Participating Contracts and Solvency Capital

Why Participating Benefits Matter for Solvency

A participating contract may provide both benefits the insurer must pay and benefits that depend on future surplus, investment performance, or a declared bonus scale. For solvency, these are not interchangeable. A vested bonus generally cannot be removed merely because assets perform poorly, while a future discretionary bonus may be reduced if the contract and the insurer’s established practices permit it. That distinction affects both the best-estimate liability and how much loss a stress can absorb.

The valuation must reflect the benefits policyholders can reasonably expect, not only the minimum contractual guarantee. At the same time, a solvency calculation must not treat a discretionary benefit as an unconditional guarantee if the insurer can credibly reduce it. The relevant assumptions and permitted management actions depend on the contract and valuation regime. The principles below are aligned with the SOA Exam ALTAM (Advanced Long-Term Actuarial Mathematics) syllabus; numerical capital measures are simplified illustrations, not regulatory formulas for a particular jurisdiction.

Definition: A guaranteed benefit is a benefit the insurer is contractually required to provide when the specified conditions are met. A declared or vested bonus is a bonus that, once declared under the contract, has become part of the benefit that must be paid. A future discretionary benefit (FDB) is a possible future benefit, such as a future bonus, whose amount can still be influenced by the insurer’s discretion, subject to contract terms, applicable law, established practice, and policyholder expectations.

A bonus label alone does not determine its solvency treatment. For example, an annual bonus may become guaranteed when declared, while a terminal bonus may remain discretionary until it is awarded. The actuary must identify the actual contractual status and any relevant policyholder expectations. A management action is an action the insurer assumes it can take in response to future conditions, such as reducing a future bonus scale. It must be consistent with the contract, the insurer’s established practices, and the assumptions required by the applicable valuation basis.

Separating the Liability Components

For a simplified valuation, divide the present value of benefits into guaranteed and discretionary components. The guaranteed component includes contractual benefits and bonuses already vested. The discretionary component is the present value of projected future benefits that remain discretionary but are included because policyholders are expected to receive them under the valuation assumptions. Expenses and other cash flows may also belong in a full best-estimate liability. A risk margin may be required separately, depending on the valuation basis.

\text{BEL}=\text{PV of guaranteed benefits}+\text{PV of future discretionary benefits}+\text{other best-estimate cash flows}.

The expected future discretionary benefits are not automatically equal to a fixed fraction of current assets or surplus. They should follow an explicit projection of future benefits and the assumed bonus policy, using appropriate assumptions for interest, decrements, expenses, and other relevant experience. If outcomes are modelled across scenarios, the valuation reflects the expected present value under the prescribed valuation approach. A guarantee remains in the liability even in a scenario where the insurer would prefer to reduce bonuses.

Worked Example: Valuing a Vested Bonus and a Projected Bonus

A hypothetical participating policy pays benefits at the end of year 2. The guaranteed maturity benefit is $1,000, and a declared, vested bonus of $120 is payable with it. The projected future discretionary bonus is $50 at maturity. Assume a flat effective annual discount rate of 4%, no mortality or lapse before maturity, and no expenses or risk margin. Find the present value of each component and the simplified benefit liability.

Method. Discount each amount due at year 2 by $v^2=(1.04)^{-2}$. The vested bonus is included with the guarantee because it is already payable under the contract; the projected $50 remains separately identified as discretionary.

v^2=\frac{1}{1.04^2}=\frac{1}{1.0816}=0.9245562\ldots

The guaranteed benefit including the vested bonus is $1{,}000+120=\$1{,}120$. Its present value is $1{,}120(0.9245562\ldots)=\$1{,}035.50$ to the nearest cent. The projected discretionary bonus has present value $50(0.9245562\ldots)=\$46.23$.

\text{Simplified benefit liability} =1{,}035.50+46.23 =\$1{,}081.73.

The component values and total are rounded to cents only at the end. As a check, the total undiscounted maturity benefit is $1{,}000+120+50=\$1{,}170$, and discounting it directly gives $1{,}170/1.0816=\$1{,}081.73$. The method avoids the mistake of excluding the vested bonus because it was originally declared as a bonus.

