4a Probability-of-Failure-Based Decision Rules to Manage Sequence Risk in Retirement JFP Nov 2011.pdf

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44 Journal of Financial Planning | November 2011
Contributions F r a n k | M i t c h e l l | B l a n c h e t t
• This paper demonstrates how
practitioners can better use the
often-overlooked probability of
failure as a decision tool.
• Withdrawal rates depend on the
retiree’s age (distribution time
remaining), and therefore withdrawal
rates alone do not tell a complete
sustainable distribution story.
• Probability of failure does not
depend on the retiree’s age and
is therefore useful for comparison
of withdrawal rates over any time
period or asset allocation.
• Comparison of probability-of-
failure curves, and their shift
between strategies, illustrates how
effective one strategy is compared
with another.
• The methodology presented
provides an ability to evaluate the
withdrawal rate and exposure to
sequence risk together.
• This paper seeks to answer the
question: how can you determine
when a withdrawal rate is too high,
as well as subject to poor (or good)
markets as the retiree ages?
• The paper concludes with practical
applications for practitioners from
two key insights: (1) results from a
prior simulation would be different
for a current simulation (differ-
ent transient states as defined
in the paper), and (2) a range of
probability of failure is desired
over trying to maintain a steady
probability of failure.
Executive Summary
Probability-of-Failure-Based
Decision Rules to Manage
Sequence Risk in Retirement
by Larry R. Frank Sr., CFP®; John B. Mitchell, D.B.A.; and David M. Blanchett, CFP®
, CLU, AIFA®
, QPA, CFA
Larry R. Frank Sr., CFP®
, is a registered investment
adviser in Rocklin, California.
John B. Mitchell, D.B.A., is professor of finance at
Central Michigan University.
David M. Blanchett, CFP®
, CLU, AIFA®
, QPA, CFA,
is the director of consulting and investment research
for the Retirement Plan Consulting Group at Unified
Trust Company in Lexington, Kentucky.
P
ast research on sustainable
withdrawal rates has focused
primarily on static simulations
based on the perspective of an “initial,”
or safe, sustainable withdrawal rate.
This approach ignores the fact that
the variables affecting retirement
income are dynamic over time. This has
been demonstrated by recent market
upheavals, which have caused many
practitioners to question the long-term
sustainability of withdrawal strategies.
In this paper, the authors demonstrate
a methodology in which the withdrawal
dollar amount dynamically adjusts as
the retiree ages.1
This dynamic concept is captured
using the term “current” as opposed
to “initial.” This becomes an iterative
process as the retiree continues to age
and the other variables subsequently
also change over time.
Past research has tended to focus on
safe withdrawal rates combined with
withdrawal-rate-based decision rules;
see for example Guyton (2004), Guyton
and Klinger (2006), Pye (2008), Stout
(2008), and Mitchell (2011). If the
retiree continues to strive to maximize
withdrawals as he or she ages, a result is
increased exposure to sequence risk. This
problem is exacerbated by unpredictable,
significant market movements (black
swans) as discussed by Mandelbrot and
Hudson (2004) and Taleb (2007). The
challenge is to manage both withdrawal
sustainability and ever-present sequence
risk (Frank and Blanchett 2010) when
adverse events occur (for example,
market declines or unexpected, large
required withdrawals).
The problem with a withdrawal rate
approach is that the withdrawal rate
alone does not directly inform the
observer whether ruin is imminent
for the (unknown) time remaining;
hence, various past researchers estab-
lished decision rules to manage this
exposure to sequence risk. Research

www.FPAnet.org/Journal November 2011 | Journal of Financial Planning 45
Contributions
F r a n k | M i t c h e l l | B l a n c h e t t
by Blanchett and Frank (2009)
suggests that withdrawal rates are
relatively “low” for longer planning
horizons, but increase as the retiree’s
distribution period shortens (as he or
she ages). Thus, withdrawal rates are
time-dependent (values that change
as the retiree ages), and therefore
are not useful variables when making
sequence risk decisions. This paper
demonstrates a methodology for evalu-
ating the use of probability of failure,
a time-independent variable (values
do not change as the retiree ages).
The retirement distribution problem
is a function of four variables that
can be plotted three-dimensionally:
time, withdrawal rate percentage,
portfolio allocation, and probability of
failure (POF). Our hypothesis is that
probability-of-failure-based decision
rules can be developed to warn a retiree
that adverse return sequences may put
distributions at risk of depletion within
his or her lifetime. With such a warning,
these same decision rules may suggest a
method for practitioners to adjust either
the portfolio allocation and/or with-
drawal amount to avoid running out of
money before the retiree’s death. This
paper uses fixed distribution periods.
