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Which of the following best describes the Mack chain ladder method as a stochastic reserving technique?

A fully parametric model that assumes incremental losses follow a log-normal distribution

A distribution-free model that reproduces chain ladder reserves and supplies prediction error estimates

A Bayesian credibility model that requires prior distributions for each accident year

A bootstrap procedure that simulates pseudo-triangles by resampling unscaled residuals

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Practice Pages

CAS Exam 5 Basic Ratemaking and Estimating Claim Liabilities Practice100 questions CAS Exam 6 Regulation and Financial Reporting (US) Practice100 questions CAS Exam 8 Advanced Ratemaking Practice100 questions CAS Exam 9 Financial Risk and Rate of Return Practice100 questions CAS Exam MAS-I Modern Actuarial Statistics I Practice100 questions CAS Exam MAS-II Modern Actuarial Statistics II Practice100 questions

2026 Statistics

Key Facts: CAS Exam 7 Exam

100

Practice Questions

OpenExamPrep CAS Exam 7 bank

4 hrs

Exam Length

CAS 2026 Admissions Schedule

30-35%

Recent Pass Rate

CAS sittings 2024-2025

~$1,200

Exam Fee

CAS 2026 fee schedule

2x/yr

2026 Sittings

Apr 14-21 and Oct 19-27

400-600 hrs

Recommended Study

Typical CAS Fellowship guidance

CAS Exam 7 is a primarily essay-format four-hour CBT taken on the Fellowship pathway, with a recent pass rate of about 30-35% and a fee near $1,200. It is administered twice a year (April 14-21 and October 19-27 in 2026) and tests reserving methodologies (Mack, bootstrap, GLM, stochastic) at roughly 25%, insurance company valuation at 20%, capital allocation at 15%, ERM frameworks at 15%, reinsurance strategy at 10%, cat modeling at 10%, and ASOP-based professionalism at 5%. Candidates should already hold ACAS or be near-ACAS standing before sitting.

Sample CAS Exam 7 Practice Questions

Try these sample questions to test your CAS Exam 7 exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Which of the following best describes the Mack chain ladder method as a stochastic reserving technique?

A.A fully parametric model that assumes incremental losses follow a log-normal distribution

B.A distribution-free model that reproduces chain ladder reserves and supplies prediction error estimates

C.A Bayesian credibility model that requires prior distributions for each accident year

D.A bootstrap procedure that simulates pseudo-triangles by resampling unscaled residuals

Explanation: Mack's method is a distribution-free stochastic chain ladder. It uses only the first two moments of age-to-age factors so the central estimate matches the deterministic chain ladder, and it adds a closed-form formula for the mean squared error of prediction.

2Mack's three core assumptions for the chain ladder model include all of the following EXCEPT:

A.Expected cumulative losses in column j+1 are proportional to those in column j

B.Cumulative losses for different accident years are independent

C.The variance of cumulative losses in column j+1 is proportional to the cumulative loss in column j

D.Incremental losses are independently and identically log-normally distributed

Explanation: Mack's assumptions are (i) linearity of expected cumulative losses by development period, (ii) independence between accident years, and (iii) a variance proportionality condition. The model is distribution-free, so a log-normal i.i.d. assumption is not part of it.

3Mack decomposes the mean squared error of the reserve estimate into two components. They are best described as:

A.Process variance and parameter (estimation) variance

B.Aleatory uncertainty and demand surge

C.Tail-factor risk and operational risk

D.Quantile risk and prior misspecification risk

Explanation: Mack's MSEP formula splits prediction error into process variance, the irreducible random fluctuation around the model, and parameter variance, the uncertainty from estimating the age-to-age factors and sigma squared from limited data.

4An actuary computes Mack's age-to-age factor variance estimator sigma squared for development period j. Which formula is correct?

A.sigma squared sub j = (1/(I-j-1)) * sum over i of C sub i,j * (f sub i,j - f hat sub j) squared

B.sigma squared sub j = (1/(I-j)) * sum over i of (C sub i,j+1 - C sub i,j) squared

C.sigma squared sub j = mean squared development factor minus one

D.sigma squared sub j = product of historical age-to-age factors minus the mean

Explanation: Mack defines sigma squared sub j as a weighted variance of the individual development factors f sub i,j around the volume-weighted f hat sub j, with weights C sub i,j and the standard 1/(I-j-1) degrees of freedom adjustment.

