瑞士再保險系列培訓課件-精算及利潤測試 profit testing

1、Introduction to Profit Testing,Intro Profit TestingKenneth LoActuarial Associate,,,3 Objectives,Illustrate the differences of profit testing (by cash flow methods) over traditional methodsGive practical examples of ho

2、w profit testing can be used for pricingOutline some useful techniques, based on the cash flow approach, which will enable us to better understand the business that we write,Intro to Profit TestingKenneth LoActuarial

3、Associate,Agenda,Profit Testing IIntroductionTechniquesPremium calculationProfit measurement,Intro to Profit TestingKenneth LoActuarial Associate,Profit Testing II Sensitivities testing Surrenders and lapses Ad

4、ding a rider Model office New business projections,Traditional method,Developed before computers were widely availableUse tables of annuity (äx) and assurance (Ax) factors, and commutation functions (Cx, Dx, Nx,

5、Mx, Rx, etc)Determining premiums involved solving an equation like:whereP, S = premium, sum insuredI , m =initial, maintenance expenses,Intro to Profit TestingKenneth LoActuarial Associate,Problems wit

6、h traditional method,Assumptions are inflexible (e.g. interest rate cannot be varied over time)Difficult to allow for complex benefits (e.g. return of premiums on death)Difficult to allow for more than one decrement(e

7、.g. no allowance for profits and losses on surrenders, difficult to include rider benefits),Intro to Profit TestingKenneth LoActuarial Associate,Profit testing - cash flow methods (1),Make use of computers for complex

8、calculationsMore complicated models are possible allowing us to overcome these disadvantagesMore intuitive and easier to understand for non-actuaries,Intro to Profit TestingKenneth LoActuarial Associate,Profit testin

9、g - cash flow methods (2),Can incorporate assumptions about:surrenders and lapses ?riders and additional benefits ?valuation basis and method ?new business ?profitability targets ?bonuses and distribution of surplu

10、s ?reinsurance ?,Intro to Profit TestingKenneth LoActuarial Associate,Profit testing - cash flow methods (3),The basic idea:Set up a column for every cash flow relevant to the policy, and some columns for intermediat

11、e calculations if requiredFor each column, multiply the possible cash flow by the probability of that cash flow occurring to get an expected cash flowTest the cash flows to arrive at the desire profit,Intro to Profit T

12、estingKenneth LoActuarial Associate,Life product’s control cycle,Intro to Profit TestingKenneth LoActuarial Associate,Profit testing - applications,Profit testing using a cash flow approach is used to manage the life

13、 products such as:Endowment InsuranceTerm InsuranceIt is very easy to adapt cash flow pricing techniques to other products (e.g. annuities, unit-linked, etc),Intro to Profit TestingKenneth LoActuarial Associate,Prof

14、it testing - techniques (1/2),Premium calculations premium rating adding expenses reserves & surplusProfit measurement methods applications,Intro to Profit TestingKenneth LoActuarial Associate,A Simple Exampl

15、e,10 year endowment policy45 year-old malenon-profitSum Insured = RMB 10,000Mortality = A67/70 Ult4% InterestNo expenses,Intro to Profit TestingKenneth LoActuarial Associate,Premium Rating (1),Traditional way of

16、setting premium:Solve for P (premium) by looking up tablesPremium = RMB 819.35,Intro to Profit TestingKenneth LoActuarial Associate,Premium Rating (2),The Cash Flow Pricing ApproachSet up columns of cash flows(Pr

17、emiums, Death & Maturity Claims, Interest, Accumulated Cash Flow)Guess a reasonable premiumUse “Goal Seek” or “Solver” to find the premium which makes the accumulated cash flow equal to ZERO at the end of the polic

18、y term,Intro to Profit TestingKenneth LoActuarial Associate,Premium Rating (3),The results:Annual premium of RMB 819 will give an accumulated Cash Flow of ‘0’ at the end of 10 years,Intro to Profit TestingKenneth Lo

19、Actuarial Associate,Adding Expenses (1),Initial Expenses: RMB 80 per policyMaintenance Expenses:RMB 10 per policy (including 1st year)New Equation:P (Premium) = RMB 838.98,Intro to Profit TestingKenneth LoActuaria

20、l Associate,,Adding Expenses (2),The results: Annual premium of RMB 839 will give an accumulated Cash Flow of ‘0’ at the end of 10 years, after allowing for expenses,Reserving (1),The Traditional Method implicitly assum

21、es that: Reserving Assumptions = Pricing Assumptions(Reserves = Accumulated Cash Flow)What if our reserving basis is different to (more conservative than) our pricing basis?,Intro to Profit TestingKenneth LoA

22、ctuarial Associate,Reserving (2),What happens now?We no longer have an Accumulated Cash Flow - instead, we have ReservesWe need to set up Reserves at each valuation date (assume this happens just before a policy annive

23、rsary) for the expected number of policies at that dateWe need to adjust the cash flows to hold the correct reserve at each valuation date - we may have insufficient or excess cash,Intro to Profit TestingKenneth LoAct