A future paper by the authors will
integrate longevity with the methodol-
ogy presented here.
The point of reference for Guyton-
type decision rules is based on an
initial withdrawal rate. This is, by
definition, a time reference to some
point in the past. But what past time
point is relevant for this decision? This
paper shifts the point of reference for
decision rules into the future by using a
future-oriented reference point for the
time function. Therefore, this paper
always uses current withdrawal rates as
opposed to a previous initial, or safe,
withdrawal rate perspective.
The previously retired person who
may have experienced portfolio value
decline and hence seen his current
withdrawal rates go up (even though his
initial withdrawal rate from a previous
simulation may suggest they were
fine), needs to decide when to retrench
spending to the level suggested for new
retirees. This paper provides guidelines
for withdrawal management specifically
as a result of variable portfolio values
from market sequences.
Asset Classes, Time Sequencing, and
Simulation Periods
Monthly real returns for the five asset
classes shown below were collected
from January 1926 through December
2010. Inflation is measured by the
increase in the Consumer Price Index
for Urban Consumers, data obtained
from the Bureau of Labor Statistics.
• Cash: 30-day T-bill
• Bond: Ibbotson Associates Long-
Term Corporate Bond Index
• Domestic large-cap equity: S&P 500
• Domestic small-cap equity:
Ibbotson Associates U.S. Small
Stock Index
• International large-cap equity:
Global Financial Data Global ex
USA Index from January 1926 to
December 1969; MSCI EAFE from
January 1970 to December 2009
Portfolios are assumed to be com-
posed of cash/fixed and equity. The cash/
fixed component is 25 percent cash and
75 percent bond. The equity component
is 50 percent domestic large-cap equity,
25 percent domestic small-cap equity,
and 25 percent international large-cap
equity. For example, a 60/40 portfolio
(60 percent equity and 40 percent cash/
fixed) would be composed of 10 percent
cash, 30 percent bond, 30 percent
domestic large-cap equity, 15 percent
domestic small-cap equity, and 15
percent international large-cap equity.
Simulation distribution periods in
Figure 1 are 40 through 10 years, in
one-year increments. The purpose of
this first step in the investigation is to
parse out where probability-of-failure
landscapes plot (0–5 percent landscape,
5.1–10 percent landscape, etc.), which is
a new approach.
Probability of Failure Serves as a Baseline
for Subsequent Comparison
Step 1 generates fixed-withdrawal-
rate data (Figure 1) to provide the
baseline data for subsequent strategy
comparisons. Fixed real (inflation-
adjusted) distributions are taken from
the portfolio at the beginning of each
year in a 10,000-run Monte Carlo
generator. Probability of failure is
defined as the percentage of portfolios
with negative values at the end of the
planning horizon.
The withdrawal rate problem is
three-dimensional. A dynamic approach
investigates changes along all three axes
simultaneously. Most research consists
primarily of keeping the allocation
within a single static asset allocation for
the duration of the distribution time.
Little research (see Garrison, Sera, and
Cribbs 2010 for a recent exception) has
explored the dynamic effect of changing
the portfolio allocation within the simula-
tion, as has been done for dynamically
changing withdrawal rates within the
simulation over time (Blanchett and
Frank 2009).
All points graphed in Figure 1 have
the same approximate probability-
of-failure rate throughout the same
probability-of-failure landscape. Higher
probability-of-failure landscapes would
map out higher on the withdrawal rate
axis because corresponding withdrawal
rates are higher; that is, the 5 percent
probability-of-failure landscape would
lie under the 20 percent probability-of-
failure landscape, which in turn is below
the 30 percent probability-of-failure
landscape for all periods and asset allo-
cations. Note that as distribution time
shortens, withdrawal rates may increase,
all with a similar approximate exposure
to probability of failure. For example,
with 60 percent equity allocation, a 3.5

percent withdrawal rate is possible for
30 years, and a 6.05 percent withdrawal
rate is possible for 15 years, both with
a 10 percent probability of failure;
correspondingly, withdrawal rates of
4.75 percent for 30 years and 7.6 percent
for 15 years co-exist on the 30 percent
probability-of-failure landscape.
Figure 2 shows four cross-sections of
Figure 1 at various distribution periods
to illustrate longer-term distributions
for early retirees (35 years), mid-term
periods (25 and 20 years), and a short-
term distribution period (10 years) for
older retirees (all other cross-sections
co-exist throughout the time-remaining
axis). These sample cross-sectional
views through the probability-of-failure
landscapes allow better visualization of
how the withdrawal rates with the same
probability of failure shift up as distribu-
tion time shortens. Consistent tenden-
cies also emerge as to asset allocations.
