introduction to property & casualty actuarial presenter: matt duke

Introduction to Property & Casualty Actuarial

Presenter: Matt Duke

What does a PC Actuary do?Examine past and present experience to

predict the future.

• Pricing– Rate adequacy / rate filings.

• Reserving– Reserve reviews.

• Predictive Modeling– Generalized linear or additive model.

What is an Actuary?Actuaries are experts in:

• evaluating the likelihood of future events,

• designing creative ways to reduce the likelihood of undesirable events,

• decreasing the impact of undesirable events that do occur.

www.beanactuary.org

Actuarial Vocabulary• Premium = Rate * Exposures

• Exposure (exposure bases)

• Expenses– Loss Adjustment Expense (ALAE & ULAE)– Other Underwriting Expenses

• Commissions & Brokerage• General Expenses (OIE)• Taxes, Licenses, and Fees

– Investment Expenses– Variable vs. Fixed

Actuarial Vocabulary• Losses• Claim Counts

– claims/claimants, open/closed

• Ratios: Loss, Expense, Combined• Frequency = Claim Count / Exposures• Severity = Losses / Claim Count• Pure Premium = Frequency * Severity

= Losses / Exposures

A Dollar of Premium• 60% Loss (&ALAE) Ratio = $0.60

• ULAE = 10% Loss+ALAE = $0.06

• Commissions = 18% prem = $0.18

• Fixed Expenses = 10% prem = $0.10

• Taxes = 5% prem = $0.05

• The rest is left for: Profit! $0.01

• What about investment income?

Investment Income• In my example, for every $1.00 we collect,

we pay out $0.99.

• However, we get to invest the $1.00 for a length of time before we have to pay any losses.

• The extent that we rely on investments for profit varies by line of business.

Written vs. Earned Premium• Written Premium:

All Premium for a policy is assigned to a single year - the year in which the policy was “written” (when coverage became effective.)

• Earned Premium:

Premium is distributed to each year the policy is in effect, based on the proportion of the policy period in each year.

Written vs. Earned Premium

Policy Effective Date July 1, 2001Policy Expiration Date July 1, 2002Total Policy Premium $1,000

2001 2002

Written Premium ??? ???

Earned Premium ??? ???

Written vs. Earned PremiumPolicy Effective Date July 1, 2001Policy Expiration Date July 1, 2002Total Policy Premium $1,000

2001 2002

Written Premium $1,000 $0

Earned Premium ??? ???

2001 2002

Policy Effective PeriodSince the Policy waswritten in 2001, allwritten premium

goes to 2001

Written vs. Earned PremiumPolicy Effective Date July 1, 2001Policy Expiration Date July 1, 2002Total Policy Premium $1,000

2001 2002

Written Premium $1,000 $0

Earned Premium $500 $500

Since 1/2 of the policyperiod is in 2001 and

1/2 is in 2002, theearned premium is

split 50/50%

Written vs. Earned PremiumPolicy Effective Date July 1, 2001Policy Expiration Date July 1, 2002Total Policy Premium $1,000

2001 2002

Written Premium $1,000 $0

Earned Premium $500 $500

2001 2002

Since 1/2 of the policyperiod is in 2001 and

1/2 is in 2002, theearned premium is

split 50/50%

1/2 1/2

Written vs. Earned PremiumPolicy Effective Date October 1, 2001Policy Expiration Date October 1, 2002Total Policy Premium $1,000

2001 2002

Written Premium ???? ????

Earned Premium ???? ????

Written vs. Earned PremiumPolicy Effective Date October 1, 2001Policy Expiration Date October 1, 2002Total Policy Premium $1,000

2001 2002

Written Premium $1,000 $0

Earned Premium ???? ????

Since the Policy waswritten in 2001, allwritten premium

goes to 2001

Written vs. Earned PremiumPolicy Effective Date October 1, 2001Policy Expiration Date October 1, 2002Total Policy Premium $1,000

2001 2002

Written Premium $1,000 $0

Earned Premium $250 $750

2001 2002

Since 1/4 of the policyperiod is in 2001 and

3/4 is in 2002, theearned premium is

split 25/75%

1/4 3/4

Written vs. Earned Premium

• Additional Note:

– It doesn’t matter when the premium is actually collected from the policyholder for either written or earned premium.

Different Types of “Years”• Accident Year (Loss Only)

• Policy Year (Loss or Written Premium)

• Calendar Year (Loss or Written/Earned Premium)

• Report Year (Loss Only)

• Exposure Year (Earned Premium Only)

Different Types of “Years”• Accident Year (Loss Only)

– Groups losses by the year in which the loss event (accident) occurred.

