Tom O'Haver, University of Maryland, March 1997. Revised April
This is a simulation of saving and investing for retirement. It
shows how much you can accumulate in a tax-deferred retirement
account (e.g. an IRA or 401k account) by saving a certain amount
each year and investing it in a combination of fixed-interest and
variable (equity) instruments. You can control the amount invested,
the rate at which that amount is increased with time, the return on
the fixed-interest and equity portions of your investment, and the
volatility (uncertainty) of the returns of the equity portion.
Graphs show the amount invested per month,, the growth of your
principal with time, and the return on equities vs time for a
35-year period (for example, from age 30 to the normal retirement
age of 65). (A companion simulation, the
Income Simulation Spreadsheet, can be used to estimate the
income that you can obtain from your investments in retirement).
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: annual
contribution limitations; income and capital gains taxes; IRS
minimum required withdraws from tax-deferred accounts after age 70
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 of this spreadsheet is still
available. This version has mouse-controlled sliders for input
control and was developed using WingZ 1.1, an object-oriented
spreadsheet that is available for Windows, Macintosh, and UNIX
from Investment Intelligence
Systems Corp. 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
First month investment. Amount invested (saved) in
the first month. The yearly investment is automatically
calculated and displayed under "Outputs".
Yearly Increase. This is the percent increase in
investment each year. If you set this to zero, it means that you
invest the same amount each year. If you set this to 5, it means
that each year you invest 5% more than the previous year.
Because your income is likely to increase with time as you
obtain raises, promotions, and cost-of-living adjustments, you
should be able to afford to increase the amount that you invest
by a few percent per year.
Initial assets at start of year 1. The number of
dollars (if any) that you initally transfer into this investment
program from previous investments, gifts, or other sources. This
will be zero if you are "starting from scratch".
Expected Return on Fixed. The average annualized
return on the fixed-interest portion of your investment
portfolio (such as bonds, certificates of deposit, or money
market accounts). Typical fixed account returns are 3 - 6%.
Expected Return on Equities. The average long-term
annualized return on the equity (stock and stock mutual fund)
portion of your investment portfolio. Returns on equity
investments are typically greater than on fixed investments.
Typical long-term equity returns average 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 volatility towards the lower end
of this range.
Yearly Investment: Total investment in the first
Principal in Year 35: The total value of your
investments in Year 35, assuming that all interest is
re-invested and not taxed. Of course, not everyone will have a
full 35-year investment period. If you are starting late or
retiring early, then the total principal you will have can be
read off the Principal graph that is displayed on the
Out-of-pocket expense: The total amount that you have
actually paid into your retirement accounts 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 investments in each
year, assuming that all interest is re-invested and not taxed.
The horizontal axis is years from the beginning of your
investment program. If you are planning to retire, say, 20 years
from the beginning of your investment program, then you would
read off your expected principal at year 20 from this graph.
$ invested per month: The amount you invest per month.
This will be a flat line if "Yearly increase" is zero.
Return on equities: The simulates year-to-year
variation in annualized return on the equity (stock and stock
fund) portion of your investment portfolio. The average is
controlled by the "Expected Return on Equities" and the
fluctuation (variation) is controlled by the "Volatility". Every
time you recalculate the spreadsheet (by pressing F9), another
random set of returns is calculated.
Start with all the inputs set to zero. Obviously in this case
you never accumulate anything and all the graphs stay at zero.
Set the "First month investment" to $170. This means you are
investing roughly $2000 per year, but since there is no annual
increase in savings and since the return on your investments is
zero, the money simply accumulates. The principal graph in this
case is just a straight line. By retirement at age 65, you would
have accumulated a little over $70,000. You might call this the
"stick the money under the mattress" scenario. You can do much
better than this.
Now let us assume that you invest your savings in a
fixed-return account earning 5% yearly, such as a certificate of
deposit or money market account. Set the "Expected Return on
Fixed" to 5. Now the principal graph shows an upward curve as
the interest from your investment compounds from year to year.
By retirement at age 65, you would have accumulated roughly
$184,000. And note that this does not increase your
out-of-pocket expense. Not bad, but you can do better than this.