Stopping the illustrations at any
particular probability of failure is
arbitrary (the authors stop illustration
at 50 percent probability of failure).
Probability-of-failure landscapes exist
along the full spectrum between 0 to
100 percent.
This paper extends previous research
in order to answer the following ques-
tions: what are more refined decision
rules for a retiree? At what withdrawal
rate does a retiree need to reduce his
withdrawal amount? More importantly,
is a single “withdrawal-rate-adjustment
rule” true at any probability of failure,
time period, or asset allocation? These
are questions the practitioner needs to
be able to answer.
Past research has usually stopped at
this point without a good answer as to
when the withdrawal rate may be exces-
sive. Additional comparative data are
required to properly address this issue.
The objective of our research is
to separate out two strategies over
which a retiree has any real control:
(1) changing the asset allocation, or
(2) changing the withdrawal amount.
The final step is to determine what
decision rules emerge to aid distribu-
tion decisions as the retiree continues
to encounter sequence risk, positive
or negative, throughout retirement. In
summary, Step 1 established a baseline
upon which to compare subsequent
research Steps 2 and 3 in order to
develop a decision-rule regime.
Recall the fundamental withdrawal
rate equation: withdrawal rate equals
the withdrawal dollar amount divided
by the portfolio value. Because portfolio
values fluctuate as a result of market
sequences, a retiree’s withdrawal rate
fluctuates inversely to portfolio value;
hence, probability of failure fluctuates
along with the withdrawal rate. This
dynamic suggests that a practical
application would be to accept a range
of acceptable probability of failure. At
any particular probability of failure,
as portfolio value shrinks from a bad
market sequence, probability of failure
would increase, but may not yet require
a retrenchment decision to remain
at a reasonable risk level. Is there a
maximum probability of failure at which
a retiree must retrench spending or
face runaway risk? The high end of the
probability-of-failure range emerges
from data in Step 2.
Transient States
The above baseline data set represents
starting a fixed withdrawal at each
moment in time and is developed in
order to evaluate and compare strate-
gies. Although the simulations are run
with fixed withdrawals, in reality each
simulation data point is transient
Figure 1: Probability-of-Failure (POF) Landscapes for Fixed
Withdrawals (F$)
40
35
30 25 20 15 10
0%
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
0
%
2
0
%
4
0
%
6
0
%
8
0
%
1
0
0
%
Allocation (Equity %) Years Remaining
10% POF Landscape
9–10%
8–9%
7–8%
6–7%
5–6%
4–5%
3–4%
2–3%
40
35
30 25 20 15 10
0%
1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
11%
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Allocation (Equity %) Years Remaining
30% POF Landscape
10–11%
9–10%
8–9%
7–8%
6–7%
5–6%
4–5%
3–4%
Withdrawal
Rate
Withdrawal
Rate
Withdrawal
Rate
Withdrawal
Rate

Contributions
depending on factors beyond the
retirees’ control: (1) the decreasing time
remaining for the retirees’ distribution
as they age (Blanchett and Frank 2009,
Frank and Blanchett 2010) and (2) the
portfolio value.
Practitioners tend to think in terms
of simulations and project a single
result (the “safe withdrawal rate”)
“forever” into the future. However, in
truth, simulations or calculations are
projected results representing only that
single point in time, which is in a tran-
sient state. If we run a simulation at
time T1
, we get a certain single result.
However, the variables change as time
passes. Later, at time T2
, when for
example the market has declined 5 per-
cent, we run another simulation and
get a different single result. The same
occurs at time T3
, when the market is
now down 10 percent relative to T1
.
The same process continues to happen
as long as the market declines at each
period. All of these results are correct
for their given conditions. Should the
market recover, the reverse occurs. So
practitioners need to look not only at
probability-of-failure decision points
while the market deteriorates but
also at decision points to reverse the
process as the market recovers.
Each data point in Figures 1 and 2
represents the transient state defined
by the results of a particular simulation
run. The probability-of-failure results of
that simulation would plot somewhere
within the three-dimensional space
defined by time, withdrawal rate, and
portfolio allocation and represent the
current transient state of that retiree
at that moment. Other retirees would
be at different transient states based
on their simulation parameters. Thus
all transient states co-exist (Figure 1);
the exercise is to determine the current
retiree state and the implications of the
current state as the retiree transitions to
another state and needs to dynamically
recalculate to her new circumstances.
