Provisions Specification¶

Basel 3.1 provision treatment: expected loss calculation with revised LGD parameters, Art. 158(6A) EL monotonicity, and EL shortfall/excess comparison.

Regulatory Reference: PRA PS1/26 Art. 158–159, Art. 36(1)(d), Art. 62(d) Test Group: B31-G

Requirements Status¶

Overview¶

Basel 3.1 modifies the provision and expected loss (EL) framework primarily through the reduction of F-IRB supervisory LGD from 45% to 40% for non-FSE senior unsecured exposures. This change flows through to the EL calculation, reducing expected loss estimates and consequently affecting the EL shortfall/excess comparison.

Key Changes from CRR¶

SA Provision Treatment (Unchanged)¶

For SA exposures, provisions are deducted from the exposure value before risk weighting:

EAD_net = EAD_gross - specific_provisions - other_provisions_allocated

This is the drawn-first deduction approach per Art. 111(1)(a)–(b):

1. Specific credit risk adjustments reduce the exposure value
2. General credit risk adjustments may be included in Tier 2 capital

No changes from CRR for the SA provision mechanism.

IRB Expected Loss Calculation¶

F-IRB Expected Loss¶

EL = PD x LGD x EAD

Where LGD is the supervisory LGD from the F-IRB Specification:

The reduction from 45% to 40% for non-FSE senior exposures directly reduces F-IRB expected loss by approximately 11% ((45−40)/45 ≈ 11.1%), leading to:

• Lower EL shortfall (or higher EL excess)
• More capital available as Tier 2 credit
• Structural reduction in the capital penalty for under-provisioned portfolios

A-IRB Expected Loss¶

A-IRB uses the firm's own LGD estimates, subject to LGD floors (see A-IRB Specification):

EL = PD x LGD_floored x EAD

Art. 158(6A) — EL Monotonicity¶

Basel 3.1 addition. When post-model adjustments (PMA) are applied to A-IRB exposures:

EL_adjusted >= EL_unadjusted

PMA can increase RWA and EL but must never decrease EL below the pre-adjustment level. This ensures that conservative overlays do not inadvertently reduce expected loss estimates.

EL Shortfall / Excess Comparison (Art. 159)¶

The comparison of total expected loss against total provisions determines the capital impact:

EL Excess (Provisions > EL)¶

When total provisions exceed total expected loss:

el_excess     = total_provisions - total_el
t2_credit_cap = 0.006 × IRB_credit_risk_RWA
t2_credit     = min(el_excess, t2_credit_cap)

The excess (up to the cap) is added to Tier 2 capital per Art. 62(d). See Art. 62(d) — T2 Cap on EL Excess below for the verbatim cap text and a worked example.

EL Shortfall (EL > Provisions)¶

When total expected loss exceeds total provisions:

el_shortfall   = total_el - total_provisions
cet1_deduction = el_shortfall      (full amount)

Art. 159 Component Definitions¶

The Art. 159 comparison uses four labelled amounts (A, B, C, D):

Art. 159(3) — Two-Branch Rule¶

The Art. 159 EL-vs-provisions test has two distinct branches depending on whether the non-defaulted (A vs B) and defaulted (D vs C) pools are aligned in sign.

Branch 1 — split branch (A > B AND D > C, simultaneously):
    negative amount = B − A    (non-defaulted shortfall)
    positive amount = D − C    (defaulted excess)

Branch 2 — combined branch (all other cases):
    if (A + C) > (B + D):
        negative amount = (B + D) − (A + C)
    if (B + D) > (A + C):
        positive amount = (B + D) − (A + C)

The split branch prevents specific CRAs on defaulted exposures from offsetting expected loss amounts on other (non-defaulted) exposures.

The negative amount is deducted in full from CET1 (Art. 36(1)(d)). The positive amount is admitted to T2 (Art. 62(d)), subject to the cap formalised below.

Art. 62(d) — T2 Cap on EL Excess¶

The Art. 159(3) positive amount (EL excess) flows into Tier 2 capital under Art. 62(d) of the Own Funds (CRR) Part of the PRA Rulebook, capped at:

T2_credit_cap = 0.006 × IRB_credit_risk_RWA      # 0.6% of IRB credit-risk RWA
T2_credit     = min(EL_excess, T2_credit_cap)

Worked example — both branches¶

Scenario A: combined branch with shortfall (CET1 deduction)

Inputs (£m):
  A = 100   (non-defaulted EL, with Art. 158(6A) PMA increase already applied)
  B =  60   (non-defaulted Pool B: GCRA + non-defaulted SCRA + AVA + other reductions)
  C =  40   (defaulted EL — BEEL × EAD for A-IRB; 1 × LGD × EAD for F-IRB)
  D =  30   (defaulted SCRA)
  IRB credit-risk RWA = 12,500

Branch test: A > B (100 > 60) AND D > C? D = 30, C = 40, so D < C.
  → Split branch does NOT apply. Use combined branch.

