Actuarial Notes

Valuation Principle

Study guides: Exam CP-321, Exam GH-201C, Exam GH-201U, Exam ILA-101, Exam ILA-201I, Exam ILA-201U

A Valuation Principle is the set of rules a reporting framework lays down for measuring insurance contract liabilities (reserves). It says which cash flows count; whether assumptions are prescribed, best-estimate, or best-estimate with margins; what discount rate to use; whether assumptions are locked in or updated; and when profit emerges. U.S. statutory, GAAP, IFRS 17, tax and the health-reserving standards each apply their own, so one block of business has several reserves.

\text{Liability} = \text{PV}(\text{benefits} + \text{expenses}) - \text{PV}(\text{premiums})

\text{IFRS 17 liability} = \text{PV(net outflows)} + \text{RA} + \text{CSM}

\text{GAAP reserve} = \text{PV(benefits)} - \text{NPR} \times \text{PV(gross premiums)}

  • Statutory (ILA-201U, ILA-101). The aim is solvency, so the basis is conservative. Formulaic reserves (CRVM for life, CARVM for annuities) use prescribed mortality and interest. Principle-based reserves (VM-20 for life, VM-21 for variable annuities) project cash flows on prudent-estimate assumptions. Under VM-20 the reserve is the largest of the formulaic net premium reserve, the deterministic reserve and the stochastic reserve.
  • U.S. GAAP (LDTI). The aim is matching revenue and expense. The net premium ratio (NPR) is the share of gross premium needed to fund benefits. Cash-flow assumptions are reviewed and updated at least annually, the discount rate is an upper-medium-grade bond yield, and acquisition costs go into a separate DAC asset.
  • IFRS 17 (ILA-201I). The aim is current measurement. Fulfilment cash flows are unbiased and current, plus an explicit risk adjustment (RA). The CSM holds unearned profit so that no gain is recognised at inception. An onerous group recognises its loss immediately.
  • Short-duration health (GH-201, CP-321). Claim reserves are best estimates of unpaid claims, often with an explicit margin for adverse deviation. They are governed by ASOP No. 5 for incurred claims and ASOP No. 42 for other health liabilities. Contract and premium-deficiency reserves sit alongside them.

Same Term Block, Two Bases A fully discrete 3-year term insurance of $100,000 is valued on two bases with level net premiums. Basis A is prescribed and conservative: q = 0.010, 0.014, 0.019 in years 1 to 3, and i = 3.5\%. Basis B is best estimate: q = 0.008, 0.011, 0.015, and i = 4.5\%. Expenses are ignored, so on Basis B the NPR times the gross premium is just the net premium. Find each basis's reserve at time 1.

Answer On each basis, P = 100{,}000\,A^1_{x:\overline{3}|}/\ddot{a}_{x:\overline{3}|}. Then {}_1V = 100{,}000\,A^1_{x+1:\overline{2}|} - P\,\ddot{a}_{x+1:\overline{2}|}.

\begin{align*}
P_A &= \frac{3{,}932.83}{2.86776} \\
&= 1{,}371.39 \\
{}_1V_A &= 3{,}101.50 - 1{,}371.39(1.95266) \\
&= 423.63 \\
P_B &= \frac{3{,}054.38}{2.84769} \\
&= 1{,}072.58 \\
{}_1V_B &= 2{,}411.12 - 1{,}072.58(1.94641) \\
&= 323.43
\end{align*}

The conservative basis holds about 31\% more reserve for the same contract. The difference is profit that the conservative basis releases later.

IFRS 17 at Initial Recognition A group of life contracts has a PV of future premiums of 1,000 and a PV of future claims and expenses of 820, with RA = 60. Find the CSM and the liability at initial recognition. Repeat with outflows of 970.

Answer

\begin{align*}
\text{FCF} &= 820 + 60 - 1{,}000 \\
&= -120 \\
\text{CSM} &= 120 \\
\text{Liability} &= -120 + 120 \\
&= 0 \\
\text{FCF}' &= 970 + 60 - 1{,}000 \\
&= +30
\end{align*}

The profitable group carries a CSM of 120 and no day-one gain. With outflows of 970 the group is onerous: no CSM, a loss component of 30, and a loss of 30 recognised at once.

How it appears on the exam

  • ILA-201U tests the U.S. statutory (formulaic and principle-based) and GAAP (including DAC) principles. Questions ask for a reserve under a stated principle, or ask candidates to evaluate which method or assumption the principle requires.
  • ILA-201I describes and evaluates IFRS 17 for life and annuity products: fulfilment cash flows, risk adjustment, CSM release over coverage units, and onerous groups.
  • GH-201 and CP-321 test reserving principles for group and health contracts and for long-duration contracts, through claim reserve calculations and written answers on adequacy, margins and the relevant ASOPs.

Exam traps

  • One basis per answer. Statutory mortality and interest are prescribed. GAAP and IFRS 17 assumptions are current. Valuing with the pricing basis because "it was given" is the usual slip.
  • Locked-in vs updated. Under LDTI, cash-flow assumptions are updated with a catch-up, while the discount rate for interest accretion stays locked in at issue. Updating both, or neither, misstates the reserve change.
  • CSM is never negative. An unfavourable fulfilment cash flow at inception makes a group onerous. A negative CSM in an answer means a loss has been deferred that should have been recognised.
  • Conservatism is not a margin everywhere. Statutory reserves are deliberately prudent, while IFRS 17 puts the margin into the explicit RA. Adding a statutory-style margin to IFRS 17 cash flows counts it twice.