The Solvency Balance Sheet And Capital Resources

Why a Solvency Balance Sheet Matters

A capital figure is meaningful only when its underlying assets and liabilities are measured on a defined basis. An insurer can report positive statutory surplus and still have a smaller amount of net resources on a regulatory solvency basis if assets are valued differently or obligations are measured more conservatively. The solvency balance sheet makes that comparison explicit: it lists recognized assets and liabilities on the regulatory valuation basis, then calculates the residual.

The central task here is to calculate and interpret that residual. It is not the same as calculating a capital requirement or deciding which forms of capital meet particular eligibility limits. Those further questions depend on the applicable framework. This tutorial is aligned with the CAS Exam 9 (Risk Management for Actuaries) syllabus.

Definition: A regulatory solvency balance sheet is a statement of an insurer’s assets and liabilities, valued and recognized according to a specified regulatory framework at a particular valuation date. Net own funds are the excess of recognized assets over recognized liabilities on that balance sheet. In this tutorial, regulatory available capital refers to this net amount before any framework-specific tier limits, deductions, or eligibility restrictions are applied.

What Goes on the Balance Sheet?

An asset is recognized when the insurer has an economic resource that the applicable framework permits it to include. Typical examples include cash, investments, premium receivables, and amounts recoverable from reinsurers. Recognition and valuation are separate questions: an item may exist but be excluded, or it may be included at an amount that differs from its accounting carrying value.

Liabilities represent obligations of the insurer at the valuation date. They can include claims, policy benefits, debt, and other payables. A framework may prescribe how insurance obligations are valued. For example, it may specify a best estimate of future cash flows and a risk margin, but the exact method and components depend on the framework. Use the rule stated in the problem rather than assuming every jurisdiction uses the same valuation approach.

In particular, keep reinsurance recoverables distinct from the associated insurance liability unless the stated rules explicitly require a net presentation. Showing the gross obligation as a liability and the recoverable as an asset makes the valuation and counterparty exposure visible. It also reduces the risk of subtracting a recoverable twice.

\text{Net own funds} = \text{recognized assets} - \text{recognized liabilities}

This calculation is a balance-sheet residual, not a statement that the insurer holds that exact amount in cash. Assets can be investments or receivables, and liabilities can be estimates of future obligations. Nor does the equation itself establish whether the resulting amount satisfies a regulatory capital requirement.

Fix the valuation date and basis.
Identify which regulatory framework applies and which valuation assumptions the problem supplies.

Determine recognized asset values.
Include permitted assets at their regulatory values; do not automatically copy statutory carrying values.

Determine recognized liability values.
Apply the stated valuation method to insurance obligations and include other recognized liabilities.

Subtract liabilities from assets.
Report the net own funds and state clearly that it is measured on the regulatory basis.

From Insurance Cash Flows to a Liability Value

When a problem specifies future liability cash flows and a discount rate, the present value of those cash flows can be calculated using the effective annual interest rate $i$. The calculation below assumes payments occur at the ends of the specified years, the rate is constant, and the amounts are deterministic. A problem involving uncertain cash flows, mortality, or a different valuation rule would require those assumptions to be treated explicitly.

Worked Example: Valuing a Claims Provision and Calculating Own Funds

A hypothetical insurer has recognized assets of $260 thousand and other recognized liabilities of $35 thousand. It expects deterministic claims payments of $100 thousand at the end of each of the next two years. The regulatory rule in this example defines the claims liability as the present value of those payments plus a $12 thousand risk margin. Use an effective annual interest rate of $i=4\%$. No mortality assumption or probability distribution is used because the cash flows are supplied as fixed amounts.

Method. Discount each payment to the valuation date, add the risk margin to obtain the specified claims liability, then subtract all recognized liabilities from recognized assets.

The year-one discount factor is $1/1.04$, so the present value of its payment is:

\frac{100}{1.04}=96.153846\text{ thousand}

The year-two discount factor is $1/(1.04)^2=1/1.0816$, so the second payment has present value:

\frac{100}{1.0816}=92.455621\text{ thousand}

Thus, the best-estimate present value of the specified claims cash flows is $96.153846+92.455621=188.609467$ thousand. Adding the risk margin gives a claims liability of $188.609467+12=200.609467$ thousand. Total recognized liabilities are $200.609467+35=235.609467$ thousand.

Net own funds are $260-235.609467=24.390533$ thousand. Rounded only at the final step to two decimal places, the insurer has $24.39 thousand of net own funds.

Check. Assets exceed liabilities by $260-235.609467=24.390533$ thousand, consistent with the reported result. A common mistake is to add the risk margin to assets or omit it from liabilities; either changes the balance-sheet residual incorrectly.

Why the Residual Formula Holds

The calculation follows directly from the balance-sheet identity. At the valuation date, recognized assets fund the insurer’s obligations and leave a residual for its owners or capital providers. If liabilities increase while assets are unchanged, that residual must decrease by the same amount. If assets increase while liabilities are unchanged, the residual must increase by the same amount.

OF=A-L $$ $$ \Delta OF=(A+\Delta A)-(L+\Delta L)-(A-L) =\Delta A-\Delta L

Here $A$ denotes recognized assets, $L$ recognized liabilities, and $OF$ net own funds. The second equation shows why valuation adjustments affect capital through both sides of the balance sheet. A downward adjustment to assets reduces own funds; an upward adjustment to liabilities also reduces own funds. These changes are not interchangeable with changes in a separate capital requirement.

