Credit risk modelling — PD, LGD, EAD, Basel

Modern bank credit risk runs on a small set of equations whose elegance hides the institutional weight behind them. The core equation is so simple it fits on a single line of text, yet it is the calculation a credit risk committee, a regulatory capital officer, and a loan pricing model all use, every working day, on every exposure on the bank's balance sheet. The Basel framework codifies the equation into regulatory capital rules that govern roughly USD 200 trillion of global banking assets. The implementation is hard enough that whole departments are dedicated to it; the fundamentals are simple enough that every credit analyst should be able to carry them.

The core equation

  Expected Loss  =  PD  ×  LGD  ×  EAD

Variable glossary — every input explained

• Expected Loss (EL) — the average loss the lender expects to incur over the next period (usually one year) on this exposure, expressed in the currency of the exposure. Not what the bank actually loses on this loan in any given year — that's a draw from a distribution — but the long-run statistical average. The bank prices this average into the interest rate it charges.
• PD — probability of default. The probability that the borrower defaults at any point in the next year, expressed as a decimal between 0 and 1. A 3% PD means three defaults per hundred borrowers of this credit quality in an average year. Sources: statistical models fit on historical defaults, agency rating-implied default tables, or market-implied PD backed out of bond or CDS spreads.
• LGD — loss given default. The fraction of exposure that the lender ultimately loses, after recoveries from collateral, guarantees, and restructuring negotiations. Expressed as a decimal. A 40% LGD means the lender recovers 60% of what was outstanding at default. Driven primarily by seniority and collateral: senior secured 15-40% LGD, senior unsecured 40-60%, subordinated 60-80%, unsecured retail 70-90%.
• EAD — exposure at default. The amount actually outstanding when default occurs, in currency. For an amortising term loan, EAD is the remaining principal at the default date. For a revolving credit line, EAD typically exceeds the current drawn balance because distressed borrowers draw down available headroom before defaulting — captured by a credit conversion factor (CCF) applied to the undrawn portion.

A worked example with every variable explicit

Loan profile:
  Borrower:         Kenyan mid-cap manufacturer, rated B+ (S&P-equivalent)
  Loan size (EAD):  KES 10,000,000 — fully drawn term loan, no undrawn headroom
  Collateral:       Building valued KES 12,000,000 at origination
  Recovery:         Liquidation typically recovers 60% of building's market value
                    after costs, time, and forced-sale discount

Step 1 — PD: B+ rating → historical 1-year PD ≈ 3%
                                     PD = 0.03

Step 2 — LGD: Recovery from collateral = 12,000,000 × 0.60 = 7,200,000
              Exposure = 10,000,000
              Loss     = 10,000,000 − 7,200,000 = 2,800,000
              LGD      = 2,800,000 / 10,000,000 = 0.28 (28%)

Step 3 — EAD: Term loan, no undrawn portion.
              EAD = 10,000,000

Step 4 — Expected Loss:
              EL  =  0.03  ×  0.28  ×  10,000,000  =  KES 84,000 per year

Interpretation: in expectation the bank loses KES 84,000 a year on this
loan. To break even on credit losses, the loan must earn at least 84 bp
in spread above its funding cost. To clear the bank's full pricing hurdle
it must also cover opex and the capital cost — see the RAROC walkthrough
in Module 10 [[leverage-haircuts-secured]].

Probability of Default — three sources

PD is the variable most subject to analyst judgement and the one most often disputed in credit-risk committees. Three independent sources are used in combination:

• Statistical models fitted to historical default data. Logistic regression or machine-learning models trained on years of defaulted vs non-defaulted loans, with financial-statement variables (leverage, interest coverage, working-capital ratios) and behavioural variables (account-conduct history, late payments, bureau data) as inputs.
• Credit ratings. Each agency rating maps to a historical 1-year and lifetime PD: AAA <0.1%, BBB roughly 0.3-0.5%, BB roughly 2-3%, B roughly 5-8%, CCC roughly 25-30%. Banks calibrate internal grades to one of these scales.
• Market-implied measures. CDS spreads and bond spreads back out a market-implied PD assuming a recovery rate (typically 40% by convention). Markets see information that bank analysts miss; the gap between bank-rated PD and market-implied PD is itself a signal worth investigating.

Banks distinguish 'through-the-cycle' PDs (long-run averages across an economic cycle, used for regulatory capital under Basel) from 'point-in-time' PDs (today's conditional probability, used for IFRS 9 expected credit loss provisions). The same borrower can have a 2% through-the-cycle PD and a 5% point-in-time PD if conditions are weakening. Both numbers are real; they answer different questions.

Loss Given Default — driven by seniority and collateral

LGD is the fraction of exposure lost in default. It is shaped primarily at deal-structuring time and is the lever credit officers pull when negotiating term sheets. Three settings drive most of the variation across loans:

• Seniority: where the loan sits in the capital-structure waterfall. Senior secured paid first, then senior unsecured, then subordinated. Empirical LGDs by tier are tracked publicly by Moody's, S&P, and Fitch and have remained roughly stable for decades.
• Collateral: pledged assets that the lender can liquidate against the outstanding exposure in default. The Kenyan SACCO model's robustness comes from heavy collateralisation — share collateral plus guarantor cover often drives LGD below 20%.
• Bankruptcy regime: jurisdictions with strong creditor protection (US Chapter 11, English law) deliver higher recoveries than weak regimes. Kenya's Insolvency Act 2015 modernised the regime but enforcement timelines remain long, which depresses recoveries.

Exposure at Default and credit conversion factors

For a fully-drawn term loan, EAD equals the outstanding principal at the default date. For revolving facilities — credit cards, commercial lines of credit, working-capital facilities — the problem is harder: borrowers under stress draw down available headroom before missing payments. A KES 10m line with KES 6m drawn could become KES 9m drawn just before the default. Basel and bank internal models address this by applying a Credit Conversion Factor (CCF) to the undrawn portion:

  EAD  =  Drawn balance  +  CCF  ×  Undrawn balance

where:
  Drawn balance   =  what the borrower has actually borrowed today
  Undrawn balance =  the remaining limit the borrower could still draw
  CCF             =  the credit conversion factor, in decimal form
                     A regulatory or internally-estimated number
                     reflecting how much of the undrawn headroom
                     typically gets drawn before default.
                     Basel standardised CCFs: 0% for unconditionally
                     cancellable retail lines (cards), 20-50% for
                     short-term trade and corporate lines,
                     50-100% for committed term-out facilities.

Example: KES 10m line, KES 6m drawn. CCF = 50%.
  EAD  =  6,000,000  +  0.50  ×  4,000,000  =  KES 8,000,000

Basel III in plain terms

• Banks must hold capital proportional to risk-weighted assets (RWA). High-risk loans count for more than low-risk loans.
• Risk weights are either standardised (regulator-set, by asset type) or internal-ratings-based (the bank's own models, subject to regulatory approval).
• Minimum Common Equity Tier 1 ratio (CET1 / RWA): 4.5%, with conservation buffer + countercyclical buffer pushing the effective minimum to 7-10%.
• Leverage ratio (Tier 1 / Total Assets): 3% minimum, regardless of risk weight.
• Liquidity Coverage Ratio: must hold enough high-quality liquid assets to survive 30-day stress.