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THE INSURANCE EXPENSE EXHIBIT AND THE ALLOCATION OF INVESTMENT INCOME - PDF
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1 THE INSURANCE EXPENSE EXHIBIT AND THE ALLOCATION OF INVESTMENT INCOME prepared by Shalom Feldblum (Fifth Edition: May 1997) [The author is indebted to David Eley and Martin Rosenberg for extensive comments on earlier versions of this paper, as well as to Martin Simons, Richard Roth, James Wilson, and Donald Manis for additional reviews. Mr. Eley, of the Texas Insurance Department, is the architect of the investment income allocation procedures in the new Insurance Expense Exhibit. Mr. Simons (Chief Property & Casualty Actuary of the South Carolina Insurance Department) was chairman of the NAIC Insurance Expense Exhibit working group, to which Mr. Rosenberg (former Assistant Insurance Commissioner of New Jersey) and Mr. Roth (Assistant Insurance Commissioner of California) contributed. Mr. Wilson reviewed the first version of this paper for the CAS Forum and greatly enhanced its readability. Mr. Manis reviewed the final version of this paper for publication in the Proceedings of the CAS, and he revised its structure to appeal to a more general actuarial audience. Any errors remaining in this paper are the author s own and should not be ascribed to the regulators and actuaries mentioned above.]
2 THE INSURANCE EXPENSE EXHIBIT AND THE ALLOCATION OF INVESTMENT INCOME Table of Contents Introduction... 1 The Structure of the Insurance Expense Exhibit...,2 IEE Part II: Allocation to Lines of Business Net of Reinsurance... 4 Allocation of Investment Income by Line of Business... 4 Conceptual Level... 5 Component Level... 5 The Allocation... 6 Data-Level.. _.... _ The1992 Revisions... 9 Profit or Loss Allocation Procedures: An Illustration Allocation of Surplus to. Lines of Business Investment Gain Ratio Prepaid ( Acquisition ) Expenses... _ Investment gain on funds attributable to insurance transactions Investment gain attributable to capital and surplus Part III - Allocation to Lines of Direct Business Written Profit or Loss The Measurement of Profitability Prospective versus Retrospective Allocation of Surplus retrospective surplus allocation prospective surplus assumptions Reserve Run-Off versus New Business Insurance Returns and Investment Returns Perspectives on the IEE Procedures Appendix A: The Part II Entries Premiums Dividends Losses and Loss Adjustment Expenses Agents' Balances Underwriting Expenses Appendix B: The Part III Entries References
3 THE INSURANCE EXPENSE EXHIBIT AND THE ALLOCATION OF INVESTMENT INCOME Introduction The statutory Annual Statement enables state regulators to monitor the profitability and financial strength of insurance enterprises. Most revenues and expenditures that relate to particular policies, such as premiums and losses, are shown by line of business. Revenues and expenditures that cannot be directly associated with particular policies, such as investment income and general expenses, are shown only in the aggregate. The primary focus of state regulation is on the ability of the insurance company to meet its obligations to policyholders and claimants. Profitability is an important consideration, since a consistently unprofitable insurer may soon find itself in financial distress. But the focus is on overall profitability, not on the profitability of each business segment. But aggregate information does not suffice for all users. Rate regulators, for instance, must determine if premium rates by line of business are inadequate or excessive. Investors must determine if the capital used to support a given block of business is earning a satisfactory return. The insurer s management mustdetermine which segments of the company are meeting desired profit levels. The Insurance Expense Exhibit (IEE), filed by April 1 as a supplement to the statutory Annual Statement, provides the needed additional information, All revenues and expenditures, whether or not they are associated with particular policies, are allocated to lines of business. Various sets of operating returns are calculated, so that profitability by line of business may be measured. Expense allocation may be complicated, but it is. not conceptually difficult. Investment income allocation, however, particularly when used to measure the total return by line of business, requires subjective assumptions: How should surplus be allocated to lines of business? Should the investment returns on policyholder supplied funds differ from those on capital and surplus funds? How should policyholder supplied funds be defined? These are not idle questions. They have been debated for years by actuaries and regulators, and their answers form the framework of the new investment income allocation procedure in the IEE. This paper reviews this allocation procedure and the resultant measures of profitability by line of business in the NAIC financial statements. Casualty actuaries are often asked to complete the investment income columns in their The Insurance Expense Exhibit and the Allocation of Investment Income Page 7