Regulatory Values Are Not Automatically Statutory Values

Statutory accounting surplus is generally calculated using statutory accounting values and rules. Regulatory net own funds are calculated using the valuation and recognition rules of the solvency framework being applied. The two measures can differ because of asset valuation, liability valuation, recognition rules, or presentation. A comparison must use a common valuation date and must identify the basis for each figure.

A useful reconciliation starts with statutory surplus, then separately identifies changes to assets and changes to liabilities. If regulatory assets are lower, the adjustment reduces own funds. If regulatory liabilities are higher, that adjustment also reduces own funds. Keeping the two columns separate helps reveal whether a difference comes from asset valuation, liability valuation, or both.

Worked Example: Reconciling Statutory Surplus to Regulatory Own Funds

A hypothetical insurer reports statutory assets of $290 million and statutory liabilities of $230 million. On the regulatory basis, the relevant items are valued as follows: cash, $70 million; bonds, $174 million; premium receivables, $40 million; reinsurance recoverables, $24 million; and equipment, $8 million. Regulatory insurance liabilities are $250 million, and other regulatory liabilities are $20 million. All figures are valuation-date amounts, so no interest rate is applied in this reconciliation. No mortality assumption or probability distribution is used.

Method. First calculate statutory surplus. Then total the regulatory asset values and regulatory liabilities separately, and take their difference.

Statutory surplus is $290-230=60$ million. Regulatory assets total $70+174+40+24+8=316$ million. Regulatory liabilities total $250+20=270$ million. Therefore regulatory net own funds are $316-270=46$ million.

The reconciliation gives the same result. Regulatory assets are $316-290=26$ million higher than statutory assets, while regulatory liabilities are $270-230=40$ million higher than statutory liabilities. The net change in own funds is $26-40=-14$ million, so regulatory own funds are $60-14=46$ million. The calculation checks.

Common mistake. Subtracting the $40 million increase in liabilities from statutory surplus but ignoring the $26 million increase in regulatory assets would produce $20 million. The correction is to include both sides of the balance sheet: $60+26-40=46$ million.

Worked Example: Keeping Recoverables Separate From Gross Liabilities

A hypothetical insurer has recognized cash of $85 million, investments of $145 million, and a reinsurance recoverable of $22 million. Its gross claims liability is $210 million, and its other liabilities are $18 million. The stated regulatory basis recognizes the recoverable as a separate asset and the claims liability at its stated gross amount. All figures are already valued at the balance-sheet date; no interest rate, mortality assumption, or probability distribution is used.

Method. Add the recognized assets, including the recoverable once, and add the liabilities, retaining the gross claims amount. Then calculate the residual.

Recognized assets are $85+145+22=252$ million. Recognized liabilities are $210+18=228$ million. Net own funds are $252-228=24$ million.

The same result can be checked by treating the recoverable as a separate positive asset: assets other than the recoverable total $85+145=230$ million, and $230+22-228=24$ million. A common error is to reduce the $210 million gross claims liability by $22 million and also include the $22 million recoverable as an asset. That would count the recoverable twice and overstate own funds by $22 million.

Common Exam Traps and Interpretation

Using statutory surplus as the regulatory answer. Statutory surplus is not automatically net own funds. Apply the stated regulatory recognition and valuation rules.
Mixing valuation dates. Assets and liabilities must be measured at the same date for the residual to be meaningful.
Netting a recoverable twice. If a recoverable is shown as an asset and the liability is stated gross, do not also deduct that recoverable from the liability.
Forgetting a specified liability component. If the problem defines a liability as a present value plus a risk margin, include both before subtracting liabilities from assets.
Calling own funds the capital requirement. Net own funds describe resources on the balance sheet. A requirement is a separate benchmark against which resources may later be assessed.

These distinctions matter in solvency analysis because a reported capital resource is only interpretable once its basis and components are clear. A balance-sheet reconciliation can also help identify whether a change in resources arose from asset values, liability estimates, or both. The framework may impose further rules on the capital that can be counted, but those rules must be applied after the balance-sheet amounts have been established.

Check Your Understanding

For each problem, use only the valuation rules and assumptions stated. Amounts are in the units shown.

A hypothetical insurer has regulatory assets of $145 million and regulatory liabilities of $132 million. No further valuation adjustment is required. What are its net own funds? (Answer: $13 million)
A hypothetical insurer has assets of $120 million and other liabilities of $10 million. Its insurance liability is the present value of fixed payments of $50 million at the end of each of the next two years, plus a $7 million risk margin. Use $i=5\%$ effective annually. No mortality assumption or probability distribution is used. Calculate net own funds, rounding only the final answer to the nearest $0.01 million. (Answer: $10.03 million)
Statutory assets are $200 million and statutory liabilities are $160 million. Regulatory assets are $193 million and regulatory liabilities are $169 million. Calculate statutory surplus, regulatory net own funds, and the change between them. (Answer: statutory surplus $40 million; regulatory net own funds $24 million; decrease $16 million)
A hypothetical balance sheet lists cash of $60 million, investments of $180 million, and a recognized reinsurance recoverable of $20 million. Liabilities are a gross claims provision of $250 million and other liabilities of $20 million. The recoverable is shown separately and is not netted against the claims provision. Calculate net own funds. (Answer: $-10 million)
A framework specifies a claims best estimate of $380 million and a risk margin of $14 million. Other liabilities are $30 million, and recognized assets are $450 million. Calculate net own funds, showing the claims liability and total liabilities first. No discounting or stochastic model is needed because the liability values are supplied. (Answer: claims liability $394 million; total liabilities $424 million; net own funds $26 million)

What You'll Learn