• Policy Year (Loss or Written Premium)

• Calendar Year (Loss or Written/Earned Premium)

• Report Year (Loss Only)

• Exposure Year (Earned Premium Only)

Different Types of “Years”• Accident Year (Loss Only)

• Policy Year (Loss or Written Premium)– Groups losses or premiums by the year in

which the associated policy was effective.

• Calendar Year (Loss or Written/Earned Premium)

• Report Year (Loss Only)

• Exposure Year (Earned Premium Only)

Different Types of “Years”• Accident Year (Loss Only)

• Policy Year (Loss or Written Premium)

• Calendar Year (Loss or Written/Earned Premium)– All transactions (losses paid, reserves posted,

etc.) counted in the year they actually took place.

• Report Year (Loss Only)

• Exposure Year (Earned Premium Only)

Different Types of “Years”• Accident Year (Loss Only)

• Policy Year (Loss or Written Premium)

• Calendar Year (Loss or Written/Earned Premium)

• Report Year (Loss Only)– Groups losses by the year in which we (the

insurance company) were notified of the claim.

• Exposure Year (Earned Premium Only)

Different Types of “Years”• Accident Year (Loss Only)

• Policy Year (Loss or Written Premium)

• Calendar Year (Loss or Written/Earned Premium)

• Report Year (Loss Only)

• Exposure Year (Earned Premium Only)– Similar to calendar year, but premium

adjustments after expiration are reassigned to the year(s) the coverage was effective.

1994 1995 1996 1997 1998 1999

Car Accident Happened

Claim paid in full for $1,000

Accident Reported to Insurer

Different Types of “Years”12 Month Auto Policy Written 7/1/1994

Premium Audit of $100

1994 1995 1996 1997 1998 1999

Car Accident Happened

Claim paid in full for $1,000

Accident Reported to Insurer

Different Types of “Years”

Paid Loss1994 1995 1996 1997 1998 1999

Accident Year ?? ?? ?? ?? ?? ??

Report Year ?? ?? ?? ?? ?? ??

Calendar Year ?? ?? ?? ?? ?? ??

Policy Year ?? ?? ?? ?? ?? ??

12 Month Auto Policy Written 7/1/1994

Premium Audit of $100

1994 1995 1996 1997 1998 1999

Car Accident Happened

Claim paid in full for $1,000

Accident Reported to Insurer

Different Types of “Years”

Paid Loss1994 1995 1996 1997 1998 1999

Accident Year -$ 1,000$ -$ -$ -$ -$

Report Year -$ -$ 1,000$ -$ -$ -$

Calendar Year -$ -$ -$ -$ -$ 1,000$

Policy Year 1,000$ -$ -$ -$ -$ -$

Premium Audit of $100

12 Month Auto Policy Written 7/1/1994

1994 1995 1996 1997 1998 1999

Car Accident Happened

Premium Audit of $100

Claim paid in full for $1,000

Accident Reported to Insurer

Different Types of “Years”

Audit Premium1994 1995 1996 1997 1998 1999

Policy Year ?? ?? ?? ?? ?? ??

Calendar Year ?? ?? ?? ?? ?? ??

Exposure Year ?? BONUS QUESTION ??

12 Month Auto Policy Written 7/1/1994

1994 1995 1996 1997 1998 1999

Car Accident Happened

Premium Audit of $100

Claim paid in full for $1,000

Accident Reported to Insurer

Different Types of “Years”

Audit Premium1994 1995 1996 1997 1998 1999

Policy Year 100$ -$ -$ -$ -$ -$

Calendar Year -$ -$ -$ 100$ -$ -$

Exposure Year 50$ 50$ -$ -$ -$ -$

12 Month Auto Policy Written 7/1/1994

Paid vs. Incurred vs. Outstanding Loss

• Paid Loss = Total $$ actually paid out to policyholders for claims.– Calendar Year 2001 Paid Loss = Total $$ for

claim payments made during 2001, even on accidents from prior years.

– Accident Year 2001 Paid Loss = Total $$ paid for accidents that occurred in 2001, even if the claim was paid after 2001.

Paid vs. Incurred vs. Outstanding Loss

• Outstanding Loss = $$ that the claim department has set aside for future payments on existing claims.– Outstanding Loss = Case Reserves– Case Reserves are estimates of the $$

amount remaining to be paid on individual claims.

Paid vs. Incurred vs. Outstanding Loss

• Case Incurred Loss = Paid + Outstanding– Accident Year 2001 Incurred Loss =

All paid $$ + case reserves on claims from accidents that occurred in 2001.

– Calendar Year 2001 Incurred Loss =

All claim payments made in 2001 + all new case reserves posted in 2001 (including reserve increases/decreases on existing claims).

Loss Development

Loss Development =

The process by which the losses on a defined group of claims changes

over time.

