Reserves
James Miles, FSA, MAAA
October 5, 2006
October 5, 2006
Purdue University
What is a reserve?
• Current income set aside, or reserved, for
a future contingent payment.
• An accounting device for matching
revenues of one period with benefits and
expenses in another period.
• An estimate.
October 5, 2006
Purdue University
A Life Insurance Company
Balance Sheet
Assets
$
$
October 5, 2006
1,672,672,230
Reserves
$ 1,346,059,480
Other Liabilities
$
216,403,978
Capital & Surplus
$
110,208,772
1,672,672,230
$ 1,672,672,230
Purdue University
A Life Insurance Company
Income Statement
Premium
$ 275,684,995
Investment Income
$
Benefits
$ 171,380,772
Change in Reserves
$
72,169,080
Expenses
$
93,114,150
Policyholder Dividends
$
24,671,978
Federal Income Tax
$
555,019
Realized Capital Gains
$
(451,226)
Net Income
$
1,328,303
October 5, 2006
Purdue University
87,985,533
Impact
• For an insurance company reserves are
the major item on the balance sheet.
• A small change or error in the reserves
can have a major impact on income.
• Actuaries calculate the reserves!
October 5, 2006
Purdue University
Impact Potential
•
•
•
•
Reserves: $1,346,059,480
Change in reserves: $72,169,080
Net income: $1,328,303
In this example a 0.1% error in the
reserves would wipe out the net income.
• A company
• A career
October 5, 2006
Purdue University
Differing Points of View
• A US life insurance company will calculate
at least three reserve values for every
policy every financial reporting period.
– Statutory reserve using methods specified by
state insurance departments
– GAAP reserve using methods specified by the
Financial Accounting Standards Board (FASB)
– Tax reserve using methods specified in the
Internal Revenue Code
October 5, 2006
Purdue University
A simple case
• Your six-month automobile insurance
premium is $600.
• After you mail in your payment the
insurance company has $600 of cash.
• The company wants to present a pro-rata
portion of the premium in their income
statement each month.
• The company sets up an unearned
premium reserve as a liability.
October 5, 2006
Purdue University
Unearned Premium Reserve
Change in
unearned
premium
reserve
Premium
received
minus
change in
reserve
Month
Premium
received
Unearned
premium
reserve
(upr)
1
600
500
500
100
2
400
-100
100
3
300
-100
100
4
200
-100
100
5
100
-100
100
6
0
-100
100
October 5, 2006
Purdue University
A simple case continued
• During the sixth month of your automobile policy
you are involved in a traffic accident. The
estimated damage to the other car is $1,350.
• As the sixth month comes to a close the other
driver has not settled with your insurance
company.
• Your insurance company wants the claim to be
reported on their income statement in the month
of the accident.
• The company sets up a claim reserve as a
liability.
October 5, 2006
Purdue University
Claim Reserve
Month
Premium
received
minus
change
in upr
Claim
reserve
Change in
claim
reserve
Claim
payments
Claim
payments
plus
change in
claim
reserve
1
100
0
0
0
0
2
100
0
0
0
0
3
100
0
0
0
0
4
100
0
0
0
0
5
100
0
0
0
0
6
100
1,350
1,350
0
1,350
October 5, 2006
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Claim Reserve
Month
Premium
received
minus
change
in upr
Claim
reserve
Change in
claim
reserve
Claim
payments
Claim
payments
plus
change in
claim
reserve
1
100
0
0
0
0
2
100
0
0
0
0
3
100
0
0
0
0
4
100
0
0
0
0
5
100
0
0
0
0
6
100
1,350
1,350
0
1,350
7
0
0
-1,350
1,350
0
October 5, 2006
Purdue University
Claim Reserve
Month
Premium
received
minus
change
in upr
Claim
reserve
Change in
claim
reserve
Claim
payments
Claim
payments
plus
change in
claim
reserve
1
100
0
0
0
0
2
100
0
0
0
0
3
100
0
0
0
0
4
100
0
0
0
0
5
100
0
0
0
0
6
100
1,350
1,350
0
1,350
7
0
0
-1,350
1,400
50
October 5, 2006
Purdue University
A Life Insurance Example
• You purchase a ten-year term life
insurance policy.