4 companies Insurance Expense Exhibits.1 In addition, they are often asked to evaluate the IEE profitability measures: to tell their managements whether the operating returns shown in the IEE accurately reflect the performance of each line of business. Careful study of the investment income allocation procedures in the IEE is needed to respond to such questions. The Structure of the Insurance Expense Exhibit The structure of the IEE is as follows: l Part I - Allocation to Expense Groups l Part II - Allocation to Lines of Business Net of Reinsurance l Part III - Allocation to Lines of Direct Business Written Part I of the IEE, like Part 4 of the Underwriting and Investment Exhibit, divides expenses along two dimensions: a Expense classification, such as advertising, rent, salaries, or equipment, and b. Expensegroups, which are loss adjustment expenses, other underwriting expenses, and investment expenses. The IEE has a more refined division of other underwriting expenses into l Acquisition, field supervision and collection expenses l General expenses l Taxes, licenses and fees Part II of the IEE shows the allocation of all revenues and expenditures to lines of business, where the figures are net of reinsurance. Part III shows a similar allocation for direct business, except that investment income is not included in Part III. In Parts II and Ill, lines of business are shown along the vertical axis (i.e., they are rows), and revenue and expenditure categories are shown along the horizontal axis (i.e., they are columns). A decimal point in an IEE line of business indicates that a finer breakdown is being used than is shown in the Underwriting and Investment Exhibit. Automobile liability provides a good illustration. The pre-1995 Underwriting and Investment Exhibit in the Annual Statement 1 The statutory procedures for completing the IEE are documented in the IVAlC Proceedings, 1992, Volume IA, pages , Summary of Changes to the Proposal of the Insurance Expense Exhibit Working Group to the Blanks (EX4) Task Force, as well as in the NAIC instructions to the IEE. The Insurance Expense Exhibit and the Allocation of Investment Income Page 2
5 showed a single Line 19: Auto liability. 2 The IEE shows Lines 19.1, 19.2: Private Passenger Auto Liability and Lines 19.3, 19.4: Commercial Auto Liability. The exhibits of premiums and losses by state (page 15 of the Annual Statement) show all four components separately: Line 19.1: Private passenger auto no-fault (personal injury protection) Line 19.2: Other private passenger auto liability Line 19.3: Commercial auto no-fault (personal injury protection) Line 19.4: Other commercial auto liability Personal and commercial auto often have different expense characteristics (e.g., agents contract- may provide a higher commission rate on personal auto), so this subdivision is appropriate for the IEE. This paper concentrates on the investment income allocation procedures used for completing Part II of the IEE, columns 18 and 20. There are only passing references to Parts I and III of the IEE; in particular, there is no discussion of the expense classifications in Part I of the IEE. Moreover, the first 16 columns of Part II of the IEE, which contain the data needed for the investment income allocation procedure, are described in Appendix A, not in the body of the paper. The text of the paper deals with the computations needed to determine the entries for columns 18 and 20, and it provides an arithmetic example,of the procedure. 2 In 1995, automobile liability was split in the Underwriting and Expense Exhibit as well into personal and commercial auto liability, following the IEE split. In the Underwriting and Investment Exhibit, 19.1 is now private passenger auto liability and 19.2 is now commercial auto liability. The Insurance Expense Exhibit and the Allocation of investment Income Page 3
6 IEE Part II: Allocation to Lines of Business Net of Reinsurance The purpose of Part II is to allocate elements of total profit (or loss) net of reinsurance to lines of business. - NAIC Proceedings, 1992, Volume IA, pages 339 The completion procedures for the first 16 columns of Part II of the Insurance Expense Exhibit are documented in detail in Appendix A. Readers who are preparing to complete an actual IEE will find the information in Appendix A to be essential. The focus of this paper is on the allocation of investment income in the IEE, so we begin with column 17 of Part II. Allocation of Investment Income by Line of Business The allocation of investment income by line of business in the 1992 and subsequent Insurance Expense Exhibits differs from the corresponding allocation in previous years. However, the allocation in the IEE is now the same as the allocation in the NAIC Profitability by Line by State reports. Before 1992, the allocation procedure was documented in the footnotes to the IEE. Now the allocation procedure appears in the instructions to the IEE. The allocation procedure is also described in the Proceedings of the NAG, 1992, Volume IA, pages s This paper examines the allocation procedure on three levels: l Conceptual: the philosophy underlying the allocation procedure. l Components: the insurance elements comprising the allocation formula, as well as the adjustments made to several of these elements. l Data: the data sources for the elements of the allocation formula (primarily the previous columns of Part II of the IEE). The NAIC instructions to the IEE show the arithmetic formula, with little or no explanation of the allocation philosophy or the rationale for the adjustments. This paper describes the concepts and formulas of the allocation procedure, and it provides a detailed example to assist the reader in understanding the method. 3 The allocation procedure is strictly prescribed by the NAIC: Although various methodologies might result in reasonable allocations of investment income to lines of business, the following formulae for allocating investment gain must be used in completing the allocation for Column 18, Investment Gain on Funds Attributable to Insurance Transactions and the allocation for Column 20, Investment Gain Attributable to Capital and Surplus (page 339). The Insurance Expense Exhibit and the Allocation of Investment Income Page 4
