What an Asset Share Measures
An asset share is a retrospective measure of the assets attributed to a policy under a specified allocation basis. It starts with an opening amount, adds policy receipts and any other allocated inflows, subtracts allocated outgo, and reflects investment accumulation between cash-flow dates. The result depends on which items the basis allocates to the policy and when those items are recorded.
A per-policy ledger makes those choices visible. It records each receipt and outgo as a separate dated item rather than combining amounts without regard to timing. This is particularly important when a policy has acquisition expenses, later premiums, benefits, or an exit payment at different dates.
The ledger may include premiums, allocated expenses, claims or benefits, surrender payments, and other cash flows assigned to the policy. An allocation can be an actual amount paid for one policy or a defined per-policy share of a common amount. The ledger should say which interpretation is being used. It should not imply that every item is directly observable for an individual policy.
An asset share is not automatically a policy reserve, a surrender value, or the amount contractually payable to a policyholder. A reserve is a prospective valuation under its own assumptions and definition; an asset share is retrospective. A benefit may be greater than, equal to, or less than an asset share. Depending on the opening amount and allocated cash flows, an asset share can also be negative.
Building a Dated Per-Policy Ledger
A useful ledger has a row for each cash-flow date and enough detail to identify the components of the net amount. Keep receipts and outgo in separate columns, even if the final calculation uses their difference. A suitable layout is:
| Date | Receipt item | Receipts | Outgo item | Outgo | Net cash flow |
|---|---|---|---|---|---|
| Stated date | Premium or other allocated inflow | Amount received | Expense, claim, or benefit | Amount paid or allocated | Receipts less outgo |
For a basic annual calculation, suppose entries occur at integer times \(0,1,\ldots,n\), and the effective annual investment return is a constant \(i\). The ledger is valued immediately after the entries at time \(n\). A net entry at time \(j\) is then accumulated for \(n-j\) years. If \(C_j\) denotes receipts less outgo recorded at time \(j\), and \(AS_0\) is the opening asset share immediately before time-0 entries, then:
This expression assumes the same effective annual return in each year and the stated date convention. It does not by itself determine which expenses or benefits belong in the ledger. With changing returns, irregular dates, or a different convention for whether a valuation is before or after transactions, the accumulation factors or dates must be adjusted to match the stated basis.
Why Dated Entries Accumulate This Way
The accumulation formula follows from the definition of an effective annual return. One dollar invested at time \(j\) becomes \(1+i\) dollars at time \(j+1\). Repeating that annual accumulation \(n-j\) times gives \((1+i)^{n-j}\) dollars at time \(n\). Multiplying by the signed cash flow \(C_j\) gives its value at the valuation date. Since accumulation is linear, the dated entries can be added, along with the similarly accumulated opening asset share.
A receipt is represented by a positive \(C_j\); an outgo is negative. Thus a benefit paid exactly at the valuation date has no investment period after payment: its factor is \((1+i)^0=1\). The date convention is part of the model, not a cosmetic detail.
Worked Ledger Calculations
Worked Example: Premiums, Expenses, and a Benefit
A hypothetical policy has zero opening asset share. At time 0 it receives a premium of $600 and incurs an acquisition expense of $120. At time 1 it receives a $600 premium and incurs a $50 allocated expense. At time 2 it pays a benefit of $200. The effective annual return is 4%, applied between successive integer dates. Find the asset share immediately after the time-2 benefit.
Method. Record receipts and outgo at their actual dates, form each date's net entry, and accumulate each net entry to time 2. This avoids treating all amounts as if they were received or paid at the same time.
| Time | Receipts | Outgo | Net entry | Accumulated to time 2 |
|---|---|---|---|---|
| 0 | $600 | $120 | $480 | $480(1.04)2 = $519.168 |
| 1 | $600 | $50 | $550 | $550(1.04) = $572.00 |
| 2 | $0 | $200 | −$200 | −$200 |
The time-0 net entry is $600 − $120 = $480 and earns two years of return. The time-1 net entry is $600 − $50 = $550 and earns one year. The time-2 benefit is paid at the valuation date and earns no return after payment. Therefore:
Rounded to the nearest cent, the asset share is $891.17. The calculation is checked by summing the ledger's accumulated entries: $519.168 + $572.00 − $200 = $891.168.
Common mistake avoided: Giving the time-0 entry only one year's return would use $480(1.04), even though it is invested from time 0 to time 2. The correct duration is two years.
Worked Example: Separating Issue Costs From Later Outgo
A hypothetical endowment policy starts with zero asset share. At time 0 it receives a premium of $900 and is allocated a $90 commission and $60 of issue expenses. At time 1 it receives a premium of $900 and incurs a $45 renewal expense. At time 2 it pays a maturity benefit of $1,500. Assume a constant effective annual return of 3%, with the ledger valued immediately after time-2 entries. Find the asset share.
