The standalone charge is not what an asset costs an insurer. The increase in the aggregated total is, and it depends on what the insurer already holds.
The marginal SCR of an investment is the insurer's diversified capital requirement after adding the asset, less the requirement before it. Run the standard-formula aggregation twice and subtract. On an illustrative insurer with 911.2 million of aggregated market risk, a real estate fund carrying a 37.50 million property charge adds only 26.72 million, 71.25 per cent of its standalone charge. At an insurer of the same size whose book is already heavy in property, the same fund adds 35.18 million.
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 quote the standalone charge because it belongs to the fund. The insurer pays the marginal one, because capital is held on the whole balance sheet, after diversification. The two differ by enough to reorder a shortlist.
Two fictional insurers with identical total market-risk charges, 1,135 million before diversification and 911.2 million after, differing only in mix: one is heavy in spread risk, the other in property. Charges are combined with the market risk correlation matrix in Article 164 of the Delegated Regulation (EU) 2015/35, taking the downward interest scenario, in which interest rate risk correlates 0.5 with equity, property and spread. Each fund's charge is added to its own sub-module as if perfectly correlated with what is there, a simplification.
| Sub-module | Insurer A, spread-heavy | Insurer B, property-heavy |
|---|---|---|
| Interest rate | 180 | 180 |
| Equity | 240 | 240 |
| Property | 95 | 520 |
| Spread | 520 | 95 |
| Currency | 60 | 60 |
| Concentration | 40 | 40 |
| Aggregated market risk | 911.25 | 911.25 |
The aggregation itself, square root of the correlation-weighted sum of every pair of charges, is worked in how to aggregate Solvency II market risk charges.
SCRmkt = √(Σi,j Corri,j × SCRi × SCRj)
Marginal SCR = SCRmkt(book + asset) − SCRmkt(book)
In Excel, with the six charges in B6:B11 and the matrix in B40:G45: =SQRT(SUMPRODUCT(B6:B11,MMULT(B40:G45,B6:B11))), once on the existing book and once with the fund's charge added to its row.
Step 1: the existing book. The correlation-weighted sum of squares for insurer A is 830,375; its square root is 911.25.
Step 2: add the fund. The real estate fund, 150 million at a 25 per cent property charge, adds 37.50 to the property row: 95 becomes 132.5. The weighted sum rises to 879,781, and its square root to 937.97.
Step 3: subtract. 937.97 − 911.25 = 26.72 million. The fund's standalone charge is 37.50; the insurer's requirement rises by 71.25 per cent of it.
A quick estimate without rerunning the matrix: each sub-module's gradient, its correlation-weighted row over the total. For insurer A, property's gradient is 0.702 and spread's 0.936; for insurer B they swap. Multiply by the charge added and you are close: 0.702 × 37.50 is within half a million of the exact 26.72. For large additions, rerun the formula.
| Fund | Standalone | Marginal, A | % of standalone | Marginal, B | % of standalone |
|---|---|---|---|---|---|
| Listed equity fund | 58.50 | 52.15 | 89.14 | 52.15 | 89.14 |
| Private equity fund | 73.50 | 65.63 | 89.29 | 65.63 | 89.29 |
| Direct real estate fund | 37.50 | 26.72 | 71.25 | 35.18 | 93.80 |
| Private credit fund | 28.35 | 26.58 | 93.74 | 20.13 | 71.00 |
The equity funds cost the same at both insurers, because their equity books are identical. The real estate and credit funds swap places. At insurer A, the real estate fund costs 26.72 million and the credit fund 26.58, almost the same capital for very different standalone charges. At insurer B the real estate fund costs 8.46 million more, and the credit fund 6.45 million less.
Turned into return on capital, at expected returns of 6.80 per cent for real estate and 8.90 for credit on 150 million each, the real estate fund earns 38.18 per cent on marginal capital at insurer A and 29.00 at insurer B; the credit fund 50.23 and 66.32. The standalone figures, 27.20 and 47.09, describe neither insurer. The standalone ranking is set out in return on Solvency II capital for a fund.
Marginal costs are measured one at a time against the existing book, so they do not add up exactly when several assets arrive together. At insurer A the four marginals sum to 171.1 million; adding all four funds together raises the aggregate by 171.9 million, to 1,083.2. The gap is 0.87 million, 0.51 per cent, positive because the new charges crowd each other. At insurer B the gap is 0.65 million. Against 197.85 million of standalone charges, both totals are far lower, but neither is the simple sum of the parts.
Aggregate with and without the asset and subtract: 26.72 million for a fund whose own charge is 37.50, at an insurer whose risk sits elsewhere. Insurance Capital for Asset Managers is built around this point, why the same fund costs two insurers different amounts, and the free workbook for this case prices the four funds against both insurers, one at a time and all together.
The standalone charge is the asset's own capital charge, before diversification. The marginal SCR is how much the insurer's diversified total rises when the asset is added. An illustrative real estate fund with a 37.50 million property charge raises one insurer's market-risk SCR by only 26.72 million, because property is a small part of that insurer's existing risk.
Because diversification depends on the existing book. Two illustrative insurers each carry 911.2 million of aggregated market risk, one heavy in spread risk, the other in property. A 37.50 million property charge adds 26.72 million at the first and 35.18 million at the second; a 28.35 million spread charge adds 26.58 million at the first and 20.13 at the second.
Not exactly. Each marginal is measured against the book without the others. On an illustrative insurer, four funds have marginal costs summing to 171.1 million, but added together they raise the aggregate by 171.9 million, a gap of 0.87 million or 0.51 per cent, because the new charges crowd each other.
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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