Equity Approach Specification¶
Equity exposure treatment under SA and IRB, including CIU look-through and Basel 3.1 transitional schedule.
Regulatory Reference: CRR Articles 132 (omitted)–133, 155; PRA PS1/26 Articles 132–132C, 133, 147A
Test Group: CRR-J
Regulatory History — UK CRR Art. 132 / 132a omitted
UK CRR has no live Art. 132, 132a, 132A, or 132B. Article 132 ("Exposures in the form of units or shares in CIUs") and Article 132a ("Approaches for calculating risk-weighted exposure amounts of CIUs") were omitted from UK CRR by SI 2021/1078, regs. 1(1), 6(3)(b)–(c), effective 1 January 2022. From 1 Jan 2022 to 31 Dec 2026, the equivalent CIU rules are housed in the PRA Rulebook (CRR firms — Standardised Approach Part) rather than CRR itself.
Pre-omission paragraph structure of Art. 132 contained paragraphs (1)–(5), with paragraph (4) covering the look-through approach and paragraph (5) covering the mandate-based approach (Annex III correlation table, page 451 of the UK-onshored CRR PDF, references Art. 132(4) and Art. 132(5) explicitly). Some later versions of EU CRR (post-CRR2 amendment by Reg. 2017/2401) split these into Art. 132 + Art. 132a; UK onshoring omitted both.
Article 132A and Article 132B are Basel 3.1 (PRA PS1/26) constructs, not CRR articles:
- PRA PS1/26 Art. 132A — Approaches for calculating risk-weighted exposure amounts of CIUs (look-through = Art. 132A(1); mandate-based = Art. 132A(2)).
- PRA PS1/26 Art. 132B — Exclusions from the approaches for calculating risk-weighted exposure amounts of CIUs (separate exclusion treatment, not a CRM equivalent).
- PRA PS1/26 Art. 132C — Treatment of off-balance sheet exposures to CIUs.
These come into force on 1 January 2027. See Basel 3.1 Equity Approach Specification for the B31 treatment.
Within this CRR specification, references to the look-through and mandate-based approaches use the pre-omission Art. 132(4) and Art. 132(5) citations.
Requirements Status¶
| ID | Requirement | Priority | Status |
|---|---|---|---|
| FR-1.7 | Equity risk weights: SA (Art. 133) and IRB Simple (Art. 155) | P1 | Done |
| FR-1.7a | Basel 3.1 equity SA weights (Art. 133(3)-(6)) | P1 | Done |
| FR-1.7b | CIU treatment (CRR Art. 132 (omitted, pre-omission paras (4)–(5)); PRA PS1/26 Art. 132A / 132B) | P2 | Done |
| FR-1.7c | Equity transitional schedule (PRA Rules 4.1-4.3) | P2 | Done |
CRR SA Equity Risk Weights (Art. 133)¶
Art. 133(2): "Equity exposures shall be assigned a risk weight of 100%, unless they are required to be deducted in accordance with Part Two, assigned a 250% risk weight in accordance with Article 48(4), assigned a 1250% risk weight in accordance with Article 89(3) or treated as high risk items in accordance with Article 128."
| Equity Type | Risk Weight | Reference |
|---|---|---|
| Central bank / sovereign equity | 0% | Sovereign treatment |
| All other equity (listed, unlisted, PE, etc.) | 100% | Art. 133(2) flat |
| CIU (fallback) | 1,250% | Art. 132(2) (pre-omission) |
| CIU (look-through) | Underlying RW | Art. 132(4) (pre-omission) |
| CIU (mandate-based) | Mandate RW | Art. 132(5) (pre-omission) |
Previous Spec Error Corrected
This table previously claimed CRR Art. 133 had differentiated weights: unlisted=150% (Art. 133(3)) and PE/VC=190% (Art. 133(4)). These paragraph numbers and values were fabricated. CRR Art. 133 has only 3 paragraphs and assigns a flat 100% to all equity. The 150%/190% values are from Art. 155 (IRB Simple Method), not Art. 133. Under the Art. 112 Table A2 waterfall, equity (priority 3) takes precedence over high-risk items (priority 4). PE/VC is classified as equity under Art. 133, not as a high-risk item under Art. 128. Note: Art. 128 was omitted from UK CRR by SI 2021/1078 (effective 1 Jan 2022) and is only active under Basel 3.1 (from 2027).
