Beyond Monte Carlo An Algorithmic Replacement for a Misunderstood Practice

1. Beyond Monte Carlo An Algorithmic Replacement for a Misunderstood Practice Shawn Brayman President, PlanPlus Inc.

2. Shawn Brayman • PlanPlus Founder • 20+ years experience in financial services IT sector • B.Sc. (Applied & Computational Math), MES (Expert Systems) York University • Canadian Institute of Financial Planning (1994) prescribed course of study • Software, training, speaking on financial planning in 9 countries Shawn Brayman President PlanPlus Inc.

3. Our industry is filled withconflicting information. For both advisors and clients it is almost impossible to sort out “truth” from “fiction”.

4. Executive Summary SECTION ONE – MCS Myths • MCS challenges on assumptions • MCS tests higher & lower returns • MCS tests bad years, client goals (sequence risk) • Randomizing life expectancy tests longevity risk

5. Executive Summary SECTION TWO – Reliability Forecast • Precision challenges with MCS • Creating an algorithmic solution • Validating the algorithmic solution • Improved sensitivity analysis for a financial plan

6. Disclaimer! • MCS is simply a statistical procedure and as such cannot “be wrong”. It is how it is applied and interpreted that there may be issues. • My research specifically looked at MCS for long-term financial planning. I am sure many academics and researchers have valid applications of MCS in specific instances.

7. A Last Aside • FPA Seattle had 7 of 30 sessions that deal directly with Monte Carlo or aspects of it (just over 23%) • 3 are supportive/use it, 3 question it and 1 is “yes, but buyer beware” • I went back and to FPA conference programs from Nashville, San Diego and Denver • Did a randomization with 100,000 simulations and determined in 4 years the entire FPA conference will be about MCS with no “winner”

8. A Last Aside • FPA Seattle had 7 of 30 sessions that deal directly with Monte Carlo or aspects of it (just over 23%) • 3 are supportive/use it, 3 question it and 1 is “yes, but buyer beware” • I went back and to FPA conference programs from Nashville, San Diego and Denver • Did a randomization with 100,000 simulations and determined in 4 years the entire FPA conference will be about MCS with no “winner” Kidding!

9. A Last Aside

10. Financial Planning is a Balancing Act

11. Financial Planning is a Balancing Act Return Risk Sequence Risk

12. Financial Planning is a Balancing Act Return Risk Longevity Risk Sequence Risk

13. Financial Planning is a Balancing Act Return Risk Longevity Risk Sequence Risk

14. Inflation & Return Assumptions

15. Case 1: Tom and Mary • Both age 60 • Assume mortality at age 85; • Indexed pensions of $5,675 at age 60, $4,653 at 65 • Both have $400,000 in retirement savings • They have $5,000 in a joint savings • Goal $60,000 after-tax during their lifetime; • Assume a 15% average tax rate

16. Case 1: Tom and Mary Portfolio is • Cash 15% • Fixed income 40% • Canadian equity 25% • US equity 20%

17. What Have the Returns Looked Like?

18. Case 1: Tom and Mary Based on data from 1950 to 2005 (56 years) • Inflation averaged 3.94% (geometric mean) • Return on this mix averaged 8.96% (geometric mean) • Real Return is (Nominal-Inflation)/(1+inflation) = 4.83%

19. Case 1: Tom and Mary Results • Tom and Mary’s plan is perfect and they run out of money at the end of age 85, leaving an estate of $0 to their cat.

20. Monte Carlo

21. What is Monte Carlo? • A statistical procedure where we pass an expected return and standard deviation and get random series of returns that “average” to our assumptions. • If we passed a standard deviation of 0%, it would be identical to an algorithmic solution.

22. Monte Carlo and Returns – 3 Benefits • It tests different returns – higher and lower? • It tests for bad years up front or the impact of the order of returns? (Sequence risk) • Gives an overall chance of success? You have a 74.6% chance of achieving your plan!

23. Run a Monte Carlo • Enter 8.96% with standard deviation of 8.07% • Results indicate 65% failure – timing?

24. Run a Monte Carlo • Enter 8.96% with standard deviation of 8.07% • Results indicate 65% failure – timing? • NO • You just entered a different return than your plan (8.55%)

25. Geometric vs. Arithmetic Mean • Planning uses geometric means • Monte Carlo uses arithmetic mean • G approx R – V/(2(1+R)) Many advisors attribute increased failures to timing when really different assumptions!

26. Test Higher and Lower Returns? • For Tom and Mary, 8.96% return was “perfect”. • The geometric mean is by definition the point of 50/50 probability.

27. Test Higher and Lower Returns? • Enter proper 9.26% rate, 50.5% failures

28. Test Higher and Lower Returns? • What if we increase arithmetic return and standard deviation with maintain the same 8.96% geometric mean? ?

29. Test Higher and Lower Returns? • What if we increase arithmetic return and standard deviation with maintain the same 8.96% geometric mean? !

