Tom O'Haver, University of Maryland, April 1998. Revised April, 2008.
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 You can control the income withdrawn,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).
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 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 formats:
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 this variable.
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 this.
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)
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
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
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 varies.
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
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 aggressively.
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 returns.
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 volatility.
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 strategies.
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%).
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 Web sites.
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.