Actuarial Notes

Experience Study Calculations

By David B. Atkinson and John K. McGarry · Society of Actuaries · 2016

Study guide: Exam ILA-101

An October 2016 Society of Actuaries paper, revised March 2024, that presents and explains the methods for determining rates based on experience, such as mortality and claim utilization rates. The objective of experience studies is to develop rates or probabilities from data collected from sources such as insurance companies, consulting firms or governmental bodies, which actuaries use to develop assumptions for financial planning, valuation, pricing and risk management.

On the syllabus

  • Exam ILA-101 — Experience Study Calculations, SOA, Oct 2016 (revised Mar 2024), sections 2-4, 11, 12, 15, 17 and 18, excluding 18.2, 18.8 and 18.9; outcomes 2e.

Preface: Revisions Made to this Report Subsequent to October 2016

1 Acknowledgements

2 Introduction

  • 2.1 Scope
  • 2.2 Guide to Usage

3 Experience Study Overview

  • 3.1 Basic Terminology
  • 3.2 Experience Study Segmentation

4 Simple Mortality Study Examples

  • 4.1 Cohort Study with Deaths only
    • 4.1.1 Summary Rates with Deaths Only
  • 4.2 Cohort Study with Deaths and Withdrawals
    • 4.2.1 Individual Exposure Calculation
    • 4.2.2 Grouped Exposure Calculation
    • 4.2.3 Summary Rates with Deaths and Withdrawals
  • 4.3 Period Study with Deaths and Withdrawals
    • 4.3.1 Individual Exposure Calculation
    • 4.3.2 Grouped Exposure Calculation
  • 4.4 Amount-Weighted Studies
    • 4.4.1 Individual Amount Weights
    • 4.4.2 Grouped Amount Weights

5 Distributed Exposure

  • 5.1 Period Study

6 Fractional Rates

  • 6.1 Half-Year Period Study
  • 6.2 Average Fractional Rates
  • 6.3 Annual Period Study by Calendar Year

7 Average Daily Rates and Exposure

  • 7.1 Period Study with Daily Exposure

8 Average Force of Mortality

  • 8.1 Period Study with Constant Force
  • 8.2 Changing Force of Mortality

9 Distributions of Deaths

  • 9.1 Comparison of Distributions
    • 9.1.1 Balducci Hypothesis
    • 9.1.2 Uniform Distribution of Deaths
    • 9.1.3 Constant Mortality Rates
    • 9.1.4 Increasing Force
  • 9.2 Estimating Errors

10 Decrement Studies

  • 10.1 Decrement Types
  • 10.2 Rate Intervals
    • 10.2.1 Partial Rate Intervals
  • 10.3 Time Intervals
  • 10.4 Discrete Decrements
  • 10.5 Population States

11 Simple Withdrawal Study Example

  • 11.1 Period Study
    • 11.1.1 Exposure Calculation

12 Actual to Expected Analysis

  • 12.1 Period Study with Deaths and Withdrawals
  • 12.2 Amount-Weighted Period Study
  • 12.3 Period Study with Calendar Year
  • 12.4 Half-Year Study
  • 12.5 Half-Year Study with Daily Decrement Rates

13 Central Rates

  • 13.1 Annual Period Study
  • 13.2 Force of Decrement

14 Dependent Rates

  • 14.1 Cohort Study with Deaths and Withdrawals
  • 14.2 Period Study with Deaths and Withdrawals
  • 14.3 Population Projection
  • 14.4 Formula Derivation

15 Utilization Studies

  • 15.1 Frequency and Severity
  • 15.2 Utilization of Maximum Limits
  • 15.3 Loss Ratio
  • 15.4 Variable Annuity Withdrawal Utilization

16 Exposure and Rate Comparisons

17 Practical Considerations

  • 17.1 Amount-Weighted Distortions
  • 17.2 Data Extracts for Multi-Year Studies
  • 17.3 Homogeneity of Data
  • 17.4 Reporting Lags
  • 17.5 Non-Uniform Distribution of Events
  • 17.6 Partial Policy Years
    • 17.6.1 Overview
    • 17.6.2 Inclusion of Partial Policy Years
    • 17.6.3 Overview of Exposure Methods
    • 17.6.4 Annual Exposure Method
    • 17.6.5 Distributed Exposure Method

18 Product-Related Considerations

  • 18.1 Individual Life Insurance
    • 18.1.1 Grace Period
    • 18.1.2 Compromised and Denied Claims
    • 18.1.3 Study Variables Changing Over Time
    • 18.1.4 Treatment of Reinsured Amounts
    • 18.1.5 Use of Net Amount at Risk
    • 18.1.6 Inclusion of Substandard or Uninsurable Lives
    • 18.1.7 Backdated New Business
  • 18.2 Group Life Insurance
  • 18.3 Morbidity Products
    • 18.3.1 Claim Incidence Studies
    • 18.3.2 Claim Severity Studies
    • 18.3.3 Claim Termination Studies
  • 18.4 Disability Income
    • 18.4.1 Elimination Periods
    • 18.4.2 Partial Disability Benefits
    • 18.4.3 Recovery Followed by Relapse
    • 18.4.4 Claim Settlements
    • 18.4.5 Other DI Considerations
  • 18.5 Long-Term Care
    • 18.5.1 Elimination Period
    • 18.5.2 Inflation Protection
    • 18.5.3 Benefit Utilization Rate
    • 18.5.4 Other LTC Considerations
  • 18.6 Deferred Annuities
    • 18.6.1 Deferred Annuity Utilization Rates
    • 18.6.2 Contract Year Data Challenges
  • 18.7 Payout Annuities
  • 18.8 Retirement Pensions
  • 18.9 Credit Life and Disability
    • 18.9.1 Credit Life Insurance
    • 18.9.2 Credit Disability Income

19 Standard Method Error Derivation

  • 19.1 Errors from Fractional Exposure Method
    • 19.1.1 Error for Partial Year Running from Age 𝒙 to 𝒙+𝒔
    • 19.1.2 Error for Partial Year Running from Age 𝒙+𝒔 to 𝒙+𝟏
    • 19.1.3 Error for Fractional Period
  • 19.2 Errors for Annual Exposure Method
    • 19.2.1 Error for Partial Year Running from Age 𝒙+𝒔 to 𝒙+𝟏
    • 19.2.2 Error for Partial Year Running from Age 𝒙 to 𝒙+𝒔
    • 19.2.3 Error for Fractional Period
  • 19.3 Errors from Distributed Exposure Method
    • 19.3.1 Error for Partial Year Running from Age 𝒙 to 𝒙+𝒔
    • 19.3.2 Error for Partial Year Running from Age 𝒙+𝒔 to 𝒙+𝟏
    • 19.3.3 Error for Fractional Period

20 Linear Force Method

  • 20.1 Formula Development
    • 20.1.1 Partial Year Running from Age 𝒙 to 𝒙+𝒔
    • 20.1.2 Partial Year from Age 𝒙+𝒔 to 𝒙+𝟏
    • 20.1.3 Fractional Periods
  • 20.2 Increasing Force Example

21 Glossary

22 About the Society of Actuaries

Sources