EDUCATIONAL NOTE DISCOUNTING COMMITTEE ON PROPERTY AND CASUALTY INSURANCE FINANCIAL REPORTING. APRIL Canadian Institute of Actuaries

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1 EDUCATIONAL NOTE Educational notes do not constitute standards of practice. They are intended to assist actuaries in applying standards of practice in specific matters. Responsibility for the manner of application of standards in specific circumstances remains that of the practitioner. DISCOUNTING COMMITTEE ON PROPERTY AND CASUALTY INSURANCE FINANCIAL REPORTING APRIL Canadian Institute of Actuaries Ce document est disponible en français Canadian Institute of Actuaries Institut Canadien des Actuaires

2 Canadian Institute of Actuaries Institut Canadien des Actuaires MEMORANDUM TO: All Members and Students of the Canadian Institute of Actuaries Interested in Property and Casualty Issues FROM: James K. Christie, Councillor Responsible for Property and Casualty Matters DATE: April 12, 1999 SUBJECT: Educational Note on Discounting This package consists of two documents: an updated educational note on discounting; and a survey of actual discounting practice, as described in year-end 1996 valuation reports. The educational note updates and replaces the educational note on discounting issued by the Committee on Property & Casualty Insurance Financial Reporting (PCFRC) in There are no major changes in the body of the note, but there is an increased emphasis on book yields. Etracts from Section 5.04 of the Recommendations for Property-Casualty Insurance Financial Reporting are included for ease of reference. In addition, a new appendi is added which discusses the impact of different investment portfolios on the selection of discount rate(s) for a hypothetical company. The survey of practice was compiled by the Québec Regulator s Office (IGIF), based on a review of yearend 1996 valuation reports. Jean Côté first presented the core of the survey results at the 1997 Seminar for the Appointed Actuary in Montréal. With the assistance of the PCFRC, this version highlights best practices among those noted in the survey. Both of these documents should assist members in reviewing procedures and documentation. JKC Secretariat : 360 Albert #820, Ottawa, Ontario, Canada, K1R 7X7 (613) FAX : (613)

3 Educational Note on Discounting These educational notes on Section 5.04 of the Recommendations for Property-Casualty Insurance Company Financial Reporting address the issue of discounting of policy liabilities (including claims liabilities) in the contet of financial reporting of insurance companies. The discounting of policy liabilities involves two fundamental concepts. The first is the payment pattern of the liabilities to be discounted. The second is the discount rate used to present-value future payments. We will address both in turn below. Sections in the right margin are etracted directly from the Recommendations for Property-Casualty Insurance Company Financial Reporting Present Value of Policy and Claims Liabilities, and Rate of Return Used in the Valuation The member should establish a present value provision for the policy or claim liabilities using the following guidelines: PAYMENT PATTERN Before any consideration of a provision for adverse deviation, discounted liabilities for future payments to settle claims are estimated by applying discount rates to epected payment patterns. Payment patterns selected should reflect the actuary s best estimates with regard to the timing and amount of payments (indemnity and claim adjustment epenses) in connection with the settlement of claims subsequent to the valuation date. They would normally vary from one grouping of claims to the net. They might also vary by accident year within a grouping, especially when there have been known changes in the insurance environment. Selected payment patterns would normally be derived from the individual company s historical eperience insofar as possible. To the etent that such individual company historical data does not eist (e.g., for a new line not previously written by the company) or does not have a reasonable level of credibility (e.g., for a company with very low claims volume), it may be necessary to supplement such eperience with other eternal eperience before selecting the payment patterns. Such other eternal eperience should reflect the payment and timing characteristics of the grouping under consideration to the etent possible. If historical eperience is used as the basis for the derivation of the payment pattern, then it is necessary to take into consideration known and ascertainable changes. For eample, the historical information may not be reflective of the current reinsurance agreements (level of ecess layer) or the current claim settlement practices of the company. Where historical eperience is judged to have low predictive value, which might be the case in some lines such as surety, the actuary will need to apply significant levels of informed judgment. The selected payment patterns should be consistent with the assumptions used in the estimation, if any, of the undiscounted liabilities. Reasonably homogenous groups of claims (or subclaims) with a schedule of payments which are fied and predetermined with respect to both quantum and timing ecept, perhaps, for such contingencies as inflation-linked indeation, death, recovery, and relapse should be valued separately, if practical. For eample, weekly indemnity subclaims within the automobile insurance accident benefits coverage will usually fall into this category. Other claims should be subdivided into reasonably homogeneous groups for the selection of payment patterns for evaluation purposes. Such groupings would normally be the same as those used in the evaluation, if any, of the ultimate (undiscounted) liabilities. They would not normally mi types of claims of a short-tail nature with those of a long-tail nature. Timing of epected salvage, subrogation, loss transfer, and any reinsurance recovery amounts should be considered in the selection of payment patterns. 3 PAYMENT PATTERN a. claims which are paid according to a schedule which has pre-determined amounts and times of payment should be valued individually, if practical. Alternatively, claims that are similar can be grouped into blocks of claims and each block evaluated For eample, total disability claims in the accident benefits section; b. all other claims should be divided into homogeneous sub-groups, as far as is practical, and the present value of such claims should be determined using an epected payment pattern. The liability at zero rate of return should be calculated for the purpose of testing the runoff pattern;

