Free CAS Exam 6-U.S. (Regulation and Financial Reporting) Formula Sheet (2026)

Every Exam 6U formula you need on the test, grouped by topic and rendered with full math notation. 72 formulas across 8 topics, calibrated to the 2026 syllabus. Free forever, no signup required.

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All Exam 6U Formulas

Regulation Foundations & the NAIC 1 item
Risk-Based Capital ratio
RBC ratio=TACACL RBC\text{RBC ratio} = \dfrac{\text{TAC}}{\text{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−Dnt−Dt\text{TAC} = \text{PHS} - D_{nt} - D_{t}, PHS = policyholders' surplus, DntD_{nt} = non-tabular discount, DtD_t = tabular discount on medical reserves
Authorized Control Level RBC
ACL RBC=0.5×(RBCcov×1.03)\text{ACL RBC} = 0.5 \times (\text{RBC}_{\text{cov}} \times 1.03), RBCcovRBC_{cov} = covariance result, 1.03 applies the 3% basic operational risk add-on before halving
Risk-based capital covariance result
RBCcov=R0+R12+R22+R32+R42+R52+Rcat2\text{RBC}_{\text{cov}} = R_0 + \sqrt{R_1^{2} + R_2^{2} + R_3^{2} + R_4^{2} + R_5^{2} + R_{\text{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×tT = 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∧C∧¬PA = S \wedge C \wedge \neg P, A = acceptable factor, S = statistically significant, C = cost-rational link, P = proxy for a protected class
Price-optimized premium
Popt=R×mP_{opt} = R \times m, PoptP_{opt} = optimized premium, R = cost-based indicated rate, m = demand/elasticity multiplier (m>1 for inelastic insureds)
Cost-based indicated rate
R=PP1−VR = \dfrac{PP}{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 = D + 0.20(L - D), R = insurer retention, D = deductible (20% of prior-year premium), L = insured loss
Subsidy per insured
Si=Pirb−PicS_i = P^{rb}_i - P^{c}_i, SiS_i = subsidy for insured i, PirbP^{rb}_i = risk-based premium, PicP^{c}_i = charged premium
Treasury mandatory recoupment under TRIA
RC=1.40×FRC = 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=AVPs = \dfrac{A}{VP}, s = surcharge rate, A = assessment owed (market share × deficit), VP = insurer's voluntary premium base in the line
Total tort cost breakdown
Ctotal=Cnet+Cplaintiff+Cdefense+CadminC_{total} = C_{net} + C_{plaintiff} + C_{defense} + C_{admin}, CnetC_{net} = claimant net compensation, C_plaintiff = plaintiff legal costs, CdefenseC_{defense} = defense costs, CadminC_{admin} = administrative overhead
Post-reform award with cap and collateral source offset
A=(E−O)+min⁡(N,K)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
Ld=A×fdL_d = A \times f_d, LdL_d = amount owed by the defendant, A = total post-reform award, fdf_d = defendant's fault share
TRIA federal reimbursement (federal share)
R=0.80×(L−D), L>DR = 0.80 \times (L - D),\ L > D, R = federal reimbursement, L = insurer's certified losses, D = insurer deductible
TRIA insurer deductible
D=0.20×PD = 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×(L−D), L>DI = 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=Reserves13∑t=13Paidt\text{Survival ratio} = \frac{\text{Reserves}}{\tfrac{1}{3}\sum_{t=1}^{3}\text{Paid}_t}, Reserves = current held reserves, PaidtPaid_t = paid loss in each of last 3 years
Change in policyholder surplus from reserve strengthening
ΔSurplus=− ΔLoss Reserves\Delta \text{Surplus} = -\,\Delta \text{Loss Reserves}, ΔSurplus = change in policyholder surplus, ΔLoss Reserves = change in loss-reserve liability
Pro-rata by time on risk allocation share
Insurer share=yT×L\text{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=Premium+Reserves+BackstopExpected losses+Cat load\text{Funding ratio} = \frac{\text{Premium} + \text{Reserves} + \text{Backstop}}{\text{Expected losses} + \text{Cat load}}, ratio ≥1\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
RM=CoC∑t≥0SCRt(1+rt+1)t+1RM = CoC \sum_{t \ge 0} \frac{SCR_t}{(1 + r_{t+1})^{t+1}}, RM = risk margin, CoC = cost-of-capital rate (6%), SCRtSCR_t = projected solvency capital requirement at time t, r = risk-free rate
Solvency II technical provision
TP=BE+RMTP = BE + RM, 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
EGAAP=SSAP+DAC+NA+AFS+DTAE_{GAAP} = S_{SAP} + DAC + NA + AFS + DTA, 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=PV(CF)+RA+CSML = PV(CF) + RA + CSM, 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
