Why Reconcile the Solvency Balance Sheet?
A solvency ratio is only meaningful if its numerator and denominator are measured consistently. Before interpreting coverage, an actuary should be able to trace the amount of eligible own funds back to admitted assets, technical provisions and other liabilities. A reconciliation also helps locate errors: a missing liability, an asset counted on the wrong basis, or an eligibility limit applied to the wrong amount can all produce a plausible-looking but incorrect ratio.
The examples use hypothetical insurers and a simplified solvency framework. They are designed to show the accounting identities and calculation sequence, not to state the rules of any particular jurisdiction. Real regimes specify their own valuation bases, own-fund classifications, eligibility limits and capital requirements. The method is aligned with the SOA Exam ALTAM (Advanced Long-Term Actuarial Mathematics) syllabus.
Keep the balance-sheet identity distinct from the capital test. The identity determines the basic own-fund amount; eligibility rules determine how much of that amount may count; and the capital requirement is the benchmark against which eligible own funds are compared.
If technical provisions are separated into a best estimate and a risk margin, their total is the sum of those components. In the examples below, recoverables are included in admitted assets and technical provisions are stated on the corresponding basis. Do not also subtract those recoverables from provisions unless the problem explicitly gives gross provisions and asks for a net calculation. That would count the same adjustment twice.
A Reliable Reconciliation Sequence
Use a fixed order. First identify which asset amounts are recognized and total them. Next total technical provisions and other liabilities separately. Their sum is total liabilities for this reconciliation. Subtract that amount from admitted assets to obtain basic own funds. Then apply any stated eligibility limits to the own-fund components, and compare eligible own funds with the stated capital requirement.
Confirm the valuation date and whether assets, provisions and recoverables are stated on consistent bases.
Add admitted assets; add technical provisions and other liabilities; calculate their difference.
Confirm the stated own-fund components sum to basic own funds before applying eligibility limits.
Calculate eligible own funds, then divide by the capital requirement and report any surplus or shortfall.
Worked Balance-Sheet Reconciliations
Worked Example: Reconcile Assets, Provisions and Capital Coverage
A hypothetical insurer reports admitted assets of $150 million. Its best-estimate technical provisions are $112 million and its risk margin is $8 million. Other liabilities are $10 million. Basic own funds comprise $17 million of Tier 1 and $3 million of Tier 2 own funds; both amounts are fully eligible under the stated rules. The solvency capital requirement (SCR) is $16 million. Reconcile the balance sheet and calculate coverage and surplus.
Method. Total technical provisions first, then calculate basic own funds from the balance-sheet identity. Verify that the stated own-fund components match that result before calculating coverage.
Step 1: Total technical provisions.
Step 2: Total liabilities in this reconciliation. Add technical provisions and other liabilities:
Step 3: Calculate basic own funds.
Step 4: Check the own-fund components. The stated components sum to \(17+3=20\) million, agreeing with the balance-sheet surplus. As both are fully eligible, eligible own funds are also $20 million.
Step 5: Calculate coverage and surplus.
Check. The balance sheet reconciles because \(150=120+10+20\), and the eligible own funds of $20 million exceed the $16 million SCR by $4 million. The common mistake this method avoids is comparing the $20 million balance-sheet surplus with the SCR before checking that all own funds are eligible.
Worked Example: Exclude a Non-Admitted Asset
A hypothetical insurer’s ledger lists investments of $71.5 million, cash of $10.5 million, reinsurance recoverables of $10 million and a $4 million asset that is not admitted under the stated solvency basis. The best-estimate provisions are $72 million, the risk margin is $4 million, and other liabilities are $6 million. Tier 1 own funds are $8 million and Tier 2 own funds are $2 million, both fully eligible. The SCR is $12 million. Calculate admitted assets, basic and eligible own funds, the coverage ratio and any shortfall.
Method. Remove the non-admitted item from the ledger total before applying the balance-sheet identity. Then check own-fund components and calculate coverage using eligible own funds.
Step 1: Calculate admitted assets. The recognized assets are investments, cash and recoverables:
The ledger total, including the non-admitted asset, is \(92+4=96\) million. The solvency balance sheet uses $92 million, not $96 million.
Step 2: Calculate total technical provisions and liabilities.
Step 3: Calculate basic own funds.
Step 4: Reconcile components and eligibility. Tier 1 plus Tier 2 is \(8+2=10\) million, matching basic own funds. Both are fully eligible, so eligible own funds are $10 million.
Step 5: Calculate coverage and shortfall.
Check and trap. Using the ledger total of $96 million would incorrectly give \(96-82=14\) million of own funds and a coverage ratio of \(14/12=116.7\%\). That calculation counts the $4 million non-admitted asset. The corrected calculation uses admitted assets and gives $10 million of eligible own funds, or 83.3% coverage.
Worked Example: Apply Stated Tier Eligibility Limits
A hypothetical insurer has admitted investments of $150 million, cash of $42 million, reinsurance recoverables of $28 million and other admitted assets of $20 million. Its best-estimate provisions are $174 million, its risk margin is $8 million, and other liabilities are $18 million. Basic own funds are classified as $25 million Tier 1, $11 million Tier 2 and $4 million Tier 3. For this example only, the eligibility rules cap the combined recognized Tier 2 and Tier 3 amounts at $10 million, cap recognized Tier 3 at $2 million, and impose no further limit on Tier 1. The SCR is $32 million. Calculate the reconciliation, eligible own funds, coverage and surplus.
Method. First establish total basic own funds from the balance sheet. Then apply both stated caps to the lower-tier components; do not treat the nominal classification amounts as automatically eligible.
Step 1: Total admitted assets.
Step 2: Total technical provisions and liabilities.
