October 5, 2006Purdue University Reserves James Miles, FSA, MAAA 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, 2006Purdue University A Life Insurance Company Balance Sheet Assets $ 1,672,672,230Reserves $ 1,346,059,480 Other Liabilities $ 216,403,978 Capital & Surplus $ 110,208,772 $ 1,672,672,230

October 5, 2006Purdue 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, 2006Purdue 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, 2006Purdue 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, 2006Purdue 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, 2006Purdue 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, 2006Purdue University Unearned Premium Reserve Month Premium received Unearned premium reserve (upr) Change in unearned premium reserve Premium received minus change in reserve

October 5, 2006Purdue 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, 2006Purdue 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 ,350 0

October 5, 2006Purdue 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 , ,3501,3500

October 5, 2006Purdue 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 , ,3501,40050

October 5, 2006Purdue 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, 2006Purdue University Premium versus Expected Loss

October 5, 2006Purdue University Benefit Reserve The present value of future benefits less the present value of future premium

October 5, 2006Purdue University Benefit Reserve

October 5, 2006Purdue University Expected Loss versus Change in Benefit Reserve

October 5, 2006Purdue University Expected Loss plus Change in Benefit Reserve

October 5, 2006Purdue 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 –Second year is

October 5, 2006Purdue University Benefit Reserve The present value of future benefits less the present value of future premium

October 5, 2006Purdue 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, 2006Purdue 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 ]/ (1.04) + [100,000 x (1 – ) x ] / ((1.04)^2) =

October 5, 2006Purdue 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 ( ) / (1.04) =

October 5, 2006Purdue University Benefit Reserve – = $115 premium was received. $ is reserved for expected benefit payments. If no deaths occur the reported income in year one is $ $ or $8.87.

October 5, 2006Purdue 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, 2006Purdue University Approaches Standards –Formula based –Principles based Level of Detail –Seriatim –Grouped Projection –Deterministic –Stochastic

October 5, 2006Purdue University Expected Loss plus Change in Benefit Reserve

October 5, 2006Purdue University Exercise 1

October 5, 2006Purdue University Exercise 2

October 5, 2006Purdue University Questions