When a Dutch pension fund moves to the solidarity contribution scheme (SPR), it has to decide how the solidarity reserve is funded, how much goes in at the start and when it pays out. Every choice shifts value between generations. I calculated this for a fictitious fund, using the DNB scenario set for the third quarter of 2026 and the AG2026 mortality projection table.
Key results
- Funding the reserve with 10% of positive excess return makes every existing age group a net payer. Members aged 35 to 50 contribute most (−4.3% of their assets including future contributions), pensioners least (−0.1%). Future members receive a net +1.6%.
- An initial funding of 5% shifts the bill to older members. For pensioners, the net value transfer moves from −0.1% to −2.4%. Members younger than about 40 at conversion gain, older members lose.
- Without initial funding the median reserve grows to 3.7% of total assets after 10 years and 9.1% after 30 years. The probability that a pensioner loses more than 5% of their benefit in a given year falls from 7.8% without a reserve to 2.3% with one.
The question
The solidarity reserve is the collective buffer in the solidarity contribution scheme. It is funded from part of the contributions or of members' returns, and used to absorb setbacks, mostly for pensioners. The people who pay in and the people who benefit are not the same group at the same time. So the question is not only whether the reserve becomes large enough, but also whether the rules are balanced between generations.
Answering that takes two kinds of calculation. Under a risk-neutral scenario set (Q) you calculate the market value of what each generation pays in and gets back: the value transfer. Under a real-world scenario set (P) you look at how the reserve develops and how often it is needed.
The legal framework
- The reserve is at most 15% of total pension assets, including the reserve itself, and never negative (Article 10d of the Dutch Pensions Act).
- Funding from contributions is at most 10% of the contribution, funding from excess return at most 10% of the positive collective excess return.
- Anything above 15% is distributed to the personal pension accounts according to rules set in advance.
- After conversion, the reserve may temporarily exceed 15%, until 1 January 2037 or until it first falls below 15% (Article 150n(9) of the Pensions Act).
The model
The fund
A fictitious fund with 25,000 members and €4.3 billion of converted assets: 11,960 active members, 7,540 deferred members and 5,500 pensioners. Assets per member are synthetic, but realistic in size and age profile. Active members pay a flat contribution of 24% of salary above an offset of €17,500. For forty years, 400 new members aged 25 join each year. Retirement age is 68.
The model works by cohort: year of birth by sex by group (active or inactive). Because all reserve rules are proportional to assets and everyone in a cohort has the same age, this gives the same percentage outcome for the reserve rules as a calculation per member. Only the contribution differs slightly, because it is based on the cohort's average salary and the offset is not linear.
Scenarios
The DNB CP2022 scenario set for the third quarter of 2026, in both the P and Q version, using all 20,000 scenarios over 100 years. The nominal yield curve follows from three state variables of the KNW model:
ln P(t, n) = φ(n, t) + Ψ(n) · X(t)
Equity returns and Dutch price inflation come straight from the set. Under Q, the stochastic discount factor from the set is the numeraire.
Mortality
AG2026 projection table, best estimate by sex, used as a generation table. No fund-specific experience adjustment is applied. Mortality follows the AG2026 probabilities exactly, so no mortality results arise. The assets of members who die, including before retirement, pass to the survivors in the same cohort.
Allocation of returns
- Protection return: the return on a zero-coupon hedge of the cohort's expected benefit cash flow. The hedge ratio runs from 0% at age 25 through 20% at 45 to 100% from 68.
- Excess return: equity return minus the one-year interest rate, allocated with an exposure of 90% at age 25, 80% at 45, 35% at 68 and 25% at the highest ages.
Benefits
At retirement, assets are converted into a benefit using the scenario's current yield curve and AG2026 survival probabilities, without a projected return:
B = V / ( N · Σ P(t, m) · ₘpₓ )
The benefit is recalculated every year. Shocks are not spread over several years.
The reserve in the base case
- Funding: 10% of positive excess return, as long as the reserve is below 15%.
- Investment: 30% equities, 70% at the one-year rate.
- Smoothing: if a pensioner cohort's benefit falls by more than 5%, the reserve tops it up to −5%. At most 20% of the reserve is paid out for smoothing per year.
- Surplus above 15%: distributed to all members in proportion to their assets.
How balance is measured
For each cohort k, the net value transfer is the market value under Q of what the cohort receives from the reserve, minus what it pays in:
VT(k) = EQ[ Σ D(t) · ( R(k, t) − C(k, t) ) ]
D(t) is the deflator, R the receipts (smoothing and distribution above 15%), C the contributions to the reserve (levies and any initial funding). The result is expressed as a percentage of converted assets plus the market value of the cohort's future contributions. Across all cohorts, the value transfers plus the reserve left after 100 years add up to zero.
Results
How the reserve grows
In the base case the reserve grows slowly: a median of 3.7% after 10 years and 9.1% after 30 years, with a range of 5.6% to 12.7%. With 5% initial funding the median after 30 years is 11.5%. In the most favourable scenarios the reserve then reaches the maximum (14.7% at the 95th percentile).
| Variant | Median t = 10 (%) | Median t = 30 (%) | Cut (% per year) | Cut > 5% (% per year) |
|---|---|---|---|---|
| No reserve | 0.0 | 0.0 | 32.1 | 7.8 |
| Base: 10% of excess return | 3.7 | 9.1 | 29.7 | 2.3 |
| Base plus 5% initial funding | 7.2 | 11.5 | 29.6 | 1.6 |
| 5% of contributions, no excess return | 1.0 | 2.3 | 31.7 | 5.8 |
| Base, smoothing from a 2% cut | 3.5 | 7.5 | 30.5 | 6.8 |
| Base, smoothing also for those near retirement | 3.6 | 8.1 | 30.1 | 5.2 |
The probability of a benefit cut stays around 30% a year in every variant. The reserve only absorbs large cuts. A lower smoothing threshold (2%) helps less than you might expect: the reserve is drawn on more often, stays smaller, and the probability of a cut above 5% becomes 6.8% instead of 2.3%.
