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Free CAS Exam 6-U.S. Formula Sheet PDF, No Signup (2026)

Regulation Foundations & the NAIC 1 item

Risk-Based Capital ratio

RBC ratio = \frac{TAC}{ACL RBC}

, TAC = total adjusted capital, ACL RBC = Authorized Control Level risk-based capital

Solvency, Specialty Markets & Emerging Regulation 7 items

Total Adjusted Capital

TAC = PHS - D_{n t} - D_{t}

, PHS = policyholders' surplus, D_nt = non-tabular discount, D_t = tabular discount on medical reserves

Authorized Control Level RBC

ACL RBC = 0.5 \times (RBC_{cov} \times 1.03)

, RBC_cov = covariance result, 1.03 applies the 3% basic operational risk add-on before halving

Risk-based capital covariance result

RBC_{cov} = R_{0} + R_{1}^{2} + R_{2}^{2} + R_{3}^{2} + R_{4}^{2} + R_{5}^{2} + R_{cat}^{2}

, R0 = affiliate risk, R1-R5 = fixed income/equity/credit/reserving/premium risk, Rcat = catastrophe risk

Surplus lines premium tax (home state, NRRA)

T = P \times t

, T = tax owed to insured's home state, P = full policy premium, t = home-state surplus lines tax rate (no multi-state allocation)

Acceptable predictive rating factor gate

A = S \land C \land \neg P

, A = acceptable factor, S = statistically significant, C = cost-rational link, P = proxy for a protected class

Price-optimized premium

P_{o pt} = R \times m

, P_opt = optimized premium, R = cost-based indicated rate, m = demand/elasticity multiplier (m>1 for inelastic insureds)

Cost-based indicated rate

R = \frac{P P}{1 - V}

, R = indicated rate, PP = expected pure premium, V = combined expense-and-profit load (as a fraction)

Tort Environment & Government Programs 14 items

Total insurer retention under TRIA

R = D + 0.20 (L - D)

, R = insurer retention, D = deductible (20% of prior-year premium), L = insured loss

Subsidy per insured

S_{i} = P_{i}^{r b} - P_{i}^{c}

,

S_{i}

= subsidy for insured i,

P_{i}^{r b}

= risk-based premium,

P_{i}^{c}

= charged premium

Treasury mandatory recoupment under TRIA

R C = 1.40 \times F

, RC = amount recouped via policyholder surcharges, F = federal outlay (applies below the $37.5B aggregate retention)

Residual-market deficit recoupment surcharge rate

s = \frac{A}{V P}

, s = surcharge rate, A = assessment owed (market share × deficit), VP = insurer's voluntary premium base in the line

Total tort cost breakdown

C_{t o t a l} = C_{n e t} + C_{pl ain t i f f} + C_{d e f e n se} + C_{a d min}

, C_net = claimant net compensation, C_plaintiff = plaintiff legal costs, C_defense = defense costs, C_admin = administrative overhead

Post-reform award with cap and collateral source offset

A = (E - O) + min (N, K)

, A = post-reform award, E = economic damages, O = collateral source offset, N = non-economic damages, K = non-economic cap

Defendant liability under modified joint-and-several reform

L_{d} = A \times f_{d}

, L_d = amount owed by the defendant, A = total post-reform award, f_d = defendant's fault share

TRIA federal reimbursement (federal share)

R = 0.80 \times (L - D), L > D

, R = federal reimbursement, L = insurer's certified losses, D = insurer deductible

TRIA insurer deductible

D = 0.20 \times P

, D = insurer deductible, P = prior-year direct earned premium in TRIA-eligible commercial P&C lines

TRIA insurer retention

I = D + 0.20 \times (L - D), L > D

, I = insurer retention, D = insurer deductible, L = insurer's certified losses

Three-year survival ratio

Survival ratio = \frac{Reserves}{\frac{1}{3} \sum _{t = 1}^{3} Paid _{t}}

, Reserves = current held reserves, Paid_t = paid loss in each of last 3 years

Change in policyholder surplus from reserve strengthening

Δ Surplus = - Δ Loss Reserves

, ΔSurplus = change in policyholder surplus, ΔLoss Reserves = change in loss-reserve liability

