CFA Level II Exam · Credit Analysis Models

Credit Risk Basics: Expected Loss, PD and LGD

Updated 7 October 2026 · Fact-checked

Credit risk is the chance a borrower fails to pay in full and on time. You measure it with probability of default (PD), exposure at default, and loss given default (LGD). Expected loss = PD × LGD × exposure. Credit spread is the extra yield over the risk-free rate that compensates for this risk.

Understand Basics of Credit Risk and Credit Analysis

Credit risk is the risk of loss because a borrower does not meet its payment obligations. It has two parts. Default risk is the chance the borrower fails to pay. Loss severity is how much you lose if it does. A bond can have a high chance of default but small loss, or the reverse. You must keep the two ideas apart.

Probability of default (PD) is the likelihood of default over a stated period, usually one year. Exposure at default is the amount owed when default happens. Loss given default (LGD) is the share of that exposure you lose after recoveries. Recovery rate is the share you get back, so LGD = 1 − recovery rate (when both are stated as a share of exposure). Loss given default can also be stated as a currency amount.

Expected loss is the average loss you would predict: PD × LGD × exposure. It is a mean, not the loss you will actually see. Actual loss is either zero or large. The uncertainty around the expected loss is unexpected loss, and it is what capital and risk limits are meant to cover. Credit risk is often described with a skewed return profile: limited upside (coupons and par) and a long left tail.

The credit spread is the yield on a risky bond minus the yield on a comparable-maturity risk-free bond. It compensates investors for expected loss and also for bearing the uncertainty (a risk premium) and often for lower liquidity. So the spread is usually larger than the expected loss alone. Spreads widen when the market sees more risk and narrow when it sees less.

In the exam, the vignette gives you PD, recovery or LGD, exposure and yields. Your job is to pick the right inputs, keep the time period consistent, and combine them. Be careful with words: a recovery rate is not LGD.

Key formulas to remember

Loss given default: LGD = Exposure × (1 − Recovery rate); Recovery rate is the share of exposure recovered. LGD can also be quoted as a percentage: LGD % = 1 − recovery rate.
Expected loss: EL = PD × LGD × Exposure at default; If LGD is already a currency amount, EL = PD × LGD amount. Use the same time period for PD as for EL.
Credit spread: Credit spread = Yield on risky bond − Yield on risk-free bond of same maturity; Compensates for expected loss, a risk premium for uncertainty and liquidity effects.
Probability of survival over two years (given annual PDs): P(survive 2 yrs) = (1 − PD₁) × (1 − PD₂); PD₁ and PD₂ are conditional annual default probabilities, treated as independent here. Cumulative PD = 1 − survival probability.

How to solve Basics of Credit Risk and Credit Analysis questions

Use this method for any expected loss or credit risk question in a vignette.

1Read the question first, then find the credit data in the vignette: PD, recovery rate or LGD, exposure, yields and horizon.
2Decide what is being asked: PD, LGD, expected loss or spread.
3Convert recovery to LGD if needed: LGD % = 1 − recovery rate. Check whether recovery is on exposure or on par value.
4Check the time period. Use annual PD for a one-year loss. For longer horizons, build survival probabilities.
5Multiply: EL = PD × LGD % × exposure.
6For spread questions, subtract the matching risk-free yield of the same maturity from the risky yield.
7Sanity-check: EL must be below exposure, and spread should usually exceed annual PD × LGD.

Quickest way: Three-number shortcut

When to use it: When the vignette gives PD, recovery rate and exposure and you need expected loss quickly.

Write PD, LGD % (1 − recovery) and exposure on scratch space.
Multiply PD × LGD % first to get expected loss as a percentage of exposure.
Multiply by the exposure.
Eliminate options that use recovery instead of LGD: they are usually the trap.

Common mistakes in Basics of Credit Risk and Credit Analysis

Using the recovery rate in place of LGD in the expected loss formula.
Both numbers appear in the vignette and look similar.
Fix: Always compute LGD = 1 − recovery rate before multiplying.
Treating PD and LGD as the same thing.
Both describe 'how bad' a credit is.
Fix: PD is how likely default is. LGD is how much is lost if default happens. Ask 'likelihood or size?'
Saying expected loss equals the credit spread.
Both are compensation for credit risk.
Fix: The spread also includes a risk premium and liquidity compensation, so it is usually larger than expected loss.
Mixing time horizons, such as using a one-year PD for a three-year loss.
The vignette gives annual figures and the question gives a longer holding period.
Fix: Use survival probabilities for multi-year horizons: cumulative PD = 1 − Π(1 − PDₜ).
Applying LGD to the wrong base, such as the loan's original size instead of exposure at default.
Exposure can change, for example a drawn credit line.
Fix: Use the exposure stated at default in the vignette.
Calling expected loss the worst-case loss.
The word 'loss' suggests a maximum.
Fix: Expected loss is a probability-weighted average. Unexpected loss relates to variability around it.

Worked examples

Example 1

A bank has a term loan of ₹8,00,00,000 outstanding to a manufacturer. The vignette states a one-year probability of default of 2.5% and an expected recovery of 40% of exposure if default occurs. Q1: What is the LGD in rupees? Q2: What is the one-year expected loss?

Show the solution

Recovery rate is 40%, so LGD % = 1 − 0.40 = 60%.
LGD in rupees = ₹8,00,00,000 × 0.60 = ₹4,80,00,000.
Expected loss = PD × LGD amount = 0.025 × ₹4,80,00,000 = ₹12,00,000.

Answer: Q1: ₹4,80,00,000. Q2: ₹12,00,000.

Example 2

A corporate bond has an annual PD of 3% in year 1 and 4% in year 2 (conditional on surviving year 1). The bond yields 6.2% and a risk-free bond of the same maturity yields 4.5%. Q1: What is the credit spread? Q2: What is the probability the issuer survives both years?

Show the solution

Credit spread = 6.2% − 4.5% = 1.7%, or 170 basis points.
Survival in year 1 = 1 − 0.03 = 0.97.
Survival in year 2 = 1 − 0.04 = 0.96.
Two-year survival = 0.97 × 0.96 = 0.9312.

Answer: Q1: 1.70% (170 bps). Q2: 93.12%.

Exam tips

Underline whether the vignette gives recovery rate or LGD. Many wrong options come from mixing them.
Check the horizon before multiplying. Annual PD answers an annual question only.
When asked what the spread compensates for, remember expected loss plus risk premium and liquidity, not expected loss alone.
If a question asks which credit has the higher expected loss, compare PD × LGD × exposure for each; do not rank on PD alone.

Basics of Credit Risk and Credit Analysis in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Basics of Credit Risk and Credit Analysis: frequently asked questions

What is the difference between probability of default and loss severity?

Probability of default is how likely the borrower is to fail to pay. Loss severity, measured by loss given default, is the share of exposure lost when it does. Expected loss needs both.

How do I calculate loss given default from recovery rate?

Subtract the recovery rate from 1. If recovery is 35% of exposure, LGD is 65%. Multiply by exposure to get the amount.

What is exposure at default?

It is the amount the borrower owes at the moment it defaults. It can differ from the original amount, for example if a credit line has been drawn further or a loan partly repaid.

Is the credit spread the same as expected loss?

No. The spread is the yield difference over a risk-free bond of the same maturity. It covers expected loss plus compensation for uncertainty and often liquidity, so it is usually higher.