Skip to content
Actuably

Non-Life Standard Deviation

Calculate the Total Non-Life Standard Deviation instantly.

#Annex II SegmentSegment Volume MeasureSegment Standard Deviation
1Motor Vehicle Liability
€
2Other Motor
€
3Marine, Aviation and Transport
€
4Fire and Property
€
5General Liability
€
6Credit and Suretyship
€
7Legal Expenses
€
8Assistance
€
9Miscellaneous Financial Loss
€
10Non-Proportional Casualty
€
11Non-Proportional MAT
€
12Non-Proportional Property
€

Total Non-Life Standard Deviation

8.59%

=

Square-Root Portfolio Variance

€10 175 603

÷

Total Volume Measure

€118 518 929

Non-life standard deviation correlation build-up

Waterfall chart showing standalone component risk amounts, diversification benefit, and diversified result.
StepImpactRunning
Motor Vehicle Liability10175603.07686957210175603.076869572
Segment Sigma-Volume Sum10175603.07686957210175603.076869572
Square-Root Portfolio Variance10175603.07686957210175603.076869572
Segment sigma-volume shares
Segment sigma-volume sharesShare of each segment in the total.Motor VehicleLiability100.0% · €10M
ModuleShareAmount
Motor Vehicle Liability100.0%€10M

Annex IV correlation matrix

1.000.250.50
Annex IV correlation matrix
01Motor Vehicle Liability02Other Motor03Marine, Aviation and Transport04Fire and Property05General Liability06Credit and Suretyship07Legal Expenses08Assistance09Miscellaneous Financial Loss10Non-Proportional Casualty11Non-Proportional MAT12Non-Proportional Property
01Motor Vehicle Liability
1.00
0.50
0.50
0.25
0.50
0.25
0.50
0.25
0.50
0.25
0.25
0.25
02Other Motor
0.50
1.00
0.25
0.25
0.25
0.25
0.50
0.50
0.50
0.25
0.25
0.25
03Marine, Aviation and Transport
0.50
0.25
1.00
0.25
0.25
0.25
0.25
0.50
0.50
0.25
0.50
0.25
04Fire and Property
0.25
0.25
0.25
1.00
0.25
0.25
0.25
0.50
0.50
0.25
0.50
0.50
05General Liability
0.50
0.25
0.25
0.25
1.00
0.50
0.50
0.25
0.50
0.50
0.25
0.25
06Credit and Suretyship
0.25
0.25
0.25
0.25
0.50
1.00
0.50
0.25
0.50
0.50
0.25
0.25
07Legal Expenses
0.50
0.50
0.25
0.25
0.50
0.50
1.00
0.25
0.50
0.50
0.25
0.25
08Assistance
0.25
0.50
0.50
0.50
0.25
0.25
0.25
1.00
0.50
0.25
0.25
0.50
09Miscellaneous Financial Loss
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
1.00
0.25
0.50
0.25
10Non-Proportional Casualty
0.25
0.25
0.25
0.25
0.50
0.50
0.50
0.25
0.25
1.00
0.25
0.25
11Non-Proportional MAT
0.25
0.25
0.50
0.50
0.25
0.25
0.25
0.25
0.50
0.25
1.00
0.25
12Non-Proportional Property
0.25
0.25
0.25
0.50
0.25
0.25
0.25
0.50
0.25
0.25
0.25
1.00
1Step 1

Pair each Annex II segment volume measure with its segment standard deviation

Xs=σsVsX_s=\sigma_s V_s
2Step 2

Aggregate segment standard deviations using the Annex IV correlation matrix

σNL=∑i∑jCorrijσiViσjVj∑iVi\sigma_{NL}=\frac{\sqrt{\sum_i\sum_j Corr_{ij}\sigma_iV_i\sigma_jV_j}}{\sum_i V_i}

Understand the Non-Life Standard Deviation

Overview

This calculator implements the portfolio-level Non-Life Standard Deviation calculation within the Solvency II standard formula.[1] It combines segment volume measures and segment standard deviations with the Annex IV correlation matrix.

Input Terms

  • Segment Volume Measure: The Article 116 volume amount for one Annex II segment.[2]
  • Segment Standard Deviation: The Article 117 volatility amount for the selected Annex II segment.[1]
  • Total Non-Life Standard Deviation: The Article 117 portfolio volatility after applying Annex IV correlations.[1]

Technical Rationale

Article 117 makes non-life standard deviation the volatility driver for the Premium & Reserve Risk requirement because the capital amount must reflect the undertaking's risk profile and line-of-business diversification. The prescribed correlation matrix recognizes that non-life lines can diversify while still preserving exposure to simultaneous claims volatility across the portfolio.

The volatility measure is combined with the Non-Life Volume Measure because volatility without volume is not yet a capital amount.[3][2]

Important Notes

  • Reporting: The volatility result supports the combined-standard-deviation fields in the S.26.05.01 non-life underwriting risk reporting view; it is not a standalone SCR component.[4]

Sources

  1. Delegated Regulation (EU) 2015/35 - Art. 117 (Standard deviation for non-life premium and reserve risk) - EIOPA
  2. Delegated Regulation (EU) 2015/35 - Art. 116 (Volume measure for non-life premium and reserve risk) - EIOPA
  3. Delegated Regulation (EU) 2015/35 - Art. 115 (Non-life premium and reserve risk sub-module) - EIOPA
  4. Commission Implementing Regulation (EU) 2023/894 - QRT S.26.05.01 (SCR non-life underwriting risk) - 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.