CR=LossEP+LAEEP+UW expenseWPCR = \frac{\text{Loss}}{EP} + \frac{\text{LAE}}{EP} + \frac{\text{UW expense}}{WP}, Loss = incurred loss, LAE = loss adjustment expense, EP = earned premium, WP = written premium; below 100% = underwriting profit
Capital and surplus account roll-forward
Send=Sbeg+NI+ΔU+ΔT+ΔN−ΔR−D+CS_{end} = S_{beg} + NI + \Delta U + \Delta T + \Delta N - \Delta 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\text{Surplus} = \text{Admitted assets} - \text{Liabilities}, Admitted assets = readily marketable assets (nonadmitted excluded); Liabilities = total statutory liabilities
Statutory underwriting income
UW income=EP−Loss−LAE−UW expense\text{UW income} = EP - \text{Loss} - \text{LAE} - \text{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
IGline=y×(R‾L+LAE+UEPR‾−AB‾)IG_{line} = y \times (\overline{R}_{L+LAE} + \overline{UEPR} - \overline{AB}), y = investment yield, mean loss/LAE reserves, mean unearned premium reserve, mean agents' balances
One-year reserve development
D1=(Pyr+Rnow)−RpriorD_1 = (P_{yr} + R_{now}) - R_{prior}, PyrP_{yr} = paid this year on all prior accident years, RnowR_{now} = reserves now held on those years, RpriorR_{prior} = reserves held one year ago; positive is adverse
IRIS ratio 11 one-year reserve development to surplus
IRIS 11=D1S\text{IRIS 11} = \dfrac{D_1}{S}, D1D_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×O\text{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=RBCcov×1.03\text{Total RBC} = \text{RBC}_{\text{cov}} \times 1.03, RBCcovRBC_{cov} = covariance result R0+R12+⋯+Rcat2R_0 + \sqrt{R_1^2+\cdots+R_{\text{cat}}^2}, 1.03 applies the 3% operational risk add-on
Basic operational risk charge
Op=0.03×RBCcov\text{Op} = 0.03 \times \text{RBC}_{\text{cov}}, Op = basic operational risk add-on, RBCcovRBC_{cov} = Total RBC after covariance before operational risk
IRIS two-year overall operating ratio
OR=(LR+ER)−IIROR = (LR + ER) - IIR, 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
D1PHSprior\frac{D_1}{PHS_{prior}}, D1D_1 = one-year adverse reserve development, PHSpriorPHS_{prior} = prior year-end policyholders' surplus; usual < 20%
IRIS surplus aid estimate
Surplus aid=CCRPC×UPC\text{Surplus aid} = \frac{CC}{RPC} \times UPC, CC = ceding commissions, RPC = reinsurance premiums ceded, UPC = unearned premiums ceded to non-affiliates
IRIS change in net premiums written ratio
NPW−NPWpriorNPWprior\frac{NPW - NPW_{prior}}{NPW_{prior}}, NPW = current net premiums written, NPWpriorNPW_{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×SM = 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−CD = L - C when C<LC < L, D = deficiency (inadequate opinion), L = low end of reasonable range, C = carried reserve
AOS adverse one-year reserve development disclosure trigger
Adverse 1yr developmentSprior>5%\frac{\text{Adverse 1yr development}}{S_{prior}} > 5\% in ≥3\geq 3 of past 5 years, SpriorS_{prior} = prior year-end surplus; triggers required AOS explanation of contributors
Risk of material adverse deviation test
(H−C)>M⇒RMAD exists(H - C) > M \Rightarrow \text{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∈[ Low, High ]  ⟹  RMAD exists\text{Carried} + M \in [\,\text{Low},\ \text{High}\,] \implies \text{RMAD exists}, M = materiality standard, Low/High = ends of actuary's range of reasonable estimates
AOS one-year adverse development disclosure threshold
Dt>0.05×St−1D_t > 0.05 \times S_{t-1}, DtD_t = one-year adverse development in year t, St−1S_{t-1} = that year's prior year-end policyholders' surplus
Reasonable reserve provision condition
Carried∈[ Low, High ]\text{Carried} \in [\,\text{Low},\ \text{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\text{RMAD present} \iff D > M, D = plausible adverse deviation from major risk factors, M = materiality standard
AOS persistent adverse-development disclosure trigger
Describe if ADtSt−1>5% in ≥3 of last 5 years\text{Describe if } \frac{AD_t}{S_{t-1}} > 5\% \text{ in } \geq 3 \text{ of last 5 years}, AD = one-year adverse development, S = prior year-end surplus
Materiality standard for the SAO
