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“Contradictions do not exist. Whenever you think you are facing a contradiction, check your
premises. You will find that one of them is wrong.” – Ayn Rand

We often have an opportunity to re-educate clients about the
mechanics of retirement finance. New clients often bring along
financial plans from previous advisors, so we can compare the
practices of advisors from many other firms. Most firms use financial
plans as a sales tool to bring new clients in the door, and then stuff
the plan with optimistic assumptions. Plans constructed in this way
offer the illusion of pleasing results, and clients eagerly sign on for
solutions which promise to deliver retirement Nirvana.
Unfortunately, these plans often leave retirees only slightly better
than a 1 in 2 chance of outliving their retirement savings (see calculations below).

This article will present a retirement planning case study, and apply two different techniques to
discover safe retirement income. The first technique should be familiar to many readers, as we
will present standard charts and tables included in plans from most wealth management firms.
Next, we will test the results of the traditional approach by applying them to a more robust
planning approach adopted from the pension and insurance field. This should be a harsh eye-
opener for readers as we demonstrate how the planning approach applied throughout the
wealth management industry delivers a 1 in 3 chance that retirement plans will fail.

The table below shows how the actuarial approach makes use of 4 inputs, while the traditional
approach only accounts for 2.

Actuarial Approach Traditional Approach

–>Inputs –>Inputs

———> Expected Return ———> Expected Return

———> Portfolio Volatility ———> Median Remaining Lifespan

———> Median Remaining Lifespan
———> Confidence Level –>Output

———> Extraction Rate

–>Output
———> Safe Extraction Rate
Source: Butler|Philbrick & Associates

Definitions:

Expected Return: the average annual return that the portfolio is expected to return over a
person’s retirement horizon, adjusted for inflation

Portfolio Volatility: the degree to which the portfolio experiences ups and downs in value as
markets rise and fall

Common weaknesses in

retirement plans:

Don’t account for fees

Aggressive assumptions

Assume no volatility

Median Remaining Lifespan: the number of years between a person’s current age, and the age
at which the person has a 50% chance of mortality.

Confidence Level: the degree to which a retiree wants to be certain of success. For example a
more conservative retiree may want to be 85% confident of outliving his or her portfolio. In
contrast, a more adventurous retiree may wish to have a higher retirement income, and thus
settle for a lower confidence level, say 70%. Note that a traditional plan, by definition, provides
for a maximum of 50% confidence.

Safe Extraction Rate: the portion of a retiree’s portfolio that can be safely withdrawn each year
for income while maintaining an appropriate level of confidence in the future success of the
plan. For the traditional plan, the extraction rate reflects a median outcome: 50% of future
outcomes will cause the plan to fail.

Case Study Scenario

Imagine a 65 year old couple, Jack and Diane, about to retire. Like so many private healthcare
professionals, they have no private pension. Jack worked outside the home for over 40 years in
Canada, and Diane worked infrequently outside the home. In concert with their Advisor, they
collect the following information and assumptions. Note that Jack and Diane are both 65, and
will retire at the end of this year.

Combined RRSP Assets $1,000,000

Expected investment returns 7% per year

Expected inflation rate 3%

Lifespan planning horizon (MRL) Age 85

The ‘Lifespan planning horizon’, also called ‘Median Remaining Lifespan’ or MRL, needs some
explanation. A person’s MRL is the age at which the person has a 50% chance of mortality. For
example, at age 65 Jack has a 50% chance of living to age 82, so his median remaining lifespan
is 17 years. In contrast, at 65 Diane can expect to live over 20 more years to age 85.

For simplicity, we will assume that Jack and Diane elect to have a constant, inflation adjusted
income until Diane’s death, so they assume a time horizon equal to Diane’s MRL of 20 years.
Couples often elect to model for retirement income to drop upon the death of the first spouse,
but our contrary assumption does not materially affect the conclusions of our comparison.

