Expected Loss Calculation: Formula & Examples

Expected loss calculation estimates the average amount a lender should expect to lose on a loan or portfolio over a set period, usually one year. The core formula multiplies three inputs: probability of default (PD), loss given default (LGD) and exposure at default (EAD).

That one product does a lot of work inside a bank. It sets the minimum credit cost built into loan pricing, and it also feeds provisioning. It frames how much capital the bank holds against losses it can’t predict. As a result, a small error in any input compounds across thousands of loans.

This post walks through the formula, two worked examples in rupees, a three-segment portfolio calculation and a short Python snippet. We’ll also compare the Basel view of expected loss with IFRS 9 expected credit loss. Then we’ll look at what RBI’s new ECL directions mean for banks in India.

What Is Expected Loss?

Expected loss (EL) is the average credit loss a lender anticipates on an exposure over a given horizon, typically one year. It’s calculated as probability of default × loss given default × exposure at default. As a result, EL is a cost of doing business: lenders price it into interest rates and cover it with provisions.

Think of EL as the loss you can plan for. Unexpected loss (UL), however, is the swing around that average, the bad year when defaults come in well above the norm. Banks recover EL through pricing and provisions, while they hold capital against UL. In the Basel IRB framework, for instance, the capital formula targets unexpected loss, whereas expected loss is compared against provisions.

The Expected Loss Formula: PD × LGD × EAD

EL = PD × LGD × EAD

Each input answers a different question. PD tells you how likely a default is, and EAD tells you how much is owed when it happens. Finally, LGD tells you what share of that amount you won’t get back.

Two caveats matter. First, the basic formula is a one-period simplification that assumes a one-year horizon. Under IFRS 9, however, lifetime measures stretch it across the life of deteriorating loans, as we cover below.

Second, the simple product treats PD and LGD as independent. In practice, both tend to worsen together in a downturn, so Basel asks for downturn LGD estimates.

For deeper dives, see our guides on probability of default , loss given default and exposure at default .

Worked Example: One Loan

Example 1: A ₹10 lakh term loan

Suppose a bank lends INR10,00,000. Its model gives a 2% one-year PD. Collateral and collections are expected to recover 60% of what’s owed after default, so LGD is 40%. Because the loan is fully drawn, EAD is INR10,00,000.

1. First, work out the loss if the borrower defaults: 40% × INR10,00,000 = INR4,00,000
2. Then weight it by the chance of default: 2% × INR4,00,000 = INR8,000

So EL = 0.02 × 0.40 × INR10,00,000 = INR8,000, or 0.8% of the loan.

In reality, no single borrower loses INR8,000. They either default or they don’t. Instead, EL is an average across many loans: in a pool of 100 identical loans, about two would default, costing INR4,00,000 each, which works out to INR8,000 per loan. That INR8,000 is the minimum the interest rate has to cover. It also has to pay for funding cost, operating cost and the cost of capital.

Example 2: A revolving credit limit

Now take a working-capital line. The limit is INR5,00,000 and the borrower has drawn INR2,00,000, so INR3,00,000 is undrawn. Typically, borrowers in trouble tend to draw down their limits before defaulting. A CCF of 50% therefore says that, on average, half the undrawn amount will be drawn by the time default occurs.

Formula: EAD = drawn + (CCF × undrawn)

Substituting: EAD = INR2,00,000 + (50% × INR3,00,000)

Result: EAD = INR2,00,000 + INR1,50,000 = INR3,50,000

So looking only at the drawn balance would understate the exposure by INR1,50,000.

Note that the 2%, 40% and 50% above are illustrative. In real banks, PD, LGD and CCF come from statistical models built on historical data, rather than judgment calls.

Calculating Expected Loss for a Loan Portfolio

Single-loan maths is easy, but portfolios are where the insight is. The table below uses hypothetical, illustrative numbers, not data from any real bank.

For example, take home loans: INR200 crore × 1.5% = INR3 crore of exposure expected to default. Then, at 25% LGD, that becomes ₹0.75 crore lost.

The split is the interesting part. Home loans are 57% of exposure, but they account for under 10% of expected loss. Personal loans and credit cards, on the other hand, are about 43% of exposure and roughly 90% of expected loss. Both are unsecured, with higher PDs and higher LGDs, so unsecured products carry higher interest rates.

Segment-level EL adds up cleanly: if you know each segment’s EL, the total is just the sum. However, unexpected loss doesn’t work this way. Because borrowers across segments don’t default in perfect lockstep, the combined volatility is lower than the sum of the parts. That diversification effect, and the correlation between borrowers, is what portfolio models try to capture. We cover this in our section on portfolio credit risk.

One more note: segment-level calculation is a simplification. Most banks, in fact, run EL at the account level, so each loan’s own PD and exposure feed in before the results aggregate upward.