Pro-rata by time on risk allocation share

Insurer share = \frac{y}{T} \times L

, y = years insurer covered, T = total trigger period in years, L = total indemnity loss

Program funding adequacy ratio

Funding ratio = \frac{Premium + Reserves + Backstop}{Expected losses + Cat load}

, ratio

\geq 1

means the program self-funds an average year; exclude any backstop drawn every year

Primary Statements & Statutory Accounting 8 items

Solvency II risk margin

R M = C o C \sum_{t \geq 0} \frac{S C R _{t}}{( 1 + r _{t + 1} ) ^{t + 1}}

, RM = risk margin, CoC = cost-of-capital rate (6%), SCR_t = projected solvency capital requirement at time t, r = risk-free rate

Solvency II technical provision

T P = B E + R M

, TP = technical provision, BE = best estimate (probability-weighted PV of future cash flows at risk-free rates), RM = risk margin

GAAP equity bridge from SAP surplus

E_{G AA P} = S_{S A P} + D A C + N A + A F S + D T A

, E = GAAP equity, S = SAP surplus, DAC = unamortized deferred acquisition costs, NA = nonadmitted assets, AFS = AFS fair-value gain, DTA = additional deferred tax asset

IFRS 17 insurance liability

L = P V (C F) + R A + C S M

, L = insurance liability, PV(CF) = present value of fulfilment cash flows, RA = risk adjustment for non-financial risk, CSM = contractual service margin (unearned profit)

Combined ratio

C R = \frac{Loss}{E P} + \frac{LAE}{E P} + \frac{UW expense}{W P}

, Loss = incurred loss, LAE = loss adjustment expense, EP = earned premium, WP = written premium; below 100% = underwriting profit

Capital and surplus account roll-forward

S_{e n d} = S_{b e g} + N I + Δ U + Δ T + Δ N - Δ R - D + C

, NI = net income, ΔU = Δ unrealized gains, ΔT = Δ net deferred tax, ΔN = Δ (decrease in) nonadmitted assets, ΔR = Δ reinsurance provision, D = stockholder dividends, C = paid-in capital

Statutory policyholders' surplus

Surplus = Admitted assets - Liabilities

, Admitted assets = readily marketable assets (nonadmitted excluded); Liabilities = total statutory liabilities

Statutory underwriting income

UW income = E P - Loss - LAE - UW expense

, EP = earned premium, Loss = incurred loss, LAE = loss adjustment expense, UW expense = other underwriting expense

Annual Statement Schedules & the IEE 4 items

IEE investment gain allocated to a line

I G_{l in e} = y \times (\overline{R}_{L + L A E} + \overline{U E P R} - \overline{A B})

, y = investment yield, mean loss/LAE reserves, mean unearned premium reserve, mean agents' balances

One-year reserve development

D_{1} = (P_{y r} + R_{n o w}) - R_{p r i or}

, P_yr = paid this year on all prior accident years, R_now = reserves now held on those years, R_prior = reserves held one year ago; positive is adverse

IRIS ratio 11 one-year reserve development to surplus

IRIS 11 = \frac{D _{1}}{S}

, D_1 = one-year reserve development on all prior accident years, S = policyholders' surplus; unusual value if exceeds 20%

Schedule F provision for reinsurance

Provision = (R - C) + 0.20 \times O

, R = unauthorized recoverable, C = collateral held, O = over-90-day overdue amount (penalty only if O > 20% of that reinsurer's total)

