Solvency Capital Requirements and Available Capital

Comparing Capital With a Solvency Requirement

A solvency balance sheet gives a view of an insurer’s assets and obligations at a particular valuation date. The solvency capital requirement (SCR) is a separate amount of capital specified by the applicable solvency framework. To assess whether the insurer meets that requirement, compare the eligible own funds available to meet it with the SCR. The comparison is meaningful only when the figures use the same valuation date, currency, and applicable basis.

This is a threshold test, not a valuation of the insurance liabilities. Technical provisions measure obligations under the stated valuation basis; own funds represent the excess of recognized assets over recognized liabilities, subject to the applicable rules. Eligibility limits may mean that not all own funds count toward meeting the SCR.

Definition: For a stated solvency framework and valuation date, eligible own funds are the own funds permitted to meet the SCR after applying the framework’s eligibility rules and limits. The solvency surplus is eligible own funds minus the SCR. A positive result is a surplus; a negative result is a shortfall.

The framework matters. There is no single set of tier limits or adjustments that applies to every solvency regime. Whenever a problem provides eligibility limits, use those stated limits; do not silently substitute limits remembered from another framework. If no limit or adjustment is stated, use the treatment specified in the problem.

From the Balance Sheet to Eligible Own Funds

In a simplified solvency balance sheet, basic own funds are calculated as recognized assets less recognized liabilities. The liabilities may include technical provisions and other recognized liabilities. The calculation is not generally the same as subtracting only technical provisions from assets.

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

Own funds may also include other items, and some frameworks distinguish capital by quality or impose eligibility limits. Therefore, first identify the own funds before eligibility adjustments, then apply the specific limits to determine the eligible amount. Do not assume the SCR itself is a liability on the balance sheet: it is the requirement against which eligible own funds are compared.

Why the Surplus Test Works

Suppose $E$ denotes eligible own funds and $C$ denotes the stated SCR. The amount $C$ is the capital threshold to be met. If $E$ is greater than $C$, the amount beyond the threshold is $E-C$. If $E$ is less than $C$, the amount by which the available funds fall short is $C-E$. These two cases can be represented by one signed quantity.

\text{Solvency surplus (signed)} = E-C

This result follows directly from the comparison: meeting the requirement means $E \ge C$. Subtracting $C$ from both sides gives $E-C \ge 0$. Conversely, if $E-C<0$, then $E<C$, and the shortfall is $C-E=-(E-C)$. The sign is therefore essential: reporting only the absolute difference would hide whether the insurer has met the requirement.

Establish own funds.
Calculate basic own funds from recognized assets and liabilities, adding or deducting other items only as specified.

Apply eligibility rules.
Determine the amount of each own-funds item that is permitted to count, including any individual or combined limits.

Compare with the SCR.
Subtract the stated SCR from eligible own funds. A nonnegative result is a surplus; a negative result is a shortfall.

State the interpretation.
Give the amount, currency, and whether it is a surplus or shortfall, and identify any assumptions used.

Worked Applications

Worked Example: Calculating a Surplus From a Solvency Balance Sheet

A hypothetical life insurer reports recognized assets of $\$12.40$ million, technical provisions of $\$10.85$ million, and other recognized liabilities of $\$0.35$ million. Assume there are no additional own-funds items or eligibility restrictions. The stated SCR is $\$1.05$ million. Calculate eligible own funds and the surplus or shortfall.

Method. First find recognized liabilities by adding the two liability amounts:

\$10.85\text{ million}+\$0.35\text{ million} =\$11.20\text{ million}.

Basic own funds are assets less recognized liabilities:

\$12.40\text{ million}-\$11.20\text{ million} =\$1.20\text{ million}.

Under the assumption that all these own funds are eligible, $E=\$1.20$ million. Subtract the SCR:

E-C =\$1.20\text{ million}-\$1.05\text{ million} =\$0.15\text{ million}.

The insurer has a $\$0.15$ million surplus over the stated SCR. As a check, eligible own funds of $\$1.20$ million exceed the $\$1.05$ million requirement by $\$0.15$ million.

Common mistake avoided: Subtracting only technical provisions from assets gives $\$1.55$ million and overstates own funds by omitting the other $\$0.35$ million of recognized liabilities.

Worked Example: Applying Individual and Combined Tier Limits

A hypothetical framework has an SCR of $\$0.50$ million and specifies these limits: Tier 3 own funds may count up to 20% of the SCR, and combined Tier 2 and Tier 3 own funds may count up to 25% of the SCR. The insurer has $\$0.36$ million of Tier 1, $\$0.075$ million of Tier 2, and $\$0.20$ million of Tier 3 own funds. Assume Tier 1 and the stated Tier 2 amount are otherwise eligible. Find eligible own funds and the resulting position.

Method. Calculate the Tier 3 individual limit:

0.20(\$0.50\text{ million})=\$0.10\text{ million}.

The combined Tier 2 and Tier 3 limit is:

0.25(\$0.50\text{ million})=\$0.125\text{ million}.

Tier 2 already uses $\$0.075$ million of this combined limit. The remaining combined capacity for Tier 3 is:

\$0.125\text{ million}-\$0.075\text{ million} =\$0.050\text{ million}.

