The standard formula spread charge from rating and modified duration, worked on a private credit fund, with the grid and what rating drift and longer loans do to it.
Under the Solvency II standard formula, the spread risk charge on a bond or loan is read from Article 176 of the Delegated Regulation: a fixed amount plus a rate per year of modified duration, both set by the exposure's credit quality step and its duration band. A BB loan book with a modified duration of 4.2 years is charged 4.5 per cent per year, 18.90 per cent of market value, which on a €150.0 million holding is €28.35 million of capital.
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 spread risk sub-module stresses the market value of credit exposures for a widening of spreads. For bonds and loans, the stress on each exposure is a function of two inputs only: its credit quality step, which maps from the rating of a nominated rating agency (step 0 for AAA down to step 6), and its modified duration in years. The charge is the sum across exposures of market value times stress, capped at 100 per cent. Exposures to EU member state governments in their own currency are exempt, and interest rate risk and concentration risk are charged in other sub-modules.
Stress = a + b × (duration − lower bound of the band)
Spread charge = market value × stress
Excel, with the table in a range: =INDEX(a,band)+INDEX(b,band)*(Dur-INDEX(lb,band)), where band is =MATCH(Dur,lb,1) on the row for the rating
For a BB exposure (step 4), the bands are: up to five years, 4.5 per cent a year; five to ten years, 22.5 per cent plus 2.5 per cent a year above five; ten to fifteen, 35 per cent plus 1.8 per cent; fifteen to twenty, 44 per cent plus 0.5 per cent; above twenty, 46.5 per cent plus 0.5 per cent.
Calder Life, an illustrative European life insurer, is considering €150.0 million in a private credit fund that makes senior secured loans to mid-market borrowers, BB equivalent, with a modified duration of 4.2 years. The manager provides a full look-through inventory, so the insurer can charge the loans rather than the fund units. The fund is expected to return 8.9 per cent net.
| Step | Value |
|---|---|
| Credit quality step | 4 (BB) |
| Modified duration | 4.2 years |
| Band | 0 to 5 years |
| Stress = 0 + 4.5% × 4.2 | 18.90% |
| Market value | €150.0m |
| Capital required | €28.35m |
| Expected income at 8.9% | €13.35m |
| Return on capital | 47.09% |
Return on capital, income over the capital the asset consumes, is the number an insurer's investment committee actually ranks on. At 47.09 per cent the credit fund is cheap to hold, which is why credit managers court life insurers. Without the look-through inventory, the same fund would be charged as type 2 equity at 49.00 per cent before the symmetric adjustment, €73.5 million of capital; that gap is worked in what a missing look-through pack costs.
The same formula across ratings and durations gives the grid every insurance client's capital function has pinned to the wall.
| Rating | 2 years | 4.2 years | 7 years | 12 years | 18 years |
|---|---|---|---|---|---|
| AAA | 1.80% | 3.78% | 5.50% | 8.00% | 11.00% |
| AA | 2.20% | 4.62% | 6.70% | 9.40% | 12.40% |
| A | 2.80% | 5.88% | 8.40% | 11.50% | 14.50% |
| BBB | 5.00% | 10.50% | 15.50% | 22.00% | 28.00% |
| BB | 9.00% | 18.90% | 27.50% | 38.60% | 45.50% |
| B | 15.00% | 31.50% | 45.90% | 59.50% | 62.50% |
| Unrated | 6.00% | 12.60% | 18.40% | 25.90% | 33.10% |
Take the seven-year column as a check on the bands: BBB is 12.5 per cent plus 1.5 per cent for each of the two years above five, 15.50 per cent; BB is 22.5 plus 2.5 times two, 27.50 per cent.
Duration can outweigh rating. A 15-year AA bond is charged 10.90 per cent, more than a two-year BB loan at 9.00 per cent; a ten-year BBB bond, at 20.00 per cent, costs less than a five-year BB at 22.50. An insurer cannot rank two credit funds by their rating alone.
The charge is computed on the portfolio at each reporting date, not on the fund's prospectus. Two kinds of drift change it.
| Portfolio | Stress | Capital, €m | Change, €m | Return on capital |
|---|---|---|---|---|
| BB, 4.2 years (base) | 18.90% | 28.35 | 0.0 | 47.09% |
| BB, 3.0 years | 13.50% | 20.25 | −8.1 | 65.93% |
| BB, 6.0 years | 25.00% | 37.50 | 9.1 | 35.60% |
| B, 4.2 years | 31.50% | 47.25 | 18.9 | 28.25% |
| BBB, 4.2 years | 10.50% | 15.75 | −12.6 | 84.76% |
| Unrated, 4.2 years | 12.60% | 18.90 | −9.5 | 70.63% |
Each year of duration on a BB book below five years costs 4.5 points, €6.75 million here. A drift from BB to B at the same duration adds €18.9 million, two thirds of the original charge. The unrated row is real, not a misprint: debt with no rating from a nominated agency and no collateral has its own row in Article 176, and below five years it is charged less than BB. Whether a given loan may sit in that row, or must be assessed under the alternative provisions for unrated bonds and loans, is a question for the insurer's capital function, not for the manager's marketing deck.
The most frequent error is quoting the charge on the fund's target duration or average rating instead of computing it exposure by exposure. The formula is linear within a band but jumps in slope between bands and between ratings, so a BB portfolio with half its loans at two years and half at eight is charged 19.50 per cent, not the 22.50 per cent of a portfolio at five. The fix is to compute the stress on each line of the look-through inventory and sum the capital, then report the implied average for convenience only.
The full Article 176 table, the grids and a sheet for your own fund are in the free workbook for this case.
For BBB (credit quality step 3) the charge is 2.5 per cent per year of modified duration up to five years, then 12.5 per cent plus 1.5 per cent a year from five to ten. A five-year BBB bond is charged 12.50 per cent, a seven-year 15.50 per cent and a ten-year 20.00 per cent. The charge applies to market value.
Because the charge multiplies a rating factor by duration. A 15-year AA bond is charged 10.90 per cent, more than the 9.00 per cent on a two-year BB loan. An insurer comparing a long investment-grade fund with a short high-yield one cannot rank them by rating alone; it has to read the grid at each fund's actual duration.
Directly. A BB loan book at 4.2 years is charged 18.90 per cent; if new loans lengthen the portfolio to six years the charge rises to 25.00 per cent, because the second duration band starts at 22.5 per cent and adds 2.5 per cent a year. On €150.0 million that is €9.1 million more capital with no change in credit quality.
The spread charge grid is set out in chapter 4 and Appendix A of 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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