Sources of Earnings: Tools for Managing Your LTC Business

1. Sources of Earnings:Tools for Managing Your LTC Business John K. Heins, FSA, MAAA PolySystems Robert J. LaLonde, FSA Insight Decision Solutions, Inc Mark A. Walker, FSA, MAAA Genworth Financial

2. The Way It Was Meant To Be

3. Earnings Include… • Percent of Premium • Plus Gain on Interest • Plus Gain on Persistency • Plus Gain on Claim Experience • Plus Expense Gain • Plus Interest on Surplus (Capital,Equity)

4. Sample Quarterly Statement

5. Profit from Premium • To quantify, you must have an idea of the valuation net premium(s) • Should be able to obtain once a product is priced • Best obtained from valuation system – the more granular the better

6. Gain From Interest (iActual – iAssumed) x Net Liability • Net liability for GAAP is all reserves less DAC (or VOBA for PGAAP blocks) • Have to know assumptions, actual experience, and the exposure (net liability)

7. Gain From Persistency (qActual – qAssumed) x Net Liability • q includes all forms of termination • Net liability for GAAP is all reserves less DAC (or VOBA for PGAAP blocks) • Gain could be split into pieces • Have to know assumptions, actual experience, and the exposure

8. Gain on Claim Experience Tabular Cost of Claims Less Incurred Claims • If you don’t know about tabular cost, it is not readily available • If you know about tabular cost, it is probably not readily available

9. Paid Claims + Chg in Reserves – Interest = (PaidCp + PaidPp + PaidOld ) + (CpV1 + PpV1 + OldV1 - V0 ) + (CpIBNR1 + OldIBNR1 - IBNR0 ) – (IntIBNR + IntV ) = (PaidCp + CpV1 + CpIBNR1 )(1) – (IBNR0 + IntIBNR - PaidPp - PpV1 - OldIBNR1)(2) – (V0 + IntV - PaidOld - OldV1 )(3) • Estimated total claims for current period • IBNR gain • Case Reserve gain

10. If you don’t know where to begin… …start with DAC (fewer moving parts other than deferrals) DACReported = (pActual/pAssumed) x DACSched. The Scheduled DAC is the amortized amount from the prior period if all assumptions are met

11. DACReported x pAssumed / pActual = DACPrevious x (1+ i) - NPDAC x (1+ i)(1/2) You must know interest and net premium. Actual persistency (or termination) can be measured from premium, policy count, or other units in force. Assumed terminations are the unknown and will be used for…

12. Reserves VReported x pAssumed / pActual = VPrevious x (1 + i) - (NPBenefit – Tabular Cost) x (1 + i)(1/2) You must know interest and net premium. Tabular Cost is the unknown.

13. Earnings by Source

14. The more granular the better • At the product level • At the issue year level • Formulae may be refined • The more the assumptions are known and the more accurate actual is, the more accurate the calculations

15. Sources of Earnings:Tools for Managing Your LTC Business John K. Heins, FSA, MAAA PolySystems, Inc.

16. Sources of Earnings:Tools for Managing Your LTC Business The SOE Calculation

17. The SOE Calculation Recall that Source of Earnings is all about the increase in reserves.

18. Let’s start with a traditional Fackler reserve formula: V(t+1) = [ (V(t) + P(t)) * (1 + i(t)) - C(t) ]  [ 1 - qd(t) -qw(t) ]

19. Move the survivorship factor to the other side: V(t+1) = [ (V(t) + P(t)) * (1 + i(t)) - C(t) ]  [ 1 - qd(t) -qw(t) ]

20. Move the survivorship factor to the other side: V(t+1) * [ 1 - qd(t) -qw(t) ] = [ (V(t) + P(t)) * (1 + i(t)) - C(t) ]

21. Distribute the components of the survivorship factor V(t+1) – [V(t+1) * qd(t)] – [V(t+1) * qw(t)] = [ (V(t) + P(t)) * (1 + i(t)) - C(t) ]

22. Then isolate V(t+1) V(t+1) = [ (V(t) + P(t)) * (1 + i(t)) - C(t) ] + [V(t+1) * qd(t)] + [V(t+1) * qw(t)]

23. Multiply through by lives inforce – let’s call this equation #1 V(t+1) * l(t) = l(t) * [V(t) + P(t)) * (1 + i(t)] - C(t) * l(t) + V(t+1) * qd(t) * l(t) + V(t+1) * qw(t) * l(t)

24. Now . . . V(t+1) * l(t+1) = V(t+1) * l(t+1) + V(t+1) * [ l(t) - l(t) ]

25. And, rearranging a bit . . . V(t+1) * l(t+1) = V(t+1) * l(t) - V(t+1) * [ l(t) - l(t+1) ]

26. And V(t+1) * l(t+1) = V(t+1) * l(t) - V(t+1) * [ qd(t) + qw(t) ]

27. Now it gets just a little tricky V(t+1) * l(t+1) = V(t+1) * l(t) - V(t+1) * [ qd(t) + qw(t) ]

28. We replace the valuation lapse and mortality with actual V(t+1) * l(t+1) = V(t+1) * l(t) - V(t+1) * [ qda(t) + qwa(t) ]