7 Conceptual Level The allocation of investment income to line of business in the IEE rests upon three principles: 0 Investment income is allocated to each line of business in proportion to the investable funds associated with each line of business. Investable funds consist of (i) funds attributable to insurance transactions and (ii) funds attributable to capital and surplus. 0 Funds attributable to insurance transactions. are loss reserves plus unearned premium reserves minus prepaid expenses and minus uncollected premiums. jthe adjustments to the unearned premium reserves for prepaid expenses and uncollected premiums occur in some.parts of the allocation procedure, not in all parts (see below).] 0 Capital and surplus are allocated to lines of business in proportion to total reserves plus earned premium for the year. Component Level The allocation procedure uses the following principles to derive the items in the conceptual level :.i 1 _ For balance sheet items, the averages of the current year-end values and the prior year-end values are used. These balance sheet items are l Net loss and loss adjustment expense reserves l Net unearned premium reserves l Net agents balances l Policyholders surplus The.allocation procedure refers to these as mean surplus, mean net agents balances, and so forth. [For example, mean surplus is the average of policyholders surplus at December 31 of the current year and policyholders surplus at December 31 of the prior year.] 2. Prepaid expenses, or acquisition expenses, are Commission and brokerage expenses incurred + Taxes, licenses, and fees incurred + Other acquisition, field supervision, and collection expenses incurred + One half (r/2) of general expenses incurred. 3. Net investment gain or loss is composed of net investment income earned and net realized capital gains or losses. It does nut include unrealized capital gains or losses. The Insurance Expense Exhibit and the Allocation of Investment Income Page 5
8 The Allocation The allocation procedure works as follows: A. Allocate the company s mean surplus to line of business in proportion to Mean net loss and loss adjustment expense reserves + Mean net unearned premium reserves + Earned premium for the year Unearned premium reserves are not adjusted for agents balances or for prepaid expenses, in this part of the allocation procedure. The unearned premium reserves represent the amount the insurer is required to hold, not the amount of investable funds derived from premiums.?cis B. Determine the company s overall investment gain ratio as Net investment gain + (Mean net loss and loss adjustment expense reserves + Mean net unearned premium reserves - Mean net agents balances + Mean policyholders surplus). Net investment gain (or loss) is composed of net investment income earned and net realized capital gains or losses. It does not include unrealized capital gains or losses. Agents balances are a component of written premium and therefore of the unearned premium reserve. But agents balances are not an investable asset, so they are subtracted from the unearned premium reserve in determining the investment gain ratio. In statutory accounting, prepaid expenses are an expenditure, not an asset. Prepaid expenses reduce policyholders surplus, so they are already subtracted from the investable assets in the denominator of the investment gain ratio. [In contrast, the agents balances considered here are admitted assets, so they do not reduce policyholders surplus.41 In this part of the formula, the reserves, agents balances, and surplus are for all lines combined. C. For each line of business, the investment gain on funds attributable to insurance transactions (column 18) is the company s investment gain ratio times the funds attributable to insurance transactions for that line of business. This latter item is determined as Funds attributable to insurance transactions = 4 Non-admitted agents balances do not appear on the balance sheet, since they are already deducted from policyholders surplus. The Insurance Expense Exhibit and the Allocation of investment Income Page 6