Basel 3.1 SA Equity Risk Weights (PRA PS1/26 Art. 133)¶
Significant increase in equity risk weights under Basel 3.1:
| Equity Type | Risk Weight | Reference |
|---|---|---|
| Standard equity (listed, exchange-traded) | 250% | Art. 133(3) |
| Higher-risk equity | 400% | Art. 133(4) |
| Subordinated debt / non-equity own funds instruments | 150% | Art. 133(5) |
| Legislative equity (carve-out, see below) | 100% | Art. 133(6) |
Correction: PRA vs BCBS Equity Categories
- No "CQS 1-2 speculative" tier in PRA: The BCBS framework (CRE60.20) includes speculative unlisted equity tiers differentiated by CQS. PRA PS1/26 Art. 133 does not include these tiers — all non-legislative, non-subordinated equity is either standard (250%, Art. 133(3)) or higher-risk (400%, Art. 133(4)).
- Higher-risk definition: Under PRA PS1/26 Glossary (p.5), "higher risk equity exposure" means equity that is (1) not listed on a recognised exchange AND (2) the underlying business has existed for less than five years. PE/VC is only higher-risk if it meets both criteria — there is no automatic PE/VC = 400% rule. The prior definition here (short-term resale / derivative position / PE-VC) was the BCBS CRE60.20 definition, not PRA.
- Art. 133(5) is subordinated debt / non-equity own funds: 150% risk weight for subordinated debt and capital instruments that are not classified as equity exposures.
- Art. 133(6) is a carve-out: Legislative equity at 100% is a carve-out for government-mandated holdings (e.g., holdings required by national development policy legislation). It is not a general 100% weight category.
Classification Decision Tree¶
Is it subordinated debt / non-equity own funds instruments?
→ Yes: 150% (Art. 133(5))
Is it legislative equity (government-mandated, Art. 133(6) carve-out)?
→ Yes: 100% (Art. 133(6))
Is it listed on a recognised exchange?
→ Yes: 250% (Art. 133(3))
Is it higher risk (unlisted AND business < 5 years)?
→ Yes: 400% (Art. 133(4))
Otherwise (unlisted, business ≥ 5 years, including PE/VC not meeting higher-risk criteria):
→ 250% (Art. 133(3))
Unlisted Non-Higher-Risk Treatment
Unlisted equity where the business has existed for five years or more receives the standard 250% weight under Art. 133(3), including PE/VC holdings in established businesses. Only unlisted equity in undertakings whose business has existed for less than five years qualifies as higher-risk (400%). The BCBS framework would differentiate via CQS speculative tiers, but PRA does not use that structure.
CRR IRB Equity Approaches (Art. 155)¶
Art. 155(1) gives firms with IRB permission three approaches for equity, to be chosen consistently and not for regulatory arbitrage:
- Simple Risk Weight Approach (Art. 155(2))
- PD/LGD Approach (Art. 155(3))
- Internal Models Approach (Art. 155(4))
Equity exposures deducted under Part Two or assigned 250% under Art. 48 are excluded from Art. 155 altogether.
Simple Risk Weight Approach — Art. 155(2)¶
| Equity Category | Risk Weight | Reference |
|---|---|---|
| Private equity in sufficiently diversified portfolios | 190% | Art. 155(2), RW bullet 1 |
| Exchange-traded equity | 290% | Art. 155(2), RW bullet 2 |
| All other equity exposures | 370% | Art. 155(2), RW bullet 3 |
Short cash positions and derivatives held in the non-trading book may offset long positions in the same individual stock provided the hedge is explicit and covers at least one year. Other short positions are treated as long with the relevant RW applied to their absolute value.
PD/LGD Approach — Art. 155(3)¶
Under the PD/LGD approach, equity risk-weighted exposure amounts are calculated using the
Art. 153(1) corporate IRB formula (same K × 12.5 × 1.06 × EAD × MA mechanics), with
equity-specific PD floors (Art. 165(1)) and LGD values (Art. 165(2)):
| Equity Category | PD Floor (Art. 165(1)) | LGD (Art. 155(3) / 165(2)) |
|---|---|---|
| Exchange-traded, long-term customer relationship | 0.09% | 90% (65% if in sufficiently diversified PE portfolio, Art. 155(3)) |
| Non-exchange-traded, returns from regular/periodic cash flows (not capital gains) | 0.09% | 90% (65% if diversified) |
| Exchange-traded equity (other short positions in Art. 155(2)) | 0.40% | 90% (65% if diversified) |
| All other equity exposures | 1.25% | 90% (65% if diversified) |
Key rules (Art. 155(3)):
M = 5 yearsfor all equity under PD/LGD (Art. 165(3)).- Where the firm does not have sufficient information to use the default definition in Art. 178, a scaling factor of 1.5 is applied to the risk weights.
