Why Lapse Stress Is Not Just a Policy-Count Change
A higher lapse rate can reduce future guarantee exposure, but it also removes future charges and may require an immediate surrender payment. For participating contracts, declared reversionary bonuses can increase both the liability released at lapse and the amount payable to a departing policyholder. The net effect therefore depends on what the insurer pays, what liabilities it releases, and what future income it gives up.
The useful comparison is not simply “fewer policies means less risk.” A lapse can improve own funds when the reserve released exceeds the surrender payment, or weaken own funds when the surrender payment exceeds that reserve. Even a positive change in own funds does not by itself establish that the solvency position improves: required capital may also change under the stressed scenario.
The liability \(L\) is the net liability being released, not necessarily just the guaranteed benefit. It can include the present value of benefits and guarantees less the value of future charges or other income included in the valuation. Once the policy lapses, those future charges will not be received, so they reduce the net liability release. The surrender amount \(S\) must reflect the payment actually made under the contract, including any amounts due because of declared or vested bonuses.
Deriving the Own-Funds Effect
Suppose a lapse causes the insurer to pay \(S\) immediately and to remove a liability of \(L\). Other balance-sheet items are unchanged. Assets therefore decrease by \(S\), while liabilities decrease by \(L\). Since own funds equal assets minus liabilities, the change is:
This calculation isolates the lapse itself. For a group of identical policies, with no interaction between policies, \(n\) additional lapses change own funds by \(n(L-S)\). In a full valuation, the remaining policies may also have different liabilities after the lapse stress. Their revaluation must be added separately; it is not captured by simply multiplying the per-lapse result.
Include the relevant guarantee and bonus commitments, then allow for future charges or margins that will no longer be received.
Use the payment due on lapse, not automatically the account value or the full guaranteed benefit.
Subtract the surrender payment from the released liability, then multiply by the number of additional lapses when the policies are sufficiently alike.
Combine the own-funds change with the change in required capital and any revaluation of the policies that remain in force.
Worked Applications
Worked Example: Linked Account, Guarantee, and Lost Charges
Method. Calculate the net liability per lapse, compare it with the surrender payment, and apply the result to the increase in lapses. A hypothetical linked contract has an account-value liability of $10,000 and an additional guarantee liability of $1,100. The present value of future charges included in the valuation is $500. The surrender payment is $9,700. In a block of 1,000 contracts, the annual lapse rate rises from 10% to 25%. Find the change in own funds attributable to the additional lapses. Assume the per-policy values are the same for all contracts and ignore any revaluation of survivors.
Step 1: Find the net liability released. The account-value and guarantee liabilities total \(10{,}000+1{,}100=11{,}100\). Subtract the $500 present value of future charges that will be lost:
Step 2: Find the own-funds effect per lapse. The reserve release exceeds the surrender payment by:
Each lapse therefore increases own funds by $900 on the stated valuation basis. As a component check, the $300 difference between the account value and surrender payment, plus the $1,100 guarantee release, less $500 of lost future charges, also equals \(300+1{,}100-500=900\).
Step 3: Find the additional lapses. The increase in rate is \(25\%-10\%=15\%\), so the number of additional lapses is \(1{,}000(0.15)=150\).
Step 4: Scale the result.
The lapse stress increases own funds by $135,000, before any change in the valuation of continuing contracts or required capital. The common mistake is to treat all $1,100 of guarantee liability as the gain and omit both the surrender payment and lost charges. The net result is $900, not $1,100.
Worked Example: A Declared Bonus and the Surrender Amount
Method. Recalculate both the released liability and the surrender payment after including the declared bonus. A hypothetical participating contract has a guaranteed base liability of $10,000. A declared reversionary bonus adds $1,000 to the guaranteed liability. The present value of future shareholder margins is $400. The surrender payment is $9,700 without the declared bonus and $10,500 with it. In a block of 600 contracts, the lapse rate rises from 5% to 15%. Assume these values apply consistently to each additional lapse.
Step 1: Calculate the net liability released after declaration.
Step 2: Compare the release with the bonus-inclusive surrender payment.
Each additional lapse increases own funds by $100. The increase in lapse rate is \(10\%\), giving \(600(0.10)=60\) additional lapses. The total own-funds change is \(60(100)=\$6{,}000\).
For comparison, without the declared bonus the net liability would be \(10{,}000-400=\$9{,}600\), and the surrender payment would be $9,700. The per-lapse effect would then be \(9{,}600-9{,}700=-\$100\). The bonus increases the liability release by $1,000 but increases the surrender payment by $800, shifting the lapse effect by \(1{,}000-800=\$200\), from a $100 decrease to a $100 increase per lapse. The common mistake is to include the bonus in the liability but leave the surrender payment at its pre-bonus value.
