Tom O'Haver, University of Maryland, April 1998. Revised April,
translation by Weronika Pawlak. Dutch
translation by Johanne Teerink.
This simulation shows how much income you can withdraw from a
retirement account of (e.g. an IRA or 401k account) that is
invested it in a combination of fixed-interest or variable
(equity) instruments, assuming that all interest and capital gains
are re-invested and not taxed. You can control the income
withdrawn, the return on the fixed-income and equity portions of
your investments, and the volatility (uncertainty) of the equity
portion. Graphs show the variation of principal and monthly income
vs time for a 35-year period of retirement (for example, from age
65 to 100, or from age 60 to 95). (A companion simulation, the Investment Simulation Spreadsheet
can be used to estimate the principal that can be accumulated by
investing in your working years). Instructions and further
explanation is available on https://terpconnect.umd.edu/~toh/simulations/Instructions.html
Note: This simulation was developed for instructional purposes
and is not intended a tool for detailed personal financial
planning. It does not take into account certain personal and legal
factors that may apply to citizens of the USA, such as: additional
income from pensions, Social Security, or wage earnings; income
taxes and capital gains taxes; IRS penalties for early withdrawal
before age 59 or for excess withdrawls above $150,000 per year;
and IRS minimum required withdrawls from tax-deferred accounts
after age 70 1/2.
This simulation is available in three different spreadsheet
The Microsoft Excel version is in
Excel 97/2000/XP format. You must own Excel or Microsoft Office
in order to run this version.
The original WingZ version is still available. This version
uses mouse-controlled sliders for input control and was
developed using WingZ 1.1, an object-oriented spreadsheet for
Windows, Macintosh, and UNIX. You must own a copy of WingZ 1.1
to run this version. You may download this version of the
simulation in binary or HQX format.
Initial principal: This is the total amount invested in
your retirement accounts at the beginning of retirement. You may
use the Investment Simulation
Spreadsheet to estimate the principal that you are likely
to have at retirement.
Yearly income, initial $: This is used if you wish to
withdraw a certain dollar amount from your principal each year
as income, no matter how your principal may fluctuate because of
variable investment returns. This will be the dollar amount
taken in the first year (which may increase in following years,
as determined by the next input item, Yearly Increase).
Yearly Increase: The percentage factor by which you
wish to increase your income each year (i.e. to compensate for
inflation). If this is set to zero, it means you will take the
same income each year.
Yearly income as % of principal: This is used if you
wish to withdraw a fixed percentage of your principal each year
as income, which may therefore fluctuate from year to year
because of variable investment returns. Note: Your total income
will be the sum of the dollar amount specified by the above two
input variables and the percentage of principal specified by
Expected Return on Fixed. The average annualized
return on the fixed-interest portion of your investment
portfolio (such as bonds or certificates of deposit). Typical
fixed account returns are 3 - 6%. Returns on these types of
accounts vary so little from year to year that they can be
considered effectively "fixed".
Expected Return on Equities. The average annualized
return on the equity (stock and stock fund) portion of your
investment portfolio. Returns on equity investments are
typically greater than that on fixed investmentss. Typical
equity returns are 10 - 20%.
Fraction in equities. The fraction of your portfolio's
value that is invested in equities (stocks and stock funds). If
you set this to zero, it means that all your portfolio is in
fixed investments (an ultra-conservative stance); if it is set
to 100, all your investments are in equities (a more aggressive
Volatility (Sigma). This simulates the volatility of
the equity portion of your portfolio, by controlling the
year-to-year fluctuation of the equity returns. If you set this
to zero, it means that there is no fluctuation in the returns
(an unrealistic supposition). Volatility is measured in "sigma"
(standard deviation). Typical sigmas for individual equity
mutual funds are 10 to 20%, but a well-balanced portfolio of
diverse fund types may have a volitility somewhat less than
Principal in Year 35: The principal remaining in the
35th year of retirement (age 100 if you retire at 65).
Total income: The total amount that you have taken as
income over the 35-year period of the simulation.
Annualized return: The average annual return on your
entire portfolio (fixed and equity portions combined) over the
35-year period of the simulation. This will typically differ
somewhat from the "Expected return" set in the Inputs because of
the volatility of equity investments.
Principal: The total value of your invested principal.
The x-axis is the number of years of retirement.
Annual income withdrawn: This is your total gross
(pre-tax) yearly income. The x-axis is the number of years of
retirement. If your principal is held in a tax-deferred
retirement account (e.g. an IRA or company-sponsored qualified
401k plan), you will have to pay ordinary income taxes on this
income. If your principal is held in a Roth IRA account, you
will have already paid the income taxes and therefore this
represents your after-tax (take home) income.
Annual return on equities: This simulates the
year-to-year variation in the annualized return on the equity
(stock and stock fund) portion of your investment portfolio. The
average is controlled by the "Equity Return" variable and the
fluctuation (variation) is controlled by the "Volatility"
variable. Every time you recalculate the spreadsheet, another
random set of returns is calculated.
