Total market risk capital · RiskAtoms Academy

By the end you will be able to

1Build the bank's full standardised market risk capital and place Module 4.1's £417.7m in it.
2Aggregate capital when some desks use the internal model and others the SA, with the cap and the add-back.
3Compute the capital surcharge for amber desks and explain what it charges for.
4Explain why the SA stays essential for a bank with model permission.

Why it matters

From 1 January 2027 RiskAtoms Bank plc's market risk capital is the standardised approach: £39.657m, RWA £495.7m. The internal model of the last three lessons would give £35.465m once three desks pass its tests, a saving of £4.19m of capital, £52.4m of RWA. The rules do not simply add the model desks to the SA desks: they cap the total at the SA, add back anything the model charges above it, and make amber desks pay a surcharge. This lesson puts the pieces together.

Core explanation

From desk capital to one number

Illustrative dataRiskAtoms Bank plc's trading desk under the internal models approach

The same made-up Markets desk as Module 3.2: eight positions on four desks (Equities, Rates, FX and commodities, Credit), eight risk factors and 750 days of seeded history with a stressed spell, every position revalued in full. Figures are in £ millions at 31 December 2025.

Every internal-model figure is illustrative. The UK internal model approach for market risk starts on 1 January 2028 (PRA PS1/26, para 1.24), and the bank has no model permission: its capital is the standardised approach of the earlier lessons. The pages show what the bank's models would give if it had one.

The SA figures on this page are the bank's capital from 1 January 2027. The IMA figures, and the aggregate built from them, are illustrative.

Where £417.7m sits

L4.1.04: Risk-weighted assets gave the bank's market risk RWA as £417.65m. That is the SBM alone, its high-correlation scenario binding. The full SA adds the DRC and the RRAO of L4.3.04: Default risk charge and residual risk add-on:

RWA = 12.5 × capital. Module 4.1 is short by £78.06m of RWA, almost all of it DRC.
Component	Capital, £m	RWA, £m
SBM (Module 4.1)	33.412	417.65
DRC	6.140	76.75
RRAO	0.105	1.31
Full SA	39.657	495.71

Desk by desk

Each desk can be costed both ways. On its own, the model is cheaper than the SA for Rates and Credit and dearer for Equities and FX and commodities. The Equities desk on its own would have 5 backtesting exceptions and m_c = 1.70. FX and commodities has no default risk, so its comparison is ES against its SBM of 6.429 plus its RRAO of 0.100.

£m. The IMA column is each desk alone, with its own multiplier: a comparison, not the rule. The rules aggregate the model desks together.
Desk	SA: SBM + DRC + RRAO	IMA alone: C_A + DRC	Cheaper
Equities	16.405	11.902 + 6.0 = 17.902	SA
Rates	9.401	4.498 + 0.0 = 4.498	IMA
FX and commodities	6.529	8.298 + 0.0 = 8.298	SA
Credit	16.862	5.965 + 6.0 = 11.965	IMA

Adding desks loses diversification. The four desks' SA, one by one, sums to £49.197m; on the whole book it is £39.657m. The same holds for the model. So the rules take the model desks as one group.

The aggregation

L4.3.07: Backtesting and the P&L attribution test left three desks on the model: Equities and Credit green, Rates amber. FX and commodities failed the P&L attribution test and uses the SA. Three numbers come from the two approaches (MAR33.41–33.45):

IMA_G,A, the model capital of the three model desks together: C_A = 15.891, worked below with the IMCC recomputed on the three model desks alone (10.071, not the whole-desk figure of L4.3.05: Internal models: expected shortfall), plus the IMA DRC of 12.0 from L4.3.06: Non-modellable risk factors and the internal DRC, so £27.891m.
SA_G,A, the same three desks under the SA: £37.371m.
C_U, the SA of the desks off the model, FX and commodities: £6.529m.