How Bonus Actions Affect Stressed Capital

Solvency capital measures the effect of adverse experience on the insurer’s financial position. In a simplified balance sheet, own funds equal the value of assets less technical provisions and any other relevant liabilities. A stress may reduce asset values, increase guaranteed liabilities, or change the projected future discretionary benefits. The change in own funds, not the change in one liability component by itself, shows the net financial loss in the stress.

\text{Own funds}=A-\text{TP}, \qquad \text{loss in stress}=\text{Own funds}_{0}-\text{Own funds}_{1},

Here $A$ denotes assets, $\text{TP}$ denotes technical provisions, subscript 0 denotes the position before stress, and subscript 1 denotes the position after stress. In a full capital assessment, the capital requirement may also reflect multiple stresses, aggregation, risk margins, tax effects, and rules specific to the regime. Therefore, the isolated loss in a single stress is an illustration of the mechanism, not necessarily the complete required capital.

A reduction in future bonuses can reduce a stressed liability, but only to the extent the assumed action is credible and permitted. Previously declared bonuses cannot generally be released as though they were still discretionary. Nor should an assumed bonus reduction be counted twice—for example, first as a fall in the liability and again as a separate capital benefit. The calculation should compare complete pre-stress and post-stress balance sheets with a consistent treatment of management actions.

Worked Example: Measuring a Stress Loss with a Bonus Reduction

A hypothetical insurer has assets of $125 million. Its technical provisions comprise a guaranteed-benefit liability of $96 million, an FDB liability of $12 million, and a $2 million risk margin. Under a one-year stress, assets fall to $114 million, the guaranteed-benefit liability rises to $101 million, and a credible reduction in future bonuses lowers the FDB liability to $7 million. Assume the risk margin remains $2 million for this illustration. Calculate own funds before and after stress and the isolated stress loss.

Method. Calculate technical provisions and own funds on both balance sheets, then take the difference in own funds. The bonus reduction affects only the future discretionary component.

Before stress, technical provisions are $96+12+2=\$110$ million, so own funds are $125-110=\$15$ million. After stress, technical provisions are $101+7+2=\$110$ million, so own funds are $114-110=\$4$ million. Therefore, the isolated stress loss is $15-4=\$11$ million.

As a check, assets have fallen by $11 million and technical provisions are unchanged in total, so own funds also fall by $11 million. If the FDB had incorrectly been left at $12 million after stress, stressed technical provisions would be $115 million and own funds would be $-\$1$ million, suggesting a $16 million loss. That calculation ignores the assumed credible bonus action; the correction is to include the FDB reduction once, in the stressed liability.

Why the Bonus Action Has Limits

The liability reduction from a future bonus action is limited by what can actually be changed. If a benefit has vested, it belongs in the guaranteed component for this purpose. If future bonuses are discretionary, the amount projected after stress must still reflect contractual constraints and policyholder expectations. An assumption that all future bonuses can be cancelled may overstate the insurer’s ability to absorb losses. Conversely, treating every projected future bonus as irrevocable may overstate the stressed liability when a reduction is genuinely available.

A useful way to show the mechanics is to write the post-stress liability as the stressed guaranteed component plus the FDB that remains after the assumed action. The difference between the pre-action and post-action FDB is a reduction in expected future payments; it is not a recovery of assets. Only its effect on the net balance sheet contributes to the change in own funds.

Worked Example: Applying a Floor to a Discretionary Bonus Reduction

A hypothetical participating fund has assets of $120 million, a guaranteed-benefit liability of $100 million, an FDB liability of $15 million, and a $2 million risk margin. Under stress, assets fall to $112 million and the guaranteed-benefit liability rises to $104 million. Before management action, the projected stressed FDB is $13 million. The insurer can reduce that projected FDB, but policyholder expectations and the assumed bonus policy require at least $6 million to remain. Assume the risk margin stays at $2 million. Find the maximum permitted reduction from the stressed FDB, the stressed own funds, and the isolated stress loss.

Method. Apply the floor to the stressed FDB, not to the pre-stress FDB. The amount that can be removed is $13-6=\$7$ million, leaving an FDB of $6 million.

Before stress, technical provisions are $100+15+2=\$117$ million, so own funds are $120-117=\$3$ million. After stress and the permitted action, technical provisions are $104+6+2=\$112$ million. Stressed own funds are $112-112=\$0$ million, so the isolated stress loss is $3-0=\$3$ million.