Solvency Metrics: RBC & IRIS 6 items

Total RBC after covariance including basic operational risk

Total RBC = RBC_{cov} \times 1.03

, RBC_cov = covariance result

R_{0} + R_{1}^{2} + \dots + R_{cat}^{2}

, 1.03 applies the 3% operational risk add-on

Basic operational risk charge

Op = 0.03 \times RBC_{cov}

, Op = basic operational risk add-on, RBC_cov = Total RBC after covariance before operational risk

IRIS two-year overall operating ratio

O R = (L R + E R) - I I R

, LR = 2-yr loss ratio, ER = 2-yr expense ratio, IIR = 2-yr investment income ratio; usual < 100%

IRIS one-year reserve development to surplus ratio

\frac{D _{1}}{P H S _{p r i or}}

, D_1 = one-year adverse reserve development, PHS_prior = prior year-end policyholders' surplus; usual < 20%

IRIS surplus aid estimate

Surplus aid = \frac{C C}{R P C} \times U P C

, CC = ceding commissions, RPC = reinsurance premiums ceded, UPC = unearned premiums ceded to non-affiliates

IRIS change in net premiums written ratio

\frac{N P W - N P W _{p r i or}}{N P W _{p r i or}}

, NPW = current net premiums written, NPW_prior = prior-year net premiums written; usual range −33% to +33%

The Appointed Actuary: SAO, AOS & Professionalism 10 items

Materiality standard as a percentage of surplus

M = p \times S

, M = materiality standard, p = chosen percentage (e.g. 10%), S = statutory policyholders surplus

Reserve deficiency below the range of reasonable estimates

D = L - C

when

C < L

, D = deficiency (inadequate opinion), L = low end of reasonable range, C = carried reserve

AOS adverse one-year reserve development disclosure trigger

\frac{Adverse 1yr development}{S _{p r i or}} > 5%

in

\geq 3

of past 5 years, S_prior = prior year-end surplus; triggers required AOS explanation of contributors

Risk of material adverse deviation test

(H - C) > M \Rightarrow RMAD exists

, H = high end of reasonable range, C = carried reserve, M = disclosed materiality standard (gap at or below M does not rule out RMAD)

ASOP 36 risk of material adverse deviation bright-line test

Carried + M \in [Low, High] ⟹ RMAD exists

, M = materiality standard, Low/High = ends of actuary's range of reasonable estimates

AOS one-year adverse development disclosure threshold

D_{t} > 0.05 \times S_{t - 1}

,

D_{t}

= one-year adverse development in year t,

S_{t - 1}

= that year's prior year-end policyholders' surplus

Reasonable reserve provision condition

Carried \in [Low, High]

, Carried = carried reserves, Low = low end of range, High = high end of actuary's range of reasonable estimates

Risk of material adverse deviation condition

RMAD present ⟺ D > M

, D = plausible adverse deviation from major risk factors, M = materiality standard

AOS persistent adverse-development disclosure trigger

Describe if \frac{A D _{t}}{S _{t - 1}} > 5% in \geq 3 of last 5 years

, AD = one-year adverse development, S = prior year-end surplus

Materiality standard for the SAO

M = p \times S

, M = materiality standard, p = selected percentage (e.g. 10%), S = policyholders' surplus

Insurer Taxation & Reinsurance Accounting 22 items

Expected reinsurer deficit

E R D = p \times \overset{s}{ˉ}

, p = probability of an NPV loss to the reinsurer,

\overset{s}{ˉ}

= average loss severity as a percent of premium; risk transfer indicated when ERD > 1%

Reinsurer present-value loss as a percent of premium

L % = \frac{P V ( losses + expenses ) - P}{P}

, PV = present value of losses and expenses in a scenario, P = reinsurance premium paid

Ten-ten rule risk transfer condition

Pr (L % \geq 10%) \geq 10%

,

L %

= reinsurer PV loss as a percent of premium; both a 10% probability and a 10% loss size are required to pass

Slow-paying test ratio on paid recoverables

ratio = \frac{O P}{T P + R P} \geq 0.20

, OP = paid recoverables over 90 days overdue not disputed, TP = total paid recoverables not disputed, RP = amounts received in prior 90 days

