In the last post I looked at the new overall market risk regulation, and its split into Trading Book (TB) and CVA. In this note I will focus on FRTB-TB.

The major changes that FRTB-TB brings can be summarized as:

  • Much stronger and prescriptive separation of trading and banking books
  • Very detailed and prescriptive Standardised Approach (SA) charge
  • Calculation and publication of SA charge is mandatory for all institutions (for comparison and fallback purposes), regardless of whether they can use Internal Model Approach (IMA) to calculate the actual capital charge
  • IMA now requires using Expected Shortfall (ES), not Value at Risk (VaR)
  • IMA considers liquidity of instruments, introducing liquidity horizons
  • IMA accreditation is now much more granular, at a trading desk level. Any desk can fail its IMA accreditation checks, and temporarily fall back to SA capital charge until the accreditation conditions are met again.

Trading book boundary

A major goal of the regulators was to at least limit, at best remove, any potential regulatory arbitrage resulting from different capital treatment for banking and trading books.  Existing regulation uses intentional definition of the trading book (for example FCA’s BIPRU uses defines as trading book as “positions […] held either with trading intent or in order to hedge other elements of the trading book”.

This approach is clearly subject to interpretation. in 2008 liquidity in some instruments evaporated overnight. As a result, migrating a position from trading to banking book could provide significant capital relief.

FRTB’s approach to the trading book is now prescriptive. Specific instruments (such as any options, any listed equities, and any instruments that are accounted for using fair value – in effect any financial instruments for which a reasonable market exists) are automatically presumed to be in the trading book. Any exceptions to these are at supervisory discretion, and require explicit regulatory approval. FX and commodity risk continues to be subject to market risk capital charges regardless of what book it is captured in.

Additionally, the boundary between trading and banking book hardened. Only under exceptional events (mergers, restructuring and similar) can be any positions moved from a trading book to a banking book. Moreover, any such move cannot result in a lower capital charge.  If moving a position from a trading book to a banking book results in a lower charge, the FI must hold the difference as a regulatory capital surcharge under Pillar 1, subject to a run-off agreed with regulator[1].

Standardised Approach Charge

SA charge is one of the areas that underwent the most changes in the various FRTB iterations.

In the final version, SA charge is made of three different components.

The first is so called Enhanced Delta Plus (EDP) charge. This consist of two linear (delta and vega) sensitivity based charges, and a curvature charge, intended to capture any non-linearities[2].

The charge is calculated across seven different asset classes (although it would be better to call it risk classes, as three are variations on credit risk), with no hedging or diversification benefits recognized across the classes. Within each asset class, a standard deviation/variation like formulas with predefined correlations[3] and risk weights are used to calculate the capital charge for the asset class. Both baseline and stressed correlations are prescribed, and the worst-case result is then used.

While the formulas themselves are fairly simple, the calculations rely on a very large number of regulatory parameters and rules.  Of the sixty six pages of the accord released in January, fully thirty pages were specifying the SA calculations, compared with just ten for the IMA[4].

The second component is Default Risk Charge (DRC). This charge covers only debt (and equity) instruments, and is intended to capture any Jump To Default risk. It has similarly prescriptive rules and parameters to EDP, although it is considerably lighter (and thus ambiguous).

The last component is Residual Risk Add-On.  It is a simple risk-weight times notional charge, meant to capture risks that are subject to vega and curvature charges in EDP, but where the pay-off cannot be expressed as a simple linear combination of European or American options (such as gap risk, prepayment risk, correlation risk etc.). The risk weight is 0.1% or 1%, depending on whether the risk is exotic or not.[5]

Despite the highly prescriptive nature to SA, I believe that there is still some ambiguity and space for misunderstanding, especially around Residual Risk Add-On and DRC charges.

Another issue that BCBS wishes to address with SA charges is comparability. It is hard for both regulators and investors to make capital-adequacy comparisons between institutions using IMA, with its relative freedom of assumptions.  BCBS decided to solve this by requiring all FIs, including those with IMA accreditations, to calculate and publish their SA capital charges.