30. Test Higher and Lower Returns? Conclusions: • MCS results are strictly a function of the geometric mean and not sensitive to the level of risk. • If MCS reports a single “probability of success”, it will average out results so no “test” of the range of returns is occurring. Recommendation: • The success/failure result must be subtotaled to allow reporting based on higher or lower returns.

31. Does MCS Test Sequence Risk? • Even withdrawal of $52,159 indexed; • $57,423 for the first 5 years (10% increase) then reduce the withdrawal to $49,932 for the duration of the plan. • $65,000 for the first 5 years (25% more); • $78,000 for the first 5 years (50% more); • $104,300 for the first 5 years (100% more); • Withdraw an additional lump sum of $100,000 in the 12th year of the plan; • Withdraw an additional lump sum of $100,000 in the 20th year of the plan. All scenarios have the same PV for the withdrawals.

32. Test Sequence Risk?

33. Test Sequence Risk? • So all withdrawal strategies with same PV of withdrawals resulted in the same 52% failure rate. • Repeated the same 7 withdrawal strategies using 11% return +/- 20.63% (8.96% geometric mean). From 51.8% to 52.1% failures. No change. • Why??

34. Test Poor Initial Returns? • Same PV of withdrawal and geometric mean results in same failures

35. Test Poor Initial Returns? • Conclusion: If the PV of the withdrawals is constant, no difference in success/failure. • Yes MCS can creates initial poor returns but no more so than great returns. If reports a single “probability of success”, it will average out results so no “test” regardless. • Observation: Unless strategies exist to deal with initial poor returns without compromising initial great returns – so what?

36. Sidebar on Inflation • Given consistent indexation of revenues and goals, planning is totally driven by the real rate of return. • Changing inflation assumptions and return assumptions only matter to the extent they change the real rate of return. • 10,000 simulations of inflation at 3.99% +/- 3.3% resulted in 49.1 success, assuming savings & withdrawals use the random variable for the indexation rate and constant real return.

37. Mortality Assumptions/Longevity Risk

38. Mortality Assumptions What mortality assumption would you use in financial plans? • Mortality tables (77 for Tom) • Age 85 • Age 90 • Age 99

39. Mortality • Tom and Mary are 60 • Tom’s life expectancy is age 77 • Mary’s life expectancy is age 85

40. What is the Impact of Mortality?

41. How do we Randomize? • Select a random number between 1 and the number of lives (i.e. 87,813) • Map to the tables to determine mortality

42. Results of Randomized Mortality • When we randomize mortality, ½ will be less than expected mortality and ½ will be more. • If we average the results, we have generated a plan based on the average life expectancy. • If we sum Success/Failure, any scenario with mortality 85 or less succeeds, 86 or more fails • Our results are 31% failure, 69% success – the same as the initial mortality assumption

43. Another Planning Risk • In respect to life expectancy, aside from longevity risk, need to consider RAK-IT Risk • Retire And Kick IT (IT = The Bucket!) • When we obsess on Longevity Risk we may be planning for our compliance department, not the client • I would say “Forget longevity risk if it means delaying my retirement and getting to my boat!”

44. Another Planning Risk

45. Longevity Risk • Conclusion:By randomizing mortality to represent longevity, advisors are, on average, basing their planning on a lower mortality assumption than would be used in traditional plans. • The success/failure is identical to initial mortality assumptions • Observation: Results can be subtotaled based on the age parameter, which would allow reporting based on mortality bands.

46. Section One Summary • Use of arithmetic means is subject to error and misinterpretation • The practice of reporting a single result washes out all concept of testing extremes and results in a plan based on the mean. • People talk as if randomization tested only a portion of the distribution – poor returns initially, living longer than planned, but it is a statistical process that equally looks at great initial returns or dieing sooner. • MCS returns the same results as the geometric mean when consistent assumptions are maintained.

47. Pre-Decease Age 85 (69%) Outlive Age 85 (31%) Returns Above 8.96 (50%) A 34 ½ % chance the client will die before age 85 and have higher than projected returns (Surplus – Success) A 15 ½ % chance the client will outlive age 85 with higher than projected returns (Unclear outcome) Returns Below 8.96 (50%) A 34 ½ % chance the client will die before age 85 but have lower than projected returns (Unclear outcome) A 15 ½ % chance the client will outlive age 85 with lower than projected returns (Capital shortfall – Failure) Section 2: Reliability Forecasts MCS provides an interesting “partial probabilities” removing ambiguity around the “unclear outcomes”

48. MCS for Returns & Mortality • 10,000 simulations • 9.26% return +/- 8.07% or 8.96% geometric • Randomized mortality • 72.9% successful and 27.1 failed sims • Is this good? • Dying at age 61 is success because $ remain • Living to 105 with funds exhausted at 103 is a failure

49. A Challenge with Precision… Simulated Returns/Age Planning Tool

50. A Challenge with Precision… Simulated Returns/Age Planning Tool Win/Loose Count