Potential Future Exposure

[al66440]

Hi David,

What is the difference between Potential Future Exposure (PFE) and VAR? Is this part of the FRM material?

Greatly appreciate your guidance on this one.

Alex

 

[David Harper CFA FRM]

Hi Alex,

Although PFE has a technical definition, I do consider it a type of VaR. Say you simulate the (counterparty) exposure of an interest rate swap over the life of the swap; at each point in future time, there is a distribution of simulated exposures. At each point in future simulated time, then, a simulted distribution exists and PFE(t) is just the VaR (confidence) of that distribution; e.g, the worst exposure that will be exceeded 5% of the time (so Jorion calls PFE by "wost credit exposure" and, i think maybe jorion has the PFE as the "class" that includes WCE. Whereas assigned Canabarro uses PFE(t) which itself is a VaR quantile. So, I think maybe Canabarro PFE(t) = Jorion WCE but mathematically both are VaRs).

So, in this way, PFE(t) is nothing more than a future "point in time" VaR for a monte carlo simulated distribution of exposures

Is it part of the FRM: IMO, it had a minor role in 2009 (I did cover in the Canabarro reading) but I also definitely expect its role to GROW in prominence b/c counterparty exposure is a vital topic. Hope that helps, David

 

[LloydDagdag]

Hi David

I have a practice related query.

Since PFE is like VaR, should it be also backtested like VaR?

let's say for example, a company sets pre-settlement risk limits using PFE calculations, and is approved by the board annually.
How do we backtest this?

(unlike VaR where we can simply compare the actual PnL or PnL of the hypothetical portfolio against the VaR computed)

Any comments would be much appreciated
Thank you very much.

 

[[email protected]]

Hi LloydDagdag,

VaR is used to measure the market risk of a portfolio. PFE, as David mentioned, is used to measure the maximum potential loss in the case of credit events. Number of credit events are too few in a given time period compared to market events, meaning that number of exceptions may be too few to be able to make a sensible statistical analysis (backtesting).

Hope this makes sense.

 

[LloydDagdag]

Thanks

 

[TomNg12]

Hi LloydDagdag,

VaR is used to measure the market risk of a portfolio. PFE, as David mentioned, is used to measure the maximum potential loss in the case of credit events. Number of credit events are too few in a given time period compared to market events, meaning that number of exceptions may be too few to be able to make a sensible statistical analysis (backtesting).

Hope this makes sense.

Hi, thanks for this! However, the VaR you mentioned is Market VaR right? So what is the difference between Credit VaR and PFE then? As far as I understand, Credit VaR also measures the loss in case counterparty defaults?
Thank you very much!

 

[David Harper CFA FRM]

Hi @TomNg12 It's still a great question. PFE and CVaR are essentially similar, or at worst analogs. I would say this difference is merely contextual connotation. But in terms of denotation (definition) they are both quantiles (e.g., 99%) of an estimated credit loss distribution. In this way, PFE is a counterparty credit value at risk. The connotation difference is context: whereas CVaR implies principal at risk (e.g., a traditional loan or portfolio with an expected loss), PFE implies (connotes) a bilateral derivative position. Gregory, in itemizing exposure profiles, includes "loans and bonds" such that these instruments do have PFE but he writes "although not generally characterised as counterparty risk, the exposures of debt instruments such as loans and bonds can usually be considered almost deterministic and approximately equal to the notional value." So PFE is a CVaR but it explicitly suggests counterparty credit risk (as a subclass of credit risk) and it suggests we'll need to simulate the long-term future distribution (compared to CVaR which suggests we have analytical approaches such as IRB in Basel). I hope that's helpful!

Gregory's Counterparty Credit Risk [1st Edition because he explicates in more detail]:

"2.5.3 Potential future exposure: In risk management, it is natural to ask ourselves what is the worse exposure we could have at a certain time in the future? A PFE will answer this question with reference to a certain confidence level. For example, the PFE at a confidence level of 99% will define an exposure that would be exceeded with a probability of no more than 1% (one minus the confidence level). We see that the definition of PFE is exactly the same as the traditional measure of value-at-risk (VAR) with two notable exceptions:

• PFE may be defined at a point far in the future (e.g. several years) whereas VAR typically refers to a short (e.g. 10-day) horizon.
• PFE refers to a number that will normally be associated with a gain (exposure) whereas traditional VAR refers to a loss.

This last point is important; VAR is trying to predict a worst-case loss whereas PFE is actually predicting a worst-case gain10 since this is the amount at risk if the counterparty defaults." -- Gregory, Jon. Counterparty Credit Risk: The new challenge for global financial markets (The Wiley Finance Series) (Kindle Locations 1502-1513). Wiley. Kindle Edition.

 

[TomNg12]

Thank you very much David, it clarifies a lot!
I actually preferred your own explanation. Gregory's quote refers to Market VaR I think, and that's exactly what I am confused. In my research I was almost saying VaR refers to a loss, while PFE refers to a gain, however as I was talking explicitly about Credit VaR in context, I realized it was not true anymore. Gregory's sentence is only true with Market VaR I think