1、On the Calculation of Embedded Value Summary In the past in Switzerland the performance of life insurance companies was judged primarily, both within the company and externally, on the basis of its published, statutory results. With the increased focus on earnings on the part of management and share
2、holders, and with the growing demand on all sides for transparency and detailed information, a more appropriate analysis and assessment of an insurance companys performance has become necessary. Such an examination should look closely at the companys products and their profitability. It should also
3、incorporate the so-called “embedded value” of a company. This figure represents the value of the company, taking into account its current business (i.e. without goodwill or future new production) under current expectations, and among other things, also serves stock market analysts as an additional e
4、lement of information for the evaluation and comparison of different insurance companies. Since such figures are highly dependent on the specific model used and the overall conditions assumed, a subcommission has been set up by the Board of the SVV with the aim of drawing up specific guidelines for
5、the calculation of embedded values to facilitate improved comparison of the results of different companies. The present document sets out requirements for a model for the calculation of embedded values. At the same time, recommendations are offered concerning the setting of parameters. Companies wan
6、ting to publish their embedded value figure can refer to these guidelines. Especially in the case of deviations from these guidelines, a great need exists to explain the differing methods by which the parameters were fixed as well as the individual procedures followed. Finally, it is also the aim of
7、 this document to propose useful standards, which should be taken into account in the case of a public presentation (or an internal company publication). Table of Contents 1. INTRODUCTION . 3 1.1 SUBDIVISION OF EMBEDDED VALUE 4 1.2 PRESENT VALUE OF FUTURE PROFITS 4 2. ASSUMPTIONS INFLUENCING THE PVF
8、P AND THEIR DETERMINATION . 6 2.1 INTRODUCTION. 6 2.2 RISK DISCOUNT RATE . 7 2.3 INVESTMENT RETURNS. 7 2.3.1 Basic principles 7 2.3.2 Long term projected yields . 9 2.3.3 Yields in the first calculation year12 2.3.4 Transition to long-term projected yields 13 2.3.5 Possible refinement with the bond
9、yield . 13 2.4 BONUS PARTICIPATION 14 2.5 INFLATION 14 2.6 SALARY INFLATION 14 2.7 TAX 14 2.8 EXPERIENCED MORTALITY AND INVALIDITY . 14 2.9 SURRENDERS AND LAPSES . 152 2.10 ACTUAL EXPENSES 15 2.11 NEW BUSINESS. 15 2.12 REINSURANCE 15 2.13 OTHER REQUIRED RESERVES 15 2.14 FREE BONUS RESERVE . 16 2.15
10、CALCULATION OF THE PVFP FOR GROUP INSURANCE . 16 3. DETERMINATION OF ADJUSTED NET ASSET VALUE 16 3.1 EQUITY (STATUTORY EQUITY). 16 3.2 ADJUSTMENTS TO CAPITAL ASSETS AND APPORTIONING OF HIDDEN RESERVES 16 3.3 COSTS FOR TIED CAPITAL . 17 4 PUBLICATION 17 A EXAMPLE . 17 A.1 CALCULATION OF THE PVFP. 17
11、A.2 SENSITIVITY ANALYSES. 20 B OPEN POINTS 213 1. Introduction The Embedded Value (EV) and its development over several years is useful in assessing the performance of a life insurance company and can be divided into two parts. On one side, there is the present value of future profit earnings, broug
12、ht in from the companys own ongoing insurance business. In order to determine this quantity, which in the English- speaking world is called PVFP (present value of future profits), model calculations are necessary. In addition to the PVFP, embedded value is also composed of the funds belonging to the
13、 shareholder which were accumulated in the past through the companys capital resources and undistributed profits, as well as from that part of the hidden reserves (i.e. the difference between the market value and the book value of the investments) which can be assigned to the shareholder. In the Ang
14、lo-Saxon world this shareholder capital is known as “adjusted net asset value” (ANAV) and is applied as follows: EV = PVFP + ANAV The ANAV can consist of free (unrestricted) capital or capital tied up in the run-off of the business, after consideration of the taxes to be paid by the company. The com
15、pany could reimburse the free capital immediately to the shareholder; however in the event of non-reimbursement, the capital remains freely at the companys disposal for the financing of its long-term business activity. (It just has to make sure it gains a corresponding risk- adjusted return on its c
16、apital investment ). With embedded value the purpose is to present the financial worth of the existing portfolio: thus no future new business is taken into consideration. It is not concerned with a market valuation of the entire enterprise (i.e. appraisal value = EV + goodwill). Underlying the calcu
17、lation of embedded value is a tapering off of the reserves (run-off assumption). However, as a basis for establishing the assumptions to be followed in determining a projection of future earnings (according to statutory principles), the “going concern” principle is used: i.e. a continuation of the b
