http://www.wam.umd.edu/~toh/investment/
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, the
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
that may apply to citizens of the USA, 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 OpenOffice Calc version will
work on both the Windows and
the Macintosh version of OpenOffice, which is available for free
download from openoffice.org.
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.
The Inputs:
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
stance).
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.
The Outputs:
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.
The Graphs:
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.
Experiments.
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%) 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
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 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
Standard
Deviation
Fidelity Growth & Income
20 %
15
Fidelity Puritan
15 %
10
Washington Mutual Investors
17.6 %
14
Income Fund of America
15 %
11
Fundamental Investors
17.9 %
13
New Perspectives
14 %
10
Investment Company of America
16.8 %
12
Invesco Dynamics
18.5 %
21
MAS Equity
16.7 %
13
VALIC Growth fund
15.5 %
13
VALIC Science and Technology
22.7 %
22
Lincoln Global Asset Allocation
8.3 %
11
Lincoln Growth and Income
13.4 %
13
Lincoln Managed Fund
10.4 %
10
Lincoln Social Awareness
14.2 %
17
Lincoln Special Opportunities
13.3 %
16
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)
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
returns.
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.