In other words, old calculations
no longer represent current facts.
A retiree moves vertically to other
probability-of-failure landscapes
(Figure 1) over time because of
fluctuating portfolio values. These
values can only follow a landscape if
she constantly adjusts her withdrawal
amount. Changing allocation also
shifts the retiree’s position on a
landscape. This dynamic perspective is
different than a static perspective and
may eventually lead to physics-type
formulas to determine the retiree’s
ability to sustain distributions during
her lifetime.
The transient nature of results as a
function of time and sequence risk,
good or bad, is the impetus for evaluat-
ing the relative transient states of other
possible withdrawal strategies. If a
retiree changes her allocation and/or
Figure 2: Time Cross-SectionsThrough Figure 1,FixedWithdrawals (F$)
0%
2%
4%
6%
8%
10%
12%
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
Withdrawal
Rate
%
Allocation (Equity %)
35-Year Fixed (F$) (POF % Surfaces)
POF %
0%
2%
4%
6%
8%
10%
12%
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
Withdrawal
Rate
%
0%
2%
4%
6%
8%
10%
12%
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
Withdrawal
Rate
%
0%
2%
4%
6%
8%
10%
12%
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
Withdrawal
Rate
%
50% 40% 30% 20% 10%

her withdrawal amount at any time,
how does this change her probability
of failure?
The Next Two Steps
For Step 2, the distribution withdrawal
dollar amount changes (potentially
each year) based on the previous annual
return of the portfolio. If the portfolio
return is greater than 0.5 standard
deviations above the average, then the
dollar withdrawal is increased by 3
percent (for example, a portfolio with
an average expected real return of 5
percent and standard deviation of 10
percent would need to experience a real
return of 10 percent (5 percent + (0.5
x 10 percent)) or greater. If the port-
folio return is more than 0.5 standard
deviations below the average, then the
dollar withdrawal is decreased by 3
percent. Use of 3 percent is an arbitrary
rate of adjustment. Higher rates of
adjustment would more effectively
manage probability-of-failure exposure
through fewer adjustments, but at the
expense of greater changes in lifestyle
for the retiree. The portfolio allocation
is not changed in this step, only the
dollar withdrawal amount. Standard
deviation is used as the decision variable
in order to properly scale results three-
dimensionally for asset allocations.
For Step 3, the equity allocation of the
portfolio changes (potentially each year)
based on the previous annual return of
the portfolio. If the portfolio return is
more than 0.5 standard deviations above
(or below) the average, the equity alloca-
tion would be increased (or decreased)
by 10 percent. The dollar withdrawal
is not changed in this step, only the
allocation.
By comparing the differences
between the withdrawal rates along the
same probability-of-failure landscapes
between the fixed withdrawal and
dynamically changing variable with-
drawal simulations in Steps 2 and 3, the
practitioner can evaluate the efficacy of
various dynamic strategies.
Step 2. Comparison of POF Landscapes
Between Varying Withdrawals (V$) Within
Simulations and Fixed-Dollar (F$)
Step 2 adjusts the withdrawal dollar
amount in response to negative or
positive market return sequences.
Figure 3, illustrating a commonly
researched period, is similar to Figure
2, but shows both a variable dollar
(V$) amount (spending retrench-
ment/expansion) strategy (Step 2)
and the fixed-dollar (F$) strategy
(Step 1) in order to illustrate the
differences in withdrawal rate at the
same probability of failure (POF).
Notice that the variable-dollar
probability-of-failure landscapes
shift up; that is, the corresponding
variable-dollar withdrawal rate is
higher for each probability-of-failure
landscape (Blanchett and Frank
2009). For example, at a 10 percent
probability of failure, a 60 percent
equity allocation results in a fixed
3.5 percent withdrawal rate, and the
variable-dollar withdrawal rate is 4.2
percent.
When there is a difference along all
time periods between comparative data
sets, this suggests a possible strategy
application (the greater the differences,
the more effective the strategy and
vice versa). The left side of Figure 4
represents a negative, or bad, market
sequence for 35-, 25-, and 10-year
periods for a strategy of withdrawal
dollar amount adjustment (V$). The
right side of Figure 4 represents a
positive, or good, market sequence for
the given period.