As a check on the action limit, cancelling the full $13 million stressed FDB would violate the $6 million floor. Without any bonus reduction, stressed technical provisions would be $104+13+2=\$119$ million and own funds would be $-\$7$ million, a $10 million loss from the initial $3 million. The permitted $7 million reduction improves stressed own funds by $7 million, bringing the loss to $3 million. The vested or guaranteed benefits have not been reduced.

A Practical Solvency Calculation

For a participating contract, a disciplined calculation keeps the guarantee, discretionary projection, and capital comparison visible. This makes it easier to identify whether an apparent capital benefit is coming from an asset movement, a change in guaranteed obligations, or a permitted future bonus action.

Classify each benefit.
Identify contractual guarantees, bonuses already vested, and benefits that remain discretionary. Do not classify solely by the name of the bonus.

Project the best-estimate cash flows.
Use the valuation assumptions and the assumed bonus policy to determine the expected future benefits and other relevant cash flows.

Apply the stress and management actions.
Recalculate asset values, guarantees, and future discretionary benefits. Apply only actions that are consistent with the contract and valuation basis.

Compare own funds consistently.
Subtract post-stress technical provisions from post-stress assets, then compare with pre-stress own funds. Include other components of the capital framework where required.

This separation matters because policyholder protection depends on the guaranteed floor, while the insurer’s actual liability may also include expected discretionary distributions. A stress can make the guaranteed component more costly at the same time that a reduction in future bonuses partly offsets the increase. The net capital effect depends on both sides of the balance sheet and on the credibility of the assumed action.

Common Exam Traps

Removing a declared bonus. A vested bonus is not a future discretionary benefit merely because it was once called a bonus. Keep it in the guaranteed cash flows when the contract requires payment.
Omitting expected future bonuses. A bonus that remains discretionary may still be included in the best-estimate liability when the valuation basis requires expected policyholder benefits to be projected.
Assuming unrestricted discretion. Do not reduce future bonuses below contractual constraints or a defensible level of policyholder expectation.
Calculating capital from liabilities alone. Capital impact is measured through the change in own funds, which depends on stressed assets as well as stressed technical provisions.
Counting the same action twice. If the FDB reduction is already reflected in post-stress technical provisions, do not add that same reduction again as a separate benefit to own funds.

Key takeaway: In solvency valuation, distinguish what is guaranteed from what remains discretionary. Project future discretionary benefits consistently, allow only credible bonus actions under stress, and measure the capital effect by comparing complete pre-stress and post-stress financial positions.

Check Your Understanding

Work through each question by separating guaranteed benefits from future discretionary benefits before calculating present values or stressed own funds.

A hypothetical policy pays a guaranteed $2,000 and a vested bonus of $100 at the end of year 4. A projected discretionary bonus of $80 is also expected then. At an effective annual interest rate of 3%, with no decrements or expenses, find the simplified present value of the benefits, rounded to cents. (Answer: $1,936.90)
An insurer has assets of $140 million, guaranteed-benefit liability of $110 million, FDB liability of $18 million, and risk margin of $3 million. After stress, the corresponding values are $130 million, $115 million, $12 million, and $3 million. Calculate pre- and post-stress own funds and the isolated stress loss. (Answer: $9 million before stress, $0 after stress, $9 million loss)
Before stress, assets are $120 million, guaranteed-benefit liability is $100 million, FDB is $15 million, and risk margin is $2 million. After stress, assets are $112 million, the guaranteed liability is $104 million, and the projected FDB before action is $13 million. The permitted action must leave at least $6 million of FDB, and the risk margin remains $2 million. Find the maximum reduction, stressed own funds, and stress loss. (Answer: $7 million reduction, $0 stressed own funds, $3 million loss)
A simplified liability has a guaranteed component of $80 million and an FDB component of $20 million. A stress leaves the guarantee unchanged and changes the FDB to $5 million after a credible action. Ignoring other cash flows and risk margin, by how much does the liability fall, and what share of the original liability is the fall? (Answer: $15 million; 15%)
A hypothetical insurer has pre-stress assets of $200 million and technical provisions of $185 million. Under stress, assets fall by $12 million, the guaranteed liability rises by $5 million, and the FDB falls by $4 million through a permitted action; all other provisions are unchanged. Calculate pre- and post-stress own funds and the stress loss. (Answer: $15 million before stress, $2 million after stress, $13 million loss)

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