SA’s design goal was also to provide a credible backstop to IMA, allowing regulators to withdraw IMA accreditations on a very short notice, and be able to control IMA accreditation with greater granularity.

Internal Model Approach Charge

A FI can apply to use IMA to calculate its capital charges.

IMA is applicable only for some of the asset classes. In particular, all securitization (including correlation trading book – check), must have its capital charges calculated using SA (as if it was a separate portfolio, foregoing any diversification and hedging benefits from the rest of the portfolio).

There is a number of substantial changes introduced by FRTB for IMA.

The most visible change is that VaR is replaced by ES. Unlike VaR, ES provides a better view of how the tail risk in the portfolio looks like. At the same time, if an institution can generate VaR PnL vectors now, switching to ES can be fairly straightforward.

The complexity of new IMA does not come from VaR being replaced by ES, but rather with fact that to come up with the final charge, a number of ES values for different scenarios needs to be calculated. This is a result of introducing a new concept of Liquidity Horizons.

The existing regulation assumed a holding period of 10 days, and that all instruments could be safely liquidated without undue impact on market prices within this period. This was usually calculated by scaling a return period of one day assuming normality and independence of returns.

BCBS now recognizes that in a period of stress, 10 days is too optimistic except for the most liquid assets. A set of different liquidity horizons has been defined, with each asset class (and risk factors associated with it) assigned to a liquidity horizon. These can be as short as 10 days (for major interest rates markets and listed large-cap equities), to as long as 120 days (for structured and exotic credit spreads). While the initial proposals were vary of scaling and the underlying assumptions, in the end calculation uses scaling[6] although it requires that the shortest (10 day) is calculated directly, without any scaling. ES charges are calculated for each liquidity horizon, and form input into the next step.

Basel 2.0 required the VaR to be calculated using scenarios defined by the last two years. Basel 2.5 recognised the procyclicality of this calculation, and included a requirement to calculates Stressed VaR, with the resulting charge being a sum of “normal” VaR and stressed VaR (SVaR).  While this was conservative for the upside in the cycle, at the cycle’s downside it was unnecessarily punitive.

For IMA, FRTB requires an identification of one period of stress – 12 months calibrated to produce most severe stress over a reduced set of risk factors relevant to FI’s portfolio[7]. The resulting ES charge on this set[8] is then multiplied by a scaling factor to compensate for the reduction of the risk factor set.

Unlike under SA, using IMA allows cross-asset correlation, with some limitations. Institutions are required to add a surcharge, calculated by using uncorrelated per-asset-class ES measures and a regulator correlation parameter to the unrestricted ES calculation.

Next component of IMA is a default charge[9]. This is an incremental charge intended to capture losses that would stem from an obligor actually defaulting – a sort of Jump to Default charge. A VaR model with 99.9% confidence level is required. An important fact is that this model is not allowed to rely on market implied probabilities of default (PDs), but an “objective probability of default”.

IMA’s last component is risk for non-modellable risk factors (NMRF). These are factors that affect pricing, but are not allowed (or cannot be) included in the ES calculation. FRTB specifies, that any risk factors with insufficient pricing history[10] is deemed NMRF hence any risk factor that has no observable price (including implied price) is automatically qualified as NMRF.  NMRF are capitalised using a stressed scenario calculation[11].

Some observations

Firstly, it becomes more important than ever to have well integrated and architected IT systems, with clean data and good interfaces.  For example, before FRTB, financial institutions could use shortcuts and crutches to get their PnL reconciliation working. Now, a few days of PnL explain going wrong can force a trading desk on SA capital charge, punishing the banks with bad data, systems and processes.  An institution wishing to take advantage of IMA approach must ensure that their the front-to-back systems, data and models align[12] or it will not be able to use the advantage to the full extent.

The new system also penalizes new products, as they may have to start their life under SA treatment. Even under IMA, they are likely to suffer from high LH charges, and a need to use NRMF stress-scenario.

There may be exceptions to that, where the industry embraces the product and a reasonably liquid market for it is created very quickly, but proprietary and highly bespoke products are likely to be capitalised highly, and priced accordingly.