The aggregate capital requirement is then

\text{ACR} = \min\big(\text{IMA}_{G,A} + \text{surcharge} + C_U,\ \text{SA}_{\text{all}}\big) + \max\big(\text{IMA}_{G,A} - \text{SA}_{G,A},\ 0\big)

Each piece of M-A11: Min, max, floors and caps does a job. The min is a cap: whatever the mix, the bank never holds more than the full SA because some desks are on the model. The max is a floor on the add-back: if the model charges more than the SA on its own desks, the excess comes back on top, so the cap cannot make a cautious model cheaper. And the capital surcharge gives back part of the model's saving when desks are amber:

\text{surcharge} = k \times \max\big(\text{SA}_{G,A} - \text{IMA}_{G,A},\ 0\big), \qquad k = 0.5 \times \frac{\sum_{i \in \text{amber}} \text{SA}_i}{\sum_{i \in G,A} \text{SA}_i}

On the book, the Rates desk's stand-alone SA of 9.401 is 22.0% of the model desks' 42.668, so k = 0.1102 and the surcharge is 0.1102 × (37.371 − 27.891) = £1.044m. Then ACR = min(27.891 + 1.044 + 6.529, 39.657) + 0 = £35.465m, RWA £443.31m.

IMA_G,A (3 model desks)

£27.891m

Surcharge (Rates amber)

£1.044m

C_U (FX and commodities)

£6.529m

ACR

£35.465m

Full SA: £39.657m

The SA never goes away

A bank with model permission still runs the SA on every desk. The aggregation needs SA_G,A, C_U, SA_all and each amber desk's SA; a desk that fails its tests falls back to the SA at once; and the Basel Committee revised the SA in 2019 partly so that it could serve as a credible fall-back to the models. There is a floor on the model's weight too: the desks passing both tests must carry at least 10% of the aggregate capital, or the bank uses the SA for the whole book (MAR32.2). Here IMA_G,A is 78.6% of the ACR, the reading this page takes of that test.

Questions on the book

The formal version

For the model desks G,A (green or amber, passing backtesting), the amber desks Y and the SA desks U, with m_c from the bank-wide backtest (MAR33.41–33.45; PRA Rulebook, IMA Part, Article 325ba(1)–(5)):

\begin{aligned} C_A &= \max\big(\text{IMCC}_{t-1} + \text{SES}_{t-1},\ m_c \cdot \overline{\text{IMCC}} + \overline{\text{SES}}\big) \\ \text{IMA}_{G,A} &= C_A + \text{DRC}_{\text{IMA}} \\ k &= 0.5 \cdot \frac{\sum_{i \in Y} \text{SA}_i}{\sum_{i \in G,A} \text{SA}_i}, \qquad \text{surcharge} = k \cdot \max\big(\text{SA}_{G,A} - \text{IMA}_{G,A},\ 0\big) \\ \text{ACR} &= \min\big(\text{IMA}_{G,A} + \text{surcharge} + C_U,\ \text{SA}_{\text{all}}\big) + \max\big(\text{IMA}_{G,A} - \text{SA}_{G,A},\ 0\big) \end{aligned}

Averages are over 60 business days (IMCC, SES) and 12 weeks (DRC, which takes the greater of the latest and the average). SA_i is each desk's stand-alone SA; SA_G,A, C_U and SA_all are SA on each group taken together. If IMA_G,A ≤ SA_G,A the ACR is at most SA_all.

Try it

Start from the book. Turn Rates green and watch the surcharge go; push the exceptions up and see where the cap at the full SA starts to bind. Then put only one desk on the model, amber, and see k reach 0.5.

Try itAggregate the bank's market risk capital

Equities

Rates

FX & comm.

Credit

Bank-wide backtesting exceptions of the model desks (99%, 250 days)2 → m_c 1.50

The slider starts at the model desks' own count; a red desk leaves the model and goes to the SA.