Eligible Tier 3 is the smallest of its available amount, its individual limit, and the remaining combined capacity:

\min(\$0.20,\ \$0.10,\ \$0.05)\text{ million} =\$0.05\text{ million}.

Thus eligible own funds are:

\$0.36+\$0.075+\$0.05 =\$0.485\text{ million}.

The signed comparison is:

\$0.485\text{ million}-\$0.50\text{ million} =-\$0.015\text{ million}.

The insurer has a $\$0.015$ million shortfall. As a check, $\$0.485$ million is $\$0.015$ million less than the $\$0.50$ million SCR.

Common mistake avoided: Counting Tier 3 up to its $\$0.10$ million individual limit without applying the combined limit, which restricts eligible Tier 3 to $\$0.05$ million.

Worked Example: Reassessing the Position After an Asset Loss

A hypothetical insurer has recognized assets of $\$6.80$ million, technical provisions of $\$5.60$ million, and other recognized liabilities of $\$0.30$ million. Assume all resulting own funds are eligible. Its SCR is $\$0.82$ million. An asset loss of $\$0.12$ million occurs. For this calculation, assume liabilities and the SCR are unchanged by the loss. Find the position before and after the loss.

Before the loss. Recognized liabilities are:

\$5.60+\$0.30=\$5.90\text{ million}.

Own funds are:

\$6.80-\$5.90=\$0.90\text{ million}.

The initial signed surplus is:

\$0.90-\$0.82=\$0.08\text{ million}.

So the insurer initially has a $\$0.08$ million surplus. After the loss, assets are $\$6.80-\$0.12=\$6.68$ million. With liabilities unchanged, post-loss own funds are:

\$6.68-\$5.90=\$0.78\text{ million}.

The post-loss comparison is:

\$0.78-\$0.82=-\$0.04\text{ million}.

After the loss, the insurer has a $\$0.04$ million shortfall. The change in the signed position is $-\$0.04-\$0.08=-\$0.12$ million, exactly equal to the assumed asset loss. This is a check on the calculation.

Common mistake avoided: Reporting the initial surplus after the asset loss. The balance sheet must be recalculated using post-loss assets, even when the problem holds liabilities and the SCR fixed.

Interpretation and Exam Checks

The comparison answers a specific question: do eligible own funds meet the stated SCR, and by how much? It does not by itself explain why the SCR has its stated value, establish whether the technical provisions are adequate, or determine how the insurer should raise or manage capital.

Before concluding, check that the available capital and requirement are stated on a consistent basis. In particular, confirm the currency and units, the valuation date, whether the own-funds figure is before or after eligibility limits, and whether the SCR is the amount to be used in the comparison. If a problem supplies a signed difference, preserve its sign; if it asks for a shortfall, report the positive magnitude and label it as a shortfall.

Comparison	Interpretation
Eligible own funds > SCR	Positive surplus: eligible funds exceed the requirement.
Eligible own funds = SCR	Neither surplus nor shortfall: funds exactly meet the requirement.
Eligible own funds < SCR	Shortfall: eligible funds are less than the requirement.

Key takeaway: Calculate own funds on the stated solvency balance sheet, apply all specified eligibility limits, and then compare the resulting eligible amount with the SCR. The sign of eligible own funds minus the SCR determines whether the result is a surplus or shortfall.

Check Your Understanding

For each problem, use only the assumptions and eligibility rules stated. Amounts are in millions unless otherwise noted.

A hypothetical insurer has assets of $\$4.75$ million, technical provisions of $\$4.10$ million, and other recognized liabilities of $\$0.15$ million. All resulting own funds are eligible, and the SCR is $\$0.46$ million. What is the surplus or shortfall? (Answer: $\$0.04$ million surplus)
An insurer has $\$1.26$ million of basic own funds, of which $\$0.11$ million is ineligible. The SCR is $\$1.10$ million. Find eligible own funds and the resulting position. (Answer: $\$1.15$ million eligible own funds; $\$0.05$ million surplus)
A stated framework allows Tier 3 up to 10% of the SCR and combined Tier 2 and Tier 3 up to 30% of the SCR. The SCR is $\$1.20$ million. Own funds are $\$0.55$ million Tier 1, $\$0.26$ million Tier 2, and $\$0.30$ million Tier 3. Assume Tier 1 and Tier 2 are otherwise eligible. Calculate eligible own funds and the shortfall or surplus. (Answer: $\$0.91$ million eligible own funds; $\$0.29$ million shortfall)
A hypothetical insurer has assets of $\$9.20$ million, technical provisions of $\$8.15$ million, and other liabilities of $\$0.25$ million. All own funds are eligible. Its SCR is $\$0.75$ million. An asset loss of $\$0.09$ million occurs, and the SCR increases by 8%; liabilities are unchanged. Find the post-change position. (Answer: $\$0.71$ million eligible own funds and $\$0.81$ million SCR; $\$0.10$ million shortfall)
An insurer has $\$1.04$ million of eligible own funds and an SCR of $\$0.98$ million. It makes a distribution of $\$0.10$ million, reducing eligible own funds dollar for dollar, while the SCR is unchanged. Find its position after the distribution. (Answer: $\$0.94$ million eligible own funds; $\$0.04$ million shortfall)

What You'll Learn