This document is provided as the basis for discussion with the objective to develop an ACLI
    position on the subject ma...
Scope
The scope of the discussion should take into account all contract types, i.e., short-duration and long-
duration con...
contracts, the rate may not be explicitly stated in the contract. The crediting rate for long-duration
contracts (life con...
IAS 17
        At the commencement of the lease term, lessees shall recognise finance leases as assets and
        liabili...
IAS 37
           The discount rate (or rates) shall be a pre-tax rate (or rates) that reflect(s) current market
         ...
Appendix A
Discount Rates for Insurance Contracts
Prepared by Bill Schwegler (Aegon) and Carrie Morton (Principal Financia...
Background:
In IASB Agenda Paper 17D: Discounting, the IASB staff expresses the view that the discount rate for
a liabilit...
o   Prescribing an observable market rate would tend to reduce diversity in practice.
o Some alternatives (e.g. high-quali...
Appendix B
ACLI Discount Rate Modeling Project – Fixed Deferred Annuities
Prepared by Carrie Morton, Principal Financial G...
resulting discount rate was applied to all cash flows, regardless of duration – i.e. for cash flows
occurring at time 10, ...
The calculations in the graph above are based on approach (1). The following paragraphs describe
how the various discount ...
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  1. 1. This document is provided as the basis for discussion with the objective to develop an ACLI position on the subject matter. These notes are based on staff’s analysis of tentative views of the IASB and FASB, reference to various resource documents, and prior ACLI discussions and position statements expressed in letters to accounting standard setters on the topic. INFORMATION FOR DEPUTIES SUBGROUP Project: Insurance Contracts Topic: Discount rate ______________________________________________________________________________ Purpose This paper discusses various approaches to setting and applying the discount rate to the expected cash flows in measuring the insurance contract liabilities (for a portfolio of contracts) based upon the building blocks approach set forth in the 2007 IASB Discussion Paper: Preliminary Views on Insurance Contracts (DP). The proposed measurement approach would be a quasi-fair value model, i.e., current value. This paper concentrates on those methods having the greatest likelihood of meeting the measurement objective. The American Academy of Actuaries (AAA) September 2009 White Paper1 titled “Discussion on the use of Discount Rates in Accounting Present Value Estimates” is a key resource used in developing the content of this paper. The Subgroup, however, should not rule out other methods not described herein if such methods are determined to be a candidate. The following methods have been identified (not in any order of significance or importance): 1. Asset earned rate 2. Crediting rate implicit in the contract 3. High quality corporate bonds 4. Risk-free rate adjusted for liquidity While the discount rate is the topic of discussion, the Subgroup must be careful in its deliberations not to make a decision prematurely, i.e., the Subgroup must consider the effects of the decision on other elements of the measurement, e.g., explicit margins. The Subgroup has noted the significant interrelationship of insurance contract features and options. Consequently, a decision without consideration of the interrelationships could result in an inconsistent measurement approach. Structure of the paper a. Scope b. Discount rate candidates c. Existing IASB accounting guidance about discount rates d. Questions for the Subgroup e. Appendix A- Discount Rates for Insurance Contracts memo by Bill Schwegler and Carrie Morton f. Appendix B- ACLI Discount Rate Modeling Project – Fixed Deferred Annuities prepared by Carrie Morton 1 The White Paper is an addendum to this staff paper and serves as additional material to be taken into account in developing the ACLI position on discount rate. 1
  2. 2. Scope The scope of the discussion should take into account all contract types, i.e., short-duration and long- duration contracts, participating (including UL) and non-participating contracts, variable and fixed contracts. In addition, the discussion should consider subsequent measurement of the discount rate based on current market inputs. Any decision about the discount rate should not carve-out any segment of the insurance business unnecessarily. This paper does not provide detailed research, commentary or examples. Rather, the paper describes in a summarized way key points for and against the various methods to assist the Subgroup in the decision making process. Discount rate candidates The IASB has tentatively decided that: a) the discount rate for insurance liabilities should conceptually adjust estimated future cash flows for the time value of money in a way that captures the characteristics of that liability rather than using a discount rate based on expected returns on actual assets backing those liabilities b) the standard should not give detailed guidance on how to determine the discount rate. The FASB has not yet arrived at a decision on this topic. The IASB’s tentative view, while consistent with a principles-based approach, may not provide sufficient guidance for preparers. In the ACLI February 6, 2009 letter to the IASB regarding “Should credit characteristics of insurance liabilities affect their measurement?” the position expressed in the letter was: “Consequently, we