9 Mean net loss and loss adjustment expense reserves + Mean net unearned premium reserves x [I - (prepaid expenses + written premiums)] - Mean net agents balances. Prepaid expense are funded from surplus, not from insurance transactions, since the full (gross) unearned premium reserve must be held as a liability. The ratio of prepaid expenses to written premiums shows the percentage of each premium dollar that must be funded from surplus. The mean net unearned premium reserves are therefore multiplied by the complement of this ratio. D. For each line of business, the investment attributable to capital and surplus (column 20) is the total investment gain for that line of business minus the investment gain on funds attributable to insurance transactions. The total investment gain for that line of business is the company s investment gain ratio times the investable funds associated with that line of business. The investable funds associated with that line of business equal that line s Mean net loss and.loss adjustment expense reserves + Mean net unearned premium reserves - Mean net agents balances + Allocated policyholders surplus. ; Since policyholders surplus is already reduced by prepaid expenses in statutory accounting, there is no need to reduce the unearned premium reserves by these expenses. This completes the allocation procedure for investment income. The section below shows the data sources for each element of the procedure. Data Level All the data elements for the allocation of investment income to line of business are taken from the Annual Statement or from prior columns of the IEE. The following abbreviations clarify the formulas+ LRlob Mean net loss and loss adjustment expense reserves by line of business Rot Mean net loss and loss adjustment expense reserves for all lines combined UEPRi,b Mean net unearned premium reserves by lines of business UEPRtot Mean net unearned premium reserves for all lines combined P&b Net prepaid expenses, or net acquisition expenses, by line of business Abob Mean net agents balances by line of business Ahot Mean net agents balances for all lines combined WPlob Net written premium by line of business for the current year 5 The NAIC instructions use different abbreviations: Al for LRk,b, A2 for LRrot, Bl for UEPRr,b, and so forth, through L for IGe and M for IGcs. Actuaries familiar with ancient BASIC variable naming conventions should have no difficulty with the NAIC abbreviations. The insurance Expense Exhibit and the Allocation of Investment Income Page 7
10 Ehob EPtot PWot H%b PHSrat IG IGR IGit 6s Net earned premium by line of business for the current year Net earned premium for all lines combined for the current year Mean policyholders surplus for all lines combined Policyholders surplus allocated to the line of business Policyholder surplus ratio Net investment gain Investment gain ratio Investment gain by line of business on funds attributable to insurance transactions Investment gain by line of business attributable to capital and surplus 1. Net loss and loss adjustment expense reserves are taken from page 11 of the Annual Statement, Underwriting and Investment Exhibit, Part 3A, column 5, net losses unpaid excluding loss adjustment expenses, plus column 6, unpaid loss adjustment expenses. The mean value is determined by averaging the amounts in the current and prior Annual Statements. 2. Net unearned premium reserves are taken from page 9 of the Annual Statement, Underwriting and Investment Exhibit, Part 2A, column 5, total reserve for unearned premium. The mean value is determined by averaging the amounts in the current and prior Annual Statements. 3. Net prepaid expenses are determined from the prior columns in Part II of the IEE, as Net prepaid expenses = (column 12 + column 13 + column 14 + t/2 column 15) 4. Net agents balances for all lines combined is taken from page 2 of the Annual Statement, line 10.1 plus line Agents balances by line of business are taken from column 11 of Part II of the IEE: The mean values are determined by averaging the amounts in the current and prior Annual Statements and Insurance Expense Exhibits. 5. Written and earned premium: Net written premium is taken from column 1 of Part II of the IEE, and net earned premium is taken from column Mean policyholders surplus for all lines combined is the average of columns 1 and 2 on line 26 of page 3 of the Annual Statement. 7. The policyholders surplus ratio is defined as the ratio of policyholders surplus to the sum of loss reserves, unearned premium reserves, and annual earned premium, or PHSrat = PHSt,t + (LRtot + UEPRtot + EPr,r) 8. The policyholders surplus allocated to each line of business is determined as the product of the policyholders surplus ratio and the sum of loss reserves, unearned premium reserves, and annual earned premium for that line of business, or The Insurance Expense Exhibit and the Allocation of Investment Income Page 8
11 Pf-tsl,b = PHSrat X (LRf,b + UEPRr,b + EP& 9. The net investment gain is taken from the Annual Statement, page 4, Statement of Income, line 9A, net investment gain or loss. Line 9A of page 4 is the sum of line 8 ( net investment income earned, or interest, dividends, and rent) and line 9 ( realized capital gains or losses ). Unrealized capital gains and losses, which appear on line 19 of page 4, are not included in line 9A. 70. The investment gain ratio is defined as the investment gain divided by investable assets, or IGR = IG + (LRtot + UEPRtot + PHStot - ABtot).e 11. The investment gain by line of business on.funds attributable to insurance transactions is determined as IGit = IGR X (LR lob + UEPRlob.tl - (PPElob + WPlob)l - ABlob) This is the entry for column The investment gain by line of business attributable to capital and surplus is determined as lgcs = [IGR X (LRrob + UEPRrob + PHSrob - ABlob)] - lgit