Desks on the model3

C_U (the SA desks together)£6.529m

C_A: m_c × average IMCC + SES binds£15.891m

+ IMA DRC£12.000m

IMA_G,A£27.891m

SA_G,A (model desks under the SA)£37.371m

Surcharge: k = 0.1102£1.044m

Cap: not binding£35.465m

+ max(IMA_G,A − SA_G,A, 0)£0.000m

Model desks' share of ACR78.6%

RWA (12.5 × ACR)£443.3m

ACR£35.465m

IMA_G,A

£27.89m

Surcharge

£1.04m

C_U

£6.53m

ACR

£35.46m

SA, whole book: £39.66m

Zones now:Equities greenRates amberFX & comm. redCredit green

A desk's zone here is its PLA zone; every desk is assumed to pass desk-level backtesting. The IMA figures for each group of desks (IMCC, SES, DRC) are computed in advance from the book. Illustrative, £ millions.

Worked example

Aggregating the book

31 December 2025, illustrative, £m.

ACR for RiskAtoms Bank plc

Step 1 of 5

1
C_A
IMCC 10.071, SES 0.785, 2 exceptions so m_c = 1.5: $C_A = \max(10.071 + 0.785,\ 1.5 \times 10.071 + 0.785) = \text{£}15.891\text{m}$ . The averaged term binds.

£m, from the same pinned figures as the Try it
What if	m_c	Surcharge	Cap binds	ACR
The book: Rates amber, FX and commodities red	1.50	1.044	no	35.465
Rates fixed to green: no surcharge	1.50	0.000	no	34.420
FX and commodities fixed too: all four on the model	1.50	0.000	no	31.655
As the book, but 6 exceptions: m_c 1.76	1.76	0.756	no	37.795
As the book, but 10 exceptions: m_c 2.0	2.00	0.490	yes	39.657
Only Rates on the model, amber	1.50	2.452	yes	39.657

Regulatory lens

Basel: MAR33.41–33.45 and MAR32.2. Status as at 3 November 2026 as at 3 Nov 2026.

In the UK

The standardised approach (the PRA's ASA) applies from 1 January 2027 (PS1/26, para 1.23) and the internal model approach from 1 January 2028 (para 1.24). The aggregation, with the surcharge for desks in the yellow zone, is in the PRA Rulebook's Market Risk: Internal Model Approach (CRR) Part, Article 325ba. The PRA keeps central government and central bank exposures out of the IMA DRC (PS17/23, para 3.41; L4.3.06: Non-modellable risk factors and the internal DRC), so the book's UK IMA_G,A would differ; the figures here follow Basel. The PRA's CP9/26 (June 2026) proposes to replace C_U, the stand-alone SA of the non-model desks, with the full SA less the SA of the model desks, keeping the SA's diversification between the two groups, and to replace the cap at the full SA with a permission to apply one (paras 2.26–2.27). On the book that C_U would be £2.286m instead of £6.529m, and the ACR about £31.22m. Not final as at 3 November 2026.

In the EU

The market risk rules, the internal model approach included, apply from 1 January 2027 after two postponements (Delegated Regulation (EU) 2026/1221, recital 2). Until 31 December 2029 the same regulation lets desks that fail the P&L attribution test keep the model (Article 495i), so failing that test does not by itself move a desk into C_U.

In the US

The agencies' proposals of 19 March 2026 would introduce a standardised approach for market risk “to serve as a credible fallback approach” and move the models approach from VaR to expected shortfall (Federal Reserve fact sheet, 19 March 2026). They were not final as at 3 November 2026 (L4.3.11: Market risk and CVA capital: what changes from 2027).

Spark Atoms

Spark AtomAdding up standalone SA costs diversification

The SA of the model desks together (37.371) plus the SA of FX and commodities alone (6.529) is 43.900, 4.243 more than the SA of the whole book. Splitting the book loses that diversification, which is why the cap at SA_all matters and why the PRA has proposed changing C_U.

Spark AtomA bad backtest year can wipe out the saving

With 6 exceptions m_c rises to 1.76 and the ACR to £37.795m; with 10 it is 2.0, the cap binds and the bank holds the full SA of £39.657m. With only Rates on the model, amber, k = 0.5 and the cap binds too: £39.657m.