Because your earned income is likely to increase with time, as
you get raises or cost-of-living adjustments, you should be able
to afford to increase the amount that you invest each year. For
example, suppose you increase your savings 5% per year (set the
"Yearly increase" to 5). In this case by retirement at age 65,
you would have accumulated nearly $400,000! In fact, if you feel
you will have trouble investing in the early years (when your
salary is low), you can always reach the same goal by reducing
the "First month investment" and increasing the "Yearly
increase" to compensate. This means that you invest less in the
beginning but more in later years, when you can presumably
afford it. (However, doing this does increase your total
"out-of-pocket expense"). But you can do even better than this
by increasing the return on your investments.
Typically, returns on equity (stock and stock mutual fund)
investments are greater than for fixed investments. The
long-term historical average return of the stock market as a
whole is 10% including the Great Depression and 12% excluding
the Depression. To simulate investment in equities, set the
"Fraction in equities" to 100% and the "Expected Return on
Equities" to 10% - 12%. In this case by retirement at age 65,
you would have accumulated close to one million dollars, at no
further increase in out-of-pocket expense! Of course, there is
really no way to predict the future; past returns are no
guarantee of future results. The future may be better or worse
than the past, but most likely it will be about the same. The
best we can do is to use historical trends to predict the most
likely future results.
It is actually possible to do even better than the above by
carefully selecting your equity investments in order to maximize
returns. A good way to do this is to invest in high-quality
equity mutual funds. The long-term average return of the
high-quality equity mutual funds with the longest track records
is in the range of 13 to 14% over a 30 - 50 year period. (For
example, the American Fund's Investment Company of America
has had an annual return of 13.7% since it was founded in 1934,
during the Great Depression). Your employer's 401k plan will
probably allow you to choose from an assortment of mutual funds
(or variable annuities, which are similar) which achieve similar
long-term returns. Try putting these returns into the "Expected
Return on Equities" and observe the result. Clearly, even small
(1%) increases in investment return can result in huge increases
in wealth over a long investment period.
Note that the Principal graph is now a very curved line,
starting out almost flat and sweeping up sharply in the later
years. This is an important and natural characteristic of
investing. Why is this important? It means that it is very
important to begin your investment program as early as
possible and not to keep putting it off because you can't
afford it. If you delay starting by one year, it has the same
effect as retiring one year early - in either case your
investment period is reduced by one year. One year can make
a lot of difference. Just look at the Principal graph. If
you have accumulated $1,000,000 by year 34, and you are making a
10% return on your investments, then in the last year you make
$100,000 in interest (10% of $1,000,000). So reducing your
investment period by one year (by starting one year later or by
retiring one year early) would cost you $100,000!! Are you
willing to throw away $100,000 just to delay biting the bullet
for one year?
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. In some years
it even looses money (has a negative return). Nevertheless, the
long-term average return is still better for equities
than for bonds or other fixed investments. Saving for retirement
is a long-term investment, so you are generally better of
investing heavily in equities.
You can simulate the effect of market fluctuations by setting
the "Volatility" to some non-zero value. Typical volatility
values for equity mutual funds are 10 to 20%. Every time you
recalculate the spreadsheet (by pressing F9), 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 times to
observe how much the total value of your principal varies. As
you can discover, small amounts of volatility pose little real
risk - there is some "bumpiness" in the rising principal curve,
but it ultimately rises nonetheless. If the volatility is high
enough (relative to the average return), you will see that in
some years the returns are negative; that is, your
principal actually looses money. But even so, over the
long term, the principal gradually grows. Volatility is
unavoidable when investing in equities. What it really means is
that you can not predict exactly how rich you will be at the end
of your investment period. You may end up with $1,000,000, or
maybe only $800,000, or maybe $1,200,000, or maybe even more or
less. You can never be exactly sure how rich you will be. But,
like the man said, don't you wish you had that problem!