Traditional Approach

The traditional planning model assumes that the couple will experience 7% returns on their
portfolio every year throughout retirement, with no ups or downs. This allows us to model a
simple pro-forma portfolio value and cash-flow forecast for each year of retirement, as shown
in the tables and charts below. These tables and charts should look familiar to those who have
worked through a financial plan with one of the major investment or accounting firms.

Year Age Starting Value Income Ending Value

1 66 $1,000,000 $70,102 $994,991

2 67 $994,991 $72,205 $987,380

3 68 $987,380 $74,371 $976,919

4 69 $976,919 $76,603 $963,339

5 70 $963,339 $78,901 $946,349

6 71 $946,349 $81,268 $925,637

7 72 $925,637 $83,706 $900,866

8 73 $900,866 $86,217 $871,675

9 74 $871,675 $88,803 $837,673

10 75 $837,673 $91,468 $798,439

11 76 $798,439 $94,212 $753,524

12 77 $753,524 $97,038 $702,440

13 78 $702,440 $99,949 $644,665

14 79 $644,665 $102,947 $579,638

15 80 $579,638 $106,036 $506,754

16 81 $506,754 $109,217 $425,365

17 82 $425,365 $112,494 $334,772

18 83 $334,772 $115,868 $234,227

19 84 $234,227 $119,344 $122,925

20 85 $122,925 $122,925 $0

$0

$20,000

$40,000

$60,000

$80,000

$100,000

$120,000

$140,000

$0

$100,000

$200,000

$300,000

$400,000

$500,000

$600,000

$700,000

$800,000

$900,000

$1,000,000

66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85

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End of Year Portfolio Value and Inflation Adjusted Income

Savings $1,000,000

Expected Return 7%

Inflation 3%

Portfolio Income $70,102

Source: Butler|Philbrick & Associates

You can see that a traditional model provides for Jack and Diane to extract $70,104 from their
portfolios each year, adjusted for inflation. This equates to an extraction rate of about 7% per
year from the portfolio ($70,000 / $1,000,000). We will use this 7% rate in our second analysis
below.

It is important to identify the salient features of the traditional plan as illustrated above.
Specifically, the solution above assumes:

constant returns to the portfolio of 7% every year with no variability
constant inflation of 3%
a fixed lifespan of 85 years.

The use of averages in the models without accounting for the variability around the averages
implies a great deal of ambiguity about the model’s likelihood of success. For example, if
expected average returns are to be 7% per year, by definition one must acknowledge a near
50% possibility of experiencing returns below this average, which would result in a failed
retirement plan. Further, if we assume an average (median) expected lifespan of another 20
years, there is by definition a 50% chance of living beyond this age, which would again result in
a failed retirement.

Actuarial Approach

Next we will contrast the results from the standard planning exercise above with an actuarial
approach. Our actuarial approach allows us to tailor the model inputs in ways that account for
the random nature of lifespan, inflation, and market returns.

The purpose of an actuarial approach is to tailor plans to accommodate the level of safety
needed by each individual retiree. In our experience with retirees, couples are uncomfortable
with the 50% chance of failure that is implied by the traditional approach above. In contrast,
the actuarial model allows couples to raise their level of confidence to 80% or more.

This approach also facilitates annual reviews which quantify whether a plan is on track based on
whether current portfolio values fall into a certain confidence level range. For example, a plan
can be reviewed each year, and incomes can be adjusted if confidence levels rise above, or fall
below certain thresholds, say 90% or 70% respectively.

Example of ‘Milestones Report’ tracking funded status of retirement portfolio.

What happens when we input the results from the traditional model into our actuarial model?
Before we can run this analysis, we must compute the ‘Portfolio Volatility’ input discussed
above. This is computed by finding the combination of stocks and bonds in a portfolio that
would provide for the 7% expected return assumed in our case study. In fact, if we use
historical returns as a guide a portfolio consisting of 70% stocks and 30% bonds would average
7% annual returns. This combination has a ‘Portfolio Volatility’ of 13.25%. (Source: Shiller, Yale,
2010)

The table and chart below summarize our assumptions and the results of our actuarial analysis.