- The per-exposure capital is capped:
EL × 12.5 + RWEA ≤ EAD × 12.5— i.e. the PD/LGD output cannot require more capital than a 100% loss assumption. - Unfunded credit protection may be recognised per Chapter 4 but the guarantor LGD is 90% (65% only if the hedged exposure is PE in a sufficiently diversified portfolio).
- EL = PD × LGD (using the Art. 165 PD floor and the relevant 65%/90% LGD); EL is not deducted — for equity, EL enters the expected-loss cover test against provisions under the general IRB machinery.
Internal Models Approach — Art. 155(4)¶
The IMA risk-weighted exposure amount is 12.5 × potential loss on the institution's equity exposures, where potential loss is derived from an internal VaR model at the 99th percentile, one-tailed confidence level on the difference between quarterly returns and an appropriate risk-free rate, computed over a long-term sample period.
Floor (Art. 155(4)): The portfolio-level RWEA under IMA must not be lower than the sum of:
- the RWEA that would be produced under the PD/LGD approach (Art. 155(3)), and
- the corresponding expected-loss amounts × 12.5,
each computed using the Art. 165(1) PD values and Art. 165(2) LGD values.
IMA requires PRA permission (embedded in the general Art. 143 IRB permission). Unfunded credit protection may be recognised on an equity position.
Art. 165 — Equity Minimum PD Values and LGDs¶
Art. 165 sets the IRB equity-specific inputs referenced by Art. 155(3) and (4):
| Paragraph | Parameter | Value(s) |
|---|---|---|
| 165(1)(a) | PD floor — exchange-traded, long-term customer relationship | 0.09% |
| 165(1)(b) | PD floor — non-exchange-traded, returns from regular cash flows | 0.09% |
| 165(1)(c) | PD floor — exchange-traded equity incl. other short positions (155(2)) | 0.40% |
| 165(1)(d) | PD floor — all other equity incl. other short positions (155(2)) | 1.25% |
| 165(2) | LGD — private equity in sufficiently diversified portfolios | 65% |
| 165(2) | LGD — all other equity exposures | 90% |
| 165(3) | Maturity for all equity exposures | M = 5 years |
The 0.09% / 0.40% / 1.25% values in Art. 165(1) are the PD floors used inside Art. 155(3) (PD/LGD) and as inputs to the Art. 155(4) IMA floor; they do not modify the flat risk weights of Art. 155(2), which are already calibrated.
Art. 153(3) — Double-Default Adjustment for Guaranteed Exposures¶
Art. 153(3) provides a double-default credit-protection adjustment for IRB exposures (including equity under Art. 155(3)) meeting the Articles 202 and 217 requirements on the guarantor and the protection contract:
where PD_pp is the PD of the protection provider and RW is the risk weight computed
from the obligor's PD but the guarantor's LGD (comparable direct exposure). The maturity
factor b uses the lower of the obligor and protection-provider PD.
Double-default — practical status
The full Art. 153(3) formula is recorded here for completeness; the current calculator
does not apply the (0.15 + 160 × PD_pp) double-default adjustment and instead falls
back to Art. 236 parameter substitution or Art. 235 risk-weight substitution. Under
PRA PS1/26 (Basel 3.1), Art. 153(3) is "[Provision left blank]" and the double-default
treatment is removed entirely.
IRB Equity Removal Under Basel 3.1¶
Under Basel 3.1 (PRA PS1/26 Art. 147A), all three IRB equity approaches (Simple, PD/LGD, Internal Models) are removed. All equity exposures must use SA risk weights (Art. 133). This is a mandatory restriction — firms cannot opt to continue using IRB equity methods.
CIU Treatment (Pre-omission Art. 132)¶
Collective Investment Undertakings (CIUs / funds) have three possible treatments under the pre-omission UK CRR Art. 132 framework. Recall that Art. 132 was omitted from UK CRR by SI 2021/1078 with effect from 1 January 2022; the paragraph references below are the pre-omission citations preserved here for historical and pre-2022 reporting completeness. The equivalent live UK rules through 31 December 2026 sit in the PRA Rulebook (CRR firms — Standardised Approach Part); from 1 January 2027 they are reintroduced as PRA PS1/26 Art. 132A (look-through and mandate-based) and Art. 132B (exclusions) — see Basel 3.1 Equity Approach Specification.
Look-Through Approach (pre-omission Art. 132(4))¶
Where the firm has sufficient information about the CIU's underlying holdings:
- Each underlying exposure is risk-weighted as if directly held
- The CIU's leverage is applied to gross up the risk weights
- Requires daily knowledge of the fund's composition
Reintroduced under Basel 3.1 as PRA PS1/26 Art. 132A(1) (and Art. 152(4) for IRB CIUs).