M=p×SM = p \times S, M = materiality standard, p = selected percentage (e.g. 10%), S = policyholders' surplus
Insurer Taxation & Reinsurance Accounting 22 items
Expected reinsurer deficit
ERD=p×sˉERD = p \times \bar{s}, p = probability of an NPV loss to the reinsurer, sˉ\bar{s} = average loss severity as a percent of premium; risk transfer indicated when ERD > 1%
Reinsurer present-value loss as a percent of premium
L%=PV(losses+expenses)−PPL\% = \dfrac{PV(\text{losses} + \text{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%≥10%)≥10%\Pr(L\% \ge 10\%) \ge 10\%, L%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=OPTP+RP≥0.20\text{ratio} = \frac{OP}{TP + RP}\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×OD, R]P = \min[(R - C) + 0.20 \times OD,\ 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×(OP+D)P = 0.20 \times (OP + D), OP = overdue paid balances, D = paid balances in dispute more than 90 days, P = provision charged when reinsurer is not slow-paying
Slow-paying reinsurer provision
Pslow=0.20×max⁡(R−C, OP)P_{slow} = 0.20 \times \max(R - C,\ OP), R = recoverable, C = funds held plus collateral, OP = paid recoverables over 90 days overdue, P = provision
Proration reduction to the loss deduction
Δ=p (TEI+DRD)\Delta = p\,(TEI + DRD), p = reduction percentage = 5.25%/21% = 25%, TEI = tax-exempt interest, DRD = dividends-received deduction; reduces losses incurred
Tax loss reserve discount amount
D=Rundisc(1−f)D = R_{undisc}(1 - f), RundiscR_{undisc} = statutory undiscounted reserve, f = discount factor = Rdisc/Rundisc≤1R_{disc}/R_{undisc} \le 1; D is added to current taxable income
Tax-earned premium under the revenue offset
EPtax=WP−0.80 ΔUEPREP_{tax} = WP - 0.80\,\Delta UEPR, WPWP = written premium, ΔUEPR\Delta UEPR = increase in unearned premium reserve; equals statutory earned premium plus 20% of ΔUEPR\Delta UEPR
Discounted unpaid loss reserve under Section 846
Rdisc=∑tPt (1+i)−(t−0.5)R_{disc} = \sum_{t} P_{t}\,(1+i)^{-(t-0.5)}, PtP_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=LmaxPrem\ell = \dfrac{L_{max}}{\text{Prem}}, ℓ\ell = worst-case loss as fraction of premium, LmaxL_{max} = maximum present-value loss to reinsurer, Prem = ceded premium; significant if ℓ≥10%\ell \ge 10\%
10-10 rule risk transfer screen
P(L≥0.10×Prem)≥0.10P(L \ge 0.10 \times \text{Prem}) \ge 0.10, LL = 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−CD = \text{Prem} - C, DD = deposit (asset for cedant, liability for reinsurer), Prem = premium paid, CC = ceding commissions; carried forward at the effective yield
Reinsurance accounting qualification condition
Reinsurance accounting=Rins∧Sloss\text{Reinsurance accounting} = R_{ins} \wedge S_{loss}, RinsR_{ins} = significant insurance risk transferred, SlossS_{loss} = reasonable possibility of significant loss; both must hold or use deposit accounting
Surplus relief from ceding a quota share
Surplus aid=c×UPRceded\text{Surplus aid} = c \times \text{UPR}_{\text{ceded}}, c = ceding commission rate, UPRcededUPR_{ceded} = ceded unearned premium reserve
Surplus aid as a percent of policyholders' surplus
Surplus aid %=c×UPRcededSurplus\text{Surplus aid \%} = \frac{c \times \text{UPR}_{\text{ceded}}}{\text{Surplus}}; 15% or more trips the IRIS Ratio 4 unusual value
Net premium-to-surplus leverage
Net leverage=NWPSurplus\text{Net leverage} = \frac{\text{NWP}}{\text{Surplus}}, NWP = net written premium (net of ceded), Surplus = policyholders' surplus
Taxable gain on a commutation under IRC 846
Gtax=Rtax−PG_{tax} = R_{tax} - P, GtaxG_{tax} = taxable gain, RtaxR_{tax} = IRC 846 discounted reserve released, PP = commutation payment
Reinsurer statutory gain on a commutation
G=Rreleased−PG = R_{released} - P, GG = reinsurer gain, RreleasedR_{released} = assumed statutory reserves released, PP = commutation payment made
Book-tax difference on a commutation gain
Δ=Rstat−Rtax\Delta = R_{stat} - R_{tax}, Δ\Delta = book-tax difference (equals reserve discount), RstatR_{stat} = statutory reserve, RtaxR_{tax} = IRC 846 discounted reserve
Cedant underwriting result on a commutation
U=P−CU = P - C, UU = cedant result (loss if negative), PP = commutation cash received, CC = recoverable the cedant carried

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