The differences in Figure 4 represent
the percentage magnitude of change
between the fixed-dollar withdrawals
data (F$) in Step 1 and variable-dollar
withdrawals data (V$) in Step 2 (as
illustrated in Figure 3). For example,
a 1 percent withdrawal rate change
from 4 percent to 5 percent for a rising
withdrawal rate (bad market, left side:
portfolio value declines; hence, with-
drawal rate increases) would represent
a 25 percent change ((V$ – F$)/F$). Or
a 20 percent change for the 1 percent
withdrawal rate change from 5 percent
to 4 percent for a declining withdrawal
rate (good market, right side: portfolio
value increases; hence, withdrawal rate
decreases, (|(F$ – V$)/V$|). Absolute
value is used here so that the magni-
tudes of change can be compared side
by side in Figure 4. The comparison is
between similar landscapes, for example
Figure 3: Comparison of Probability-of-Failure Landscapes Between
Fixed-Dollar (F$) andVariable-Dollar (V$) Strategies for
30-Year Plane
0%
1%
2%
3%
4%
5%
6%
7%
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
Withdrawal
Rate
%
50% V$
50% F$
40% V$
40% F$
30% V$
30% F$
20% V$
20% F$
10% V$
10% F$
POF %

Contributions
10%F$ to 10%V$ and so on.
The purpose of this strategy compari-
son is to see where probability-of-failure
landscapes emerge as a decision point.
Notice in Figure 4 that the differ-
ences between both strategy data sets
compress and move closer to zero as
the probability of failure increases; for
example, the 50 percent POF percent
data set differences are smaller than
the 10 percent data set differences. This
compression becomes more pronounced
from 30 percent to 50 percent POF.
The compression of the withdrawal
rate curves in Figure 4, or reduced
differences between data sets (which
means dollar adjustments are not as
effective at this point), suggests that the
withdrawal dollars should be adjusted as
the probability of failure approaches 30
percent (probability of failure not to be
confused with withdrawal rate), because
this is when the compression of data
differences begin to occur. Thus, results
here suggest that a probability-of-failure
range is a more useful approach. Of
course, practitioners and their clients
Figure 4: Left Half:Negative Sequence (Bad Market);Right Half:Positive Sequence (Good Market) for
35-,25-,and 10-Year Periods
0%
5%
10%
15%
20%
25%
30%
35%
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
Withdrawal
Rate
%
Differences
Between
V$
and
F$
35-Year Bad Market Sequence
0%
5%
10%
15%
20%
25%
30%
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
Withdrawal
Rate
%
Differences
Between
V$
and
F$
35-Year Good Market Sequence
0%
5%
10%
15%
20%
25%
30%
35%
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
0%
5%
10%
15%
20%
25%
30%
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
–5%
0%
5%
10%
15%
20%
25%
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
–5%
0%
5%
10%
15%
20%
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
10% 15% 20% 25% 30% 40% 50%
POF %
Withdrawal
Rate
%
Differences
Between
V$
and
F$
Withdrawal
Rate
%
Differences
Between
V$
and
F$
Withdrawal
Rate
%
Differences
Between
V$
and
F$
Withdrawal
Rate
%
Differences
Between
V$
and
F$
Please take note of the difference in scale among charts within this figure.

are free, indeed encouraged, to adopt
lower probability-of-failure thresholds,
for example, 20 percent, for the upper-
range decision value.
The withdrawal rate differences
are not consistent as the distribution
period shortens; for example, for
the bad market, 60 percent equity at
35 years, the data difference is 18.1
percent, but it is 7.9 percent at 10 years
(both on the 15 percent probability-of-
failure landscape).
Why 30 percent probability of failure
as a maximum decision point? For
probability-of-failure rates higher than
30 percent, differences in withdrawal
rate data are much smaller, more sensi-
tive to portfolio value changes, regard-
less of allocation. Thus more withdrawal
dollar amount adjustments would be
necessary to change probability-of-
failure exposure; that is, at high prob-
ability of failure, risk changes quickly.
The results in Figure 4 show that the
amount of withdrawal rate change is not
a constant, but changes depending on
distribution period, portfolio allocation,
and the probability of failure with which
the retiree is comfortable.
Waiting for markets to improve the
portfolio value later in order to improve
the probability of failure (depending on
the historical improvement of markets)
may not be prudent because market
improvements may be long in coming.
The methodology developed here
measures the probability of failure in
order to prudently adjust the withdrawal
rate sooner rather than later in response
to what is actually occurring. Monitor-
ing the improvement of probability
of failure during moments
of positive sequence risk
provides a signal to increase
the withdrawal dollar amount
as well.
Practitioners should
think in terms of returning
their clients to within an
acceptable range of prob-
ability of failure in both
good and bad markets. The
acceptable range for prob-
ability of failure should be
client-specific per his risk
tolerance. However, the
higher the probability of
failure (hence, withdrawal
rate) the greater the necessary vigilance
because it takes less of a portfolio value
change to move quickly into even higher
probability-of-failure rates (Figure 4).
