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