The sub-module that charges a single name for being large, why it is computed on the look-through, and why the same fund triggers it at one insurer and not another.
The Solvency II concentration risk charge takes each single name's exposure, subtracts a threshold set as a percentage of the insurer's relevant assets, and charges the excess at a factor that depends on the name's credit quality; the name-by-name charges are then combined as the square root of their sum of squares. At an illustrative insurer with 5,000m of relevant assets, 120m of unrated loans to one borrower held through a private credit fund exceeds its 75.0m threshold by 45.0m and costs 32.85m, more than twice the spread charge on the same loans.
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 →
The concentration sub-module is invisible on a fund factsheet. It is computed by the insurer, on its whole balance sheet, after looking through every fund it holds to the names underneath. A private credit fund with one large borrower, or a property fund with one dominant building, can trigger it at one insurer and not at another, purely because of the insurer's size. It is the clearest case of the book's theme: the same fund costs two insurers different amounts.
| Single name | Exposure E | Threshold CT | Factor g |
|---|---|---|---|
| Borrower A, unrated loans via a private credit fund | 120.0 | 1.5% | 73% |
| Bank B, bonds rated CQS 1 | 220.0 | 3.0% | 12% |
| Office building, held through a property fund | 600.0 | 10.0% | 12% |
Relevant assets, the base for the threshold, are 5,000m: total assets less those excluded from the sub-module, such as unit-linked assets and exposures covered by the counterparty default module. The thresholds and factors follow Articles 182 to 187 of Delegated Regulation (EU) 2015/35: 3 per cent for names with an average credit quality step of 0 to 2, 1.5 per cent for steps 3 to 6, and 10 per cent for property in the same building. The factor runs from 12 per cent at the top steps to 73 per cent at the bottom; unrated non-insurance names are treated here at the 1.5 per cent threshold and the 73 per cent factor. Exposures to EU governments are outside the sub-module.
XSi = max(0, Ei − CTi × Assetsxl)
Conci = XSi × gi
SCRconc = √(Σ Conci2)
Excel, exposure in B2, threshold in C2, factor in D2 and assets in B1: =MAX(0,B2-C2*$B$1)*D2, then =SQRT(SUMSQ(E2:E4))
| Name | Threshold | Excess XS | Charge | Squared |
|---|---|---|---|---|
| Borrower A | 75.0 | 45.0 | 32.85 | 1,079.12 |
| Bank B | 150.0 | 70.0 | 8.40 | 70.56 |
| Office building | 500.0 | 100.0 | 12.00 | 144.00 |
| Total | 53.25 | 1,293.68 |
SCRconc = √1,293.68 = 35.97m. The square root saves 17.28m against the simple sum, because the regulation treats defaults of different names as independent.
Borrower A dominates: 32.85m of the 53.25m before aggregation, from an exposure that is the smallest of the three. Two things make it expensive. The threshold is low, 1.5 per cent of assets, and the factor is high, 73 per cent of the excess. The bank exposure is almost twice as large but rated, so it breaches a threshold twice as high and is charged at 12 per cent.
Put the 32.85m beside the spread charge on the same loans. Unrated debt with a duration of 4.2 years is charged 3.0 per cent per year of duration under Article 176, 12.60 per cent, or 15.12m on 120m; the derivation is in how to calculate the Solvency II spread risk charge. The concentration charge adds 217.3 per cent of that on top. Taken alone, the charge is 27.38 per cent of the exposure.
| Case | Threshold | Excess | Charge |
|---|---|---|---|
| Exposure 75.0, assets 5,000 | 75.0 | 0.0 | 0.00 |
| Exposure 90.0, assets 5,000 | 75.0 | 15.0 | 10.95 |
| Exposure 120.0, assets 5,000 | 75.0 | 45.0 | 32.85 |
| Exposure 150.0, assets 5,000 | 75.0 | 75.0 | 54.75 |
| Exposure 120.0, assets 2,000 | 30.0 | 90.0 | 65.70 |
| Exposure 120.0, assets 3,000 | 45.0 | 75.0 | 54.75 |
| Exposure 120.0, assets 8,000 | 120.0 | 0.0 | 0.00 |
The same 120m holding costs 65.70m at an insurer of 2,000m and nothing at one of 8,000m. A rating changes it too: at credit quality step 3 the factor falls to 27 per cent and the charge to 12.15m; at step 2 the threshold doubles to 150.0m and the charge disappears.
A manager who confirms that no borrower exceeds 10 per cent of the fund has answered the wrong question. The test runs on the insurer's balance sheet: the borrower's weight in the fund times the insurer's commitment, plus anything the insurer already holds in the same name directly or through other managers. A 12 per cent position in a 1,000m fund is 120m to an insurer that owns all of it; an insurer with 5,000m of assets needs that number in the look-through file, not the fund's percentage. Without a look-through pack, the insurer cannot compute the charge at all and the whole fund falls into the equity bucket, as costed in what a missing look-through pack costs.
The sub-module enters market risk with a correlation of zero to every other sub-module, so its marginal effect on the aggregated market charge is smaller than its standalone size. Removing Borrower A cuts the sub-module from 35.97m to 14.65m, 21.32m before aggregation; how much survives aggregation depends on the insurer's other charges, as worked in how to aggregate Solvency II market risk charges.
Conc = max(0, E − CT × assets) × g, combined as a root sum of squares. Unrated names breach at 1.5 per cent of the insurer's assets and are charged 73 per cent of the excess: 32.85m on a 120m exposure at a 5,000m insurer. Holding the look-through exposure to one name below 75.0m at that insurer removes the charge. Every equity and debt charge an insurer reads off a fund, with the Article 176 grid as a table the formulas read, is in the free workbooks for this book. All figures are illustrative.
The relative excess exposure threshold is 3 per cent of the insurer's relevant assets for names with an average credit quality step of 0 to 2, 1.5 per cent for steps 3 to 6 and for unrated names in the illustrative treatment used here, and 10 per cent for a single property. At 5,000m of assets that is 150.0m, 75.0m and 500.0m. Government and certain exempt exposures are outside the sub-module.
Yes, on the look-through. The insurer adds what it holds in each name through every fund to what it holds directly. Unrated loans of 120m to one borrower inside a private credit fund count in full against that borrower, and at 5,000m of assets they breach the 75.0m threshold by 45.0m, costing 32.85m.
The name-by-name charges are combined as the square root of the sum of their squares: 32.85m, 8.40m and 12.00m give 35.97m, not 53.25m. The result then enters the market risk aggregation with a correlation of zero to every other sub-module, so its marginal effect on the total market charge is smaller than its standalone size.
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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