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An Insurance Buying An Insurance Buying QuestionQuestion
An Insurance Buying An Insurance Buying QuestionQuestion
Mary Frances Miller, FCAS, MAAA, FCA, CPCUMary Frances Miller, FCAS, MAAA, FCA, CPCUUniversity of IllinoisUniversity of IllinoisOctober 27, 2005October 27, 2005
What is an Actuary?• An expert in the evaluation and management
of the financial impact of uncertain future events
• A member of a small, highly respected profession that is essential to maintaining a strong economy
• A math techie who also succeeds in business• Someone who really wanted to be an
accountant - but it was too exciting
What’s the value of an uncertain future event?• Start with a certain event
– What’s the value today of a dollar tomorrow?– That’s the magic of compound interest
• Now add uncertainty– What’s the value today of a dollar tomorrow if you’re
dead? That’s life insurance – What’s the value today of a dollar tomorrow if you’re
still alive? That’s a pension!– What’s the value today to replace your car if you
crash it next month? That’s casualty insurance!
What kinds of problems do actuaries work on?
• Insurance– What’s a fair price for auto insurance in Illinois? – If the legislature increases workers compensation benefits, how much will
that cost employers?• Pensions
– How much does an employer need to contribute each year to fund retiree benefits?
– How much is my pension worth?• Private industry
– Should a large company buy insurance or manage risk internally?– How likely is it that a new capital project will yield a return greater than
the cost of capital?• Social questions
– Is Social Security really bust?– How much is the new Medicare drug benefit going to cost?
When should you buy insurance?
• Should you insure your car?– Let’s say you are an exceptionally good driver
• Your accident risk is low• Insurance is expensive
– But – can you afford to replace the car if it does get totaled?
– What if you kill somebody in an accident?
• Should you (or your parents) insure your house?– The probability of your house burning down is very,
very small– But would you take that risk?
A less clear example• You are the Risk Manager for a large
manufacturing company, with 1000’s of employees
• Your employees have on the job injuries– Despite the best safety efforts, accidents happen!– The employer is responsible for the costs under
workers compensation laws– Costs can include lifetime medical costs and lost
wages
• Should you buy insurance, or just budget for the workers comp costs?
Your choices• Average annual losses are $55,000,000• Option 1: Insure it all
– Pay an insurance premium of $65,000,000• Option 2: Only insure for the big claims
– Pay an insurance premium of $18,000,000 to cover claims over $500,000
– Budget $45,000,000 for the other losses• Option 3: Only insure for the really big claims
– Pay an insurance premium of $3,000,000 to cover claims over $1,000,000
– Budget $50,000,000 for the other losses
Average Costs• On average, your costs for the
three options would be:• Full Insurance - $65,000,000• Some Insurance - $63,000,000• Little Insurance - $60,000,000• No Insurance - $55,000,000
What else do you need to know?
• If the losses were totally predictable, you’d just budget the $55,000,000.
• How likely is it that the losses will be more than $55,000,000? – Or $65,000,000?– How much more?
• Can the company afford to cover the difference if the results are bad?– Are there enough assets?– Would you lose your job?
What is the distribution of possible results?
Workers Comp Loss Distribution(No Insurance)
$0
$50
$100
$150
0% 20% 40% 60% 80% 100%
Probability
Ou
tco
me
($m
illi
on
)
“Distributions”• The average is $55,000,000 (we
already knew that)• About 1/2 of the time, losses are
less than $45,000,000• About 10% of the time, losses are
more than $90,000,000
What is the distribution of possible results?
Workers Comp Loss Distribution(No Insurance)
$0
$50
$100
$150
0% 20% 40% 60% 80% 100%
Probability
Ou
tco
me
($m
illi
on
)
Full InsuranceCosts are fixed - at $65,000,000
$20$30$40$50$60$70$80$90
$100
0% 20% 40% 60% 80% 100%
Probability
Ou
tco
me
($m
illi
on
)
Full Insurance vs No Insurance
Full Insurance Eliminates the Risk
$20
$40
$60
$80
$100
0% 20% 40% 60% 80% 100%
Probability
Ou
tco
me
($m
illi
on
)
Insurance No Insurance
Maybe I can take some risk?