Worked Example: Combining Product Effects and Capital
Method. Calculate the additional own-funds effect for each block, add the effects, and then compare the stressed own funds with stressed required capital. All values are hypothetical. A linked block has 800 policies; its lapse rate rises from 8% to 23%, its released liability is $10,600 per lapse, and its surrender payment is $10,900. A participating block has 500 policies; its lapse rate rises from 5% to 15%, its released liability, including declared bonuses and net of future margins, is $10,400 per lapse, and its surrender payment is $10,100. Before the stress, own funds are $1,500,000 and required capital is $1,200,000. After the stress, the full capital calculation gives required capital of $1,240,000. Ignore other balance-sheet changes.
Linked block. The lapse-rate increase is \(23\%-8\%=15\%\), so \(800(0.15)=120\) additional policies lapse. The own-funds effect per lapse is \(10{,}600-10{,}900=-\$300\). The block effect is \(120(-300)=-\$36{,}000\).
Participating block. The lapse-rate increase is \(15\%-5\%=10\%\), so \(500(0.10)=50\) additional policies lapse. The effect per lapse is \(10{,}400-10{,}100=\$300\). The block effect is \(50(300)=\$15{,}000\).
Combined own-funds change. The total is \(-36{,}000+15{,}000=-\$21{,}000\), so stressed own funds are \(1{,}500{,}000-21{,}000=\$1{,}479{,}000\).
Solvency comparison. Before stress, the margin of own funds over required capital is \(1{,}500{,}000-1{,}200{,}000=\$300{,}000\). After stress, it is \(1{,}479{,}000-1{,}240{,}000=\$239{,}000\). The margin falls by \(300{,}000-239{,}000=\$61{,}000\). This agrees with the $21,000 decrease in own funds plus the $40,000 increase in required capital. The common mistake is to conclude that the own-funds effect alone gives the change in solvency margin.
How to Interpret a Lapse Stress
The sign of \(L-S\) is a useful first test, not a complete description of the stress. In linked business, the liability release may include an account-value component and a guarantee component, while the surrender payment may differ from the account value. If the payment exceeds the net reserve release, additional lapses reduce own funds. The loss of future charges can make this outcome more adverse by reducing the net liability released.
In participating business, distinguish amounts already declared and guaranteed from future discretionary bonuses. A declared reversionary bonus may increase the amount payable on surrender as well as the liability released. Do not assume that a future discretionary bonus is a guaranteed liability or that it is automatically included in surrender value; use the contract terms and the stated valuation basis. Bonus treatment can change the sign of the lapse effect, as the worked example shows.
A stressed lapse rate also changes the number and composition of policies that remain. If their guarantee exposure or liability changes under the stress, revalue them using the applicable assumptions rather than treating the additional lapses as the only effect. Finally, calculate required capital under the stressed scenario on its own basis. The change in solvency margin is the change in own funds minus the change in required capital.
Check Your Understanding
For each problem, use the stated assumptions and include all specified items in the net liability release.
- A hypothetical linked contract has an account-value liability of $8,200, an additional guarantee liability of $900, and a present value of future charges of $300. Its surrender payment is $8,450. What is the own-funds effect per lapse? (Answer: +$350 per lapse)
- A block has 200 more lapses under a stress than under the baseline. The reserve released is $9,500 per policy and the surrender payment is $9,620 per policy. What is the aggregate own-funds change, ignoring survivor revaluation? (Answer: −$24,000)
- A participating block of 900 policies has a lapse rate increase from 4% to 14%. Per policy, the guaranteed base liability is $8,000, the declared bonus adds $600, and future margins have a present value of $250. The surrender payment, including the declared bonus, is $8,200. Find the own-funds effect of the additional lapses. (Answer: +$13,500)
- Before a lapse stress, own funds are $2,400,000 and required capital is $1,900,000. The stress reduces own funds by $75,000 and increases required capital by $25,000. Find the stressed solvency margin and its change from the baseline. (Answer: stressed margin $400,000; decrease of $100,000)
- A linked block of 500 policies has a lapse rate increase from 12% to 20%. Per lapse, the account-value liability is $12,000, the guarantee liability is $1,600, future charges have a present value of $700, and surrender is $12,500. A participating block of 300 policies has a lapse rate increase from 5% to 15%. Per lapse, its guaranteed liability is $9,000, declared bonuses add $900, future margins have a present value of $200, and surrender is $9,800. What is the combined own-funds change, ignoring survivor revaluation? (Answer: +$13,000)