4 All considerations concerning the payment patterns for claim liabilities also apply for other policy liabilities. However, when selecting the payment pattern for other policy liabilities, the actuary should consider the characteristics that affect those liabilities. For eample, the calculation of the impact of the time value of money when testing the adequacy of the unearned premium reserve should reflect the timing associated with the earning of the unearned eposure and its associated average date of accident. c. the investment rate of return depends on: i) the method of reporting investment return and valuing assets; DISCOUNT RATE Discount rates based on investment returns are used to reduce epected future claim payment streams to their equivalent present value. They would normally be deterministic and not stochastic. They may or may not vary from one claim grouping to the net, from one future calendar period to the net, or from one underlying accident period to the net. Selection of discount rates (and their potential variation as alluded to above) should be based on the purpose behind the valuation, and might be different for different purposes. Such purposes include but are not limited to the following: Capital Adequacy For eample, some solvency or capital adequacy tests mark invested assets to market value. Currently, there is no corresponding mark-to-market required for the liabilities, and so a valuation on this basis is uncommon. Balance Sheet and/or Income Statement For eample, the current annual regulatory return balance sheet and income statement mark invested assets to book value. This is the most common situation faced by the Canadian P&C actuary today. The situation may be different for nonstatutory balance sheets and income statements. Purchase or Sale of an Entire Insurance Company or of a Portfolio In this situation, assets would normally be valued at market. One part of the assessment of an insurance transaction sale may be the valuation of the policy liabilities at a rate realizable by the purchaser or the seller. While these valuations are important in the contet of current merger and acquisition activity, they are not currently part of financial reporting. Valuation for Income Ta At the current time, the discounting carried out for the valuation for the regulatory return should form the basis for the liabilities used in determining income ta. Possible candidates for selected discount rates include, depending on the purpose, the following: Market Rates These would reflect the current (i.e., new money ) achievable investment rates for a risk-free or other prudently invested portfolio of assets with appropriate duration. While these rates should be considered in determining reinvestment assumptions (see below), they are not otherwise appropriate when assets are valued at book. Market rates are, however, an essential part of determining the fair value of liabilities. 4

5 Portfolio Rates These would reflect the epected returns of the asset portfolio that supports the policy liabilities. For most P&C companies today, this support will be based on a notional matching of assets and liabilities. Allocated assets must be sufficient to support the PFADs, in addition to the epected payments. With respect to short-term and fied-income securities, such epected returns would represent book yields, assuming investments are held to redemption. Care should be taken to understand the formulas used to determine any quoted book yields. For instance, it is common for the book yield on a bond portfolio to be quoted as a nominal yield, compounded semi-annually, while short-term money market instruments are usually simple discount rates. The actuary may need to convert this number to the equivalent annual effective interest rate. For such a notional matching, it has been traditional to assume that an insurance company s most risky assets should be matched with its capital and surplus, while its most risk-free assets should be matched with policy liabilities. This includes appropriately considering the epected cash flows (dividends and normal trading activity) on any equity investments in the asset portfolio. Using notional matching, the rates might vary from one grouping to the net. In this contet, the matching of assets to the various policy liabilities may be done on a basis different from the grouping selected to derive the payment patterns. It is often useful to partially match premium liabilities with premium receivable and installment premiums (net of commission payable). ii) iii) the allocation of investment return and assets among classes of business; the projected rate of return on its assets at the valuation date; Prescribed Rates If a prescribed rate is used, the member s report may have to be qualified. The rates used to discount the policy liabilities should be consistent with the valuation of the related assets, if any. For this reason, the use of a prescribed rate may be inappropriate for the purpose of evaluating capital adequacy status. The basis for the selection of the discount rate(s) used must be clearly identified to the user of the work. Aside from considering the purpose of the valuation, in selecting the discount rates, the following considerations should be taken into account: 5

