Credit risk: probability of default and loss given default

Where does credit risk come from?

Credit risk is the risk of loss because a borrower does not pay interest or principal in full and on time. A borrower that misses a promised payment is in default . A lender who takes that risk wants to be paid for the loss it can expect, which is the idea the rest of this module measures.

Where the money to repay comes from depends on the borrower:

• A company with unsecured debt pays from cash flow from its operations. If it defaults, lenders have a claim on its general pool of assets.
• A company with secured debt also pays from cash flow, but specific pledged assets give the lender a second source of repayment.
• A government pays from taxes and other revenue.

Analysts organize the questions they ask into the Cs of credit analysis . Five look at the borrower itself (bottom-up) and three at the world it operates in (top-down).

Cs of credit analysiseight lenses on whether a borrower will pay

• Bottom-up: the borrower Memorize five factors specific to one issuer
  • Capacity Memorize ability to pay on time from cash flow
  • Capital Memorize other resources, less reliance on debt
  • Collateral Memorize quality and value of pledged assets
  • Covenants Memorize legal terms the borrower must keep
  • Character Memorize management quality and willingness to repay
• Top-down: the environment Memorize three factors that touch every borrower
  • Conditions Memorize economic, competitive and business climate
  • Country Memorize legal, political and geopolitical system
  • Currency Memorize exchange-rate effects, foreign-currency debt

Capacity and capital are mostly numbers taken from the financial statements. Collateral, covenants and character are mostly judgments about the company’s history and its managers. The top-down Cs apply to every borrower in a country, to a greater or lesser degree.

Why does a borrower fail to pay? Usually because it lacks cash on the day. An illiquid borrower cannot raise the cash in time: it may be unable to draw a credit line or sell assets quickly, even though its assets are worth more than its debts. An insolvent borrower is a deeper problem: its assets are worth less than its liabilities. Either one can lead to default.

Go deeper Pari passu and cross-default: why one missed payment is a problem for all the debt

Unsecured bonds usually rank pari passu, meaning equally, with the issuer’s other unsecured debt. They also usually carry cross-default wording: a default on one obligation puts the others in default too. So a missed coupon on one bond makes all of the issuer’s unsecured debt claim against the same general pool of assets at the same time. Secured lenders, in addition, can look to their specific pledged assets before they share in what is left.

How do you measure expected loss?

Two questions give you the loss a lender should expect. How often does the borrower default, and how much is lost when it does? The first is the probability of default (POD) , usually stated for one year. The second is the loss given default (LGD) .

Loss given default has two inputs. The first is the size of the claim when default happens, the expected exposure (EE) , also called exposure at default. It is what the borrower owes (face value plus accrued interest) less the current value of any collateral.

$$EE = \text{face value} + \text{accrued interest} - \text{collateral value}$$

The second input is how much of that claim comes back. The recovery rate (RR) is the percentage of the claim recovered. The part that does not come back, 1 − RR, is the loss severity .

$$LGD = EE \times (1 - RR)$$

Loss given default can be stated as an amount (EUR 450,000) or as a percentage of principal (45%). The percentage is easier to compare across borrowers and positions of different sizes.

Multiply how often by how much and you have the expected loss (EL) :

$$EL = POD \times LGD = POD \times EE \times (1 - RR)$$

Expected loss (EL)POD × LGD: how often you lose times how much

• Probability of default (POD) Memorize how often; usually a one-year figure
  • Profitability Use it higher means lower POD
  • Coverage Use it higher means lower POD
  • Leverage Use it higher means higher POD
• Loss given default (LGD) Memorize how much; EE × (1 − RR)
  • Expected exposure (EE) Memorize face + accrued − collateral
  • Recovery rate (RR) Memorize share of the claim recovered
  • Seniority and security Use it drive recovery; secured and senior means lower LGD

Exam tip Before multiplying, ask what the percentage means. A recovery rate is what you get back. The formula needs what you lose, so use 1 − RR.

Go deeper Expected loss is not the loss you will see

Expected loss exists before any default happens. It is a probability-weighted average of two outcomes: no loss in most years and a large loss in a few. A lender who prices a loan to cover only the expected loss would, on average, earn nothing for bearing the risk. That is why lenders also care about the variation around the average, not just the average.

Go deeper Which time period does POD cover?

Probability of default is normally an annual figure. The chance that a bond defaults at some point over its whole life is larger. This module works with one-year numbers, because the spread formula below is also a yearly figure.

Is the credit spread enough?

The extra yield a credit-risky bond pays over a government bond of similar maturity is its credit spread. If the market is pricing credit risk sensibly, that spread should cover the expected loss.

$$\text{credit spread} \approx POD \times LGD$$

Put both numbers on the same yearly scale first. Then compare:

• spread equal to expected loss: the investor is fairly compensated;
• spread above expected loss: more than fairly compensated;
• spread below: less than fairly compensated.

What moves each part? Probability of default rises as profitability and coverage fall and as leverage rises. Loss given default depends mainly on where the claim ranks and what backs it: secured and senior claims recover more, so their loss given default is lower. That explains how different investors protect themselves. An investor in unsecured investment-grade bonds faces a high loss given default if something goes wrong, so the main danger is a rise in the probability of default. A high-yield investor expects defaults to be likelier, so they look for security and covenants to lower the loss given default.