Portfolio Management Pathway · Fixed-Income Active Management: Credit Strategies

Expected Loss, Probability of Default and Loss Given Default

Updated 8 October 2026 · Fact-checked

Expected loss is the average credit loss you should anticipate on a bond. It equals probability of default × loss given default, where LGD = 1 − recovery rate, scaled by exposure. To solve a question, find each input, multiply them, and state which risk the figure leaves out.

Understand Credit Risk Analysis: Default Probability and Loss Given Default

Credit risk is the chance you lose money because a borrower fails to pay as promised. Two numbers describe most of it. Probability of default (PD) is how likely the issuer is to default over a set period. Loss given default (LGD) is the share of exposure you lose if default happens.

LGD is linked to the recovery rate, the share you get back. LGD = 1 − recovery rate. A bond that recovers 40% of its value has an LGD of 60%. Recovery depends on seniority, security and the value of the assets left. Senior secured debt usually recovers more than subordinated debt.

Expected loss combines the two: PD × LGD, applied to exposure. It is an average, not a worst case. The actual loss is either zero or large, so the average hides the risk. The spread over a risk-free bond must pay for expected loss and also for the uncertainty around it, plus liquidity and other factors. That is why spreads are usually wider than expected loss alone.

Credit migration (downgrade) risk is the chance that an issuer's rating changes. A downgrade widens the spread and cuts the bond's price even with no default. A transition matrix shows the probability of moving from one rating to another over a period. Spread widening on a downgrade is roughly spread change × spread duration, with the sign negative for price.

Creditworthiness analysis looks at the issuer's capacity (cash flow, leverage, coverage, business strength) and willingness to pay, plus covenants and structure. For investment grade, the main concern is spread changes and downgrades, especially the fall to high yield. For high yield, default and recovery matter more, so analysis leans on cash flow, liquidity, covenants and the position in the capital structure.

The credit valuation adjustment (CVA) is the present value of expected credit loss on a derivative or other exposure to a counterparty. It is the value reduction from counterparty default risk. In the simplest form it is the sum over periods of expected exposure × PD × LGD × discount factor.

Key rules to remember

Loss given default: LGD = 1 − Recovery rate; Recovery rate is the share of exposure recovered. Both are usually a percentage of exposure.
Expected loss: EL = PD × LGD × Exposure; Use the same time period for PD as for the loss you want. Without exposure, EL is a percentage.
Expected loss rate (no exposure): EL % = PD × (1 − Recovery rate); A simple annual credit cost to compare against the spread.
Multi-period survival: Survival to T = (1 − PD) ^ T; Holds only when annual PD is constant and independent across years. Cumulative PD = 1 − (1 − PD) ^ T.
Price change from spread move: %ΔPrice ≈ −Spread duration × ΔSpread; Use for migration risk. Convert ΔSpread to decimal form.
Credit valuation adjustment: CVA = Σ [Expected exposure_t × PD_t × LGD × Discount factor_t]; PD_t is the probability of default in period t. It is a present value, so discount.

How to solve Credit Risk Analysis: Default Probability and Loss Given Default questions

Use the same sequence for any question on credit risk inputs, expected loss or issuer analysis.

1Read the command word. Is it calculate, compare, justify or recommend?
2List the inputs given: PD, recovery rate or LGD, exposure and time horizon.
3Convert recovery rate to LGD if needed: LGD = 1 − recovery.
4Match the time basis. If PD is annual and the question spans several years, use survival or cumulative PD.
5Multiply to get expected loss, in rupees or currency units if exposure is given, otherwise in percent.
6For migration, use spread duration × spread change, and give the sign of the price effect.
7Tie the result to the client or mandate: compare to the spread, then say whether it compensates for the risk.
8Write the number with its unit, plus one short reason if the command word asks for justification.

Quickest way: Three-line credit loss check

When to use it: Use when a vignette gives PD and recovery and asks whether a spread is adequate or what loss to expect.

Write LGD = 1 − recovery.
Write EL = PD × LGD and compare it with the spread.
If the spread is not much larger than EL, say the extra return for uncertainty, liquidity and migration risk is thin.

