# Insurance Company – Mathematical Reserves

1

### Application and Definitions

1.1

Unless otherwise stated, this Part applies to a non-directive insurer which carries on long-term insurance business, other than a non-directive friendly society.

1.2

Except for 16.3(1) this Part does not apply to final bonuses.

1.3

In this Part, the following definitions shall apply:

benefits payable

means benefits payable under a long-term insurance contract, including:

1. (1) all guaranteed benefits including guaranteed surrender values and paid-up values;
2. (2) vested, declared and allotted bonuses to which the policyholder is entitled;
3. (3) all options available to the policyholder under the terms of the contract; and
4. (4) discretionary benefits payable in accordance with any relevant provisions of the FCA Handbook.

dividend yield

has the meaning given in 9.6(1).

earnings yield

has the meaning given in 9.6(2).

means the value attributed to a premium due in any future financial year.

internal rate of return

has the meaning given in 9.7.

non-attributable expenses

means expenses which are not directly attributable to a particular contract of long-term insurance.

recoverable acquisition expenses

means the amount of expenses, after allowing for the effects of taxation, which it is reasonable to expect will be recovered from future premiums payable under the contract.

means the risk-adjusted yield calculated in accordance with 9 and 10.

running yield

has the meaning given in 9.5.

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2

### Basic Valuation Method

2.1

1. (1) Subject to (2), a firm must establish its mathematical reserves using a prospective actuarial valuation on prudent assumptions of all future cash flows expected to arise under, or in respect of, each of its contracts of long-term insurance.
2. (2) A firm may use a retrospective actuarial valuation where:
1. (a) a prospective method cannot be applied to a particular type of contract; or
2. (b) the firm can demonstrate that the resulting amount of the mathematical reserves would be no lower than would be required by a prudent prospective actuarial valuation.

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3

### Methods and Assumptions

3.1

In the actuarial valuation under 2.1, a firm must use methods and prudent assumptions which:

1. (1) are appropriate to the business of the firm;
2. (2) are consistent from year to year without arbitrary changes;
3. (3) are consistent with the method of valuing assets;
4. (4) include appropriate margins for adverse deviation of relevant factors which are sufficiently prudent to ensure that there is no significant foreseeable risk that liabilities to policyholders in respect of contracts of long-term insurance will not be met as they fall due;
5. (5) recognise the distribution of profits (that is, emerging surplus) in an appropriate way over the duration of each contract of insurance;
6. (6) take into account its regulatory duty to treat its customers fairly under any relevant provision of the FCA Handbook; and
7. (7) are in accordance with generally accepted actuarial practice.

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4

### Valuation of Individual Contracts

4.1

1. (1) Subject to (2) and (3), a firm must determine the amount of the mathematical reserves separately for each contract of long-term insurance.
2. (2) Approximations or generalisations may be made:
1. (a) in the case of non-attributable expenses, in relation to a group of contracts with the same or similar expense risk characteristics, provided that the mathematical reserves in respect of such expenses established by the firm in relation to that group of contracts have a minimum value of at least zero; and
2. (b) in any other case, where they are likely to provide the same, or a higher, result than a determination made in accordance with (1).
3. (3) A firm must set up additional mathematical reserves on an aggregated basis for general risks that are not specific to individual contracts.

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5

### Negative Mathematical Reserves

5.1

A firm may calculate a negative value for the mathematical reserves in respect of a contract of long-term insurance provided that:

1. (1) this is based on assumptions which meet the general requirements for prudent assumptions as set out in 3.1;
2. (2) the contract does not have a surrender value which at the actuarial valuation date is guaranteed; and
3. (3) the total mathematical reserves established by the firm have a minimum value of at least:
1. (a) where the firm's contracts of long-term insurance include linked long-term contract of insurance, the sum of the surrender values of all its linked long-term contract of insurance at the actuarial valuation date; and
2. (b) in any other case, zero.

