Actuarium

CAS Exam 5Basic Techniques for Ratemaking & Estimating Claim Liabilities

Associateship (ACAS)
4 hours·25–30 written-answer items, ~80 points·≈400 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.

Ratemaking (Werner & Modlin)

55%
  • Adjust premium to current rate level via the parallelogram method and extension of exposures.
  • Select loss and premium trend factors and project experience to the future policy period.
  • Calculate rate level indications using the loss ratio and pure premium methods, including credibility weighting to a complement of credibility.
  • Develop classification, territorial and increased limit rating relativities from loss experience.
  • Incorporate expense provisions, underwriting profit and contingency loads into the overall rate indication.

Estimating unpaid claims (Friedland)

45%
  • Estimate ultimate claims using development-triangle methods including chain ladder, Bornhuetter-Ferguson, Cape Cod and expected claims techniques.
  • Diagnose and adjust for changes in case reserve adequacy, claim processing speed, and other distortions in a triangle.
  • Apply frequency-severity methods to estimate unpaid claims separately from counts and average severities.
  • Reconcile and select a best estimate from multiple reserving methods and assess reasonableness.

Lecture videos for this exam

Open the full video library →

Actuarial Reserving 1 | Development Method

Mancinelli's Math Lab · Loss Reserving

Reserve Calculation Basic Chain Ladder and Bornhuetter Ferguson Method

Pradnya Ambatipudi · Loss Reserving

Actuaries CT6 Run off Triangles Introduction

Pradnya Ambatipudi · Loss Reserving

Overview

Exam 5 is the gateway to Associateship: half ratemaking (Werner & Modlin's Basic Ratemaking) and half reserving (Friedland's Estimating Unpaid Claims Using Basic Techniques). It is a written-answer exam that rewards clean, labeled calculations and short justifications.

Duration
4 hours
Questions
25–30 written-answer items, ~80 points
Style
Computer-based written answer (spreadsheet-style)
Credit
Required for ACAS
Passing
Pass mark set by Examination Committee

Syllabus map

Ratemaking (Werner & Modlin)
55%
Ratemaking FundamentalsWorkers' Compensation RatemakingGL, Auto & Umbrella Pricing: Increased Limits and Excess Ratemaking
Estimating unpaid claims (Friedland)
45%
Loss Development Triangles: Construction and Age-to-Age FactorsReserving Methods: Chain Ladder, Bornhuetter–Ferguson, Benktander, and Cape CodReserving Diagnostics and the Berquist–Sherman Adjustment

Key formulas

Fundamental insurance equation   P=L+EL+EF+V⋅P+Q⋅P\;P=L+E_L+E_F+V\cdot P+Q\cdot P

Loss ratio indication Indicated change=Trended, developed LR+F1−V−QT−1\text{Indicated change}=\frac{\text{Trended, developed LR}+F}{1-V-Q_T}-1

Pure premium indication   Pˉ=Lˉ+EˉF1−V−QT\;\bar P=\dfrac{\bar L+\bar E_F}{1-V-Q_T}

Parallelogram on-level factor   OLF=current rate levelaverage rate level in period\;OLF=\dfrac{\text{current rate level}}{\text{average rate level in period}}

Chain ladder   C^i,∞=Ci,k∏j≥kf^j\;\hat C_{i,\infty}=C_{i,k}\prod_{j\ge k}\hat f_j, f^j=∑iCi,j+1∑iCi,j\hat f_j=\dfrac{\sum_i C_{i,j+1}}{\sum_i C_{i,j}}

Bornhuetter–Ferguson   IBNR^i=Pi⋅ELR⋅(1−1CDFi)\;\widehat{IBNR}_i=P_i\cdot ELR\cdot\left(1-\tfrac{1}{CDF_i}\right)

Cape Cod   ELR=∑iCi,k∑iPi/CDFi\;ELR=\dfrac{\sum_i C_{i,k}}{\sum_i P_i/CDF_i}

Study strategy

  1. Build a personal formula sheet from the source texts, then reproduce it from memory weekly — the exam gives no formulas.

  2. Do every problem in the CAS examiner's reports at least twice; the same structures recur with new numbers.

  3. Label every intermediate quantity in your answer; graders award partial credit for correct method.

  4. Practice the 'explain why' items: when BF beats chain ladder, when to use paid vs reported, how a change in case-reserve adequacy distorts each method.

Common traps

  • Trending losses to the average accident date of the future policy period, not to the effective date.

  • Applying fixed expense as a ratio to premium instead of per exposure (or vice versa).

  • Forgetting the tail factor or applying an all-year average when a change in settlement rate calls for a recent average.

  • BF: using 1−1/CDF1-1/CDF on paid CDF when losses are reported (or the reverse).

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