This is the entry for column 20. The 1992 Revisions The major differences introduced in the 1992 IEE- regarding the allocation of investment income are as follows: l Before 1992, there was a separate capital and surplus account, similar to a line of business. The investment income attributable to capital and surplus was not allocated to 6 In theory, one might make other adjustments to investable assets, such as for bills receivable, taken for premiums (line 11 of page 2 of the Annual Statement). Most of these other adjustments are minor, and would not materially affect the allocation procedures. David Eley has pointed out to me that the investment gain ratio is applied to the investable assets by line of business. It would be extremely difficult, if at all practical, to make these adjustments by line of business. To properly allocate investment income, the investable assets by line of business should sum to the total investable assets used in the allocation procedure. Moreover, although the investment gain ratio without these adjustments may be slightly inaccurate in any one year, over a period of several years the ratio works well. Mr. Eley is correct. These practical considerations overwhelm any theoretical advantages from additional adjustments. The Insurance Expense Exhibit and the Allocation of investment Income Page 9
12 lines of business. In 1992, the separate capital and surplus account was removed, and the investment income attributable to capital and surplus is allocated to lines of business. l Before 1992, the investment income allocated to lines of business reflected primarily bond returns, not common stock dividends or capital gains. 7 Thus, the investment yield on funds attributable to capital and surplus differed from the investment yield on funds attributable to insurance transactions. In 1992, stock dividends and realized capital gains are treated as other investment income, so the difference in investment yields has been eliminated.8 7 In the 1991 IEE, the adjusted investment income that is allocated to lines of business is defined as Annual Statement, page 6, part 1, column 8, lines (see step B of footnote D in the 1991 IEE). Part 1 of page 6 shows interest, dividends, and real estate income, not capital gains. Column 8 shows the amount earned during the year. Line IO shows the total (gross) investment income. Column 11 shows the investment expenses incurred, and column 12 shows the real estate depreciation. Lines 2.1, 2.11, 2.2, and 2.21 show dividends on (i) unaffiliated preferred stock, (ii) affiliated preferred stock, (iii) unaffiliated common stock, and (iv) affiliated common stock, respectively. The investable assets to which the adjusted investment income was compared also excluded common stocks. The investment income ratio used for the allocation of investment income to line of business therefore reflected primarily bond returns, not stock returns. Step J of footnote D to the 1991 IEE defines investment income attributable to the capital and surplus accounts as Annual Statement page 4, line 8, less the investment income allocated to lines of business. Page 4, line 8, equals page 6, column 8, lines Line 13 is aggregate write-ins for deductions from investment income, and it is usually a small amount. A major portion of net investment income attributed to the capital and surplus account reflected the difference between stock and bond returns. Step K of footnote D to the 1991 IEE says Realized capital gains attributable to capital and surplus accounts = Annual Statement, page 4, line 9. Page 4, line 9, comprises all realized capital gains, as shown on page 6, part IA, line 11. This separation of stock dividends and realized capital gains from other investment income was no longer considered appropriate. In 1992, the division between investment income attributable to insurance transactions and that attributable to capital and surplus relates to the earnings base (Le., the amount of funds in each section), not to the type of investments associated with each section. 8 Cf. the NAIC Proceedings, 1991 Volume IIA, Insurance Expense Exhibit Working Group of the Blanks (EX4) Task Force, March 22, 1991, Attachment Four-B, page 450: The separate treatment of realized capital gains was eliminated with the effect of relating the same rate of return to capital and surplus that is related to insurance transaction funds. Compare also the letter from David F. Eley to Dan Atkinson of February 22, 1991, Formula for Allocating Investment Income to Lines of Business in the NAlC Proceedings, 1991 Volume IIA, page 454: A second change is that all investment gain, including realized capital gain or loss, The Insurance Expense Exhibit and the Allocation of Investment Income Page 10
