Mortality Experience Profit in Universal Life

Introduction

Universal life mortality profit depends on more than the number of death claims. The insurer receives cost-of-insurance charges, pays death benefits, and may release reserves when policies terminate. To isolate mortality experience, compare actual and expected profit on a consistent basis, keeping the other cash flows and assumptions fixed.

This tutorial develops two compatible ways to make that comparison. One uses net claim costs, such as the death benefit less the account value supporting it. The other uses a profit calculation that explicitly includes the reserve released on death. The methods are alternatives for different accounting setups: do not subtract an account value as a net claim cost and then subtract the same value again as a reserve release.

Definition: Mortality experience profit is actual profit less the profit expected under a specified mortality basis, with other assumptions and cash flows held fixed. A positive difference is a mortality gain; a negative difference is a mortality loss. In a universal life model, cost-of-insurance charges are mortality-related income, while death claims and the release of reserves on death are mortality-related outgo and offsets.

Set the Mortality Accounting Basis

For a group of policies, let $N$ be the number in force at the start of a period, $q$ the expected probability of death during that period, and $D$ the actual number of deaths. Assume the policies are otherwise treated alike for the calculation. The expected number of deaths is $Nq$, and the expected number of survivors is $N(1-q)$. Expected counts can be fractional; they are calculation averages, not predictions that a fractional person will die.

Let $C$ be total cost-of-insurance charges collected during the period. In a mortality-only comparison, hold $C$ fixed between expected and actual results. This isolates the effect of actual deaths differing from expected deaths. If charges vary with account values, timing, or the number of policies in force, those effects must either be modeled explicitly or attributed separately; they should not silently be treated as mortality differences.

When the account value is paid as part of the death benefit, a useful claim measure is the net amount at risk (NAR): the death benefit less the account value available to support it. Under a level death benefit $B$ and account value $AV$, for example, $\text{NAR}=B-AV$. The net claim cost for $D$ deaths is $D$ times the applicable NAR, if that amount is constant for the group and period.

A different but equivalent bookkeeping approach can be used when reserves are shown explicitly. Let $R_0$ be the reserve per policy at the start of the period and $R_1$ the end-of-period reserve per surviving policy. Let $B$ be the gross death benefit paid per death. With no other cash flows in the mortality calculation, profit is charges plus opening reserves, less claims and closing reserves. The reserve for a policy that dies is not included in closing reserves: it is released.

\begin{aligned} \text{Actual profit} &= C+NR_0-DB-(N-D)R_1,\\ \text{Expected profit} &= C+NR_0-NqB-N(1-q)R_1. \end{aligned}

These equations assume deaths occur during the period and that the stated death benefit and reserve timing match the accounting convention. They do not include interest, expenses, premiums, lapses, or changes in reserves for other reasons. Include those items in a full profit test, but do not attribute them to mortality unless the analysis specifically calls for it.

Why Excess Deaths Create a Net Claim Cost

The reserve formula can be rearranged to show the effect of each death. Add and subtract $NR_1$ in the actual profit expression:

\begin{aligned} C+NR_0-DB-(N-D)R_1 &=C+N(R_0-R_1)-D(B-R_1). \end{aligned}

The closing reserve that would have been held for all $N$ policies is reduced by the reserve released on the $D$ deaths. Consequently, each death has a net cost of $B-R_1$: the benefit is paid, but the reserve $R_1$ is released. Subtract expected profit from actual profit. The common charges and opening reserves cancel, giving

\text{Mortality experience profit} =(Nq-D)(B-R_1).

If $B>R_1$, actual deaths above expected produce a loss, and actual deaths below expected produce a gain. If $B=R_1$, the net death cost in this simplified model is zero. The sign depends on actual minus expected profit, not on whether the actual profit itself is positive or negative.

Choose one accounting method.
Use net claim costs such as NAR when account values are already netted from claims, or use gross benefits and explicit reserve releases when reserves are modeled. Do not combine the two treatments for the same amount.

Calculate expected mortality.
For each group, multiply the number in force by the expected death probability to obtain expected deaths.

Calculate expected and actual profit.
Apply the same charge and reserve conventions to both results; change only the mortality experience being tested.

Subtract expected from actual.
Report the difference as a gain if positive or a loss if negative, and check that its direction agrees with the difference between actual and expected deaths.

