Modern credit risk management would not have been possible without the potential future exposure (PFE) measure. Taken as the maximum expected loss over a given period at a specified level of confidence, PFE is essential to setting credit risk limits and monitoring risk within a bank, giving it a similar status as value at risk used in market risk.
Of course, since the crisis, the industry has steadily been moving away from VAR. Dubbed ‘the number that killed us’, VAR rapidly fell out of favour for its inability to capture tail risk, as the losses beyond the set confidence threshold are ignored – a problem, when those losses turn out to be catastrophically large.
Regulations such as the Fundamental Review of the Trading Book (FRTB) have pushed banks away from VAR towards expected shortfall – a measure that does a better job of averaging the tail distribution of losses.
Given the wide acceptance of expected shortfall now, some question why the same development has not happened for PFE, VAR’s counterpart in credit risk management.
In this month’s first technical, Counterparty trading limits revisited: from PFE to PFL, three senior quants – Chris Kenyon, EMEA head of XVA quant modelling at MUFG Securities, Mourad Berrahoui, head of counterparty credit risk modelling at Lloyds Banking Group, and Benjamin Poncet, a senior manager within the same team – argue PFE has several flaws as a counterparty credit risk measure, and propose a replacement that better captures tail risk.
They dub their solution potential future loss, or PFL, which can be expressed as a product of a portfolio’s expected shortfall multiplied by its loss given default (LGD). This is similar in principle to expected shortfall, as the losses in the tail are averaged and the measure also includes LGD, which means the differences in recovery rates are already factored in.
Typically in credit risk monitoring using PFE, counterparties are assigned a particular risk limit for each netting set or seniority set they belong to based on creditworthiness, before being allowed to trade with a bank’s trading desks. If any of the risk limits are filled, then all desks would stop trading with that counterparty.
The trouble with that is, PFE alone does not tell whether a counterparty is more risky than another, or even make comparisons between different levels of seniorities of debt issued by the same counterparty. This is because the PFE calculations are based on exposure distributions. This ignores recovery rates, which can differ widely across counterparties and seniorities. Different recovery rates mean different loss distributions, essentially making it difficult to compare PFEs for different counterparties and express the risk appetite of the bank without making subjective adjustments.
“If you have a PFE for two different counterparties, you don’t know which one is bigger,” says Kenyon. “In order to understand how you’ve set that limit in the first place, you have to start looking into what is the counterparty like – in the sense of what is the LGD of the counterparties in that sector, for example. So you can’t compare the PFE numbers for two different counterparties. Expressing a bank’s risk appetite is really not transparent with PFE.”
PFE was invented sufficiently long ago that although it may have been a really significant step for its time, now, I think we can do betterChris Kenyon, MUFG Securities
This is significant, because recovery rates can vary quite widely. Historically, in the case of savings and loans, the median recovery was reckoned to be about 1%; in public finance it’s typical to have much higher rates, usually well above 60%.
This means most banks set risk limits only for one counterparty netting set or seniority set at a time, through very careful analysis of that specific counterparty, which can be very time consuming. Loss relationships across different seniorities are accounted for subjectively.
“If you’ve filled up one risk limit and you want to move [capacity] from another netting set, it’s not fungible, because typically different seniorities have different recovery rates, and generally the difference between senior unsecured and subordinated can be at least a factor of two. It slows down the process by which you can address customer needs,” argues Kenyon.
Even for comparisons between collateralised and uncollateralised trades, PFE fails as a good metric, the quants argue; the loss distributions are different for both cases, so the numbers aren’t comparable. This is an even more significant flaw given the rapid rise in collateralisation across the industry thanks to regulations such as margin rules for non-cleared derivatives.
PFL, says Kenyon, “gives you the expected loss above the quantile, so you know you’ve captured the contribution of all the possible losses above the quantile. If it’s very low you can relax, because you know it’s genuine; there is nothing hiding. Whereas in PFE, above the quantile, you can have anything.”
Back in 2012, when regulators suggested FRTB would require banks to start using expected shortfall, many smaller market participants argued it would be a very difficult shift, requiring massive changes to decades’ worth of work on infrastructure and systems. But regulators persisted and the industry has more or less accepted the new measure. Doing the same for credit risk monitoring might be another big step for the industry, but the issues with PFE, and the past lessons learned from VAR should be motivation enough.
“PFE was invented sufficiently long ago that although it may have been a really significant step for its time, now, I think we can do better,” says Kenyon.
Editing by Tom Osborn