The formula, the index levels at which it hits its bounds, and what it does to the capital and the return on capital of a private equity fund held by an insurer.
The symmetric adjustment is added to the Solvency II standard formula equity charge: half of the equity index's distance from its 36-month weighted average, less 8 per cent, bounded at 10 percentage points either way. It moves the 49 per cent charge on type 2 equity anywhere between 39 and 59 per cent, so a €150.0 million private equity fund can cost an insurer €58.5 million or €88.5 million of capital, €30.0 million apart, with nothing about the fund changed.
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 →
Article 106 of the Solvency II Directive requires the equity risk sub-module to include a symmetric adjustment, and Article 172 of the Delegated Regulation sets the formula. EIOPA computes it from a basket of equity indices and publishes it every month; insurers do not compute their own. But an asset manager selling to insurers should understand it, because it moves the capital cost of every equity-like fund at once.
SA = ½ × ((CI − AI) / AI − 8%), bounded between −10% and +10%
CI = current index level; AI = weighted average of daily index levels over the previous 36 months
Type 1 equity charge = 39% + SA; type 2 equity charge = 49% + SA
Excel: =MAX(-0.1,MIN(0.1,0.5*((CI-AI)/AI-0.08)))
Two features of the formula are easy to miss. The 8 per cent term means the adjustment is zero only when the index stands 8 per cent above its average; with the index exactly on its average it is minus 4.00 points. And the factor of one half means each point the index moves relative to its average moves the charge by 0.5 point, until a bound is hit. The bounds are reached when the index is 12 per cent below or 28 per cent above its average.
| Category | Base charge | Share of SA | Range within the bounds |
|---|---|---|---|
| Type 1 equity (listed in the EEA or OECD) | 39% | 100% | 29% to 49% |
| Type 2 equity (unlisted, private equity, other) | 49% | 100% | 39% to 59% |
| Qualifying infrastructure equity | 30% | 77% | 22.30% to 37.70% |
| Qualifying infrastructure corporate | 36% | 92% | 26.80% to 45.20% |
| Long-term equity investment (Article 171a) | 22% | none | 22% fixed |
| Property (separate sub-module) | 25% | none | 25% fixed |
Calder Life, an illustrative European life insurer, holds €150.0 million in a private equity fund. With no look-through to listed holdings, it is type 2 equity. The fund is expected to return 11.5 per cent, €17.25 million a year. Take three index states.
Index on its average. (CI − AI) / AI = 0. SA = ½ × (0 − 8%) = −4.00%. Charge = 49% − 4.00% = 45.00%. Capital = €67.5 million.
Index 8 per cent above. SA = ½ × (8% − 8%) = 0. Charge = 49.00%. Capital = €73.5 million. This is the state most published examples assume, and it is not neutral: it is an index well above its own history.
Index 40 per cent above. The raw adjustment is ½ × (40% − 8%) = 16.00%, cut to the 10 point bound. Charge = 59.00%. Capital = €88.5 million.
| Index vs 36-month average | SA | Type 1 | Type 2 | Capital, €m | Return on capital |
|---|---|---|---|---|---|
| −30% | −10.00% | 29.00% | 39.00% | 58.50 | 29.49% |
| −12% | −10.00% | 29.00% | 39.00% | 58.50 | 29.49% |
| −5% | −6.50% | 32.50% | 42.50% | 63.75 | 27.06% |
| 0% | −4.00% | 35.00% | 45.00% | 67.50 | 25.56% |
| +8% | 0.00% | 39.00% | 49.00% | 73.50 | 23.47% |
| +15% | 3.50% | 42.50% | 52.50% | 78.75 | 21.90% |
| +28% | 10.00% | 49.00% | 59.00% | 88.50 | 19.49% |
| +40% | 10.00% | 49.00% | 59.00% | 88.50 | 19.49% |
The adjustment is countercyclical by design. After a fall, equity becomes cheaper to hold, so insurers are not forced to sell into a falling market; after a long rally it becomes dearer. The same fund's return on capital runs from 29.49 to 19.49 per cent across the range, on identical expected income.
A fund manager pitching a private equity fund on a 23.47 per cent return on capital has quietly assumed an index 8 per cent above its average. Quote the range, or at least the month's published adjustment, beside it.
The common mistake is treating the base charge as the charge. A model built when the adjustment was near zero, then left alone, can be several points wrong by the time the committee meets, and in both directions. The second mistake is applying the full adjustment to infrastructure: qualifying infrastructure equity takes only 77 per cent of it, infrastructure corporates 92 per cent, and long-term equity none. The fix is a single input cell for the current published value, with every equity-like charge in the model reading it at its own share. Also check the corridor in force at your reporting date: the 2025 amendments to the Directive widen it once they apply.
For credit funds the equivalent exercise is the spread charge, worked in how to calculate the Solvency II spread risk charge. The spread charge does not read the adjustment at all.
The adjustment computed from the index, every charge that reads it and the levers a manager controls are in the free workbook for this case.
It is a countercyclical add-on to the standard formula equity charge, published monthly by EIOPA. It equals half of the difference between the current level of an equity index and its weighted average over 36 months, expressed as a share of that average, less 8 per cent, and is bounded at 10 points either way. Type 1 equity is charged 39 per cent plus the adjustment, type 2 equity 49 per cent plus the adjustment.
No. Because of the 8 per cent term in the formula, the adjustment is zero only when the index is 8 per cent above its 36-month average. With the index exactly on its average it is minus 4.00 points, so type 2 equity is charged 45.00 per cent rather than 49.00, and a €150.0 million holding needs €67.5 million of capital instead of €73.5 million.
Partly. Qualifying infrastructure equity is charged 30 per cent plus 77 per cent of the adjustment, and qualifying infrastructure corporates 36 per cent plus 92 per cent of it. Long-term equity investments carry a fixed 22 per cent with no adjustment. At the upper bound, infrastructure equity reaches 37.70 per cent while long-term equity stays at 22.00.
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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