believe that the credit risk of the insurance contract at initial recognition should reflect credit characteristics equivalent to a high quality debt instrument, e.g., AA - AAA rating and that subsequent measurement should not reflect changes in credit standing. Because of the capital requirements and guaranty funds, no change in the credit risk assumption is necessary for subsequent measurement. The rationale is that policyholders and beneficiaries are first in line in the event of insolvency of the insurer and that regulators typically take action well in advance to significantly minimize additional loss in value of the assets to ensure payment. Where there are not sufficient assets to pay claims as they come due, the guaranty fund system provides additional resources.” While the letter was specific to the issue of credit risk, it is relevant in the discussion on discount rate. Critical to the discussion of the discount rate is the way that the provision for risk should be taken into account. For example, should the discount rate reflect market-observable discount rates for cash flow streams with similar timing and risk characteristics or should the cash flows be risk adjusted? Asset earned rate Many industry responses to the DP commented on the discount rate urging the Board not to use a risk-free rate since the result would likely mean a loss at issue on profitable business. A typical response from US organizations was “we recommend using a discount rate that reflects the rate of return that the reporting entity expects to earn on the portfolio of assets backing the liability.” While the industry has often argued that the asset earned rate is fundamental in the pricing of insurance contracts especially long-duration contracts, nevertheless, the IASB has tentatively rejected the use of the asset earned rate in the measurement of insurance contracts. The junk bond example is often cited as the scenario against using the asset earned rate noting that the earned rate of a portfolio of junk bonds cannot serve as the discount rate for the insurance contract liabilities-especially non-par contracts. While the asset earned rate may not be appropriate for all insurance contracts, it may be appropriate for certain contracts such as participating contracts, UL contracts, and variable contracts, where the policyholder assumes the investment risk. Crediting rate implicit in the contract A modified version of the asset earned rate is the crediting rate, which is defined herein as the rate used by the pricing actuary in setting the gross premium. For some contracts, such as short-duration 2
  3. 3. contracts, the rate may not be explicitly stated in the contract. The crediting rate for long-duration contracts (life contracts) may be determined by regulation, i.e., the guaranteed rate. Whether the rate is implicit or explicit in the contract, the crediting rate is typically the asset earned rate reduced by an amount to recover operating costs and profit margin. High quality corporate bonds A view expressed by some standard setters when the topic of discount rate has been discussed is that there should be a single rate to achieve consistency and comparability. While a single rate may be a noble objective, such a rate would appear to be inconsistent with a principles-based approach and would not necessarily reflect the nature of the business. Current accounting guidance for defined benefit pension plans requires that the discount rate be based upon the rate for high quality corporate bonds. Measurement of insurance contract liabilities has many of the same characteristics as pensions-payments payable over a long period of time that will vary based upon the life expectancy of the plan participant. The discount rate referencing high quality corporate bonds may serve as a proxy for the rate used to price insurance contracts. Risk-free rate adjusted for liquidity Both the IASB staff and the CFO forum have expressed support for the use of a risk-free rate with an adjustment to reflect the liquidity characteristics of the liability. In 2006 a CFO Forum document titled “Elaborated Principles for an IFRS Phase II Insurance Accounting Model” articulated the following view (not sure if they continue to hold this view but used here only to illustrate an example): Discount rate EP10) A discount rate is required to adjust the insurance liability for relevant financial factors, notably the time value of money. The appropriate discount rate is the risk free rate of return specific to the liabilities being measured. EP11) Certain liabilities may not be subject to particular aspects of financial risk, such as liquidity risk. In such cases, the market risk free rate should be adjusted to reflect the absence of these risks. As a proxy for determining this adjustment, it may be appropriate to consider the yield on debt instruments with similar characteristics, such as corporate bonds. The yield should be adjusted to remove any premium for risks that are not relevant to the liability being evaluated, for example default risk. In the AAA White Paper, examples are provided illustrating that the provision for risk taken be taken into account in the estimate of cash flows or in the discount rate. Using a risk-free rate presumes that the cash flows have been risk adjusted. While there are proponents for the use of a risk-free rate, issues remain such as how to determine the risk-free rate, e.g., should the rate be determined used the swap rate and/or adjusted for liquidity? Existing IASB accounting guidance about discount