Worked Examples

Worked Example: Net Claim Costs and Cost-of-Insurance Charges

A hypothetical insurer has two universal life blocks. In block A, 100 policies have expected mortality $q=0.020$ and a net claim cost of $50,000 per death. In block B, 200 policies have expected mortality $q=0.010$ and a net claim cost of $20,000 per death. Total cost-of-insurance charges collected are $100,000. Actual deaths are 1 in block A and 3 in block B. Calculate expected profit, actual profit, and mortality experience profit. No separate reserve-release amount is provided; the stated net claim costs are the claim measure for this calculation.

Method. Calculate expected and actual net claim costs by block. Subtract these costs from the same $100,000 of charges. This compares the two mortality outcomes without inventing a separate reserve item.

Expected claims in block A. Expected deaths are $100(0.020)=2$. Expected net claim cost is $2($50{,}000)=$100{,}000$.

Expected claims in block B. Expected deaths are $200(0.010)=2$. Expected net claim cost is $2($20{,}000)=$40{,}000$. Total expected net claim cost is $$100{,}000+$40{,}000=$140{,}000$.

Expected profit is charges less expected net claim cost: $$100{,}000-$140{,}000=-$40{,}000$.

Actual claims in block A. One death at $50,000 gives an actual net claim cost of $$50{,}000$.

Actual claims in block B. Three deaths at $20,000 each give an actual net claim cost of $3($20{,}000)=$60{,}000$. Total actual net claim cost is $$50{,}000+$60{,}000=$110{,}000$.

Actual profit is $$100{,}000-$110{,}000=-$10{,}000$. Therefore, mortality experience profit is $-$10{,}000-(-$40{,}000)=+$30{,}000$, a gain. The result checks: actual net claim costs are $30,000 below expected costs, while charges are unchanged.

Common mistake avoided. Do not confuse a negative actual profit with a mortality loss. Here both profits are negative, but actual profit is $30,000 higher than expected, so mortality experience is favorable.

Worked Example: Including a Reserve Release on Death

A hypothetical universal life block has 500 policies in force. Each policy has a beginning reserve of $18,000. The cost-of-insurance charge is $120 per policy for the period. The expected death probability is $q=0.020$, the death benefit is $100,000, and the end-of-period reserve for each survivor is $20,000. Actual deaths are 14. Find expected profit, actual profit, and the mortality experience result. Assume no other cash flows, and assume the $20,000 reserve is released for each policy that dies.

Method. Use the gross-benefit reserve equation. The charge income and opening reserves are included in both profit calculations. The closing reserve applies only to survivors.

Total charges are $500($120)=$60{,}000$, and total opening reserves are $500($18{,}000)=$9{,}000{,}000$.

Expected deaths are $500(0.020)=10$, so expected claims are $10($100{,}000)=$1{,}000{,}000$. Expected survivors are $500-10=490$, giving expected closing reserves of $490($20{,}000)=$9{,}800{,}000$. Thus expected profit is $$60{,}000+$9{,}000{,}000-$1{,}000{,}000-$9{,}800{,}000=-$1{,}740{,}000$.

Actual claims are $14($100{,}000)=$1{,}400{,}000$. Actual survivors are $500-14=486$, with closing reserves of $486($20{,}000)=$9{,}720{,}000$. Actual profit is $$60{,}000+$9{,}000{,}000-$1{,}400{,}000-$9{,}720{,}000=-$2{,}060{,}000$.

Mortality experience profit is $-$2{,}060{,}000-(-$1{,}740{,}000)=-$320{,}000$, a loss. As a check, actual deaths exceed expected deaths by $14-10=4$, and the net cost per death after reserve release is $$100{,}000-$20{,}000=$80{,}000$. Four excess deaths produce a loss of $4($80{,}000)=$320{,}000$.

Common mistake avoided. Subtracting all 500 end-of-period reserves would incorrectly retain a reserve for policies that died. The correct closing reserve is based on the 486 actual survivors.

Worked Example: Checking a Mortality Result Against NAR

A hypothetical block has 250 policies in force. Each has a $150,000 death benefit and a $50,000 account value, so the net claim cost is $100,000 per death. Total cost-of-insurance charges are $20,000. Expected mortality is $q=0.005$, and actual deaths are 3. Calculate expected and actual mortality results using net claim costs, then determine the experience gain or loss. No separate reserve release is specified.

Method. First determine the NAR, then use it as the claim cost per death. Because this method already uses the net cost, do not also subtract a reserve release.

The NAR per policy is $$150{,}000-$50{,}000=$100{,}000$. Expected deaths are $250(0.005)=1.25$, so expected net claim cost is $1.25($100{,}000)=$125{,}000$. Expected mortality result is charges less expected cost: $$20{,}000-$125{,}000=-$105{,}000$.

