IFoA SP2 cheat sheet

Net premium reserve (prospective): V_t = A_{x+t} − P·ä_{x+t} using the valuation basis; gross premium reserve replaces P with the gross premium and loads expenses explicitly.

Recursive reserve identity: (V_t + G − e)·(1+i) = q_{x+t}·S + p_{x+t}·V_{t+1}, where S is the sum assured payable at end of year of death; solve forward from V_0 = 0 to test premium adequacy.

Profit signature: profit in year t = (premium + investment income + reserve release) − (claims + expenses + reserve held); discount at the risk discount rate to get NPV, and accumulate at the RDR to get the profit margin per unit premium.

Zeroisation test: alternative profit vectors with the same NPV but different timing reveal the effect of margins; a reserve basis with margins front-loads profit, a best-estimate basis back-loads it.

Asset-liability matching: immunise with duration and convexity; for a life fund with guaranteed surrender values, the liability duration shortens when lapse rates rise, so matching must be stress-tested for dynamic lapse behaviour.

With-profits: asset share = accumulated premiums less charges and cost of cover, plus investment return; smoothing of payouts is funded by the estate, and the estate must be sufficient to avoid a cut in payout on a 1-in-200 style stress.

Universal life / unit-linked: account value = previous value + premium − charges, rolled up at the credited rate; no-profit (NGE) charges must cover mortality and expense risk, tested by projecting the account value to zero under adverse lapse and yield scenarios.

Solvency II life SCR modules: mortality, longevity, morbidity, lapse, expense and revision risk are shocked separately and aggregated with a correlation matrix; longevity shock is a permanent 20% reduction in mortality rates for the SCR standard formula.

Premium bases: gross premium = expected claim cost + expenses + profit margin + risk margin, where the risk margin reflects the cost of holding capital above the best-estimate reserve over the policy lifetime.

Mortality improvement: use a projection model such as the CMI (e.g. 20xx series) with a long-term rate and convergence period; the cohort effect means a 65-year-old today has different improvement than a 65-year-old in 20 years.

Select mortality: deaths in the first years of a policy are lower than ultimate; q_{[x]+t} < q_{x+t}. Ignoring select factors overstates reserves for new business and understates them for in-force blocks priced on select rates.

Surrender and lapse assumptions: lapse rates are typically highest in early durations and vary with interest rates (dynamic lapse); a rise in interest rates increases lapses on low-guarantee products, worsening liquidity and reserve strain.

Expense reserves: per-policy expenses are a fixed cost that does not fall with policy size, so expense inflation and the fixed/variable split drive the reserve; overruns in per-policy expense hit small policies hardest.

Risk discount rate: set as risk-free rate plus a risk premium reflecting the cost of capital and the systematic risk of the profit stream; a higher RDR penalises back-loaded profit and favours front-loaded products.

Participating fund surplus: surplus = assets − liabilities − estate target; distribution policy determines the reversionary bonus and terminal bonus split, and terminal bonus cannot be used to disguise a deficit in the asset share.

Reinsurance: quota share reduces both reserve strain and profit; surplus (risk premium) reinsurance reduces new business strain on large sums assured; the reinsurance credit in reserves depends on counterparty default risk.

Cash-flow projection: model monthly or annual cash flows, apply decrements (death, surrender, maturity) in the correct order, and check the fund roll-forward reconciles opening assets plus investment return less outgo to closing assets.

Unit pricing: bid-offer spread and the treatment of expenses determine the unit price; the fund must not be materially disadvantaged by the pricing basis, and the price must be published and applied consistently.

Guaranteed annuity options (GAOs): value as a put option on the annuity rate; the cost rises with interest rate volatility and falls with mortality improvement; reserves must be held even when the option is currently out of the money.

Annuity reserves: a_{x} = Σ v^t·p_x; with longevity risk, the reserve is highly sensitive to the interest rate and to the mortality improvement assumption, so a 1% fall in yields can raise reserves by more than 10% for a young annuitant.

Term assurance pricing: the single premium is A^1_{x:n} = Σ v^{t+1}·p_x·q_{x+t}; for level premiums use the equivalence principle P = A^1_{x:n} / ä_{x:n}.

Endowment: A_{x:n} = A^1_{x:n} + A_{x:n}^1 (pure endowment); the reserve at duration t is the difference between the benefit value and the future premium value.