rates A review of existing IASB accounting standards involving the use of a discount rate resulted in the identification of a number of accounting standards where a discount rate is described that are relevant in the discussion of the discount rate for insurance contract liabilities. The following references are listed as examples and do not represent a comprehensive list of all accounting standards where discount rates are specified. IFRS 1 to the extent that the liability is within the scope of IFRIC 1, estimate the amount that would have been included in the cost of the related asset when the liability first arose, by discounting the liability to that date using its best estimate of the historical risk-adjusted discount rate(s) that would have applied for that liability over the intervening period;2 2 Extracted from IFRS 1, First-time Adoption of International Financial Reporting Standards. © IASC Foundation. 3
  4. 4. IAS 17 At the commencement of the lease term, lessees shall recognise finance leases as assets and liabilities in their statements of financial position at amounts equal to the fair value of the leased property or, if lower, the present value of the minimum lease payments, each determined at the inception of the lease. The discount rate to be used in calculating the present value of the minimum lease payments is the interest rate implicit in the lease, if this is practicable to determine; if not, the lessee's incremental borrowing rate shall be used. Any initial direct costs of the lessee are added to the amount recognised as an asset.3 IAS 19 The rate used to discount post-employment benefit obligations (both funded and unfunded) shall be determined by reference to market yields at the end of the reporting period on high quality corporate bonds. In countries where there is no deep market in such bonds, the market yields (at the end of the reporting period) on government bonds shall be used. The currency and term of the corporate bonds or government bonds shall be consistent with the currency and estimated term of the post-employment benefit obligations.4 One actuarial assumption which has a material effect is the discount rate. The discount rate reflects the time value of money but not the actuarial or investment risk. Furthermore, the discount rate does not reflect the entity-specific credit risk borne by the entity's creditors, nor does it reflect the risk that future experience may differ from actuarial assumptions.5 BC31 The Board has not identified clear evidence that the expected return on an appropriate portfolio of assets provides a relevant and reliable indication of the risks associated with a defined benefit obligation, or that such a rate can be determined with reasonable objectivity. Therefore, the Board decided that the discount rate should reflect the time value of money but should not attempt to capture those risks. Furthermore, the discount rate should not reflect the entity's own credit rating, as otherwise an entity with a lower credit rating would recognise a smaller liability. The rate that best achieves these objectives is the yield on high quality corporate bonds. In countries where there is no deep market in such bonds, the yield on government bonds should be used.6 BC34 The reference to market yields at the balance sheet date does not mean that short-term discount rates should be used to discount long-term obligations. The new IAS 19 requires that the discount rate should reflect market yields (at the balance sheet date) on bonds with an expected term consistent with the expected term of the obligations. 7 IAS 36 The discount rate (rates) shall be a pre-tax rate (rates) that reflect(s) current market assessments of: (a) the time value of money; and (b) the risks specific to the asset for which the future cash flow estimates have not been adjusted.8 3 Extracted from IAS 17, Leases. © IASC Foundation. 4 Extracted from IAS 19, Employee Benefits. © IASC Foundation. 5 Extracted from IAS 19, Employee Benefits. © IASC Foundation. 6 Extracted from IAS 19, Basis for Conclusions. © IASC Foundation. 7 Extracted from IAS 19, Basis for Conclusions. © IASC Foundation. 8 Extracted from IAS 36, Impairment of Assets. © IASC Foundation. 4
  5. 5. IAS 37 The discount rate (or rates) shall be a pre-tax rate (or rates) that reflect(s) current market assessments of the time value of money and the risks specific to the liability. The discount rate(s) shall not reflect risks for which future cash flow estimates have been adjusted.9 IAS 41 …an entity incorporates expectations about possible variations in cash flows into either the expected cash flows, or the discount rate, or some combination of the two. In determining a discount rate, an entity uses assumptions consistent with those used in estimating the expected cash flows, to avoid the effect of some assumptions being double-counted or ignored.10 Questions for the Subgroup In order to advance the discussion and decision making with respect to the discount rate, the Subgroup is asked the following questions. 1. Does the Subgroup agree or disagree with the IASB tentative decision on the discount rate? What is the basis for agreement or disagreement? 2. Is more detailed guidance needed and if yes what should that guidance be? 3. How should the risk characteristics-credit risk, liquidity risk, be reflected in the measurement, i.e., in the discount rate or cash flows? What is the rationale? 4. What discount rate(s) should be used in the measurement of insurance contract liabilities at inception, subsequent measurement? What is the rationale? 5. What discount rate(s) should be used in measurement of insurance contracts with participating features? 9 Extracted from IAS 37, Provisions, Contingent Liabilities and Contingent Assets. © IASC Foundation. 10 Extracted from IAS 41, Agriculture. © IASC Foundation. 5