6 General Cash Flow Considerations For a going-concern, the actuary should consider whether epected cash flow(s) from future business is likely to be sufficient to cover the payments needed under the epected payment patterns in relation to the runoff of the current policy liabilities, or whether covering these payments will require the liquidation of some currently invested assets. The actuary should be familiar with and consider the insurance company s investment philosophy. Liquidation and Reinvestment Risks If, in the judgment of the actuary, it will likely be necessary to liquidate some currently invested assets, the actuary should consider whether or not the potential or current actual asset portfolio has appropriately scheduled maturity dates and/or liquidity to cover the payments needed. To the etent that mismatches eist, the actuary should consider the epected future reinvestment rate for new money (by appropriately melding the current asset-based rate with epected future reinvestment rates to derive future calendar-period discount rates), and the epected capital gain or loss on any assets which may require premature liquidation. Investment Epenses The actuary should consider the epected epenses to be incurred in connection with the investment of assets. The simplest method may be to reduce the investment yield by a few basis points, based on review of historical investment epenses. Asset Default Risk The actuary should consider the epected losses, if any, arising from the potential default of obligations by the issuer of the invested assets. The actuary should be concerned with the impact of a concentration of investment on such default risk. iv) where cash flow is epected to be positive, the epected new money rate of return on its assets acquired after the valuation date; v) where cash flow is epected to be negative, the epected capital gains or losses on its assets disposed of after the valuation date; vi) vii) its epected investment epense rates; and its epected losses from default. The member need not verify the eistence and the ownership of the assets owned at the valuation date. He should, however, base his assumptions upon their characteristics and his appraisal of their quality. 6

7 Appendi Sample Co. Introduction Sample Co. was developed as a way of focussing on the selection of the interest rate(s) and the interest PFAD(s) and the mechanics of their application. All the hard work is presented as given and agreed. That is, ultimate premium and claim liabilities have been determined, including gross/ceded splits. Epected payment patterns are known for all of these combinations. Finally, development and reinsurance MADs have been selected. The only tricky piece is that four scenarios are presented for the assets. The asset scenarios also reflect different investment policies. Data A complete underwriting income statement and balance sheet was determined for the company. The figures are based on a composite of the Canadian industry as at December 31, As such, the company can be assumed to be in good financial health, although MAT figures were not calculated. To reduce compleity, complete investment income, ta and capital flow information was not provided. The underwriting income and balance sheets are as follows: Premiums Written: Ratios Year Ended Direct 100.0% 100.0% 72,114 69,818 Ceded 10.0% 10.0% 7,211 6,982 Net 90.0% 90.0% 64,903 62,836 Decrease(increase) in Net Unearned Premiums (1,221) (1,741) Net Premiums Earned 100.0% 100.0% 63,682 61,095 Net Claims and Adjustment Epenses 71.7% 73.0% 45,660 44,600 Acquisition Epenses: Commissions 14.6% 14.5% 9,298 8,859 Taes 3.6% 3.5% 2,293 2,138 General Epenses 13.0% 13.1% 8,279 8,003 Total Claims and Epenses 102.9% 104.1% 65,528 63,600 Underwriting Income -2.9% -4.1% (1,847) (2,505) 7

8 As of Dec. 31st As of Dec. 31st Payables: Cash 1,974 1,599 Agents and Brokers 4,411 3,684 Investment Income Due and Accrued 1,391 1,450 Policyholders Nil Nil Investments 100,000 91,093 Subsidiaries and Affiliates 3,088 2,579 Other 1,323 1,105 Receivables: Agents and Brokers 8,786 8,142 Unearned Premiums 34,435 33,078 Installment Premiums 5,857 5,428 Unpaid Claims and Adjustment Epenses 65,409 62,008 Facility Association and the P.R.R. 6,548 7,264 Subsidiaries and Affiliates 1, Other 2,592 2,703 Other Unearned Commissions Recoverable from Reinsurers: Unearned Premiums 3,443 3,308 Unpaid Claims and Adjustment Epenses 3,270 3,100 TOTAL LIABILITIES 111, ,817 Deferred Income Taes Reserves Required 4,015 3,721 Investments in Subsidiaries Capital Stock Paid 13,311 12,939 and Affiliates 2,946 2,817 Other 12,536 12,530 Contributed Surplus 2,825 2,840 Deferred Policy Acquisition Earned Surplus 22,403 18,537 Epenses 6,041 5,812 General and Contingency Reserves Total Capital, Surplus and Reserves 42,754 38,286 TOTAL ASSETS 154, ,251 TOTAL LIABILITIES, CAPITAL, SURPLUS AND RESERVES 154, ,251 8

