Lesson 1.1: What credit risk is: PD, LGD, EAD and expected loss
Learn what credit risk is and how lenders split it into PD, LGD and EAD to calculate expected loss, price loans and plan for a bad year.
By the end of this lesson you will be able to say what credit risk is, break it into three measurable parts, and combine them into one number, the expected loss, that a lender can price, provide for and manage. You will calculate expected loss for a single loan and for a portfolio, work out the minimum interest rate that covers it, and see why a lender must plan for more than the average loss. You need no background in finance or statistics beyond simple percentages. Every number is small enough to check with a calculator.
Credit risk is the oldest risk in banking and the one that sinks most lenders. A bank that lends well can survive a poor year. A bank that misjudges who will repay, and how much it will lose when they do not, cannot be rescued by good marketing. Everything in this track, from scorecards to roll rates to stress tests, is a method for measuring one thing more carefully. This first lesson defines that thing.
What credit risk is
Credit risk is the risk that a borrower does not repay what they owe, on time and in full, and that the lender therefore loses money. The borrower might be a salaried person with a ₹2 lakh personal loan, a small shop with a working-capital line, or a large company with a bond. The risk is the same in kind. A promise to pay in the future may be broken.
Notice three features of that definition, because they shape everything that follows.
It is about the future. When you lend, you do not know who will repay. You estimate it from what you can observe today.
It is about a probability, not a certainty. Even a very good borrower might default, and even a poor one might repay. A lender does not predict individuals. It estimates rates across many borrowers.
Loss is not the same as default. A borrower can default and the lender can still recover most of the money, especially if there is collateral such as gold or a house. A lender needs to know how often borrowers default and how much is lost when they do.
That last point leads to the central idea of the lesson: the risk of a loan is the product of three separate questions.
The three parts: PD, LGD and EAD
Ask three questions about any loan.
1. How likely is the borrower to default? This is the probability of default, or PD. It is a percentage over a stated period, usually the next 12 months. A PD of 4 per cent means that out of 100 similar borrowers, about 4 are expected to default within a year.
2. If they default, what share of the money is lost? This is the loss given default, or LGD. It is a percentage of the amount owed at default. If the lender recovers 40 per cent through collections and selling collateral, the LGD is 60 per cent.
3. How much will be owed at the moment of default? This is the exposure at default, or EAD. For a term loan it is the outstanding balance at that time, not the amount originally lent. For a credit card or an overdraft it is whatever has been drawn by then, which may be more than today's balance.
The three combine in one line:
Expected loss = PD × LGD × EAD
Read it as a story. The chance of default, times the share lost if default happens, times the amount at stake. It is an average. It is the loss a lender should expect over many similar loans, not the loss on any one of them. On any single loan the loss is either zero or a lot.
Predict first: a borrower has a ₹10 lakh loan, but has already repaid some, and ₹8 lakh is outstanding. The PD is 4 per cent and the LGD is 60 per cent. Before you read on, estimate the expected loss in rupees.
The expected loss is 0.04 × 0.60 × ₹8,00,000 = ₹19,200. Notice that the EAD used is the ₹8 lakh outstanding, and not the ₹10 lakh originally lent. Notice also that ₹19,200 is a figure that will almost never appear as an actual loss on this one loan. If the borrower repays, the loss is zero. If the borrower defaults, the loss is 0.60 × 8,00,000 = ₹4,80,000. The expected loss is the probability-weighted average of those two outcomes: 0.96 × 0 + 0.04 × 4,80,000 = ₹19,200.
Try it yourself, and watch what each input does.
At the defaults the expected loss rate is 2.4 per cent of the exposure, and adding a 9 per cent funding cost and a 3 per cent operating cost gives a break-even rate of 14.4 per cent a year. Anything charged below that loses money on average. This is the first use of credit risk numbers: they tell you what a loan has to earn.
The three parts differ by product
PD, LGD and EAD are not fixed properties of a borrower. They depend on the product, the borrower and the collateral. Compare five illustrative loan types.
The ranking is the point. A gold loan can have a fairly high default rate and still lose little, because the gold covers the debt and can be sold quickly. A home loan has a low PD and a modest LGD. A digital micro-loan with no collateral may lose most of what it lends when a borrower defaults, so even a modest PD becomes a heavy cost. Lenders price the products accordingly, which is why unsecured small loans carry much higher interest rates than secured ones. The difference is not greed. It is arithmetic.
What moves each part
PD is driven by the borrower: income stability, repayment history, existing debt, the economy, and the lender's own underwriting. Later lessons build scorecards and models that estimate it.
LGD is driven by the loan: whether there is collateral, how easily it sells, how strong the legal recovery process is, and how effective collections are. A better collections team lowers LGD without changing PD.