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6

### Avoidance of Future Valuation Strain

6.1

1. (1) A firm must establish mathematical reserves for a contract of insurance which are sufficient to ensure that, at any subsequent date, the mathematical reserves then required are covered solely by:
1. (a) the assets covering the current mathematical reserves; and
2. (b) the resources arising from those assets and from the contract itself.
2. (2) For the purposes of (1), the firm must assume that:
1. (a) the assumptions adopted for the current valuation of liabilities remain unaltered and are met; and
2. (b) discretionary benefits and charges will be set so as to fulfil its regulatory duty to treat its customers fairly under any relevant provision of the FCA Handbook.
3. (3) Subject to (4), the requirements in (1) may be applied to a group of similar contracts instead of to the individual contracts within that group.
4. (4) The requirements in (1) must be applied to a group of contracts in relation to which mathematical reserves in respect of non-attributable expenses are established for that group of contracts in accordance with 4.1(2)(a), instead of to the individual contracts within that group.

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7

### Cash Flows to Be Valued

7.1

In a prospective valuation, a firm must:

1. (1) include in the cash flows to be valued, the following:
2. (b) expenses, including commissions;
3. (c) benefits payable; and
4. (d) subject to (2), amounts to be received or paid in respect of contracts of long-term insurance under contracts of reinsurance or analogous non-reinsurance financing agreements; but
2. (2) exclude from those cash flows amounts recoverable from an ISPV.

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8

### Valuation Rates of Interest

8.1

In calculating the present value of future net cash flows, a firm must determine the rates of interest to be used in accordance with 8.2, 9 and 10.

8.2

1. (1) The rates of interest required by 8.1 to be used by a firm for the calculation of the present value of a long-term insurance liability must not exceed 97.5% of the risk-adjusted yield that is expected to be achieved on:
1. (a) the assets allocated to cover that liability;
2. (b) the reinvestment of sums expected to be received from those assets; and
3. (c) the investment of future premium receipts.
2. (2) The requirements in (1) do not apply to a contract of long-term insurance in respect of which the firm has calculated a negative value for the mathematical reserves in accordance with 5.1.
3. (3) For the purposes of (1), the rates of interest assumed must allow appropriately for the rates of tax that apply to the investment return on policyholder assets.
4. (4) For the purposes of (3), the rates of tax assumed must be such that the firm's total implied liability for tax arising from the allocation of assets to liabilities is not less than the firm's actual expected liability for tax for the period in respect of which tax is to be assessed.

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9

9.1

A risk-adjusted yield on an asset must be calculated by:

1. (1) taking the asset together with any covering derivatives, forward transactions and quasi-derivatives;
2. (2) assuming that the factors which affect the yield will remain unchanged after the valuation date;
3. (3) valuing the asset (together with any offsetting transaction) in accordance with Insurance Company – Overall Resources and Valuation 3 to 8;
4. (4) making reasonable assumptions as to whether, and if so when, any options or other rights embedded in the asset (or in any offsetting transaction) will be exercised.

9.2

For the purpose of 9.1(2), the factors that affect yield should be ascertained as at the valuation date (that is, the date to which present values of cash flows are being calculated). All changes known to have occurred by that date must be taken into account including:

1. (1) changes in the rental income from real estate;
2. (2) changes in dividends or audited profit on equities;
3. (3) known or forecast changes in dividends which have been publicly announced by the issuer by the valuation date;
4. (4) known or forecast changes in earnings which have been publicly announced by the issuer by the valuation date;
5. (5) alterations in capital structure; and
6. (6) the value (at the most recent date at or before the valuation date for which it is known) of any determinant of the amount of any future interest or capital payment.

9.3

1. (1) for equities and real estate, a running yield; or
2. (2) for all other assets, the internal rate of return.

9.4

The risk-adjusted yield on a basket of assets is the arithmetic mean of the risk-adjusted yield on each asset weighted by that asset's market value.

9.5

The running yield:

1. (1) for real estate, is the ratio of:
1. (a) the rental income arising from the real estate over the previous 12 months; to
2. (b) the market value of the real estate.
2. (2) for equities, is:
1. (a) the dividend yield, if the dividend yield is more than the earnings yield;
2. (b) otherwise, the sum of the dividend yield and the earnings yield, divided by two.