Start with the Initial principal set to, say, $1,000,000 and
all the other variables set to zero. Obviously in this case you
are taking no income, so the income graph stays at zero and
principal graph stays flat.
Increase the "Yearly income, initial $" variable and notice
the effect: the annual income graph is a flat line (constant)
and the principal graph is a straight line sloping down, showing
the depletion of principal. Set the $ income to $100,000/year.
In this case you can do the math in your head - you are
obviously going to run out of money in 10 years, and this is
shown by the graphs as you would expect. Question: What is the
largest annual income you can take that will cause your money to
last for at least 35 years? Do you consider that a reasonable
annual income for someone starting out with a million dollars?
Return the "Yearly income, initial $" to zero. Increase the
"Yearly income as % of principal" and notice the effect: the
both the annual income graph and the principal graph are now
curved lines. This is because the income is calculated as a
fixed percentage of the principal, so as the principal
is depleted, income drops. If you set this variable to 10% (of a
$1,000,000 initial principal), the initial income $100,000/year
as before, you will see that you don't run out of money
suddenly; rather, your annual income decreases substantially
with time as the principal is depleted.
Now let us assume that you have invested your entire principal
in a fixed-return account earning 5% yearly. Set the "Fixed
Return" variable to 5. Set your annual income to $30,000. Now
the principal graph shows an upward curve as the
interest from your investment, compounded from year to year,
more than compensates for the $30,000 annual income withdrawn.
You could now increase your income without running out of money.
Question: What income can you take that will cause your
principal to remain unchanged for the full 35 year duration of
the simulation? Limiting your income to this amount, you will
never run out of money, no matter how long you live, and you
will have all of the original principal to pass on to your
heirs. However, perhaps you do not care to leave anything
behind, in which case you can increase your income even further.
The advantage of investing your principal in fixed-return
instruments is predictability - that is, you can predict exactly
how much income you will make from your investment and how long
your principal will last. If you have accumulated a sufficiently
large principal, then you may have the luxury of investing in
predictable, worry-free fixed-return investments. However, many
retirees find that they need to obtain more retirement income
than fixed-return investments allow.
How much income will you need in retirement? Many financial
advisors say you will need between 80% and 100% of your
pre-retirement income. Some expenses will be reduced in
retirement (no daily commuting to work, possibly lower clothing
costs, lower housing costs if your home is paid off by that
time), but some expenses may be greater. (Most retirees report
that they spend more on travel, entertainment, eating out, and -
especially as they get older - medical expenses). But if you are
many years from retirement, how can you estimate what your
income will be just before retirement? At the vary least, it is
likely that your income will keep up with inflation, which has
averaged between 3 and 5% over the last several decades.
Moreover, it's likely that you will receive raises, promotions,
or better job opportunities at some points in your working life.
That means that over a 30-year period, your income could easily
be 5-10 times your starting income, even though that may seem
like a lot of money from the perspective of someone just
beginning their working life. Social Security will clearly not
be enough, even if that system is still in operation when you
retire. Consider yourself fortunate if you will get a pension
from your employer - such pensions are becomming less and less
common. It's most likely that you will need to generate most or
all of your retirement income yourself, from your retirement
savings and investments.
A favorite way to increase retirement income is to increase
the investment return on your retirement savings. Typically,
returns on equity investments (stocks and stock mutual funds)
are greater than that for fixed investments. The long-term
historical average annual return of the stock market is 10%
including the Great Depression and 12% excluding the Depression.
To simulate investment in equities, set the "Fraction in
equities" variable to 100% and the "Equity Return" to between
10% to 12%. Question: Now what annual income can you
take that will leave your principal unchanged?
The down side of investing in equities is the risk of
fluctuating returns (called "volatility"). In some years the
stock market does better than in other years. The volatility is
the degree to which the returns fluctuate around their average;
it is expressed in terms of standard deviation. The higher the
standard deviation, the higher the fluctuation.
You can simulate the effect of these fluctuations by setting
the "Volatility" variable to some non-zero value. Doing so
will introduce some "bumpiness" in the principal curve (and in
the income curve, if you are basing all or some of your income
on a percentage of principal). Every time you recalculate the
spreadsheet, another random set of returns is calculated. This
is like simulating various alternative possible "futures".
Every time you try out a different set of input variables, you
should press F9 several time to observe how much your income
An obvious effect of fluctuation in investment returns is
that it makes precise planning impossible. In fact, the effect
of fluctuation is greater in your retirement years, when you
are withdrawing income from your retirement accounts, than in
your wealth-accumulation years, when you are contributing to
to your retirement accounts. This is illustrated in the
following graph, which shows a simulation of random
fluctuating returns on investment principal for two scenarios.
