Comparing and Designing Strategies for
Lifetime Income and Asset Management for
Retirees With 401(k) Accounts/IRAs
SYSTEMATIC WITHDRAWALS, LIFE ANNUITIES AND INVESTMENTS
M A R K J . WA R S HAWS K Y, PH.D .,
PRESIDENT, RELIAS LLC
AUTHOR, RETIREMENT INCOME: RISKS AND
ST R AT E G I E S
JANUARY 10, 2014
SECURITY AND FLEXIBILITY IN RETIREMENT
Workers in baby boom generation increasingly rely on DC plans and IRAs as their primary source
of retirement financing outside of Social Security
Disciplined lifetime withdrawal is being lost with the decline of traditional DB plans
A sound strategy is needed for DC plan participants
 To generate a reliable lifetime flow of retirement income
 To preserve some wealth for varied liquidity needs (e.g., family emergency) and bequest
Focus of this presentation
 Compare the performance of several existing and possible products and strategies in
retirement, by evaluating the trade-offs between income security and wealth preservation, in
inflation-adjusted terms
 Put forward a good strategy that is efficient, low risk, robust and strikes a reasonable balance
between income and wealth, while emphasizing the former
 Use a methodology which is comprehensive and scientific, based on solid research, to
determine the “best” or “optimal” strategy designed for each retired household
Based directly on Chapters 5 and 7 of my book, Retirement Income: Risks and Strategies, 2012,
MIT Press (also influenced by Chapters 4 (participant survey) and 6 (formal theoretical
economic model)), and also based on our paper, “Retirement Income Strategies in Expected
Utility and Loss Aversion Frameworks”
2
COMPARING SOME STRATEGIES FOR INCOME
MANAGEMENT IN RETIREMENT
Strategy 1. Systematic withdrawals from account balances invested in mutual
funds (personal endowment)
 Fixed percentage withdrawal from balances of a mix of mutual funds – does not
exhaust wealth entirely, as “Bengen rule” fixed dollar approach commonly used
by financial advisors might
 Liquidity to investors and upside potential
 Income fluctuates with investment performance (and, in real terms, with
inflation)
Strategy 2. Fixed payout income immediate life annuity (SPIA)
 One-time purchase at retirement with all retirement account wealth
 Fixed level of nominal income for life guaranteed
 “Traditional” problems: extra cost owing to adverse selection of mortality risks,
illiquidity, timing risk in the purchase price due to changing interest rates
3
COMPARING SOME STRATEGIES FOR INCOME
MANAGEMENT IN RETIREMENT (CONT.)
Strategy 3. Immediate variable life annuity (IVA)
 One-time purchase at retirement with all wealth, but no pricing risk
 Underlying mutual funds selected by investors, within menu offerings
 Income for life, fixed in units, but variable with investment performance
 Wealth and liquidity needs not serviced
Strategy 4. Deferred variable annuity plus guaranteed minimum withdrawal benefit
rider (VA+GMWB)
 One-time purchase at retirement with entire account balance
 Underlying mutual funds selected by investors, within offerings and limits
 Variable income for life, but nominal level no lower than GMWB
 GMWB is a certain fixed percentage of the guaranteed income base (GIB), which
is non-decreasing; amount can step up on the GMWB rider anniversary if the
investments perform well
 Basic death benefit with remaining account value paid to beneficiaries or
withdrawn by account holder
4
COMPARING SOME STRATEGIES FOR INCOME
MANAGEMENT IN RETIREMENT (CONT.)
Strategy 5. Mix of systematic withdrawals from account with mutual funds and fixed
payout immediate life annuity, one-time wealth split at retirement
 Mutual funds give liquidity, flexibility, and opportunities for realization of equity
premium (higher return)
 Fixed life annuity guarantees a (nominal) consumption floor
 Actual real income fluctuates with investment performance and inflation
Strategy 6. Mix of systematic withdrawals from account and fixed payout immediate life
annuity, gradual annuitization at certain ages (ladder)
 Start with all (or almost all) wealth in mutual funds, shift to life annuities with age,
and complete annuitization (full or partial) by certain age
 Help ease the impact of annuity rate fluctuations (dollar cost averaging)
 Help circumvent the psychological obstacle to the (irreversible) purchase of life
annuities
 “Mortality credit” increases with age of life annuity purchases, overcoming “extra
costs”
 Provides an “option” to stop annuitization mid-stream if personal circumstances (e.g.