9.6

For the purposes of 9.5(2):

1. (1) the dividend yield is the ratio (expressed as a percentage) of dividend income over the previous 12 months from the equities for which the running yield is being calculated ("the relevant equities") to the market value of those equities;
2. (2) the earnings yield is the ratio (expressed as a percentage) of the audited profit (including exceptional items and extraordinary items) for the preceding financial year of the issuer of the relevant equities to the market value of those equities;
3. (3) the earnings yield must be calculated in accordance with whichever is most appropriate (to the issuer of the relevant equities) of UK, US or international generally accepted accounting practice.

9.7

The internal rate of return on an asset is the annual rate of interest which, if used to calculate the present value of future income (before deduction of tax) and of repayments of capital (before deduction of tax) would result in the sum of those amounts being equal to the market value of the asset.

9.8

In both the running yield and internal rate of return the yield must be reduced to exclude that part of the yield that represents compensation for credit risk arising from the asset.

9.9

Provision for credit risk for securities that are not credit-rated must be made on principles at least as prudent as those adopted for credit-rated securities.

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10

### Investment and Reinvestment

10.1

The risk-adjusted yield assumed for the investment or reinvestment of sterling sums (other than sums expected to be received within the next three years) must not exceed the lowest of:

1. (1) the higher of:
1. (a) the long-term gilt yield; and
2. (b) the greater of:
1. (i) the forward gilts yield; and
2. (ii) the forward rate on sterling interest rate swaps, reduced to exclude that part of the rate that represents compensation for credit risk;

where the forward yields and forward rates corresponding to the time when the sums are expected to be received are weighted so as to reflect the investment and reinvestment characteristics of the liabilities covered;

1. (2) 3% per annum, increased by two thirds of the excess, if any, of the percentage in (1) over 3% per annum; and
2. (3) 6.5% per annum.

10.2

The risk-adjusted yield assumed for the investment or reinvestment of those sterling sums expected to be received within the next three years must not exceed the risk-adjusted yield on the assets actually held adjusted linearly over the three-year period to the risk-adjusted yield determined under 10.1.

10.3

The risk-adjusted yield assumed for the investment or reinvestment of sums denominated in a currency other than sterling must be at least as prudent as in 10.1 and 10.2 taking into account the yields on government securities denominated in that currency.

10.4

For the purpose of 10.3 the yields on the government securities must be reduced to exclude that part of the yield that represents compensation for credit risk unless, in relation to the issuer of those securities, a credit rating is available from at least one of the following rating agencies in the corresponding rating categories;

1. (1) for A.M. Best Company, ‘aaa’ or ‘aa’;
2. (2) for Fitch Ratings, ‘AAA’ or ‘AA’;
3. (3) for Moody's Investors Service ‘Aaa’ or ‘Aa’; or
4. (4) for Standard & Poor's Corporation ‘AAA’ or ‘AA’.

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11

11.1

This Chapter applies to with-profits policies, except accumulating with-profits policies written on a recurring single premium basis.

11.2

A future premium must not exceed the lower of the value of:

1. (1) the actual premium payable under the contract; and
2. (2) the net premium, which may be increased for deferred acquisition costs in accordance with 12.1.

11.3

Where the terms of a contract of insurance have changed since it was first entered into, a firm must, in determining the net premium for the purpose of 11.2(2), treat that change as if either:

1. (1) it had been included in the original contract but came into effect from the time the change became effective; or
2. (2) the original contract were cancelled and replaced by a new contract (with an initial premium paid on the new contract equal to the liability under the original contract immediately prior to the change); or
3. (3) subject to 11.4, it gave rise to two separate contracts where:
1. (a) all premiums are payable under the first contract and that contract provides only for such benefits as those premiums could have purchased from the firm at the date the change became effective; and
2. (b) no premiums are payable under the second contract and that contract provides for all the other benefits.

11.4

For the purposes of 11.3(3), a firm must not treat the change referred to in 11.3 as giving rise to two separate contracts unless a meaningful comparison can be made between the terms of the contract (as changed) and the terms upon which the firm was newly effecting contracts of insurance at the time the contract was changed.

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12

12.1

1. (1) The amount of any increase to the net premium for deferred acquisition costs must not exceed the equivalent of the recoverable acquisition expenses spread over the period of premium payments and calculated in accordance with the rates of interest, mortality and morbidity assumed in calculating the mathematical reserves.
2. (2) The recoverable acquisition expenses in (1) must not exceed the lower of:
1. (a) the value of the excess of actual premiums over net premiums; and
2. (b) 3.5% of the relevant capital sum.
3. (3) Recoverable acquisition expenses may be calculated as the average for a group of similar contracts weighted by the relevant capital sum for each contract.