Who pays and who benefits
| Variant (net value transfer, %) | < 35 | 35–49 | 50–67 | 68+ | New members |
|---|---|---|---|---|---|
| Base: 10% of excess return | −3.2 | −4.3 | −1.3 | −0.1 | +1.6 |
| Base plus 5% initial funding | −1.9 | −4.9 | −3.5 | −2.4 | +2.5 |
| 5% of contributions, no excess return | −1.1 | 0.0 | +1.3 | +0.8 | −1.0 |
| Base, smoothing from a 2% cut | −1.6 | −2.1 | +1.3 | +1.2 | −0.2 |
| Base, smoothing also for those near retirement | −2.4 | −3.7 | −2.7 | −1.2 | +1.8 |
Under Q, funding from excess return works like a written option on each cohort: those who carry the most equity risk give up the most. These are members aged 35 to 50, who have both sizeable assets and a high exposure. Pensioners pay in little, but also get little back through smoothing. Part of the value goes to future members, and 1.7% of converted assets is still in the reserve after 100 years.
Funding from contributions instead of excess return reverses the picture: older active members and pensioners become net beneficiaries, while the youngest and new members pay.
The effect of initial funding
Initial funding is taken pro rata from converted assets. Everyone pays the same per euro, but for a pensioner the converted assets are all there is, while most of a 25-year-old's assets still have to come from future contributions. The effect is +1.6 percentage points at age 25 and −2.4 percentage points at age 75. The break-even point is around age 40.
| Source (% of assets incl. future contributions) | Age 25, base | Age 25, initial funding | Age 75, base | Age 75, initial funding |
|---|---|---|---|---|
| Paid in via initial funding | 0.00 | 0.04 | 0.00 | 5.00 |
| Paid in via excess-return levy | 10.39 | 9.85 | 1.70 | 1.65 |
| Received via smoothing | 6.33 | 6.70 | 1.54 | 4.08 |
| Received via distribution above 15% | 1.38 | 2.10 | 0.00 | 0.00 |
| Net | −2.68 | −1.08 | −0.16 | −2.58 |
The 75-year-old pays in 5% and gets about half of it back through smoothing in their remaining years. The 25-year-old hardly contributes, gives up slightly less excess return because the reserve is full more often, and later receives more through smoothing and through distribution above 15%. Part of the older members' initial funding ends up with the younger members.
Checks
- Martingale test on the Q set with the DNB deflator: the expected deflated value of equities, zero-coupon bonds and a 10-year bond deviates by less than 1% from its starting value after 10 and 30 years. At very long horizons (60 years and beyond) the sampling noise rises to a few percent.
- Value conservation: in the base case the net value transfers plus the remaining reserve add up to −3.0 million euros, with a standard error of 3.2 million. That is within Monte Carlo noise and less than 0.1% of converted assets.
- With a full interest rate hedge and no equity exposure, the nominal benefit stays exactly constant (deviation below 10−14).
Limitations
- The fund is fictitious. For a real fund, the age profile, inflow of new members and the mix of active, deferred and retired members drive the results.
- The calculation is by cohort, without transitions from active to deferred or a flexible retirement age.
- No risk-based partner pension is modelled. Under the Wtp, the assets of members who die fall to the collective. The model distributes them over the survivors in the same cohort. Because the risk premium is missing, assets and benefits are slightly overstated.
- Benefits have no projected return and no spreading of shocks. Both affect how often the reserve is drawn on.
- Mortality is deterministic. Longevity risk as a shock is not included.
- The scenario set only contains interest rates, inflation and one equity index, so no credit, real estate or currencies, and no wage inflation.
- The rules are applied mechanically every year. Board decisions are not modelled.
Reproducibility
The model itself is not public. Everything that determines the results is fixed, so the calculation can be checked and rebuilt:
| Scenarios | DNB CP2022 P and Q set 2026Q3, 20K version (xlsx), all 20,000 scenarios, Dutch inflation |
| Mortality | Royal Dutch Actuarial Association, "Parameters en best estimate sterftekansen van Prognosetafel AG2026" |
| Source files (SHA-256) | 7adab0da9d2c (P), 60d5fb8276c5 (Q), 8880c47fce18 (AG2026) |
| Member data | Synthetic, fixed file of 25,000 records (c03ca4c75d99) |
| Software | R 4.3.3 with OpenBLAS, packages yaml 2.3.8, readxl 1.4.3, ggplot2 3.4.4, svglite 2.1.3 |
| Parameters | One configuration file with all scheme, allocation, reserve and scenario settings, as described above (594d93bdfd05) |
| Randomness | None. Given the source files, member data and configuration, the result is deterministic. |
| Run time | About 25 minutes for seven variants under P and Q, on two processor cores |
What this means for a fund
The choice of funding rule and any initial funding determines which generation pays for the reserve. That is not a technical detail but a distribution question the board must be able to explain and justify. A calculation like this makes the distribution per generation visible before the rules are fixed.
Would you like this calculated for your own fund, or a second opinion on an existing analysis? Get in touch.