The charge sits on the gap between asset and liability duration, so the same credit fund can raise one insurer's capital and lower another's.
The Solvency II interest rate risk charge is the loss in own funds, assets minus liabilities, when the whole risk-free curve is shocked up and then down by the factors of Articles 166 and 167; the charge is the worse of the two. On an illustrative €3,200 million annuity block with 12-year liabilities at a flat 3 per cent, assets of 4 years' duration cost €149.5 million, set by the downward shock, while assets matched at 12 years cost nothing. The charge measures the duration gap, not the bonds.
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 →
That is the point most asset managers miss. A fund does not have an interest rate charge of its own: the same four-year credit fund raises the charge of an insurer with long liabilities, costs much less against short ones, and can even lower the charge of an insurer whose existing assets are already longer than its liabilities. The calculation below shows why, and what lengthening a mandate is worth in euros.
| Input | Value |
|---|---|
| Liabilities (best estimate) | €3,200m |
| Duration of the liabilities | 12 years |
| Flat risk-free rate | 3.00% |
| Assets | €3,200m |
| Minimum upward move (Article 166) | 1.00 point |
The shock factors are relative: the up factor multiplies the rate by (1 + sup), the down factor by (1 − sdown), and both shrink with maturity. Selected values from the tables as originally calibrated:
| Maturity | Up | Down |
|---|---|---|
| 4 years | 59% | 50% |
| 6 years | 52% | 42% |
| 8 years | 47% | 36% |
| 10 years | 42% | 31% |
| 12 years | 37% | 29% |
The review of Solvency II recalibrates these shocks, including for low and negative rates, with a transition. Check which calibration your insurer's reporting uses. The method that follows, liabilities first and then the gap, does not change.
Shocked rate up = max(r × (1 + sup), r + 1 point); shocked rate down = r × (1 − sdown)
ΔOwn funds = ΔAssets − ΔLiabilities, under each shock
Interest rate SCR = max(loss under up, loss under down, 0)
For one cash flow worth V today at maturity t: =V*(1+r)^t/(1+r_shocked)^t-V. Between tabulated maturities, interpolate the factor linearly.
Step 1, the liabilities. At 12 years the down factor is 29 per cent, so the rate falls from 3.00 to 2.13 per cent. The up factor is 37 per cent, so it rises to 4.11, above the 4.00 the one-point floor would impose. Discounting the same cash flow at 2.13 per cent raises the liabilities by €342.9 million, to €3,542.9 million; at 4.11 per cent they fall by €386.2 million.
Step 2, the assets. At 4 years the rate moves to 1.50 per cent down and 4.77 per cent up. The assets gain €193.4 million under the downward shock and lose €210.8 million under the upward one.
Step 3, own funds. Down: assets +193.4, liabilities +342.9, own funds −149.5. Up: assets −210.8, liabilities −386.2, own funds +175.4. Only the downward shock produces a loss, so the charge is €149.5 million, 4.67 per cent of the liabilities.
| Asset duration | Own funds, down | Own funds, up | Interest rate SCR | Binding shock |
|---|---|---|---|---|
| 4 years | -149.5 | 175.4 | 149.5 | down |
| 6 years | -97.6 | 110.3 | 97.6 | down |
| 8 years | -61.3 | 56.4 | 61.3 | down |
| 10 years | -39.1 | 19.9 | 39.1 | down |
| 12 years (matched) | 0.0 | 0.0 | 0.0 | none |
| 14 years | 45.8 | -26.1 | 26.1 | up |
| 16 years | 105.1 | -72.1 | 72.1 | up |
Moving the block's assets from four years to ten releases €110.4 million of capital without touching their credit quality. Past the liabilities, the binding shock flips to the upward one and the charge rises again. Notice also that the curve is not symmetric: the floor of one point starts to bind at 15 years here (37 per cent of 3 per cent is more than a point at 12 years, but 33 per cent at 15 is not), and the down factors stop shrinking around 14 years.
Take a €150.0 million private credit allocation with a duration of 4.2 years, held against €150.0 million of the same 12-year liabilities. Interpolated, the factors at 4.2 years are 49.2 per cent down and 58.2 per cent up, giving shocked rates of 1.524 and 4.746 per cent. The interest rate charge on the pair is €6.70 million. Lengthen the fund to 10 years and it falls to €1.83 million: €4.87 million released, 3.24 points of the allocation. Held instead against €150.0 million of two-year non-life liabilities, the same 4.2-year fund costs €4.29 million, and under the upward shock, because now the assets are the longer leg.
Use the four-year factors for the 4.2-year fund instead of interpolating and the charge is €6.54 million and the release €4.71 million. A small difference, but the kind that makes a capital function distrust the rest of a manager's pack.
Set that beside the spread charge on the same fund, 18.90 per cent or €28.35 million (worked in the spread risk charge on a bond). Duration is a smaller lever than look-through data, but it is one only the manager can pull, and it compounds with the rest once the sub-modules are aggregated, as in the market risk aggregation.
Quoting the interest rate charge of the assets alone. A manager running the up shock on the four-year book would report a loss of €210.8 million and call it the interest rate risk. The insurer is charged €149.5 million, under the opposite shock, because its liabilities move more than its assets. A fund presented as "low duration, low rate risk" can be the expensive choice for a life insurer and the cheap one for a non-life insurer with two-year claims.
Two smaller errors follow from the same habit: forgetting the one-point floor on the upward shock at long maturities, and shocking a single rate instead of the whole curve. A real block has cash flows at every maturity, each discounted at its own shocked rate; the single-cash-flow version above shows the mechanism, not the reporting number.
The interest rate sheet, with the full factor tables and the interpolation, is in the free workbook for this case.
The downward shock, when assets are shorter than liabilities, which is the usual case for annuity and savings books. In the illustrative block with 12-year liabilities, any asset duration from 4 to 10 years is charged under the downward shock, €149.5 million at 4 years. The upward shock only binds once assets are longer than the liabilities: at 14 years the charge is €26.1 million, set by the up shock.
No. Interest rate risk is charged on the insurer's balance sheet, assets and liabilities together. A €150.0 million credit fund of 4.2 years' duration held against 12-year liabilities adds €6.70 million of interest rate charge; against two-year non-life liabilities the same fund costs €4.29 million, under the upward shock instead. It lowers the charge only where the insurer's existing assets are already longer than its liabilities. Managers can only state the fund's duration and cash flow profile accurately so the insurer can run it.
Under the original Article 166 calibration, the upward shock must raise each rate by at least one percentage point. At a flat 3 per cent rate it starts to bind at 15 years, where 33 per cent of 3.00 per cent is less than a point, so the shocked rate is 4.00 per cent rather than 3.99. The review of Solvency II recalibrates the shocks, so confirm which version applies.
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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