(the defined group of claims could, for instance, be all claims from

accident year 2000)

Loss Development

2 Types of Loss Development

• Paid Loss Development =

Changes over time in total $$ paid to date for a defined group of

claims.

• Incurred Loss Development =

Changes over time in total $$ incurred to date for a defined group of claims.

Loss Development

Why do losses develop?

Loss Development

Why do losses develop?

Examples:

• Unreported claims

• Development on case reserves (under/overestimating the total loss when it is first recorded)

• …other influences

Loss Development

A Hypothetical Workers’ Compensation Claim

Date Event Paid Outst. Incurred1/1/2001 A worker is injured - - - 3/15/2002 The claim is reported to the agent - - - 4/10/2002 The adjuster posts a case reserve

and the claim is recorded in our data systems - 10,000 10,000

6/1/2003 New information leads the adjuster to increase the reserve on the claim - 20,000 20,000

12/1/2003 A partial payment is made 15,000 5,000 20,000 3/1/2004 A second payment is made - claim is

closed 20,000 - 20,000 8/1/2004 New back injuries surface - claim

reopens 20,000 10,000 30,000 1/1/2005 Final payment is made - claim is

closed 30,000 - 30,000

Cumulative

LO

SS

DE

VE

LO

PM

EN

T

Loss Development

• Age = The amount of time that has elapsed since the beginning of an accident or policy period.

E.g. - What is the “age” (in months) of accident year 2000 at 7/1/2001?

Loss Development

• Age = The amount of time that has elapsed since the beginning of an accident or policy period.

E.g. - What is the “age” (in months) of accident year 2000 at 7/1/2001?

Answer: 18 months (From 1/1/2000 to

7/1/2001)

Loss Development

• Ultimate Loss =

The total $$ that will “ultimately” be paid to settle a claim or group of

claims after all development is finished.

It can take as little as a few months to over 50 years for losses to reach “ultimate”.

Loss Development

• IBNR = (“Incurred but not reported”)– Pure IBNR = Losses on claims for accidents

that have occurred that have not yet been reported to the insurer.

– “IBNR” usually includes “everything else” that causes case incurred losses to develop in addition to “Pure IBNR.”

Paid + Outstanding + IBNR = Ultimate

Case Incurred

Loss Development

• IBNR = (“Incurred but not reported”)– Pure IBNR = Losses on claims for accidents

that have occurred that have not yet been reported to the insurer.

– “IBNR” usually includes “everything else” that causes case incurred losses to develop in addition to “Pure IBNR.”

– As opposed to case reserves, IBNR is not assigned to individual claims!

Loss Development

• Loss Development that occurs at late ages is called the “tail” (e.g. - development after > 20 years).

• Short Tailed Lines / Long Tailed Lines

Short tailed lines - Claims settle quickly

Long tailed lines - Claims can take many

years to settle

Which lines are short tailed? Long tailed?

Loss Development

Age (in years)

Los

s $$

5 10 15 20

$10MM

$20MM

$30MM

$40MM

Paid Loss

Case ReservesIBNR

Ultimate Loss

“Tail”

Credibility• Predictive power of a statistic depends on

the volume and homogeneity of the data behind it.

• The more reliable the statistic is, the more weight (credibility) we give it in determining the final estimate.

• Each credibility weighted item needs at least one complement.

• Actuarial Exam C/4 material.

Credibility Example• Which has more credibility?

Loss Ratios (including ALAE) (%) 4-yrState 1997 1998 1999 2000 Avg

NC 40 100 50 90 70CT 70 70 69 71 70

Loss Limiting/LayeringLosses limited at X:

– All losses < or = X are counted at their full value

– All losses > X are “capped” at X

Claims

Los

s $$ Loss Limit

Loss Limiting/LayeringLoss Limited

Claim # Date Total Loss at $10,000

1 1/1/01 8,000 8,000

2 4/16/01 12,000 10,000

3 11/14/01 2,000 2,000

TOTAL 22,000 20,000

Loss Limiting/LayeringLoss Layering = Similar to loss limiting but

also may eliminate losses below a fixed limit, as well as above a higher limit.

Loss Layer

Claims

Los

s $$

Loss Limiting/LayeringLoss in $5,000

Claim # Date Total Loss to $10,000 layer

1 1/1/01 8,500 3,500

2 4/16/01 12,000 5,000

3 11/14/01 500 0

TOTAL 21,000 8,500

Loss Limiting/LayeringWhy would we look at limited/layered

losses?

Loss Limiting/LayeringWhy would we look at limited/layered

losses?

1) Policy provisions limit coverage (deductibles, policy limits, etc.)

2) Smooth volatile experience in high loss layers

• Trend = the changing value of claims over time

• Caused by:– inflation– environment (litigiousness, social attitudes)– tech. advances (new medicines, air bags)– just about anything

Trend

Questions