Current Exposure and Potential Future Exposure

Why Exposure Depends on When It Is Measured

A counterparty position can have a different value today than it will have when the counterparty defaults. If the position is an asset to the reporting party, the amount at risk from replacement is positive; if it is a liability, the reporting party does not have a positive replacement-cost exposure on that position at that instant. Because market values change, a zero or small exposure today does not establish that exposure will remain zero or small.

This tutorial considers a single position with no netting or collateral adjustment. That boundary matters: the exposure measure here is based on the position’s signed market value, while agreements that combine positions or reduce exposure through collateral require additional treatment. Exposure is also not itself a credit loss. It measures the amount that could be at risk if the counterparty defaulted; recovery and default likelihood are separate considerations.

Definition: Let $V_t$ be the signed market value of a position at time $t$, measured from the reporting party’s perspective. A positive value means the position is an asset to that party; a negative value means it is a liability. The position’s exposure at time $t$, before netting or collateral, is the positive part of its value: $$ E_t=(V_t)^+=\max(V_t,0). $$ Current exposure is $E_0$, the exposure calculated using the market value at the present measurement time. Future exposure at horizon $T$ is the random variable $E_T=(V_T)^+$, because the future market value is uncertain.

Current Exposure, Expected Exposure, and PFE

Current exposure is a measurement of the position now. For one position, it is the replacement-cost amount if the signed market value is positive, and zero if the signed value is negative. Taking the positive part is essential: a negative value is not a negative exposure that offsets a different future outcome in the same scenario.

At a future horizon, different market outcomes can produce different signed values and therefore different exposures. Two summaries answer different questions. Expected exposure is the probability-weighted average of future exposure at the stated horizon. Potential future exposure (PFE) at level $q$ is a quantile of the future exposure distribution. Both depend on the specified horizon and the model or scenarios used to describe future market values.

Definition: For a specified future horizon $T$, expected exposure is $EE(T)=E[E_T]$. For $0<q<1$, define the $q$-level PFE by the quantile convention $$ PFE_q(T)=\inf\{x:F_{E_T}(x)\ge q\}, $$ where $F_{E_T}(x)=P(E_T\le x)$ is the cumulative distribution function of future exposure. Thus PFE is a threshold at the specified horizon, while expected exposure is an average at that horizon.

The quantile definition gives a precise probability interpretation. At least probability $q$ is at or below the PFE. Consequently, the probability strictly above the PFE is at most $1-q$; it can be less when probability is concentrated at the quantile. For a continuous distribution with no probability mass at the quantile and cumulative probability $q$ there, the probability strictly above is $1-q$. A PFE is not an expected value, a hard upper bound, or a statement that exposure stays below the threshold at every time before the horizon.

The following calculation justifies the discrete quantile procedure. Sort the possible exposure outcomes from smallest to largest and add their probabilities cumulatively. The first outcome whose cumulative probability reaches or exceeds $q$ is the $q$-quantile: every smaller outcome has cumulative probability below $q$, while the selected outcome has cumulative probability at least $q$. This is why a discrete PFE need not leave exactly $1-q$ probability strictly above it.

Use the stated horizon.
Identify the future time $T$ at which market values are being assessed. A PFE at one horizon does not summarize all intervening times.

Find signed values by scenario.
Use the model or scenario data to determine $V_T$ in each outcome, including whether each value is positive or negative.

Convert values to exposure.
For each outcome, calculate $E_T=\max(V_T,0)$. Do this before calculating averages or quantiles.

Calculate the requested summary.
Weight exposure outcomes by their probabilities for expected exposure; sort them and accumulate probabilities for PFE.

Worked Examples

Worked Example: Current Exposure and an 80% PFE

A hypothetical counterparty position has a current signed market value of $-\$850$. At a specified future horizon, its signed market value is $-\$200$ with probability 0.30, $\$400$ with probability 0.50, and $\$1{,}600$ with probability 0.20. Find current exposure, expected future exposure, and the 80% PFE.

Model assumptions and method. Treat the stated outcomes as the complete discrete distribution of signed market value at this one horizon. The probabilities sum to $0.30+0.50+0.20=1.00$. The values are horizon market values, so no separate interest adjustment is made; mortality is not relevant to this position. First apply the positive-part function to each signed value.

