FRM Exam Part II · Future Value and Exposure

Exposure Measures for Capital and Limits: Maximum PFE vs EEPE

Updated 11 October 2026 · Fact-checked

Exposure measures turn a counterparty's changing exposure profile into one number for a purpose. Credit limits use maximum PFE, a high-percentile peak. Basel regulatory capital uses EEPE, a one-year average of non-decreasing expected exposure. To solve questions, match the measure to the purpose, then compute or interpret it.

Understand Exposure Measures for Capital and Limits

A derivative's exposure changes every day. If the counterparty defaults, you lose only if the contract is worth more than zero to you. So exposure at any date is max(V, 0), where V is the netted portfolio value less collateral held. Because future values are uncertain, exposure is a distribution at each future date.

From that distribution you build profiles. Expected exposure (EE) is the average of the positive exposure at each date. Potential future exposure (PFE) is a high percentile, such as 95% or 99%, at each date. Plot either against time and you get a profile. The maximum PFE is the highest point of the PFE profile. Expected positive exposure (EPE) is the time average of the EE profile.

Different uses need different summaries. Credit limits are about the worst plausible exposure, so desks use peak PFE. A limit based on the peak makes sure that exposure stays inside appetite at the riskiest date, even if the average is much lower. Peak measures are conservative and treat a short-lived spike the same as a long-lasting one.

Capital is about losses spread across a portfolio and over time, so Basel uses an average. Effective EE is the EE profile forced to be non-decreasing within the first year: at each date it is the larger of the current EE and the previous effective EE. This reflects that short-dated trades are rolled over, so exposure does not fall away. EEPE is the time-weighted average of effective EE over the first year, or until the longest maturity in the netting set if that is under one year. The non-decreasing rule applies only within that horizon. Exposure at default for capital is then EEPE multiplied by a scalar alpha, which is 1.4 under the Basel internal model method unless supervisors approve an own estimate.

Stress testing adds a third lens. You shock the market factors, such as rates, FX or credit spreads, and recompute exposure under the stressed scenario. You also stress collateral, for example larger haircuts or a longer margin period of risk. The result shows exposures that normal-condition limits and capital may miss, and it feeds limit changes and capital planning.

Key formulas to remember

Exposure at a date: Exposure = max(V, 0), after netting and collateral; V is the netted portfolio value less collateral held. Exposure is never negative.
Expected exposure (EE): EE(t) = E[max(V(t), 0)]; Average positive exposure at date t. Not the same as the average value.
Potential future exposure (PFE): PFE(t) = the α-percentile of exposure at date t; Typically 95% or 99%. Higher confidence gives a higher PFE.
Maximum PFE: Max PFE = max over t of PFE(t); The peak of the PFE profile. Used for limits.
Effective EE: Effective EE(t) = max(EE(t), Effective EE(t−1)); Makes the EE profile non-decreasing within the first year. Reflects rollover of short trades.
EEPE: EEPE = time-weighted average of Effective EE over the first year; Use the first year, or the longest maturity if shorter than one year. With equal intervals, the simple average of the interval values is the time-weighted average.
Regulatory EAD: EAD = alpha × EEPE, alpha = 1.4; Alpha is 1.4 under the Basel IMM unless a supervisor-approved estimate is used.

How to solve Exposure Measures for Capital and Limits questions

Use this order for any question on exposure measures, limits, capital or stress tests.

1Identify the purpose: limit setting, regulatory capital, or stress testing.
2Pick the matching measure: maximum PFE for limits, EEPE for capital, stressed profile for stress testing.
3Check the netting set and collateral. Exposure is after netting and collateral, floored at zero.
4If asked for EEPE, list EE at each date in the first year, then build effective EE by carrying forward the running maximum.
5Take the time-weighted average of effective EE over the first year, weighting by time interval if dates are unequally spaced. With equal intervals, the simple average of the interval values is the time-weighted average.
6If asked for EAD, multiply EEPE by alpha of 1.4.
7If asked for maximum PFE, scan the PFE profile and take the highest point, not the last.
8State the interpretation: peak versus average, and what risk the measure does or does not capture.

Quickest way: Purpose-to-measure shortcut

When to use it: Use when the question gives a profile and asks which measure fits, or a short table of EE values.