Readers are reminded to think in terms
of an acceptable range of probability of
failure because probability of failure will
fluctuate as portfolio values fluctuate.
Maintaining a fixed probability of failure
is only possible by maintaining a fixed
withdrawal rate, which translates to vari-
able income when most retirees prefer a
steady income (fewer retrenchments).
Step 3. Comparison of POF Landscapes
Between Variable Portfolio Allocation (VA)
Within Simulations and Fixed-Dollar (F$)
Garrison, Sera, and Cribbs (2010)
dynamically change portfolio allocation
during simulations using a trailing
12-month simple moving average as the
portfolio-switching signal. Here we use
the change in the portfolio value itself as
the signal to switch between portfolios
as described in methodology above. The
results from this step will be compared
with the fixed-dollar results from Step 1.
Figure 5 illustrates the withdrawal rate
differences and compares fixed-dollar
data (Step 1) to variable-allocation data
(Step 3) between comparable probability-
of-failure landscapes during either
negative sequence (bad markets, left
side) or positive sequence (good markets,
right side). Percentage changes in the
withdrawal rate are calculated the same
here as in Figure 4.
In Figure 5, the tolerable change of the
withdrawal rate (the withdrawal amount
compared with the portfolio value) is
around 1 percent or less for bad market
sequences. The probability-of-failure
data differences are so small (values less
than 1 in most cases) during bad market
sequences that in this case a portfolio
adjustment strategy would not enhance
the retiree’s probability of failure.
The right side of Figure 5 represents a
positive (good) market sequence for the
stated distribution period. The percent
change in withdrawal rate is much
larger, comparable to that of increasing
the withdrawal dollar amount in Step 2.
However, that effect tends to disappear
as the equity allocation is reduced to
approximately 50 percent or less.
Changing portfolio allocation in
response to sequence risk is ineffec-
tive in changing the probability of
failure. The negative sequence (bad)
market series (left side of Figure 5),
has values so small, or even negative
(indicating the fixed strategy has
higher withdrawal rates), that they are
essentially the same as the fixed-rate
withdrawal rate values. Although the
change in withdrawal rate values is
large for the positive sequence (good)
market series (right side of Figure 5),
the dilemma is that this would imply
allocating more aggressively during
growing markets to take advantage
of opportunities to increase the
portfolio values but not allocating
more conservatively during declining
“Practitioners should think
in terms of returning their
clients to within an acceptable
range of probability of
failure in both good and bad
markets.
”

Contributions
markets, which is not a practical or
logical combination strategy.
These results suggest that changing
portfolio allocation may be a more
effective behavioral management tool.
However, changing allocation solely to
manage exposure to sequence risk and
reduce exposure to probability of failure
is not as effective as retrenchment.
The general flatness of the withdrawal
rate curves in Figures 2 and 3 also
suggests this ineffectiveness because the
withdrawal rates across the allocation
spectrum are very close in value.
Further research combining a different
allocation switching rule, for example
one used by Garrison, Sera, and Cribbs
(2010), with this probability-of-failure-
based methodology would be interesting.
Subsequent research is needed on
integrating model-based rules with
retiree behaviors during both adverse and
positive sequence-risk periods.
Practical Applications
A retiree’s withdrawal rate, in
reality, is not fixed. Recall that the
Figure 5: Left Half:Negative Sequence (Bad Market);Right Half:Positive Sequence (Good Market) for
35-,25-,and 10-Year Periods
10% 15% 20% 25% 30% 40% 50%
POF %
–0.6%
–0.4%
–0.2%
0.0%
0.2%
0.4%
0.6%
0.8%
1.0%
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
Withdrawal
Rate
%
Differences
Between
Allocation
Chg
and
F$
–0.4%
–0.2%
0.0%
0.2%
0.4%
0.6%
0.8%
1.0%
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
–0.4%
–0.2%
0.0%
0.2%
0.4%
0.6%
0.8%
1.0%
1.2%
1.4%
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
–15%
–10%
–5%
0%
5%
10%
15%
20%
25%
30%
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
Withdrawal
Rate
%
Differences
Between
Allocation
Chg
and
F$
–10%
–5%
0%
5%
10%
15%
20%
25%
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
–5%
0%
5%
10%
15%
20%
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
Withdrawal
Rate
%
Differences
Between
Allocation
Chg
and
F$
Withdrawal
Rate
%
Differences
Between
Allocation
Chg
and
F$
Withdrawal
Rate
%
Differences
Between
Allocation
Chg
and
F$
Withdrawal
Rate
%
Differences
Between
Allocation
Chg
and
F$
Please take note of the difference in scale among charts within this figure.

