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Tail Factors Working Party: Part 2. The Work Product Mark R. Shapland, FCAS, ASA, MAAA Casualty Loss Reserve Seminar Boston, MA September 12-13, 2005. Organized by “Type” of Method Sections Describe: Mechanics of each method, Examples for most methods, Results of our Testing, and

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Tail Factors Working Party:Part 2. The Work Product Mark R. Shapland, FCAS, ASA, MAAACasualty Loss Reserve SeminarBoston, MASeptember 12-13, 2005

paper overview
Organized by “Type” of Method

Sections Describe:

Mechanics of each method,

Examples for most methods,

Results of our Testing, and

Results of our Surveys

Paper Overview
paper overview1
Standard Notation:


Started with Notation from Reserve Variability Working Party

Added new notation where lacking

Summarize Areas for Future Research

Paper Overview
section overview
Bondy-Type Methods

Algebraic Methods

Benchmark Methods

Open Claim Methods

Curve Fitting Methods

Lifespan Methods

Miscellaneous Methods

Section Overview
bondy type methods
Bondy Method

Use last link ratio:

Modified Bondy Method

Double or square:

Generalized Bondy Method (Weller)

For 0<B<1:

Fully Generalized Bondy Method (Gile)

Let Vary by Accident Year

Bondy-Type Methods
bondy type methods1

Simple to Implement

Pattern Described with One Factor

Only Requires Cumulative Paid Data


Not Always Useful for Incurred Data

Will Fail with Increasing Development

May Fail with “More Complicated” Patterns

Bondy-Type Methods
algebraic methods
Equalizing Paid & Incurred Loss Estimates

Use Cumulative Incurred / Cumulative Paid

Boor’s Method

Adjust Case Reserves

Mueller’s Method

Adjust Incremental Factors

NCCI Method

Algebraic Methods
algebraic methods1

Simple to Implement

Only Requires Cumulative Data

Statistically Unbiased


May Not be Sophisticated Enough

Subject to Case Reserve Distortions

Some Methods Not Generally Well Known

Algebraic Methods
benchmark methods
Benchmark Development / Link Ratios

Adjusted Benchmark Development / Link Ratios

Use Link Ratios to Adjust Tail Factor

Benchmark Average Severity

Benchmark Adjusted by Claims Audit

Benchmark Methods
benchmark methods1

Supplement when Little Data

Adds Credibility

Various Degrees of Sophistication


Need Similar Data

Claim Handling Procedures

Relative Case Reserve Strength

Benchmark Methods
open claim methods
Maximum Possible Loss

Judgment of Open Claim Costs / Audit

Open Claim Methods
open claim methods1

Incorporates Particulars of Open Claims

Uses Knowledge of Claim Staff

Can Provide Bounds


Requires Access to Individual Claims

Subject to Judgment/Availability of Auditors

May Underestimate for Severe Cases

Open Claim Methods
curve fitting methods
Exponential Decay

Constant Rate of Factor Decay

McClenahan’s Method

Constant Monthly Incremental Paid Decay

Skurnick’s Method

Simplify Using Annual Decay

Sherman’s Method

Use “Inverse Power” Curves

England-Verrall Method

Smooth & Extrapolate Incremental Data

Curve Fitting Methods
curve fitting methods1

Straightforward & Intuitive

Extrapolate Beyond End of Data

Various Levels of Sophistication


May Underestimate Tail for Long-Tail Lines

Sub-Optimal If Pattern Not Consistent

Sometimes No Closed Form Solution

Curve Fitting Methods
lifespan methods
Static Mortality Method

Frequency / Severity Using Mortality Rates

Trended Mortality Method

Greatest Impact on “Distant” Years

Sherman-Diss Method

Separate Impact of Inflation & Mortality

Corro’s Method

Modeling of “Pension” Claims

Lifespan Methods
lifespan methods1

Extrapolate “Very-Long” Tail

Can Include “Increasing” Factors

Detailed Assumptions/Some Non-Subjective


More Complex

Need “Very Old” Data to Parameterize

Need Specific Mortality Rates

Lifespan Methods
miscellaneous methods1

Improves “Other” Methods

Adjustments Readily Understood

Add Claim Professional Judgment


Difficult to Reconstruct Old Claim Files

Auditor Must Ignore Prior Development

Auditor Must Evaluate at Multiple Points

Miscellaneous Methods