24、uarial Associate,The Concept of Transfers/Surplus (1),The Transfer (Surplus) is the remainder of the cash flow after the reserves have been set up for the yearIn General:Transfer (surplus) =+ Cash Inflows (premiums,

25、 interest, etc) - Cash Outflows (expenses, claims, etc)+Previous Year’s Reserves - This Year’s Reserves,Intro to Profit TestingKenneth LoActuarial Associate,The Concept of Transfers/Surplus (2),Back to our example

26、:If Reserves are set equal to the Accumulated Cash Flow (i.e. reserving basis = pricing basis)…A67/70 mortality4% interestRMB 80 Zillmer adjustment for initial expenses,Intro to Profit TestingKenneth LoActua

27、rial Associate,,The Concept of Transfers/Surplus (3),The results: All transfers are equal to zero (i.e. nothing is left over after the reserves are set up),The Concept of Transfers/Surplus (4),Now we make our reser

28、ving basis more conservative than our pricing basis:A67/70 mortality (same as pricing basis)3% interest (instead of 4%)RMB 40 Zillmer adjustment for initial expenses (instead of RMB 80),Intro to Profit TestingKenneth

29、 LoActuarial Associate,,The Concept of Transfers/Surplus (5),The results:Our pattern of transfers changes to: (1) negative at the start (2) positive at the end,The Concept of Transfers/Surplus (6),Why??O

30、ur reserves are conservativeOur cash flows are inadequate to set up the reserves at the beginning - we need to inject capital (negative transfers)We recoup this capital over the term of the policy as we expect experien

31、ce to be better than the reserving basis (positive transfers),Intro to Profit TestingKenneth LoActuarial Associate,The Profit Signature (1),The pattern or shape of transfers over time - showing the amount of capital in

32、vested and its recovery over time,Intro to Profit TestingKenneth LoActuarial Associate,The Profit Signature (2),Ideally, the valuation basis should result in the following pattern of transfersabsolute amount not too l

33、arge(reserving basis not too strong)negative then positiveshould not turn negative in later years(reserving basis not too weak),Intro to Profit TestingKenneth LoActuarial Associate,Why calculate Transfers?,Now that

34、 we have injections and releases of capital (transfers), what do we use them for?ANSWER: Measuring Profit !!!(NB: these are expected profits),Intro to Profit TestingKenneth LoActuarial Associate,Measuring Profit (1),

35、How did we measure profit using traditional actuarial methods?ANSWER: We didn’tThe traditional actuarial approach was to build in some implicit conservatism in the premium rates so that we expected a profitExpected pr

36、ofit was never quantified !!!,Intro to Profit TestingKenneth LoActuarial Associate,Measuring Profit (2),Ideally, a measure of profit should considerall cash flowstime value of money (i.e. interest)tax,Intro to Profi

37、t TestingKenneth LoActuarial Associate,Measuring Profit (3),Measures of ProfitPayback PeriodInternal Rate of ReturnNet Present Value,Intro to Profit TestingKenneth LoActuarial Associate,Payback Period,Expected num

38、ber of years to recover original cash investmentProblemsignores cash flows after the payback periodignores the rate of return required by shareholdersNot a good measure of profitability,Intro to Profit TestingKennet

39、h LoActuarial Associate,Internal Rate of Return (IRR),The discount rate which makes the expected net present value of transfers equal to zeroProblemsmultiple solutions possiblereinvestment assumption,Intro to Profit

40、 TestingKenneth LoActuarial Associate,Net Present Value (NPV) - (1),Which discount rate?rate earned on investmentsshareholders’ required rate (risk rate)Transfers involve the use of shareholder capital - therefore w

41、e should use the shareholders’ required rate of return,Intro to Profit TestingKenneth LoActuarial Associate,Net Present Value (NPV) - (2),The expected NPV (discounting at either the earned rate or the required sharehol

42、der rate) is sometimes expressed as a percentage of premium (or present value of premiums) for scaling purposesi.e. the NPV per unit of premium,Intro to Profit TestingKenneth LoActuarial Associate,What does it all m

43、ean?,The IRR can be thought of as the return expected to be earned on the policyIf the IRR is greater than the risk rate required by shareholders, then shareholders should be happy,Intro to Profit TestingKenneth LoAct

44、uarial Associate,The NPV (discounted at the shareholder risk rate) can be thought of as the expected contribution to shareholder wealthIf the NPV is greater than zero, shareholders should be happy,,Applying profit measu

45、rement (1),Back to our example:NPV @ earned rate = 0.00NPV @ risk rate =- 34.11IRR = 4% (assuming earned rate= 4% , shareholders’ risk rate= 10%),,Applying profit measurem

46、ent (2),The results: Premium RMB 838.98 -> RMB 844.39We need to increase the premium to ensure that we are earning the rate our shareholders require, I.e. 10%,The profit signatures changes to be less negative

