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Hypotheses:
The problems addressed by this dissertation
are stated below in the form of hypotheses that are proven or disproven
by this research. Discussions
and data supporting or disproving these hypotheses are provided in
chapter four.
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Hypothesis 1 - It is expected that this research will show that
dollar value averaging is superior to dollar cost averaging and asset
allocation in all cases but two on the basis of return on investment and
cumulative investment.
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Hypothesis 2 - When the growth rate and volatility are flat, it
is anticipated that both the math and the computer simulations will show
that dollar cost averaging and dollar value averaging are equivalent.
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Hypothesis 3 - When the growth rate is consistently negative,
dollar cost averaging is expected to be superior although the investor
will essentially be pouring money into a "black hole" in
either case.
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Hypothesis 4 - If there is any positive growth, no matter how
short-lived, in conjunction with any volatility, no matter how small, it
is expected that the research will show dollar value averaging is the
superior technique.
Finally,
a practical implementation plan will be derived and presented.
This plan will require modifications of the pure theory which
appear more significant than they really are.
However, it is not intuitively obvious what the final
conclusions, with respect to the real-world limitations, will be prior
to performing the computer simulations.
Definitions
of Terms and Symbols
Several terms and the context of these terms used in this
dissertation are presented below.
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Automatic Investment Techniques
The term “automatic investment
technique” is used in this dissertation to refer to a technique of
periodically investing or changing investments based on a mathematical
plan independent of fundamental issues such as predicting the economy,
interest rates, the new president, impacts of weather on business, war,
business plans, etc. The
nature of “automatic investment techniques” specifically excludes
trying to “time the market.” Examples
of these techniques include dollar value averaging, dollar cost
averaging, and asset allocation.
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Dollar Cost Averaging
Dollar cost averaging is an “automatic”
investment technique where the investor invests a fixed dollar amount on
a periodic basis regardless of the “share value” of the underlying
investment. When “share
value” (e.g., Net Asset Value for mutual funds) is low, dollar cost
averaging forces one to automatically buy more shares since a fixed
amount is invested. When
“share value” is high, dollar cost averaging forces one to
automatically buy fewer shares. Therefore,
over the long term, the average cost per share actually purchased by the
investor is lower than the average cost per share during the same
period.
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Dollar Value Averaging
Dollar value averaging, also called value
averaging, is an “automatic” investment technique where the investor
invests a variable dollar amount on a periodic basis where the actual
amount invested is dependent on the difference between current account
value and the target account value at that point in time.
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Asset Allocation
When using asset allocation, the investor
invests specific percentages of assets available in multiple investment
vehicles. At pre-determined
time intervals, the percentage of investment among the investment
vehicles is reviewed and modified, if necessary, to return to the
original percentage per investment vehicle or to new percentage
allocations based on the investor's stage in life. The allocation among
the different investment types will vary over time based on changes in
“share value” of one category versus another. Thus, at the end of a
specified time interval (e.g., one year), the investor should sell
portions of the investments that have risen in value and purchase more
of the investments that have fallen, or risen less, in value to return
to the pre-defined percentage allocations.
This concept automatically invokes the “buy low, sell high”
convention since one will buy more when share values are lower, and one
will actually sell some of the "shares" when share values are
higher.
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Base Trend Rate of Growth
The base trend rate of growth (or base
rate) is the smoothed average growth in value of a selected investment
vehicle (i.e., short-term volatility is extracted).
On an annual basis, the base rate of growth is synonymous with
the annual percentage rate.
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Volatility Function
The volatility function is a function
describing the variation in “share value” when the base trend rate
of growth is removed from the function describing the total change in
“share value.” The
volatility function describes the short-term changes in share value.
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Mutual Funds
A mutual fund is an investment vehicle
where a large number of people pool their investment funds together in a
common account that is invested and managed by a professional investor
called the “fund manager.” The
fund manager buys and sells equities, bonds, and other assets
commensurate with objectives published in the fund prospectus.
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Share Value
In this dissertation, “share value” is
used to refer to the unit value of an investment vehicle.
For example, if one is investing in stocks, the “share value”
is the market price of a single share of the stock.
If one is investing in mutual funds, the “share value” is the
Net Asset Value (NAV) which is the value of one share of the mutual fund
that represents a percentage ownership of all stocks, bonds, etc. held
by the fund. If one is
investing in physical silver, “share value” would generally be the
value of one ounce of silver. The
term “share value” allows the discussion to generalize across
different types of investments.
