by Craig Lemoine, CFP®; David M. Cordell, Ph.D., CFA, CFP®, CLU; and A. William Gustafson, Ph.D.
Executive Summary
- This article contrasts sustainable retirement withdrawals from strategies with annuity components and strategies without annuity components.
- The authors discuss today's market environment as it affects retirement planning strategies with and without annuity components.
- This study evaluates common retirement planning strategies by analyzing the withdrawal stability for portfolios consisting of equity, fixed income, variable annuity, and fixed annuity assets.
- This article uses replacement Monte Carlo methodology to determine retirement success over investor accumulation and withdrawal phases. The goal of each trial was to secure calculated retirement funding rather than to maximize wealth.
- Five retirement portfolio strategies are evaluated: (1) 50 percent in equities and 50 percent in bonds, (2) 100 percent in equities, (3) a combination of equities and bonds in which the equities percentage is calculated as 128-minus-attained-age, (4) a variable annuity with a 5 percent withdrawal rate, and (5) 100 percent equities with a fixed annuity lock.
- Different rebalancing strategies were modeled to capture any variances between frequency. Portfolios composed of a higher portion of equities outperformed those with a higher portion of bonds. The trials using 50 percent equities and 50 percent bonds yielded the lowest chance of success. Attempting to reduce portfolio risk by reallocating to fixed-income assets annually is less likely to provide long-term success than an allocation that remains fully invested in equities.
- The results indicate that using an equity portfolio with a fixed annuity component provides a higher chance of maintaining retirement distributions than other alternatives.
Craig Lemoine, CFP®, is an assistant professor of
financial planning at the American College. He also works with
retirees and is completing a doctoral dissertation at Texas Tech
University.
David M. Cordell, Ph.D., CFA, CFP®, CLU, is director of finance programs at the University of Texas at Dallas.
A. William Gustafson, Ph.D., is an associate professor at Texas Tech University.
Domestic and international equities markets have experienced
dramatic volatility over the past two years. Fixed income positions
have offered some relief, but typical equities portfolios have lost
more than 30 percent of their value, even after rebounding from the
market bottom. Consumer sentiment is low, and investors may be
looking for alternative asset allocations.
Traditional retirement portfolio management holds that the
percentage allocated to equities should be high when an investor is
young and should decline over time. In theory, the higher
percentage in the early years provides needed growth while the long
time horizon ameliorates the accompanying risk. In contrast, an
older investor with a shorter time horizon is less able to absorb
the risk of an extended bear market.
Of course, rules of thumb do not always stand up to scrutiny, and
with a generation of baby boomers reaching retirement, the need for
identifying successful strategies is becoming increasingly
critical. Those who retired in 2007 or 2008 may find that equity
and bond markets alone are not able to sustain their anticipated
retirement needs.
This research tests five retirement portfolio asset allocation
strategies through both the retirement accumulation and
distribution phases. Three of the strategies tested involve stocks
and/or bonds, and two incorporate annuity contracts. Three of the
portfolio strategies tested are often used as baseline cases in
literature: (1) a portfolio that consists of 50 percent equities
and 50 percent bonds, (2) a portfolio that consists of 100 percent
equities, (3) a portfolio that adjusts asset allocation during the
life cycle, reducing the equities percentage as the client ages,
(4) a variable annuity strategy that includes a 5 percent living
benefit guarantee, and (5) a 100 percent equities model that
annuitizes upon achieving a predetermined value.
Review of Literature
Asset allocation tools and techniques have been studied over
many time horizons. (Anderson and Faff, 2004; Hau and Rey, 2004;
Donohue and Yip, 2003; Ibbotson and Kaplan, 2000; Athanassakos,
1992). Literature suggests that investors experience higher overall
returns in portfolios composed primarily of equity investments over
5-, 10-, and 20-year periods (Ciccotello, Grant, and Field, 2002).
Investment data (Ibbotson and Kaplan, 2000) support the generally
accepted belief that equity portfolios (particularly U.S.
value-based portfolios) historically outperform their fixed and
domestic bond counterparts. However, historical returns vary
greatly depending on the date an investor begins investing and
accessing his/her portfolio, and returns also vary based on any
portfolio rebalancing tools that are implemented.
Studies of portfolio rebalancing strategies tend to look at initial
asset allocation, trading frequency, trading styles, rebalancing
triggers, and other aspects of investment decision making
(Hlawitschka and Tucker, 2005; Jensen and Mercer, 2003; Judd,
Kubler, and Schmedders, 2003). Of course, portfolio rebalancing
strategies are typically aimed at creating a portfolio with a
risk-return profile that is consistent with the investor's risk
tolerance.