Contributions
withdrawal rate is a function of the
withdrawal dollar amount divided by
the portfolio value (with an inverse
relationship to the market sequence):
as market values go down, withdrawal
rates go up and vice versa. Thus, over
time, the withdrawal rate changes as
a result of market effects on the port-
folio value. The fundamental question
is: at what withdrawal rate should
a retiree be concerned during poor
markets? Or, during good markets:
how much more can the retiree afford
to spend for a vacation?
However, as demonstrated above,
using the withdrawal rate alone as the
primary factor to answer these questions
is problematic because the withdrawal
rate depends on the retiree’s age (dis-
tribution time remaining). This paper
shows that probability of failure auto-
matically accounts for the withdrawal
rate that corresponds to the remaining
distribution period for each retiree. Thus,
probability of failure forms the basis for
adjusting the withdrawal amount. With
his withdrawal dollar amount, a retiree
transitions through various transient
states as the markets change his portfolio
values; that is, he transitions through
probability-of-failure landscapes in Figure
1 as his portfolio values change.
For example, a retiree with a
20-year horizon and 60 percent equity
allocation in a $1 million portfolio
may currently have a 4.75 percent
withdrawal rate that provides $47,500
annually with a 10 percent probability
of failure (transient state 1). Shortly
after, a poor market sequence may
reduce the portfolio value to $913,462
for a withdrawal rate of 5.2 percent
(transient state 2 with $47,500) at a 15
percent probability of failure. Con-
tinued poor markets may reduce the
portfolio value to $772,358
for a 6.15 percent withdrawal
rate with a corresponding
30 percent probability of
failure (transient state n with
$47,500). See Figure 2.
Therefore, the practical
application comes from the
ability to pre-calculate the
corresponding portfolio
values by using the with-
drawal rates that correspond
to various probabilities of
failures, and have a discussion
with the retiree beforehand
about what his portfolio value
thresholds may be for spend-
ing retrenchment decisions as well as
providing time to make those spending
changes as needed. Thus, this retiree
needs to consider reducing expenditures
to $36,687 (4.75 percent withdrawal
rate of $772,358 to return back to the 10
percent probability-of-failure landscape)
if he chooses to wait to make this decision
at 30 percent probability of failure. Note
that it is not certain the portfolio value
will reach $772,358; however, should
it do so, spending retrenchment is
suggested at this point.
Most retirees would probably choose
to retrench sooner, at a lower prob-
ability of failure, in order to have a
higher distribution amount. However,
prior to this paper, it was not clear at
what point that retrenchment decision
should be made. These portfolio values
would be different for an older retiree
who may have an 8 percent withdrawal
rate (10-year distribution period), or
a younger retiree who would have
lower withdrawal amounts (30 years);
however, the range of probability of
failure up to a maximum value is useful
in predetermining portfolio values for
decisions for all retirees.
Because this is a dynamic process: a
retiree who retrenches (or increases)
spending needs to recalculate a new set
of retrenched (or increased) portfolio
values that represent his adjusted
transient state rather than his prior
state. That is, when his withdrawal
dollar amount changes, the prior
set of calculations no longer applies
(for example, recalculating decision
portfolio values based on $36,687 in the
example above).
Notice that the authors are not sug-
gesting either a 0 percent probability
of failure or 30 percent probability
of failure as absolutes. Rather, the
suggestion is that portfolio values
float as a result of market forces and
thus a practical range of acceptable
probability of failure needs to be
recognized (otherwise, the retiree is
constantly adjusting his withdrawal
dollar amounts to maintain any
given probability-of-failure landscape
(Figure 1)). A range of probability-
of-failure values generates a range of
useful portfolio values with which
a retiree can make more informed
decisions beforehand.
The opposite applies for good market
sequences. In the above example, the
retiree may consider returning to his
higher spending level as markets improve
his portfolio value. For example, the
retiree now has $1.2 million, and a 4.75
percent withdrawal rate (10 percent
probability of failure) provides $57,000
this year; thus the retiree may consider
using the $9,500 ($57,000–$47,500) for
his vacation this year (with the under-
standing that poor market sequences may
require future retrenchments).
“This paper shows that
probability of failure
automatically accounts for
the withdrawal rate that
corresponds to the remaining
distribution period for each
retiree.
”

Contributions
Conclusion
The objective of our research is to
establish probability-of-failure-based
decision rules to aid practitioners in a
forward-looking evaluation of retirees’
current exposure to sequence risk and to
pre-determine portfolio values that may
trigger retrenchment.
