Headroom divided by the standalone charge is the wrong answer, and the right one gets more expensive with every euro.
Divide the capital headroom above the target ratio by the private equity charge, then correct for diversification, because the insurer's SCR rises by less than the standalone charge. On an illustrative insurer with €1,400m of own funds and a 180.3 per cent ratio, the 49 per cent type 2 equity charge suggests €319.9m of private equity before the ratio falls to 150 per cent; run through the standard-formula aggregation, the answer is €445.5m, 39 per cent more.
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 →
Asset managers usually see one side of this: the charge on their fund. The insurer's investment committee sees the other: how much of the fund it can hold before the solvency ratio reaches the level its risk appetite statement treats as a floor. The answer depends on the capital it has to spare and on how the new charge combines with what is already on the balance sheet.
| Item | Value |
|---|---|
| Eligible own funds | 1,400 |
| Interest rate risk | 120 |
| Equity risk, type 1 (listed) | 150 |
| Property risk | 60 |
| Spread risk | 250 |
| Currency risk | 40 |
| Counterparty default risk | 50 |
| Life underwriting risk | 400 |
| Operational risk, held constant | 40 |
| Target ratio from the risk appetite | 150% |
Unlisted private equity is usually type 2 equity, charged at 49 per cent plus the symmetric adjustment (within plus or minus 10 points), taken here as zero. Holdings that qualify as long-term equity investments are charged 22 per cent, and some fund structures, such as qualifying ELTIFs, EuVECA and EuSEF funds, can fall under type 1 instead; this insurer's fund qualifies for neither. The purchase is funded from cash and short-dated EEA government bonds, which carry no spread charge, and the interest rate charge is assumed unchanged. Each simplification is stated so that it can be replaced with the insurer's own figures.
Market risk aggregates the six sub-modules with the correlation matrix of Article 164 of Delegated Regulation (EU) 2015/35: 620 undiversified becomes 506.1. BSCR combines market, default and life risk at a correlation of 0.25 between each pair: 736.6. Adding operational risk, SCR = 776.6 and the ratio is 1,400 ÷ 776.6 = 180.3 per cent.
Maximum SCR at 150 per cent = 1,400 ÷ 1.50 = 933.3. Headroom = 933.3 − 776.6 = 156.8.
156.8 ÷ 49% = 319.9. This treats every euro of charge as a euro of SCR.
Add X × 49% to type 2 equity, combine it with type 1 at a correlation of 0.75, re-run both aggregations, and solve for the X that makes SCR equal 933.3. In Excel, put the aggregation in one cell and use Goal Seek, or =SQRT(SUMPRODUCT(V,MMULT(Corr,V))) nested twice, with X as the changing cell. The answer is 445.5.
| Item | Before | After €445.5m of PE |
|---|---|---|
| Type 2 equity charge | 0.0 | 218.3 |
| Equity risk | 150.0 | 345.4 |
| Market risk | 506.1 | 686.4 |
| SCR | 776.6 | 933.3 |
| Solvency ratio | 180.3% | 150.0% |
A standalone charge of 218.3 raises SCR by 156.8, 71.8 per cent of it. On average each euro of private equity costs 35.2 cents of SCR, not 49. But the cost is not flat: the first euro adds 27.6 cents and the last 39.6, because the larger equity becomes, the more of the book it dominates and the less diversification is left. The first €100m costs only 30.2 of SCR and leaves the ratio at 173.5 per cent, which is why a pilot allocation looks cheaper than the full programme.
What is left out. Loss-absorbing capacity of deferred taxes would lower the net SCR and raise the capacity; a higher symmetric adjustment lowers it, while funding the purchase by selling corporate bonds rather than cash releases spread charge and raises it. The method does not change: recompute the whole aggregation each time.
| Target ratio | 22% (long-term equity) | 49% (type 2) | 54% (type 2, adjustment +5) |
|---|---|---|---|
| 140% | 1,359 | 610 | 554 |
| 150% | 992 | 446 | 404 |
| 160% | 655 | 294 | 267 |
| 175% | 176 | 79 | 72 |
The target ratio dominates. Raising it from 150 to 160 per cent cuts the capacity by a third, and at 175 per cent, close to where the insurer already stands, there is almost nothing left. Long-term equity treatment at 22 per cent more than doubles capacity at every target, which is the practical meaning of the saving worked in how much long-term equity status saves.
Dividing headroom by the standalone charge understates capacity here by €125.6m. The opposite error is just as common: taking the first-euro marginal cost of 27.6 per cent and scaling it up, which gives 567 rather than 446 and overshoots the target. Both are shortcuts for an aggregation that has to be run on the whole balance sheet, as in the marginal SCR of an investment.
Capacity = the allocation at which the recomputed SCR meets own funds ÷ target ratio. Solve for it rather than dividing, quote it at two or three target ratios, and remember the price per euro rises as the allocation grows. The aggregation, the correlation matrix and the marginal capital are all in the free workbooks for this book.
Unlisted private equity is usually type 2 equity under the standard formula: 49 per cent plus the symmetric adjustment, which moves within plus or minus 10 points. Qualifying long-term equity investments are charged 22 per cent, and some qualifying fund structures fall under type 1. In the illustrative case the 22 per cent treatment more than doubles the private equity an insurer can add at a 150 per cent target, from 446 to 992 million euros.
Because the charge is aggregated with existing risks through correlation matrices below one. A 218.3 million euro type 2 charge combines with listed equity at 0.75 and with other market and underwriting risks at lower correlations, so the illustrative insurer's SCR rises by 156.8 million, 71.8 per cent of the standalone charge.
Strongly. With 1,400 million euros of own funds and an SCR of 776.6 million, the illustrative insurer can add 610 million of private equity at a 140 per cent target, 446 million at 150, 294 million at 160 and only 79 million at 175 per cent.
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.
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