Insurer investment risk and the ORSA · RiskAtoms Academy

By the end you will be able to

1Compute the market risk module on an insurer's portfolio: interest, equity, property and spread.
2Aggregate risk modules with a correlation matrix to the BSCR and the SCR, and share the total back out by module.
3Explain the risk margin as a cost of capital, and what the 2025 review changes.
4Build an ORSA projection with stresses, management actions and a risk appetite, and say where the standard formula does not fit the firm.

Why it matters

RiskAtoms Insurance SE takes nearly half of its capital risk on the asset side, not in its policies. Its market module, €3,391m, is the largest of the five, and after diversification it is 48% of the BSCR. The book's market and insurance stresses in the same year would take its solvency ratio from 186% to 94%. The standard formula gives one number; the ORSA asks what could happen next, and what the board would do.

Core explanation

From the investment portfolio to the board's own view

Illustrative dataRiskAtoms Insurance SE's insurance book

The same composite European insurer as Modules 1.8 and 2.2, reporting in € millions at 31 December 2025: €70bn of assets, €9.0bn of non-life premiums, annuities, savings with guarantees and term business, a cat event set, a reinsurance programme and a Solvency II standard formula in outline (SCR €5,000m, own funds €9,300m, a ratio of 186%). Every line, event, bond, treaty and price is made up for teaching and seeded so it never changes; none is any insurer's data. The same book runs through every lesson in Module 3.8, so the figures agree.

This lesson relies on the book's standard formula in outline: the equity symmetric adjustment set at 0; no concentration or currency risk (all euro, diversified issuers); money-market funds looked through and not charged; counterparty default stated at €150m; the cat charge from the event set; the risk margin and the deferred-tax adjustment as balancing items, the latter held at 19.4% in every stress; own-funds changes before tax.

The market risk module

L2.7.05: Solvency I to Solvency II introduced the SCR as a 1-in-200 one-year loss. The market risk module asks what each market shock would do to own funds (Delegated Regulation (EU) 2015/35, Arts 164–176). On RiskAtoms' €70bn balance sheet:

Sub-module	Exposure	Shock	Charge
Interest rate	Bonds against best estimates	Relative up and down shocks; up binds (L3.8.11: Insurer asset-liability management)	393.0
Equity, type 1	Listed 3,000 + strategic 1,000	39% + SA; 22% strategic	1,390.0
Equity, type 2	Private equity 500	49% + SA	245.0
Equity, combined		Types correlated 0.75	1,582.1
Property	3,000	25% fall	750.0
Spread	Covered and corporate bonds 26,000	Factor by rating step × duration	1,428.5
Concentration, currency		Not material here	0

The type 1 shock of 39% and the strategic 22% apply to RiskAtoms' listed shares and its participation in a related asset manager; the symmetric adjustment, which EIOPA publishes monthly, is set at 0 in the book. The money-market funds (€1,500m) are looked through to short deposits. The spread charge works bond by bond:

Holding	Value	Duration	Factor	Charge
CB4	5,000	3.75	2.63%	131.4
AA5	5,000	4.59	5.05%	252.7
A4	6,000	3.71	5.20%	312.0
A7	4,000	6.15	7.81%	312.2
BBB3	6,000	2.80	7.00%	420.2
Spread charge				1,428.5

The factor rises with both duration and lower credit quality, so the three-year BBB bonds are charged almost as much per euro as the seven-year A bonds. The €28bn of Euro area government bonds in euro carry no spread charge at all: the rules treat member states' own-currency debt as free of spread risk (Art 180(2)). That is a choice, not a fact about markets, and it comes back in the ORSA.

The four sub-modules are aggregated with the market correlation matrix of Art 164. Because the up interest scenario binds, the parameter $A$ linking interest to the others is 0:

Market risk correlations, A = 0
	Interest	Equity	Property	Spread
Interest	1.00	0.00	0.00	0.00
Equity	0.00	1.00	0.75	0.75
Property	0.00	0.75	1.00	0.50
Spread	0.00	0.75	0.50	1.00

The sub-modules add up to €4,153.6m; aggregated they need €3,391.4m, a diversification of €762m (18.4%). The saving is modest because equity, property and spread are correlated 0.5 to 0.75 with one another; only interest, at 0 with the rest, diversifies fully. Had the down scenario bound, $A$ would be 0.5 and the same amounts would need €3,603m.