Mandate-Based Approach (pre-omission Art. 132(5))¶
Where full look-through is not available but the fund's mandate is known:
- The fund is assumed to invest to the maximum extent permitted by its mandate in the highest-risk asset class
- Then the next highest-risk class, and so on until the maximum total investment capacity is filled
- This produces a conservative weighted-average risk weight
Reintroduced under Basel 3.1 as PRA PS1/26 Art. 132A(2) (and Art. 152(5) for IRB CIUs).
Fallback Approach (pre-omission Art. 132(2))¶
Where neither look-through nor mandate-based approaches are feasible:
| CIU Type | CRR Risk Weight | Basel 3.1 Risk Weight |
|---|---|---|
| Standard CIU fallback | 1,250% | 1,250% |
The 1,250% fallback originates from CRR2 (Regulation 2019/876) and is carried forward unchanged in PRA PS1/26 Art. 132(2). This is a punitive weight designed to incentivise firms to use look-through or mandate-based approaches.
PRA PS1/26 Art. 132B Exclusion — Not the Same as Fallback
Under Basel 3.1, certain CIU equity exposures are excluded from CIU treatment by Art. 132B (e.g., 0% sovereign entities, legislative programme holdings) and instead receive standard Art. 133 equity treatment: 100% (CRR) / 250% listed or 400% unlisted (Basel 3.1). These are NOT the Art. 132(2) "fallback" — they are reclassified equity exposures. Art. 132B has no CRR equivalent; under UK CRR the analogous exclusion criteria sat within the omitted Art. 132 itself (and now within the PRA Rulebook).
Fixed in v0.1.181
The CIU fallback is correctly applied as 1,250% for both CRR and Basel 3.1,
matching Art. 132(2). Prior to v0.1.181 the code incorrectly applied Art. 133
equity weights (150% CRR / 250%–400% Basel 3.1) for ciu_approach = "fallback".
Equity Transitional Schedule (PRA Rules 4.1–4.10)¶
PRA PS1/26 provides a transitional phase-in for the increased equity risk weights from 2027 to 2030. The transitional has two distinct pathways depending on whether the firm had IRB permission at 31 December 2026.
SA Transitional (Rules 4.1–4.3) — Firms Without IRB Permission¶
Rule 4.1 restricts Rules 4.2–4.3 to firms that did not have IRB permission under Art. 143 of CRR on 31 December 2026.
Standard equity (Rule 4.2 — modifies Art. 133(3)):
| Period | Risk Weight |
|---|---|
| 2027 | 160% |
| 2028 | 190% |
| 2029 | 220% |
| 2030+ (Steady state) | 250% |
Higher-risk equity (Rule 4.3 — modifies Art. 133(4)):
| Period | Risk Weight |
|---|---|
| 2027 | 220% |
| 2028 | 280% |
| 2029 | 340% |
| 2030+ (Steady state) | 400% |
IRB Transitional (Rules 4.4–4.6) — Firms With IRB Permission¶
Rule 4.4 scopes Rules 4.5–4.6 to firms that had IRB permission on 31 December 2026. These firms bifurcate their equity portfolio per Rule 4.5:
- SA equities (Rule 4.5(1)): Equity exposures on the Standardised Approach (Art. 148/150) at 31 Dec 2026 use the same phase-in schedule as Rules 4.2/4.3 above.
- IRB equities (Rules 4.5(2) + 4.6): Equity exposures on IRB at 31 Dec 2026 use the
higher of:
- the risk weight from the firm's legacy IRB methodology (Art. 155, as in force on 31 Dec 2026), and
- the transitional SA risk weight from Rules 4.2/4.3.
CIU Transitional (Rules 4.7–4.8)¶
During the 3-year transition period (2027–2029), Rules 4.7–4.8 apply to firms with IRB permission at 31 December 2026. CIU equity underlyings that were subject to the simple risk weight approach (Art. 155(2)) use the higher of the old simple risk weight and the transitional SA equity weight from Rules 4.2/4.3.
Opt-Out (Rules 4.9–4.10)¶
Firms may elect to skip the transitional and apply full Basel 3.1 steady-state weights (Art. 133: 250%/400%) immediately. This election is irrevocable and requires prior PRA notification. The opt-out covers both direct equity (Rules 4.5–4.6) and CIU underlyings (Rule 4.8).
Transitional Scope
The transitional is time-period-based, not vintage-based — all equity exposures receive the transitional weight applicable to the reporting period, regardless of when they were acquired. The schedule does not apply to legislative equity (100%, Art. 133(6)) or subordinated debt (150%, Art. 133(5)).
