CAS Exam 7 common mistakes
CAS Exam 7 · Understand the traps and how to avoid them.
Computing a stochastic reserve estimate (e.g., Mack standard error or a bootstrap distribution) and reporting only the point estimate or only the coefficient of variation, without stating whether the interval is a prediction interval for a single accident year versus the aggregate reserve, and without reconciling the process variance and parameter/estimation variance components.
Candidates memorize the Mack variance formula as a single plug-in expression and never internalize that the total mean squared error of the reserve combines two distinct sources; exam questions frequently ask for one component or for the effect of aggregating across accident years, and under time pressure candidates default to the familiar total and skip the decomposition.
What to do instead
Before computing, write down explicitly which quantity is being estimated (single-year vs. total reserve) and which variance component is requested. Practice deriving the process-variance and parameter-variance terms separately, then show how correlation across accident years changes the aggregate (parameter variance does not simply add). Sanity-check that the aggregate MSE is less than the sum of individual MSEs when parameter uncertainty is shared.
Applying a development-factor or curve-fitting method (e.g., Sherman, Zehnwirth, or a log-linear decay fit) without first testing and documenting the underlying assumptions, and then reporting fitted ultimates as if the assumptions held.
The syllabus methods each rest on specific structural assumptions (e.g., constant development patterns, proportionality of cumulative claims to exposure, log-normality or specified variance structure). Candidates learn the mechanics of the fit but treat assumption diagnostics as optional narrative, so they skip residual plots, slope tests, and outlier checks that the question is actually testing.
What to do instead
For each method, maintain a one-page assumption checklist and a matching diagnostic. When a question asks to evaluate a method, structure the answer as: state assumptions, state the diagnostic that would reveal violation, apply it to the given data, then conclude. If a diagnostic is not computable from the data provided, say so explicitly rather than assuming validity.
Treating case-outstanding or case-incurred estimates as unbiased and using them directly in a Bornhuetter-Ferguson or Cape Cod calculation without adjusting for case-reserve inadequacy or for the difference between reported and ultimate emergence patterns.
BF and Cape Cod blend an a priori expected loss ratio with reported-to-date experience; the credibility of that blend depends on the reported data being on a consistent basis. Candidates often plug reported incurred losses straight into the expected-loss-ratio term, ignoring that case reserves may be redundant or deficient and that the emergence pattern used must match the data basis.
What to do instead
Before any BF/Cape Cod calculation, state the data basis (paid vs. incurred), state whether case reserves are believed adequate, and if not, adjust to a paid or adjusted-incurred basis. Show the credibility weight explicitly as a function of the percent reported and the chosen expected loss ratio, and test sensitivity to the a priori loss ratio rather than presenting a single number.
Confusing the roles of the indicated rate change, the selected rate change, and the written-to-earned or on-level premium adjustment, and applying an on-level factor in the wrong direction or to the wrong exposure base.
Rate-indication problems chain several multiplicative adjustments (trend, development, benefit/limit, catastrophe, credibility) and candidates lose track of which factors belong in the numerator versus the denominator, or apply an on-level factor to losses instead of premiums. The direction error is easy to make and hard to catch without a dimensional check.
What to do instead
Set up the indication as an explicit equation with labeled numerator and denominator before substituting numbers, and carry units (loss dollars vs. premium dollars) through each step. Verify direction by asking whether the adjustment should raise or lower the indicated change, and confirm the on-level factor converts historical premium to current rate level, not the reverse.
Valuing an insurer or block using a discounted cash flow or dividend-discount model without reconciling the discount rate to the cash flow definition (e.g., discounting statutory surplus flows at a cost of equity built from GAAP earnings) and without a terminal-value consistency check.
Valuation questions mix statutory and GAAP bases, and the cost of capital, growth rate, and payout assumptions must be internally consistent. Candidates often take a provided cost of equity at face value and apply it to a flow measured on a different basis, or let the terminal growth rate exceed the discount rate, producing an infinite or negative value they fail to flag.
