Management Actions and Their Solvency Trade-Offs

Introduction

When a life insurer faces pressure on its solvency position, management may consider actions such as changing charges, reducing future bonuses, or changing the investment mix. These actions do not have a single effect. A charge increase may improve projected income while reducing policyholder account values. A bonus reduction may lower the liability but reduce benefits. A more conservative investment mix may reduce stress losses while also lowering expected return.

The useful comparison is not simply “Does the action improve solvency?” It is: How does it change assets, liabilities, required capital, and policyholder outcomes, under which assumptions? This tutorial uses a simplified solvency measure to make those comparisons explicit. The scenarios and data are hypothetical.

Definition: Let $A$ be the value of assets, $L$ the value of liabilities, and $K$ the required capital under a specified basis. Define solvency surplus above required capital as $E=A-L-K$. For an action, its change in this measure is $\Delta E=\Delta A-\Delta L-\Delta K$. A positive $\Delta E$ improves this measure; it does not by itself establish that the action is suitable, contractually permitted, or beneficial to policyholders.

This measure is a deliberately simplified comparison. A real solvency assessment must use the applicable valuation and capital rules, reflect relevant risks and interactions, and account for implementation constraints. In the examples, all amounts are in dollars, no tax or transaction costs apply unless stated, and the same valuation basis is used before and after each action.

Separate the Solvency Effect from the Policyholder Effect

For a proposed action, first identify which cash flows or values change. Then evaluate each effect on the same basis. An increase in charges may increase assets through fees, but may also reduce the account value backing a policyholder’s benefit. A bonus reduction may lower liabilities, but is not a reduction in assets. Required capital may also move: its change must be included rather than assumed to be zero.

The equation for $\Delta E$ follows directly by subtracting the initial surplus from the revised surplus:

E_{\text{before}}=A_{\text{before}}-L_{\text{before}}-K_{\text{before}}, \qquad E_{\text{after}}=A_{\text{after}}-L_{\text{after}}-K_{\text{after}}.

\Delta E =E_{\text{after}}-E_{\text{before}} =(A_{\text{after}}-A_{\text{before}}) -(L_{\text{after}}-L_{\text{before}}) -(K_{\text{after}}-K_{\text{before}}) =\Delta A-\Delta L-\Delta K.

This identity explains why a liability reduction improves the measure, while an increase in required capital worsens it. It also prevents a common double count: a single economic effect must not be recorded both as an asset increase and as a liability decrease unless those are genuinely two distinct consequences of the action.

Worked Example: Increasing a Monthly Policy Charge

A hypothetical universal life block has assets of $10,000,000, liabilities of $8,400,000, and required capital of $1,200,000. Management considers increasing a monthly charge for one year. The projected fee income increases assets by $300,000. The lower policy account values reduce the measured liabilities by $250,000. Required capital increases by $20,000. Assume the fixed persistency basis used for these projections does not change. Calculate the revised solvency surplus and describe the policyholder effect.

Method. Calculate the initial surplus, then apply the three changes separately. The fee income is an asset effect; the reduction in policy account values is represented by the stated liability change.

Initially,

E_{\text{before}} =10{,}000{,}000-8{,}400{,}000-1{,}200{,}000 =400{,}000.

The action gives $\Delta A=300{,}000$, $\Delta L=-250{,}000$, and $\Delta K=20{,}000$. Therefore,

\Delta E =300{,}000-(-250{,}000)-20{,}000 =530{,}000.

The revised surplus is $400{,}000+530{,}000=\$930{,}000$. This agrees with calculating the revised components directly: assets are $10{,}300{,}000$, liabilities are $8{,}150{,}000$, and required capital is $1{,}220{,}000$, so $10{,}300{,}000-8{,}150{,}000-1{,}220{,}000=\$930{,}000$.

The policyholder cost is not zero: account values are lower by the amount represented in this projection, and the charge increase may affect persistency in practice. The calculation holds persistency fixed by assumption; it does not claim that policyholder behavior would remain unchanged.

Common mistake. A wrong calculation is $300{,}000-20{,}000=\$280{,}000$, which omits the liability reduction. Another error would be to count the $250,000 liability decrease as additional fee income. The correct change is $530,000 because the asset and liability changes are distinct inputs supplied by the scenario.