9 The epected future liability cash flows and the selected MADs are shown below. For simplicity, this is all assumed to come from one homogeneous line of business. Note that the information is presented NET and ceded, not GROSS and ceded. Gross epected liabilities could be derived by adding the ceded to the net. None of the asset scenarios call for the allocation of any specific assets to any specific cash flows. Epected Future Liability Cash Flows NET CEDED Calendar Unpaid Claims & Premium Unpaid Claims & Premium Year Adjustment Epenses Liabilities Adjustment Epenses Liabilities ,831 13,445 1,799 1, ,365 5, ,385 1, ,992 1, , , , , , Total 62,138 25,639 3,270 2,755 Development MADs Reinsurance MADs MADs 10.0% 7.0% 2.5% 2.5% In practice, P&C cash flows are likely to be noisy, at least for long-tail lines that generate most of the industry s claim liabilities. Given the current state of the art, only one liability cash flow scenario is presented above. This is consistent with general epectations that P&C cash flows are not closely correlated with interest rate movements. However, there is clearly a link between inflation (which does affect cash flows) and interest rates. In addition, some items, such as prejudgment interest, are directly related to interest rates. Eperience with DCAT inflation and interest rate scenarios may give some indication of the value of considering multiple liability cash flow scenarios. 9

10 Epected Payment Patterns Ceded UEP Ceded Claims Net UEP Net Claims As indicated earlier, the assets scenarios consist of a pairing of invested assets owned on December 31, 1996, and a summary of the investment policy. All investments held in all scenarios are high quality. Bond coupon rates quoted are nominal rates, compounded semi-annually. T-Bill coupon rates are really the nominal simple discount rate quoted in the trade. This is the normal convention used for these and similar instruments in Canada. The market convention can be different in other countries. Scenario 1: Investment policy is to buy to match, more or less, the liabilities, with terms to maturity restricted to five years, and with the intention to hold investments to maturity. Scenario 1 Investment Portfolio as at 31 December 1996 (Amounts in $000 s) Class Maturity Coupon Par Value Book Value Market Value T-Bill T-Bill Provincial Bond Provincial Bond Corporate Bond Canada Bond Canada Bond Canada Bond 30/Jan/97 20/Feb/97 1/Oct/97 15/Jul/98 1/Jun/99 1/Sep/99 1/Mar/00 1/Dec/ % 2.70% 11.00% % 9.20% 7.75% 8.50% 9.75% $ 5,028 $ 5,032 $20,202 $ 9,131 $ 9,693 $20,060 $ 9,089 $18,411 $ 20,000 $ 10,000 $ 10,000 $ 20,000 $ 10,000 $ 20,000 $ 21,269 $ 10,011 $ 10,671 $ 21,568 $ 10,024 $ 21,687 Total $96,646 $100,000 $105,230 10