From modules to the BSCR and the SCR

The five modules are combined the same way, with the matrix of Annex IV of the Directive. This is the covariance-matrix arithmetic of L3.1.06: Many assets and the covariance matrix, applied to capital amounts instead of portfolio weights:

Annex IV correlations between modules
	Market	Counterparty	Life	Health	Non-life
Market	1.00	0.25	0.25	0.25	0.25
Counterparty	0.25	1.00	0.25	0.25	0.50
Life	0.25	0.25	1.00	0.25	0.00
Health	0.25	0.25	0.25	1.00	0.00
Non-life	0.25	0.50	0.00	0.00	1.00

Module	Alone	Diversified contribution	Share of BSCR
Market	3,391.4	2,760.0	47.9%
Counterparty	150.0	77.0	1.3%
Life	2,054.0	1,064.8	18.5%
Health	198.1	54.9	1.0%
Non-life	2,801.2	1,809.2	31.4%
Total	8,594.8	5,765.9	100%

The BSCR is €5,765.9m, €2,829m less than the sum: 32.9% diversification, much of it because Annex IV puts life and non-life at zero correlation. With every correlation at 0 the BSCR would be €4,861m; at 0.5, €6,982m; at 1, the plain sum. The diversified contributions (L3.1.14: Risk contributions and risk budgeting) show where the capital goes: market risk is 39% of the sum of the modules but 48% of the BSCR, because it is correlated 0.25 with everything else while life and non-life offset each other.

Then the SCR (Directive, Art 103): BSCR €5,765.9m, plus operational risk €438.6m (the provisions-based figure, above the premiums-based €358.2m), less the deferred-tax adjustment €1,204.4m: €5,000m. Own funds of €9,300m give a ratio of 186%.

The risk margin

The technical provisions on the balance sheet are the best estimate plus a risk margin. It is the price another insurer would charge to take the liabilities over: a cost-of-capital rate of 6% a year (Art 39) on the SCR it would need for the risks it cannot hedge, every year until the liabilities run off, discounted (Art 37). The reference undertaking holds underwriting, reinsurance counterparty and operational risk, and market risk only where it cannot be avoided (Art 38). In the book the risk margin is €1,878m, what the best estimates leave of Module 1.8's technical provisions; a 6% cost-of-capital check, running off the non-hedgeable SCR of €4,033m with the liability cash flows, gives €1,848m.

Year t	Share of liabilities left	SCR(t)	Discount factor	6% × SCR(t) × DF
0	100.0%	4,033	0.9804	237.2
1	89.5%	3,611	0.9602	208.0
2	82.1%	3,312	0.9396	186.7
3	76.1%	3,070	0.9175	169.0
4	70.8%	2,856	0.8947	153.3
All 56 years				1,848.4

The ORSA: the board's own view

The standard formula is one calibration for every insurer in the EU, at one date. The ORSA (Directive 2009/138/EC, Art 45) is the firm's own assessment of (a) its overall solvency needs given its risk profile, risk tolerances and strategy, (b) whether it will keep meeting its capital requirements and the rules on technical provisions, and (c) how far its risk profile deviates from the assumptions behind the SCR. It is forward-looking, owned by the board, done at least once a year and after any major change in risk profile, and reported to the supervisor. It cannot be used to set a capital requirement (Art 45(7)).

Extra for this lessonRiskAtoms' risk appetite

For this lesson only, the board's risk appetite is a target ratio of at least 160% in the plan, and a tolerance of 130% that the ratio must not go below after a severe but plausible stress. These are not part of the book.

