Actuarial Mathematics for Modelling · Non-unit reserves for unit-linked contracts (zeroisation)

Unit-Linked Contracts and Non-Unit Cash Flows Explained

Updated 11 October 2026 · Fact-checked

A unit-linked contract invests the allocated part of each premium in a unit fund owned by the policyholder. The non-unit fund is the insurer's own account. Non-unit cash flow each year is premium less allocation, less expenses, plus charges, plus interest, less any death or other benefit cost above the unit fund value. Project it year by year.

Understand Unit-Linked Contracts and Non-Unit Cash Flows

A unit-linked contract ties the policyholder's benefit to the value of a pool of assets. The policyholder pays a premium. Part of it buys units in a fund. The value of those units moves with the investment return. This is the unit fund.

The insurer does not pay for the unit fund out of its own pocket. The unit fund belongs to the policyholder and is matched by assets of equal value. Everything else sits in the non-unit fund (also called the sterling or non-unit account). It holds the insurer's money: the part of the premium not allocated, the charges taken from the unit fund, the expenses paid, and any extra benefit cost.

The allocation percentage is the share of the premium that buys units. It is often low in the first year and higher later, because the insurer recovers commission and set-up costs early. If a bid-offer spread applies, units are bought at the offer price, so the allocated premium is further reduced by the spread. The part of the premium not allocated goes to the non-unit fund.

Charges move money from the unit fund to the non-unit fund. The common one is the annual management charge, a percentage of the fund value. There may also be a fixed policy fee. In return, the non-unit fund pays the expenses (initial, renewal, claim) and the benefit costs not covered by the fund. A typical death benefit is the higher of the unit fund value and a guaranteed sum. The unit fund pays its own value. The non-unit fund pays only the excess.

The non-unit cash flow is the net amount the insurer receives or pays each year on this account. It is often negative in year 1 because expenses are high and allocation is high. A negative flow means the insurer must put in capital. That is why we later calculate non-unit reserves (zeroisation). First you must get the cash flow right.

Key rules to remember

Allocated premium: A_t = α_t × P_t × (1 − s); α_t is the allocation percentage, P_t the premium, s the bid-offer spread as a proportion of the offer price (s = 0 if there is none). Check how the question defines the spread.
Unit fund roll-forward (charge at start of year): U_t = (U_(t−1) + A_t) × (1 − m) × (1 + g); m is the management charge as a proportion of the fund after allocation, g is the net unit fund growth rate. This is the fund per policy in force at start of year t, before deaths and withdrawals.
Management charge: AMC_t = m × (U_(t−1) + A_t); Charged at the start of the year in this layout. Use the timing stated in the question.
Non-unit cash flow at start of year: P_t − A_t − e_t + AMC_t (+ fixed fee if any); e_t is the expense at start of year t. The unallocated premium and charges come in. Expenses go out.
Non-unit cash flow at end of year, per policy in force at start: NUCF_t = (P_t − A_t − e_t + AMC_t) × (1 + j) − q_(x+t−1) × max(0, S − U_t); j is the non-unit (reserve or earned) interest rate. q is the death probability in the year. S is the guaranteed death benefit. Add other items such as surrender strain if the question gives them.
Expected cash flow per policy in force at time 0: Expected NUCF_t = (t−1)p_x × NUCF_t; Weight by the probability of being in force at the start of year t. Include lapses in the survival probability if given.

How to solve Unit-Linked Contracts and Non-Unit Cash Flows questions

Use this order for any projection question. Work per policy in force at the start of each year, and weight at the end only if asked.

1Write down the basis: premium, allocation percentages, bid-offer spread, charges, expenses, unit growth rate, non-unit interest rate, death and withdrawal rates, and the benefit definition.
2Compute the allocated premium for the year (allocation percentage times premium, then spread if given).
3Roll the unit fund forward: add the allocation to the opening fund, deduct the management charge, then grow at the unit fund rate.
4Compute the start-of-year non-unit cash flow: premium minus allocation, minus expenses, plus charges and fees.
5Add interest on that amount at the non-unit rate to bring it to the end of the year. Use the same rate for negative amounts unless told otherwise.
6Deduct the end-of-year extra benefit costs: death probability times the excess of the guarantee over the fund value, plus any surrender or maturity strain.
7If the question asks for expected values, multiply by the probability that the policy is in force at the start of the year.
8State the result with sign and timing, and say what a negative figure means: the insurer funds it.

Quickest way: Five-line column layout

When to use it: Use it for multi-year projections in the written paper where you must fill a table quickly.

Set up columns: Premium, Allocation, Opening fund, Charge, Closing fund.
Set up columns: Expense, Start-of-year flow, Interest, Extra death cost, NUCF.
Fill the first column fully for all years before the second, since the fund feeds the death cost.
Check one row with a sanity test: start flow equals premium minus allocation minus expense plus charge.
Mark each row's timing (start or end of year) so you do not add them together without interest.