One approach to setting the equity percentage in the retirement
portfolio is the 100-minus-attained-age algorithm, which holds that
subtracting the investor's age from 100 provides an appropriate
percentage to allocate to equities (Bodie and Treussard, 2007). Of
course, this approach fails to consider the investor's risk
tolerance or the actual time horizon. Empirical studies have
provided an improvement to this rule of thumb by evaluating the
likelihood that the portfolio can be maintained throughout
retirement. According to this approach, the optimal equities
percentages should be 115-minus-attained-age for a conservative
investor, 128-minus-attained-age for moderate investors, and
140-minus-attained-age for aggressive investors (Bengen, 1997).
Another approach to asset allocation treats each projected
retirement withdrawal as if it were a separate goal with its own
time horizon. Asset allocation for each of these hypothetical
portfolios is based on the investor's risk tolerance (Cordell,
2005). The asset allocations for all the hypothetical portfolios
are amalgamated to generate an allocation for the actual portfolio.
Relative to the 128-minus-attained-age approach, this technique
tends to generate higher equities allocations in early years and
lower allocations in the later years.
Variable annuity use has increased dramatically over the past five
years. Variable annuity assets held in management by financial
advisers and institutions grew 38.2 percent in 2006 to $1.36
trillion (Chen et. al, 2007), compared to mutual fund
growth of under 20 percent by the same institutions. This growth,
and the study of variable annuity products, has not been
incorporated into investment literature with the same level of
depth as traditional investment and mutual fund research. Indeed,
variable and fixed annuity insurance tools are not often considered
in the discussion of asset allocation and sustainable portfolio
withdrawals.
The analytical approach in this study, Monte Carlo
analysis,1 is commonly used in academic research (Fink
and Fink, 2005). Monte Carlo modeling allows users to test
investment risk by simplifying more complex modeling methods and
has been repeatedly used to test systematic and unsystematic risk
in relation to returns (Minderhoud, 2006; Boscaljon, 2006). It has
also been promoted as an effective tool for practitioners, most
notably by the late Lynn Hopewell, a former editor of the Journal
of Financial Planning (Kautt and Hopewell, 2000).
Methodology and Assumptions
This research evaluates five models for managing the retirement
portfolio utilizing Ibbotson data for equities to evaluate each
model's efficacy and compare it to other approaches. Monte Carlo
analysis is performed to determine the chance of success out of
1,000 trials. Success is defined as a trial that successfully
sustains an inflation-adjusted retirement need beginning at
retirement age and continuing through age 100. Age 100 is used to
reflect a conservative life expectancy and is often used by
practitioners in retirement and survivor needs planning. Failure is
defined as a trial that is unable to sustain continued
withdrawals.
Two asset categories are evaluated: stocks and bonds. Stocks are
represented by the Russell 1000 Index, which is composed of the
1,000 largest publicly traded U.S. companies. This index accounts
for 90 percent of equity on U.S. stock exchanges. From its 1986
inception through 2008, the Russell 1000 has had a historical
return of 12.86 percent and a standard deviation of 18.32 percent,
which are the equity return and risk factors used in this
analysis.
Bond data are modeled in the same manner as stock data. Bond data
are derived from a blend of 50 percent corporate and 50 percent
government bonds over broad bond markets. This combination has a
historical return of 5.3 percent and standard deviation of 8.87
percent, with an average duration of 10 years (CRSP 20 Year Bond
Data from 1998–2008).
Five retirement planning approaches are evaluated:
1. 50 percent equities and 50 percent bonds
2. 100 percent equities
3. An equities percentage equal to
128-minus-attained-age
4. A variable annuity with a "living benefit"
5. 100 percent equities with a fixed annuity lock
Each model assumes a 20-year accumulation phase and 35-year
distribution phase, creating a case study with a beginning age of
45, retirement age of 65, and life expectancy of 100. Inflation is
assumed to be 3 percent during both the accumulation and
distribution phases. Different rebalancing strategies were modeled
to capture any variances between frequency. We found that
portfolios composed of a higher portion of equities outperformed
those that had a higher portion of bonds. Portfolios that
rebalanced more often to bonds had less of a chance of sustaining
success than those that allowed equities to accumulate more
frequently. In other words, the pile of money available at
retirement to sustain withdrawals was larger in portfolios that
allowed equities to experience style drift.