Step 3: Calculate and check basic own funds.
The classified components also sum to \(25+11+4=40\) million, so they reconcile to basic own funds.
Step 4: Apply eligibility limits. Tier 3 is nominally $4 million, but its stated cap is $2 million, so recognized Tier 3 is $2 million. The combined Tier 2 and Tier 3 recognition cannot exceed $10 million. With $2 million of Tier 3 recognized, at most \(10-2=8\) million of Tier 2 can be recognized. Tier 2 has $11 million available, so $8 million is recognized. Eligible own funds are therefore:
Step 5: Calculate coverage and surplus.
Check. Recognized lower-tier funds total \(8+2=10\) million, exactly the combined cap; recognized Tier 3 is $2 million, exactly its separate cap. Eligible own funds of $35 million do not exceed basic own funds of $40 million. The calculation avoids the trap of adding all nominal tiers and reporting $40 million as eligible.
Why the Identity Holds—and What It Does Not Say
The reconciliation is an application of the definition of a balance-sheet surplus. On the stated valuation basis, the insurer’s net resources after settling recognized obligations are the assets remaining after liabilities are deducted. If the balance sheet classifies technical provisions and other liabilities separately, total recognized liabilities are their sum. Subtracting that total from admitted assets gives the residual assigned to basic own funds.
This is a balance-sheet identity, not a prediction of future profit and not a claim that all basic own funds can count toward a capital requirement. Eligibility limits can reduce the amount recognized for capital coverage. Nor does the identity determine the SCR: the SCR is a separately calculated capital requirement supplied by the applicable framework or problem data.
For clarity, define the coverage ratio as eligible own funds divided by the capital requirement. A ratio above 100% indicates eligible own funds exceed that requirement; a ratio below 100% indicates a shortfall. The amount of surplus or shortfall is the difference between those two amounts, not the percentage-point difference from 100%.
| Quantity | Calculation | What it answers |
|---|---|---|
| Basic own funds | Admitted assets less technical provisions and other liabilities | What is the balance-sheet surplus before eligibility limits? |
| Eligible own funds | Basic own funds after applicable eligibility adjustments | How much may count toward the capital requirement? |
| Coverage ratio | Eligible own funds divided by the capital requirement | What proportion of the requirement is covered? |
| Surplus or shortfall | Eligible own funds less the capital requirement | How many currency units are above or below the requirement? |
Reconciliation Checks and Common Traps
A sound answer should make it possible to check each subtotal without retracing the entire calculation. Write down admitted assets, technical provisions, other liabilities, basic own funds, recognized eligible own funds and the capital requirement separately. Keep amounts in the same currency units throughout, and report whether a final difference is a surplus or a shortfall.
- Using total ledger assets instead of admitted assets. Exclude any asset the stated solvency basis does not recognize.
- Omitting a provision component. If technical provisions are given as best estimate plus risk margin, include both in their total.
- Double-counting recoverables. Check whether they are already included in assets or reflected in net provisions before making another adjustment.
- Equating basic and eligible own funds. They are equal only when no eligibility adjustment or limit reduces recognition.
- Reversing a surplus or shortfall. Compare eligible own funds with the requirement explicitly: own funds minus requirement is positive for a surplus and negative for a shortfall.
Check Your Understanding
For each hypothetical case, reconcile the stated amounts before calculating coverage or surplus. Monetary amounts are in millions.
- An insurer has admitted assets of $84 million, best-estimate provisions of $62 million, a $3 million risk margin and $5 million of other liabilities. All basic own funds are eligible and the SCR is $16 million. Find basic own funds, coverage and the surplus or shortfall. (Answer: Basic own funds $14 million; coverage 87.5%; shortfall $2 million.)
- A ledger reports investments of $78 million, cash of $20 million, recoverables of $12 million and a non-admitted asset of $3 million. Best-estimate provisions are $84 million, the risk margin is $6 million, other liabilities are $8 million, and all basic own funds are eligible. The SCR is $15 million. Find admitted assets, own funds, coverage and the surplus or shortfall. (Answer: Admitted assets $110 million; own funds $12 million; coverage 80.0%; shortfall $3 million.)
- Admitted assets are $205 million. Best-estimate provisions are $157 million, the risk margin is $8 million and other liabilities are $10 million. Own funds comprise $21 million Tier 1, $7 million Tier 2 and $2 million Tier 3. A stated rule caps recognized Tier 2 and Tier 3 combined at $6 million and Tier 3 at $2 million; all Tier 1 is eligible. The SCR is $24 million. Find basic and eligible own funds, coverage and surplus or shortfall. (Answer: Basic own funds $30 million; eligible own funds $27 million; coverage 112.5%; surplus $3 million.)
- Admitted assets are $132 million, technical provisions are a $96 million best estimate plus a $5 million risk margin, and other liabilities are $9 million. The insurer reports $18 million Tier 1 and $4 million Tier 2, both fully eligible. The SCR is $20 million. Check the balance-sheet and own-fund subtotals, then calculate coverage. (Answer: Technical provisions $101 million; basic own funds $22 million, matching the stated components; eligible own funds $22 million; coverage 110.0%; surplus $2 million.)
- An insurer initially has admitted assets of $160 million, technical provisions of $120 million plus a $6 million risk margin, and other liabilities of $9 million. It pays a $3 million dividend before the valuation date; assume the payment reduces admitted assets and own funds dollar for dollar, with liabilities and the $22 million SCR unchanged. All remaining own funds are eligible. Find post-payment own funds, coverage and surplus or shortfall. (Answer: Post-payment admitted assets $157 million; technical provisions $126 million; basic and eligible own funds $22 million; coverage 100.0%; no surplus or shortfall.)