11 Scenario 2: Investment policy is to buy short term, constantly rolling portfolio over. Scenario 2 Investment Portfolio as at 31 December 1996 (Amounts in $000 s) Class Maturity Coupon Par Value Book Value Market Value T-Bill T-Bill T-Bill 30/Jan/97 20/Feb/97 27/Mar/ % 2.70% 2.80% $40,227 $30,191 $30,253 $40,000 $30,000 $30,000 $40,000 $30,000 $30,000 Total $100,671 $100,000 $100,000 Scenario 3: Investment policy is to buy to match, more or less, the liabilities, with no restriction on terms to maturity, and with the intention to hold investments to maturity. Scenario 3 Investment Portfolio as at 31 December 1996 (Amounts in $000 s) Class Maturity Coupon Par Value Book Value Market Value T-Bill T-Bill Provincial Bond Provincial Bond Corporate Bond Canada Bond Canada Bond Corporate Bond Canada Bond Provincial Bond Provincial Bond 30/Jan/97 20/Feb/97 1/Oct/97 15/Jul/98 1/Jun/99 1/Mar/00 1/Dec/01 1/Nov/02 1/Dec/03 15/Sep/04 1/Dec/ % 2.70% 11.00% % 9.20% 8.50% 9.75% 11.00% 7.50% 9.00% 7.75% $ 5,028 $ 5,032 $20,202 $ 9,131 $ 9,693 $ 9,089 $18,411 $ 5,028 $ 4,949 $ 4,956 $ 4,995 $ 20,000 $ 10,000 $ 10,000 $ 10,000 $ 20,000 $ 21,269 $ 10,011 $ 10,671 $ 10,024 $ 21,687 $ 6,150 $ 5,353 $ 5,738 $ 5,400 Total $96,514 $100,000 $106,303 Scenario 4: Investment policy is changing effective 1 January 1997 from that of scenario one to one of actively trading for higher yields. Scenario 4 Investment Portfolio as at 31 December 1996 (Amounts in $000 s) Class Maturity Coupon Par Value Book Value Market Value T-Bill T-Bill Provincial Bond Provincial Bond Corporate Bond Canada Bond Canada Bond Canada Bond 30/Jan/97 20/Feb/97 1/Oct/97 15/Jul/98 1/Jun/99 1/Sep/99 1/Mar/00 1/Dec/ % 2.70% 11.00% % 9.20% 7.75% 8.50% 9.75% $ 5,028 $ 5,032 $20,202 $ 9,131 $ 9,693 $20,060 $ 9,089 $18,411 $ 20,000 $ 10,000 $ 10,000 $ 20,000 $ 10,000 $ 20,000 $ 21,269 $ 10,011 $ 10,671 $ 21,568 $ 10,024 $ 21,687 Total $96,646 $100,000 $105,230 11

12 Results Five members of the committee determined the actuarial (i.e., discounted plus PFAD) net claim liabilities for each of the four investment scenarios. All results were determined independently. Note that the epected net payments (i.e., the booked liability) are 62,137. The valuation results were as follows: Scenario 1 Scenario 2 Scenario 3 Scenario 4 Matched to 5 years hold Stay in T-Bills Matched hold Matched to 5 years trade D 58,204 64,548 57,673 58,245 A 60,616 64,833 60,353 60,876 T 58,538 62,465 57,995 59,945 H 58,466 59,284 58,244 58,466 P 58,235 64,248 57,473 58,235 The results are generally very close for scenarios one and three. In both cases, the cash flows from the invested assets are reasonably matched with the liability cash flows, and there is little reinvestment risk. Scenario three is better matched, as its cash flows etend beyond five years. Because of the upward sloping yield curve, the book yield on this portfolio was higher than scenario one. All participants recognized this, in combination with the lower reinvestment risk, in lower valuations for scenario three than for scenario one. Compared to scenario one, the only difference in scenario four was the future reinvestment policy. Two participants made small changes in margins in response, while one of the participants changed the interest rate margin significantly to reflect this policy change. The other two adopted a wait-and-see approach, as there was no difference in current assets. Finally, there was a considerable spread in the results of scenario two. In most cases, the actuarial liabilities on this basis are higher than the undiscounted, which does raise some questions about the balance sheet above. However, the key differences were in the assumed reinvestment rates. This topic will be eamined in more detail below. Lessons Learned: Basic Approach Book Invested Asset Yield The simplest method is to determine the book yield on the (allocated) invested asset portfolio, select an appropriate PFAD, and take the present value. However, there are a number of potential pitfalls even in this simple method. In some cases, the investment professional will provide the actuary with a book yield to maturity. It is worth asking a few questions before taking the figure at face value. First, it may eclude some assets (such as T-Bills) that are held in a different account. Second, it is likely to be a nominal rate, compounded semi-annually. Third, it is worth asking for the formula used, and plugging the parameters into your own calculator at least once, etc. In the scenarios presented above, the actuary needs to calculate the book yield. To do this, the actuary must properly understand the cash flows. T-Bills are sold at a discount and mature at par. Bond coupon rates are nominal rates, paid semi-annually. Some bonds may have call features that result in redemption prior to maturity. Early principal repayments are also a feature of mortgage-backed securities, and the amount will vary with the interest rate environment. The dates of the payments must also be established. Specific days may be necessary to avoid the potential bias involved in using midpoints (i.e., assuming all payments on June 30), especially when there is a significant T-Bill portfolio. 12