  6. 6. Appendix A Discount Rates for Insurance Contracts Prepared by Bill Schwegler (Aegon) and Carrie Morton (Principal Financial Group) Date: September 23, 2009 Introduction IASB Agenda Paper 17D: Discounting describes several possible approaches for selecting a discount rate for insurance contracts. These approaches can be summarized as follows: 1. Earned rate (paragraph 12) 2. Risk-free rate with adjustment for liquidity (paragraphs 17-21) 3. Observable market rates (paragraph 23) a. High-quality corporate bonds b. High-quality fixed-income debt instruments (this appears to be similar to 3.a.) c. Risk-free rate The purpose of this paper is to describe the advantages and disadvantages of each of the approaches presented in the IASB Agenda Paper. Earned rate Background: A few respondents to the DP argued that the discount rate should reflect the expected returns on the assets backing the liabilities. However, these respondents were in the minority, and the IASB does not support this approach. Advantages: o Consistent with common pricing practices for insurance contracts o Would not cause an artificial loss to be reported at inception (unless other elements of the accounting standard introduce excess conservatism) o Measures liabilities and assets at a consistent discount rate, thus reducing “artificial volatility” o If the liability is discounted at the risk-free rate, a change in credit spreads after inception would cause a reduction in the value of the assets backing the liability, with no corresponding reduction in the liability value. However, discounting at the earned rate would eliminate this mismatch. Disadvantages: o May reduce comparability between companies o Suppose that two companies sell products with identical product features, premiums and cash flows, but Company A invests in treasury bonds, while Company B invests in BBB- rated corporate bonds. Company B would use a higher discount rate than Company A, and therefore, Company B would report a lower present value of future cash flows. However, because the margin is calibrated to the initial premium, the two companies would likely report the same total liability (provided that they charge the same premium). o The earned rate is a characteristic of the assets, not the liability o The IASB staff and the majority of respondents to the DP have expressed the view that the liability measurement should reflect only the characteristics of the liability, independent of the assets backing the liability. o Could create perverse management incentives o In a “current value” framework, an increase in the riskiness of the asset portfolio would increase the discount rate and reduce the liabilities. Therefore a company could appear to improve its financial standing by taking on additional asset risk. Risk-free rate with adjustment for liquidity 6
  7. 7. Background: In IASB Agenda Paper 17D: Discounting, the IASB staff expresses the view that the discount rate for a liability should be based on the risk-free rate, plus a liquidity premium reflecting the liquidity characteristics of the liability. Advantages: o Reflects only the characteristics of the liability (not the assets backing the liability) o Uses an observable market value (the risk-free rate) as a starting point Disadvantages: o The liquidity premium generally is not a readily observable market value o To estimate the liquidity premium, we could start by looking at the difference in yields between highly liquid instruments (e.g. government bonds) and less liquid instruments (e.g. corporate bonds). However, the difference in yield is due to differences in both liquidity characteristics and credit quality. It may be difficult to determine precisely which portion of the yield differential is due to a liquidity premium and which portion is due to credit risk. o Could lead to diversity in practice, as different companies may assign different values to the liquidity premium for similar products o May lead to a loss at issue for many products o When pricing a product, insurers generally consider the yield that they expect to earn on the assets backing the liability. This yield is composed of a risk-free rate, a liquidity premium, and a credit spread. Excluding the credit spread from the discount rate may result in a discount rate that is significantly lower than the earned rate assumed in pricing. This may result in a loss at issue for many products, even those that are expected to be profitable. o May create “artificial volatility” in the income statement, even if assets and liabilities are properly matched o A change in credit spreads after inception would cause a reduction in the value of the assets backing the liability, with no corresponding reduction in the liability value. Other notes: o We feel that additional clarification is needed regarding the context in which the risk-free rate should be determined. For example suppose that a US-based company issues an insurance contract in Latin America. Should the discount rate be based on the US risk-free rate or the risk- free rate in the country in which the liability is issued? o Agenda Paper 17D’s description of liquidity premium is not fully consistent with the liquidity premium paper that Bill wrote for ACLI last year. IASB staff defines