Profit testing: iterate the model with the reserve basis, the pricing basis and the actual experience basis separately; a positive profit at the pricing basis with zero at the reserving basis means the margins are released over time.

Mortality catastrophe risk: the SCR shock is a 1.5 per mille absolute increase in mortality rates for the following 12 months on the in-force sum at risk; it binds for protection business, not for annuities.

Lapse risk: the SCR combines a mass lapse shock (typically 40% of policies lapse immediately) and a lapse up/down shock; mass lapse hurts when acquisition costs are unrecouped and reserves are low.

Pricing for options and guarantees: charge explicitly for the guarantee or hold a reserve; the cost of the guarantee is the difference between the guaranteed benefit and the best-estimate value under the risk-neutral measure.

Asset-liability modelling: project assets and liabilities on a consistent basis, apply stochastic scenarios for yields and equity returns, and report the distribution of surplus, not just the mean.

Investment return attribution: split total return into income yield, capital gain and currency effect; for with-profits, the smoothed return credited to policyholders may differ from the earned return, with the difference held in the estate.

Capital requirements: economic capital = the loss at a chosen confidence level (e.g. 99.5% over one year) above the best-estimate liability; the cost of holding this capital is a charge in the pricing and profit test.

New business strain: the excess of acquisition expenses and reserves over the first premium; strain is recovered over the policy term, so rapid growth consumes capital and must be funded by the estate or by reinsurance.

Embedded value: EV = net assets + value of in-force business; the value of in-force is the present value of future profits after tax and the cost of capital, and it falls when the RDR rises.

Experience monitoring: compare actual to expected mortality, lapse, expense and investment return; a persistent A/E ratio above 100% on mortality means the pricing basis is too light and reserves need strengthening.

Treating customers fairly: product design, charges and surrender values must be tested for fairness across cohorts; the with-profits actuary must certify that payouts reflect asset shares and that the estate is not excessive.

Regulatory reporting: under Solvency II, the best-estimate liability plus risk margin equals technical provisions; the risk margin is the cost of capital of 6% per annum on the SCR for future years.

Life expectancy: e_x = Σ_{t≥1} p_x; a change of 1 year in life expectancy changes an annuity reserve by roughly the value of one year's payment discounted, so longevity risk is material for pension annuities.

Mortality table construction: crude rates q_x = deaths / exposed to risk, graduated with a smooth curve (e.g. Gompertz-Makeham or splines), and standardised for comparison using the SMR (actual/expected deaths).

Standardised mortality ratio: SMR = observed deaths / expected deaths, where expected uses a standard table; an SMR of 90 means 10% lighter mortality than the standard.

Select and ultimate tables: the select period is typically 2-5 years; the ultimate table applies after that, and the select effect is larger at younger ages and for larger sums assured.

Annuity mortality: annuitants have lighter mortality than the general population (self-selection), and the gap widens over time; using population tables for annuities understates the reserve.

Joint-life annuities: the last-survivor annuity value is a_x + a_y − a_{xy}; the reserve depends on the age gap and the correlation of the two lives' mortality.

Reversionary annuities and contingent benefits: value the benefit as a deferred annuity on the second life, contingent on the first life having died; the reserve is the expected present value of the contingent payments.

Pricing with expenses: the gross premium solves G·ä_{x:n} = A_{x:n} + e_initial + e_renewal·ä_{x:n} + e_claim·A_{x:n}; the expense loading per unit of premium falls as the sum assured rises.

Model documentation: record the purpose, the basis, the data and the limitations of every model; a model is only as good as its assumptions, and sensitivity testing shows which assumption dominates the result.

Deterministic vs stochastic: deterministic projections give a single scenario and are used for reserving; stochastic projections (e.g. Monte Carlo) give a distribution and are used for capital and for options and guarantees.

Risk-neutral vs real-world: price and reserve options on the risk-neutral measure (discount at the risk-free rate), but project capital and profit on the real-world measure with a risk premium.

Discounting: use the risk-free curve for best-estimate liabilities; the matching adjustment or volatility adjustment may be applied to the discount rate under Solvency II, subject to eligibility criteria.

Data quality: check for missing dates, duplicate policies, negative sums assured and inconsistent status codes; a small number of large misstatements can distort the A/E analysis more than many small ones.