Assumptions:

Total Return 7%

Inflation 3%

Expected Portfolio Volatility 13.25%

Median Remaining Lifespan 20 years

The red bar on the chart represents the 7% portfolio income rate per the results of the
traditional retirement analysis. Note the red line drawn from the red bar to the y-axis which
highlights the confidence level that arises from this 7% income extraction rate. The actuarial
analysis suggests that a 7% extraction rate, which equates to $70,000 income from Jack’s and
Diane’s $1 million portfolio, has a 66% chance of success. In other words, if they choose to take
$70,000 per year in income, adjusted each year for inflation, there is a 1 in 3 chance that Jack
and Diane will run out of retirement savings before Diane passes away. This is an unacceptable
risk for most retirees.

40%

45%

50%

55%

60%

65%

70%

75%

80%

85%

90%

95%

100%

3.0% 3.5% 4.0% 4.5% 5.0% 5.5% 6.0% 6.5% 7.0% 7.5% 8.0%

Probability of a Fully Funded Retirement at Various Income Extraction Rates
30% Bonds / 70% Stock Allocation

Income Extraction Rate (Inflation adjusted)

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Source: Moshe Milevsky, “A Sustainable Spending Rate without Simulation”, Financial Analysts Journal, 2005;

Butler|Philbrick & Associates

When we run this analysis with clients, we generally suggest that they target a confidence level
somewhere between 75% and 90%. The green bar on the chart above marks a 4.5% extraction
rate, which represents an 85% chance of successful retirement. Many clients feel that a
confidence level of 80% to 85% offers the right mix of income for lifestyle, and safety for the
future.

On Monte-Carlo Analysis

Some firms have begun to offer retirement plans based on Monte-Carlo analysis. This type of
analysis enables Advisors to provide a similar ‘confidence interval’ to the actuarial approach
described above. A Monte-Carlo approach is substantially better than the traditional approach,
because it accounts for the wide variety of possible futures by creating ‘alternative histories’
from historical market data. If used properly, this approach can provide a slightly more accurate
confidence interval than the actuarial approach described above.

Unfortunately, this approach is rarely used properly. Before engaging in a planning exercise that
incorporates Monte-Carlo simulations, it is imperative to ask your Advisor the time period the
model uses to source its data. For example, many Monte-Carlo models often use data just from
the past 20 or 30 years. By using data from 1990 or 1980 on, the results will be skewed to
higher returns than were experienced over longer time periods. An analysis based on this data
will suggest a higher withdrawal rate than might be advisable based on data over longer time
periods. This allows the Advisor to provide a more palatable answer for prospective clients, but
the answer may not be in the clients’ long-term interests.

Conclusion and Future Applications

We have examined two different approaches to retirement planning, and demonstrated how a
traditional planning model leaves unacceptable ambiguity about the likelihood of retirement
success. The vast majority of financial plans delivered to Canadian clients by major wealth
management, accounting and legal firms, apply the traditional approach. These plans make it
simple to present clients with many pages of detailed pro-forma retirement cash-flow
forecasts. Unfortunately, the traditional approach to planning is like playing Monty Hall’s ‘Let’s
Make a Deal’ with your retirement dreams. These plans are very precise, but not very accurate.

We propose that retirees should demand that Advisors apply an actuarial approach to calculate
their safe retirement income rate. This technique allows retirees to quantify their likelihood of
success, and track their progress. Further, investors should make sure that plans account for
after-tax management and/or trading fees, which might easily represent a drag of 2% or more
for most investors.

It is important to note that the analysis above is not a prescription, and should not be used for
planning purposes. The assumptions used are not necessarily appropriate for many investors,
and each retiree will have a different mix of values, goals, risk tolerances, and financial means.
Investors should consult their Advisor or contact us to discuss the creation of a customized

plan.

Future articles will discuss how introducing inexpensive simple annuities to cover non-
discretionary retirement expenses can substantially enhance overall after-tax retirement
income. Other topics will include investment strategies that can substantially improve
retirement income potential. More information is available at our website and blog.

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