MAS-I common mistakes
MAS-I · Understand the traps and how to avoid them.
On a rate-filing item, applies a prior-approval waiting period by default and concludes the filed rate cannot be used until the state approves it, even when the stem describes a competitive-rating state or a file-and-use law.
Most study time goes to the numerically heavy domains, so the regulatory handful gets compressed into a single 'rates must be approved' slogan and prior approval becomes the default assumption.
What to do instead
Before answering any rate-filing item, write down the regime named in the stem (prior approval, file-and-use, use-and-file, competitive/no-file) and the rule it implies for when a rate may be used and how long it stays on file. If the stem names no regime, do not import prior approval by default.
States that the NAIC can order an insurer to change a rate, examine its books, or suspend its licence when the insurer violates a model regulation.
Model laws are drafted by the NAIC and adopted by states, and the two names appear side by side in study material, so the drafting body is credited with the enforcement powers of the state department.
What to do instead
Fix the division of roles: the NAIC drafts model laws and regulations, runs the accreditation programme, and maintains financial databases, but has no statutory authority; only the state insurance department/commissioner can examine, approve rates and forms, and act against a licence.
Computes a posterior or reverse-conditional probability by dividing by the prior P(A) or by the likelihood, instead of by the total probability of the observed event.
Bayes' formula is remembered as a ratio of two familiar pieces, and the denominator slot gets filled with whichever probability appears first in the stem.
What to do instead
Write P(A|B) = P(B|A)P(A) / [P(B|A)P(A) + P(B|A^c)P(A^c)] with the full partition written out before substituting numbers, and check that the denominator sums correctly across the partition.
When asked for the density of Y = g(X) (for example Y = sqrt(X), Y = 1/X, or Y = e^X), substitutes the inverse function into f_X and reports that expression as the density of Y.
The CDF route F_Y(y) = F_X(g^{-1}(y)) is correct and familiar, but the short-cut density version silently drops the derivative factor.
What to do instead
Use f_Y(y) = f_X(g^{-1}(y)) * |d/dy g^{-1}(y)|, or carry out the CDF route and differentiate at the end; for decreasing g remember the absolute value and transform the support bounds as well.
Uses normal critical values with the sample standard deviation for a small-sample mean or two-sample comparison, and reports n1 + n2 - 2 degrees of freedom for an unequal-variance (Welch) comparison.
The normal-based formula is the first template learned and the most practised, so small-sample and unequal-variance variants look like minor cosmetic changes to it.
What to do instead
Check sample size and whether sigma is known before choosing: t with n - 1 df for a single mean with unknown sigma, pooled t with n1 + n2 - 2 df only when equal variances are stated, and Welch with the Satterthwaite df otherwise. Write the df formula on the page before computing.
Feeds a nominal annual rate straight into accumulation or discount factors, for example computing 1000(1.06)^10 when the rate is 6% convertible semiannually.
The symbol i^(m) looks like an interest rate, and under time pressure the superscript is read as decoration rather than as a compounding instruction.
What to do instead
Convert first and write the conversion on the page: i = (1 + i^(m)/m)^m - 1, and for discount d = 1 - (1 - d^(m)/m)^m. Only then touch the cash flows.
Values a payment stream at the wrong date or uses an annuity-immediate symbol when payments fall at the start of each period, for example discounting a premium that is due at issue.
The standard a-angle-n and s-angle-n symbols are annuities-immediate, while exam stems often describe insurance premiums payable in advance.
What to do instead
Draw a timeline and mark every payment date before selecting a symbol. Use the annuity-due form for payments at the start of each period and shift by one period whenever the valuation date is not the date of the first payment.
Computes Var(S) as E[N]Var(X) or as Var(N)Var(X) for aggregate losses, omitting the other term of the decomposition.
The expression resembles the variance of a product, and the conditional variance decomposition is recalled as a single term rather than a sum.
What to do instead
Derive from Var(S) = E[Var(S|N)] + Var(E[S|N]) = E[N]Var(X) + Var(N)(E[X])^2, then sanity-check against the Poisson case where it collapses to lambda times E[X^2].
Inverts the Buhlmann credibility constant, using k = Var(hypothetical means)/E[process variance], which credits the manual rate precisely when between-group heterogeneity is large.
Both the expected value of process variance and the variance of hypothetical means are computed from the same two summaries, and the ratio is remembered without its direction.
What to do instead
Anchor on the meaning of k: it is the exposure for which Z = 1/2, so Z = n/(n + k) with k = EPV/VHM. Check the direction: more between-group heterogeneity (larger VHM) must shrink k and raise Z; more within-group noise (larger EPV) must lower Z.
Applies a deductible to the aggregate loss distribution, or uses the claim count where a payment count is required, in a frequency-severity problem with a per-claim limit.
These problems are almost always posed in terms of claims, so the distinction among losses, claims and payments reads as definitional detail rather than as a modelling choice.
What to do instead
Express the coverage modification as a per-loss random variable, Y = min(X, d) or (X - d)+, and feed E[Y] and E[Y^2] into the aggregate formulas with the original claim count. Introduce a separate payment count only when a per-claim limit can eliminate claims, and compute the probability that a claim produces a payment explicitly.