Bonus Decisions and Benefit Reductions

A reduction in a discretionary bonus can improve the stated solvency measure when it reduces the value of benefits included in liabilities. The benefit reduction should also be stated in policyholder terms. Whether a bonus is discretionary, already declared, or constrained by contractual terms matters: a projection cannot assume management may remove a benefit that is not legally or contractually reducible.

Worked Example: Reducing a Hypothetical Terminal Bonus

A hypothetical participating portfolio has 3,000 policies. Each policy has a projected terminal bonus of $800 included in the liability. Management considers reducing each projected bonus by 25%. On the same valuation basis, the total liability falls by the amount of the bonus reduction, and required capital falls by $100,000. Assets are unchanged. Assume the bonus is not guaranteed and that the proposed reduction is permitted under the product terms. Calculate the change in solvency surplus and the reduction per policy.

Method. Calculate the benefit reduction per policy, aggregate it across policies, and then apply the surplus identity. The expected number of policies and all other liability components are held fixed.

The reduction per policy is $0.25\times \$800=\$200$. Across 3,000 policies, the liability reduction is $3{,}000\times \$200=\$600{,}000$, so $\Delta L=-\$600{,}000$. Assets are unchanged, so $\Delta A=0$, and $\Delta K=-\$100{,}000$. Thus,

\Delta E =0-(-600{,}000)-(-100{,}000) =700{,}000.

The solvency surplus above required capital improves by $700,000 under the stated assumptions. The projected terminal bonus falls by $200 per policy. The capital reduction contributes $100,000 of the improvement in addition to the $600,000 liability reduction.

Common mistake. Counting only the liability reduction gives a $600,000 improvement and misses the stated capital release. Conversely, it would be wrong to report $700,000 as the aggregate bonus cut: the aggregate benefit reduction is $600,000, while the remaining $100,000 is a change in required capital.

Investment Allocation: Expected Return Versus Stress Loss

Changing the investment mix can alter both expected investment income and losses under a specified stress. These are different measures. A reduction in a particular stress loss does not prove that every risk has fallen, and an expected return is not a guaranteed outcome.

The next example uses a simple one-year comparison. The stress loss is measured from current asset value using the specified asset-class shocks. The required capital is defined in this example as that stress loss, with no other capital components. This is an illustrative comparison, not a general capital formula.

Worked Example: Shifting a Hypothetical Portfolio Toward Bonds

A hypothetical insurer has $5,000,000 invested. Bonds have an assumed expected one-year return of 3% and a stress return of $-2\%$. Equities have an assumed expected return of 7% and a stress return of $-25\%$. The current allocation is 60% bonds and 40% equities; the proposed allocation is 80% bonds and 20% equities. Liabilities are $4,400,000 and are held fixed for this comparison. Required capital equals the loss under the specified stress. Compare expected investment return, stress loss, and solvency surplus under each allocation.

Method. For each allocation, calculate the dollar amount in each asset class, the weighted expected return, and the stress loss. Then subtract liabilities and required capital from current assets.

Under the current allocation, bonds are $0.60\times \$5{,}000{,}000=\$3{,}000{,}000$, and equities are $0.40\times \$5{,}000{,}000=\$2{,}000{,}000$. Expected return is

3{,}000{,}000(0.03)+2{,}000{,}000(0.07) =90{,}000+140{,}000 =\$230{,}000.

The specified stress loss is $3{,}000{,}000(0.02)+2{,}000{,}000(0.25)=60{,}000+500{,}000=\$560{,}000$. Required capital is therefore $560,000, and the current solvency surplus is $5{,}000{,}000-4{,}400{,}000-560{,}000=\$40{,}000$.

Under the proposed allocation, bonds are $4,000,000 and equities are $1,000,000. Expected return is $4{,}000{,}000(0.03)+1{,}000{,}000(0.07)=120{,}000+70{,}000=\$190{,}000$. The specified stress loss is $4{,}000{,}000(0.02)+1{,}000{,}000(0.25)=80{,}000+250{,}000=\$330{,}000$. The revised surplus is $5{,}000{,}000-4{,}400{,}000-330{,}000=\$270{,}000$.

