FRM Exam Part II · Credit Value Adjustment

Credit Exposure Metrics: EE, PFE, EPE and Effective EPE

Updated 11 October 2026 · Fact-checked

Credit exposure is the loss you would suffer if a counterparty defaulted, floored at zero: max(V, 0). Expected exposure (EE) is the average of that at a future date. Potential future exposure (PFE) is a high percentile of it. EPE averages EE over time. Effective EPE uses a non-decreasing EE profile.

Understand Credit Exposure and Exposure Metrics

Counterparty credit exposure is the amount you would lose if a counterparty defaulted today, before recoveries. If a derivative has a positive value to you, the counterparty owes you that amount. If the value is negative, you owe them, and your loss on their default is zero. So exposure at any date is max(V, 0), where V is the contract's mark-to-market value to you.

Today's value is known. Future value is not. So we model exposure at each future date as a distribution and summarise it with a metric. Each metric answers a different question.

Expected exposure (EE) is the mean of exposure at a future date t. It is the average of max(V, 0), which includes the zeros. It is not the average of only the positive outcomes, and it is not the average of V. EE is the input to CVA, because CVA prices the expected loss.

Potential future exposure (PFE) is a high percentile, such as the 95th or 97.5th, of the exposure distribution at date t. It is a worst-case style number used for credit limits. The maximum of the PFE profile is often called peak exposure.

Expected positive exposure (EPE) is the time average of the EE profile over a horizon, usually one year for regulatory capital. Effective EE is the running maximum of EE, so it never falls over the horizon. Effective EPE is the time average of effective EE. It reflects that short-dated trades are rolled over, so exposure does not really fall as trades mature. Basel uses effective EPE to compute exposure at default (EAD) for counterparty credit risk under the internal model method.

Key formulas to remember

Exposure at date t: E(t) = max(V(t), 0); V is the portfolio value to you. For a netting set, net the trades first, then take the max.
Expected exposure: EE(t) = E[max(V(t), 0)]; Includes the zero outcomes. It is always at least max(E[V(t)], 0).
Potential future exposure: PFE(t) = the α-percentile of E(t), i.e. P(E(t) ≤ PFE) = α; Common α is 95% or 97.5%. Peak PFE is the maximum over time.
Expected positive exposure: EPE = (1 ÷ T) × ∫ EE(t) dt ≈ Σ EE(tᵢ) × Δtᵢ ÷ T; A time-weighted average of EE. Use time weights if the dates are unevenly spaced.
Effective EE: Effective EE(tₖ) = max(Effective EE(tₖ₋₁), EE(tₖ)); Running maximum, so the profile is non-decreasing.
Effective EPE: Effective EPE = Σ Effective EE(tₖ) × Δtₖ ÷ T, over the first year; Basel horizon is the shorter of one year and the longest maturity in the netting set.
Normal exposure percentile: If V ~ N(μ, σ²) and PFE > 0: PFE = μ + z × σ; z = 1.645 for 95% and 1.96 for 97.5%. Floor at zero.
Regulatory EAD (internal model method): EAD = α × Effective EPE, with α = 1.4 unless supervisors approve otherwise; α is a multiplier calibrated by Basel. State it as the default.

How to solve Credit Exposure and Exposure Metrics questions

Use this routine for any question that asks for an exposure metric or a comparison of metrics.

1Identify the metric asked for: EE (mean), PFE (percentile), EPE (time average of EE) or effective EPE (time average of non-decreasing EE).
2Write the exposure as max(V, 0) at each date. Net trades inside a legal netting set before applying the max.
3For EE, average exposure over all scenarios, counting negative-value scenarios as zero.
4For PFE, find the stated percentile of the exposure distribution. If V is normal, use μ + zσ and floor at zero.
5For EPE, average the EE values across dates, using time weights. For effective EPE, first replace each EE by the running maximum of earlier values, then average.
6Check the horizon. Regulatory effective EPE uses one year or the longest maturity if shorter.
7Apply any multiplier (α = 1.4 for EAD) only if the question asks for EAD.
8Sanity check: PFE ≥ EE at the same date, and effective EPE ≥ EPE.

Quickest way: Rank-and-run-max shortcut

When to use it: Use when the question gives a table of EE values by date and asks for EPE or effective EPE.

Write the EE values in date order.
For effective EE, run down the list and carry forward the highest value seen so far.
If dates are equally spaced, effective EPE is the simple average of the effective EE list. Otherwise weight by interval length.
Compare answers to the options. Effective EPE can never be below EPE, which often removes two options.
For PFE with a normal V, compute μ + zσ. If it is below zero, the PFE is zero.

