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Financing Retirement in Ageing Societies
William F. Sharpe
Iseo Summer School, 2013
Lifetime Income and Expenditures
Demographics
www.gapminder.org
www.gapminder.org
Old Age Support Ratios, 2008,2050 (# 20-64 / # 65+)
Percentage of Population 65+
Overall Retirement Systems
World Bank Recommendation:“Averting the Old Age Crisis,” 1994
Melbourne-Mercer Global Pension Index, 2012
Melbourne-Mercer Global Pension Index, 2012
Social Systems
Replacement Rates, Social Retirement Programs, 2010
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 %
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 %
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 %
Defined Benefit Plans
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)
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.)
Carmel-by-the-SeaCalPERS 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)
(
Defined Contribution Plans
Investment Expenses
Terminal Wealth Ratio:Lump-sum Investment held 10
YearsU.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
Retirement Income
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 ….
Retirement Income Scenario Analysis
Market Client
Account 1 Account 2
Analysis
Outcomes
Repeat annually while client alive
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 %
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 %
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
PPC t=a t Rmt−b
Price Per Chance and One-year Market Return
Price Per Chance and One-year Market Return
(logarithmic scales)
The Client
The Smiths Bob
Male 67
Sue Female 63
U.S. Society of Actuaries Mortality Table RP2000, Combined Healthy Mortality Improvement Scale BB
The Client: Mortality Projections
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
4% Rule: Probabilities of Payment
Present Values of Client Paymentsand Goals
Present Values of Client Payments and Inheritances
4% Rule: Present Values of Recipient Payments
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)
Social Security: Present Values of Recipient Payments
Total PV = $ 839,000
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)
Cumulative Distribution:Chance of Exceeding Goal
Cumulative Distribution:50/50 Outcome
Show SmithPPO
(Video)
Show SmithSSPPO
(Video)
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
Vanguard Managed PayoutGrowth 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
ShowSmithPPOS
(Video)
PPOS: 10/90 Percentile Payment Rangeswith and without Asset Smoothing
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
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
Vanguard GLWB Payment Ratcheting
Vanguard GLWB Withdrawal Rates
ShowSmithGLWB
(Video)
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
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
Useful Retirement Instrumentsfor 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