Tom O'Haver, University of Maryland, March 1997. Revised April 2008.
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 equiities vs time for a 35-year period
(for example, from age 30 to the normal retirement age of 65). (A companion simulation,
Income Simulation Spreadsheet, can be used to estimate the income that you can obtain from your
investments in retirement).
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: annual contribution limitations;
income and capital gains taxes; 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 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 format.
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 volitility towards the lower end of this range.
Yearly Investment: Total investment in the first year.
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 spreadsheet.
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
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
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%) increses 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
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 recaculate 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). Neverthelss, 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
10-year average annual return
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
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)
hve 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 10% to 14%. If possible, you should try to select the funds with the best long-term
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%).
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.