III IC-26 cheat sheet

Reserve = PV(future benefits) − PV(future net premiums), evaluated on the valuation basis (mortality table, interest rate, and method specified in the contract and regulation).

Net premium reserve uses gross premiums replaced by net (valuation) premiums; gross premium reserves subtract actual expense loadings and are used for GAAP/earnings analysis.

Prospective reserve looks forward from the valuation date (PV benefits − PV future premiums); retrospective reserve looks backward (accumulated past net premiums − accumulated past benefits) and equals the prospective reserve only if assumptions match.

Terminal reserve at the end of year t equals the reserve at the start of year t+1 accumulated one year at interest plus net premium, minus the year's expected death benefit cost.

FPT (full preliminary term) modifies the first-year reserve to zero by treating first-year expenses as a full year of modified premiums; it lowers early reserves and raises later ones relative to the net premium method.

CRVM (commissioners reserve valuation method) and its 20-year preliminary term variant are minimum standard methods for many US products; a reserve deficiency arises when the actual reserve is below the minimum standard.

Net amount at risk = death benefit − reserve; for a level-premium whole life policy it declines as reserves grow, so YRT cost of insurance charges rise with age even though the face amount is level.

Cash value is not the reserve: cash surrender value = reserve − surrender charge, and the difference is a source of lapse-supported profit or a policyholder equity issue depending on regulation.

Gross premium = net premium + expense loading; loading covers per-policy, per-unit, and percentage-of-premium expenses plus a profit and contingency margin.

Profit test: discount distributable earnings (premiums − claims − expenses − increase in reserves, after tax) at the hurdle rate; IRR of the emerging cash flows is compared with the required return on capital.

Asset share = accumulated premiums minus accumulated claims, expenses, and cost of insurance, plus interest; it is compared with the cash value to test whether a product is adequately priced.

Statutory reserves are conservative (valuation mortality and maximum valuation interest rates); GAAP reserves under FAS 60/97/120 use best-estimate assumptions and can differ materially, creating DAC amortization effects.

Risk-based capital (C1 asset risk, C2 insurance risk, C3 interest-rate/credit risk, C4 business risk, C0 affiliate risk) sets a minimum capital floor; the ratio drives regulatory action levels.

Mortality improvement, lapse/surrender assumptions, and expense inflation are the assumptions most likely to dominate a life product's profit sensitivity; test each with a defined shock.

Universal life: account value grows at credited interest minus cost of insurance and expense charges; a no-lapse guarantee is a separate secondary guarantee whose cost depends on premium funding adequacy.

Duration matching: choose asset duration ≈ liability duration; a duration gap creates surplus volatility when interest rates move, measured as −D_A × A × Δi + D_L × L × Δi.

Immunization requires matching present values, durations, and (for multi-period protection) convexity, and rebalancing as durations drift with time and rate changes.

US life insurer tax: the small life insurance company deduction and the policyholders' surplus account (PSA) phase-down affect effective tax rate; DAC tax under IRC §848 spreads acquisition costs.

Policyholder taxation: death benefits generally income-tax-free; cash value growth is tax-deferred; loans and withdrawals above basis can trigger taxable income and, for MECs, LIFO gain recognition plus a 10% penalty before age 59½.

Statutory accounting: assets at admitted value, liabilities at conservative reserves; surplus = admitted assets − liabilities, and reserve strengthening reduces surplus and reported earnings immediately.

Embedded value = adjusted net worth + PV of in-force business profits; new business value and value of new business measure the profitability of production in a period.

ALM reporting: interest maintenance reserve (IMR) amortizes realized capital gains/losses attributable to interest-rate movements, while the AVR absorbs credit-related losses.