• You agree to pay a premium of $170 each
year.
• If you die during the ten year period your
beneficiary will receive $100,000.
• Should the company set up a benefit
reserve as a liability?
October 5, 2006
Purdue University
Premium versus Expected Loss
$340
$170
$0
0
October 5, 2006
1
2
3
4
5
Purdue University
6
7
8
9
10
Benefit Reserve
The present value of future benefits
less
the present value of future premium
October 5, 2006
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Benefit Reserve
$340
$170
$0
October 5, 2006
1
2
3
4
5
Purdue University
6
7
8
9
10
Expected Loss versus Change in
Benefit Reserve
$200
$100
-$100
October 5, 2006
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10
9
8
7
6
5
4
3
2
1
$0
Expected Loss plus Change in
Benefit Reserve
$340
$170
$1
October 5, 2006
2
3
4
5
6
Purdue University
7
8
9
10
Simple Life
•
•
•
•
•
Two-year term life insurance
The death benefit is $100,000
The premium each year is $115
The annual interest rate is 4%
The probability of death in the
– First year is 0.0011
– Second year is 0.0012
October 5, 2006
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Benefit Reserve
The present value of future benefits
less
the present value of future premium
October 5, 2006
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Benefit Reserve Calculation
• Calculate the benefit reserve immediately
after the first premium payment.
• Assume premium is paid at the beginning
of each year.
• Assume death benefits are paid at the end
of each year.
October 5, 2006
Purdue University
Present value of future benefits
The expected value of each benefit payment
after the valuation date is discounted with
interest to the date of valuation.
[100,000 x 0.0011 ]/ (1.04)
+ [100,000 x (1 – 0.0011) x 0.0012] /
((1.04)^2)
= 216.59
October 5, 2006
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Present value of future premium
Each premium after the valuation date is
discounted back to the date of valuation.
In this example, only one premium remains
to be paid.
115 x (1- 0.0011) / (1.04) = 110.46
October 5, 2006
Purdue University
Benefit Reserve
216.59 – 110.46 = 106.13
• $115 premium was received.
• $106.13 is reserved for expected benefit
payments.
• If no deaths occur the reported income in
year one is $115.00 - $106.13 or $8.87.
October 5, 2006
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Assumptions
• Mortality rates
• Interest rates
• Premium is paid at the beginning of each
policy year.
• Death benefits are paid at the end of each
policy year.
October 5, 2006
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Approaches
• Standards
– Formula based
– Principles based
• Level of Detail
– Seriatim
– Grouped
• Projection
– Deterministic
– Stochastic
October 5, 2006
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Expected Loss plus Change in
Benefit Reserve
October 5, 2006
Purdue University
Exercise 1
Calculate the reserve for a three-year tem life insurance policy
immediately after the first premium is paid.
Year
1
2
3
Probability
Interest Rate
of Death
0.0011
0.0012
0.0014
0.04
0.04
0.04
Death
Benefit
Premium
100,000
100,000
100,000
Reserve for two-year term policy was
216.59 - 110.46 = 106.13
October 5, 2006
Purdue University
115
115
115
Exercise 2
Calculate the reserve for a three-year tem life insurance
policy immediately after the first premium is paid.
Year
1
2
3
Probability
of Death
Interest
Rate
0.0011
0.0012
0.0014
0.04
0.04
0.04
Death
Benefit
100,000
100,000
100,000
Premium
200
200
200
Reserve for three-year term policy with premium of
115 was 341.32 - 216.54 = 124.78
October 5, 2006
Purdue University
Questions
October 5, 2006
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