Washington State Transit Insurance Pool

Actuarial Science 101

Presented by:Kevin Wick, FCAS, MAAASeptember 30, 2008

PricewaterhouseCoopersSeptember 30, 2008

Slide 2

Agenda

• Risk Transfer/Role of Actuary• Example of calculations• What do you get from an

actuarial report?• Key questions to ask

PricewaterhouseCoopersSeptember 30, 2008

Slide 3

Risk Transfer Basics

• All entities deal with risks and uncertainties

• Ways to deal with risks include:- Retain- Transfer- Mitigate- Combination

• Actuaries are trained at quantifying and measuring risk

Slide 4 PricewaterhouseCoopers

September 30, 2008

What Specifically Do Actuaries Do?

1) Reserves Estimate the liability for costs already incurred but not yet paid Balance Sheet (solvency)

2) Rates Projected costs for accidents not yet incurred Income Statement (budgeting)

3) Other Confidence Levels, Cost Allocation, Retention Analysis

Actuarial projections do not affect the final cost of claims.

Apples to Apples

Slide 5 PricewaterhouseCoopers

September 30, 2008

Definitions

Accident Year Year in which accident occurred

Paid Loss Payments

Case Reserves Claim adjustor’s best estimate (based on info available at time)

Incurred Loss = Paid Loss + Case Reserves

IBNR Reserves = Ultimate Loss – Incurred Loss

Ultimate Loss Final cost when all claims settled

Slide 6 PricewaterhouseCoopers

September 30, 2008

Summary of Losses & ReservesWSTIP – Automobile LiabilityAs of June 30, 2008

AccidentYear Paid

CaseReserves Incurred

IBNRReserves Ultimate

TotalReserves

2004 2,558 322 2,880 15 2,895 337

2005 1,704 309 2,013 87 2,100 396

2006 1,417 2,002 3,419 281 3,700 2,283

2007 677 689 1,366 709 2,075 1,398

2008 425 1,158 1,583 417 2,000 1,575

Slide 7 PricewaterhouseCoopers

September 30, 2008

Selection of Ultimate LossWSTIP – Automobile LiabilityAs of June 30, 2008

AccidentYear

Paid Method

IncurredMethod

B-F Paid Method

B-F Incurred Method

SelectedUltimate

2004 2,925 2,908 2,796 2,898 2,895

2005 2,222 2,054 2,252 2,060 2,100

2006 2,494 3,767 2,718 3,697 3,700

2007 2,384 1,746 3,020 2,078 2,075

2008 5,606 5,462 3,829 4,199 4,800

Total 15,631 15,937 14,615 14,932 15,570

Slide 8 PricewaterhouseCoopers

September 30, 2008

More Definitions

Triangle Table displaying historical experience by accident year, as it develops over time

Development Increase in amounts over time

Development Factor

Multiple from one period to another

Trend Inflation (medical, benefit level changes)

Slide 9 PricewaterhouseCoopers

September 30, 2008

Paid Loss Development TriangleWSTIP – Automobile LiabilityAs of June 30, 2008

AccidentYear

6 18 30 42 54

2004 265 806 1,791 2,267 2,558

2005 145 634 1,603 1,704

2006 227 967 1,417

2007 222 677

2008 425

Development

Trend

Diagonal

Slide 10 PricewaterhouseCoopers

September 30, 2008

Incurred Loss Development TriangleWSTIP – Automobile LiabilityAs of June 30, 2008

AccidentYear

6 18 30 42 54

2004 900 2,390 2,506 2,885 2,880

2005 680 1,849 2,062 2,013

2006 1,077 3,015 3,419

2007 684 1,366

2008 1,583

Development

Trend

Diagonal

Slide 11 PricewaterhouseCoopers

September 30, 2008

Other Considerations

• Case reserving practices• Closure rates• Retentions

- Per claim loss limits- Aggregate stop-loss

limits• Measure and type of

exposures• Geographical area

Slide 12 PricewaterhouseCoopers

September 30, 2008

Projected Year Losses for Automobile LiabilityApples to Apples

AccidentYear

Miles (000s)

Losses Limited to

$250K

Trend Factors

Loss RateAt 2008Level

2004 51,897 2,158 1.276 53

2005 61,326 1,750 1.216 35

2006 67,961 2,994 1.158 51

2007 70,253 2,065 1.103 32

2008 74,465 4,125 1.050 58

2009 at $250,000 Retention 43

2009 at $1m + 33%QS of $3m xs

$1m56.7

Slide 13 PricewaterhouseCoopers

September 30, 2008

Confidence LevelsMargin for Error

• Reserves are ESTIMATES.• There is variability around these estimates (historical loss

emergence shows general patterns but variation remains on a year to year basis).

• Think of experiment with 1,000 trials – each trial is running off reserves until all claims settled.

• 80% confidence level:- 800 trials result in payments at or below this level- Greater than “expected” reserve need- 200 trials result in payments above this level

Slide 14 PricewaterhouseCoopers

September 30, 2008

Confidence Levels (cont’d)Margin for Error

• Confidence level of program:- Look at (Expected Reserves) + (Equity)- Ability to absorb variation around estimates

• What affects confidence levels?- Size (law of large numbers)- Variability of claim size (big spread vs. small spread)

• Confidence level applied to rates- Similar concept- How confident are you that next year’s losses will come in at or below

the amount budgeted?

Slide 15 PricewaterhouseCoopers

September 30, 2008

What an actuarial report provides?

• Financial reporting issues- people make decisions

based on financial statements

- unpaid claim estimate is critical for an insurance entity

• Budgeting/rate setting• Program integrity• Protection• Sophistication/decisions

Slide 16 PricewaterhouseCoopers

September 30, 2008

Questions to Ask

1. What significant assumptions have you made?

2. Do your reserve projections reconcile to our booked reserves on the financials?

3. How accurate is your estimate?

4. What is the scope of your services and how does that compare to your other clients?

5. What trends are you seeing?

6. How are we doing?