Follow £100,000 through investments, survivor allocations and forty annual payment dates.
The experiment tests the worked ladder in pools of 50, 200 and 500 people, with different ages and balances. Each pool is run through 1,000 investment and mortality histories. The example member joins at 65 and remains the focus of the payment results. Each rung’s full proceeds are paid one year after release; the target sets the opening investments rather than fixing the payments.
Earlier payments are close to the funding target
At age 85, the simulated certainty equivalents are about £7,364, £7,437 and £7,446 for the three pools. Each is close to the ideal-sharing target of £7,420, and every eligible release at that age is completed.
The later rungs expose the harder question. In the smaller pool, some surviving members reach dates for which the policy has already stopped. The larger pools complete more of the calendar, but the oldest-age results depend on very few surviving observations.
Eligibility is assessed at release, one year before payment. An entitlement released before a member’s death is paid to their beneficiary. Each pool size uses a different fixed cohort, so differences reflect composition as well as size.
The targets being tested
Annual targets from the same £100,000 contribution
£4,907Annual investment-only CE target. Independently funded unpooled ladder.
£7,420Annual ideal-sharing CE target. The finite-pool simulation tests delivery.
Same contribution, strategy and forty payment dates; different initial rung weights. The ideal-sharing model raises the level target by 51.2%. Actual finite-pool payments are examined in the simulations.
The two ladders each begin with £100,000 and use the same investment strategy and monthly market shocks. Each is independently allocated to fund its own level target. The unpooled assets remain available to the member or their estate; the pooled ladder shares unreleased balances.
The funding schedule shows every opening investment. The comparisons here ask how actual payments measure up to those starting targets.
Assumptions
The model uses synthetic independent mortality and a specified equity-to-bond glidepath. All amounts are nominal. Relative risk aversion is 3. The policy follows known death order and checks each ordinary single-death FTP allocation.
People, investments and dates
Members
The example member contributes £100,000 at age 65. Peers’ ages span 55–80 and contributions £60,000–£140,000, independently shuffled. All use the same forty calendar payment dates. There are no later entrants or contributions.
Investment policy
Equities have a 6.5% annual GBM drift and 16% volatility. Their weight falls from 80% at thirty years before release to zero at five years. Bonds earn a deterministic continuously compounded 3.5%; the distribution account earns the same rate for its final year.
Mortality
The monthly hazard is 0.01 × exp((entry age − 65 + elapsed years) / 10), held constant within each month. The same law supplies survival probabilities and death times.
Scope
The experiment excludes fees, tax, inflation, mortality improvements, correlated deaths and external buffers. The horizon ends with payment at age 105 for the example member.
Allocation, research stops and accounting
Survivor receipts are allocated across the recipient’s remaining rungs using conditional-survival and remaining CE weights. Existing investments stay in their own rungs.
The calculation stops when the current single-death exposure is infeasible, an audit fails, or fewer than three members retain unreleased assets. Those assets remain in the ledger pending a settlement policy. Already released entitlements continue to their scheduled payment dates.
Recorded payments include the eventual cash flows from already released assets. Retained assets are valued at the stopping date. The model note records this accounting convention and the full equations.
The next question is continuation
The experiment connects an opening funding rule to the income produced by actual FTP transfers. It also identifies the paths on which the current policy stops, leaving future payment outcomes unresolved.
The next study needs a continuation or transfer rule that accounts for those retained entitlements. The resulting complete payout distribution can then be used to recalibrate the starting investments. The capacity research supplies candidate constraints for that work.
Source and results
The package contains the generator, assumptions, fixed cohorts, every example-member outcome, pool stop records and selected event ledgers. Independent checks reconcile the funding, allocations and payment accounts.