Common mistakes in Credit Exposure and Exposure Metrics

Averaging only the positive outcomes to get EE, or averaging V itself.
The words 'expected positive exposure' suggest conditioning on positives.
Fix: EE is E[max(V, 0)] over all scenarios. Negative scenarios count as zero, not dropped.
Treating PFE as an average.
PFE and EE sound similar and both are 'future exposure'.
Fix: PFE is a percentile. It is used for limits. EE is a mean. It is used for pricing CVA.
Taking effective EPE as the average of the raw EE profile.
Students forget the non-decreasing adjustment.
Fix: Take the running maximum first. Then average. Effective EPE is at least EPE.
Using the same horizon for every case.
Students assume one year always applies.
Fix: Use the shorter of one year and the longest maturity in the netting set. Read the question for the stated horizon.
Taking max(V, 0) on each trade before netting.
Exposure feels like a per-trade idea.
Fix: Where a legally enforceable netting agreement exists, net first, then take the max on the total.
Applying the 1.4 multiplier to EE, PFE or EPE.
Students memorise 1.4 without its purpose.
Fix: The multiplier applies to effective EPE to get EAD under the internal model method, and only there.

Worked examples

Example 1

A bank's exposure to a counterparty at a future date has four equally likely scenarios for the netting-set value V: -$8m, -$2m, +$4m and +$10m. Compute the expected exposure at that date. Compare it with the expected value of V.

Show the solution

Exposure is max(V, 0): 0, 0, 4, 10.
EE = (0 + 0 + 4 + 10) ÷ 4 = 14 ÷ 4 = $3.5m.
Expected V = (-8 - 2 + 4 + 10) ÷ 4 = 4 ÷ 4 = $1.0m.
EE ($3.5m) exceeds E[V] ($1.0m) because the negative scenarios are floored at zero.

Answer: EE = $3.5m, versus an expected value of V of $1.0m.

Example 2

A netting set has the following expected exposure profile over the first year at equal quarterly intervals: EE = $6m, $9m, $7m, $5m at the end of quarters 1 to 4. Compute EPE and effective EPE over the year.

Show the solution

EPE = (6 + 9 + 7 + 5) ÷ 4 = 27 ÷ 4 = $6.75m.
Effective EE by running maximum: Q1 = 6, Q2 = max(6, 9) = 9, Q3 = max(9, 7) = 9, Q4 = max(9, 5) = 9.
Effective EPE = (6 + 9 + 9 + 9) ÷ 4 = 33 ÷ 4 = $8.25m.
Check: 8.25 ≥ 6.75, as expected.
If the question asked for EAD with α = 1.4: 1.4 × 8.25 = $11.55m.

Answer: EPE = $6.75m and effective EPE = $8.25m. EAD would be $11.55m using α = 1.4.

Exam tips

Read the metric name twice. Mean, percentile, time average and running-maximum average are four different answers.
Wrong options often come from skipping the zero floor or the running maximum. Check both before choosing.
Know the uses: EE feeds CVA, PFE feeds limits, effective EPE feeds regulatory EAD.
Expect interpretation questions, such as why a swap's exposure profile rises then falls while an option's is highest at start. Link the shape to time to maturity and volatility.
Keep the sanity checks ready: PFE ≥ EE at the same date, and effective EPE ≥ EPE.

Practice questions from Credit Value Adjustment

Credit Exposure and Exposure Metrics: frequently asked questions

What is the difference between expected exposure and PFE?

Expected exposure is the mean of future exposure at a date, with negative values set to zero. PFE is a high percentile of the same distribution, such as 95%. EE suits pricing, such as CVA, while PFE suits credit limits.

What is EPE and effective EPE?

EPE is the time average of the expected exposure profile over a horizon. Effective EPE first makes the EE profile non-decreasing by taking a running maximum, and then averages it. Basel uses effective EPE, scaled by a multiplier, to set exposure at default.

How do you calculate potential future exposure?

Model the distribution of the netting set value at a future date, floor it at zero, and read off the chosen percentile. If value is normal with mean μ and standard deviation σ, PFE is μ + zσ, floored at zero. Use z = 1.645 for 95%.

Why is effective EPE higher than EPE?

The running maximum can only keep or raise each EE value. So the average cannot fall. The idea is that maturing short trades are replaced by new ones, so exposure does not really decline.