The top graph illustrates the wealth-accumulation years
(calculated with the Investment
Simulation Spreadsheet) and the bottom graph illustrates
the retirement income years. The average annual return (10%)
and standard deviation (15%) are identical for these two
scenarios. The only difference is that in the top graph,
regular contributions are made, while in the bottom graph,
regular withdrawls are made. Clearly, the effect of volatility
is much greater in the retirement income. This is one reason
that retired persons are often advised to keep their principal
invested in a balanced portfolio of conservative equity funds
and fixed-return funds, in order to reduce volatility. People
in their wealth-accumulation investment phase, however, can
tolerate more volatility and can afford to invest more
But there is another and even more serious problem. If the
standard deviation is suficiently large relative to the
average return, it is possible that your principal may be
exhausted within your life expectancy. Once that happens,
there is no way to recover your principal, because you are no
longer making contributions. Try increasing the volatility and
see if you can observe such a "go broke" scenario. Obviously,
you want to eliminate this possiblity. There are several ways
to reduce the likelyhood of going broke: you could reduce your
rate of withdrawls, increase the rate of return on your
investments, or reduce the volatility of your investment
What are the values of typical standard deviations for various
types of investments? The following chart shows the percent
average annual return (on the horizonatal axis) plotted against
the annual standard deviation (on the vertical axis) of several
different investment types. (These are real examples of
well-known funds computed over the period 1987-1997). Clearly
there is a trend evident here: the investments with the highest
potential rate of return are generally the ones with the highest
Obviously, both high average return and low standard deviation
are desirable. In general, funds that use "higher-risk"
investment strategies yield greater average returns and greater
standard deviations than funds that use more conservative
You can simulate the effect of investing in these types of
funds by using these values to set the "Equity Return" and
"Volatility" variables. (In the WingZ version, full-scale on
the Volatility slider represents a standard deviation of 60%.
The standard deviation is displayed at the top right of the
slider). Question: based on the mutual fund data list in this
table, which of these fund types would allow the greatest
annual income to be withdrawn without significant risk of
going broke before year 35?
Despite the greater risk of equities compared to
fixed-return investments, the long-term average return
is still better for equities. Life expectances are now long
enough that many of us will spend 30 years or more in
retirement, which most people would consider a long-term
investment. For this reason many retired people keep a
substantial fraction of their principal invested in equities.
The effect of volatility depends on whether you take your
income as a percentage of principal or as a fixed dollar amount.
To demonstrate this, try the following experiment. Set the
standard deviation to zero and the % income to zero. Then adjust
the $ income until the principal is just exhausted in year 35.
Now increase the standard deviation to 5% and note the large
effect. Now set the % income to this same income and set the $
income to zero. Recalculate the spreadsheet and note the greater
stability of your income in the later years. In effect, this
strategy reduces your income when investment returns are low and
increases it when returns are high, greatly reducing the chance
that you will go broke.
One way to reduce risk is to invest in a mix of fixed
investments and equities. You can simulate this by setting the
"Fraction in equities" somewhere between 0 and 100%. You will
find, however, that diluting your equity investents with
fixed-return investments will reduce your average annualized
returns. For example, if you have a portfolio of 50% equities
(returning 12%) and 50% fixed investments (returning 6%), then
the overall return of this mixed portfolio would be 9% (half-way
between 12% and 6%). Most financial investors recommend that
retired investors should have 50-80% of their principal invested
in equity funds.
A better way to reduce volatility, while maximizing returns,
is to construct a portfolio that allocates its assets between
different fund types and sectors, for example, a mix of domestic
and foreign funds, large-company, small-company, and mid-size
company funds, industry sectors such as technology,
pharmaceuticals, and financial funds, and funds utilizing
different investment strategies such as "growth", "value", and
"income" funds. The idea is that if some types of funds are
doing poorly one year, other types of funds may be doing better
in that year, which will help to smooth out returns from year to
year. If each of the funds achieves good long-term returns on
its own, then this strategy can reduce volatility without
reducing the overall long-term returns of the portfolio. You can
learn about the holdings, historical rates of return and
volatility, and investment strategies of mutual funds by
researching the funds on Morningstar (www.morningstar.com) or in
Value Line (www.valueline.com) or by looking on the funds' own
Compensating for inflation. Because of improved medical care,
people are living longer and longer. It's not unusual to live 20
or 30 years in retirement - or even longer. That is why this
retirement income simulation has a 35-year time-line. Over this
period of time, inflation (at the rate of 3-5% per year) is
likely to decrease your purchasing power by a factor of about
three. For that reason you can not expect to live easily on a
fixed income over a long time period. To compensate for this
effect, you should plan to increase your retirement income
gradually over time, at the rate of 3-5% per year. If your
retirement principal is invested at least partially in equity
funds, and you are computing your income as a percentage of your
principal (show above to be the safest mathod), then the best
way to do this is to take an income which is less than the
expected rate of return on your principal by the expected rate
of inflation. For example, if you expect to obtain a 12% annual
return on your overall protfolio, and you expect inflation to
average 4%, then take 8% of your principal as income, leaving
the remaining 4% to grow your principal (and your income) to
compensate for inflation.