5When the latest development period only has one observation, Mack's standard variance estimator cannot be computed. The most common practical fix is to:

A.Set sigma squared for the tail to zero and ignore tail uncertainty

B.Extrapolate sigma squared sub j using sigma squared sub I-2 squared divided by sigma squared sub I-3

C.Use the bootstrap variance from the prior development period as a substitute

D.Replace the tail factor with the industry average from a Schedule P benchmark

Explanation: Mack himself proposes extrapolating sigma squared in the tail by min(sigma squared sub I-2 squared / sigma squared sub I-3, sigma squared sub I-3, sigma squared sub I-2). It is a pragmatic way to avoid assuming zero tail variance.

6The ODP bootstrap method for reserves resamples residuals derived from which underlying GLM?

A.An over-dispersed Poisson GLM with log link, fit to incremental losses

B.A gamma GLM with identity link, fit to cumulative losses

C.A Tweedie GLM with power 1.7, fit to ultimate losses

D.A binomial GLM with logit link, fit to closure rates

Explanation: The ODP bootstrap is built on an over-dispersed Poisson GLM with log link, fit to incremental claim payments. England and Verrall showed this GLM reproduces the chain ladder reserves and supports residual resampling for prediction error.

7In the ODP bootstrap, after fitting the chain ladder to each pseudo-triangle, the next step required to obtain a full predictive distribution of ultimate losses is:

A.Add a Monte Carlo process error step using the over-dispersion parameter phi

B.Apply Mack's MSEP formula to each pseudo reserve

C.Re-estimate development factors with a generalised additive model

D.Discount each pseudo reserve at the risk-free rate

Explanation: Bootstrapping pseudo-triangles captures parameter uncertainty, but each simulated reserve must then be combined with a Monte Carlo draw of process error (often Poisson or gamma based on the over-dispersion parameter) to produce a full predictive distribution.

8Pearson residuals used in the ODP bootstrap are typically scaled by which quantity to keep their variance comparable across cells?

A.The square root of the fitted incremental value

B.The cumulative loss to date

C.The sample mean of all observed incrementals

D.The triangle's grand total

Explanation: Pearson residuals divide each (observed minus fitted) incremental by the square root of the fitted incremental value, so that under the Poisson assumption their variance is approximately constant and they can be resampled without bias.

9Which statement about the relationship between the ODP GLM reserve estimate and the deterministic chain ladder reserve is correct?

A.The ODP GLM reserve equals the chain ladder reserve when fit to incremental data with log link

B.The ODP GLM always produces a higher reserve than the chain ladder

C.The ODP GLM only matches the chain ladder for short-tail lines

D.The ODP GLM reserve diverges from the chain ladder as soon as the triangle has a missing cell

Explanation: England and Verrall demonstrated that an over-dispersed Poisson GLM with log link, fit to incremental claim payments, reproduces the volume-weighted chain ladder reserve exactly when the triangle is complete.

10An actuary fits a gamma GLM with log link to a severity triangle. Which property of the gamma distribution makes it well suited to severity modelling?

A.Variance proportional to the mean squared, capturing positive skew

B.Variance equal to the mean, like the Poisson

C.Constant variance across all observations

D.Symmetric distribution centred on zero

Explanation: The gamma family has variance proportional to the square of the mean, which fits the right-skewed, strictly positive shape of claim severities well and makes it a common choice for severity GLMs.

About the CAS Exam 7 Exam

CAS Exam 7 is a Fellowship-track essay exam that tests stochastic reserving (Mack, bootstrap, Bayesian), insurance company valuation (DCF, embedded value, appraisal value), capital allocation methods, enterprise risk management frameworks, reinsurance strategy and optimization, catastrophe modeling, and the professionalism standards in ASOPs 36, 41, 43, and 56.

