Expected Loss Formula Explained: PD, LGD and EAD for IIBF Risk Management

Every banker who clears the IIBF Risk Management certification eventually realises that the entire credit-risk syllabus rests on one deceptively simple equation. The Expected Loss formula ties together how often a borrower defaults, how much is at stake, and how much you actually lose when default happens. Master this single relationship and the rest of the credit-risk paper, from provisioning to RAROC, falls into place.

This guide breaks down the Expected Loss formula into its three components, PD, LGD and EAD, with worked examples calibrated to how Indian banks and the IIBF exam treat them in 2026.

The Expected Loss Formula: PD x LGD x EAD

The Expected Loss formula is the cornerstone of modern credit-risk measurement and the most heavily tested concept in the IIBF Risk Management certification. It is expressed as:

• EL = PD x LGD x EAD

Here Expected Loss (EL) is the average loss a bank statistically anticipates from a credit exposure over a one-year horizon. It is not a worst-case number; it is the loss the bank should plan for and price into the loan, which is why EL is covered by provisions and the credit spread rather than by capital.

Why the three factors multiply

The logic is intuitive. A loss only occurs if the borrower defaults (captured by PD), and only to the extent the exposure is not recovered (captured by LGD), applied to the amount outstanding at the time (captured by EAD). Multiply the three and you get the probability-weighted rupee loss.

Consider a working-capital loan with EAD of Rs 1,00,00,000, a PD of 2% and an LGD of 45%:

• EL = 0.02 x 0.45 x 1,00,00,000 = Rs 90,000

That Rs 90,000 is the expected annual cost of carrying this loan. Banks recover it through pricing. For deeper drilling on Basel-aligned credit topics, the overlapping CAIIB risk management course material is a useful companion. You can also test these calculations under exam conditions on our practice tests.

Probability of Default (PD): How Likely Is a Default?

Probability of Default is the likelihood that a borrower fails to meet contractual obligations within a defined period, conventionally one year, and is the first input to the Expected Loss formula. It is expressed as a percentage between 0% and 100%.

How banks estimate PD

• Internal rating models map each borrower grade to a historical default rate. A AAA-equivalent grade may carry a PD of 0.03%, while a sub-investment grade may exceed 5%.
• Through-the-cycle vs point-in-time PDs differ: through-the-cycle smooths economic swings, while point-in-time reflects current conditions and is used in IFRS 9 / Ind AS 109 expected-credit-loss staging.
• Days-past-due triggers: in India, the RBI's 90-day NPA norm anchors the practical definition of default for most retail and corporate exposures.

A key exam point is that PD is borrower-specific, not facility-specific. The same borrower carries one PD across all their loans because default is an event that happens to the obligor, not to an individual account. Two facilities to the same firm therefore share a PD but can have very different LGDs and EADs.

PD is sensitive to the macro cycle, so banks recalibrate models periodically against actual default experience. Watching policy signals such as the repo rate helps; our live RBI rates tracker is handy when you study how monetary tightening pushes corporate PDs upward.

Loss Given Default (LGD) and Exposure at Default (EAD)

The remaining two inputs to the Expected Loss formula describe the severity and the size of the loss.

Loss Given Default (LGD)

LGD is the proportion of the exposure a bank expects to lose if the borrower defaults, after accounting for recoveries from collateral, guarantees and legal action. It is the mirror image of the recovery rate:

• LGD = 1 - Recovery Rate

If a defaulted loan is expected to recover 60 paise on the rupee, the LGD is 40%. Well-secured home loans typically show low LGDs (often 10-25%), whereas unsecured personal loans show high LGDs (frequently 65% or more). Collateral quality, seniority and enforceability under the SARFAESI and IBC frameworks all shape LGD in the Indian context.

Exposure at Default (EAD)

EAD is the total amount the bank stands to lose at the moment of default. For a fully drawn term loan, EAD is simply the outstanding balance. For revolving facilities such as cash credit or credit cards, EAD must estimate likely additional drawdowns before default using a Credit Conversion Factor (CCF):

• EAD = Drawn Amount + (CCF x Undrawn Commitment)

A borrower with Rs 60 lakh drawn, Rs 40 lakh undrawn and a 50% CCF has an EAD of Rs 80 lakh. Reinforce these mechanics with the quick-recall drills on our match-the-concept game.

From Expected Loss to Pricing, Provisioning and Capital

Understanding the Expected Loss formula matters because EL feeds directly into how a bank runs its credit book.

Expected vs Unexpected Loss

EL is the average; actual losses fluctuate around it. The volatility above the average is Unexpected Loss (UL), and that is what regulatory and economic capital are designed to absorb. A clean way to remember the split:

• Expected Loss is covered by provisions and pricing (the credit spread).
• Unexpected Loss is covered by capital.

Where EL appears in practice

• Loan pricing: the risk premium in a loan's interest rate should at minimum recover the EL; a 0.9% EL on the earlier example implies at least 90 bps of spread.
• IFRS 9 / Ind AS 109 ECL: 12-month and lifetime expected credit losses are computed using PD, LGD and EAD across staging buckets.
• RAROC: risk-adjusted return on capital subtracts EL from revenue, so RAROC = (Revenue - Costs - EL) / Economic Capital. A loan that does not clear the bank's hurdle RAROC destroys value even if it looks profitable on paper.

This is why the IIBF treats EL as the spine of the credit-risk module rather than an isolated formula. Keep current with regulatory shifts through our IIBF news feed, and browse more explainers on the iibf.store blog.

For authoritative guidance, refer to the official resources of the Reserve Bank of India and the Indian Institute of Banking & Finance.

Frequently Asked Questions

Conclusion: Lock In the Expected Loss Formula Before Exam Day

The Expected Loss formula, EL = PD x LGD x EAD, is the single most rewarding concept to master for the IIBF Risk Management certification. Once you can decompose any exposure into its probability, severity and size, the harder topics of provisioning, ECL staging and RAROC become straightforward extensions rather than new material. Practise numericals until the multiplication and the CCF adjustment feel automatic. Ready to check your readiness under timed conditions? Attempt a full Risk Management mock test now, or strengthen the Basel and capital foundations with the CAIIB risk course.