13 l More funds are attributable to insurance transactions in the 1992 and subsequent Insurance Expense Exhibits than were attributed to policyholders in the pre-1992 IEE. Profit or Loss Part II of the IEE shows three columns of profit or loss: l Column 17: Pre-tax profit or loss excluding all investment gain l Column 19: Profit or loss excluding investment gain attributable to capital and surplus l Column 21: Total profit or loss All three columns are pre-federal income tax, though the pre-tax caption appears only in column 17. The profit or loss equals revenues minus expenditures, on an accrual (not paid).basis. Thus l Column 1, premium written, is on a paid basis. Column 2, premium earned, is on an accrual basis. Earned premium (column 2) is used.in the profit and loss calculation, not written premium (column 1). i, l Columns 7 through 10, the loss reserves, loss adjustment expense reserves, and unearned premium. reserves, are liabilities, not expenditures. Column 11, agents balances, is an asset, not a revenue item. Columns 7 through 11 do not enter the profit or loss calculation. l Column 16, other income is a revenue item. Columns 3 through 6 (policy benefits, or losses incurred, loss adjustment expenses incurred, and policyholder dividends) and 12 through 15 (expenses) are expenditure items, so they enter the profit or loss calculation. The formula for column 17 is therefore column 17 = columns Investment income is a revenue item. Thus column 19 equals column 17 + column 18, and column 21 equals column 19 + column 20. This completes Part II of the IEE. Allocation Procedures: An Illustration The discussion above is abstract; an illustration should clarify the procedures. The example below reviews the various steps in the allocation of investment income: is allocated equally. There is no longer any disparity between the rate of return earned on funds derived from the insurance transaction and the rate of return earned on capital and surplus. The Insurance Expense Exhibit and the Allocation of Investment income Page 11
14 l Allocating surplus to lines of business l Calculating the investment gain ratio l Calculating the prepaid ( acquisition ) expense ratio. Determining the investment gain on funds attributable to insurance transactions. Determining the investment gain attributable to capital and surplus In the illustration, we are completing the investment gain columns in Part II of the 1996 Insurance Expense Exhibit, using data from the 1995 and 1996 statutory financial statements. The IEE is for a commercial lines insurer that writes only two lines of business: workers compensation and other liability. All amounts in the illustration are in millions of dollars. Allocation of Surplus to Lines of Business We must first allocate policyholders surplus to lines of business. Line 26 of page 3 of the 1996 Annual Statement shows statutory surplus of $500 million at December 31, 1995, and of $700 million at December 31, The earned premiums, unpaid losses, unpaid allocated loss adjustment expenses, unpaid unallocated loss adjustment expenses, and unearned premium reserves for workers compensation and other liability shown in the table below are taken from the 1995 and 1996 Insurance Expense Exhibits, columns 2, 7, 8, 9, and IO, for rows 16 and 17. Alternatively, these figures may be taken from the Underwriting and Investment Exhibits in the 1995 and 1996 Annual Statements: earned premiums from Part 2 (page 7), column 4; unearned premium reserves from Part 2A (page 8), column 5; unpaid losses from Part 3A (page IO), column 5; and unpaid loss adjustment expenses from Part 3A (page 111, column 6. (Figures in millions of dollars) Workers Compensation Other Liability ~. * ,Earned premium, year ending 12/31/g gloss and LAE reserves, 12/31/9-1,400 1, Unearned premium reserves, 12/31/g The IEE investment income allocation procedure requires that we allocate the company s me&n surplus to line of business in proportion to Mean net loss and loss adjustment expense reserves + Mean net unearned premium reserves + Earned premium for the year. In this allocation, there is no adjustment of the unearned premium reserves for agents balances or for prepaid expenses. Mean surplus is the average of the December 31, 1995, surplus and the December 31, 1996, surplus, or ($500 million + $700 million) + 2 = $600 million. Mean surplus is used because investment income is earned over the course of the year. The Insurance Expense Exhibit and the Allocation of Investment Income Page 12
15 Mean reserves are used, both for loss and loss adjustment expenses and for unearned premium. The 1996 earned premium is used, not the average 1995 and 1996 earned premiums. l For workers compensation, the sum of mean reserves and annual earned premium is [(I, ,700) [( ) f = $2,100 million.. For other liability, the sum of mean reserves and annual earned premium is [( ) f 21 + [(IO ) f = $900 million. l The mean surplus allocated to workers compensation is (600) x [2,100 + (2, ) ] = $420 million. l The mean surplus allocated to-other liability is / i (600) x [900 + (2, ) ] = $180 million. Investment Gain Ratio We proceed,to determine the investment gain ratio. The workers.compensation and other liability figures are reproduced below. (Figures in millions of dollars) Workers Compensation Other Liability Agents balances, 12/31/ Earned premium, year ending 12/31/ Loss and LAE reserves, 12/31/g- 1,400 1, Unearned premium reserves, 12/31/g In addition, we take the following investment income and capital gains figures from the 1995 and 1996 Annual Statements, from the following exhibits: l Net investment income: Page 4, line 8 = Underwriting and Investment Exhibit, page 6, Part 1, item 15. l Realized capital gains: Page 4, line 9 = Underwriting and Investment Exhibit, page 6, Part IA, item 11.. Unrealized capital gains: Page 4, line 19 = Underwriting and Investment Exhibit, page The Insurance Expense Exhibit and the Allocation of Investment income Page 13