EAD is driven by the structure: for a term loan it falls as the borrower repays, and for revolving lines it can grow as the borrower draws down before default.
This matters because each part has a different owner inside the lender. Underwriting and data science focus on PD. Collections and legal focus on LGD. Product design and limit management focus on EAD. A rise in expected loss could come from any of the three, and the fix is different for each.
Estimating the three parts in practice
Here is how a lender gets numbers for each part. The details come in later lessons, but the outline helps you see where the track is going.
PD is usually estimated from history. Take a group of loans that started at the same time, follow them for 12 months, and count how many defaulted. If 400 of 10,000 loans defaulted, the observed default rate is 4 per cent. A scorecard or model then splits the borrowers into groups with different rates, perhaps 1 per cent for the best and 9 per cent for the worst. Defining "default" precisely is its own topic, and Lesson 1.4 covers it.
LGD is estimated from recoveries. For every defaulted loan, add up the money recovered over time, subtract the cost of collecting it, bring it back to a present value, and divide by the exposure at default. If a lender recovered ₹3.2 lakh, net of costs and discounted, on a defaulted exposure of ₹8 lakh, the recovery rate is 40 per cent and the LGD is 60 per cent. Recoveries often arrive slowly, over years, so LGD needs a long history.
EAD is straightforward for a loan that follows a repayment schedule, since the outstanding balance at any date is known. For a revolving facility such as a credit line or card, borrowers tend to draw more as they get into trouble. Lenders use a credit conversion factor, or CCF, to estimate what share of the unused limit will be drawn by the time of default. With a limit of ₹5 lakh, ₹3 lakh drawn and a CCF of 50 per cent, the EAD is 3 + 0.5 × (5 − 3) = ₹4 lakh. The ₹3 lakh balance today understates the exposure.
python
import pandas as pd
loans = pd.readcsv("loans.csv") # one row per loan with outcome after 12 months
pdhat = loans["defaulted12m"].mean() # observed default rate
defaulted = loans[loans["defaulted12m"] == 1]
lgdhat = 1 - (defaulted["recoveredpv"].sum() / defaulted["ead"].sum())
ead = loans["outstanding"] # term loans: balance at the date
loans["el"] = pdhat lgdhat ead # expected loss per loan
loans["el"].sum() # portfolio expected loss
This snippet uses single portfolio-wide figures, which is the simplest case. Real models estimate a PD per loan, so the last two lines sum different values for each row.
From one loan to a portfolio
Lenders do not hold one loan. A portfolio of 1,000 loans, each with an EAD of ₹4 lakh, a PD of 4 per cent and an LGD of 60 per cent, has an expected loss of 1,000 × 4 × 0.04 × 0.60 = 96 lakh, or ₹0.96 crore. In that portfolio the lender expects 1,000 × 0.04 = 40 defaults over the year.
But the lender does not experience exactly 40 defaults. Some years it sees 31 and some years 52. The expected loss is an average, and the actual loss moves around it. This variation is the heart of why lenders hold capital, and it has a name: unexpected loss.
The simplest way to see it is to treat each loan as a weighted coin. Each loan defaults with probability p, independently of the others. The number of defaults then has an average of n × p and a standard deviation of √(n × p × (1 − p)). With n = 1,000 and p = 0.04, the standard deviation is √(1,000 × 0.04 × 0.96) = √38.4 = 6.2 defaults. A bad year, defined as roughly the worst 1 in 100, is about 2.33 standard deviations above the average: 40 + 2.33 × 6.2 = 54.4 defaults.
At the default values, the expected loss is ₹0.96 crore and the bad-year loss is ₹1.31 crore, about 36 per cent more. Now slide the number of loans up to 20,000. The expected number of defaults rises to 800, but the bad year is only about 10 per cent above the average. This is the law of large numbers at work, and it is why lending can be a business: the more independent loans you hold, the closer reality gets to the average. It is also why a lender with a few large loans is far riskier than one with many small ones.
The word "independent" is the catch. In a real downturn, many borrowers lose income together, so defaults rise across the board. Because of that, actual bad years are much worse than this arithmetic suggests, and stress tests and correlation models exist to capture it. You will meet those later in the track. For now, hold the lesson that an average can be safe while a bad year is not.
Expected loss, provisions and capital
The split between expected and unexpected loss gives lenders a way to organise what they do about each.
Concept · What it is · How the lender deals with itExpected loss · The average loss over many loans and years · Price it into interest rates and set aside provisions for it
Unexpected loss · The chance that the loss is worse than average · Hold capital, which is shareholders' money, as a buffer
Stress loss · The loss in a severe downturn · Test the portfolio against it and plan actions
Provisions are amounts the lender sets aside from its profit for losses it already expects. They appear as a cost in the profit and loss account, and they reduce the reported value of the loans. Capital is the cushion that absorbs losses beyond those provisioned. Pricing covers expected loss loan by loan, provisions cover it on the balance sheet, and capital covers the surprise. Regulators set minimum capital rules because a lender's failure harms depositors and the wider economy, which Module 10 of this track covers.
