october 5, 2006purdue university reserves james miles, fsa, maaa october 5, 2006
Post on 21-Dec-2015
217 views
TRANSCRIPT
October 5, 2006 Purdue University
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 $ 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
October 5, 2006 Purdue University
A Life Insurance Company Income Statement
Premium $ 275,684,995
Investment Income $ 87,985,533
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
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
MonthPremium received
Unearned premium reserve
(upr)
Change in unearned premium reserve
Premium received
minus change in
reserve
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 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 1,350 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
$0
$170
$340
0 1 2 3 4 5 6 7 8 9 10
October 5, 2006 Purdue University
Benefit Reserve
The present value of future benefits
less
the present value of future premium
October 5, 2006 Purdue University
Benefit Reserve
$-
$170
$340
0 1 2 3 4 5 6 7 8 9 10
October 5, 2006 Purdue University
Expected Loss versus Change in Benefit Reserve
-$100
$0
$100
$200
October 5, 2006 Purdue University
Expected Loss plus Change in Benefit Reserve
$-
$170
$340
1 2 3 4 5 6 7 8 9 10
October 5, 2006 Purdue University
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 Purdue University
Benefit Reserve
The present value of future benefits
less
the present value of future premium
October 5, 2006 Purdue University
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 Purdue University
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 Purdue University
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 Purdue University
Approaches
• Standards– Formula based– Principles based
• Level of Detail– Seriatim– Grouped
• Projection– Deterministic– Stochastic
October 5, 2006 Purdue University
Expected Loss plus Change in Benefit Reserve
October 5, 2006 Purdue University
Exercise 1
YearProbability
of DeathInterest Rate
Death Benefit
Premium
1 0.0011 0.04 100,000 115 2 0.0012 0.04 100,000 115 3 0.0014 0.04 100,000 115
Reserve for two-year term policy was 216.59 - 110.46 = 106.13
Calculate the reserve for a three-year tem life insurance policyimmediately after the first premium is paid.
October 5, 2006 Purdue University
Exercise 2Calculate the reserve for a three-year tem life insurance
policy immediately after the first premium is paid.
Year Probability
of Death Interest
Rate Death
Benefit Premium
1 0.0011 0.04 100,000 200 2 0.0012 0.04 100,000 200 3 0.0014 0.04 100,000 200
Reserve for three-year term policy with premium of 115 was 341.32 - 216.54 = 124.78
October 5, 2006 Purdue University
Questions