liquidity in the sense of a contractual demand feature. Bill defined liquidity as predictability, i.e. the property that allows an insurer to invest in illiquid assets to back a group of contracts. Observable market rates Background: The IASB staff noted that some observers support a prescribed discount rate. These prescribed rates would not necessarily point the practitioner to the exact rate or set of rates to use, but they would provide directional guidance. IASB staff provided the following examples from other accounting standards: o High quality corporate bonds (from IAS 19) o High quality fixed-income debt instruments (from FAS 87 and FAS 106) o Risk-free rate based on government bonds (from FAS 163) In addition, the CFO Forum’s Market Consistent Embedded Value principles currently prescribe the use of the swap yield curve. Advantages: 7
  8. 8. o Prescribing an observable market rate would tend to reduce diversity in practice. o Some alternatives (e.g. high-quality fixed income securities) would mitigate the perceived problem of an “artificial” loss at inception. o These alternatives would allow realization of some degree of asset credit risk in the discount rate while avoiding arguably anomalous results of other approaches, i.e. a reduced liability value resulting from an increase in asset risk or a decrease in the credit standing of the liability. o The use of swaps is justified on the assertion that, in many countries, the market for swaps is deeper, longer and more liquid than the market for government bonds. o The CFO Forum has, at various times, positioned the use of swaps as a proxy for risk-free rates and as containing a provision for liquidity spread (although the premium is really for credit risk). The Forum is currently exploring the addition of a liquidity premium. Disadvantages: o The prescribed rate or set of rates might not reflect the characteristics of the liability. o For instance, the credit risk in a set of bonds underlying an index may be inconsistent with the credit risk of the liability. o A prescribed standard might need to be supplemented by a more principles-based standard. o What if the prescribed market rate is not available or is deemed to be unreliable? o Even with a “prescribed” rate, there is still likely to be diversity in practice. o For instance, a high quality corporate bond rate could be based on numerous indices with different definitions of “high quality.” Other general comments Agenda Paper 17D does not address the question of whether or how the measurement of insurance liabilities should reflect non-performance risk. In order to perform a meaningful evaluation of the various discount rate alternatives, we need to evaluate the discount rate in its entirety, including any adjustment for non-performance risk. Without a discussion of non-performance risk, the discount rate discussion in Agenda Paper 17D is incomplete. 8
  9. 9. Appendix B ACLI Discount Rate Modeling Project – Fixed Deferred Annuities Prepared by Carrie Morton, Principal Financial Group 5/1/2009 Background  In 2008, the Deputies’ Subgroup on Accounting Issues completed a discount rate modeling project that illustrated the impact of discounting liability cash flows at the risk-free rate and the asset earned rate.  In a February 2009 letter to the IASB, the ACLI recommended that insurance liabilities use a discount rate equivalent to a highly rated corporate debt instrument.  This paper updates our prior analysis to reflect the ACLI’s discount rate recommendation.  The calculations are based on an exit value approach, with risk margins reflecting the cost of bearing the risk. The risk margins are not calibrated to the premium.  Please see Attachment 1 for a description of the assumptions and methodology. Results The following graph shows the annual pre-tax earnings for the first 10 years. Liabilities were calculated using the risk free rate, the earned rate, corporate AAA bond yields, and Corporate AA bond yields. IFRS Income for SPDA w/ 5-year Guarantee $10M initial premium, based on expected crediting rate 400,000 200,000 - Pre-tax earnings Risk-free (200,000) Earned Corp AAA Corp AA (400,000) (600,000) (800,000) 0 1 2 3 4 5 6 7 8 9 10 Year Observations Corporate AA bond yields Discounting at the AA bond yield produces a substantial gain at issue. The gain is significantly larger than the gain that results from discounting at the asset earned rate. The difference in results is primarily due to the slope of the yield curve. Because the product has a 5-year interest rate guarantee, I assumed that a typical insurer would invest the premium in 5-year bonds. Therefore, I set the asset earned rate equal to the 5-year corporate bond yield, based on a blend of A and BBB rated bonds. This resulted in a net earned rate of 5.4%. The 9