13 The portfolio yield is the IRR that produces the book value. Again, care is required in defining the book value. This is because accrued interest income is often held in a separate account. For Sample Co., this means that the book value is $101,391 (investments plus investment income due and accrued). An alternative approach is to reduce the initial cash flow by the investment income due and accrued, and solve for the interest rate that produces the invested assets book value of $100,000. This should arrive at similar book yields, but will understate the asset cash flows in any cash flow tests. In some real life cases, the actuary will not have enough detail to calculate asset cash flows, but will have duration, yield and value for each asset. Using the product of duration and value as weights, the weighted average yield is an approimation of the asset IRR. Of course, it would still need to be converted from a nominal to an effective rate. Finally, an interest MAD needs to be included, together with an allowance for investment epenses and default. For Sample Co., the allowance for default may actually be zero, given the high quality of the assets. In the absence of specific information about Sample Co. s investment epenses, most participants avoided an eplicit assumption, instead incorporating this implicitly in their interest or interest MAD assumption. Actual MADs selected to produce the results for scenarios one and three were between 0.5% and 1.0%. This seems appropriate given the overall quality of the assets and the relatively small mismatch. The key advantage of this approach is its simplicity; particularly if the actuary can rely on the investment professional s determination of book yield. Its key disadvantage is the handling of reinvestment risk. There is also no real attempt to compare asset and liability cash flows. While there is some fleibility to deal with mismatch by judgmental increases in the interest MAD, this approach has limitations. Scenario two seems to require eplicit consideration of reinvestment interest rates. Yield Curve 9% 8% 7% Yield 6% 5% 4% 3% Bid Yield Interpolated Yield Reinvestment Rate 2% Duration 13

14 Reinvestment Rate Selection One popular approach seems to be to use an ultimate reinvestment rate of 5.0%, probably derived by reference to life insurance VTP 3. This figure should probably be reduced for investment epenses and epected defaults, but is not generally reduced further for an interest margin. In life insurance, liability cash flows are often longer than can be matched by readily available marketable fied-income assets. This is not the case for most P&C liabilities (obvious eceptions are accident benefit and environmental/mass tort liabilities). It is specifically not the case for Sample Co. Accordingly, market rates are generally available for periods represented by P&C liability cash flows, and these are a viable alternative. Market yield curves are based on the yield to maturity of representative assets. When the reinvestment policy calls for assets other than risk free Canada s, an appropriate reduction for default should be used. The yield curve can be decomposed into period-by-period reinvestment rates. However, the risk premium built into the normal upward sloping yield curve will usually result in the overstatement of the reinvestment rate. This can be compensated for by a higher interest MAD on the reinvestment rate. A viable alternative is to look to quotations in the forward interest rate market, although this may not yet be a liquid enough market at the medium terms. Stochastic approaches are probably unnecessarily sophisticated compared to the liability cash flow uncertainties. Whatever approach is chosen, care should be taken to ensure that the final reinvestment rates are conservative. The reinvestment rate(s) must then be blended with the eisting rate(s). One judgmental approach is to use portfolio information for payments up to and including the epiry year of the oldest asset in the portfolio, and the reinvestment rate(s) thereafter. This makes some sense when the assets are fied income, and more than sufficient to cover the liabilities at shorter durations. Another judgmental approach is to look at the investment portfolio in isolation, and to gradually blend the portfolio rate with the reinvestment rate(s) as the portfolio matures. This makes some sense in a DCAT/planning eercise. In a valuation eercise, this brings in the new money rates even if asset cash flows are perfectly matched and sufficient. Hence, it probably misstates the interest rate(s). For Sample Co., the book yields eceed the likely reinvestment rates, and the interest rate would consequently be understated. This accounts for much of the reason behind the higher valuations in result set A. Finally, specific asset/liability cash flows could be reviewed, and projected shortfalls/ecesses could be determined for reinvestment at the selected rates. This approach may also call for more detail on the reinvestment assumptions, particularly if reinvestment is made for more than one year. For instance, ecess cash flows could be reinvested until the net anticipated shortfall. In this case, it may be necessary to determine the evolution of the zero coupon curve, instead of merely forecasting one-year T-Bill rates. Cash Flow Determination Invested asset cash flows are determined first for each asset in the portfolio, based on the characteristics of the asset. Although daily timing may be necessary to determine an accurate internal rate of return, a coarser grouping will suffice for reviewing cash flow matching, especially when, as is the case for Sample Co., only annual liability flows are provided. Asset cash flows should reflect epected defaults when these could be material. 14