health) change
 Potentially greater wealth creation and certainly more account availability prior to
complete annuitization
 Even with nominal annuities, laddering gives some degree of inflation hedge
5
ASSUMPTIONS UNDERLYING FIRST-STAGE ANALYSIS OF
STRATEGIES – ASSET AND ANNUITY ALLOCATION AND
MORTALITY
Investor’s risk preference represented for this initial stage of analysis: equal
proportion (50-50) of account between high-risk assets (equity) and low-risk
assets (bonds and/or life annuities)
With account being annuitized, the equity share increases (up to 100%) to maintain
same overall risk exposure (based on result from Chapter 6)
One-time split of wealth in Strategy 5: 70% in mutual funds and 30% in fixed payout
life annuity
Gradual annuitization in Strategy 6: start with 100/0 fund/annuity split at age 65
and reach full annuitization at 75, for example
Investors retire at 65 with initial wealth of $1m, die at 100 if not earlier, with
mortality based on unisex mortality table for general population (unisex table is
legal requirement for qualified retirement plans)
6
STOCHASTIC SIMULATIONS AND OTHER STRATEGY
CONSIDERATIONS
Model only qualified plan/IRA accounts – distributions and annuity payouts are
taxable income
Asset returns and inflation and annuity pricing modeled using an estimated
stochastic system (VAR, Campbell specification), based on 1962-2008 data
Used 2008 retail price and product information in this stage of analysis, but results
are maintained if fees/costs are changed proportionately, e.g. for institutional
pricing
Mutual fund management expense ratio: 1.20%
Mortality, expense & admin. fees on VAs (M&E&A): 1.20%
GMWB rider fee: 0.60%
Immediate life annuity conservatively priced with load, Treasury yields, and
annuitant mortality
GMWB lifetime distribution guarantee is 5%
GMWB features have tightened considerably since 2008
7
INITIAL MEASURES OF SUCCESS AND RISK
Measures A – probability distribution of income levels and also shortfall
risk among those still alive
 Income amount = 5% of mutual fund balance or of GIB, and/or annuity
payout
 Average, 50th percentile (median, most likely), 5th percentile (bad), and
95th percentile (good) outcomes
 Income shortfall risk – likelihood of income falling below $45k (slightly
below nominal guarantee by GMWB at initial age)
Measure B – probability distribution of account balances among those still
alive
 Wealth balance = mutual fund balance or account value
 Average, most likely, bad, and good outcomes
All values are adjusted for stochastic realizations of inflation
8
RESULTS: STOCHASTIC OUTCOMES OF REAL INCOME
ACROSS STRATEGIES
1. Mutual Fund
2. Fixed Annuity
160
160
Good (95th pctile)
Likely (50th pctile)
Bad (05th pctile)
Average
80
120
$000
$000
120
40
0
65
80
40
70
75
80
85
90
95
0
65
100
70
75
80
Age
120
120
80
40
100
90
95
100
40
70
75
80
85
90
95
0
65
100
70
75
80
85
Age
5. Mut.Fund + Fixed Annuity, one-time
6. Mut.Fund + Fixed Annuity, gradual
160
160
120
120
$000
$000
95
80
Age
80
40
0
65
90
4. VA + GMWB
160
$000
$000
3. Variable Annuity
160
0
65
85
Age
80
40
70
75
80
85
Age
90
95
100
0
65
70
75
80
85
Age
90
95
100
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RESULTS: PROBABILITY OF REAL INCOME FALLING
BELOW $45,000
1. Mutual Fund
2. Fixed Annuity
80
80
60
60
%
100
%
100
40
40
20
20
0
70
80
90
Age
3. Variable Annuity
0
100
80
80
60
60
80
90
Age
4. VA + GMWB
100
%
100
%
100
70
40
40
20
20
0
0
70
80
90
100
Age
5. Mut.Fund + Fixed Annuity, one-time
80
80
60
60
80
90
100
Age
6. Mut.Fund + Fixed Annuity, gradual
%
100
%
100
70
40
40
20
20
0
70
80
Age
90
100
0
70
80
Age
90
100
10
RESULTS: STOCHASTIC OUTCOMES OF REAL ACCOUNT
BALANCES ACROSS STRATEGIES
1250
1000
1000
750
500
250
250
70
75
80
85
90
Age
3. Variable Annuity
95
0
65
100
1500
1500
1250
1250
1000
1000
750
500
250
250
70
0
65
75
80
85
90
95
100
Age
5. Mut.Fund + Fixed Annuity, one-time
1500
1500
1250
1250
1000
1000
750
500
250
250
70
75
80
85
Age
90
95
100
75
70
75
70
75
80
85
90
Age
4. VA + GMWB
95
100
80
85
90
95
Age
6. Mut.Fund + Fixed Annuity, gradual
100
750
500
0
65
70
750
500
0
65
Good (95th pctile)
Likely (50th pctile)
Bad (05th pctile)
Average
750
500
$000
$000
$000
1250
0
65
$000
2. Fixed Annuity
1500
$000
$000
1. Mutual Fund
1500
0
65
80
85
Age
90
95
100