Can the volatility ever be too great, or is total return the
only factor that is ultimately important? It is often said that
for the long term investor, total returns are more important
than volatility. Nevertheless, if the volatility is too
great, there is a chance that your principal may be wiped out or
reduced to a small fraction of its former glory. Try increasing
the volatility and see if you can observe such a "go broke"
scenario. (Fortunately, even if if this does happen, it is
possible to recover to some extent, assuming that you continue
to make your regular contributions. You can always hope that,
after a big market "crash", there will be a period of market
recovery). Nevertheless, I think you can prove to yourself that
it is possible to have too much volatility.
One way of reducing the risk of investing in stocks is to buy
equity mutual funds. Individual stocks may have long- term
standard deviations or 20% or more. Mutual funds reduce risk by
spreading your investment over many stocks. What are the typical
returns and variations in returns (volatility) of equity mutual
funds? The table below lists the performance of sixteen mutual
funds and variable annuities over the last 10 years, listing the
average annualized return and the standard deviation of the
annual returns over that period.
Name of fund
Fidelity Growth & Income
Washington Mutual Investors
Income Fund of America
Investment Company of America
VALIC Growth fund
VALIC Science and Technology
Lincoln Global Asset Allocation
Lincoln Growth and Income
Lincoln Managed Fund
Lincoln Social Awareness
Lincoln Special Opportunities
Obviously, both high average return and low standard deviation
are desirable. In general, funds that use more aggressive
investment strategies (such as Invesco Dynamics) yield greater
average returns and greater standard deviations than funds that
use more conservative strategies (such as the Lincoln Managed
Fund). Your employer's 401k plan will not have these particular
funds available, but they will hopefully have a range of
different equity funds, some conservative and some more
agressive, for you to choose from. Most people like to spread
out their contributions between several funds. You can simulate
the effect of investing in these types of funds by using these
values to set the "Expected Return on Equities" and "Volatility"
inputs. However, keep in mind that these numbers are only for
the 10-year period 1988-1998. This period has been a
better-than-average period for the US economy and it includes
the longest-running bull market ever. The long-term average
returns of the equity mutual funds with the longest track
records (such as Investment Company of America) have been only
13 to 14% over a longer 30 - 50 year period. It is likely that
the equity funds in your employers 401k plan selection will have
long-term returns somewhere in the range of 7% to 11%. If
possible, you should try to select the funds with the best
Another way to reduce risk is to invest in a mix of fixed
investments and equities. Most employer-sponsored 401k plans
have both types of funds available. You can simulate this by
setting the "Fraction in equities" somewhere between 0 and 100%.
You will find, however, that diluting your equity investments
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 long-term investors should have 80% to 100% of
their principal invested in equity funds.
Perhaps the best way to reduce volatility, without reducing
your investment returns, is to construct a portfolio that
distributes 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-tern 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 (http://www.morningstar.com)
or in Value Line (http://www.valueline.com)
or by looking on the funds' own Web sites.
How to get started. See your employer's payroll department or
officer to learn if they have a 401k plan. Many employers have a
automatic payroll deduction plan that can be set up to withdraw
a specified amount from your paycheck before taxes and invest it
in one or more mutual funds or other investment instruments in
your 401k account. This is usually the most painless and the
most reliable way of insuring your continued contributions. Some
employers will even "match" a portion of your contributions with
their own contributions, up to some limit. If you don't take
advantage of that, you are in effect throwing away perfectly
good money. A 401k plan also has the beneficial effect of
reducing your income tax rate during you working years.
Contributions to your 401k are made with untaxed dollars and
accumulate tax-free until you begin to make withdrawals after
you retire, at which time you play regular income taxes on the
amount that you withdraw. (If you leave your current employer,
it is always possible to "roll over" your 401k account into
another tax-deferred retirement plan). Or you can set up your
own IRA (Individual Retirement Account) to which you can
contribute up to $2000 per year. A regular IRA, like a 401K
plan, is funded with pre-tax dollars, and you pay regular income
taxes on the amount you withdraw in retirement. A newly
available option is the "Roth IRA"; contributions to a Roth IRA
are made with after-tax dollars, but there are no taxes on
investment gains, and withdrawals are tax-free when you retire.
See a personal financial planner for detailed advice on these
and other retirement investment options.