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Bond Risk Factor CQS3 Simplification

Calculate the Effective Risk Factor instantly.

%

Article 105a Conditions

Pass

=

ECAI Coverage Test

Pass

×

Bond Eligibility Tests

Pass

×

Exclusion Tests

Fail

Assigned CQS

CQS 3

=

CQS 3

CQS 3

×

Article 105a Conditions

Pass

Effective Risk Factor

1.80%

=

CQS 3 Risk Factor

1.80%

×

Article 105a Conditions

Pass

1Step 1

Confirm that at least 80% of the portfolio value is covered by nominated ECAI assessments

CoverageFlag=CoverageECAI≥80%CoverageFlag = Coverage_{ECAI} \ge 80\%
2Step 2

Check the individual bond has no nominated assessment and has fixed redemption with regular coupons

BondFlag=NoAssessment×FixedRedemptionBondFlag = NoAssessment \times FixedRedemption
3Step 3

Exclude structured, collateralised, profit-participation, unit-linked, index-linked, and matching-adjustment liability covers

Eligibility=CoverageFlag×BondFlag×(1−Structured)×(1−ExcludedLiabilityCover)Eligibility = CoverageFlag \times BondFlag \times (1-Structured) \times (1-ExcludedLiabilityCover)
4Step 4

Assign CQS 3 and the Article 105a risk factor only when all conditions pass

RiskFactoreffective=RiskFactorCQS3×EligibilityRiskFactor_{effective} = RiskFactor_{CQS3} \times Eligibility

Understand the Bond Risk Factor CQS3 Simplification

Overview

This calculator implements the simplified bond risk factor (`b_i`) used within the Spread Risk sub-module of the Solvency II standard formula.[1] It computes the per-instrument spread-risk factor as a function of modified duration and credit quality step, providing the factor input needed by the Spread Risk Bonds Simplification to derive the standalone capital charge. This calculator does not itself output a standalone capital requirement.

Input Terms

  • Market Value (MV_i): The current market value of the bond or loan.[1]
  • Modified Duration (dur_i): The modified duration of the bond used as a proxy for price sensitivity.
  • Credit Quality Step (CQS): The regulatory rating step used to determine the applicable risk factor.

Technical Rationale

The Bond Risk Factor Simplification derives the `b_i` spread-risk factor for each bond by expressing it as a linear function of the instrument's modified duration and its credit quality step, as defined in Article 104.[1] This factor measures the percentage loss in value of a bond for a given unit change in credit spreads scaled to the instrument's duration profile. The resulting `b_i` value feeds directly into the Spread Risk Bonds Simplification to produce the per-instrument capital charge.

This method is governed by the principle of proportionality (Article 109), ensuring that smaller or captive undertakings can calculate their solvency capital requirements without the operational burden of a full-scale valuation calculator. The resulting factor is used as an intermediate input, not as a final capital requirement.

Important Notes

  • Proportionality Bound: This factor is only valid where the nature, scale, and complexity of the risks justify use of the Article 104 simplification. If the bond portfolio contains complex embedded derivatives or non-standard trigger events, a fuller build is required.
  • Factor Output Only: This calculator outputs the `b_i` factor per instrument. The full simplified standalone Spread Risk SCR is produced by the Spread Risk Bonds Simplification calculator, which applies this factor to the instrument market values.
  • Regulatory deviation: Material deviation from the standard-formula assumptions or from the conditions supporting this simplification may support a capital add-on or a move toward a fuller or internal-model approach where justified.[2]
  • Reporting: The simplified result is intended to support the corresponding standard-formula component feeding the S.25.01.01 standard-formula reporting view, not to replace the connected article-chain result where the simplification is not justified.[3]

Sources

  1. Delegated Regulation (EU) 2015/35 - Art. 104 (Simplified calculation for spread risk on bonds and loans) - EIOPA
  2. Directive 2009/138/EC - Art. 37 (Capital add-on) - EIOPA
  3. Commission Implementing Regulation (EU) 2023/894 - QRT S.25.01.01 (SCR standard formula) - EUR-Lex

Default values are illustrative sample inputs for navigation, training, and QA. Replace them with controlled data before using the result in capital analysis, governance, or reporting decisions.