Equity Exposures¶

Equity exposures receive dedicated risk weight treatment separate from credit risk. Under CRR, the calculator supports SA (Article 133) and IRB Simple (Article 155). Under Basel 3.1, only SA applies.

Overview¶

Equity exposures are routed directly from classification to the equity calculator, bypassing CRM processing (collateral is not applied to equity holdings).

flowchart LR
    A[Classified Exposures] --> B{Exposure Class}
    B -->|Equity| C[Equity Calculator]
    B -->|Other| D[CRM Processor]
    C --> E[Aggregator]
    D --> E

CRR Article 133 - Standardised Approach (SA)¶

Under CRR, Art. 133(2) assigns a flat 100% risk weight to all equity exposures (except central bank sovereign equity at 0%). There is no differentiation by equity type — listed, unlisted, PE, and speculative all receive 100%.

Under Basel 3.1, equity that is unlisted and where the business has existed for less than five years is classified as "higher-risk" (400%, Art. 133(4)). PE/VC is only higher-risk if it meets both criteria — long-established PE holdings receive standard 250%.

Calculation:

RWA = EAD x Risk Weight

Article 155 - IRB Simple Risk Weight Method¶

For firms with IRB permission, a different risk weight schedule applies:

Diversified Portfolio Treatment¶

Private equity holdings in a diversified portfolio receive a reduced risk weight of 190% (vs 370% for non-diversified). This is flagged via the is_diversified_portfolio attribute.

Short-Position Netting (Art. 155(2))¶

Art. 155(2) permits limited netting of short equity positions against long positions under the Simple Risk Weight Approach. The conditions are strict:

• Same individual stock — short cash positions and derivatives held in the non-trading book may offset long positions in the same individual stock.
• Explicit hedge — the hedging relationship must be explicit (designated and documented), not an incidental offset.
• Minimum residual maturity of 1 year — the hedge must cover the long position for at least one year.

Short positions that do not meet these criteria are treated as if they were long positions, with the relevant Art. 155(2) risk weight applied to the absolute value of the short position. Netting cannot reduce the gross long exposure for risk-weighting purposes outside the explicit-hedge case.

PD/LGD Approach Per-Exposure Cap (Art. 155(3))¶

Firms with permission to use the Art. 155(3) PD/LGD approach for equity compute RWEA via the Art. 153(1) corporate IRB formula, using the equity-specific PD floors (Art. 165(1): 0.09% / 0.40% / 1.25%) and LGDs (Art. 165(2): 90%, or 65% for sufficiently diversified PE), with M = 5 years (Art. 165(3)).

CRR Art. 155(3) imposes an individual-exposure capital cap on the PD/LGD output:

EL × 12.5 + RWEA  ≤  EAD × 12.5

Equivalently, the total risk-based capital implied by a single equity exposure (expected-loss cover plus 8% × RWEA) cannot exceed a 100% loss assumption on the exposure value. This bites when the underlying PD and LGD combination would otherwise drive the per-exposure capital above one-for-one EAD coverage — typically only for near-default equity holdings.

The cap operates per individual exposure, not at portfolio level. It is the counterpart to (but distinct from) the portfolio-level IMA floor in Art. 155(4) below.

Worked Example — Non-Binding Case¶

Listed PE holding under PD/LGD, EAD = £100, PD = 0.40%, LGD = 90% (Art. 165(2) non-diversified), giving an Art. 153(1) RW ≈ 370% (illustrative — exact value depends on the corporate K-formula with the 0.40% PD floor):

RWEA      = £100 × 370%       = £370
EL        = £100 × 0.40% × 90% = £0.36
EL × 12.5 = £0.36 × 12.5      = £4.50
LHS       = £370 + £4.50      = £374.50
RHS       = £100 × 12.5       = £1,250
Cap       = LHS ≤ RHS         → not binding (£374.50 ≪ £1,250)

Worked Example — Binding Case¶

Same exposure but with PD = 80% (a near-default unrated holding) and the Art. 178 default-definition information condition unmet, so the 1.5× scaling factor in Art. 155(3) applies. With LGD = 90% and an illustrative scaled RW = 1,500% from the PD/LGD formula:

RWEA       = £100 × 1,500%     = £1,500
EL         = £100 × 80% × 90%  = £72
EL × 12.5  = £72 × 12.5        = £900
LHS        = £1,500 + £900     = £2,400
RHS        = £100 × 12.5       = £1,250
Cap        = LHS ≤ RHS         → BINDING (£2,400 > £1,250)

Capped RWEA = (RHS − EL × 12.5) = £1,250 − £900 = £350

Result: PD/LGD RWEA is reduced from £1,500 to £350 to satisfy the Art. 155(3) cap.

Internal Models Approach (Art. 155(4))¶

Firms with PRA permission for the IRB Internal Models Approach (IMA) for equity calculate RWEA as 12.5 × potential loss, where potential loss is derived from an internal VaR model at the 99th percentile, one-tailed confidence interval on the difference between quarterly returns and an appropriate risk-free rate, computed over a long-term sample period.

Art. 155(4) IMA floor — the IMA portfolio-level RWEA must not be lower than the floor computed as the sum of:

Floor RWEA (Art. 155(4)) = PD/LGD RWEA (Art. 155(3)) + EL × 12.5

where both PD/LGD RWEA and EL are computed using the Art. 165(1) PD floors and Art. 165(2) LGD values for equity. This is a portfolio-level floor that bites when the firm's internal VaR estimate is more optimistic than the regulatory PD/LGD output.

See the CRR Equity Approach Specification for the full IMA mechanics including Art. 165 PD floors and LGD values used in the floor computation.

Approach Determination¶

The equity approach depends on the regulatory framework and IRB permissions:

Example¶

Equity holding: Listed shares, £2m

SA Treatment (Article 133):

RWA = £2,000,000 x 100% = £2,000,000

IRB Simple Treatment (Article 155):

RWA = £2,000,000 x 290% = £5,800,000

Regulatory References¶