The book projects three years from 2026 with retained profit and an SCR growing 3% a year:

Scenario (shock at the start of 2026)	Shock	2026	2027	2028
Base plan, dividends paid	–	193%	200%	206%
Market: rates −100bp, equities −30%, spreads +100bp; no dividend	2,823	137%	151%	165%
Insurance: 1-in-200 cat, reserves 10% short, half the longevity stress; no dividend	2,339	156%	171%	185%
Both in the same year; no dividend	5,162	94%	110%	125%

The market stress takes the ratio to 137%: inside the tolerance but well below target, so the board stops the dividend and rebuilds to 165% by 2028. Had it kept paying, the ratio would be 129% in 2026, below tolerance. The two stresses together break the SCR (94%). A reverse stress test makes the same point from the other end: at today's SCR, a loss of €4,300m takes the ratio to 100%. The ORSA must say how plausible such a combination is and what the firm would do: de-risk the equities, buy more reinsurance, raise capital.

The ORSA projection, 2025 to 2028

Scenario (shock at the start of 2026)

Dividend

Solvency ratioTargetToleranceSCR (100%)

Shock to own funds€2,823m

Ratio after the shock (end 2026)137%

Own funds, end 2028€9,627m

Ratio, end 2028165%

End 2026: inside tolerance but below target: management actions.

The book's ORSA rule: the shock hits at the start of 2026, profit of €1,050m a year is added, less the dividend if paid; the SCR grows 3% a year and starts 7.1% higher, because lower rates raise it. Target and tolerance are a lesson extra, not part of the book. Illustrative data.

Where the standard formula does not fit

Art 45(1)(c) asks the firm to say where its risk profile departs from the formula's assumptions. Open each card for RiskAtoms' answer.

Deviations from the standard formula

The formal version

The market module on the book. With $s$ the interest, equity, property and spread charges and $R$ the matrix above (M-E02: Matrix multiplication and quadratic forms, M-C10: Covariance and correlation):

\begin{aligned} s &= (393.0,\ 1{,}582.1,\ \\ &\qquad 750.0,\ 1{,}428.5)' \\ Rs &= (393.0,\ 3{,}216.0,\ \\ &\qquad 2{,}650.8,\ 2{,}990.1)' \\ s'Rs &= 393.0 \times 393.0 \\ &\quad + 1{,}582.1 \times 3{,}216.0 \\ &\quad + 750.0 \times 2{,}650.8 \\ &\quad + 1{,}428.5 \times 2{,}990.1 \\ &= 11{,}501{,}897 \\ \text{SCR}_{\text{mkt}} &= \sqrt{11{,}501{,}897} = 3{,}391.4\text{m} \end{aligned}

The contributions $c_i = s_i (Rs)_i / \sqrt{s'Rs}$ are interest 45.6, equity 1,500.2, property 586.2, spread 1,259.5: interest, uncorrelated with the rest when $A = 0$ , contributes only $s_1^2/\text{SCR}$ .

The BSCR works the same way on the five modules:

\begin{aligned} Rs &= (4{,}692.3,\ 2{,}961.5,\ 2{,}988.9,\ \\ &\qquad 1{,}597.0,\ 3{,}724.0)' \\ \text{BSCR} &= \sqrt{s'Rs} = \sqrt{33{,}245{,}077} \\ &= 5{,}765.9\text{m} \\ \text{SCR} &= \text{BSCR} + \text{SCR}_{\text{op}} + \text{Adj} \\ &= 5{,}765.9 + 438.6 -1{,}204.4 \\ &= 5{,}000\text{m} \end{aligned}

The risk margin (Delegated Regulation 2015/35, Art 37), with $r(t+1)$ the risk-free rate for $t+1$ years:

\begin{gathered}\text{RM} = \text{CoC} \sum_{t \ge 0} \frac{\text{SCR}(t)}{\big(1 + r(t+1)\big)^{t+1}} \\[4pt] \text{CoC} = 6\% \;\to\; 4.75\%\end{gathered}

The sum is linear in CoC, so on the book's check the new rate alone, from 30 January 2027, gives €1,463m instead of €1,848m. The review also multiplies future SCRs by a factor that falls over time; that is not modelled here.

Try it

Change the size of any module, or the correlation assumption, and watch the BSCR, the diversification and each module's share. What happens to the contributions when you double life risk? When every correlation is 1?

