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
Policy Expiration Date
Total Policy Premium
July 1, 2001
July 1, 2002
$1,000
2001
Written Premium
???
2002
???
Earned Premium
???
???
Written vs. Earned Premium
Policy Effective Date
Policy Expiration Date
Total Policy Premium
July 1, 2001
July 1, 2002
$1,000
2001
$1,000
Written Premium
Earned Premium
Since the Policy was
written in 2001, all
written premium
goes to 2001
2002
$0
???
???
Policy Effective Period
2001
2002
Written vs. Earned Premium
Policy Effective Date
Policy Expiration Date
Total Policy Premium
July 1, 2001
July 1, 2002
$1,000
Written Premium
2001
$1,000
2002
$0
Earned Premium
$500
$500
Since 1/2 of the policy
period is in 2001 and
1/2 is in 2002, the
earned premium is
split 50/50%
Written vs. Earned Premium
Policy Effective Date
Policy Expiration Date
Total Policy Premium
July 1, 2001
July 1, 2002
$1,000
Written Premium
2001
$1,000
2002
$0
Earned Premium
$500
$500
Since 1/2 of the policy
period is in 2001 and
1/2 is in 2002, the
earned premium is
split 50/50%
1/2
2001
1/2
2002
Written vs. Earned Premium
Policy Effective Date
October 1, 2001
Policy Expiration Date October 1, 2002
Total Policy Premium
$1,000
Written Premium
2001
????
2002
????
Earned Premium
????
????
Written vs. Earned Premium
Policy Effective Date
October 1, 2001
Policy Expiration Date October 1, 2002
Total Policy Premium
$1,000
Written Premium
Earned Premium
Since the Policy was
written in 2001, all
written premium
goes to 2001
2001
$1,000
????
2002
$0
????
Written vs. Earned Premium
Policy Effective Date
October 1, 2001
Policy Expiration Date October 1, 2002
Total Policy Premium
$1,000
Written Premium
2001
$1,000
2002
$0
Earned Premium
$250
$750
Since 1/4 of the policy
period is in 2001 and
3/4 is in 2002, the
earned premium is
split 25/75%
1/4
2001
3/4
2002
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.
Different Types of “Years”
12 Month
Auto Policy
Written
7/1/1994
1994
Car
Accident
Happened
1995
Accident
Reported
to Insurer
1996
Premium Audit
of $100
1997
Claim paid in
full for $1,000
1998
1999
Different Types of “Years”
12 Month
Auto Policy
Written
7/1/1994
1994
Car
Accident
Happened
1995
Accident
Reported
to Insurer
1996
Premium Audit
of $100
1997
Claim paid in
full for $1,000
1998
1999
Paid Loss
1994
Accident Year
Report Year
Calendar Year
Policy Year
??
??
??
??
1995
??
??
??
??
1996
??
??
??
??
1997
??
??
??
??
1998
??
??
??
??
1999
??
??
??
??
Different Types of “Years”
12 Month
Auto Policy
Written
7/1/1994
1994
Car
Accident
Happened
1995
Accident
Reported
to Insurer
1996
Premium Audit
of $100
1997
Claim paid in
full for $1,000
1998
1999
Paid Loss
1994
Accident Year
Report Year
Calendar Year
Policy Year
$ $ $ $ 1,000
1995
$ 1,000
$ $ $ -
1996
$ $ 1,000
$ $ -
1997
$
$
$
$
-
1998
$
$
$
$
-
1999
$ $ $ 1,000
$ -
Different Types of “Years”
12 Month
Auto Policy
Written
7/1/1994
1994
Car
Accident
Happened
1995
Accident
Reported
to Insurer
1996
Premium Audit
of $100
1997
Claim paid in
full for $1,000
1998
1999
Audit Premium
1994
Policy Year
Calendar Year
Exposure Year
??
??
1995
??
??
??
1996
1997
??
??
??
??
