1. Financing Retirement in Ageing Societies William F. Sharpe Iseo Summer School, 2013

2. Lifetime Income and Expenditures

3. Demographics

4. www.gapminder.org

9. Old Age Support Ratios, 2008,2050 (# 20-64 / # 65+)

10. Percentage of Population 65+

11. Overall Retirement Systems

12. World Bank Recommendation: “Averting the Old Age Crisis,” 1994

13. Melbourne-Mercer Global Pension Index, 2012

16. Social Systems

17. Replacement Rates, Social Retirement Programs, 2010

18. GDP 2012 $15.7 Trillion

21. U.S. Social Security, 2012 Present Value ofUnfunded obligation for past and current participants: $ 21.6 Trillion GDP: $ 15.7 Trillion Present Value of cost for future participants over the infinite horizon: $ 45.9 Trillion Present Value of dedicated tax increase for future participants over the infinite horizon: $ 47.0 Trillion Real Interest Rate used to compute Present Values: 2.9 %

22. Annual Average Realized U.S. Treasury Real Rates PERIOD REAL RATE 1970 – 1980 0.36 % 1980 – 1990 6.10 % 1990 – 2000 4.43 % 2000 – 2010 2.11 % 1970 – 2010 3.23 %

23. U.S. Treasury Inflation Protected Security Real Yields, May 29, 2013 MATURITY ANNUAL REAL YIELD 5 years - 0.89 % 7 years - 0.45 % 10 years - 0.10 % 20 years 0.57 % 30 years 0.91 %

24. Defined Benefit Plans

25. U.S. Pension Liability Discount Rates Government Plans  The long-term expected rate of return on the investments in the pension plan Corporate Plans  Corporate Bond Rates Unfunded Liabilities, US State and Local Government Plans, 2010  Reported (7.5% to 8.25%): $ 766 Billion  Corporate rates (5.5%): > $ 2 Trillion (Moody's estimates)

26. CalPERS Termination Discount Rate “The discount rate..., will be a weighted average of the 10 and 30 year US Treasury yields.. [to] equal the duration of the expected benefit payment cash flows...the inflation assumption used to project the expected benefit payment cash flows.. will be the inflation imbedded in the US Treasury Inflation Protected Securities (TIPS)..” (For inflation-indexed benefits, equivalent to discounting at the TIPS real yield.)

27. Carmel-by-the-Sea CalPERS Valuations, 2011 Actuarial Market Value of Assets $ 44.9 $ 40.1 Value of Liabilities $ 56.0 $ 79.9 Funded Ratio 80.2 % 50.2 % Unfunded Liabilities $ 11.1 $ 39.8 Discount Rate 7.5 % 2.87 % (values in $ Millions) (

28. Defined Contribution Plans

30. Investment Expenses

31. Terminal Wealth Ratio: Lump-sum Investment held 10 Years U.S. Stock Market Index Fund Expense Ratio: 0.06 % per year U.S. Stock Market Average Actively-managed Fund Expense Ratio: 1.12 % per year

34. Retirement Income

35. The U.S. Market for Retirement Income In the United States 10,000 Baby Boomers retire each day Defined contribution balances are growing Products and services are being offered by:  Financial advisors  Mutual fund companies  Insurance companies  Retirement plan providers  ….

36. Retirement Income Scenario Analysis MarketClient Account 1 Account 2 Analysis Outcomes Repeat annually while client alive

37. The Market: Returns The Riskless Asset  Annual Real Return = 1.0 % The Market Portfolio  Market-weighted World bonds and stocks  Annual Returns Independent year-to-year Identically Distributed each year  Lognormal Distributions  Annual Expected Return = 4.5 %  Annual Standard Deviation of Return = 10.0 %

38. The Market: Inflation Annual Inflation  Independent year to year  Identically Distributed in each year  Uncorrelated with the Market Portfolio Real Returns  Lognormal Distributions  Annual Expected Inflation = 2.5 %  Annual Standard Deviation of Inflation = 1.0 %