The proposed mix reduces expected one-year return by $40,000 and the specified stress loss by $230,000. On this simplified basis, solvency surplus improves by $270{,}000-40{,}000=\$230{,}000$. This conclusion is limited to the assumed returns, stress shocks, fixed liabilities, and capital definition; it does not establish that the proposed allocation is superior across all market outcomes or risks.

Common mistake. Applying the stress percentages to the expected-return amounts, or treating the 3% and 7% expected returns as stress returns, mixes two different scenarios. Use the expected return assumptions for the expected-income calculation and the specified negative stress returns for the stress-loss calculation.

Making the Comparison Decision-Useful

A management action is best evaluated with a consistent before-and-after projection, not by focusing on a single favorable line item. The following sequence makes the comparison auditable.

Define the action and constraints.
Specify what changes, when it takes effect, which contracts are affected, and whether the action is permitted by product terms and applicable requirements.

Set a common basis.
Keep the valuation date, assumptions, and capital definition consistent before and after the action. State explicitly any assumption that changes, such as persistency or investment return.

Measure each financial effect once.
Separate changes in assets, liabilities, and required capital. Use $\Delta E=\Delta A-\Delta L-\Delta K$ to reconcile the result.

Report the policyholder consequence.
Translate the action into a benefit, account-value, charge, or expected-return effect where the scenario permits. Do not present a solvency gain as though it were costless.

Test sensitivity and interaction.
Consider whether behavior or other risks could offset the projected gain. A charge increase, for example, may change lapses; a changed allocation may alter more than one stress measure.

The fixed-persistency assumption in the charge example illustrates an important limitation. If an action causes more policies to lapse, future fee income may be lower, expenses per remaining policy may rise, and guarantees or surrender benefits may become more costly. The net liability and capital effects must then be recalculated; the original fixed-persistency result cannot simply be carried forward.

Similarly, a bonus reduction should be distinguished from a change to a guaranteed benefit, and an investment shift should be assessed against the risks it actually changes. The most defensible conclusion identifies both the measured improvement and the assumptions or policyholder costs behind it. That approach is aligned with the SOA Exam ALTAM (Advanced Long-Term Actuarial Mathematics) syllabus.

Key takeaway: Compare actions using a consistent solvency measure, but do not confuse a solvency improvement with an unqualified improvement in the product. Report $\Delta A$, $\Delta L$, and $\Delta K$, state the policyholder consequence, and make the assumptions that could change the result visible.

Check Your Understanding

For each hypothetical case, use the stated assumptions and report the requested comparison.

A charge change increases assets by $14,400, reduces liabilities by $10,800, and increases required capital by $2,000. Calculate the change in solvency surplus and the average liability reduction per policy if 1,200 policies are affected. (Answer: surplus increases by $23,200; liability reduction averages $9 per policy.)
A hypothetical bonus of $500 per policy is reduced by 20% for 850 policies. Assets are unchanged and required capital falls by $15,000. Calculate the aggregate benefit reduction and the change in solvency surplus. (Answer: benefit reduction is $85,000; surplus increases by $100,000.)
A $2,000,000 portfolio shifts from 50% bonds and 50% equities to 70% bonds and 30% equities. Expected returns are 2% for bonds and 8% for equities; stress returns are $-3\%$ and $-20\%$, respectively. Calculate the change in expected return and the reduction in stress loss. (Answer: expected return falls from $100,000 to $76,000, a $24,000 decrease; stress loss falls from $230,000 to $162,000, a $68,000 reduction.)
A portfolio initially has assets of $4,800,000, liabilities of $4,100,000, and required capital of $500,000. A combined action increases assets by $90,000, reduces liabilities by $55,000, and increases required capital by $10,000. Calculate the initial and revised surplus. (Answer: initial surplus is $200,000; revised surplus is $335,000, an increase of $135,000.)
A proposed charge action increases fee assets by $120,000 and directly reduces liabilities by $100,000. A modeled lapse response then increases liabilities by $70,000 relative to the fixed-persistency projection, while required capital rises by $25,000. Calculate the net liability change and change in surplus, and compare with the fixed-persistency result. (Answer: net liabilities fall by $30,000; surplus increases by $125,000, compared with $195,000 under fixed persistency.)

What You'll Learn