18、usiness activity is stipulated. Thus, in particular, cost projections are determined on the basis of the current infrastructure. As a result, the embedded value will be strongly influenced by the assumptions used in the calculation. The factors assumed, and especially changes to them from year to ye
19、ar, are to be specified in any internal presentation of embedded values and, where applicable, in external publications. The calculation of the present value of future results carried out using the risk discount rate corresponds to the present value of future earnings minus the present value of futu
20、re expenditures, in which all projection assumptions are to be made as realistically as possible. That is, the projections should be neither knowingly over- nor underestimated. As a rule the projections contain no safety margin, and in the Anglo-Saxon world are termed “best estimate”. In principle,
21、the following points should be taken into account in the calculation of the embedded value insofar as they are significant and influence the future, projected results : explicitly formulated legal supervisory conditions, for example legislative texts, ordinances, decrees, etc. implicitly applied sup
22、ervisory rules (practices of the authorities); statutes of the life insurance company; applied auditing guidelines;4 business plans and business practice; market rules, customary practices. Included under the above-mentioned points are also the surplus to policyholders (promised or projected end ben
23、efits), as well as the procedures used in determining the amount and crediting of the bonus participation (business plan). All of these aspects, which are generated from the existing portfolio, are to be taken into account in the embedded value model. In the same way, actuaries proceed according to
24、a certain system in constituting reserves at the year-end closure and build up specific reinforcements (longevity reserves, lump sum reserves, fluctuation reserves, etc.) They tie up a certain capital in the future, which is only released later in the projections and only then flows back into the re
25、sults and thus today is not available at the nominal value. The tied capital achieves the market interest rate gained by the company in the form of a return on investment. Because the risk discount rate as a rule is higher than the market interest rate, one can also say that todays capital will be r
26、educed by those opportunity costs which are caused by the so-called “lock-in” effect. Thus the goal of this model is to model the business policy and make it transparent. 1.1 Subdivision of Embedded Value Embedded value is divided into the PVFP and the ANAV. By the PVFP we mean the present value of
27、future profits. The ANAV is calculated starting from the following two values: “equity” (Statutory Capital) “adjustments” (adjustments to Statutory Capital) by means of: ANAV = equity + adjustments The adjustments comprise among other things: hidden reserves, in particular the unrealised gains attri
28、buted to shareholders in the capital investments, and reserves which are tied up for use in the run-off of the business, but which are attributed to the shareholder, etc. 1.2 Present Value of Future Profits This section provides an introduction to the topic. Here it is necessary to distinguish betwe
29、en the two principal components of embedded value. The PVFP involves a figure derived from long-term model calculations. In contrast, the ANAV is a snapshot at a particular point in time of the EV calculation.5 The idea behind the calculation of the PVFP, is to adopt the standpoint of the shareholde
30、r and to calculate the expected statutory profit or loss for each policy year. Time t t + t tV i (t) + P Inflow: Premium and Reserves t -a i Pre (t) Outflow: Annuity Payments t Costs Outflow: Expenses t Others t + t -V j (t+ t) Outflow: Reserves t + t + Capital yield Income: Investments t + t -a ij
31、Post (t) Outflow: Insurance Benefits t + t Bonuses Outflow: Bonuses t + t Others Table 1: Payment streams for calculation of profits in a policy year In addition, effects should be taken into account which influence profit or loss. From this statement it becomes clear that in calculating the PVFP, a
32、 model adapted to the nature of the problem should be applied. This model is first and foremost dependent on the products examined. Moreover it should reflect a managerial approach as well as the apportioning of the profits between the shareholder and the policyholder. In deriving a model for the PV
33、FP, one adopts the standpoint of the insurance company and looks at what occurs in the course of a policy year. At the beginning of the year (or of the time period being considered) the insurance company receives the actuarial reserves and the premiums. From this money it has to finance expenditures