Other kinds of credit risk
PD, LGD and EAD describe default risk. A complete view includes others.
Concentration risk: too much exposure to one borrower, sector, region or product. If the lender has 30 per cent of its book in one industry, a shock to that industry becomes a shock to the lender.
Migration risk: borrowers drifting into worse risk grades without defaulting. This reduces the value of the loans and raises provisions even before any loss. Module 4 covers credit migration.
Counterparty risk: the other side of a trade or derivative contract fails before settling.
Country and sovereign risk: losses from a government's actions or an economy's collapse.
For an Indian non-banking lender, the day-to-day work is mostly about retail and small business loans: personal loans, vehicle loans, gold loans and microfinance. These have large numbers of small loans, so the statistical methods in this track apply directly.
Common mistakes
Using the original loan amount as EAD. EAD is what is owed at default. For an amortising loan, it is the outstanding balance then, and for a credit line it may be more than the balance today.
Reading expected loss as a forecast for one loan. It is an average over many loans. One loan loses nothing or a lot.
Treating PD and LGD as the same thing. A high PD with a low LGD, such as gold loans, can be safer than a low PD with a high LGD.
Ignoring the time horizon. A 12-month PD and a lifetime PD are different numbers. State which one you mean.
Assuming independence in a downturn. Real defaults cluster. The binomial arithmetic in this lesson understates a bad year.
Pricing to the average and forgetting costs. The expected loss is only one part of the minimum rate. Funding and operating costs come on top.
Key takeaways
Credit risk is the chance that a borrower does not repay and the lender loses money. It is estimated as a rate across many borrowers, not predicted for individuals.
Expected loss = PD × LGD × EAD: the chance of default, the share lost if it happens, and the amount owed at that moment.
PD comes from borrower behaviour, LGD from collateral and recoveries, and EAD from the loan structure. Each has a different owner inside a lender.
Expected loss sets the floor for pricing and the amount to provision. Capital covers the unexpected loss beyond the average.
A larger, more diversified portfolio sits closer to its average, but real defaults cluster in downturns, so a bad year is worse than simple arithmetic suggests.
Credit risk has other forms too, including concentration and migration, which later modules measure.
Check yourself
1. A loan has PD 2 per cent, LGD 50 per cent and an EAD of ₹6 lakh. What is the expected loss?
0.02 × 0.50 × 6,00,000 = ₹6,000.
2. Why can a gold loan with a 3 per cent PD be less risky than an unsecured loan with a 2 per cent PD?
The gold loan's LGD is very low because the gold can be sold, so PD × LGD is small. The unsecured loan loses most of its exposure on default.
3. A credit line has a limit of ₹10 lakh, ₹6 lakh drawn and a CCF of 50 per cent. What is the EAD?
6 + 0.5 × (10 − 6) = ₹8 lakh.
4. A lender holds 2,500 loans, each with a PD of 4 per cent. How many defaults does it expect, and what is the standard deviation under the independence assumption?
Expected defaults are 100. The standard deviation is √(2,500 × 0.04 × 0.96) = √96 = about 9.8.
5. Expected loss is 2.4 per cent, funding cost 9 per cent and operating cost 3 per cent. What is the minimum yearly rate to break even?
2.4 + 9 + 3 = 14.4 per cent.
Try this
Pick one loan product you know, such as a two-wheeler loan, a personal loan or a gold loan, and build a rough expected loss table for it. Set aside thirty-five to forty-five minutes.
1. Write the product's typical loan size and tenure. Decide what EAD would be on a typical default, given when defaults usually happen in the life of the loan.
2. Look for a published default or delinquency rate for the product, such as an annual report, a rating agency note or a regulator's data. Use it for a rough PD and note the source and the period it covers. If you cannot find one, use an example PD and label it.
3. Estimate the recovery rate. Think about collateral, the cost of collection and how long recovery takes, and write down your LGD with a reason.
4. Calculate expected loss in rupees per loan and as a share of the exposure.
5. Use the first simulator to find the minimum rate, using a funding cost and an operating cost you can justify. Compare it with the rate lenders actually charge for the product.
6. Use the second simulator with 500 loans, and then 5,000. Note how the gap between the average and the bad year changes.
7. Write one paragraph: which of the three parts is the largest source of risk in this product, and what a lender could do to reduce it.
A good result is a half-page note with each assumption labelled as sourced or illustrative, and a clear statement of what would change the answer. The next lesson looks at where the data for all of these numbers comes from: the life of a loan from application to closure.
Tags: Credit Risk Analytics Expected loss PD LGD EAD Lending Beginner