16 6, Part IA, item 12. Policyholders surplus was $500 million at December 31, 1995, and $700 million at December 31, 1996, as shown on page 3, line 26. Investment Income and Policyholders Surplus ($000,000) Net investment income, year ending 12/31/9- Realized capital gains, year ending 12/31/g- Unrealized capital gains, year ending 12/31/g- Policyholders surplus, year ending 12/31/g The company s overall investment gain ratio is defined as Net investment gain + (Mean net loss and loss adjustment expense reserves + Mean net unearned premium reserves - Mean net agents balances + Mean policyholders surplus) Net investment gain for 1996 is used, not the average of the.i 995 and 1996 values. It consists of net investment income earned (line 8 of page 4) and net realized capital gains or losses (line 9 of page 4). It does not include unrealized capital gains or losses (line 19 of page 4). In this example, net investment gain, or line 9A of page 4 of the Annual Statement, equals $250 million + $50 million = $300 million. The reserves, agents balances, and surplus figures are needed for the company as a whole, not for each line of business. In this example, the figures are l Mean net loss and loss adjustment expense reserves are ($1,400 M + $1,700 M + $600 M + $600 M) + 2 = $2,150 million l Mean net unearned premium reserves are ($75 M + $125 M + $100 M + $100 M ) + 2 = $200 million l Mean net agents balances are ($35 M + $45 M + $10 M + $10 M) + 2 = $50 million The Insurance Expense Exhibit and the Allocation of Investment income Page 14
17 l Mean policyholders surplus is ($500 M + $700 M) + 2 = $600 million The investment gain ratio is [$300 M + ($2,150 M + $200 M - $50 M + $600 M) ] = 10.34% Prepaid ( Acquisition ) Expenses. We now proceed to determine the prepaid expenses by line of business. We take the following data from the 1995 and 1996 Insurance Expense Exhibits (figures in millions of dollars): II (Figures in millions of dollars) II : Workers Other Compensation Liability Written premium, year ending 12/31/g Commission & brokerage, year ending 12/31/g- 40,' 50 Taxes, licenses & fees, year ending 12/31/g- 8 IO Other acquisition expenses, year ending 12/31/g General expenses, vear endina 12/31/g L 6 5 5' Prepaid expenses, or acquisition expenses, are defined as Commission and brokerage expenses incurred + Taxes, licenses, and fees incurred + Other acquisition, field supervision, and collection expenses incurred c One half (t/2) of general expenses incurred. For prepaid expenses, we use the 1996 figures, not the average of the 1995 and 1996 figures. l For workers compensation, prepaid expenses are [$50 M + $10 M + $10 M + (0.5)($60 M) ] = $100 million l For other liability, prepaid expenses are [$30 M + $5 M + $5 M = (O-5)($20) ] = $50 million The prepaid expense ratio is prepaid expenses divided by written premium, not earned premium (see the calculations below). Acquisition expenses, underwriting expenses, and premium taxes all relate to written premiums (or written exposures), not to earned premiums. The Insurance Expense Exhibit and the Allocation of Investment Income Page 15
18 Investment gain on funds attributable. to insurance transactions Column 18 of the Insurance Expense Exhibit asks for the investment gain on funds attributable to insurance transactions. We now determine the appropriate column 18 entries for workers compensation and other liability, using the accounting information from the company s 1995 and 1996 financial statements, as shown above. For each line of business, the investment gain on funds attributable to insurance transactions is the company s investment gain ratio times the funds attributable to insurance transactions for that line of business. In this example, the investment gain ratio is 10.34%, as determined above. The funds attributable to insurance transactions are defined as Funds attributable to insurance transactions = Mean net loss and loss adjustment expense reserves + Mean net unearned premium reserves x [I - (prepaid expenses + written premiums)] - Mean net agents balances Prepaid expenses were determined above as $100 million for workers compensation and $50 million for other liability. The 1996 written premium is $500 million for workers compensation and $200 million for other liability, so the factor of 1 - (prepaid expenses + written premiums) is 80% for workers compensation and 75% for other liability. The mean values for reserves and agents balances were determined above. the funds attributable to insurance transactions are as follows: Using these values, l For workers compensation: [(1,400+1,700) {[(75+125) + 21 x 80%) - [(35+45) + 21 = $1,590 t-dion. l For other liability: [( ) ([(IO ) + 21 x 75%) - [(IO + 10) + 21 = $665 million. The investment gain on funds attributable to insurance transactions is therefore 10.34% x $1,590 million = $165 million for workers compensation and 10.34% x $665 million = $69 million for other liability. Investment gain attributable to capital and surplus Column 20 of the Insurance Expense Exhibit asks for the investment gain attributable to capital and surplus. We now determine the appropriate column 20 entries for workers compensation and other liability, using the accounting information from the company s 1995 The insurance Expense Exhibit and the Allocation of Investment Income Page 16
