Fair value of insurance liabilities: unit linked / variable business

Transcription

1 Fair value of insurance liabilities: unit linked / variable business The fair value treatment of unit linked / variable business differs from that of the traditional policies; below a description of a possible approach with regard to this type of business. The underlying idea is that premium payments and interest earned are immediately passed on to the policyholder accounts. Therefore, these payments as well as the corresponding increase in reserves are excluded from the P&L. The same goes for death and surrender payments: these are also excluded from the P&L to the extend that they are offset by release of reserves. Only payments in excess of the account values are included in the P&L. Basically, this business is -in this example- treated as a savings deposit: only the charges or margins that the company receives and the expenses and claims in excess of the fund value are of concern to the company. The following steps will need to be taken to determine the market value of the liabilities (below each of these steps will be further explained): 1. Determine the gross margins at best estimate assumptions for all future years 2. Calculate the present value of the gross margins from step 1 3. Determine the MVM per assumption 4. Determine the gross margins at best estimate + MVM for all future years 5. Calculate the present value of the gross margins from step 4 Based on the information generated by these 5 steps, the P&L and balance sheet for the current year can be set up. Moreover, the projected run-off P&L and balance sheets for all future years can be estimated: 6. Set up profit and loss accounts 7. Set up balance sheets Below an example of each of these steps : Step 1: Determine the gross margins at best estimate assumptions for all future years: The gross margin will include: a. Amounts expected to be earned on investments of policyholder accounts less interest credited to policyholders: b. Charged for mortality coverage less benefit claims in excess of policyholder balance c. Expense charges less policy administration costs incurred d. Surrender charges

2 Therefore, gross margin = Interest earned -/- interest credited + Mortality charges -/- death benefits in excess of contract balance + Expense charges -/- policy administration + Policy surrender charges Before this projection can be made, (best estimate) assumption will have to be set with regard to the amount of premium to be received in the future, the expected investment return, surrender and death rates, etc. After determining the expected development of the investment funds, the gross margins can be calculated: Fund development Fund Value BOY (a) 0 10,270 11,574 12,914 14,289 15,702 Premium (b) 10,000 1,000 1,000 1,000 1,000 1,000 Mortality & expense charges (c) Proj interest Earned ,025 1,134 1,246 1,361 Proj Interest Credited (d) ,006 1,113 1,223 1,336 Release funds upon Death (e) Release funds upon Surrender (f) Fund Value EOY a+b-c+d-e-f 10,270 11,574 12,914 14,289 15,702 17,153 Projected gross margin (Best Estimates) Gross interest margin Mortality & expense charges Surrender charge Incurred Expenses Death benefit in excess of fund Projected gross margin (BE) In this example, the following assumptions are used: - Premium payments take place at the beginning of each year; - Mortality & expense charge, Projected interest earned and Projected interest credited are a percentage of the beginning of year fund value after premium payment (resp. 0,10%, 8,15% and 8,00%) - Release of funds upon death and surrender depend on their respective rates of occurrence; in this example we have assumed respectively 1,2 % and 4 % of beginning of year funds after premium payment; - Gross interest margin = projected interest earned projected interest credited, - Surrender charge is defined as 2 % of the related fund release; - Death benefit is based on a projection.

3 Step 2: Calculate the present value of the gross margins from step 1 The present value of the gross margins is calculated by discounting them at the net crediting rate (the crediting rate after mortality and expense charges): crediting rate 8.00% 8.00% 8.00% 8.00% 8.00% 8.00% Mortality & expense charge 0.10% 0.10% 0.10% 0.10% 0.10% 0.10% Net crediting rate 7.90% 7.90% 7.90% 7.90% 7.90% 7.90% If the present value of the gross margins is defined as: (Gross Margin t + Present Value Gross Margin t+1 ) / (1 + cr t ) wth cr t being the net crediting rate in year t as defined above, the present values become: Present Value of gross margins (Best Estimates) projected gross margin Net crediting rate 7.90% 7.90% 7.90% 7.90% 7.90% 7.90% PV BOY Step 3: Determine the MVM per assumption The MVM (Market Value Margin) is the price the market would charge for running uncertainty risk: risk related to mis-estimation of parameters used in setting the best estimate assumptions. In this example, this risk will be quantified by determining the impact of the mis-estimation on the present value of gross margins. For example, suppose that best estimate mortality rates are derived from prior year s observations by estimating a trend. Then, the more volatile the observations were in the past (or the fewer observations one has) the more uncertain this best estimate prediction will be. By also calculating the present value of gross margins for other possible trend developments, the distribution of (all) possible present value outcomes can be determined. The standard deviation of this distribution can then be used as a basis for the quantification of the MVM (the part of the uncertainty risk included in the market value of the liabilities). For example, determine: PV gross margin under different mortality assumpt. PV gross margin under different lapse assumpt. < 86.5 Higher Mortality $' > 86.5 Lower Mortality < 86.5 Higher Lapse $' > 86.5 Lower Lapse St. dev mortality = X St. dev lapse = Y