39. The Market: Present Values For each scenario and year  State Price (Present Value) Value today of $1 in that scenario and year  Price per Chance (PPC) State price / probability of that scenario and year Only the market return is priced for every horizon  PPC = a function of cumulative market return

40. Price Per Chance and One-year Market Return

41. Price Per Chance and One-year Market Return (logarithmic scales)

42. The Client The Smiths  Bob Male 67  Sue Female 63 U.S. Society of Actuaries  Mortality Table RP2000, Combined Healthy  Mortality Improvement Scale BB

43. The Client: Mortality Projections

44. Account Type 1: Constant Annual Real Payments The four percent rule  Initial investment: $ 1,000,000  Invest in a portfolio of bonds and stocks  First year's payment: 4% of Initial Investment $ 40,000  Subsequent annual payments: $ 40,000 + inflation  Continue until client dies or the money runs out  Typical fees: 1% or more (1% assumed) Alternatives: Different initial percentages

45. 4% Rule: Probabilities of Payment

46. Present Values of Client Payments and Goals

47. Present Values of Client Payments and Inheritances

48. 4% Rule: Present Values of Recipient Payments

49. Account Type 2: United States Social Security Contributions based on payroll Constant real payments Initial payment depends on prior contributions and age when benefits start Surviving spouse receives larger of  Own benefits  Deceased spouse's benefits The Smiths:  Bob: $ 2,500 per month ($ 30,000 per year)  Sue: $ 1,000 per month ($ 12,000 per year)

50. Social Security: Present Values of Recipient Payments Total PV = $ 839,000

51. Account Type 3: Proportional Payouts (PPO) Payment each year is a scheduled proportion of the market value of investments Investment strategy  Constant, or  Decreasing risk (Glide Path) Example:  Fidelity Income Replacement Funds  2042 Fund (fee = 0.68% per year)

53. Cumulative Distribution: Chance of Exceeding Goal

54. Cumulative Distribution: 50/50 Outcome

55. Show SmithPPO (Video)

56. Show SmithSSPPO (Video)

57. Account Type 4: Proportional Payouts with Asset Smoothing Payment each year is a scheduled proportion of the value of investments Investment strategy  Constant, or  Decreasing risk (Glide Path) Investment Value of assets is an average of prior values over some period Example:  Vanguard Managed Payout Funds

58. Vanguard Managed Payout Growth and Distribution Fund “The fund seeks to make regular monthly payouts that, over time, keep pace with inflation” Portfolio: 77% stocks Expense Ratio: 0.43% Annual Payout: 5% of average of prior 36 months' asset values

59. ShowSmithPPOS (Video)

60. PPOS: 10/90 Percentile Payment Ranges with and without Asset Smoothing

61. Account Type 5: Guaranteed Lifetime Withdrawal Benefits Payments a fixed percentage of “withdrawal base” Withdrawal base can increase with increases in the value of the underlying account but can never decrease Insurance company guarantees payments for the life of the client or clients Funds may be withdrawn at any time, decreasing the withdrawal base Fees for investment management and insurance

62. Vanguard Variable Annuities with GLWB Rider Investments  Balanced Portfolio  Moderate Allocation Portfolio  Conservative Allocation Portfolio Fees  annual fee: 0.95% of the withdrawal base  “The rider fee for future premium payments...could be higher or lower, but not more than the maximum of 2.0%” Withdrawal base increases  Once each year based on current asset value

63. Vanguard GLWB Payment Ratcheting

64. Vanguard GLWB Withdrawal Rates

65. ShowSmithGLWB (Video)

66. Fundamental Principles Fate  determines mortality risks Insurance strategies  Can allocate mortality risks among the parties Investment strategies  determine financial risks and returns Spending strategies  allocate financial risks and returns among the parties

67. Key Observations Non-market risk can be pooled Market risk cannot be pooled Spending Strategies cannot reduce market risk, they can only re-allocate it There are no magic formulas Fees matter For-warned is for-armed

68. Useful Retirement Instruments for an Ageing Population TIPS  Zero-coupon TRILLS  Zero-coupon  pay one-trillionth of GDP in specified year Tontines  Cohort of similar investors (e.g. male, born 1940)  Pay those alive at maturity date