Scenario testing: run interest rate up/down, equity fall, mortality/longevity shock, lapse shock and expense inflation shock; report the impact on surplus and on the SCR, and identify the binding scenario.

Governance: the with-profits actuary, the appointed actuary and the risk function have distinct roles; the actuarial function must report on the adequacy of reserves and on the reliability of the data.

Communication: present results with the basis, the key sensitivities and the uncertainty; a single point estimate without a range misleads decision-makers about the risk in the book.

Term assurance reserve: for a level premium, the reserve is negative in early durations (strain) and rises to the sum assured at maturity; the reserve is the excess of the present value of future benefits over future premiums.

Whole life reserve: V_t = A_{x+t} − P·ä_{x+t}; at older ages the reserve approaches the sum assured, so mortality risk on the in-force block is small relative to the reserve.

Endowment reserve: at duration t, the reserve is the present value of the maturity benefit plus death benefit less future premiums; the reserve grows steadily and peaks at maturity.

Annuity reserve: for a level annuity, the reserve falls over time as payments are made; for a deferred annuity, the reserve rises during the deferment and then falls during payment.

Surrender value: typically the asset share less a surrender charge or market value adjustment; the surrender value must not exceed the asset share, and a market value adjustment protects the fund when assets fall.

Paid-up policies: the sum assured is reduced in proportion to the premiums paid; the reserve is recalculated on the reduced benefit and the policy remains in force without further premiums.

Non-forfeiture: if a premium is missed, the policy may be converted to a paid-up policy or to an extended term assurance; the reserve must be sufficient to fund the reduced benefit.

Policy loans: the loan plus accrued interest is deducted from the claim or surrender value; the reserve must allow for the loan and the interest, and the loan may exceed the reserve if the policy is old.

Bonus systems: reversionary (compound) bonuses add to the sum assured and are guaranteed once declared; terminal bonuses are not guaranteed and are used to bring payouts up to asset share at claim.

Asset share calculation: AS_t = (AS_{t-1} + P − charges)·(1 + i_t) − cost of life cover; the asset share is the policyholder's fair share of the fund and is the anchor for payout decisions.

Smoothing: payouts are smoothed around asset share to avoid sharp falls; the estate funds the smoothing, and the smoothing policy must be documented and applied consistently across cohorts.

Estate: the estate is the excess of assets over the sum of asset shares; it must cover the cost of guarantees, smoothing and any regulatory capital, and must not be built up excessively at the expense of policyholders.

Inherited estate: the part of the estate not attributable to current policyholders; its distribution must be fair, and the with-profits actuary must consider the reasonable expectations of policyholders.

Charges: explicit charges (policy fee, fund management charge, surrender charge) and implicit charges (through the asset share) must be disclosed; a charge that is not disclosed is a conduct risk.

Guaranteed minimum: the guaranteed sum assured plus declared bonuses is a floor on the payout; the cost of the guarantee is the value of the put on the asset share, and it rises with volatility.

With-profits governance: the with-profits committee or independent examiner reviews payout decisions; the actuarial function must report on the fairness of the distribution and on the solvency of the fund.

Risk classification: mortality varies with age, sex, health, smoking, occupation and sum assured; underwriting bands and medical limits determine which risks are individually assessed.

Anti-selection: if a risk factor is not priced, those with the higher risk are more likely to buy, so the book deteriorates; genetic testing and family history must be handled within the regulatory framework.

Smoker/non-smoker: the mortality differential is large at younger ages and narrows at older ages; misclassification (a smoker declaring non-smoker) is a material leakage and is tested by random checks.

Occupation and residence: hazardous occupations and residence in high-mortality countries attract loadings; the loading must reflect the extra risk and be reviewed as the policyholder's circumstances change.

Sum assured limits: large sums assured are individually underwritten and may be reinsured; the retention limit is set by the insurer's capital and by the reinsurer's terms.

Claims: the claim amount is the sum assured plus bonuses less any policy loan and outstanding premiums; the death must be notified and the claim assessed against the policy terms and any exclusions.

Exclusions: suicide clauses (typically 12-13 months), war and hazardous pursuits exclusions; the reserve must allow for the expected claim cost net of the exclusion.

Underwriting evidence: medical examination, attending physician's report, blood tests and questionnaires; the cost of underwriting must be balanced against the mortality saving from better classification.