Questions

100 scored questions

Time Limit

4 hours

Passing Score

Scaled (6-10 = pass on the CAS 0-10 scale)

Exam Fee

~$1,200 (Casualty Actuarial Society (CAS))

CAS Exam 7 Exam Content Outline

25%

Reserving Methodologies

Mack distribution-free chain ladder, ODP bootstrap, GLM reserving (ODP, log-normal, gamma), Bayesian/MCMC stochastic reserves, MSE decomposition into process and parameter error

20%

Insurance Company Valuation

DCF using FCFE, P/E and P/B multiples for P&C, embedded value (ANW + VIF), MCEV, appraisal value, run-off value, value of new business

15%

Capital Allocation

Marginal vs allocated capital, RAROC, Myers-Cohn (CAPM-based), Merton-Perold, TVaR, CoVaR, Shapley value allocation

15%

ERM Frameworks

COSO ERM 2017 components, ISO 31000 principles/framework/process, S&P ERM rating (Strong/Adequate/Weak), risk appetite vs tolerance

10%

Reinsurance Strategy & Optimization

Treaty vs facultative, proportional (quota share, surplus share), non-proportional (XOL per risk/per occurrence/aggregate), retention selection, ROL, payback period, ceded combined ratio, reinsurance capital relief

10%

Catastrophe Modeling

AIR/RMS/KCC vendor models, AAL, PML at 1-in-100/250/500, OEP vs AEP, TVaR, epistemic vs aleatory uncertainty, demand surge, FHCF and CEA, cat bonds and ILS triggers (parametric, indemnity, industry index)

Professionalism (ASOPs)

ASOP 36 P&C reserves, ASOP 41 actuarial communications, ASOP 43 P&C unpaid claim estimates, ASOP 56 modeling

How to Pass the CAS Exam 7 Exam

What You Need to Know

Passing score: Scaled (6-10 = pass on the CAS 0-10 scale)
Exam length: 100 questions
Time limit: 4 hours
Exam fee: ~$1,200

Keys to Passing

Complete 500+ practice questions
Score 80%+ consistently before scheduling
Focus on highest-weighted sections
Use our AI tutor for tough concepts

CAS Exam 7 Study Tips from Top Performers

1Drill Mack chain ladder by hand: development factors, sigma squared estimators, and the process/parameter error decomposition of MSE

2Practice ODP bootstrap mechanics end-to-end so you can describe pseudo-triangle generation and ultimate distribution simulation in essay form

3Be able to set up and defend an embedded value calculation: ANW plus VIF less cost of capital, with MCEV adjustments where required

4Memorize the COSO ERM 2017 five components and the ISO 31000 principles, framework, and process so you can compare them on demand

5Build a one-page reinsurance cheat sheet with quota share, surplus share, XOL per risk/per occurrence/aggregate, ROL, and payback period formulas

6Re-read ASOPs 36, 41, 43, and 56 every week of your study cycle so professionalism essays become automatic

Frequently Asked Questions

How is CAS Exam 7 structured?

CAS Exam 7 is a four-hour computer-based test built primarily around essay and constructed-response items. Candidates work through multi-part problems that combine numerical calculations (chain ladder triangles, RAROC, embedded value) with written justifications grounded in the syllabus papers and ASOPs.

What is the pass rate for CAS Exam 7?

Recent sittings have cleared roughly 30 to 35 percent of candidates, which is in line with other CAS Fellowship exams. CAS reports outcomes on a 0-10 scale, where any score from 6 to 10 is a pass; CAS does not publish a fixed numeric cut score for Exam 7.

When is CAS Exam 7 offered in 2026?

Per the 2026 CAS Admissions Examination Schedule, Exam 7 has two sittings: a Spring window from April 14 to 21, 2026 and a Fall window from October 19 to 27, 2026. Registration deadlines fall several weeks before each window, and Pearson VUE handles scheduling.

How much does CAS Exam 7 cost?

The exam fee is approximately $1,200 in 2026, with discounted pricing for early registration and surcharge pricing for late registration. The total cost typically grows once you include study materials, seminar access, and any retake attempts.

What prerequisites should I have before sitting Exam 7?

CAS strongly recommends having ACAS in hand (or being one exam away from it). The syllabus assumes comfort with reserve estimation from Exam 5, regulation and accounting context from Exam 6, and statistical modeling from MAS-I and MAS-II. Without that base, the stochastic reserving and capital allocation material will be hard to follow.

How should I study for the essay format?

Most candidates spend 400-600 hours over four to six months. Build a paper-by-paper outline of the syllabus, write timed essay answers on past CAS Exam 7 problems, and practice formatting RAROC, Mack standard error, and embedded value calculations into clear bullet workings. Memorizing ASOP 36, 41, 43, and 56 requirements is also essential because professionalism shows up across multiple essay parts.