CAS Exam 5 common mistakes
CAS Exam 5 · Understand the traps and how to avoid them.
Computing a trended premium or on-level premium by multiplying the current premium by a single trend factor without first adjusting for the rate-level (on-level) change, so the trend period and rate-level adjustment are conflated into one step.
Candidates memorize 'trend to the projected period' as one operation and skip the intermediate step of restating historical premium at current rate levels using parallelogram or extension-of-exposure methods, especially when the problem gives both a rate change date and a trend rate.
What to do instead
Always separate the two adjustments: first compute the on-level factor (cumulative rate change from the policy period to the current level, using earned-exposure timing), then apply the trend factor from the current level to the projected average accident date. Write the two factors as distinct lines before multiplying.
Applying a loss-development (age-to-age or age-to-ultimate) factor to a reported loss amount that has already been adjusted for case reserves or that is on a different valuation basis than the development triangle, mixing paid and incurred bases within one calculation.
Development triangles in the problem may be paid, incurred, or reported-count based, and candidates grab whichever column is numerically convenient without checking the basis of the loss figure they are developing.
What to do instead
Before selecting any development factor, state in writing the basis of both the triangle and the loss amount (paid vs. incurred, case vs. reported). If they differ, convert one to match the other first, and label each factor with its basis in the workpaper.
Choosing a loss development factor by averaging all age-to-age factors in a column without excluding or down-weighting outliers, large-loss distortions, or immature years, and without documenting the selection rationale.
Candidates treat the arithmetic average as the default 'safe' answer and are uncomfortable making a judgment selection, so they average mechanically even when one year is obviously distorted by a catastrophe or a single large claim.
What to do instead
Compute at least simple average, volume-weighted average, and median; identify any year whose factor is driven by a known large loss orcatastrophe; then select and justify with one sentence tied to the data (e.g., 'excluded 20X3 due to hurricane; volume-weighted on remaining years'). State the selection explicitly.
Using the Bornhuetter-Ferguson or Cape Cod method without first testing whether the initial expected loss ratio (ELR) is reasonable, or applying BF to a mature year where reported losses already exceed the ELR-implied ultimate, producing an ultimate below reported.
Candidates learn BF as a formula (reported + expected unreported) and apply it uniformly, forgetting that BF is designed for immature years and that a stale ELR produces nonsensical results on mature years.
What to do instead
Screen each accident year: compare reported-to-date to the ELR-implied expected. For mature years where reported exceeds expected, use development or a credibility-weighted blend and flag the ELR as stale. Show the BF ultimate versus reported and versus development ultimate side by side before selecting.
Mixing up the direction of the rate indication formula, e.g., computing (indicated rate level / current rate level) instead of (indicated average rate / current average rate) minus one, or applying the permissible loss ratio in the numerator rather than as a divisor.
The indication is a ratio of a target loss ratio to a permissible loss ratio, and candidates invert numerator and denominator under time pressure; the algebra is simple enough that they skip writing it out.
What to do instead
Write the formula symbolically before substituting: Indication = (Projected Loss & LAE Ratio) / (Permissible Loss & LAE Ratio) − 1. Then substitute numbers. Sanity-check the sign and magnitude: a 5–15% indication is typical; a 300% answer signals an inverted ratio.
Failing to include all expense components (fixed, variable, and profit/contingency) when deriving the permissible loss ratio, or double-counting LAE by including it both in the loss ratio and as an expense.
Problems present expenses in several forms (percent of premium, percent of loss, flat per policy) and candidates add them inconsistently, or they forget that the permissible loss ratio already nets out LAE.
What to do instead
Build an explicit expense table: fixed expenses per exposure, variable expenses as % of premium, LAE as % of loss, profit and contingency as % of premium. Convert everything to a % of premium, sum, and set PLR = 1 − total expense ratio. Check that LAE appears exactly once.
Applying deductible or coinsurance adjustments to losses but not to the corresponding loss adjustment expense, or applying a deductible credit to premium while leaving the loss ratio unadjusted, so numerator and denominator are on inconsistent bases.
Deductible and coinsurance adjustments are taught as separate topics, and candidates apply them to whichever side of the ratio they remember, losing track of the requirement that both premium and loss must reflect the same coverage terms.
What to do instead
For every coverage change, write two lines: effect on losses (and LAE) and effect on premium. Apply the deductible/coinsurance factor to losses and LAE consistently, and apply the corresponding premium adjustment (or state explicitly that premium is unchanged). Verify the ratio uses matched bases.
Computing a credibility-weighted estimate using square-root credibility but applying it to the wrong quantity (e.g., weighting the loss ratio by credibility when the standard calls for weighting the complement estimate), or using full credibility standard without checking the standard's threshold.
Credibility formulas appear in several contexts and the weighting target differs; candidates recall the square-root formula but not what is being blended, and they default to full credibility whenever exposure is large.
What to do instead
State the credibility standard being used (square-root, partial, or full), the complement of credibility, and the quantity being weighted before computing. For square-root, confirm the exposure base (claims, premiums, or exposures) matches the standard. Show the weighted result as Z × subject + (1−Z) × complement.
Projecting claim counts and severities to ultimate separately and then multiplying, without ensuring the count and severity development patterns are internally consistent, or ignoring that severity should be developed on a paid basis while counts develop on a reported basis.
Frequency-severity projections feel intuitive, so candidates develop each component with whatever factor is available and multiply, producing ultimates that do not reconcile to the incurred development ultimate.
What to do instead
Develop counts and severities on explicitly stated bases, then reconcile: frequency-severity ultimate should be compared to the incurred development ultimate, and differences explained. If they diverge materially, revisit the severity trend or the count development selection.
Presenting a single point estimate for an indicated rate change or loss reserve without a range, sensitivity, or discussion of the key assumptions (trend selection, development factor selection, ELR), and without checking the result against a reasonableness benchmark.
Candidates focus on getting the arithmetic right and treat the narrative/communication portion as optional, or they run out of time and omit the discussion the grader is looking for.
What to do instead
Reserve the last portion of the answer for a short sensitivity paragraph: vary the trend and the key development factor by a reasonable range and state the effect on the indication or reserve. State the two or three assumptions that most drive the result and give a reasonableness check (e.g., implied combined ratio, comparison to prior indication).