19 ,- and 1996 financial statements, as shown above. For each line of business, the investment gain attributable to capital and surplus (column 20) is the total investment gain for that line of business minus the investment gain on funds attributable to insurance transactions. l The investment gain on funds attributable to insurance transactions for workers compensation and other liability were determined above. l The total investment gain for the line of business is the company s investment gain ratio times the investable funds associated with the line of business. The investable funds associated with the line of business equal the line s Mean net loss and loss adjustment expense reserves + Mean net unearned premium reserves - Mean net agents balances + Allocated policyholders surplus. Note carefully the distinction between investable funds attributable to insurance operations and investable funds associated with the line of business. The former has an adjustment for prepaid ( acquisition ) expenses. The latter includes policyholders surplus allocated to lines of business. As noted above, prepaid expenses are already deducted from surplus. So if surplus enters the formula, there is no deduction of prepaid expenses from the unearned premium reserves. The mean values for reserves and agents balances were determined above, as was the allocation of policyholders surplus to lines of business. Using these values, the investable funds associated with the lines of business are as follo&: l For workers compensation: [(I,400+1,700) [(75+125) [(35+45) = $2,030 million. The total investment gain = 10.34% of $2,030 million = $210 million. The investment gain attributable to funds from insurance operations is $165 million, as determined above, so the investment gain attributable to capital and surplus is $45 million. l For other liability: [( ) [(loo + I 00) [(IO + lo) = $870 million. The total investment gain = 10.34% of $890 million = $90 million. The investment gain attributable to funds from insurance operations is $69 million, as determined above, so the investment gain attributable to capital and surplus is $21 million. The Insurance Expense Exhibit and the Allocation of Investment income Page 77
20 Part Ill - Allocation to Lines of Direct Business Written The purpose of Part II! is to allocate elements of profit (or loss) on a direct basis to lines of business. Part 111 simulates what the results were without reflecting the effect of reinsurance. - NAlC Proceedings, 1992, Volume IA, pages 340 Part Ill, Allocation to Lines of Direct Business Written, is similar to Part II, except that Part III shows direct experience whereas Part II shows net experience. Two other differences result from this: l Because most Annual Statement exhibits show net experience, not direct experience, there are few direct cross-checks from Part III of the IEE to the Annual Statement. l Because investment income relates to net experience, not to direct experience, there are no investment income columns in Part III of the IEE. Profit or., Loss i Part III of the.iee shows only underwriting gain or loss, in column 17: Pre-tax profit or loss excluding a// investment gain. Column 17 of Part III is calculated in the same fashion as column 17 of Part II: revenues minus expenditures, on an accrual basis. Part III has no allocation of investment income. Investment income is earned on assets actually held by the company: that is, on assets net of reinsurance. Investment income on direct business is a theoretical amount. In 1991, the IEE Working Group of the NAIC debated whether to show a theoretical investment income figure for direct business. In April 1991, the Insurance Expense Exhibit Working Group of the Blanks (EX4) Task Force voted to show such a figure in Part III: The working group then discussed the proposal to calculate investment income on a direct basis. Members of the advisory committee expressed concerns that the proposal creates assumptions on what would exist on a direct basis; that the numbers go beyond the financial accounting data historically included in annual statement data; that companies would be projecting income that they do not have. Members of the working group indicated that it would assist a state in seeing the impact of the state s premium dollar without excluding the reinsured portion of the premium dollar. Further, the information would be qualified using italics and footnotes in order to caution users of the nature of the data. It was moved and second that investment income on funds attributable to insurance transactions be calculated on a direct basis using italics to qualify the data. Voted to adopt with California opposed. (NAB2 Proceedings, 1991 Volume IIA, Insurance Expense Exhibit Working Group of the Blanks (EX4) Task Force, April 13, 1991, Attachment Four-A, page 448). The insurance Expense Exhibit and the Allocation of Investment income Page 18
The Financial Modeling of Property/Casualty Insurance Companies by Douglas M. Hodes Tony Neghaiwi, FCAS J. David Cummins Richard Phillips Sholom
The Financial Modeling of Property/Casualty Insurance Companies by Douglas M. Hodes Tony Neghaiwi, FCAS J. David Cummins Richard Phillips Sholom Feldblum, FCAS, ASA THE FINANCIAL MODELING OF PROPERTY-CASUALTY