Common mistakes in Credit Risk Analysis: Default Probability and Loss Given Default

Using the recovery rate in place of LGD in the expected loss formula.
Both are quoted as percentages and appear close together in the vignette.
Fix: Always write LGD = 1 − recovery first, then multiply.
Treating expected loss as the maximum or typical loss.
The word expected sounds like what will happen.
Fix: Say it is a probability-weighted average. Actual outcomes are zero loss or a large loss.
Applying an annual PD to a multi-year horizon without adjusting.
Candidates multiply by the annual PD once and stop.
Fix: Use cumulative PD = 1 − (1 − PD)^T when annual PD is constant, or sum the period PDs given.
Assuming the whole credit spread is compensation for expected loss.
Spread is seen as the price of default risk only.
Fix: State that spread also compensates for uncertainty, liquidity and migration risk, so spread exceeds EL.
Ignoring migration risk for investment-grade bonds because default is unlikely.
Low PD makes the bond feel safe.
Fix: Point out that downgrades widen spreads and cut prices, and a fall to high yield can force some investors to sell.
Forgetting to discount in a CVA question.
The expected loss formula has no discount term, so it is carried over.
Fix: Multiply each period's expected loss by its discount factor, then sum.

Worked examples

Example 1

A portfolio manager holds a ₹10,00,00,000 position in a subordinated bond. The one-year probability of default is 3%. The expected recovery rate is 35%. Calculate the one-year expected loss in rupees and as a percentage of exposure.

Show the solution

LGD = 1 − 0.35 = 0.65, or 65%.
Expected loss rate = 0.03 × 0.65 = 0.0195, or 1.95%.
Expected loss = 0.0195 × ₹10,00,00,000 = ₹19,50,000.

Answer: Expected loss is ₹19,50,000, which is 1.95% of exposure.

Example 2

A bond has an annual default probability of 2% in each year, independent across years, and 40% recovery. The bond's credit spread is 1.50%. (a) Calculate the probability of default within three years. (b) Calculate the approximate annual expected loss rate and say whether the spread covers it.

Show the solution

(a) Survival over 3 years = 0.98^3 = 0.941192.
Cumulative PD = 1 − 0.941192 = 0.058808, or about 5.88%.
(b) LGD = 1 − 0.40 = 0.60.
Annual expected loss rate = 0.02 × 0.60 = 0.012, or 1.20%.
Compare: spread 1.50% exceeds 1.20% by 0.30%.

Answer: (a) About 5.88%. (b) The annual expected loss rate is 1.20%. The 1.50% spread covers it, leaving a margin of 0.30% for uncertainty, liquidity and migration risk. The margin is small.

Exam tips

A correct number typed on its own earns full credit for a calculation. Showing work is still good practice, but do not count on work earning partial credit.
Match the command word. Calculate needs a number. Justify needs a reason tied to the client. Do not write more than asked for.
In high-yield versus investment-grade questions, name the main risk for each: migration and spread widening for investment grade, default and recovery for high yield.
Check units and time horizon before multiplying. Annual PD with a multi-year question is a common trap.
Link credit exposure to the client's risk tolerance and constraints when asked to recommend.

Credit Risk Analysis: Default Probability and Loss Given Default in other exams

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

Credit Risk Analysis: Default Probability and Loss Given Default: frequently asked questions

How do you calculate expected loss in CFA Level III?

Multiply probability of default by loss given default, and by exposure if you need a currency amount. Get LGD from 1 − recovery rate. Make sure PD matches the time period you want.

What is credit migration risk?

It is the risk that an issuer's credit rating changes, usually a downgrade. A downgrade widens the spread and lowers the bond price even with no default. You estimate the price effect as −spread duration × spread change.

What does credit valuation adjustment measure?

CVA is the present value of expected loss from a counterparty failing to pay on a derivative or similar exposure. It uses expected exposure, PD, LGD and discount factors for each period. It reduces the value of the position.

How does credit analysis differ for high yield and investment grade?

Investment-grade analysis centres on spread changes and downgrade risk. High-yield analysis centres on default risk, cash flow, liquidity, covenants and recovery, since default is more likely and where the bond ranks in the capital structure matters more.