47、at the start, and more positive at the end,Applying profit measurement (3),Intro to Profit TestingKenneth LoActuarial Associate,Part I - Summary,Intro to Profit TestingKenneth LoActuarial Associate,A basic cash flow

48、model for profit testing consists of:columns of expected cash flows and intermediate calculationsexpected cash flows are derived by multiplying a possible cash flow (e.g. expenses) by the probability that the cash flow

49、 occurstransfers - expected capital requirements and releasesmeasures of profitability,End of Part I,Any questions?,Intro to Profit TestingKenneth LoActuarial Associate,Introduction to Profit Testing,,,Intro to Profi

50、t TestingKenneth LoActuarial Associate,Profit testing - techniques (2/2),Sensitivity TestingSurrender & LapsesAdding a RiderModel OfficeNew Business Projections and Capital RequirementsAdditional Features,I

51、ntro to Profit TestingKenneth LoActuarial Associate,Change one variable at a time to determine the effect on profitabilityDetermine the effect on profitability if assumptions do not turn out as expectedDetermine whic

52、h assumptions are the most crucialUnderstand your product and the risks,Sensitivity Testing,Intro to Profit TestingKenneth LoActuarial Associate,Similar to sensitivity analysis except that more than one variable is ch

53、anged at a timeExamine a set of reasonably realistic scenarios and determine the effect on profitability (e.g. a worse case scenario)In reality, some variables are linked (e.g. inflation and interest rates, interest ra

54、tes and lapses, etc),Scenario Testing,Intro to Profit TestingKenneth LoActuarial Associate,Look at two different productsEndowment InsuranceTerm Insurance (no maturity benefit)Same assumptions as previous examplePr

55、emiums have been set to earn the shareholders required return on capital,Sensitivity Testing Example (1),Intro to Profit TestingKenneth LoActuarial Associate,,Sensitivity Testing Example (2),Results for Endowment Insur

56、ance NPV @ earned rate= 44.95 NPV @ risk rate = 0.00 IRR = 10%,,Sensitivity Testing Example (3),Results for Term Insurance NPV @ earned rate= 10.12

57、 NPV @ risk rate= 0.00 IRR= 10%,Sensitivity Testing Example (4),Intro to Profit TestingKenneth LoActuarial Associate,Sensitivity TestsIncrease mortality by 5%Decrease interes

58、t earning rate by 0.25%(25 basis points),Increase Mortality by 5%,EndowmentNPV @ earned rate= RMB 37.15 (RMB44.95)NPV @ risk rate= -$6.20 (RMB0.00)IRR= 8.89% (10.00%),Intro to Profit TestingKenneth LoActuarial A

59、ssociate,TermNPV @ earned rate= -$8.06 (RMB10.12)NPV @ risk rate= -$13.09 (RMB0.00)IRR= -1.71% (9.99%),Decrease Interest Rate by 0.25%,EndowmentNPV @ earned rate= -$47.75 (RMB44.95)NPV @ risk rate= -$64.41 (RMB

60、0.00)IRR= -3.68% (10.00%),Intro to Profit TestingKenneth LoActuarial Associate,TermNPV @ earned rate= $9.29 (RMB10.12)NPV @ risk rate= -$0.96 (RMB0.00)IRR= 9.26% (10.00%),Sensitivity Test Results (1),Intro to P

61、rofit TestingKenneth LoActuarial Associate,TermSensitive to changes in mortality, but not to changes in interest ratesIt is important that you get your mortality assumptions rightUnderwriting is very importantIt is

62、 not so important where the money is invested,Sensitivity Test Results (2),Intro to Profit TestingKenneth LoActuarial Associate,EndowmentEndowment policies are sensitive to changes in interest rates, but not changes i

63、n mortalityMortality assumptions are not so importantIt is very important where the money is invested,Surrenders and Lapses (1),Intro to Profit TestingKenneth LoActuarial Associate,How were surrenders and lapses trea

64、ted under traditional actuarial methods?ANSWER: They were ignored.The traditional actuarial approach was to have surrender values which were less than the policy value so that a profit was made on surrenderThe effect

65、was never quantified,Surrenders and Lapses (2),Intro to Profit TestingKenneth LoActuarial Associate,What needs to be addedsurrender value scale (possible cash flows)surrender / lapse rates (sx)double decrement table

66、 (probabilities)(aq)x = qx * (1 - 0.5 sx)(as)x = sx * (1 - 0.5 qx)(al)x+1 = (al)x * (1 - sx) * (1 - qx)surrender claims become an extra cash flow item for calculating interest and transfers,Surrenders and Lapses (3),

67、Intro to Profit TestingKenneth LoActuarial Associate,Set the surrender basis equal (approximately) to the pricing basisA67/70 mortality4% interestRMB 80 Zillmer adjustment for initial expensesWhy only approximately

68、?the pricing basis makes no allowance for surrenders,,Surrenders and Lapses (4),The results (with surrender rate set @ 5% p.a.): NPV @ earned rate= 40.06 NPV @ risk rate = 3.74