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
1980 – 1990
1990 – 2000
2000 – 2010
0.36 %
6.10 %
4.43 %
2.11 %
1970 – 2010
3.23 %
U.S. Treasury Inflation Protected
Security Real Yields, May 29, 2013
MATURITY
5 years
7 years
10 years
20 years
30 years
ANNUAL REAL YIELD
- 0.89 %
- 0.45 %
- 0.10 %
0.57 %
0.91 %
Defined Benefit Plans
U.S. Pension Liability
Discount Rates

Government Plans


Corporate Plans


The long-term expected rate of return on the
investments in the pension plan
Corporate Bond Rates
Unfunded Liabilities, US State and Local
Government Plans, 2010

Reported (7.5% to 8.25%):

Corporate rates (5.5%):

(Moody's estimates)
$ 766 Billion
>$2
Trillion
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-Sea
CalPERS Valuations, 2011
Actuarial
Market
Value of Assets
$ 44.9
$ 40.1
Value of Liabilities
$ 56.0
$ 79.9
Funded Ratio
Unfunded Liabilities
Discount Rate
(values in $ Millions)
80.2 %
$ 11.1
7.5 %
50.2 %
$ 39.8
2.87 %
Defined Contribution
Plans
Investment Expenses
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
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 2
Account 1
Outcomes
Analysis
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)


Price per Chance (PPC)


Value today of $1 in that scenario and year
State price / probability of that scenario and year
Only the market return is priced for every
horizon

PPC = a function of cumulative market return
−b
mt
PPC t = a t R
Price Per Chance and
One-year Market Return
Price Per Chance and
One-year Market Return
(logarithmic scales)
The Client

The Smiths

Bob



Sue



Male
67
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


Subsequent annual payments:


$ 40,000
$ 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 Payments
and 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 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
ShowSmithPPOS

(Video)
PPOS: 10/90 Percentile Payment Ranges
with 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


Insurance strategies


Can allocate mortality risks among the parties
Investment strategies


determines mortality risks
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 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