15 Using asset scenario three for illustration, various cash flows are shown in the tables on the net page. Until the maturity of the last bond in 2005, asset cash flows are more than sufficient to fund the claim liabilities. However, the addition of premium liabilities causes a shortfall in When PFADs are considered, this shortfall cannot be entirely covered by the 1997 ecess cash flow. Allocated assets should generally be enough to cover PFADs. While liabilities could simply be increased for PFAD as a last step after working with the epected cash flows, this would miss many of the benefits of using the more detailed cash flow matching approaches. Invested Assets Scenario 3 Epected Claim Liabilities Epected Policy Liabilities Claim Liabilities w/pfads Policy Liabilities w/pfads ,671 21,831 35,276 24,063 38, ,318 11,365 16,684 12,526 18, ,464 8,385 10,083 9,236 11, ,028 5,992 7,459 6,595 8, ,963 4,718 5,633 5,190 6, ,785 3,279 4,126 3,607 4, ,153 2,382 2,953 2,621 3, ,789 1,672 2,113 1,839 2, ,382 1,237 1,535 1,361 1, , , Ecess of Asset Cash Flows over: Epected Claim Liabilities Epected Policy Liabilities Claim Liabilities w/pfads Policy Liabilities w/pfads ,840 3,395 14, ,953 (1,366) 2,792 (2,917) ,079 4,381 5,228 3, ,035 5,569 6,433 4, ,245 16,330 16,774 15, ,507 2,660 3,179 2, ,771 3,200 3,533 2, ,117 3,676 3,950 3, ,145 3,847 4,021 3, (786) (1,044) (865) (1,141) 2007 (426) (612) (469) (667) 2008 (64) (259) (70) (280) One possibility is to consider the cash flows from other assets and liabilities on the balance sheet. These include premium receivables from agents and brokers, installment premiums, other insurers and corresponding liabilities. For Sample Co., these net to an amount of about $12,205 more than sufficient to cover the potential shortfall in 1998, even if it just sits in the bank without interest. Accordingly, we only need to consider reinvestment rates, not borrowing rates or liquidation strategies. 15

16 In real life, some companies may take a more aggressive approach, and intentionally carry a short-term mismatch in order to take advantage of higher yields at longer durations. On a going-concern basis, initial cash flows from new and renewal policies will often cover this mismatch. In these cases, the actuary will have to choose a borrowing rate that reflects the risk, or an appropriate liquidation strategy. DCAT scenarios should help the actuary assess this risk. Asset Selection Having discussed reinvestment rates, one approach is to reformulate the problem and ignore them. This would involve selecting assets from our portfolio that would match the policy liability cash flows (with PFADs) as closely as possible, and notionally buying market assets to make up any shortfall. Unfortunately, this is not easy, especially when coupons cannot be stripped from bonds, as separate book values are needed for each. However, it does point out that the essence of discounting in the contet of an insurance company balance sheet is to identify the value of the assets required to support the liabilities. As most P&C investment policies do not currently have distinct funds, this is, perhaps, best done by determining the percentage of the invested assets that is needed to match the liability cash flows, allowing for reinvestment when there are mismatches. In the eamples below, 100% of the operating assets (i.e., premium receivable) are first allocated. Then the percentage of invested assets is determined iteratively, as follows: 1. An arbitrary initial allocation percentage of invested assets is determined. 2. Cash flows from these assets, together with the operating assets, are compared to the policy liability cash flows with PFADs. 3. Ecess cash flow is reinvested for one year. In this case, the reinvestment rate was based on the decomposed market yield curve. 4. This was done period by period and accumulated until the last liability was paid. 5. The internal rate of return on these asset cash flows was determined, using a mid-year assumption, and book values of allocated assets (including operating assets). 6. The liabilities were discounted at the asset internal rate of return, less allowances for default, epenses and an interest margin for adverse deviations. 7. If the asset book value eceeds the discounted liability value, the percentage allocation of assets was reduced (or vice versa). 8. The net iteration starts with step two, until there is a match. Note that the final selected asset allocation always produces a positive cash flow in the last year due to the interest margin. It is also worth noting that additional values, such as gross discounted premium liabilities, can be made to drop out, more or less, without any additional work. As noted earlier, only one liability cash flow is tested the liability cash flow with development and reinsurance PFAD is assumed to be independent of the discount and the allocated assets. There is no specific C-3 provision. The interest rate MAD provides for this risk in combination with the mistiming of the payments. 16