Limit or appetite wording means maximum PFE.
Capital or EAD wording means EEPE times 1.4.
For EEPE, write a running maximum down the EE column for the first year, then average it.
With equal time steps, the simple average is the time-weighted average. With unequal steps, weight by interval length.
Eliminate options that average PFE or take the last point without checking whether it is the peak.

Common mistakes in Exposure Measures for Capital and Limits

Using maximum PFE for regulatory capital.
Both are called exposure measures and PFE sounds more conservative.
Fix: Capital uses EEPE, a time average of effective EE. Maximum PFE is the limit measure.
Averaging raw EE to get EEPE.
Students confuse EPE with EEPE.
Fix: EEPE averages effective EE, which is the non-decreasing version. Apply the running maximum first.
Taking the last PFE point as the maximum PFE.
Students assume exposure rises with time.
Fix: Profiles for amortising products or swaps peak mid-life and then fall. Scan the whole profile.
Forgetting alpha when computing EAD.
Students stop at EEPE.
Fix: Under the Basel internal model method EAD = 1.4 × EEPE unless supervisors approve a different alpha.
Averaging over the full life of the trades.
EPE is often taught over the whole life.
Fix: EEPE is the time-weighted average over the first year only, or the longest maturity if shorter, and the running maximum applies only within that horizon.
Ignoring collateral and netting in stress tests.
Students shock market factors only.
Fix: Also stress haircuts, margin period of risk and netting enforceability, since these change stressed exposure.

Worked examples

Example 1

A netting set has expected exposure (USD millions) at four quarterly dates over one year: 10, 14, 12, 16. Compute EEPE and regulatory EAD under the Basel internal model method with alpha 1.4.

Show the solution

Build effective EE as a running maximum: 10, then max(14, 10) = 14, then max(12, 14) = 14, then max(16, 14) = 16.
Effective EE is 10, 14, 14, 16.
The intervals are equal, so each date has the same weight and the simple average is the time-weighted average: EEPE = (10 + 14 + 14 + 16) ÷ 4 = 54 ÷ 4 = 13.5.
EAD = 1.4 × 13.5 = 18.9.

Answer: EEPE = USD 13.5 million; EAD = USD 18.9 million.

Example 2

A bank sets a credit limit on a counterparty using 95% PFE as the limit metric. The limit horizon covers the full 4-year life of the trade. The 95% PFE profile is observed only at year-ends 1, 2, 3 and 4, and the values in USD millions are 8, 15, 19, 12. For reference, the average EE over the first year is USD 6 million. Which figure should the limit be compared with, and what is it, based on the given points?

Show the solution

Limits control the worst plausible exposure, and the limit horizon covers all four years, so use maximum PFE over the profile.
Scan the given profile points: 8, 15, 19, 12. The highest value is 19, at year 3.
The first-year average EE of 6 is an average measure, so it is not the limit comparator.
Interpretation: based on the observed points, the limit must accommodate USD 19 million at year 3, even though near-term exposure is lower.

Answer: Compare the limit with maximum PFE of USD 19 million, the highest of the given profile points (year 3).

Exam tips

Read the verb: set a limit means peak PFE; capital means EEPE.
Always apply the running maximum before averaging for EEPE.
Expect questions that ask why a peak measure and an average measure give very different numbers for the same trade.
In stress testing questions, look for the answer that stresses collateral terms and wrong-way effects as well as market factors.
Check the confidence level when comparing PFEs. A 99% PFE is not less than a 95% PFE for the same profile.

Practice questions from Future Value and Exposure

Exposure Measures for Capital and Limits: frequently asked questions

What is the difference between maximum PFE and EEPE?

Maximum PFE is the highest point of a high-percentile exposure profile and is used for credit limits. EEPE is the one-year average of the non-decreasing expected exposure and is used for Basel capital. One is a peak tail measure, the other an average.

How are credit limits set using PFE?

Banks compare the maximum of the PFE profile, at a chosen confidence level, with the limit assigned to the counterparty. This ensures the peak exposure stays within appetite on a netted, collateral-adjusted basis.

Why does Basel make expected exposure non-decreasing?

Short-dated trades are usually replaced when they mature, so the exposure to the counterparty persists. Effective EE reflects this rollover by not letting the profile fall.

How is counterparty exposure stress tested?

You shock market factors and recompute exposure. You also stress collateral terms such as haircuts and the margin period of risk. The results inform limits, capital and contingency actions.