Actuarium

CAS Exam 7Estimation of Policy Liabilities, Insurance Company Valuation & ERM

Associateship (ACAS)
4 hoursΒ·25 written-answer itemsΒ·β‰ˆ450 study hours

Syllabus learning objectives

Official syllabus

Paraphrased from the CAS syllabus so the study-plan builder and practice sets track the topics you will actually be examined on. Weights are the official topic ranges.

Advanced reserving (Mack, Clark, Brosius, HΓΌrlimann, ODP bootstrap)

45%
  • Apply Mack's method to estimate the standard error of chain-ladder reserve estimates under stated variance assumptions.
  • Apply Clark's growth-curve method (LDF/Cape Cod) using MLE to fit development patterns with measurable variability.
  • Apply Brosius's and HΓΌrlimann's credibility-based reserving approaches to blend chain-ladder and Bornhuetter-Ferguson estimates.
  • Simulate a distribution of reserve outcomes using the over-dispersed Poisson (ODP) bootstrap method.

Reserve variability & risk margins

15%
  • Quantify process and parameter risk components of overall reserve variability.
  • Construct a reserve range and select an appropriate percentile for a risk margin.
  • Assess correlation across lines of business when aggregating reserve variability estimates.
  • Communicate reserve uncertainty to management, auditors and regulators.

Insurance company valuation

15%
  • Apply appraisal value and discounted cash flow methods to value a property-casualty insurer.
  • Incorporate cost of capital and risk margins into an insurer valuation.
  • Compare embedded value and market-consistent valuation approaches.
  • Assess the impact of reserve adequacy and growth assumptions on valuation results.

Enterprise risk management

25%
  • Identify and categorize the major risk types (underwriting, reserving, credit, market, operational) facing a P&C insurer.
  • Apply economic capital modeling to quantify aggregate risk and support capital adequacy decisions.
  • Evaluate risk mitigation strategies including reinsurance and capital market solutions.
  • Assess the components of an ORSA and its use in strategic decision-making.

Overview

Exam 7 moves reserving from point estimates to distributions: Mack's variance formulas, Clark's LDF/Cape Cod curve fitting, Brosius least squares, HΓΌrlimann, ODP bootstrap, and Verrall/Meyers Bayesian views. It adds valuation (DCF, P/E, Miccolis–Feldblum) and ERM (capital allocation, risk measures, operational risk).

Duration
4 hours
Questions
25 written-answer items
Style
Computer-based written answer
Credit
Required for ACAS

Syllabus map

Advanced reserving (Mack, Clark, Brosius, HΓΌrlimann, ODP bootstrap)
45%
Stochastic Reserving: Mack's Model and the ODP BootstrapReserving Diagnostics and the Berquist–Sherman Adjustment
Reserve variability & risk margins
15%
Reserve Adequacy and ASOP 43
Insurance company valuation
15%
Forecasting Premium, Loss, and ProfitabilityP&C Financial Reporting and Schedule P
Enterprise risk management
25%
Risk Measures and CapitalStress Testing and Emerging Risk

Key formulas

Mack assumptions β€…β€ŠE[Ci,k+1∣Ci,1..k]=fkCi,k\;E[C_{i,k+1}\mid C_{i,1..k}]=f_kC_{i,k}, Var⁑(Ci,k+1βˆ£β‹…)=Οƒk2Ci,k\operatorname{Var}(C_{i,k+1}\mid\cdot)=\sigma_k^2C_{i,k}, accident years independent.

Mack variance estimate Οƒ^k2=1Iβˆ’kβˆ’1βˆ‘i=1Iβˆ’kCi,k(Ci,k+1Ci,kβˆ’f^k)2\hat\sigma_k^2=\frac{1}{I-k-1}\sum_{i=1}^{I-k}C_{i,k}\left(\frac{C_{i,k+1}}{C_{i,k}}-\hat f_k\right)^2 mse^(C^i,I)=C^i,I2βˆ‘k=I+1βˆ’iIβˆ’1Οƒ^k2f^k2(1C^i,k+1βˆ‘j≀Iβˆ’kCj,k)\widehat{mse}(\hat C_{i,I})=\hat C_{i,I}^2\sum_{k=I+1-i}^{I-1}\frac{\hat\sigma_k^2}{\hat f_k^2}\left(\frac{1}{\hat C_{i,k}}+\frac{1}{\sum_{j\le I-k}C_{j,k}}\right)

Brosius least squares β€…β€Šy^=a+bx\;\hat y=a+bx; credibility form β€…β€ŠZβ‹…xd+(1βˆ’Z)E[y]\;Z\cdot\dfrac{x}{d}+(1-Z)E[y].

Clark Weibull growth β€…β€ŠG(x)=1βˆ’exp⁑ ⁣[βˆ’(x/ΞΈ)Ο‰]\;G(x)=1-\exp\!\left[-(x/\theta)^\omega\right]; loglogistic β€…β€ŠG(x)=xΟ‰xΟ‰+ΞΈΟ‰\;G(x)=\dfrac{x^\omega}{x^\omega+\theta^\omega}.

ODP bootstrap scale β€…β€ŠΟ•^=βˆ‘rij2nβˆ’p\;\hat\phi=\dfrac{\sum r_{ij}^2}{n-p}, rij=qijβˆ’m^ijm^ijr_{ij}=\dfrac{q_{ij}-\hat m_{ij}}{\sqrt{\hat m_{ij}}}.

Cost-of-capital risk margin β€…β€ŠRM=βˆ‘tCoCβ‹…Ct vt+1\;RM=\sum_t CoC\cdot C_t\,v^{t+1}.

Study strategy

  1. Write out the Mack assumptions and the three tests for each (linearity plots, residual plots, calendar-year test) until you can reproduce them cold.

  2. Work Clark's paper end to end with a spreadsheet: fitted growth curve, expected increments, process and parameter variance.

  3. For ERM, group readings by theme (risk measures, capital allocation, operational risk, strategic risk) and memorize each author's list of criteria.

  4. Time management is decisive β€” many candidates fail on pacing; allocate points-per-minute and move on.

Common traps

  • Including the diagonal element in the count of parameters for ODP bootstrap degrees of freedom incorrectly (p=2Iβˆ’1p=2I-1 for an IΓ—II\times I triangle).

  • Forgetting the tail's contribution to Mack's mse when a tail factor is used.

  • Confusing process variance (inherent randomness) with parameter variance (estimation error).

  • Applying a cost-of-capital margin to the run-off of capital rather than to the capital held each year.

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