17 Liability Cash Flows Asset IRR PFAD Epense Claims W/PFAD Premium w/pfad Net 8.17% 0.90% 0.10% Gross Ceded Gross Ceded Total Time Factor Default 1997 $25,992 $ (1,929) $16,155 $ (1,724) $38, % 1998 $13,491 $ (965) $ 6,398 $ (690) $18, Net Rate 1999 $ 9,718 $ (482) $ 2,100 $ (276) $11, % 2000 $ 6,726 $ (132) $ 1,711 $ (138) $ 8, $ 5,190 $ $ 1,027 $ (46) $ 6, $ 3,607 $ $ 906 $ $ 4, $ 2,621 $ $ 611 $ $ 3, $ 1,839 $ $ 472 $ $ 2, $ 1,361 $ $ 319 $ $ 1, $ 865 $ $ 276 $ $ 1, $ 469 $ $ 198 $ $ $ 70 $ $ 210 $ $ Tot $71,950 $ (3,508) $30,381 $ (2,874) $95,950 NPV $61,085 $ (3,238) $26,992 $ (2,659) $82,180 $64,319 $ (3,410) $28,420 $ (2,799) Net Net $68,442 $68,442 $27,508 $27,508 <-Check NPV $57,847 $24,333 Book $60,909 $25,621 Market Asset IRR Available Total Return Selected Assets 69.0% 8.17% to Asset From 8.21% Before Insurance Asset Factor Cash out Reinvest Flows Reinvest yield Reinvest Flows Sub-total $38,494 $ 395 $38,889 $ $ 38,967 $12,206 $ 26, $18,235 $ (7,272) $10,963 $ $ 10,572 $ $ 10, $11,060 $ (8,782) $ 2,278 $ (7,684) $ 9,982 $ $ 9, $ 8,167 $ (8,580) $ (412) $ (9,385) $ 8,991 $ $ 8, $ 6,171 $ (206) $ 5,965 $ (9,163) $ 15,158 $ $ 15, $ 4,513 $ (60) $ 4,453 $ (220) $ 4,683 $ $ 4, $ 3,231 $ 943 $ 4,174 $ (64) $ 4,247 $ $ 4, $ 2,311 $ 2,688 $ 4,999 $ 1, $ 3,995 $ $ 3, $ 1,680 $ 4,889 $ 6,569 $ 2, $ 3,714 $ $ 3, $ 1,141 $ 4,076 $ 5,217 $ 5, $ $ $ $ 667 $ 3,691 $ 4,359 $ 4, $ $ $ $ 3,677 $ 3,677 $ 3,956 $ 3, $ $ $ Total $100,309 $12,206 $ 88,103 $82,180 Ass. Req. $69,014 Inv. Req. $ 82,180 $ 69,974 $ 0 Ecess 69.0% %Total Coupon 7.52% % $82,180 NPV Total Par Value $ 79,774 $13,166 $ 66,608 $82,180 Book* Book* $ 82,180 $13,166 $ 69,014 $86,530 Market Market $ 86,530 $13,166 $ 73,364 * Book for insurance flows includes share of accrued interest. 17

18 Impact of Investment Policy There are two broad uses of the investment policy in establishing the present value of the liabilities. The first is to assess the likely type and term of any reinvestment/disposal activity that will be necessary as a result of cash flow mismatches. The second, and perhaps more difficult, is to influence the actuary s judgment on the required interest risk margin. The brief descriptions given with the scenarios may have been adequate for the first purpose, but the wide range of reactions to scenario four suggests that more is needed for the second purpose. The best source for more information is probably the investment professionals themselves. Relevant questions relate to: How is the policy applied? Why are trades made? How are operating cash flows managed? How is incentive compensation determined? How is performance measured? Generally, what do the words and numbers in the policy really mean? On an ongoing basis, it may be worth reviewing the quarterly investment reports. For instance, most of the participants thought that scenario four was not much riskier than scenario one, as the assets held were identical. That attitude could change if a review of quarterly figures indicated that the portfolio had been dressed up for year-end. Conclusion Discounting does not have to be a complicated eercise. A number of simple approaches provide reasonable results in many cases, once some common pitfalls have been avoided. However, the actuary needs to realize that simple approaches incorporate a number of assumptions. The actuary should take steps to ensure that those assumptions are reasonably satisfied. Naturally, more complicated models, which require more eplicit assumptions, do take more time to develop and use. However, there may be offsetting benefits, such as increased interaction with investment professionals, and a broader, more robust set of results. Finally, most of the complicated models are still simple enough to be implemented in a spreadsheet. 18