(A + C) − (B + D) = 140 − 90 = 50 > 0
  → Negative amount = (B + D) − (A + C) = −50.
  → CET1 deduction (Art. 36(1)(d)) = £50m.
  → No T2 credit. T2 cap not engaged.

Scenario B: combined branch with excess, cap binds

Inputs (£m):
  A =  60
  B = 100
  C =  20
  D =  40
  IRB credit-risk RWA = 8,000

(B + D) − (A + C) = 140 − 80 = 60 > 0
  → Positive amount (EL excess) = £60m.

T2 cap (Art. 62(d)):
  T2_credit_cap = 0.006 × £8,000m = £48m
  T2_credit     = min(£60m, £48m) = £48m   (cap binds — £12m of excess unrecognised)

Scenario C: split branch (Art. 159(3)(a)/(b))

Inputs (£m):
  A = 100   (non-defaulted EL)
  B =  60   (non-defaulted Pool B)
  C =  20   (defaulted EL)
  D =  50   (defaulted SCRA)
  IRB credit-risk RWA = 10,000

Branch test: A > B (100 > 60) AND D > C (50 > 20)? Yes — split branch applies.

Negative amount (a) = B − A = −40   (non-defaulted shortfall £40m)
Positive amount (b) = D − C =  30   (defaulted excess £30m)

Capital impact:
  CET1 deduction (Art. 36(1)(d)) = £40m   (full non-defaulted shortfall)
  T2 cap (Art. 62(d)) = 0.006 × £10,000m = £60m
  T2 credit          = min(£30m, £60m)   = £30m  (cap not binding)

Note: Cross-pool netting is precisely what Art. 159(3) split branch prohibits
— both the full £40m CET1 deduction and the £30m (capped) T2 credit flow
through. Under combined-branch netting the institution would have shown a
net £10m excess; the split branch instead recognises both legs separately.

Art. 159(2) — Exclusions from Provisions (B and D)¶

The following amounts are excluded from the provisions side (B and D):

• Defaulted balance sheet discounts (Art. 166A(2))
• Provisions relating to securitised exposures
• Portions covered by CRM risk-weight substitution

BEEL Exception (Pool C — Art. 158(5))¶

For A-IRB defaulted exposures, Pool C of the Art. 159 comparison uses the institution's own BEEL (Best Estimate of Expected Loss), not PD x LGD. The defaulted EL amount feeding the provisions-vs-EL shortfall/excess test is therefore:

Pool C (A-IRB defaulted) = Σ (BEEL_i × EAD_i)
Pool C (F-IRB defaulted) = Σ (1 × LGD_i × EAD_i)   # standard Art. 158(5) formula, PD = 1

BEEL is an Art. 158(5) / Art. 181(1)(h)(ii) parameter, defined in the PRA Rulebook (Credit Risk: IRB Approach (CRR) Part, Rule 1.3) as "an institution's best estimate of expected loss for a defaulted exposure as referred to in point (h)(ii) of Article 181(1)". The estimation standards (downturn conditions, unexpected additional loss during the recovery period, governance and back-testing) are set out in Art. 181(1)(h)(ii). Under pre-revocation CRR the same parameter was called ELBE; PS1/26 renames it to BEEL with no substantive change.

Scope — A-IRB only. The BEEL substitution operates solely on the Pool C EL amount. F-IRB defaulted exposures use 1 × LGD (supervisory) for Pool C, since they do not benefit from own-LGD estimation permissions. The distinct A-IRB capital formula K = max(0, LGD − BEEL) (Art. 154(1)(i)) lives in the defaulted-exposures spec, not here — see Defaulted Exposures — BEEL.

Interaction with Art. 158(6A). The BEEL-based Pool C total is increased by any post-model adjustments recognised under Art. 146(3)(c) before entering the Art. 159 test (see Art. 158(6A) — EL Monotonicity above).

Key Scenarios¶

Acceptance Tests¶