Method. Show each receipt and expense separately, then accumulate the net amount for each date. The time-2 maturity payment is entered as outgo at time 2, not discounted or accumulated to another date.
| Time | Receipts | Outgo components | Net entry | Value at time 2 |
|---|---|---|---|---|
| 0 | $900 premium | $90 commission + $60 issue expenses | $750 | $750(1.03)2 = $795.675 |
| 1 | $900 premium | $45 renewal expense | $855 | $855(1.03) = $880.650 |
| 2 | $0 | $1,500 maturity benefit | −$1,500 | −$1,500 |
At time 0, the net entry is $900 − $90 − $60 = $750. At time 1, it is $900 − $45 = $855. Hence:
To the nearest cent, the asset share is $176.33. The intermediate values check: the time-0 entry accumulates for two years, the time-1 entry for one year, and the maturity benefit remains $1,500 at the time-2 valuation date. A positive result here does not establish that the policy's contractual benefit is funded under every possible basis; it is the result for the specified ledger and return.
Common mistake avoided: Combining the premiums and expenses into one total without dates would hide that the first net amount earns for two years and the second for one.
Worked Example: Carrying an Opening Asset Share Through an Exit
A hypothetical policy has an opening asset share of $250 immediately before time-0 entries. At time 0 it receives a $400 premium and is allocated a $25 expense. At time 1 it incurs a further allocated expense of $20. At time 2 it pays a $500 exit benefit and has no other entries. The effective annual return is 5%. Find the asset share immediately after the exit payment at time 2.
Method. Accumulate the opening asset share as well as each dated net entry. Include the exit benefit as negative outgo at time 2. It is not an instruction to set the asset share equal to the benefit.
The opening amount grows for two years: \(250(1.05)^2=250(1.1025)=275.625\). The time-0 net entry is \(400-25=375\), which also grows for two years: \(375(1.1025)=413.4375\). The time-1 expense is a net entry of \(-20\), which grows for one year: \(-20(1.05)=-21\). The time-2 exit benefit is \(-500\), with no accumulation after payment. Thus:
Rounded to the nearest cent, the asset share immediately after the exit payment is $168.06. The check is that the opening amount and time-0 entry each have two years of accumulation, the time-1 expense has one year, and the exit payment has none.
Common mistake avoided: Omitting the opening asset share would understate the result by its accumulated value, $275.625. The opening balance is part of the ledger even when all later cash flows are listed correctly.
Reading and Checking the Ledger
Before calculating an asset share, make the basis and date convention explicit. In particular, identify the policy, the valuation date, the opening asset share, the allocated receipts and outgo, and the investment return or accumulation factors. If an amount is allocated from a group total, record the allocation rule or the per-policy amount; do not silently treat a group total as a single-policy cash flow.
Several checks help catch errors:
- Sign check: receipts increase the asset share and expenses or benefits reduce it.
- Date check: an entry at time \(j\) is accumulated only from time \(j\) to the valuation date.
- Opening-balance check: carry the opening asset share forward under the same investment basis.
- Boundary check: under an immediately-after-entries valuation convention, a cash flow at the valuation date has accumulation factor 1.
- Interpretation check: the answer is the retrospective asset share on the stated basis, not automatically a reserve or a contractual exit amount.
A common exam trap is to apply the correct return for the wrong number of years. For example, a time-0 net receipt valued immediately after time-2 entries earns two annual returns, not one: its value is \(C_0(1+i)^2\), not \(C_0(1+i)\). Another trap is to accumulate a time-2 benefit beyond the date at which the asset share is requested. Its value at that date is simply the amount paid, with a negative sign in the ledger.
Check Your Understanding
For each problem, use the stated convention that the asset share is measured immediately after entries at the valuation date. Round dollar answers to the nearest cent.
- A policy has zero opening asset share. At time 0 it receives $200 and incurs a $30 expense. At time 1 it receives a $250 premium. The effective annual return is 2%. Find the asset share at time 2. (Answer: $431.87)
- A policy has an opening asset share of $100 before time-0 entries. At time 0 it receives $500 and incurs $80 of expense. At time 1 it pays a $100 benefit. The effective annual return is 4%. Find the asset share at time 2. (Answer: $458.43)
- A policy starts with zero asset share. At time 0 it receives a $1,000 premium and incurs a $100 commission. At time 1 it incurs $80 of expense. At time 2 it pays a $900 benefit. The effective annual return is 5%. Find the asset share after the time-2 payment. (Answer: $8.25)
- A policy has zero opening asset share. At time 0 it receives $300; at time 1 it receives $200 and incurs $40 of expense; at time 2 it incurs $25 of expense; at time 3 it pays a $400 benefit. The effective annual return is 3%. Find the asset share at time 3. (Answer: $71.81)
- A policy has an opening asset share of $300 before time-0 entries. At time 0 it receives $600 and incurs $100 of expense. At time 1 it receives $400. At time 2 it pays an exit benefit of $1,100. The effective annual return is 4%. Find the asset share immediately after the exit payment. (Answer: $181.28)