29. Replace the valuation lapse and mortality with actual – let’s call this equation #2 V(t+1) * l(t+1) = V(t+1) * l(t) - V(t+1)* [ qda(t) + qwa(t) ]

30. Now we insert equation #1 into equation #2 Equation #1 : V(t+1) * l(t) = l(t) * [V(t) + P(t)] * [1 + i(t)] - [C(t) * l(t)] + [V(t+1) * qd(t) * l(t)] + V(t+1) * qw(t) * l(t) Equation #2 : V(t+1) * l(t+1) = V(t+1) * l(t) - V(t+1)* [qda(t) + qwa(t)]

31. Now we insert equation #1 into equation #2 V(t+1) * l(t+1) = l(t) * ((V(t) + P(t)) * (1 + i(t)) - l(t) * C(t) + l(t) * V(t+1) * [ qw(t) - qwa(t) ] + l(t) * V(t+1) * [ qd(t) - qda(t) ]

32. So, the formula for the actual change in reserves at time t is: DELTAV(t) = V(t+1) * l(t+1) - V(t) * l(t) = l(t) * P(t) - l(t) * C(t) + l(t) * i(t) * (V(t)+P(t)) + l(t) * V(t+1) * [ qw(t) - qwa(t) ] + l(t) * V(t+1) * [ qd(t) - qda(t) ]

33. Let’s call this equation #3 DELTAV(t) = V(t+1) * l(t+1) - V(t) * l(t) = l(t) * P(t) - l(t) * C(t) + l(t) * i(t) * (V(t)+P(t)) + l(t) * V(t+1) * [ qw(t) - qwa(t) ] + l(t) * V(t+1) * [ qd(t) - qda(t) ]

34. Now we can write an expression for earnings as: E(t) = l(t) * G(t) - l(t) * CA(t) + ia(t) * l(t) * (V(t)+P(t)) - DELTAV(t) Where: CA(t) = actual claim rate at t, and ia(t) = actual interest rate at t

35. Let’s call this equation #4 E(t) = l(t) * G(t) - l(t) * CA(t) + ia(t) * l(t) * (V(t)+P(t)) - DELTAV(t) Where: CA(t) = actual claim rate at t, and ia(t) = actual interest rate at t

36. And finally, inserting equation #3 into equation #4 E(t) = l(t) * [ G(t) - P(t) ]   - l(t) * [ CA(t) - C(t) ]   + l(t) * [ ia(t) - i(t) ] * (V(t) + P(t))   + l(t) * V(t+1) * [ qda(t) - qd(t) ] + l(t) * V(t+1) * [qwa(t) - qw(t) ]

37. To include claim reserves for a block of disabled lives, add: li(t) * [ ia(t) – i(t) ] * [ DV(t) – B(t) ] + li(t) * [ qca(t) – qc(t) ] * DV(t)

38. Splitting claim terminations into recovery and death . . . li(t) * [ ia(t) – i(t) ] * [ DV(t) – B(t) ] li(t) * [ qcda(t) – qcd(t) ] * DV(t) + li(t) * [qcra(t) – qcr(t) ] * DV(t)

39. And finally, the equation for DAC SOE would be . . . ΔDAC(t) = G(t) * rdef * [1-qw(t-1) ] + i(t) * { DAC(t-1) - G(t) * rdef * [1-qw(t-1) ] + DEXP(t) * [1-qw(t-1)] + DEXP(t) * [1-qw(t-1) + DAC(t) * qd(t-1) * [1-qw(t-1)] + DAC(t) * qw(t-1)

40. Earnings by Source Robert LaLonde, FSA VP and Senior Account Mgr. Insight Decision Solutions, Inc.

41. Classic Approach • Profit = CF – Change in Accruals • Change of Accruals • Statutory • GAAP • Tax • Embedded Value • Management Basis

42. The LTC Claim • Disability model with incidence and continuance tables • In this model can have multiple statuses – transitions to and from statuses • Alternatively, can have claim cost approach using lag factors for run-out • Also, Case Reserves

43. DI formulation Gain from Loading Gain from Interest Gain from Surrenders Gain from Incidence Gain from Termination Gain from Expenses Claim Cost Gain from Loading Gain from Interest Gain from Surrenders Gain from Claim Cost Schedule H Gain Gain from Expenses Two Approaches for LTC

44. (+/-) • + DI approach usually on a seriatim basis. • + Can identify reserve for each policy • - Claim reserve approach often done on grouped basis, so lose individual policy association of reserves • - This screws up any kind of product analysis unless you have a rule for reserve allocation at the policy level

45. Gain From Termination Relative to Val assumptions

46. EBS = (CF - ∆ Accruals) for each component EBS = CF - ∆ Valuation Assumptions EBS = (CF – Exp) + (Exp - ∆ Val) EBS = Experience Earnings + Expected Earnings Getting at Experience Gain

47. Gain From Termination Experience and Expected

48. An Example

49. Data Warehouse Solution

50. EBS in a DW • Better equipped to balance to actual earnings • More costly but a lot more time spent on accuracy of data • Robust analytical tools • Slicing and Dicing; period to period analysis • Eliminates reruns