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13

### Future Premiums: Accumulating With-Profits Policies

13.1

This Chapter applies to accumulating with-profits policies written on a recurring single premium basis.

13.2

1. (1) A firm must not attribute any value to a future premium under the contract.
2. (2) Any liability arising only upon the payment of that premium may be ignored except to the extent that the value of that liability upon payment would exceed the amount of that premium.

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14

### Expenses

14.1

1. (1) A firm must make provision for expenses, either implicitly or explicitly, in its mathematical reserves of an amount which is not less than the amount expected, on prudent assumptions, to be incurred in fulfilling its contracts of long-term insurance.
2. (2) For the purpose of (1), expenses must be valued:
1. (a) after taking account of the effect of taxation;
2. (b) having regard to the firm's actual expenses in the last 12 months before the actuarial valuation date and any increases in expenses expected to occur in the future;
3. (c) after making prudent assumptions as to the effects of inflation on future increases in prices and earnings; and
4. (d) at no less than the level that would be incurred if the firm were to cease to transact new business 12 months after the actuarial valuation date.
3. (3) A firm must not rely upon an implicit provision arising from the method of valuing future premiums except to the extent that:
1. (a) it is reasonable to assume that expenses will be recoverable from future premiums; and
2. (b) the expenses would only arise if the future premiums were received.

14.2

The provisions for expenses (whether implicit or explicit) required by 14.1 must be sufficient to cover all the expenses of running off the firm's existing long-term insurance business including:

1. (1) all discontinuance costs (for example, redundancy costs and closure costs) that would arise if the firm were to cease transacting new business 12 months after the actuarial valuation date in circumstances where (and to the extent that) the discontinuance costs exceed the projected surplus available to meet such costs;
2. (2) all costs of continuing to service the existing business taking into account the loss of economies of scale from, and any other likely consequences of, ceasing to transact new business at that time; and
3. (3) the lower of:
1. (a) any projected valuation strain from writing new business for the 12 months following the actuarial valuation date to the extent the actual amount of that strain exceeds the projected surplus on prudent assumptions from existing business in the 12 months following the actuarial valuation date; and
2. (b) any projected new business expense overrun from writing new business for the 12 months following the actuarial valuation date to the extent the projected expenses exceed the expenses that the new business can support on a prudent basis.

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15

### Mortality and Morbidity

15.1

A firm must set the assumptions for mortality and morbidity using prudent rates of mortality and morbidity that are appropriate to the country or territory of residence of the person whose life or health is insured.

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16

### Options

16.1

1. (1) When a firm establishes its mathematical reserves in respect of a contract of long-term insurance, the firm must include an amount to cover any increase in liabilities which might be the direct result of its policyholder exercising an option under, or by virtue of, that contract of insurance.
2. (2) Where the surrender value of a contract is guaranteed, the amount of the mathematical reserves for that contract at any time must be at least as great as the value guaranteed at that time.

16.2

1. (1) Where a policyholder may opt to be paid a cash amount or a series of cash payments (including the amount or amounts likely to be paid on a voluntary discontinuance), the mathematical reserves for the contract of insurance established under 2.1 must be sufficient to ensure that the payment or payments could be made solely from:
1. (a) the assets covering those mathematical reserves; and
2. (b) the resources arising from those assets and from the contract itself.
2. (2) For the purposes of (1), the firm must assume that:
1. (a) the assumptions adopted for the current valuation remain unaltered and are met; and
2. (b) discretionary benefits and charges will be set so as to fulfil the firm's regulatory duty to treat its customers fairly under any relevant provision of the FCA Handbook.
3. (3) (1) may be applied to a group of similar contracts instead of to the individual contracts within that group, except where the cash amount or series of cash payments is the amount or amounts likely to be paid on a voluntary discontinuance.