Common mistakes in Unit-Linked Contracts and Non-Unit Cash Flows

Treating the whole premium as income to the insurer.
Students copy the traditional profit test layout, where the premium is fully in the insurer's fund.
Fix: Split the premium first. Only the unallocated part and the charges reach the non-unit fund.
Deducting the full death benefit in the non-unit cash flow.
The benefit is paid on death, so it looks like an outgo.
Fix: The unit fund pays its own value. The non-unit fund pays only the excess of the guarantee over the fund value, and zero if the fund is higher.
Charging the management charge on the opening fund instead of the fund after allocation (or the reverse).
Students do not read the timing in the question.
Fix: Read the basis. If the charge is at the start of the year after allocation, it applies to opening fund plus allocation.
Adding start-of-year and end-of-year items without interest.
All items belong to the same policy year, so they seem to belong to the same date.
Fix: Accumulate start-of-year items for one year at the non-unit rate before combining with end-of-year benefit costs.
Growing the unit fund at the non-unit interest rate.
Two interest rates appear in the question and they get mixed up.
Fix: Label them. The unit growth rate drives the fund. The non-unit rate applies to the insurer's cash flows.
Using the unit fund value per policy in force at start without adjusting for deaths when finding the death cost.
Students forget the fund at end of year is before decrements.
Fix: Take the fund per policy at end of year. Multiply the excess by the death probability for a cost per policy in force at start of year.

Worked examples

Example 1

A 10-year unit-linked policy has an annual premium of ₹50,000. In year 1, 90% of the premium is allocated to units and there is no bid-offer spread. The expense at the start of year 1 is ₹3,000. An annual management charge of 1% of the fund after allocation is taken at the start of the year. The unit fund grows at 6% a year. Non-unit cash flows earn 4% a year. The death benefit, paid at the end of the year of death, is the greater of the unit fund and ₹5,00,000. The probability of death in year 1 is 0.002. Ignore withdrawals. Find the non-unit cash flow at the end of year 1 per policy in force at the start.

Show the solution

Allocated premium = 0.90 × 50,000 = ₹45,000.
Management charge = 1% × 45,000 = ₹450.
Unit fund at end of year = (45,000 − 450) × 1.06 = 44,550 × 1.06 = ₹47,223.
Start-of-year non-unit flow = 50,000 − 45,000 − 3,000 + 450 = ₹2,450.
With interest at 4%: 2,450 × 1.04 = ₹2,548.
Extra death cost = 0.002 × (5,00,000 − 47,223) = 0.002 × 4,52,777 = ₹905.55.
NUCF at end of year 1 = 2,548 − 905.55 = ₹1,642.45.

Answer: About ₹1,642 at the end of year 1 per policy in force at the start.

Example 2

A unit-linked policy has an annual premium of ₹20,000. In year 1, 95% of the premium is allocated and there is no bid-offer spread. The expense at the start of year 1 is ₹3,000. The management charge is 1% of the fund after allocation, taken at the start of the year. Non-unit cash flows earn 5% a year. The death benefit is the unit fund value only. Find the non-unit cash flow at the end of year 1 per policy in force at the start, and say what the sign means.

Show the solution

Allocated premium = 0.95 × 20,000 = ₹19,000.
Management charge = 1% × 19,000 = ₹190.
Start-of-year non-unit flow = 20,000 − 19,000 − 3,000 + 190 = −₹2,810.
Interest at 5%: −2,810 × 1.05 = −₹2,950.50.
The death benefit equals the unit fund, so the non-unit fund pays no extra death cost.
NUCF at end of year 1 = −₹2,950.50.
The negative sign means the insurer must provide funds in year 1. The expense and the high allocation are not covered by the unallocated premium and charges.

Answer: −₹2,950.50 at the end of year 1. This is a cash strain the insurer must finance.

Exam tips

Write the timing of every item (start or end of year) next to it before you calculate. Many marks are lost on timing.
Always state whether your cash flow is per policy in force at the start of the year or an expected value from time 0.
Show the unit fund projection even if the question asks only for the non-unit flow. The death cost depends on it, and method marks are given for it.
In MCQs, check the sign and the guarantee condition first. Often the fund is above the guarantee, so the extra death cost is zero.
If you are asked to comment, say what a negative flow means and link it to the need for non-unit reserves.

Practice questions from Non-unit reserves for unit-linked contracts (zeroisation)

Unit-Linked Contracts and Non-Unit Cash Flows: frequently asked questions

What is the difference between the unit fund and the non-unit fund?

The unit fund holds the policyholder's units, and its value moves with investment returns. The non-unit fund is the insurer's own account. It receives unallocated premium and charges, and pays expenses and benefit costs not met by the unit fund.

What is the difference between a unit reserve and a non-unit reserve?

The unit reserve equals the value of the units held for the policyholder, and is backed by matching assets. The non-unit reserve is extra money the insurer holds from its own funds to cover expected future negative non-unit cash flows.

Why is the non-unit cash flow often negative in year 1?

Initial expenses and commission are high, and the allocation percentage may be high too. The unallocated premium and the first charge may not cover them. Later years usually give positive flows.

Does the insurer pay the full death benefit from the non-unit fund?

No. The unit fund pays its own value. The non-unit fund pays only the excess of any guaranteed amount over the fund value. If the fund exceeds the guarantee, the extra cost is zero.

Which interest rate do I use for non-unit cash flows?

Use the non-unit interest rate given in the basis. It is separate from the unit fund growth rate. Read the question for which rate applies to which part.