Discount the matched liabilities at the risk-free rate plus the adjustment, and the cap and the compounding take almost a third off the pitch-deck figure.
The Solvency II matching adjustment is the spread on the assets backing a matched block of liabilities, less the fundamental spread for default and downgrade, added to the risk-free rate used to discount those liabilities. On an illustrative €150.0 million BB private credit sleeve with a 4.50 per cent spread, the raw adjustment is 2.70 per cent, capped at the BBB level of 2.05 per cent, which releases €11.92 million of technical provisions over 4.2 years. The usual shorthand, adjustment times duration times liabilities, says €12.92 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 →
For a credit manager selling to annuity writers, this is the number that turns a loan book from an asset the insurer can hold into one it wants to hold: the release goes straight into own funds on day one. It is also the number most often overstated in pitch material.
| Input | Value |
|---|---|
| Matched liabilities, at the risk-free rate | €150.0m |
| Duration of the sleeve (and of the matched cash flows) | 4.2 years |
| Flat risk-free rate | 3.00% |
| Spread on the BB loans | 4.50% |
| Fundamental spread, BB | 1.80% |
| Spread on an investment-grade asset of the same duration | 2.50% |
| Fundamental spread, BBB | 0.45% |
Raw adjustment = asset spread − fundamental spread
Below investment grade: adjustment = min(raw, the adjustment a BBB asset of the same duration and class would give)
Provisions released = L − L × ((1 + r) ÷ (1 + r + MA))D
In Excel, with liabilities in B1, the rate in B2, the adjustment in B3 and duration in B4: =B1-B1*((1+B2)/(1+B2+B3))^B4.
Step 1, the raw adjustment. 4.50 per cent of spread less 1.80 per cent of fundamental spread leaves 2.70 per cent, 270 basis points.
Step 2, the cap. Under Article 77c of the Directive, a sub-investment-grade asset may not contribute more to the adjustment than an asset of credit quality step 3 (BBB) with the same duration and asset class. The BBB comparator gives 2.50 less 0.45, so 2.05 per cent. The cap cuts the adjustment by 0.65 of a point, to 205 basis points.
Step 3, the release. The matched liabilities are €150.0 million at 3.00 per cent, a cash flow of €169.83 million in 4.2 years. Discount the same cash flow at 5.05 per cent and it is worth €138.08 million. Provisions fall by €11.92 million, 7.94 per cent of the block.
| Method | Adjustment | Released |
|---|---|---|
| Shorthand: 2.05% × 4.2 × 150.0 | 2.05% | 12.92 |
| No cap applied (an error) | 2.70% | 15.45 |
| Capped and discounted | 2.05% | 11.92 |
The shorthand overstates by 8.39 per cent at 4.2 years, because duration is a first-order approximation and the discount compounds. At an adjustment of 2.70 per cent over 12 years the gap widens: €40.04 million discounted against €48.60 million by the shorthand, an overstatement of 21.38 per cent. The longer the block, the worse the rule of thumb.
Ignoring the cap is the larger error. It adds €3.53 million to the release, a figure that will not survive the insurer's actuarial review and costs the manager credibility on every other number in the deck.
| Asset | Spread | Fundamental spread | Adjustment | 4.2 years | 8 years | 12 years |
|---|---|---|---|---|---|---|
| A | 1.60% | 0.25% | 1.35% | 7.98 | 14.84 | 21.70 |
| BBB | 2.50% | 0.45% | 2.05% | 11.92 | 21.88 | 31.59 |
| BB | 4.50% | 1.80% | 2.05% | 11.92 | 21.88 | 31.59 |
| B | 6.00% | 3.50% | 2.05% | 11.92 | 21.88 | 31.59 |
The table carries the commercial point. Below investment grade, extra spread buys no extra adjustment: the B loans would give 2.50 per cent raw, and are held to the same 2.05 as BBB. Duration, by contrast, scales the release almost linearly. For an annuity writer, a longer BBB-quality loan is worth more in provisions than a shorter, higher-yielding BB one.
The release is not free. Assets in a matching adjustment portfolio must have fixed cash flows that the borrower cannot change without compensation, the liability cash flows must be replicated, and the spread risk charge on the sleeve, 18.90 per cent or €28.35 million here (see the spread risk charge on a bond), still applies, with the stress feeding back into the adjustment. Any residual duration gap between the sleeve and the matched cash flows is still charged in the interest rate risk sub-module. Loans with open prepayment at par, common in private credit, fail eligibility unless the documents add make-whole protection.
Computing the adjustment on the fund's headline spread and multiplying by duration. That stacks two errors: it skips the cap below investment grade, and it linearises a discount. On this sleeve the combination would quote roughly €17 million instead of €11.92 million. The second mistake is using the duration of the insurer's whole book rather than of the sleeve: the release is on the matched liabilities, whose cash flows the sleeve replicates, so it runs at 4.2 years, not at the annuity block's 12.
The matching adjustment sheet, with the cap and the comparison to the shorthand, is in the free workbook for this case.
It is the part of an asset's spread that compensates for expected default and downgrade losses, published by EIOPA by asset class, credit quality and duration, with a floor of 35 per cent of the long-term average spread for non-government assets under Article 77c. It is deducted from the asset's spread before the adjustment is added to the discount rate. In the illustrative case a BB loan earning 4.50 per cent loses 1.80 per cent to the fundamental spread, leaving a raw adjustment of 2.70 per cent.
They can sit in a matching adjustment portfolio, but their contribution is capped at that of an investment-grade asset of credit quality step 3 with the same duration and asset class. In the example, BB loans at 4.50 per cent and B loans at 6.00 per cent both earn 2.05 per cent, the BBB figure, so extra spread below investment grade buys no extra release.
Because duration is a linear approximation of a compounding discount. On €150.0 million of liabilities at 3 per cent, a 2.05 per cent adjustment over 4.2 years releases €11.92 million discounted, while the shorthand gives €12.92 million, 8.39 per cent too much. Over 12 years at 2.70 per cent the shorthand overstates by 21.38 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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