Aggregate the modules into the basic SCR, add operational risk, deduct the tax adjustment, divide own funds by it, then run it again with the fund in.
The Solvency II ratio is eligible own funds divided by the solvency capital requirement (SCR), where the SCR is the basic SCR aggregated across risk modules with the standard formula correlations, plus operational risk, less the loss-absorbing adjustments. On an illustrative insurer with 1,900m of own funds and an SCR of 1,152.57m the ratio is 164.85 per cent. Moving 150m from government bonds into a private equity fund adds 59.36m of SCR and takes the ratio to 156.78 per cent.
Worked in full in Insurance Capital for Asset Managers by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
An insurer's investment committee does not approve a fund on its standalone charge. It approves it on what the allocation does to the ratio it reports to its board, its supervisor and the market. The standalone charge is the manager's figure; the change in the ratio is the insurer's. Getting from one to the other takes two aggregations, which is why the second number is almost always smaller than the first.
| Component | Amount |
|---|---|
| Market risk, aggregated from six sub-modules summing to 1,135.0 | 911.25 |
| Counterparty default risk | 60 |
| Life underwriting risk | 500 |
| Health underwriting risk | 80 |
| Non-life underwriting risk | 150 |
| Operational risk | 70 |
| Loss-absorbing capacity of deferred taxes | −150 |
| Eligible own funds | 1,900 |
The market sub-modules are interest rate 180, equity 240, property 95, spread 520, currency 60 and concentration 40, aggregated with the downward interest rate scenario as in how to calculate the marginal SCR of an investment. Modules are combined with the correlation matrix of Annex IV of the Solvency II Directive: 0.25 between market and every other module, 0.5 between counterparty default and non-life, zero between life and non-life and between health and non-life, 0.25 elsewhere. The deferred tax adjustment is held fixed, a simplification.
Step 1, the basic SCR. The five modules sum to 1,701.25. Aggregate them:
BSCR = √(Σi,j Corri,j × SCRi × SCRj)
Squares 1,112,875 + cross terms 406,343 = 1,519,218; √1,519,218 = 1,232.57
Excel, modules in B2:B6 and the matrix in D2:H6: =SQRT(SUMPRODUCT(B2:B6,MMULT(D2:H6,B2:B6)))
The largest cross term is market with life, 2 × 0.25 × 911.25 × 500 = 227,812. Diversification across modules is worth 468.68.
Step 2, the SCR.
SCR = BSCR + operational risk + adjustments = 1,232.57 + 70 − 150 = 1,152.57
Step 3, the ratio.
Ratio = eligible own funds ÷ SCR = 1,900 ÷ 1,152.57 = 164.85%
Surplus = 1,900 − 1,152.57 = 747.43
The insurer sells 150m of government bonds, which carry no spread or concentration charge, and commits the money to a private equity fund charged as type 2 equity at 49 per cent: 73.50m standalone. Own funds do not change on the day, because one asset is swapped for another at fair value. The interest rate charge is assumed unchanged.
| Line | Before | After | Change |
|---|---|---|---|
| Equity sub-module | 240.0 | 313.5 | 73.50 |
| Market risk | 911.25 | 976.88 | 65.63 |
| Basic SCR | 1,232.57 | 1,291.92 | 59.36 |
| SCR | 1,152.57 | 1,211.92 | 59.36 |
| Solvency ratio | 164.85% | 156.78% | −8.07 pts |
The fund's 73.50m charge becomes 59.36m of SCR, 80.8 per cent of its standalone size. To hold the ratio at 164.85 per cent the insurer would need 97.85m of additional own funds.
| Fund | Standalone charge | SCR increase | Ratio after | Own funds to restore |
|---|---|---|---|---|
| Private equity, type 2 equity | 73.50 | 59.36 | 156.78% | 97.85 |
| Listed equity, type 1 | 58.50 | 47.11 | 158.38% | 77.66 |
| Qualifying infrastructure equity | 45.00 | 36.14 | 159.84% | 59.58 |
| Private equity, long-term equity status | 33.00 | 26.44 | 161.15% | 43.59 |
| Direct real estate | 37.50 | 24.09 | 161.47% | 39.71 |
| Private credit, BB, duration 4.2 | 28.35 | 23.96 | 161.49% | 39.50 |
Long-term equity status, worked in how much capital long-term equity status saves, more than halves the damage to the ratio: 3.70 points instead of 8.07. Real estate costs less than its standalone charge suggests at this insurer because property is a small part of its book and diversifies well; at an insurer heavy in property it would not.
For the asset manager, the lesson is in the order of the rows. Ranked by standalone charge, the private credit fund and the real estate fund are 9.15m apart; ranked by what they do to this insurer's ratio, they are almost identical. The pitch that wins is the one built on the insurer's own numbers, which is why managers that ask for the module breakdown, or at least the sub-module mix, can show the ratio effect instead of the headline charge.
Adding 73.50m straight to 1,152.57m gives 1,226.07m and a ratio of 154.97 per cent, overstating the hit by 1.81 points. On a single fund that looks small. Across a programme of allocations it is the difference between a strategy the insurer can afford and one it rejects. The reverse error is just as common: a manager quoting the diversified figure from another insurer's balance sheet. The marginal effect belongs to the insurer that will hold the fund, and has to be run on its own modules.
The ratio also moves with value. If the private equity fund fell 10 per cent, own funds would drop by 15 to 1,885 and the ratio to 155.54 per cent before any change in the charge. The capital charge and the loss it is calibrated for arrive together.
Ratio = own funds ÷ (BSCR + operational risk + adjustments). Here 1,900 ÷ 1,152.57 = 164.85 per cent. A 150m private equity allocation adds 59.36m of SCR, not 73.50m, and costs 8.07 points; with long-term equity status, 3.70. The correlation matrix in full, the aggregate and the checks that bind are in the free workbooks for this book. All figures are illustrative.
The regulatory minimum is 100 per cent: own funds equal to the SCR. Most insurers set a target range well above it in their risk appetite, often expressed as a buffer the ratio should not fall below after a stress. The illustrative insurer here runs at 164.85 per cent, with 747.43m of own funds above its SCR, and a 150m private equity allocation takes 8.07 points off the ratio.
Because the SCR is aggregated twice, first within market risk and then across modules, with correlations below 1. A private equity fund charged 73.50m standalone raises the market module by 65.63m and the SCR by 59.36m, 80.8 per cent of its standalone charge, on this insurer. Adding the full 73.50m would show a ratio of 154.97 per cent instead of 156.78.
Enough to keep the ratio where it was: own funds times new SCR over old SCR, less own funds. Keeping 164.85 per cent after the private equity allocation needs 97.85m of extra own funds; the same 150m in a real estate fund needs 39.71m, and with long-term equity status the private equity fund needs 43.59m.
This article is one calculation from Insurance Capital for Asset Managers. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
Get the book on Amazon →Free companion files
Also on Amazon UK · Amazon Germany · Amazon France · Amazon Canada
Reading guide: regulation, compliance and banking → · All 1340 articles →
If this book helped, or didn’t, a few lines on Amazon are worth more than they look: they are what the next reader goes on. Write a review. The workbook stays free either way.