Full Insurance vs Insurance for Losses over $500,000
$20
$40
$60
$80
$100
0% 20% 40% 60% 80% 100%
Probability
Out
com
e ($
mill
ion)
Full Insurance Some Insurance
Can I take some risk?
Full Insurance vs Some Insurance
$20
$40
$60
$80
$100
0% 20% 40% 60% 80% 100%
Probability
Out
com
e ($
mill
ion)
Full Insurance Some Insurance
Savings
Losses
Break Even
Can I take some risk?• Save money more often than not• Biggest potential loss is around
$10,000,000• Biggest potential savings is around
$15,000,000• Average savings is $2,000,000• Decision: Go for it
How about some more risk?
Full Insurance vs a Little Insurance
$20
$40
$60
$80
$100
0% 20% 40% 60% 80% 100%
Probability
Out
com
e ($
mill
ion)
Full Insurance Little Insurance
Savings
Losses
Break Even
How about some more risk?
Some Insurance vs a Little Insurance
$20
$40
$60
$80
$100
0% 20% 40% 60% 80% 100%
Probability
Out
com
e ($
mill
ion)
Some Insurance Little Insurance
Savings
Losses
Break Even
Can I take some more risk?
• Cheaper about 85% of the time• Biggest potential additional loss is
around $20,000,000• Biggest potential additional savings is
around $15,000,000• Average savings is $3,000,000• Decision: How much risk can my
company take on?
How do the options compare?
All 3 Options
$20
$40
$60
$80
$100
0% 20% 40% 60% 80% 100%
Probability
Out
com
e ($
mill
ion)
Full Insurance Some Insurance Less Insurance
Where do actuaries work?
• Insurance companies• Consulting firms• Accounting firms• Banks & investment companies• Large corporations• Government• Colleges & Universities
What do actuaries make?
• $40,000 to $50,000 to start• $65,000 to $90,000 with 5 exams and 5
years of experience• $100,000+ for new Associates (7 out of
9 exams)• $125,000+ for new Fellows• $150,000 - $500,000 for experienced
Fellows
DW Simpson & Company, PC
What does it take to become an actuary?
• There are two organizations that qualify actuaries in North America– Society of Actuaries for life, health,
pension & investments actuaries– Casualty Actuarial Society for property &
casualty and health actuaries• Both require demonstration of
mastery of a wide range of knowledge
What does it take to become an actuary?
• Prerequisites (not tested)– Calculus– Linear algebra– Introductory accounting– Basic statistics (SoA only)– Business law (SoA only)
What does it take to become an actuary?
• Required Courses– Econ – 2 university courses or
equivalent– Finance – 2 university courses or
equivalent– Time series & regression – university
courses or equivalent
What does it take to become an actuary?
• Preliminary exams– Probability– Financial Math (interest)– Actuarial Models and Statistics– Actuarial Modeling
What does it take to become an actuary?
• Advanced topics – Actuarial Practice– Law & Regulation– Advanced Finance– Professionalism
How long does it take?• Average “travel time” for FCAS is about
8 years• Similar times for FSA• Exams are currently offered twice a
year– Once a year for some of the upper exams
• Most people are also working full time– But most people also get some time at
work to study
What does it take?• Most employers look for 2 exams
– Or more for actuarial science majors– But not all employers require exams– Varies by geographic area
• Exams and GPA trade off– Less than 3.5 – you may need 2 exams– More than 3.8 – you may find jobs requiring
no exams
How do I get a job as an actuary if I’m from a liberal arts college?
• Get a degree in math or a related field and try to have as high a GPA as you can, especially in math
• Take econ and finance• Pass the first actuarial exam• Try for a summer internship• Be more than just a math nerd
– Hone your writing skills– Take something challenging outside your major
• You can get a listing of actuaries in your area at www.soa.org (click on “members”)
Where do I go for more information?
• www.BeAnActuary.org• www.casact.org (Casualty Actuarial
Society)• www.soa.org (Society of Actuaries)
• [email protected]– I’m happy to help
Questions?Questions?Questions?Questions?