Similar can be expected with highly bespoke and sophisticated models. The more unobservable and untradeable inputs a model has, the harder it may be to satisfy the PnL explains and justify the NMRF charges.

In other words, proprietary innovation (both of model and product) may be much more expensive under FRTB than it was under previous regimes.

Complexity now become much more costly. The desks that are most likely to fail PnL explains are the most complex cross-asset desks, with plenty of cross gamma. The failure is also most likely in the times of stress, when correlations break down. Once such a desk moves to SA, even for a month (and likely it would be for more), it becomes very costly indeed, as in addition to the higher SA charge, any cross-asset hedging or diversification the desk contained is lost – SA does not recognise any interplay between assets.

Even a complex organisational structure can become costly. If we assume that the PnL explain was calibrated to 99% confidence interval (i.e. 1% chance of a desk having to move to SA in any given twelve montsh period), 10 desks – in my opinion a minimum when IMA accreditation makes economic sense – have about one in ten chance of a desk being forced to SA over twelve months (the check is carried monthly, thus the chance is 1-0.99^12). 20 desks just over 18% chance. Of course, to get a better-then-even chance a FI would have to have more than 70 desks, but even so, the probabilities of having a trading desk on SA even with very good explains are non trivial.

I believe that all of the above is the intention of the regulation, so to say, a feature, not a bug.

The regulation also singles out securitization, which can be capitalised only using SA approach. This has some implications both on treasury business which buys and holds these securities, and potentially even larger impact on market makers, especially for the lower tranches of the more obscure ABSes.[13]

In the past, calculating VaR was often computationally expensive. While new ES measure on its own is no more computationally expensive than VaR, the numerous variations forced by different liquidity horizons, asset classes and full/scaled risk factor sets serve as a massive multiplier of the number of recalculation for the whole portfolio.  In the worst case, a trade may need up to 63 ES calculations, each for 250 business days. That translates into potentially more than 15,000 valuations[14] of a trade, which may require institutions to reevaluate their IT framework.

Indeed, it may lead to reevaluation of the need to use IMA, as the extra operational costs of doing so could in some cases outstrip the capital savings.

Institution may wish to revisit how they deal with trading limits. Historically, VaR limits were often used, but VaR is not sub-additive (i.e. VaR of two combined portfolios can be higher than any of the individual portfolios), while ES is. Of course, it’s conceivable that institutions may wish to have both VaR and ES limits, at least for a period of time.

Similarly, institutions using SA extensively may have to think about their limit structures, as SA is calculated on a consolidated portfolio. Thus SA charges on individual desks can be significantly misleading unless the risks in the desks is cleanly separated along FRTB asset classes.

Republished from

[1] Fortunately, it is not required to continue calculations on the moved positions as if it still was in a trading book, as that would introduce high level of complexity.

[2] And hence requiring a full revaluation, not just a sensitivity approximation.

[3] So that both hedging and diversification benefits are recognised.

[4] Both exclusive of default risk charges and NMRF/RAO.

[5] Undoubtedly, there will be a grey area as to what is or isn’t exotic.

[6] To do differently would present substantial problems for the long holding periods, especially the 120 days one.

[7] The reduced set must explain at least 75% of the variation of full risk-factor set.

[8] Which in itself is a comes from a formula taking ES charges for liquidity horizons.

[9] For a desk to be allowed to use IMA, it must be included both in ES and IMA default charge calculation.

[10] 24 observations in last 12 months which must be less than a month apart. This in practice mandates using proxies for any new debt or equity issuances for at least their first month.

[11] For which the only requirement is to be “as prudent as ES scenario used for modelled risks”

[12] For example, FRTB requires that the PnL explain based on risk factors is carried out using market risk models, not front office models. A number of banks may be currently using front-office risk sensitivities (and hence models) for PnL explain, and as a result may need to change their process.

[13] Holders of AAA prime-RMBS tranches are unlikely to be affected much, as these are usually floating notes.

[14] In reality, some of the asset classes do not have long liquidity horizons, and may have few if any risk factors removed. All of this would reduce number of valuations needed. 15000 is a worst-case estimate.

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