Actual net claim cost is $3($100{,}000)=$300{,}000$. Actual mortality result is $$20{,}000-$300{,}000=-$280{,}000$. The experience difference is $-$280{,}000-(-$105{,}000)=-$175{,}000$, a loss.

The check is the excess death count, $3-1.25=1.75$, multiplied by the $100,000 net claim cost: $1.75($100{,}000)=$175{,}000$ of loss. Fractional expected deaths are appropriate in an expected-value calculation.

Common mistake avoided. Using the $150,000 gross death benefit as the net claim cost would overstate mortality costs by including the $50,000 account value that supports the benefit.

Interpreting the Result and Avoiding Double Counting

The two calculation methods answer related questions but rely on different descriptions of the claim and liability:

Calculation basis	Death-related cost used	How to treat reserves or account values
Net claim cost	Deaths multiplied by NAR or another stated net cost	Do not subtract the same account value or reserve release a second time
Gross benefit with explicit reserves	Death benefit less the reserve released on each death	Include opening reserves and closing reserves for survivors

In an actual universal life profit test, the account value, the contractual death benefit, charges, and reserve basis must be identified precisely. If the death benefit is a fixed amount and the account value is paid in addition to or as part of that amount, the applicable claim measure depends on the contract’s benefit definition and the accounting basis. State that basis before calculating. A reserve release is not automatically equal to the account value.

The calculation here isolates mortality only. A separate analysis may be needed when cost-of-insurance charges depend on the account value, when policies terminate at different times, or when the valuation basis changes. In those cases, use the relevant period-specific exposures and cash flows, and keep mortality effects distinct from interest, lapse, and expense effects. This tutorial is aligned with the SOA Exam ALTAM (Advanced Long-Term Actuarial Mathematics) syllabus.

Common Exam Traps

Reporting actual profit instead of experience profit. Mortality experience profit is actual profit minus expected profit; an actual loss can still be a gain relative to a larger expected loss.
Reversing the sign. When net claim cost is positive, more deaths than expected reduce profit. Check the sign against that direction before finalizing.
Applying the reserve release to all policies. The reserve is released for deaths, while closing reserves are held for survivors only.
Counting the same value twice. If a net claim cost already subtracts account value or another supporting amount, do not subtract it again as a reserve release.
Changing charges between actual and expected results without explanation. If the task is to isolate mortality experience, hold the other cash flows fixed unless the problem explicitly says otherwise.

Key takeaway: State the accounting basis first. With net claim costs, compare cost-of-insurance charges against expected and actual net claims. With explicit reserves, calculate profit using gross benefits and survivor closing reserves. In either case, mortality experience profit is actual profit less expected profit.

Check Your Understanding

For each problem, use the stated accounting basis and report a positive experience result as a gain and a negative result as a loss.

A block has 400 policies, expected mortality $q=0.015$, a net claim cost of $30,000 per death, and $90,000 of charges. Actual deaths are 8. Find expected profit, actual profit, and the experience result. (Answer: expected profit $-$90,000$; actual profit $-$150,000$; mortality loss $$60,000$.)
A block has 300 policies, $14,000 opening reserve per policy, $200 charges per policy, expected mortality $q=0.020$, a $70,000 benefit, and a $15,000 end reserve per survivor. Actual deaths are 4. Find expected and actual profit and the experience result. (Answer: expected profit $-$570,000$; actual profit $-$460,000$; mortality gain $$110,000$.)
Group A has 200 policies, expected mortality $q=0.010$, and a $40,000 net claim cost per death. Group B has 100 policies, expected mortality $q=0.030$, and a $20,000 net claim cost per death. Total charges are $50,000. Actual deaths are 4 in A and 1 in B. Find the expected and actual results and the experience result. (Answer: expected result $-$90,000$; actual result $-$130,000$; mortality loss $$40,000$.)
A block has 800 policies, $22,000 opening reserve per policy, $180 charges per policy, expected mortality $q=0.0125$, a $90,000 death benefit, and a $25,000 end reserve per survivor. Actual deaths are 13. Calculate expected profit, actual profit, and the experience result. (Answer: expected profit $-$2,906,000$; actual profit $-$3,101,000$; mortality loss $$195,000$.)
Group A has 100 policies and expected mortality $q=0.010$; group B has 200 policies and expected mortality $q=0.020$. Both groups have a $50,000 benefit and a $10,000 end reserve per survivor. Each policy has a $9,000 opening reserve, and total charges are $45,000. Actual deaths are 0 in A and 6 in B. Find expected and actual profit and the mortality experience result. (Answer: expected profit $-$455,000$; actual profit $-$495,000$; mortality loss $$40,000$.)

What You'll Learn