See the Basel 3.1 Equity Approach Specification for detailed requirements and acceptance test scenarios.
Key Scenarios¶
CRR SA Equity (Art. 133) — CRR-J1 to CRR-J9¶
| Scenario ID | Description | Equity Type | EAD | Expected RW | Expected RWA |
|---|---|---|---|---|---|
| CRR-J1 | Listed equity SA | listed |
£500,000 | 100% | £500,000 |
| CRR-J2 | Unlisted equity SA | unlisted |
£300,000 | 100% | £300,000 |
| CRR-J3 | Exchange-traded equity SA | exchange_traded |
£200,000 | 100% | £200,000 |
| CRR-J4 | Private equity SA | private_equity |
£100,000 | 100% | £100,000 |
| CRR-J5 | Government-supported equity SA | government_supported |
£400,000 | 100% | £400,000 |
| CRR-J6 | Speculative equity SA | speculative |
£150,000 | 100% | £150,000 |
| CRR-J7 | Central bank equity SA (sovereign treatment) | central_bank |
£1,000,000 | 0% | £0 |
| CRR-J8 | Subordinated debt SA | subordinated_debt |
£250,000 | 100% | £250,000 |
| CRR-J9 | CIU fallback SA (Art. 132(2)) | ciu |
£600,000 | 1,250% | £7,500,000 |
CRR IRB Simple Equity (Art. 155) — CRR-J10 to CRR-J14¶
| Scenario ID | Description | Equity Type | Key Flags | EAD | Expected RW | Expected RWA |
|---|---|---|---|---|---|---|
| CRR-J10 | Exchange-traded equity IRB Simple | exchange_traded |
is_exchange_traded=True |
£200,000 | 290% | £580,000 |
| CRR-J11 | Diversified PE equity IRB Simple | private_equity |
is_diversified=True |
£100,000 | 190% | £190,000 |
| CRR-J12 | Other (unlisted) equity IRB Simple | unlisted |
— | £100,000 | 370% | £370,000 |
| CRR-J13 | Central bank equity IRB Simple (sovereign treatment) | central_bank |
— | £500,000 | 0% | £0 |
| CRR-J14 | Government-supported equity IRB Simple | government_supported |
is_government_supported=True |
£300,000 | 190% | £570,000 |
CRR-J14 Government-Supported Mapping
The calculator maps government_supported to Art. 155(2)(b) (diversified PE) at 190%.
Art. 155 has no "government-supported" category — only exchange-traded (a), PE diversified (b),
and all other (c). See D3.4 for the code mapping issue.
CIU Specific Tests — CRR-J15 to CRR-J17¶
| Scenario ID | Description | CIU Approach | Key Parameters | EAD | Expected RW | Expected RWA |
|---|---|---|---|---|---|---|
| CRR-J15 | CIU mandate-based SA (pre-omission Art. 132(5)) | mandate_based |
ciu_mandate_rw=0.80 |
£200,000 | 80% | £160,000 |
| CRR-J16 | CIU mandate-based + third-party 1.2× multiplier | mandate_based |
ciu_mandate_rw=0.80, ciu_third_party_calc=True |
£200,000 | 96% | £192,000 |
| CRR-J17 | CIU no approach set (default fallback) | None |
— | £100,000 | 1,250% | £1,250,000 |
CRR-J16 calculation: the 1.2× third-party multiplier (pre-omission Art. 132(5),
third sub-paragraph, third-party calculation provision) scales the mandate risk
weight: RW = 0.80 × 1.2 = 0.96 (96%). Under PRA PS1/26 the same 1.2×
multiplier sits in Art. 132A(2).
RWA Arithmetic Verification — CRR-J18 to CRR-J20¶
| Scenario ID | Description | Approach | EAD | Expected RW | Expected RWA |
|---|---|---|---|---|---|
| CRR-J18 | SA RWA arithmetic verification | SA | £1,234,567 | 100% | £1,234,567 |
| CRR-J19 | IRB Simple RWA arithmetic verification | IRB Simple | £750,000 | 370% | £2,775,000 |
| CRR-J20 | Zero EAD produces zero RWA | IRB Simple | £0 | 370% | £0 |
Basel 3.1 Equity Scenarios¶
Basel 3.1 equity scenarios are documented in the dedicated Basel 3.1 Equity Approach specification (test group B31-L).
Acceptance Tests¶
| Group | Scenarios | Tests | Pass Rate |
|---|---|---|---|
| CRR-J: Equity | J1–J20 | 32 | 100% |