The case assumes initial pre-retirement income of $1,000, initial
savings of five times income ($5,000), and an annual retirement
need of 70 percent of initial income, or $700. (Note: $700 adjusted
for 3 percent inflation for the 20-year accumulation period
generates a beginning retirement withdrawal of $1,265.) Models
assume no rebalancing costs. Annual costs of 0.53 percent were used
to proxy indexed investing costs and annuity charges were 1 percent
in addition to investment costs. A 0.53 percent proxy for
investment costs was derived from taking the average of indexed and
actively managed equity fund expense ratios in 2008 (Investment
Company Institute, 2009).
50 Percent Equities and 50 Percent Bonds. In this
approach, portfolios were invested in 50 percent equities and 50
percent bonds throughout the accumulation and distribution periods,
and the portfolios were rebalanced annually.
100 Percent Equities. This approach invested 100
percent of the portfolio in equities throughout the accumulation
and distribution periods. Fixed income instruments were not
considered.
Equities Allocation Percentage Equals
128-Minus-Attained-Age. For this trial, the asset
allocation was based on the following algorithm: equities
percentage equals 128-minus-attained-age. As noted earlier, this is
the allocation Bengen found to be most appropriate for
moderate-risk-tolerance investors (Bengen, 1997). Thus, the initial
asset allocation was 83 percent stocks (that is, 128-minus-45) and
17 percent bonds. The portfolio was rebalanced to its target
allocation every January 1, and the target allocation was
rebalanced toward bonds every 10 years as illustrated in Table 1,
which gradually reduced the equities percentage.
Variable Annuity with a Living Benefit. Another
technique is a living benefit, commonly offered by variable annuity
contracts. A living benefit allows an investor to receive a
guarantee of a percentage of the annuity value or a fixed dollar
amount at a given point (generally the contract inception date) for
life regardless of the outcome of the contract value. Living
benefits can be added to annuity contracts, and their specific
costs and features vary significantly by contract. One constant of
living benefits is that they provide a non-inflating cash flow
through the lifetime of the annuitant. (Note that specific
limitations of living benefits vary by contract, and it is
especially important for financial advisers and the public to
evaluate the annuity prospectus before making any investment
decisions.)
The cost of variable annuity contracts with living benefits varies
dramatically among different insurers. To reflect a typical
contract, this model assumes variable annuity portfolios invest in
sub-accounts equal to the allocation of the Russell 1000 and
deducts 1.53 percent from the account balance at year-end. This
model reflects a cost 1 percent higher than other equity
portfolios, for a total cost of 1.53 percent. This cost appears
reasonable because an informal review of 10 contracts offered by 5
major insurers2 revealed that they offer living benefits
on contracts with total costs ranging between 1 percent and 1.85
percent.
In this retirement planning approach, the living benefit would be
executed at any time during retirement when B (benefit) was equal
to or greater than the retirement withdrawal need. The living
benefit guarantees a non-inflating cash flow paid over the life
expectancy of the client. A 100 percent equities allocation was
used, and, as noted previously, this model factored additional
costs of using an annuity product with a lifetime benefit. Given
the above set of assumptions, an annuity must have achieved a value
of $25,285 at age 65 to produce a living benefit that would
guarantee 5 percent withdrawals at retirement. That is, $25,285 ×
.05 = $1,265, which, as noted earlier, is the $700 retirement
withdrawal increasing at the 3 percent assumed inflation rate over
the 20-year accumulation period.
100 Percent Equities with an Annuity Lock. The 100
percent equities with an annuity lock model maintains a 100 percent
equities allocation until a "trigger date" occurs. A trigger date
for this strategy is any point at which the portfolio is large
enough that it can be reallocated to a fixed annuity that will
provide all the funds necessary to cover the projected series of
retirement withdrawals from age 65 to age 100. A scenario in which
a trigger date is reached is deemed to be a successful funding of
retirement. (All contributions to the portfolio subsequent to the
trigger date can be invested in any way deemed appropriate, but the
accumulations are not evaluated because the accumulation goal has
already been achieved.) This process also implies a degree of
conservatism.
If a trigger date is not reached during the accumulation phase,
which indicates that the retirement portfolio goal is not reached,
the 100 percent equities portfolio is maintained and retirement
withdrawals begin as scheduled. At first glance these withdrawals
would seem to be ill-advised, because the portfolio would be
falling short of the calculated need and the withdrawal would
represent a larger percentage of the balance than originally
anticipated. However, the likelihood of a portfolio depleting
assets during the first year of retirement is small, especially for
portfolios that have existed for long periods. Further, because any
shortfall is likely a result of an extended bear market in the
final years of the accumulation period, it is highly probable that
the resultant market recovery will cause the distribution-phase
portfolio to recover the value needed to maintain scheduled
withdrawals.