34、 for the insurance operations and payments related to this period. At the end of the year it can add the profit to its capital, but it has to reimburse the actuarial reserves. Table 1 illustrates this process. It should be noted here that Table 1 presents this process in discrete time, and that the
35、granularity in the time axis with one year is very large. The corresponding formulae naturally also apply to shorter time intervals. Many projection tools use an interval of one month. It should furthermore be pointed out here that the benefits, premiums and actuarial reserves take into account surp
36、luses yielded in the past. Now the profit or loss has to be calculated. We are designating it here with PL t (I,j), in which this figure can be dependent on the additional attributes i,j (change of conditions from i to j). Since the PVFP shows the cash value of these payment streams, it is necessary
37、 in the next step to define the discount factor v = 1/(1+ rdr t) for the policy year (t, t + 1). The discount figure is calculated with the help of the risk discount rate (rdr t ). Now it is possible to calculate the future profits as follows: = = + = 0 0 0 ) , ( ) , ( ) , ( 1 , 0 , t t t tij t t t
38、t t j i PL j i p i i p v PVFP For normal capital insurances it is usually sufficient to consider the three conditions: alive, surrendered and dead. For the PVFP, this gives the following result h:6 + + = + + + + = = + + ) ( ) ( ) ( ) 1 ( ) 1 ( 0 0 0 0 0 0 0 0 surrender PL s death PL q ip survivorsh
39、PL s q s q v PVFP t t x t t x t t x t x t t t t x x in which q denotes mortality and s the probability of surrender. (Cf. Annex 1). 2. Assumptions influencing the PVFP and their determination 2.1 Introduction In this section guidelines will be given for determining the parameters which influence the
40、 PVFP. In this connection the following assumptions will be considered: Risk Discount Rate (rdr); Investment Returns; Bonus Participation; Inflation; Salary Inflation; Experienced Mortality and Morbidity; Tax; Surrenders and Lapses (repurchase, release or exemption of premiums for contracts, withdra
41、wal from Group Insurance); Actual Expenses; New entries into Group Insurance; Reinsurance; Other Required Reserves; Free Bonus Reserve. In general it should be emphasized that the parameters should not contradict either the overall practice of the company nor the general financial requirements and g
42、uidelines. In particular, the previous as well as future approach of management should be modeled. Moreover mutual consistency among the parameters is essential. This means that investment returns should not diverge from the projected earnings for the bonus participation. Since the PVFP reacts very
43、sensitively to certain parameters, these should be determined with the necessary prudence. This means in particular that the influence of different parameters on7 the model must be tested and that those parameters which especially influence the PVFP are to be fixed with particular caution. (See also
44、 section A.2). In establishing many of the above parameters reference is made to the planning of the company. Since much of such planning has a time horizon of perhaps 5 years, it is necessary to reset the parameters after this amount of time. In doing so, the average values of the past should be ap
45、plied for the corresponding quantities. This allows the models to be continued consistently for periods of time beyond the planning horizon. In the case of a company operating internationally, the rules for the determination of embedded value must be issued centrally and consistently (e.g. derivatio
46、n of the rdr, investment returns, solvency margin, costs). The coverage of the solvency margin is to be established by the company. Since the parameters for the calculation of the embedded value change with time, the newly calculated embedded value should also be calculated using the old parameters.
47、 The change in the embedded value coming from the change of parameters will thereby be quantified and analyzed. Through use of a compression instrument (e.g. Model Office) the model points should be chosen in such a way that any errors introduced through the grouping of the real data remain relative
48、ly small for the results to be published. In the following discussion we move from embedded value to taxes. 2.2 Risk discount rate The risk discount rate defines the yield which is expected by investors for investments in the life insurance company. It is determined according to risk-free yield rate
49、s on investment (e.g. 10-year swap) plus the risk premium for investment in the given insurance company. (The idea of fixing the risk discount rate is based in the capital asset pricing model: the investor expects a return on investment corresponding to that from a direct investment involving a similar level of risk.) The risk premium is determined on the basis of the structure of the company and the risks which the company has entered into. (Example: a risk-fr