Current exposure. The current value is negative, so $E_0=\max(-\$850,0)=\$0$.

Future exposure by outcome. The exposures are $\max(-\$200,0)=\$0$, $\max(\$400,0)=\$400$, and $\max(\$1{,}600,0)=\$1{,}600$, with respective probabilities 0.30, 0.50, and 0.20.

Expected exposure. Weight each exposure, not each signed value: $EE(T)=0.30(\$0)+0.50(\$400)+0.20(\$1{,}600)=\$0+\$200+\$320=\$520$.

80% PFE. The cumulative exposure probabilities are 0.30 at $\$0$, $0.30+0.50=0.80$ at $\$400$, and 1.00 at $\$1{,}600$. The first exposure whose cumulative probability reaches 0.80 is $\$400$, so $PFE_{0.80}(T)=\$400$.

Check and common mistake. The exposure outcomes have total probability 1.00, and 80% of the probability is at or below $\$400$. Selecting $\$1{,}600$ just because it is the largest outcome would confuse PFE with a maximum. The results are current exposure $\$0$, expected exposure $\$520$, and 80% PFE $\$400$.

Worked Example: A Higher Quantile Than the Expected Exposure

At a stated future horizon, a hypothetical position has signed market values of $-\$500$, $\$500$, $\$2{,}500$, and $\$5{,}000$, with respective probabilities 0.10, 0.25, 0.45, and 0.20. Calculate expected exposure and the 90% PFE.

Model assumptions and method. The four outcomes form the complete discrete horizon distribution; their probabilities sum to $0.10+0.25+0.45+0.20=1.00$. No separate interest rate or mortality assumption is needed because the scenario values are already stated at the horizon and mortality does not apply. Convert signed values to exposures, then compute the mean and quantile.

The exposure outcomes are $\$0$, $\$500$, $\$2{,}500$, and $\$5{,}000$. The negative signed value contributes zero exposure, not a negative amount.

Expected exposure. $EE(T)=0.10(\$0)+0.25(\$500)+0.45(\$2{,}500)+0.20(\$5{,}000)$ $=\$0+\$125+\$1{,}125+\$1{,}000=\$2{,}250$.

90% PFE. Cumulative probabilities are 0.10 at $\$0$, 0.35 at $\$500$, 0.80 at $\$2{,}500$, and 1.00 at $\$5{,}000$. Since 0.80 is below 0.90 and 1.00 reaches it, $PFE_{0.90}(T)=\$5{,}000$.

Check and common mistake. The weighted contributions are $\$0$, $\$125$, $\$1{,}125$, and $\$1{,}000$, which sum to $\$2{,}250$. Omitting the $\$1{,}000$ contribution from the last outcome would incorrectly produce $\$1{,}250$; including a negative exposure for the first outcome would also be incorrect. The 90% PFE is $\$5{,}000$, but the expected exposure is $\$2{,}250$; they are different summaries.

Worked Example: Market-Value Changes Can Reverse Exposure

A hypothetical position currently has signed market value $\$300$. By a specified future horizon, its signed market-value change is $-\$900$ with probability 0.20, $+\$200$ with probability 0.50, or $+\$1{,}200$ with probability 0.30. Calculate current exposure, expected exposure at the horizon, and the 80% PFE.

Model assumptions and method. The listed changes are complete scenario outcomes for the change in signed market value from now to the horizon; their probabilities sum to 1.00. No additional interest rate or mortality assumption is used: the scenario changes are already specified in market-value terms, and mortality is not relevant. Add each change to today’s value before taking the positive part.

Current exposure. $E_0=\max(\$300,0)=\$300$.

Future signed values and exposures. In the first scenario, the signed value is $\$300-\$900=-\$600$, giving exposure $\$0$. In the second, it is $\$300+\$200=\$500$, giving exposure $\$500$. In the third, it is $\$300+\$1{,}200=\$1{,}500$, giving exposure $\$1{,}500$.

Expected exposure. $EE(T)=0.20(\$0)+0.50(\$500)+0.30(\$1{,}500)=\$0+\$250+\$450=\$700$.

