedures, believes the borrower is unlikely to repay their debt in full, even if not yet past due.

  • Materiality:Basel regulations emphasize that a default should be based on a "material" credit obligation, meaning a significant debt, and not a minor or inconsequential one.

Indicators of Unlikeliness to Pay (Examples)

  • The bank places the exposure on non-accrual status.
  • The bank takes a charge-off or write-down on the exposure due to the borrower's financial condition.
  • The bank sells the exposure at a loss.
  • The bank consents to a distressed restructuring of the debt.
  • The bank files for the borrower's bankruptcy or the borrower seeks bankruptcy protection.

Importance of the Default Definition

  • Capital Requirements: The definition of default is crucial for calculating regulatory capital requirements for banks.

  • Risk Parameters: It influences the estimation of risk parameters like probability of default (PD), loss given default (LGD), and exposure at default (EAD).

  • Risk Weights: Default definitions affect the risk weights assigned to different assets, impacting how much capital a bank needs to hold against those assets.

  • Expected Loss Calculations: The definition directly impacts how banks calculate expected losses on their loan portfolios.

In essence, Basel's default definition is a framework that helps banks consistently and accurately assess the credit risk associated with their lending activities.

Default Mitigation Strategies

Techniques to Soften Default Provisions

What techniques can be used to take some of the bite out of default provisions?

There are basically two default softeners: the use of grace or cure provisions and the concept of materiality.

Grace Periods

A grace period is a period of time following the due date for the making of a payment during which that payment may be made and default avoided. Five days' grace beyond the due date is not uncommon; sometimes 10 or even 15 days may be granted.

Cure Periods

Cure periods apply to events of default triggered by covenant breaches. Generally, the lender will attempt to limit the application of cure periods to those covenants that are capable of being fixed (e.g., a duty to submit financial reports) but deny them for covenants that are designed to provide early warning of trouble (e.g., breach of financial ratios). The latter category of covenants typically cannot be cured and will require a waiver or amendment to avoid default. Sometimes the cure period will not begin to run until the lender has given the borrower notice of a failure to perform; in other cases, the cure period will begin to run when the borrower should have performed, whether the lender knew of the borrower's failure or not. Cure periods vary greatly from transaction to transaction and from provision to provision. However, 5-day, 10-day, and 30-day cure periods are seen from time to time, and sometimes the concept of counting only "business days" is used to extend the period by excluding Saturdays, Sundays, and nationally recognized holidays.

Materiality Concept

The concept of materiality arises when a representation turns out to be untrue, but the effect of this inaccuracy is not materially adverse to the borrower or the collateral, or to the lender's position. Therefore, the parties may agree in the loan agreement that a breach of a particular representation or warranty must be material in order to constitute a default. Materiality may not be applicable to every representation and warranty in the loan agreement.

PD Measurements

Incidence-based and Exposure-weighted Default Rate

It is not uncommon for institutions to assume that dollar-based and incidence-based default rates are equal. The standard expected loss formula is shown in Exhibit 1. Using an incidence-based default probability in this formula implicitly assumes that the two default metrics are equal. These dollar-based expected loss figures are often applied to loan loss reserves, economic capital frameworks, and various portfolio risk analyses and reporting.

The challenge with using incidence-based default probability for expected loss calculations is that it says nothing about the dollar-weighted default rate. A portfolio with exposure to 100 borrowers—99 for $10,000 and one for $1 million—could lose over half its dollar value (assuming zero recovery) and still have only a 1% incidence-based default rate. Moreover, the incidence-based rate cannot be compared directly with historical loss since it implies a loss of $9,900 (1% of $1.99 million), not the $1 million that was actually lost.

Expected loss frameworks based on incidence rates of default may implicitly assume that the underlying portfolios are perfectly granular—in other words, the portfolio is reasonably "fine-grained" with exposures being evenly spread out across a large number of obligors. If commercial portfolios were perfectly granular, banks using incidence-based default rates to calculate expected loss in dollars have to assume that there is not a significant difference between the size of defaulted credits and other credits in the portfolio. The question is, how well does this assumption hold?

In the cases of Bank B and Bank C, the use of an incidence-based PD alone may not provide for complete transparency and the resulting expected loss estimate may not reflect certain trends in the portfolio. To account for these trends, an adjustment, which we referred to as the loss severity adjustment, may be incorporated.

The loss severity adjustment is the ratio of the average charge-off balance (Line 8) to the average balance (Line 9). The loss severity adjustment restores the information buried in the averages, reconciling the incidence-based default rates with the bank’s loss in dollars. In the case of Bank B, where the largest credits have a higher propensity for default, the losses implied by incidence-based default rates need to be adjusted upward by a factor of 2.5, the loss severity adjustment. After the adjustment, the dollar losses reflect historical figures and the trend in the portfolio towards higher dollar-weighted default probabilities. The appropriate level for making this adjustment may be at the product and rating grade level.

What About Your Bank?

As the case of Bank A illustrates, the issue of incidence-based versus dollar-weighted defaults disappears when the loans that default are the same size as those that don’t. The two metrics diverge only when loans to defaulting borrowers are larger or smaller than the average credit in the portfolio.

  • To diagnose where your bank stands on this issue, it’s useful to ask:
    • Is there a consistent bias in my ratings system toward a higher or lower dollar-based default vs. incidence-based default rate? Should I redesign my ratings assignment process?
    • If large loans are more sensitive to cyclical factors, is the difference between dollar-based and incidence-based default rates driven by the recent economic cycle?
    • Is the composition of my portfolio across large corporate and smaller, middle-market borrowers driving the differences between the two default measures?
    • What impact do these ongoing trends in dollar-based vs. incidence-based default rates have on economic capital, loan loss reserves, and other risk metrics?

Know Your Metrics

The basic concepts of credit risk measurement—default probability, recovery rate, exposure at default—are easy enough to describe. But a consensus on the concepts doesn’t necessarily translate into agreement on a number representing the credit risk of a loan portfolio. Seemingly minor differences in assumptions can result in large disparities in estimates of credit risk—with potentially far-reaching effects on a bank’s ability to measure and manage credit risk.

Beyond the issue of credit measurement is a more basic theme: the importance of understanding the metrics that drive your business. There is no right or wrong way to measure the probability of default. Each method is appropriate for different uses. It is important to know which method your bank uses for what purposes. Otherwise, it’s easy to be misled by the very metrics that are intended to create transparency and improve business decisions.

Exhibit 1: Formula for Expected Loss

Expected Loss (EL) = probability of default × loss given default × exposure at default

Probability of Default: Incidence Basis = number of obligors that default during period/total number of obligors at start of period

Probability of Default: Dollar-Weighted Basis = dollar value of loans to obligor that defaulted during period/dollar value of all loans at start of period