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PRELIMINARY CONCLUSIONS
Systematic withdrawals from mutual funds have opportunities for greater
wealth at the risk of investment losses and income shortfalls
Wealth needs aside, fixed and variable immediate life annuities distribute the
highest lifelong incomes
VA+GMWB somewhat addresses both income and wealth needs but is
hampered by high fees
Strategy of mutual fund withdrawals + laddered fixed life annuities works like
VA+GMWB but provide more flexibility in the choice between income
security and maximization and wealth preservation, and lower cost
Contract terms, especially fees, are important
More research next on advanced optimal strategies
“Best” or “Optimal” in an analytical sense needs a formal framework for what
is considered better (higher welfare) for the individual or household
12
OPTIMAL STRATEGIES FOR LIFETIME INCOME AND
ASSET MANAGEMENT IN RETIREMENT
13
“LOSS AVERSION” METHODOLOGY AND ASSUMPTIONS
Focus hereafter on strategies “5” and “6” – combination of systematic withdrawals
and initial and gradual /laddered purchases of single-premium immediate life
annuities
In this second “middle” stage of our analysis, loss aversion framework minimizes the
combined probability of real income falling below $45k, and real balances falling
below $250k, based on $1M portfolio at age 65, for unisex individual, or couple,
with emphasis on income
Asset mix set is originally at 50/50, but as SPIAs are purchased, remaining
investment portfolio is moved to equities
For couples, J & 75% S annuities are purchased and income goal is cut when
widowed
Stochastic modeling is as before, but now updated to 2009 and possibility of
economic collapses is added, lowering expected returns
Search over rate of systematic withdrawals from account (0 to 10%), and
annuitization schedule (from 5 to 35 years, with life annuity share at beginning
and end in 5% increments).
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RESULTS FOR LOSS AVERSION APPROACH
Range of balances and income from optimal strategy for individual in retirement
50th
Real $000
95th percentile
percentile
A. Life annuity ladder plus systematic withdrawal
Balance
900.0
316.1
Income
80.5
51.5
B. No annuity, 50-50 equity-bond mix
Balance
1019.7
581.6
Income
70.7
41.2
C. No annuity, 70-30 equity-bond mix
Balance
1074.5
577.9
Income
74.6
41.0
5th
percentile
Mean
Std. Dev.
Shortfall Prob.
(%)
0.0
18.4
370.8
50.9
312.9
18.1
44.1
32.2
123.4
9.1
588.8
41.5
295.4
20.3
15.1
55.7
99.7
7.4
591.8
41.7
317.9
21.9
17.1
55.6
Notes: Baseline assumptions: initially $1 million at age 65 with 50-50 equity-bond mix, preference weight on income shortfall probability α=2/3, real
consumption floor C0=$45,000, and real balance threshold W0=$250,000.
A. weighted shortfall risk 36.2%, withdrawal 5%, annuity initial 10%, ending 100% by 20 years
B. weighted shortfall risk 42.2%, withdrawal 7%
C. weighted shortfall risk 42.8%, withdrawal 7%
Source: Authors’ simulations.
15
OPTIMAL LOSS AVERSION STRATEGY FOR SINGLES –
SOURCES OF REAL INCOME
Median income among survivors
60
50
Real $000
40
30
Withdrawal+annuity
Withdrawal
Annuity payout
20
10
0
65
70
75
80
85
90
95
100
Age
Strategy: Withdrawal 5%, annuity initial 10%, ending 100% by 20 years
16
OPTIMAL LOSS AVERSION STRATEGY FOR COUPLES –
SOURCES OF REAL INCOME
Median income among survivors
50
45
40
35
Real $000
30
25
Withdrawal+annuity
Withdrawal
Annuity payout
20
15
10
5
0
65
70
75
80
85
90
95
100
Age
Strategy: Withdrawal 5%, annuity initial 0%, ending 100% by 30 years
17
“EXPECTED UTILITY” METHODOLOGY AND
ASSUMPTIONS: THIRD AND FINAL STAGE OF ANALYSIS
“Expected utility” is a sophisticated model developed by mathematicians von
Neumann and Morgenstern and has been used in Nobel Prize work by several
economists. In our context, it is a mathematical function representing the
preferences and goals of the retired household for higher income and greater
wealth, but with due concern for risk.
Our algorithm to maximize expected utility produces a strategy chosen to optimize
outcomes for lifetime inflation-adjusted income and liquid net worth, in the face
of the range of several contingencies and uncertainties, such as personal
longevity, investment returns, interest rates, and inflation.