80% PFE. Cumulative probabilities for exposures $\$0,\$500,\$1{,}500$ are 0.20, 0.70, and 1.00. The cumulative probability at $\$500$ is below 0.80, so the 80% PFE is $\$1{,}500$.

Check and common mistake. The market-value changes have been added to the signed value first, and the resulting exposures are all nonnegative. Applying the positive part to the changes alone would not give the position’s future exposure: exposure depends on the future signed market value, not just on the direction of the change. The results are current exposure $\$300$, expected exposure $\$700$, and 80% PFE $\$1{,}500$.

Interpreting the Measures

Measure	What it summarizes	What it does not establish
Current exposure	The positive replacement-cost value at the present measurement time	How large exposure may become at a future horizon
Expected exposure	The probability-weighted average of exposure at a specified future horizon	A high quantile or a maximum exposure
PFE at level $q$	A $q$-quantile of exposure at a specified future horizon	An average, a hard cap, or a bound for every time before that horizon

A position with zero current exposure can have positive expected exposure and PFE if future market values can become positive. Conversely, a positive current exposure does not guarantee positive exposure in every future scenario. The scenario calculation in the third example illustrates both possibilities: the position starts as an asset, becomes a liability in one outcome, and has higher positive values in the others.

Horizon and confidence level are therefore essential parts of a PFE statement. “PFE is $\$1{,}500$” is incomplete without saying at what future horizon and at what quantile it was calculated. Nor should a horizon-specific PFE be read as the largest exposure over an entire period. A measure of exposure across time would require a different definition and analysis.

Common Exam Trap

Common mistake and correction: Do not average signed values and then take the positive part as a substitute for expected exposure. In general, $E[\max(V_T,0)]$ is not equal to $\max(E[V_T],0)$. For example, if $V_T=-\$200$ with probability 0.50 and $+\$600$ with probability 0.50, the exposure outcomes are $\$0$ and $\$600$, so expected exposure is $0.50(\$0)+0.50(\$600)=\$300$. The average signed value is $\$200$, whose positive part is $\$200$, not $\$300$. Apply the positive-part operation to each scenario before averaging.

A related quantile trap is to assume that exactly $1-q$ of outcomes must be strictly above a $q$-level PFE. With discrete outcomes, the cumulative probability can jump past $q$, leaving less than $1-q$ strictly above the quantile—or none at all. Use the cumulative-probability definition rather than trying to force an exact tail percentage.

Key takeaway: Current exposure uses today’s signed market value; expected exposure and PFE use the distribution of positive-part market values at a specified future horizon. Convert each scenario to exposure first, then calculate the requested average or quantile.

Check Your Understanding

For each problem, take the positive part of each signed future value before calculating exposure summaries. Unless stated otherwise, the scenario probabilities form the complete distribution at the stated horizon; no separate interest or mortality assumption is required.

A position’s current signed market value is $-\$2{,}400$. What is its current exposure? (Answer: $\$0$)
At a future horizon, signed values are $-\$300$, $\$900$, and $\$2{,}100$, with probabilities 0.40, 0.40, and 0.20. Find expected exposure and the 80% PFE. (Answer: expected exposure $\$780$; 80% PFE $\$900$)
At one horizon, signed values are $-\$100$, $\$400$, $\$1{,}200$, and $\$3{,}000$, with probabilities 0.15, 0.35, 0.30, and 0.20. Find expected exposure and the 85% PFE. (Answer: expected exposure $\$1{,}100$; 85% PFE $\$3{,}000$)
A position currently has signed market value $\$600$. Its future change is $-\$1{,}000$ with probability 0.25, $+\$400$ with probability 0.50, and $+\$1{,}600$ with probability 0.25. Find the future expected exposure and 75% PFE. (Answer: expected exposure $\$1{,}050$; 75% PFE $\$1{,}000$)
Future exposure is $\$0$ with probability 0.55, $\$800$ with probability 0.30, and $\$2{,}000$ with probability 0.15. Find the 80% PFE and the probability of exposure strictly above it. (Answer: 80% PFE $\$800$; probability strictly above it $0.15$)

What You'll Learn