Provision for unauthorized reinsurance

P = min [(R - C) + 0.20 \times O D, R]

, R = recoverable, C = collateral held, OD = overdue or disputed amount, P = provision (capped at R)

Below-the-line overdue and disputed provision

P = 0.20 \times (O P + D)

, OP = overdue paid balances, D = disputed paid balances, P = provision charged when reinsurer is not slow-paying

Slow-paying reinsurer provision

P_{s l o w} = 0.20 \times max (R - C, O P)

, R = recoverable, C = funds held plus collateral, OP = paid recoverables over 90 days overdue, P = provision

Proration reduction to the loss deduction

Δ = p (T E I + D R D)

, p = reduction percentage = 5.25%/21% = 25%, TEI = tax-exempt interest, DRD = dividends-received deduction; reduces losses incurred

Tax loss reserve discount amount

D = R_{u n d i sc} (1 - f)

,

R_{u n d i sc}

= statutory undiscounted reserve, f = discount factor =

R_{d i sc} / R_{u n d i sc} \leq 1

; D is added to current taxable income

Tax-earned premium under the revenue offset

E P_{t a x} = W P - 0.80 Δ U E P R

,

W P

= written premium,

Δ U E P R

= increase in unearned premium reserve; equals statutory earned premium plus 20% of

Δ U E P R

Discounted unpaid loss reserve under Section 846

R_{d i sc} = \sum_{t} P_{t} (1 + i)^{- (t - 0.5)}

,

P_{t}

= payment at time t, i = prescribed discount rate, t = full years from valuation, 0.5 = mid-year convention

Reinsurer maximum present-value loss ratio

ℓ = \frac{L _{ma x}}{Prem}

,

ℓ

= worst-case loss as fraction of premium,

L_{ma x}

= maximum present-value loss to reinsurer, Prem = ceded premium; significant if

ℓ \geq 10%

10-10 rule risk transfer screen

P (L \geq 0.10 \times Prem) \geq 0.10

,

L

= reinsurer present-value loss, Prem = ceded premium; at least a 10% probability of at least a 10% PV loss

Net consideration booked as a deposit

D = Prem - C

,

D

= deposit (asset for cedant, liability for reinsurer), Prem = premium paid,

C

= ceding commissions; carried forward at the effective yield

Reinsurance accounting qualification condition

Reinsurance accounting = R_{in s} \land S_{l oss}

,

R_{in s}

= significant insurance risk transferred,

S_{l oss}

= reasonable possibility of significant loss; both must hold or use deposit accounting

Surplus relief from ceding a quota share

Surplus aid = c \times UPR_{ceded}

, c = ceding commission rate, UPR_ceded = ceded unearned premium reserve

Surplus aid as a percent of policyholders' surplus

Surplus aid % = \frac{c \times UPR _{ceded}}{Surplus}

; 15% or more trips the IRIS Ratio 4 unusual value

Net premium-to-surplus leverage

Net leverage = \frac{NWP}{Surplus}

, NWP = net written premium (net of ceded), Surplus = policyholders' surplus

Taxable gain on a commutation under IRC 846

G_{t a x} = R_{t a x} - P

,

G_{t a x}

= taxable gain,

R_{t a x}

= IRC 846 discounted reserve released,

P

= commutation payment

Reinsurer statutory gain on a commutation

G = R_{r e l e a se d} - P

,

G

= reinsurer gain,

R_{r e l e a se d}

= assumed statutory reserves released,

P

= commutation payment made

Book-tax difference on a commutation gain

Δ = R_{s t a t} - R_{t a x}

,

Δ

= book-tax difference (equals reserve discount),

R_{s t a t}

= statutory reserve,

R_{t a x}

= IRC 846 discounted reserve

Cedant underwriting result on a commutation

U = P - C

,

U

= cedant result (loss if negative),

P

= commutation cash received,

C

= recoverable the cedant carried

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