16.3

For the purposes of 16.2, a firm must assume that the amount of a cash payment secured by the exercise of an option is:

1. (1) in the case of an accumulating with-profits policy, the lower of:
1. (a) the amount which the policyholder would reasonably expect to be paid if the option were exercised, having regard to the representations made by the firm and including any expectations of a final bonus; and
2. (b) that amount, disregarding all discretionary adjustments;
2. (2) in the case of any other policy, the amount which the policyholder would reasonably expect to be paid if the option were exercised, having regard to the representations made by the firm, without taking into account any expectations regarding future distributions of profits or the granting of discretionary additions in respect of an established surplus.

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17

### Persistency Assumptions

17.1

A firm must, when making assumptions about voluntary discontinuance rates in the calculation of the mathematical reserves, ensure that those assumptions meet the general requirements for prudent assumptions as set out in 3.1.

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18

### Reinsurance

18.1

In this Chapter, references to:

1. (1) reinsurance and contracts of reinsurance include analogous non-reinsurance financing agreements;
2. (2) reinsured risks, in relation to a contract of reinsurance entered into by a firm, means that part of:
1. (a) the risks insured by the firm under contracts of long-term insurance entered into by it; and
2. (b) the other risks arising directly from the firm's long-term insurance business;
3. that have been transferred to the reinsurer under that contract of reinsurance; and
3. (3) reinsurance cash outflows include any reduction in policy liabilities recognised as covered under a contract of reinsurance or any reduction of any debt to the firm under or in respect of a contract of reinsurance.

18.2

A firm must value reinsurance cash flows using methods and assumptions which are at least as prudent as the methods and assumptions used to value the underlying contract of insurance which have been reinsured.

18.3

For purposes of 18.2:

1. (1) reinsurance recoveries must not be recognised unless the underlying liabilities to which they relate have also been recognised;
2. (2) reinsurance cash outflows need not to be valued provided that:
1. (a) in accordance with 18.5 and 18.6, they are unambiguously linked to the emergence as surplus of margins included in the valuation of existing contract of insurance or to the exercise by a reinsurer of its rights under a termination clause; and
2. (b) the conditions in 18.4 are satisfied;
3. (3) reinsurance cash inflows that are contingent on factors or conditions other than the reinsured risks must not be valued.

18.4

The conditions referred to in 18.3(2)(b) are that:

1. (1) the reinsurance is not connected with any other transaction, which, when taken together with the reinsurance, could result in the requirements set out in 18.3(2) no longer being satisfied or in the risk transferred under the reinsurance being undermined; and
2. (2) the present value of the future reinsurance cash outflows that may be disregarded under 18.3(2) must not at any time exceed the value of the aggregate net cash inflows that have already been received by the firm under the contract of reinsurance accumulated at an assumed rate of SONIA + 6% per annum.

18.5

For the purposes of 18.3(2), the "link" must be such that a contingent liability to pay or repay the amount to the reinsurer could not arise except when, and to the extent that, the margins in the valuation of the existing contract of insurance emerge as surplus, or the reinsurer exercises its rights under a termination clause in the contract of reinsurance as a result of:

1. (1) fraudulent conduct by the firm under or in relation to the contract of reinsurance; or
2. (2) a representation as to the existence, at or before the time the contract of reinsurance is entered into, of a state of affairs which is within the knowledge or control of the firm and which is material to the reinsurer's decision to enter into the contract being discovered to be false; or
3. (3) the non-payment of reinsurance premiums by the firm; or
4. (4) a transfer by the firm of the whole or a specified part of its business without the agreement of the reinsurer, except where that agreement has been unreasonably withheld.

18.6

1. (1) Subject to (2), for the purposes of 18.3(2) and 18.5, future surplus may only be offset against future reinsurance cash outflow in respect of surplus on non-profit policies and the charges or shareholder transfers arising as surplus from with-profits policies.
2. (2) Such charges and transfers may only be allowed for to the extent consistent with the regulatory duty of the firm to treat its customers fairly under any relevant provision of the FCA Handbook.

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19

### Record Keeping

19.1

A firm must make, and retain for an appropriate period, a record of:

1. (1) the methods and assumptions used in establishing its mathematical reserves, including the margins for adverse deviation, and the reasons for their use; and
2. (2) the nature of, reasons for, and effect of, any change in approach, including the amount by which the change in approach increases or decreases its mathematical reserves.

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