The specific methodology for the 100 percent equities with annuity
lock approach is as follows. Monte Carlo analysis is run to year 16
(5 years before retirement) using 100 percent equities. At that
point (age 60), if the balance for a trial is large enough to buy a
fixed annuity that would cover aggregate projected retirement
withdrawals from age 65–100, the trial is deemed to be a
success. If the balance is insufficient, the funds for that trial
remain fully invested in equities, and the same evaluation is made
the next year. Again, if there are sufficient funds to buy the
annuity, the trial becomes a success, and if not, the money remains
invested. Retirement occurs at age 65 and, if there is still not
enough money to buy the annuity, withdrawals are made directly from
the equities portfolio. If during retirement there is eventually
enough money to buy an annuity to fund the remaining withdrawals,
the trial is a success. If a given trial never has enough money to
buy an annuity it is deemed a failure.
This model assumes that a fixed annuity can be purchased at any
time, yielding 1 percent over inflation. The annuity locks in
lifetime payments equal to the specified retirement amounts and
begins at age 65. At age 65, the required value to finance the
annuity is $34,977. The annuity amount can be discounted back
before retirement, although it will not begin making annual
payments until age 65. Discounted annuity values are illustrated in
Table 2.
Results
Figure 1 visually summarizes the success rates of the five approaches. Again, success is defined as successfully funding the entire retirement through age 100. Out of 1,000 trials for the 50 percent equities-50 percent bonds approach, 738 succeeded and 262 failed—a 73.8 percent success rate. The trials that passed maintained retirement distributions to at least age 100. For the 100 percent equities approach, out of 1,000 trials, 877 passed and 123 failed—an 87.7 percent success rate. It should be noted that the 100 percent equities model gave the client potential for the greatest wealth with the top quarter wealth of all trials being around $1.25 million.
In the 128-minus-attained-age approach, 946 of the 1,000 trials
sustained retirement withdrawals throughout retirement, while 54
trials did not sustain withdrawals—a 94.6 percent success
rate.
In the variable-annuity-with-living-benefit approach, 693 out of
1,000 trials passed, that is, reached the annuity purchase value,
by age 65, while the other 307 did not reach the annuity purchase
value by age 65. The 307 failing portfolios were aggregated in
groups in $5,000 increments, as indicated in Table 3. Each of the
groups was then modeled independently, again assuming withdrawals
of $1,265, increased for inflation, and the results were as
follows:
• 67 percent of the $20,000 portfolios could sustain
retirement withdrawals of $1,265
• 40 percent of the $15,000 portfolios could sustain
retirement withdrawals of $1,265
• 10 percent of the $10,000 portfolios could sustain
retirement withdrawals of $1,265
• 1 percent of the $5,000 portfolios could sustain
retirement withdrawals of $1,265
Of the 307 portfolios that did not achieve the targeted living
benefit value of $25,285 at retirement, about 150 were able to
maintain withdrawals through retirement. Thus, out of 1,000
portfolios using a living benefit, 843 succeeded and 157 reached
terminal failure—an 84.3 percent success rate.
For the 100 percent equities with an annuity lock approach, the
process is more complicated. Beginning at age 60 (year 16 of the
analysis), 640 portfolios met or exceeded the balance needed to
purchase an annuity capable of sustaining retirement needs, while
360 failed to reach the necessary balance. The 360 trials that
failed to meet the required balance are grouped according to the
amount of the shortfall in $5,000 increments ranging from $5,000 to
$25,000, and frequencies are noted for each group (Table 4).
One year of additional contributions and growth is applied to each
$5,000 increment—and new pass and failure frequencies are
calculated targeting the amount needed to purchase an annuity at
age 61 (year 17 of the trial), $28,702. Table 5 reports pass
frequencies for year 17.
By measuring the outcomes of failures in year 16, an additional 98
portfolios reached the target value of $28,702 by the end of year
17. A new case distribution of failed portfolios in year 17 can be
found in Table 6.
This methodology was repeated through years 17–45 finding
ending results in each year. Subsequent to retirement, portfolios
that had end-of-year values less than the next year's distribution
were considered to "terminally fail" and were removed from future
calculations.
At the end of year 20 (client age 64), 889 trials had reached the
annuity value and 111 had not. By the end of year 45 (client age
90), 968 portfolios had at some point achieved the annuity value.
The remaining 32 portfolios had reached a terminal failure. See
Table 7 for a summary of terminal failures by year.