This paper introduces a method to
demonstrate the concepts for purposes
of broadening the perspective on
sustainable distributions into three
dimensions. The authors introduce the
methodology to compare data sets of a
proposed strategy against the baseline
fixed-rate data to determine the
efficacy of the proposed strategy and
to determine refinements and possible
break points for decisions using the
proposed strategy.
A desire for low probability of failure
comes with the cost of a low withdrawal
rate requiring more assets to sustain
distributions. However, the desire for a
higher withdrawal rate (and therefore
higher probability of failure) has the
cost of increased sensitivity to sequence
risk, resulting in more frequent dollar
distribution adjustments to reduce prob-
ability of ruin. For these reasons, the
authors suggest as more practical a range
of retiree-acceptable probabilities of
failure because portfolio values, which
are what trigger the need for a deci-
sion, fluctuate—as opposed to control
of the distributions to some specific
probability-of-failure value, which
implies a fixed withdrawal rate and thus
variable withdrawal dollar amounts. In
other words, either the withdrawal rate
or the withdrawal dollar amount needs
to fluctuate.
• Rather than a single safe with-
drawal rate, there exists a range of
withdrawal rates corresponding to
varying degrees of probability-of-
failure exposure.
• A higher relative probability of
failure is more sensitive to a change
in the current withdrawal rate
(portfolio value); that is, even small
changes in portfolio value (with-
drawal rate) necessitate changes in
dollar withdrawals, or retirees risk
radical changes in probability of
failure.
• The natural tendency would be to
seek an optimal solution. Rather, an
upper limit combined with a range
of acceptable probability-of-failure
values is more realistic because
a transient-states perspective
suggests fluidity.
• Changing the withdrawal amount is
more effective in managing retiree
exposure to sequence risk than
changing the portfolio allocation.
In summary, the probability-of-failure
results of each simulation, from a given
set of distribution parameters, is a
description of a single state that can be
plotted three-dimensionally relative to
other simulation probability-of-failure
results that describe other sets of distri-
bution parameters (Figure 1). The entire
set of three-dimensional plots describes
the distribution system. Each retiree
moves through various states in a tran-
sient fashion as time and portfolio values
change. Retiree actions, for example
changing withdrawal amount or portfolio
allocation, also change the transient state
by changing the retiree’s probability of
failure. Frank and Blanchett (2010) argue
that exposure to sequence risk never goes
away. This paper develops a methodol-
ogy to evaluate that exposure to sequence
risk for any given transient state and
what retiree action may effectively
change that sequence-risk exposure.
Endnote
1. An extended version of this research working
paper is available at SSRN: http://ssrn.com/
abstract=1849868.
References
Blanchett, David M., and Larry R. Frank. 2009. “A
Dynamic and Adaptive Approach to Distribu-
tion Planning and Monitoring.” Journal of
Financial Planning 22, 4: 52–66.
Frank, Larry R., and David M. Blanchett. 2010.
“The Dynamic Implications of Sequence Risk
on a Distribution Portfolio.” Journal of Financial
Planning 23, 6: 52–61.
Garrison, Michael M., Carlos M. Sera, and Jeffrey
G. Cribbs. 2010. “A Simple Dynamic Strategy
for Portfolios Taking Withdrawals: Using a
12-Month Simple Moving Average.” Journal of
Guyton, Jonathan T. 2004. “Decision Rules and
Portfolio Management for Retirees: Is the ‘Safe’
Initial Withdrawal Rate Too Safe?” Journal of
Guyton, Jonathan T., and William J. Klinger.
2006. “Decision Rules and Maximum Initial
Withdrawal Rates.” Journal of Financial Planning
19, 3: 49–57.
Mandelbrot, Benoit, and Richard L. Hudson.
2004. The Misbehavior of Markets: A Fractal
View of Financial Turbulence. New York: Basic
Books.
Mitchell, John B. 2011. “Withdrawal Rate
Strategies for Retirement Portfolios: Preven-
tive Reductions and Risk Management.”
Financial Services Review (forthcoming). An
earlier version is available at: http://ssrn.com/
abstract=1489657.
Pye, Gordon B. 2008. “When Should Retirees
Retrench? Later Than You Think.” Journal of
Stout, R. G. 2008. “Stochastic Optimization of
Retirement Portfolio Asset Allocations and
Withdrawals.” Financial Services Review 17:
1–15.
Taleb, Nassim N. 2007. The Black Swan: The
Impact of the Highly Improbable. New York:
Random House.

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