Product design: the benefit (death, survival, annuity, critical illness), the term, the premium pattern and the guarantees must be specified before pricing; the design determines the risk profile.

Critical illness: the claim is triggered by diagnosis of a listed condition; the incidence rates rise with age and the definitions matter, so the pricing basis must use credible incidence data and allow for advances in diagnosis.

Income protection: the benefit is a replacement income during incapacity; the claim cost depends on the definition of incapacity (own occupation vs any occupation), the deferred period and the recovery rate.

Deferred period: a longer deferred period reduces the claim cost and the premium; the deferred period must match the policyholder's sick pay arrangements to avoid over-insurance.

Long-term care: the benefit is triggered by inability to perform activities of daily living; the cost depends on the incidence of care need, the duration of care and the cost of care, and is highly sensitive to the discount rate.

Indexation: benefits and premiums may be indexed to inflation; the reserve must allow for the indexation, and the pricing must allow for the cost of the option to increase cover.

Guaranteed insurability: the option to increase cover without further underwriting is valuable to the policyholder and costly to the insurer; it must be priced and reserved for.

Product review: experience emerging differently from the pricing basis triggers a review; the insurer may re-rate new business but cannot change the terms of existing policies unless the contract allows.

Premium frequency: monthly premiums cost more to administer and increase the risk of lapse; the frequency loading must cover the extra expense and the loss of interest.

Premium payment period: a shorter payment period means higher premiums but lower total cost; the reserve at any duration is higher for a shorter payment period because more benefit is pre-funded.

Waiver of premium: the premium is waived on incapacity; the benefit is a series of premium payments contingent on incapacity, and the reserve is the present value of the waived premiums.

Paid-up and surrender: the policyholder may stop paying and take a paid-up policy or surrender; the reserve must be sufficient to fund the paid-up benefit and the surrender value.

Automatic premium loan: unpaid premiums are met by a loan against the policy; the loan plus interest is deducted from the claim, and the reserve must allow for the loan.

Grace period: premiums may be paid within a grace period (typically 30 days) without lapse; the reserve must allow for the extra mortality and the administration cost.

Premium holiday: a temporary stop in premiums without lapse; the reserve must fund the benefit during the holiday, and the holiday is a cost that must be priced.

Premium review: for reviewable products, the premium may be reviewed at set intervals; the reserve must allow for the review and for the risk that the review is not taken.

Reinsurance types: quota share (a fixed proportion of every risk), surplus (a multiple of the retention), facultative (individual risks) and excess of loss (claims above a threshold).

Quota share: the reinsurer takes a fixed percentage of premiums and claims; the insurer's retention is reduced proportionally, and the reinsurance credit in the reserve is the reinsurer's share of the reserve.

Surplus reinsurance: the insurer retains a fixed amount and cedes the excess up to a limit; the retention is set by the insurer's capital, and the cession is proportional to the sum assured above the retention.

Excess of loss: the reinsurer pays claims above a retention up to a limit; the cost is a premium, and the cover protects against large individual claims or a catastrophe.

Catastrophe cover: protects against an accumulation of claims from a single event (e.g. a pandemic); the cover is priced on the expected loss and the cost of capital, and the reinsurer's default risk must be allowed for.

Reinsurance credit: the reserve is reduced by the reinsurer's share, but only if the reinsurer is solvent; the credit is subject to counterparty default risk, and the reinsurer's rating matters.

Profit commission: the reinsurer shares profits with the insurer; the commission depends on the reinsurance account's experience and must be allowed for in the profit test.

Reinsurance and new business strain: reinsurance reduces the strain on large sums assured and on protection business, but it also reduces the profit; the net effect must be tested in the profit test.

Solvency II balance sheet: assets at market value, technical provisions = best-estimate liability + risk margin, and own funds = assets − liabilities; the SCR is the capital to survive a 1-in-200 shock over one year.

Risk margin: the cost of holding the SCR for future years, calculated at 6% per annum on the projected SCR, discounted at the risk-free rate; it is higher for long-duration and option-heavy business.

Matching adjustment: an increase in the discount rate for assets held to match liabilities, subject to eligibility (fixed cash flows, ring-fenced portfolio); it reduces the technical provisions but must not be used to mask a mismatch.

Volatility adjustment: a small increase in the discount rate based on a reference portfolio; it is a spread-widening buffer and is not a substitute for matching.