  10. 10. resulting discount rate was applied to all cash flows, regardless of duration – i.e. for cash flows occurring at time 10, the discount factor was (1 + net earned rate)-10. When discounting at corporate bond yields, I used the entire corporate yield curve. I began by obtaining yields for AA corporate bonds with maturities ranging from 2 to 25 years. The nominal yields for AA bonds ranged from 3.01% at 2 years to 7.18% at 25 years. I then converted the nominal yields to spot rates and constructed a yield curve. I used this yield curve to discount the liability cash flows. The discount rates vary, depending on the duration of the cash flow – i.e. for cash flows occurring at time 5, the discount factor is (1 + 5-year spot rate)-5, and for cash flows occurring at time 10, the discount factor is (1 + 10-year spot rate)-10. Thus, the cash flows occurring at later durations are discounted at a higher discount rate than the cash flows occurring at earlier durations. At later durations, the AA discount rates exceed the asset earned rate of 5.4%, despite the fact that the earned rate is based on a slightly lower quality bond (a blend of A and BBB). This is because the earned rate was based on a 5-year yield, while the AA rates reflect the entire yield curve. For example, the 10-year AA yield is greater than the 5-year A yield. Therefore, discounting at the AA yield curve resulted in a lower initial reserve – and hence a larger gain at issue – than discounting at the earned rate. The ACLI believes that high-quality (e.g. AA) corporate bond yields provide a reasonable basis for setting the discount rate for insurance liabilities. However, due to the shape of the yield curve, this approach may produce unrealistically high discount rates for cash flows occurring at later durations. An insurer selling an SPDA with a 5-year guarantee would likely invest the premium in 5-year bonds, and then continue to reinvest in 5-year bonds after the first bonds mature. Thus, the 10-year AA spot rate (which is used to discount cash flows occurring at time 10) would likely exceed the rate that the insurer would expect to earn on its invested assets. This duration mismatch leads to an understatement of the reserve and a gain at issue. However, we could eliminate the gain at issue by calibrating the margin to the premium. Corporate AAA bond yields The Corporate AAA bond yields were only slightly higher than the corresponding risk-free rates. Discounting at the AAA bond yield produces a loss at issue, although the loss is slightly smaller than the loss that results from discounting at the risk-free rate. The discounting methodology for AAA bonds was the same as the methodology used for AA bonds. Thus, when discounting at AAA rates, we still encounter the same duration mismatch that was described above (i.e. duration 10 cash flows are discounted at the 10-year AAA spot rate, when in reality, the insurer would likely invest in shorter assets). However, the AAA discount rate produced a loss at issue, due to the lower level of the AAA yield curve. For example, the 10-year AAA yield is still less than the 5-year A yield. Thus, this approach overstates the reserve, because the discount rates are considerably lower than the expected asset earned rate. Interaction of discount rates and risk margins In Agenda Paper 5A, the IASB describes four possible approaches for setting risk margins for long- duration contracts: (1) Current exit value as proposed in the Insurance Contracts Discussion Paper (2) Current fulfillment value including a risk margin reflecting the cost of bearing risk (the IASB staff has eliminated this method from consideration) (3) Current fulfillment value as in candidate (2) plus an additional separate margin, calibrated at inception to the premium (4) Current fulfillment value including a single margin calibrated at inception to the premium (similar to candidate (3), but with one overall margin, rather than two separate margins) 10
  11. 11. The calculations in the graph above are based on approach (1). The following paragraphs describe how the various discount rates would work with each of the margin approaches. Corporate AA bond yields Under approach (1), the reserve is equal to the present value of cash flows, plus a risk margin. As discussed above, this approach produces a substantial gain at issue. The ACLI believes that it is inappropriate to recognize a gain at issue. Under approach (3), we would start with the reserve from approach (1), but we would then add a residual margin that is calibrated to the premium. Under approach (4), we would simply calculate a single margin that is calibrated to the premium (rather than calculating a risk margin and then adding a separate residual margin that is calibrated to the premium). Under both approach (3) and approach (4), there is no gain at issue. We believe that this is a more appropriate result. Corporate AAA bond yields As noted above, discounting at the AAA bond yield produces a loss at issue under approach (1). Under approach (3), we would start with the reserve from approach (1) and add a margin that is calibrated to the premium. In this case, the initial premium is less than the sum of the initial reserve from approach (1) and the acquisition expenses. Therefore, in order to break even at issue, the residual margin would have to be negative. However, negative margins are not allowed, so the residual margin would be set equal to 0, and a loss would be recognized at issue. Under approach (4), we would calculate a single margin that is calibrated to the premium. However, we would still need a negative margin in order to break even at issue. Because negative margins are not allowed, we would once again recognize a loss at issue. Risk-free rate The results for the risk-free rate are similar to the results for the AAA bond yields, although the risk- free rate produces a slightly larger loss at issue. Because negative margins are not allowed, all of the margin approaches would produce a loss at issue. Earned rate The results for the earned rate are similar to the results for the AA bond yields, although the earned rate produces a much smaller gain at issue under approach (1). The gain at issue would be eliminated under approach (3) and approach (4). 11

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