Try itAggregate the SCR

Market module€3,391m

Counterparty module€150m

Life module€2,054m

Health module€198m

Non-life module€2,801m

Correlations between modules

BSCR √(s′Rs)€5,766m

Solvency ratio186%

Sum of the modules€8,595m

Diversification€2,829m (32.9%)

Operational risk€439m

SCR after deferred taxes€5,000m

Bars show each module's diversified contribution s_i(Rs)_i ÷ BSCR; they add up to the BSCR. Operational risk is min(30% of BSCR, €439m); the deferred-tax adjustment stays at 19.4% of BSCR plus operational risk; own funds stay at €9,300m. Illustrative data, € millions.

Worked example

The market stress, step by step

All figures from the book, € millions, before tax.

Rates −100bp, equities −30% and spreads +100bp at the start of 2026

Step 1 of 5

1
Rates
Own funds fall €447m (L3.8.11: Insurer asset-liability management) and the SCR rises to €5,353m, as the guarantees and the longevity stress cost more at lower rates.

Regulatory lens

The 2025 review of Solvency II, Directive (EU) 2025/2 and Commission Delegated Regulation (EU) 2026/269, applies from 30 January 2027. It cuts the cost-of-capital rate to 4.75% (the amended Art 39) and adds a time-dependent factor that assumes risks fall by at least 3.5% a year, with the reduction capped at 50% (recital 9): on the book, the new rate alone would release about €391m of risk margin and lift the ratio to about 194% before tax. The correlation between spread and interest rate risk in the down scenario falls from 50% to 25% (recital 20); the interest rate shocks are recalibrated with a floor for negative rates (recitals 23–24); and the limits on the equity symmetric adjustment widen to ±13%. In the ORSA, insurers must factor in relevant macroprudential information where supervisors ask for it, and those with material exposure, other than small and non-complex undertakings, must analyse long-term climate change scenarios (Directive (EU) 2025/2, recitals 26 and 31). The whole framework, including internal models, the MCR and reporting, is in M4.6: Solvency II and insurance regulation.

Spark Atoms

Spark AtomThe insurer's biggest risk is often its investments

On the book, market risk is 39% of the sum of the modules and 48% of the diversified BSCR: €2,760m, nearly as much as life and non-life together (€2,874m). A composite insurer's underwriting risks partly cancel each other; its assets all sit in the same markets.

Spark AtomOne parameter switches with the scenario

The market correlation

A

is 0 when the up interest scenario binds and 0.5 when the down one does. On the book that switch alone would move the market module from €3,391m to €3,603m: the rules assume rates falling and markets falling go together, as they often have in crises.

Key takeaways

The market module charges interest (€393m), equity (39%, 49%, 22% strategic: €1,582m), property (25%: €750m) and spread (rating step × duration: €1,429m), aggregated to €3,391m.
Modules aggregate as √(s′Rs): €8,595m of modules become a BSCR of €5,766m, 33% diversification. Contributions s_i(Rs)_i/√(s′Rs) add up to the total.
SCR = BSCR + operational risk + adjustment for deferred taxes: €5,766m + €439m − €1,204m = €5,000m, a ratio of 186%.
The risk margin is a cost of capital on future non-hedgeable SCRs: about €1,848m at 6%; 4.75% from 2027.
The ORSA is the board's forward-looking view: the market stress takes the ratio to 137% with the dividend stopped, both stresses together to 94%.
The ORSA must name where the formula does not fit: zero-charged sovereign bonds, the cat model, a stated counterparty charge, behaviour the formula ignores.

Reaction

Check what stuck

Question 1 · objective 1

RiskAtoms holds €3,000m of listed shares (39% shock), a €1,000m strategic participation (22%) counted with them, and €500m of private equity (49%). Type 1 and type 2 are correlated 0.75. What is the equity charge, in €m?

€m

Question 2 · objective 2

Two modules need €300m and €400m on their own, with a correlation of 0.25. What do they need together, in €m?

€m

Question 3 · objective 3

A run-off needs an SCR (non-hedgeable risks) of €1,000m now, at the end of year 1 and at the end of year 2, then nothing. With a 6% cost of capital and a flat 3% rate, what is the risk margin, in €m? Use 6% × Σ SCR(t) / 1.03^(t+1).