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Buy Low, Sell High
“Buy low, sell high” is an investment
cliché that means one should buy a stock or commodity when the price is
low and sell the stock or commodity when its value is higher.
Alternatively, one could sell a stock or commodity at a higher
price with a delivery date in the future, and then (hopefully) buy the
stock or commodity at a lower price prior to the required delivery time.
Both of these concepts fit within the “buy low, sell high”
paradigm. The concept behind
this cliché is that the difference between the purchase price and the
selling price is the investor’s profit.
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Diversification
Diversification is a concept where the
investor spreads his investment funds across multiple investment
vehicles to reduce the risk of major decline in one or more segments of
the market. One classical
form of diversification is to allocate a portion of funds in stocks and
a portion in metals (i.e., gold, silver, and platinum) or real estate.
Thus, if inflation increases dramatically, stocks tend to decline
in value, but metals and real estate (i.e., real property) tend to grow.
Thus, the decrease in one segment is offset by the increase in
another. A mutual fund is by
definition diversified, in at least one sense, due to the Securities
Exchange Commission requirement that no more than five percent of the
fund's assets may be invested in any single stock, and no fund may own
more than ten percent of the voting stock of any given company.
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Rate Of Return/Return On Investment
The Rate Of Return (ROR), or Return On
Investment (ROI) is the rate of increase in the value of an investment.
Generally, the rate of return is calculated by the following
equation:
ROR
= ROI = [(Value @ end of
period - Value @ beginning of period) / (Value @ beginning of period)] *
100%
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Cumulative Investment
The cumulative investment is defined to be
the total money invested in equities up to the current point in time.
The cumulative investment is increased with each additional
investment and expenses (including taxes).
The cumulative investment is reduced by taking profits out of the
equity account(s). When the
cumulative investment goes below zero and income continues, the
investment becomes a “money machine.”
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Money Machine
In this dissertation, a “money machine”
refers to an investment that continues to pay the investor even after
all of the original investment has been returned to him.
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Present Value
Present value is the current value of an
investment for which the value at a future point in time is known.
Mathematically, present value can be expressed as the future
value of an investment divided by the sum of the effective interest rate
plus one raised to an exponent equal to the number of compounding
periods.
PV = FV / [(1+i)n]
where
PV = Present Value
FV = Future Value
i = Effective interest rate
n = number of compounding periods
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Future Value
The future value is the value in the future
of an investment, or series of investments, made today.
Mathematically, the future value of a one-time investment is the
present value multiplied by the sum of the effective interest rate plus
one raised to an exponent equal to the number of compounding periods.
FV = PV [(1+i)n]
where the symbols are as defined above.
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Total Account Value
Total account value (TAV) is loosely used
as a synonym for future value. In
this research, total account value includes the value of the equity
account(s) and money market account for a technique in a given market at
a given point in time.
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Average Cost per Share
Average cost per share refers to the
average price paid per share since a series of investments in an equity
account began.
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Monthly (or Periodic) Target Increment
The monthly target increment refers to the
fixed currency amount by which the investor wants an equity account to
grow per month (or period) when using dollar value averaging.
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Growth Factor
The growth factor is a percentage that
specifies the rate the monthly target increment is to grow annually.
For example, if the current monthly target increment is $100 and
the growth factor is ten percent, then the second year, the monthly
target increment will be $110.
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Flat Market
A flat market is a market where the average
return is zero. In other
words, there is no uptrend or downtrend;
share values stay the same, on average, over time.
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Individual Retirement Account
An Individual Retirement Account (IRA) is
any investment vehicle that has been labeled as a “qualified” (i.e.,
IRS-approved) retirement account for an individual.
The benefit of such a label is that all earnings within the
account are tax-deferred until the earnings are withdrawn.
In certain cases, the money invested in an IRA are also
tax-deferred until withdrawn from the account.
Most mutual funds and brokerage accounts can be tagged as IRAs.
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401(k) or 403(b)
A 401(k) or 403(b) account is a
“qualified,” defined contribution account for which the IRS allows
pre-tax investment and all earnings on investments are tax-deferred
until withdrawn. 401(k)
accounts were originally created for self-employed people to establish a
“pension” type of income upon retirement.
However, in the past ten years or so, corporations have begun
establishing 401(k) accounts for their employees as well.
403(b) accounts are similar to 401(k) accounts, but they are
designed more for specific occupations such as teachers and state
employees.
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