Discussion
A summary of the success rates of different methodologies is provided in Table 8. The trials using 50 percent equities and 50 percent stocks yielded the lowest chance of success.
Purchasing an annuity contract with a living benefit rider did not
provide a higher probability of success than using a standard 100
percent equities portfolio—84.3 percent vs. 87.7 percent.
(Recall that the expense percentage for an equities portfolio was
assumed to be 0.53 percent annually, and an additional 1 percent
was deducted to represent annuity charges.) This result is
dependent on assumptions and time frame. The variable annuity
result may outperform a 100 percent equities approach over
long-term bear market periods. Cost is critical to analyzing the
merits of using a 100 percent equities (without annuitization)
strategy or considering a variable annuity contract with a living
benefit rider. Cheaper annuity products and rougher market periods
could potentially change the results.
The 128-minus-attained-age approach provided strong results. This
approach simulated a client taking an aggressive stance
pre-retirement and less volatility risk as they approach portfolio
distribution during retirement. This model reduces portfolio
withdrawal risk by limiting equity exposure during retirement
withdrawal.
The 100 percent equities with annuity lock approach had superior
success in meeting the retirement withdrawal requirements when
contrasted to the other tested methods. Relative to the 100 percent
equities approach, the 100 percent equities with an annuity lock
method was more successful for two reasons. First, the possibility
of achieving the required annuitization balance prior to retirement
in some cases avoids the situation in which an otherwise successful
program could be undermined by a subsequent bear market. Second, it
prevents portfolios from experiencing below annuity (1 percent +
inflation) returns once the portfolio achieves an annuity
value.
The 100 percent equities with annuity lock approach does not
attempt to maximize wealth, and indeed it generates less wealth on
average than the standard 100 percent equities approach. The
specified goal, however, is to secure the calculated retirement
funding need rather than to maximize accumulations. It should also
be emphasized that this method did not provide 100 percent success,
as 32 trials experienced terminal failure (that is, they ran out of
money). On the other hand, a 96.8 percent success rate isn't bad,
especially considering the fact that age 100 is used for the life
expectancy. If age 95 had been used, or if historical mortality
experience were considered, an even larger success ratio would have
been obtained. Further, the failure percentage for the next most
successful approach was almost four times as high: 12.3 percent vs.
3.2 percent.
Note again that this study assumed a 55- year time period from the
onset of accumulation through age 100, with 35 years during the
withdrawal period. Of course, all portfolios would have higher
success rates if a life expectancy shorter than age 100 were
used.
Conclusion
Individuals have different goals. Some will be interested in
maximizing potential bequests. Others will want to minimize
variability of returns. For those clients who want to maximize the
probability of achieving financial security, defined as maintaining
projected retirement withdrawals to age 100, the 100 percent
equities with annuity lock is the preferred approach.
The results suggest that a 100 percent (or at least very high
percentage) equities allocation is more defensible when the
annuitization alternative is considered and when retirement fund
investors recognize that success can be achievable before or after
the retirement date. Another important point is that, even if the
client reaches the annuitization trigger, there is, of course, no
requirement to annuitize. Indeed, market conditions and imputed
fixed income annuity rates at the "trigger date" may indicate that
maintaining a high equities balance is a better alternative.
Given the uncertainties in investment markets, it is worth noting
that investors who reached retirement between 2007 and early 2008
would have greatly benefited from employing annuitization
strategies. Annuitization strategies are not used to maximize
wealth, but to ensure that projected retirement withdrawals can be
maintained.
By specifying the annuity purchase as a future alternative, the
financial planner can encourage a higher-equities portfolio, which
will likely lead to a larger accumulation in retirement.
Endnotes
- Monte Carlo analysis provides an ideal method of measuring the
likelihood an investment portfolio and savings plan will
successfully reach a predetermined goal. Monte Carlo method
determines aggregate portfolio performance based on a series of
randomly generated returns tied to specific asset classes.
Thousands of trials are run, each containing a unique series of
random numbers. Each trial either succeeds or fails at meeting a
predetermined goal.
The authors would like to give special thanks to Wealthcare Capital Management, creator of Financeware.com, for permitting educational use of their Monte Carlo Software Tool. - Policies from the following companies were evaluated: Allianz Life, Penn Mutual, Prudential, AXA, and Mass Mutual.
- The authors studied both 128-age and 100-age allocations. Employing a 100-age approach achieved a success rate of 75 percent and failure rate of 25 percent. A lower equity portfolio allocation during the accumulation phase led to lower success rates of sustainable withdrawals for the 100-age model.
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