The loss-absorbing capacity of deferred taxes, worked from the shock loss to the recognition cap, and why the cap decides what a new fund costs an insurer.
LAC DT is the fall in deferred taxes that the insurer's own SCR loss would trigger: apply the tax rate to the basic SCR plus operational risk (plus the technical provisions adjustment), then cap the result at what the insurer can support from net deferred tax liabilities, carry-back and probable future taxable profits. On an illustrative insurer with an 800m basic SCR, 60m of operational risk and a 25 per cent tax rate, the notional tax relief is 215.0m but only 180.0m can be supported, so LAC DT is 180.0m and the SCR is 680.0m, a 154.4 per cent ratio instead of 122.1 per cent without it.
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 adjustment is the last line of the standard formula and, for many insurers, a material deduction from it. For an asset manager it matters for a less obvious reason: whether the insurer is at its recognition cap decides whether a new fund costs it capital before tax or after tax. The calculation below shows both.
SCR = BSCR + Op + Adj, where Adj is the loss-absorbing capacity of technical provisions plus that of deferred taxes (Article 103 of the Solvency II Directive)
LAC DT = the change in deferred taxes that would result from an instantaneous loss equal to BSCR + AdjTP + Op (Article 207 of the Delegated Regulation)
The logic is that a real loss of that size would reduce the insurer's tax: it would release deferred tax liabilities, or create a deferred tax asset. The SCR can be reduced by that amount, but only to the extent the insurer can show the tax relief would really be available after the loss. That last condition is where the judgement, and the supervisory scrutiny, sits.
| Input | Value |
|---|---|
| Basic SCR (BSCR), after diversification | 800.0 |
| Operational risk (Op) | 60.0 |
| Adjustment for technical provisions (AdjTP) | 0.0 |
| Tax rate | 25% |
| Net deferred tax liability on the Solvency II balance sheet | 120.0 |
| Relief supportable by projected future taxable profits | 60.0 |
| Carry-back of losses | 0.0 |
| Eligible own funds | 1,050 |
AdjTP is nil because the insurer is assumed to have no future discretionary benefits to cut in the stress; a with-profits book would have a negative figure here, and it would reduce the shock loss below.
Shock loss = BSCR + AdjTP + Op = 800.0 + 0.0 + 60.0 = 860.0
Notional change in deferred taxes = 25% × 860.0 = 215.0
Support = net DTL 120.0 + future profits 60.0 + carry-back 0.0 = 180.0
LAC DT = min(215.0, 180.0) = 180.0; 35.0 of the notional relief is not recognised
Excel: =MIN(Tax*(BSCR+AdjTP+Op), NetDTL+FutureProfits+CarryBack)
The first 120.0 is the easier part: a loss reverses deferred tax liabilities that already sit on the balance sheet, so no profit forecast is needed, although the insurer still has to check that they reverse in a usable period and against the same tax authority. The next 60.0 requires a projection of taxable profits after the stress, which supervisors expect to be prudent, to allow for the shock itself and to fade over time. Article 207 itself, as amended in the 2019 review of the Delegated Regulation, sets conditions on that projection, and EIOPA's guidelines on the loss-absorbing capacity of technical provisions and deferred taxes add to them; check the current text and your supervisor's practice before relying on a figure. Here the insurer recognises 83.7 per cent of the notional figure.
| Measure | No LAC DT | LAC DT capped at 180.0 | Full LAC DT of 215.0 |
|---|---|---|---|
| BSCR + Op | 860.0 | 860.0 | 860.0 |
| LAC DT | 0.0 | −180.0 | −215.0 |
| SCR | 860.0 | 680.0 | 645.0 |
| Solvency ratio on 1,050 of own funds | 122.1% | 154.4% | 162.8% |
LAC DT removes 20.9 per cent of the pre-adjustment requirement and is worth 32.3 points of ratio. The full aggregation that produces the BSCR is worked in how to calculate a Solvency II ratio.
Suppose a new allocation adds 20.0 to the BSCR after diversification and earns 3.0 a year. The shock loss rises by 20.0 and the notional relief by 5.0. What happens next depends on the cap:
| Insurer | SCR before | SCR after | Increase in SCR | Return on capital |
|---|---|---|---|---|
| At its cap (support 180.0) | 680.0 | 700.0 | 20.0 | 15.0% |
| Below its cap (support 460.0) | 645.0 | 660.0 | 15.0 | 20.0% |
For the capped insurer, none of the extra relief can be recognised, so the fund costs its full 20.0 and the ratio falls from 154.4 to 150.0 per cent. For an insurer with ample deferred tax liabilities, the fund costs 20.0 × (1 − 0.25) = 15.0, and the same 3.0 of income earns 20.0 per cent on capital instead of 15.0. A manager quoting return on Solvency II capital to two insurers with identical portfolios can be a third out between them, for a reason that has nothing to do with the fund.
| Support | LAC DT | SCR | Ratio |
|---|---|---|---|
| 0 | 0.0 | 860.0 | 122.1% |
| 60 | 60.0 | 800.0 | 131.2% |
| 120 | 120.0 | 740.0 | 141.9% |
| 180 | 180.0 | 680.0 | 154.4% |
| 215 | 215.0 | 645.0 | 162.8% |
| 300 | 215.0 | 645.0 | 162.8% |
Each 60.0 of support the insurer cannot evidence costs between 9.2 and 12.5 points of ratio, more as the SCR shrinks, until the cap is reached at 215.0; beyond that, more support adds nothing.
Applying the tax rate to the SCR and stopping there. The notional 215.0 is an upper bound, not the answer: the recognised figure depends on the insurer's own balance sheet and on a profit projection its supervisor has to accept. Using 215.0 here would overstate the ratio by 8.4 points and understate the marginal cost of any new allocation by a quarter. When an insurer says it is “at its LAC DT cap”, it is telling the manager that every euro of SCR its fund adds is a full euro.
LAC DT is the tax rate times BSCR plus AdjTP plus Op, capped at the relief the insurer can support: here 180.0 of a notional 215.0, taking the SCR to 680.0 and the ratio to 154.4 per cent. Ask an insurer client whether it is at the cap before pricing your fund's capital cost. The workbooks on the companion page for the book price four funds' marginal capital at two insurers of identical size.
Reversal of net deferred tax liabilities on the Solvency II balance sheet, carry-back of losses where tax law allows, and probable future taxable profits after the stress. In the illustrative insurer 120.0m of net DTL and 60.0m of future profits support 180.0m of a notional 215.0m, 83.7% of it.
Only if the insurer is below its recognition cap. A fund adding 20.0m to the BSCR costs a capped insurer the full 20.0m of SCR, but an insurer with spare deferred tax liabilities only 15.0m at a 25% tax rate. On 3.0m of income that is a 15.0% versus 20.0% return on capital.
It depends on the tax rate and the cap. In the illustrative case, 1,050m of own funds against an SCR of 860.0m before LAC DT gives 122.1%; recognising 180.0m of LAC DT lowers the SCR to 680.0m and lifts the ratio to 154.4%, 32.3 points.
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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