BONUS QUESTION
1998
??
??
??
1999
??
??
Different Types of “Years”
12 Month
Auto Policy
Written
7/1/1994
1994
Car
Accident
Happened
1995
Accident
Reported
to Insurer
Premium Audit
of $100
1996
1997
Claim paid in
full for $1,000
1998
1999
Audit Premium
1994
Policy Year
Calendar Year
Exposure Year
$ 100
$ $
50
1995
$
$
$
50
1996
$
$
$
-
1997
$
$
$
100
-
1998
$
$
$
-
1999
$
$
$
-
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
-
10,000
10,000
15,000
20,000
5,000
20,000
20,000
20,000
-
20,000
20,000
10,000
30,000
30,000
-
30,000
LOSS DEVELOPMENT
Event
A worker is injured
The claim is reported to the agent
The adjuster posts a case reserve
and the claim is recorded in our data
systems
6/1/2003 New information leads the adjuster to
increase the reserve on the claim
12/1/2003 A partial payment is made
3/1/2004 A second payment is made - claim is
closed
8/1/2004 New back injuries surface - claim
reopens
1/1/2005 Final payment is made - claim is
closed
Date
1/1/2001
3/15/2002
4/10/2002
Cumulative
Paid
Outst. Incurred
-
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 $$ that will “ultimately” be
paid to settle a claim or group of claims
after all development is finished.
It can take as little as a few months to over
50 years for losses to reach “ultimate”.
Loss Development
• IBNR = (“Incurred but not reported”)
– Pure IBNR = Losses on claims for accidents
that have occurred that have not yet been
reported to the insurer.
– “IBNR” usually includes “everything else” that
causes case incurred losses to develop in
addition to “Pure IBNR.”
Case Incurred
Paid + Outstanding + IBNR = Ultimate
Loss Development
• IBNR = (“Incurred but not reported”)
– Pure IBNR = Losses on claims for accidents
that have occurred that have not yet been
reported to the insurer.
– “IBNR” usually includes “everything else” that
causes case incurred losses to develop in
addition to “Pure IBNR.”
– As opposed to case reserves, IBNR is not
assigned to individual claims!
Loss Development
• Loss Development that occurs at late ages is
called the “tail” (e.g. - development after > 20
years).
• Short Tailed Lines / Long Tailed Lines
Short tailed lines - Claims settle quickly
Long tailed lines - Claims can take many
years to settle
Which lines are short tailed? Long tailed?
Loss Development
“Tail”
$40MM
Loss $$
$30MM
Ultimate Loss
Paid
Loss
$20MM
$10MM
5
10
Age (in years)
15
20
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) (%)
State
1997
1998
1999
NC
40
100
50
CT
70
70
69
2000
90
71
4-yr
Avg
70
70
Loss Limiting/Layering
Losses limited at X:
Loss $$
– All losses < or = X are counted at their
full value
– All losses > X are “capped” at X
Loss Limit
Claims
Loss Limiting/Layering
Claim #
Date
1
1/1/01
8,000
8,000
2
4/16/01
12,000
10,000
3
11/14/01
2,000
2,000
22,000
20,000
TOTAL
Total Loss
Loss Limited
at $10,000
Loss Limiting/Layering
Loss $$
Loss Layering = Similar to loss limiting but
also may eliminate losses below a fixed
limit, as well as above a higher limit.
Loss Layer
Claims
Loss Limiting/Layering
Claim #
Date
1
1/1/01
8,500
3,500
2
4/16/01
12,000
5,000
3
11/14/01
500
0
21,000
8,500
TOTAL
Total Loss
Loss in $5,000
to $10,000 layer
Loss Limiting/Layering
Why would we look at limited/layered
losses?
Loss Limiting/Layering
Why 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
• Trend = the changing value of claims over
time
• Caused by:
– inflation
– environment (litigiousness, social attitudes)
– tech. advances (new medicines, air bags)
– just about anything
Questions