SCR modules: mortality, longevity, morbidity, lapse, expense, revision, counterparty and market risk; the modules are aggregated with a correlation matrix, and the operational risk is added.

Own funds tiers: tier 1 (ordinary share capital, retained earnings), tier 2 (subordinated debt) and tier 3 (deferred tax assets); the SCR must be met with at least 50% tier 1 and no more than 15% tier 3.

ORSA: the insurer's own risk and solvency assessment, forward-looking and covering the whole risk profile; it must be approved by the board and submitted to the supervisor.

Reporting: the Solvency and Financial Condition Report (SFCR) is public, the Regular Supervisory Report (RSR) is private; the quantitative reporting templates (QRTs) are submitted quarterly or annually.

IFRS 17: insurance contracts are measured as the fulfilment cash flows (best-estimate liabilities plus risk adjustment) plus the contractual service margin (CSM); the CSM is released to profit as the service is provided.

CSM: the unearned profit at initial recognition, equal to the negative of the fulfilment cash flows at inception; it is accreted with interest and released over the coverage period, and it absorbs changes in estimates.

Risk adjustment: the compensation for non-financial risk (mortality, lapse, expense); it is released over the coverage period and is not the same as the Solvency II risk margin.

Premium allocation approach: a simplified measurement for short-duration contracts (coverage of one year or less); the liability for remaining coverage is the unearned premium, and the liability for incurred claims is the expected claim cost.

Onerous contracts: if the fulfilment cash flows are positive at inception, the contract is onerous and the loss is recognised immediately; the loss is not deferred into the CSM.

Variable fee approach: for contracts with direct participation in the returns of underlying items (e.g. unit-linked), the CSM absorbs the insurer's share of the fair value returns, and the measurement is different from the general model.

Transition: full retrospective, modified retrospective and fair value approaches; the choice affects the CSM at transition and the future profit pattern.

Disclosure: IFRS 17 requires the reconciliation of the CSM, the analysis of insurance revenue and the risk adjustment; the presentation is by portfolio and by group of contracts.

Capital allocation: economic capital is allocated to lines of business by the marginal contribution to the portfolio's risk; the allocation drives pricing and performance measurement.

Return on capital: RAROC = (profit + investment income) / capital; a line is viable if RAROC exceeds the cost of capital, and the cost of capital is a charge in the pricing.

Cost of capital: the return required by shareholders, typically the risk-free rate plus a risk premium; it is used as the discount rate in the profit test and as the charge for holding capital.

Capital fungibility: capital held in a subsidiary may not be freely available to the group; the group must allow for local regulatory and currency restrictions.

Dividend policy: dividends are paid from distributable profits, and the insurer must retain enough capital to meet the SCR and the growth of the book; the dividend capacity is a key output of the ORSA.

Stress testing: the insurer must test the capital position under severe but plausible scenarios, including a pandemic, a market crash and a lapse shock, and report the results to the board.

Recovery and resolution: the insurer must have a plan for restoring the capital position after a shock, and the supervisor may require a recovery plan if the SCR coverage falls.

Group supervision: the group supervisor assesses the group's solvency on a consolidated basis; intra-group transactions and the double use of capital must be eliminated.

Professional standards: the actuarial profession's standards (e.g. TASs) require the actuary to be competent, to disclose the basis and the limitations, and to report any material uncertainty to the board.

Conflicts of interest: the with-profits actuary and the appointed actuary must manage conflicts between policyholders and shareholders; the actuarial function must be independent of the business lines.

Whistleblowing: the actuary must report to the supervisor if the insurer is not meeting its regulatory requirements, and must not be deterred by commercial pressure.

Peer review: complex models and material assumptions should be peer-reviewed; the review must be documented and the reviewer must be independent of the model builder.

Data protection: policyholder data must be handled in line with data protection law; the actuary must ensure that the data used is accurate and that the use is permitted.

Consumer duty: the insurer must act to deliver good outcomes for customers; the actuarial function must consider the fairness of charges, the clarity of communications and the suitability of the product.

Documentation: the actuarial function must document the methods, the assumptions and the judgements, and must be able to explain the results to the board and to the supervisor.

Ethical behaviour: the actuary must not mislead, must not use information improperly and must maintain the reputation of the profession; a breach may lead to disciplinary action.