Solvency Balance Sheets for Long-Term Insurers

Purpose and Structure of a Solvency Balance Sheet

A solvency balance sheet gives a snapshot of an insurer’s financial position at a specified valuation date. Its central task is to distinguish what the insurer holds from what it owes, then identify the amount left after those obligations are recognized. That residual can be compared with a separately stated capital requirement, but the requirement is not itself a liability on the balance sheet.

The figures must be measured on a consistent basis. Assets, technical provisions, and other liabilities should refer to the same date and the same scope of business. In the examples below, all amounts are hypothetical and are stated in millions of dollars. The balance-sheet arithmetic is aligned with the SOA Exam ALTAM (Advanced Long-Term Actuarial Mathematics) syllabus; it does not prescribe a particular regulatory valuation basis.

Definition: At a valuation date, let $A$ denote the value of assets, $T$ the value of technical provisions, and $L$ the value of other liabilities. The balance-sheet residual is $$ R=A-T-L. $$ It is the amount remaining after the stated liabilities are deducted from the stated assets. A capital requirement, denoted here by $C$, is a separate benchmark against which the residual may be compared; it is not included in $T$ or $L$ merely because it is a capital requirement.

Technical provisions represent obligations associated with the insurance business under the valuation basis being used. Other liabilities include obligations that are not included in those provisions, such as a separately recognized payable. The exact classification depends on the balance-sheet definitions supplied for a particular problem. The practical rule is to place each amount once, in the appropriate category, and not to omit or duplicate it.

If a problem asks whether the residual exceeds a stated capital requirement, the simple arithmetic comparison is $R-C$. A positive result is the amount by which the residual exceeds that benchmark; a negative result is the amount by which it falls short. This comparison alone does not establish that every dollar of the residual meets any separate eligibility or availability rules. Those questions require additional definitions and are outside the balance-sheet construction performed here.

Why the Balance-Sheet Identity Works

The identity follows from the basic accounting relationship: assets are funded by liabilities and the remaining net amount. In this setting, the liabilities are divided into technical provisions and other liabilities. Rearranging that relationship gives the residual directly.

A=T+L+R \qquad\Longleftrightarrow\qquad R=A-T-L.

This form also gives a useful reconciliation rule. If the valuation changes, use the changes in all three balance-sheet components:

\Delta R=\Delta A-\Delta T-\Delta L.

An increase in assets increases the residual, all else equal. An increase in either category of liabilities decreases it. A decrease in a liability increases the residual. This rule is a quick check on a calculation: if a liability rises but the reported residual also rises, there must be a sufficiently large offsetting asset increase or another liability decrease.

Worked Example: Constructing a Basic Balance Sheet

A hypothetical long-term insurer reports assets of $84.6$, technical provisions of $71.2$, and other liabilities of $4.4$, all in millions of dollars at the same valuation date. A separate capital benchmark is $7.5$. Calculate the residual and its excess over, or shortfall against, the benchmark.

Method. First calculate the residual from assets less both liability categories. Then compare that result with the capital benchmark. The common mistake avoided here is subtracting the capital benchmark as though it were an additional liability.

Total stated liabilities are $71.2+4.4=75.6$ million dollars.

The residual is $84.6-75.6=9.0$ million dollars.

The amount by which the residual exceeds the benchmark is $9.0-7.5=1.5$ million dollars.

Check. Reconstructing the asset total gives $71.2+4.4+9.0=84.6$. The identity balances. The residual is $1.5$ million dollars above the stated benchmark; subtracting the benchmark from assets before calculating the residual would mix two distinct calculations.

Reconciliation When Valuations Change

A solvency balance sheet is a snapshot, so a later valuation may show different amounts. To explain the change in the residual, calculate the residual at each date or apply the change formula. The latter is especially useful for detecting sign errors: a reduction in technical provisions is a liability decrease, so it raises the residual.

Worked Example: Explaining a Change in the Residual

At an initial valuation date, a hypothetical insurer has assets of $90.0$, technical provisions of $77.0$, and other liabilities of $3.0$ million dollars. At a later valuation, assets are $91.5$, technical provisions are $76.2$, and other liabilities are $3.2$ million dollars. Find both residuals and reconcile the change.

Method. Calculate the residual at each date, then verify the difference using $\Delta R=\Delta A-\Delta T-\Delta L$. The common mistake avoided is getting the new residual right but miscalculating its increase from the initial value.

Initially, total liabilities are $77.0+3.0=80.0$, so the initial residual is $90.0-80.0=10.0$ million dollars.

At the later date, total liabilities are $76.2+3.2=79.4$, so the revised residual is $91.5-79.4=12.1$ million dollars.

The increase in the residual is $12.1-10.0=2.1$ million dollars.

Check the change calculation directly. Assets increase by $91.5-90.0=1.5$. Technical provisions decrease by $76.2-77.0=-0.8$. Other liabilities increase by $3.2-3.0=0.2$. Therefore, $1.5-(-0.8)-0.2=2.1$ million dollars.

Check. Both methods give an increase of $2.1$ million dollars. The decrease in technical provisions contributes $0.8$ to the increase; it must not be treated as an additional liability increase.