What to do instead
Write the valuation identity first: value equals present value of distributable flows plus terminal value, with the discount rate labeled as to basis. Check that terminal growth is below the discount rate and below long-run nominal GDP growth, and that the payout/retention assumption in the terminal year matches the growth assumption. Reconcile the result to a market or book benchmark and explain any gap.
Ignoring the tax and capital frictions that make the cost of holding capital, rather than the raw cost of capital, the relevant charge in an economic value or risk-adjusted profitability calculation, and omitting the release of capital over the projection horizon.
Enterprise and valuation problems frequently require an economic value added or RAROC-style calculation where profit equals underwriting result plus investment income minus a capital charge. Candidates compute a capital charge on the full initial capital every year and forget that capital is released as the block runs off, or they apply a pre-tax cost of capital to an after-tax flow.
What to do instead
Build the projection year by year with three columns: required capital, investment income on capital and float, and capital charge. Release capital explicitly in each period and discount after-tax flows at an after-tax rate. Cross-check that the sum of capital charges plus the terminal release equals the present value of the capital commitment.
Answering an ERM question about risk appetite, tolerance, or limits with generic definitions and no linkage to the specific decision, governance body, or quantitative trigger described in the scenario.
ERM material is conceptual and candidates default to reciting definitions because they have not practiced converting framework language into operational statements. The result reads as textbook summary and earns little credit because it never states who acts, at what threshold, and with what consequence.
What to do instead
For every ERM concept, prepare a one-sentence operational template: risk appetite statement, quantified tolerance, limit structure, monitoring metric, escalation trigger, and owning committee. When answering, populate the template with the scenario's specifics and state the trade-off being made (e.g., growth versus solvency capital) rather than defining the term.
Treating economic capital, regulatory capital, and rating-agency capital as interchangeable, and computing a capital requirement without specifying the confidence level, time horizon, and risk measure (VaR vs. TVaR) being used.
The three capital concepts answer different questions and use different calibrations; candidates conflate them because the arithmetic looks similar. Omitting the risk measure and horizon makes the number uninterpretable, and comparing an economic capital figure to a regulatory ratio is a category error that examiners test directly.
What to do instead
Always label capital figures with basis, confidence level, horizon, and risk measure. When a question asks for a comparison, build a short table with rows for economic, regulatory, and rating-agency capital and columns for purpose, calibration, and treatment of diversification. Note explicitly that TVaR exceeds VaR at the same confidence level for fat-tailed distributions.
Aggregating risk capital across lines or peril modules by simple summation, or by applying a diversification benefit without stating the dependence assumption (correlation matrix, copula, or scenario-based aggregation).
Diversification benefit is the headline result in many ERM questions, and candidates reach for the sum-of-capitals or the square-root-of-sum-of-squares formula without justifying which dependence structure makes it valid. The choice matters enormously for tail risks, and the exam tests whether the candidate knows that correlation-based aggregation understates tail dependence.
What to do instead
State the aggregation method explicitly and its dependence assumption. Show the undiversified sum, the diversified total, and the implied benefit as a percentage. Where tail dependence is plausible, note that linear correlation or a Gaussian copula will understate joint extremes and that a tail-dependence or scenario approach should be used, then discuss the sensitivity of the benefit to the assumption.
Presenting a single scenario or stress-test result as the risk assessment without describing the scenario design rationale, the reverse stress test that identifies the breaking point, and the management action or contingency plan triggered by the result.
Stress testing questions reward a full cycle: identify exposures, design plausible and severe scenarios, quantify impact on capital and liquidity, and specify responses. Candidates stop after the impact number because the quantification feels like the hard part, leaving the design rationale and the action plan unaddressed and losing the governance marks.
What to do instead
Use a fixed four-part structure for every stress-test answer: exposure identification, scenario rationale including why it is severe but plausible, quantified impact on capital and liquidity with the binding constraint named, and management actions with triggers. Add a reverse stress test that solves for the loss or event that breaches the tolerance, and state the earliest observable indicator of that path.