Expected Loss under Basel vs Expected Credit Loss under IFRS 9

Basel expected loss and IFRS 9 expected credit loss (ECL) use the same three ingredients, but they differ in purpose, horizon and how forward-looking they are.

The practical difference shows up in a downturn. For example, a through-the-cycle PD barely moves when the economy weakens. A point-in-time PD, however, rises, so ECL rises with it. That’s by design, because IFRS 9 wants losses recognised earlier.

How Banks Build Expected Loss Models

Most EL and ECL engines follow the same workflow:

1. First, assemble loan-level history: balances, repayments, delinquency, collateral, recoveries and macroeconomic series.
2. PD model. Next, fit a model, often logistic regression or gradient boosting, and calibrate it to the right horizon and cycle view.
3. LGD model. Then estimate recoveries net of costs, by collateral type and recovery channel.
4. EAD and CCF. Also model how much of undrawn limits gets drawn before default.
5. Multiply the three at account level, then sum to segment and portfolio.
6. After that, test discrimination, calibration and stability, and backtest against actual losses.
7. Finally, track drift and recalibrate when the portfolio or economy shifts.

In Excel, the aggregation step is a single formula (=EAD*PD*LGD per row, then SUM). That’s fine for prototypes and reporting, but Python or SAS takes over once you’re scoring millions of accounts.

Here’s the portfolio calculation from earlier in Python:

import pandas as pd

portfolio = pd.DataFrame({

“segment”: [“Home loans”, “Personal loans”, “Credit cards”],

“ead_cr”: [200, 100, 50],

“pd”: [0.015, 0.06, 0.08],

“lgd”: [0.25, 0.65, 0.75],

})

portfolio[“el_cr”] = portfolio[“ead_cr”] * portfolio[“pd”] * portfolio[“lgd”]

total_el = portfolio[“el_cr”].sum()

total_ead = portfolio[“ead_cr”].sum()

print(portfolio)

print(f”Total EL: ₹{total_el:.2f} cr | EL rate: {total_el / total_ead:.2%}”)

The last line prints Total EL: ₹7.65 cr | EL rate: 2.19%, so the output matches the table above. In production, however, the pd column would come from a fitted model scoring each loan, not a segment average.

Common Mistakes in Expected Loss Calculation

Because the formula looks simple, these errors are easy to miss:

• Mixing horizons, such as applying a 12-month PD to a multi-year loan or dropping a lifetime PD into a one-year formula.
• Ignoring undrawn limits, so that EAD equals the current balance on cards, overdrafts and working-capital lines.
• Using a through-the-cycle PD where IFRS 9 needs a point-in-time, forward-looking one.
• Overlooking collateral haircuts, recovery timelines and cures, where a defaulted account returns to performing.
• Relying on stale LGD, because recoveries change while the estimate stays the same.

Where This Leaves You

Expected loss calculation comes down to three numbers and one multiplication. The skill is in getting each input right: the right horizon for PD, a realistic recovery view for LGD, and an honest exposure measure for EAD. Beyond that, you have to know which framework you’re working in, because Basel and IFRS 9 ask for different versions of the same idea.

If you want to build and validate these models yourself, with real datasets and Python, take a look at DexLab’s Advanced Certificate in Credit Risk Modeling with Machine Learning.

FAQ

What is the formula for expected loss?

Expected loss equals probability of default multiplied by loss given default multiplied by exposure at default: EL = PD × LGD × EAD. Here, PD is the chance of default over a set horizon, usually one year. LGD is the percentage lost after recoveries, and EAD is the amount owed at default, in rupees.

What is the difference between expected loss and ECL?

Expected loss is the basic PD × LGD × EAD product over one year, used in Basel capital frameworks. Expected credit loss, however, is the IFRS 9 accounting measure. It uses point-in-time PDs, probability-weighted forward-looking scenarios, discounting at the effective interest rate, and lifetime horizons for loans whose credit risk has risen significantly.

How do you calculate EAD for undrawn limits?

Add the drawn balance to a share of the undrawn limit. That share is the credit conversion factor (CCF). For example, with a ₹5 lakh limit, ₹2 lakh drawn and a 50% CCF, EAD is ₹2 lakh plus 50% of ₹3 lakh, which is ₹3.5 lakh.

Is expected loss the same as a provision?

No. Expected loss is a model-based estimate, while a provision, or loss allowance, is the amount a bank books. Under Basel IRB, regulators compare the two. With IFRS 9 and the RBI’s ECL framework, however, the allowance is itself an ECL estimate, although regulatory floors can also apply.

Which tools are used to calculate expected loss?

Banks commonly use SAS, Python and R to build the models, and SQL to extract data. Excel also remains common for prototypes and reporting. In production, ECL engines often run on dedicated risk and finance platforms linked to the general ledger.

Explore Dexlab Analytics’ Credit Risk Modeling certification program to build PD, LGD, and EAD models from scratch, work through IFRS 9 ECL frameworks, and learn model validation techniques used by practicing risk teams.

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