Combining Balance-Sheet Information Without Double Counting

Balance-sheet figures sometimes arrive by entity, portfolio, or business segment. Before adding them, check whether any amount is recorded on both sides of a transfer between those units. For example, an amount receivable by one unit from another may also appear as a payable. If the units are combined, that internal balance should not be counted as an asset owed by an outside party and a liability owed to an outside party.

The elimination must be consistent: remove the internal receivable from assets and the matching internal payable from other liabilities. Since equal amounts are removed from both sides, the residual is unchanged. This is an arithmetic consolidation principle, not a method for deciding which assets are available for a capital assessment.

Worked Example: Combining Two Units and Eliminating an Internal Balance

A hypothetical insurer has two units. Unit A reports assets of $60$, including a $4$ million dollar receivable from Unit B, technical provisions of $50$, and other liabilities of $3$. Unit B reports assets of $45$, technical provisions of $36$, and other liabilities of $5$, including the matching $4$ million dollar payable to Unit A. All amounts are in millions. Calculate the combined residual after eliminating the internal balance, then compare it with a separate capital benchmark of $10$.

Method. Add the two units’ figures, eliminate the matching internal receivable and payable, and calculate the residual. The common mistake avoided is counting the internal $4$ million dollar balance as though it were an external asset and an external liability of the combined insurer.

Before elimination, combined assets are $60+45=105$. The $4$ million dollar internal receivable is included in that total, so external combined assets are $105-4=101$.

Combined technical provisions are $50+36=86$. Combined other liabilities before elimination are $3+5=8$, which include the internal payable. After eliminating that payable, other liabilities are $8-4=4$.

The combined residual is $101-86-4=11$ million dollars.

The residual exceeds the separate capital benchmark by $11-10=1$ million dollar.

Check. Unit A’s residual before combination is $60-50-3=7$; Unit B’s is $45-36-5=4$. Their sum is $11$. Eliminating the same internal amount from assets and other liabilities leaves that sum unchanged, confirming the combined calculation.

Interpreting the Result and Avoiding Common Traps

The residual answers a balance-sheet question: how much remains after the specified liabilities are deducted from the specified assets? A capital requirement answers a different question: what benchmark is being used for comparison? Keeping those questions separate prevents a common structural error.

Do not treat a capital requirement as a liability. Calculate $R=A-T-L$ first. If asked, compare $R$ with $C$ afterward.
Do not subtract technical provisions twice. If a problem gives total liabilities that already include technical provisions, use the supplied breakdown carefully rather than adding the provisions again.
Keep the valuation date and scope consistent. Combining an asset figure from one date with liability figures from another does not produce a coherent snapshot unless the question explicitly asks for such an adjustment.
Track decreases with their signs. A decrease in a liability has a negative change in that liability, and subtracting that negative change increases the residual.
Check for internal balances before aggregation. A receivable and matching payable between parts of the same combined entity are not external resources or obligations.

When reporting a result, state the residual and the comparison separately. For example, “the residual is $11$ million dollars, which is $1$ million dollar above the stated benchmark” is clearer than saying only that “capital is $1$ million dollar.” The latter may blur the distinction between the balance-sheet residual and the benchmark.

Key takeaway: At a common valuation date, construct the residual as assets minus technical provisions minus other liabilities. Compare it with a capital requirement only after that calculation, and make sure each asset or liability is counted once.

Check Your Understanding

For each hypothetical balance-sheet problem, calculate the requested quantities and check that the liability categories and capital benchmark are kept distinct.

A long-term insurer has assets of $72.4$, technical provisions of $61.8$, other liabilities of $3.1$, and a separate capital benchmark of $6.9$, all in millions of dollars. Find the residual and the excess over or shortfall against the benchmark. (Answer: residual $=7.5$ million dollars; excess $=0.6$ million dollars.)
An insurer’s assets are $120.0$, technical provisions are $102.0$, and other liabilities are $8.0$ million dollars. A later valuation increases assets by $2.4$, increases technical provisions by $1.1$, and decreases other liabilities by $0.3$ million dollars. Find the initial residual, revised residual, and change. (Answer: initial residual $=10.0$ million dollars; revised residual $=11.6$ million dollars; increase $=1.6$ million dollars.)
A balance sheet reports assets of $98$, technical provisions of $84$, and other liabilities of $6$ million dollars. The stated capital benchmark is $9$ million dollars. Is the residual above or below the benchmark, and by how much? (Answer: residual $=8$ million dollars; it is $1$ million dollar below the benchmark.)
An insurer has technical provisions of $107.2$ million dollars and other liabilities of $5.3$ million dollars. It needs a residual of $12.5$ million dollars at the valuation date. What asset value is required? If a separate capital benchmark is $11.8$ million dollars, what is the residual’s excess over that benchmark? (Answer: assets $=125.0$ million dollars; excess $=0.7$ million dollars.)
Two units have combined reported assets of $105$ million dollars, including a $4$ million dollar receivable from one unit to the other. Their combined technical provisions are $86$ million dollars, and combined reported other liabilities are $8$ million dollars, including the matching payable. After eliminating the internal balance, calculate the residual and compare it with a $10$ million dollar benchmark. (Answer: residual $=11$ million dollars; excess $=1$ million dollar.)

What You'll Learn