Initial conditions, at the time of the analysis, are considered, including
demographics (such as age, single or couple, health, and so on), retirement
assets available, other sources of income, such as Social Security, employer
pensions, and so on, and current insurance and investment product
characteristics and conditions
18
“EXPECTED UTILITY” METHODOLOGY AND
ASSUMPTIONS (CONTINUED)
Information is gathered from the retired household to also determine key preference
parameters for the algorithm including attitudes toward risk, and the desire for a
bequest and liquid wealth; these parameters would be centered around
population average values, as found in the professional literature
The strategy employs the simple building blocks we identified in the last few slides:
immediate straight life annuities (single or joint-and-full-to-survivor), and index
mutual funds. The optimization tells us the rate and extent of life annuity
purchases, of systematic withdrawals from the funds, and the asset allocations
Our latest algorithm adds refinements such as inclusion of Social Security, different
product fee levels, differential mortality rates, more refined withdrawal and
annuitization approaches and details in annuity pricing, an updated VAR
stochastic return and inflation model, a model of insurer failures, and maximum
lifetime to 105.
Default preference parameters are set as found in the professional economics
literature. It is also possible to set the stochastic simulations “engine” to start
with current financial conditions, especially with regard to interest rates
19
“EXPECTED UTILITY” METHODOLOGY AND
ASSUMPTIONS (CONTINUED)
The “expected utility” model, using average preference parameters, gives somewhat greater
weight to younger ages, liquidity and bequests, especially when retirement resources are
sizeable, and results in less annuitization overall and higher rate of SW than the “loss
aversion” approach. The inclusion of Social Security also lowers somewhat the optimal
amount of annuitization purchased on the market.
Mass customization is now possible, with the inputs of different levels of risk aversion, desire for
liquidity and bequests, amounts of retirement assets, asset initial allocations, Social Security
and DB income, health status, and varied demographics for individuals and couples
The “Average Certainty Equivalent” or ACE is the best summary statistic for the strategy; higher is
better
Illustrations and examples on next slides are based on same assumptions as earlier slides, except
data extended to 2011, includes median Social Security retirement benefits, investment
expense is lowered to 25 bps, and possibility of economic collapses is removed
Simulated annual rates and returns (VAR process)
Real (%)
Equity return
Bond return
Bond yield
Mean
4.9
2.8
2.5
Std. Dev.
17.8
9.7
2.4
Nominal (%)
Mean
8.9
6.9
6.5
Std. Dev.
17.3
9.0
2.5
Source: Authors’ simulations based on 1962-2011 data.
Inflation
--4.1
2.7
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RESULTS FOR EXPECTED UTILITY APPROACH
Optimal strategy for real income and asset management in retirement
Real $000
A. Assets $1000
Balance
Income
95th percentile
50th
percentile
5th
percentile
Mean
Std. Dev.
1089.5
89.6
651.2
64.2
199.1
40.2
652.7
64.3
288.4
15.6
Notes: Baseline assumptions: single, retired age 65 with 50-50 equity-bond mix, median 2010 Social Security retirement income, preference
parameters as found in professional literature
A. ACE $56.42, withdrawal 6%, annuity initial 5%, ending 20% by 18 years
Source: Authors’ simulations.
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OPTIMAL EXPECTED UTILITY STRATEGY FOR CASE “A”
– REAL INCOME AND WEALTH RANGE OF OUTCOMES
a. Balance
b. Income
1250
100
95th
50th
05th
Avg.
750
66.6
$000
$000
1000
500
95th
50th
05th
Avg.
33.3
250
0
65
70
75
80
85
Age
90
95
100
0
65
105
70
75
100
75
75
50
25
0
65
85
Age
90
95
100
105
95
100
105
d. Prob.(Balance<$263.8k)
100
%
%
c. Prob.(Income<$58.8k)
80
50
25
70
75
80
85
Age
90
95
100
105
0
65
70
75
80
85
Age
90
22
OPTIMAL EXPECTED UTILITY STRATEGY FOR CASE “A”
– SOURCES OF REAL INCOME (MEAN)
Income
80
Total Income
Annuity Payout
M.F. Withdrawal
Social Security
$000
60
40
20
0
65
70
75
80
85
Age
90
95
100
105
Strategy: Withdrawal 6%, annuity initial 5%, ending 20% by 18 years
23
EXTENDED RESEARCH AND BUSINESS APPLICATION
Longevity insurance, delayed annuitization and other strategies marketed by other
organizations are not supported in subsequent analyses because of pricing
inefficiencies, lower income and/or higher risk
Household tax considerations for after-tax investments, as well as optimal Social
Security claiming, are also natural, if complex, extensions to be added in the
future
New rules from the Departments of Treasury (minimum distribution requirements)
and Labor (illustration of income flow disclosed annually (on a life annuity basis)
for 401(k) accounts) are expected soon; create interest and give context
Business case and plan and product description, along with further details on the
“expected utility” technology, are available for further discussion if there is
practical interest in implementation
See www.reliasllc.com
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