€m

Question 4 · objective 4

Which of these is the ORSA required to do?

AAssess how far the insurer's risk profile deviates from the assumptions behind the standard formula SCRBReplace the SCR with the insurer's own capital figureCBe produced every five years for the supervisor onlyDLeave out future business plans and look only at today's balance sheet

Question 5 · objective 2

RiskAtoms' five modules add up to €8,594.8m; its BSCR is €5,765.9m. What share of the sum is diversification, in %?

%

Glossary

Market risk module: The standard formula's market risk module: the loss of own funds under prescribed shocks to rates, equities, property, credit spreads, concentrations and currencies, combined with a correlation matrix.
Type 1 and type 2 equities: Type 1 equities: shares listed in EEA or OECD regulated markets. Type 2: other equities, such as private equity.
Strategic participation: A strategic participation: a lasting holding in a related company, such as an asset manager in the same group, charged a lower 22% shock.
Symmetric adjustment: Symmetric adjustment: a monthly add-on to the equity shock that raises it after markets have risen and lowers it after they have fallen, within set limits.
Spread risk: Spread risk: the loss when credit spreads widen. The standard formula charges a factor that rises with a bond's rating step and duration.
Basic SCR (BSCR): Basic SCR: the risk modules (market, counterparty, life, health, non-life) aggregated with the correlation matrix of Annex IV of the Directive.
Diversification benefit: The capital saved because the modules are not perfectly correlated: their sum less the BSCR.
Diversified contribution: A module's diversified contribution: its amount times the slope of the BSCR in that amount. The contributions add up to the BSCR.
Operational risk charge: Operational risk in the standard formula: a charge based on premiums or technical provisions, capped at 30% of the BSCR.
Loss-absorbing capacity of deferred taxes: The loss-absorbing capacity of deferred taxes: after a 1-in-200 loss the insurer would pay less tax, which reduces the SCR.
Risk margin: The part of technical provisions that pays another insurer for holding capital against the liabilities until they run off: a cost-of-capital rate times the future SCRs, discounted.
Cost-of-capital rate: Cost-of-capital rate: the annual return the risk margin assumes on the capital a taker-over would hold. 6% today, 4.75% from 30 January 2027.
ORSA: Own Risk and Solvency Assessment: the insurer's own, forward-looking view of its risks and the capital it needs, owned by its board and reported to the supervisor (Directive 2009/138/EC, Art 45).
Risk appetite: Risk appetite: the level of risk the board is willing to take, here written as a target solvency ratio and a lower tolerance it will not go below in a severe stress.
Reverse stress test: Reverse stress test: start from failure (here a ratio of 100%) and ask what would cause it.

Deep Dives & Origins

Deep Dives

EIOPA, Guidelines on own risk and solvency assessment, EIOPA-BoS-14/259, applying from 1 January 2016: what supervisors expect an ORSA to contain. Intermediate.
Debevoise & Plimpton, “European Commission Adopts Amendments to the Solvency II Delegated Regulation”, 2 March 2026: a short guide to the review's changes. Intermediate.

Origins

European Parliament and Council, Directive 2009/138/EC, Art 45, Art 103 and Annex IV, legislation.gov.uk.
European Commission, Delegated Regulation (EU) 2015/35, Arts 37–39, 87, 164, 169, 174 and 180 (as adopted) and Art 176 (as in force at 31 December 2020), legislation.gov.uk.
European Commission, Delegated Regulation (EU) 2026/269, Art 39 as amended and recitals 9, 20 and 23–24, EUR-Lex, 2026.
European Parliament and Council, Directive (EU) 2025/2, recitals 26 and 31, EUR-Lex, 2025.
S. Eijffinger and M. Pieterse-Bloem, “Euro area government bond spreads: A tale of different ECB policy regimes”, VoxEU column, CEPR (sovereign spreads in the 2010–2012 crisis).
EIOPA, Guidelines on own risk and solvency assessment, EIOPA-BoS-14/259 (Bank of England copy).
Debevoise & Plimpton, “European Commission Adopts Amendments to the Solvency II Delegated Regulation”, 2 March 2026 (symmetric adjustment ±13%; application date).

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