Key takeaways

Module 4.1's £417.7m of RWA is the SBM alone. The full SA adds the DRC and RRAO: £39.657m of capital, RWA £495.71m.
Desks that pass backtesting and are green or amber in PLA are aggregated together under the model (IMA_G,A); the others use the SA together (C_U).
ACR = min(IMA_G,A + surcharge + C_U, SA_all) + max(IMA_G,A − SA_G,A, 0): a cap at the full SA and an add-back when the model charges more than the SA.
The surcharge is k × max(SA_G,A − IMA_G,A, 0), with k half the amber desks' share of the model desks' stand-alone SA.
On the book: IMA_G,A 27.891, surcharge 1.044, C_U 6.529, ACR 35.465 (RWA 443.31) against the SA of 39.657. Illustrative: the UK IMA starts in 2028.
The SA stays the fall-back and the benchmark: every model bank runs it on every desk.

Reaction

Check what stuck

Question 1 · objective 2

IMA_G,A is 20, SA_G,A is 30, C_U is 10, the SA of the whole book is 38 and the surcharge is 1 (all £m). What is the ACR?

Question 2 · objective 2

Now IMA_G,A is 32 (above SA_G,A of 30), C_U is 10, the SA of the whole book is 38 and there is no surcharge. What is the ACR?

Question 3 · objective 3

The model desks' stand-alone SA capital adds up to 40, of which 10 is on desks in the amber zone. What is k?

Question 4 · objective 1

Module 4.1 gave the bank's market risk RWA as £417.7m. Under the full SA, what does that figure leave out?

AThe DRC and the RRAO: the full SA adds £78.1m of RWABNothing: £417.7m is the full SACThe capital surchargeDThe internal model's DRC

Question 5 · objective 3

On the book, the Rates desk moves from amber to green. What happens to the ACR, and why?

AIt falls by 1.044: k becomes 0, so the surcharge goesBIt rises: a green desk uses a higher multiplierCNothing: the zone only matters for red desksDIt falls to IMA_G,A alone

Glossary

Full standardised approach: Full standardised approach: SBM + DRC + RRAO on every trading desk (MAR20–23). It is the bank's capital until it has model permission, and the benchmark and fall-back once it does.
IMA_G,A: IMA_G,A: internal-model capital of the desks in the green or amber PLA zone that pass backtesting, taken together: C_A (expected shortfall and SES, with the multiplier) plus the IMA DRC (MAR33.41–33.43).
SA_G,A: SA_G,A: the standardised capital of the same model desks, taken together as if they used the SA.
C_U: C_U: the standardised capital of the desks that do not use the model, taken together.
Capital surcharge: Capital surcharge: k × max(SA_G,A − IMA_G,A, 0), with k half the amber desks' share of the model desks' stand-alone SA. It charges back part of the model's saving when desks are amber (MAR33.43–33.45).
Aggregate capital requirement (ACR): Aggregate capital requirement (ACR): min(IMA_G,A + surcharge + C_U, SA_all) + max(IMA_G,A − SA_G,A, 0).

Deep Dives & Origins

Deep Dives

Basel Committee on Banking Supervision, Minimum capital requirements for market risk, January 2019 (d457): the revised framework and its explanatory note on the SA as a fall-back. Advanced.
Prudential Regulation Authority, CP9/26, June 2026, chapter 2: the proposed changes to the UK internal model approach, the aggregation among them. Advanced.

Origins

Basel Committee on Banking Supervision, MAR33, paras 33.41–33.45, and MAR32, para 32.2, bis.org (read in the Swiss SIF copy).
Prudential Regulation Authority, PRA Rulebook: Market Risk: Internal Model Approach (CRR) Part, Article 325ba, version from 1 January 2028; PS1/26, January 2026, paras 1.23–1.24; CP9/26, June 2026, paras 2.26–2.27.
Commission Delegated Regulation (EU) 2026/1221 of 4 June 2026, recital 2 and Article 495i.
Basel Committee on Banking Supervision, d457 publication page, January 2019.
Board of Governors of the Federal Reserve System, press release and fact sheet, 19 March 2026.

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