4 If now, the MVM is defined as a number of times the standard deviation, then this multiple would reflect the market price per unit of uncertainty. The larger the price per unit of uncertainty or the uncertainty itself, the larger the MVM and visa versa. The multiple also determines what part of the uncertainty will be included in the market value of the reserves. If for example a company would like to be able to withstand adverse developments in uncertainty risk with a 99,95 % chance over a 1- year time horizon, then (based on a normal distribution) 3,29 times the standard deviations should be included as MVM in the market value of the liabilities. Suppose that the market would charge 1,3 1 times the standard deviation (90,32 % chance that the market value of the liabilities will be sufficient if uncertainty risk develops adverse). Then for all assumptions, we would need to translate the 1,3 * standard deviation, that is added to the best estimate present value, into adjustments to the assumptions. In this example, we assume that the above-described analysis of the impact on the present value of gross margins, led to such a correction of the assumptions, that all components of the gross margins decreased by 15 % (see step 4). Note: For solvency purposes, the company could hold an additional amount of capital that would, together with the MVM, add up to the required confidence level as desired by the particular company or the regulators. Step 4: Determine the gross margins at best estimate + MVM for all future years Projected gross margin (Best Estimates + MVM) Gross interest margin Mort. & exp. charges Surrender charge Expenses Death benefit in excess of fund Projected gross margin (BE+MVM) Note: all items are 15 % lower due to the inclusion of the MVM in the underlying parameters (see step 3) 1 Over time, the assessment of an appropriate level will be improved (guidance from IAA, IASC, IAIS, etc. and studies analysing the distribution functions). The 1,3 used here, is based on experience in Canada, where levels between 1 and 1,5 are typically used for these kind of calculations.

5 Step 5: Calculate the present value of the gross margins from step 4 As in step 2; discount rate is the crediting rate: Present Value of gross margins (Best Estimates + MVM) Projected gross margin Net crediting rate 7.90% 7.90% 7.90% 7.90% 7.90% 7.90% PV BOY incl MVM PV EOY incl MVM All information that is required to set up the P&L s and balance sheets for all future years is now determined. Below it is assumed that in the future, the realizations will be according to their best estimate assumptions. In practice, the actual experience would be included. Step 6: Set up profit and loss accounts (In this example, it is assumed that realizations will be according to the best estimate scenario) Projected Profits for all future years assuming the BE scenario proves to be correct: A. Change in Reserve/ PV GM (-) B. Charges* (+) C. incurred expenses (-) D. death benefit in excess of funds (-) E. Reduction in Interest (-) F. Pre tax Profit Ad A.: as premium, credited interest and the related reserve/fund increases are not included in the P&L, the change in reserves equals [PV GM BOY -/- PV GM EOY ], where PV GM stands for the present value of the gross margins including the MVM as defined in step 5. (Note: the present value of the gross margins at the begin of the first year is zero.) Ad B.: These are the actual charges incurred; as it is assumed that the best estimate scenario comes true, this item equals the sum of the first three lines of the gross margins calculated in the first step. Ad C.: Actual expense (see step 1 for value) Ad D.: Actual benefit (see step 1 for value) Ad E.: The P&L needs to be corrected for the fact that future gross margins are recognized as profits in the year of sale and therefore will not be available in the future for investments on behalf of the policyholders.

6 As the MV liabilities will be lower than the account value (by PV GM), the return generated by the assets backing the MV liab will be lower than what s needed for the fund increase, as this is based on the full account value. Therefore this amount [ PV GM t * cr t ] needs to be subtracted from the pre tax profit if the net interest item in the P&L is based on interest over the full account value. The profit in the first year will be the actual gross margin for 1999 (9.2) plus the present value of the future gross margins at the end of the first year calculated at best estimates plus MVM (61.2): 70.4 in total. After the first year, assuming that the best estimate scenario will become true, the MVM included in the calculations will be released: profits in these years equal the difference between gross margins determined at best estimate assumptions (step1) and those at best estimate plus MVM (step 4). Step 7: Setup balance sheets The following balance sheet items can be determined for every future year (again, in the example we will assume that realizations are according to best estimate assumptions): - The MV of the liabilities at the end of year t equals the difference between: a. the account value at yearend t, and b. present value of future gross margins at yearend t, as determined in step 5; (The PV GM can be viewed as a loan from the policyholder to the shareholder that will be paid back over the course of the policy term; the future gross margins will be used to pay off this loan. The amount by which the account value is lowered is therefore equal to the present value of these future margins.) - Surplus (including taxes to be paid) at year-end equals the sum of: a. the rolled forward surplus existing at the beginning of the year b. pre tax profit generated during the year Balance sheets for all future years assuming the BE scenario proves to be correct: assets 10,279 11,597 12,956 14,356 15,800 17,290 - MV liabilities 10,198 11,508 12,857 14,246 15,678 17,153 acc val 10,270 11,574 12,914 14,289 15,702 17,153 PV GM surplus liabilities 10,279 11,597 12,956 14,356 15,800 17,290 Note: interest return on surplus included above 0 6.4* * the 6.4 is the 7,9 % investment return over the 80,7 surplus that was available at the beginning of the year and is included in the surplus yearend value of year 2000: 89.0 = resp. the surplus at beginning of the year, interest on surplus and profit during the year.