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Filename : INVESTOM.DOC

INVESTOMAT (C) v1.0

Investomat has been released to the public under the Freeware
Concept. You are free to use and distribute the program under the
following conditions:

- the program must not be altered in any way
- the name INVESTOMAT is protected and may not be used for
similar programs
- while INVESTOMAT is a tool for an investor, it does not give
you investment advice. Under no circumstances is the author
responsible for any investment losses you may have taken
- you use the program entirely at your own risk.
- "The information set forth herein was obtained from sources
which I believe reliable, but I do not guarantee its accuracy.
Neither the information, nor any opinion expressed, constitutes a
solicitation by me of the purchase or sale of any securities or
futures contracts, or options thereon." This is the standard
legal talk, and if I give away a program for free, at least I
want to protect myself from any legal and/or regulatory problems.


Peter J. Morant
395 South End Ave., 30E
New York, NY 10280
March 1, 1988




What is INVESTOMAT?

INVESTOMAT is a set of fairly sophisticated utilities which are
of use primarily to the institutional investor. The program per-
forms four functions:
1) Black Scholes Option Valuation Model
2) Estimate of a Fair Market P/E
3) Dividend Discount Model / Capital Asset Pricing Model (CAPM)
4) Asset Allocation Model

A description of each function follows later in this documenta-
tion.




If you are in a hurry ...

INVESTOMAT requires no installation if you are happy with the
defaults. To start, simply type 'INVESTOM' (This is the only EXE
file which is a standalone program). There is extensive on-line
help available (F1 key). The F10 key or the ESC key are almost

1






always active and assure an orderly exit. Do not worry if INVES-
TOMAT sometimes writes to or reads from the disk during some idle
moments while you study the screen. In order to optimize the per-
formance, some house-cleaning work is sometimes performed in the
background which from time to time may involve some reading from
or writing to data files on your disk even when you did not in-
voke any specific command.



System Requirements

INVESTOMAT requires at least 256K of memory. The program checks
for the memory you have and will not run if it decides that it
may not be sufficient for safe operation. The use of a color
monitor is highly recommended, but not required.


INVESTOMAT Files

Required Files:
INVESTOM.EXE - the main program
COMB.EXE - not a standalone program
MODEL.EXE - not a standalone program
INVEST.HLP - help file

All of these four files must be present on the default drive. The
DOS 'Path' command will not be able to locate the files COMB.EXE
or MODEL.EXE.

Other Files:
INVESTOM.DEF - stores your installation data (INVESTOMAT cannot
run without this file. But if it is missing, a
new one will be recreated)
DEFAULT.INV - default data for the Asset Allocation Model
DEFAULT.SPE - default data for the P/E Model
DEFAULT.MPE - default data for the P/E Model
DEFAULT.DIV - default data for the Dividend Discount Model

The default files are automatically recreated each time you run
the Installation Option from the main program. It is not a good
idea to name any of your files DEFAULT, because chances are that
INVESTOMAT will overwrite your file sooner or later. Also, please
never use an extension when naming files to save or to retrieve.
INVESTOMAT does not accept a period (.) as a valid character.








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Installation

This program performs three functions:

1) It checks your system configuration to see whether you are
sufficiently equipped to safely run INVESTOMAT. If it decides to
abort, it will attempt to tell you why. The system check is not
performed automatically, i.e. you can run INVESTOMAT without
having invoked the installation procedure first. But you will do
so at your own risk. The program will check if you have enough
memory and if you have sufficient space on your default drive.
You will be given the option to define a path for your data files
which will be permanently stored in the file INVESTOM.DEF. If you
define a subdirectory that does not exist, INVESTOMAT will give
you an error message, but it will not create it automatically.
The three executable files, INVESTOM.EXE, COMB.EXE, and MODEL.EXE
must all reside on the same default drive, and you should take
note of the fact that INVESTOMAT temporarily disables the DOS
Path command. Do not attempt to run the programs COMB.EXE or
MODEL.EXE, because it will not work. The only standalone program
is INVESTOM.EXE which can also be invoked by typing START
(START.BAT).

2) It lets you choose the desired background and foreground
colors for the main screen, the help windows, and the error win-
dows (in case you don't like the defaults). Please make sure that
you never chose the 0,7 combination (black on white) because IN-
VESTOMAT uses these colors to highlight certain choices on the
screen.

3) It automatically recreates some of the default data files that
can be used as examples. The most complex default file,
DEFAULT.INV, is recreated automatically each time you invoke the
Asset Allocation Model.



Installation, Step by Step...

1) INVESTOMAT looks at the file INVESTOM.DEF to check whether you
have previously defined a drive/subdirectory for your data
files. If not, no problem...

The first time you run INVESTOMAT, the path drive will be your
default drive, and the path subdirectory will be your root direc-
tory. If this is ok with you, simply hit the key twice. If
you want to change the drive, hit any legal letter, without the
colon, and wait until the xxxx bytes free message changes. If you
want to change the subdirectory, do not type the final '\'. I.e.
if you want your data files to reside in C:\INVESTOM\DATA, type

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'INVESTOM\DATA'. An error message will appear if the specified
subdirectory does not exist.



2) For some internal reasons, INVESTOMAT checks the status of the
Num Lock, Scroll Lock and Insert keys. If it wants you to change
something, you will get an appropriate message.

3) On the lower right corner, 3 windows will appear. You will be
able to change the foreground and background colors of the main
screen, the help windows, and the error windows. The default
colors are:
Main screen foreground: 15 (High-intensity White)
Main screen background: 1 (Blue)
Window foreground: 0 (Black)
Window background: 3 (Cyan)
Error foreground: 15 (High-intensity White)
Error background: 4 (Red)

4) Before returning to the main program, you will be given one
last chance to restore the default colors (While you decide
whether you want to do this, the default data files will be
created).

If you are so inclined, you can modify INVESTOM.DEF directly. It
is a simple ASCII file containing the following information:
Foreground and Background colors for the main screen, the help
windows and the error windows, as well as the default path.
A typical INVESTOM.DEF file may look like this:
'15,1,0,3,15,4,"C:\INVESTOM\DATA"'.






















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Black Scholes Option Valuation Model


This model calculates the fair value of a call option. It assumes
that the price of an option is determined by the price of the
stock, the striking price, the time to expiration, interest rates
and the expected volatility of the stock. To keep things simple,
it does not take dividends into account.

Current Price of the Stock: self-explanatory
Monthly standard deviation: the expected move of the stock
(plus or minus) during the next
month. For example, if a stock
now sells at 40, and you expect
it's price to remain in the range
between 35 and 45 dollars, type 5
(40 +/- 5).
Interest rate: the annualized rate of interest
of a risk-free asset (Treasury
Bill) having a similar maturity
as the expiration date of the
call option.

Option Exercise Price: The price at which you can call
the stock at expiration date.

Number of Months: Decimals are permitted


The option market is quite efficient, and since option prices are
known, you can also use this model to solve for the implied
volatility of a stock. Once you have an opinion on a stock's
volatility, you will be able to make an intelligent guess on its
beta (see: Dividend Discount Model). You may also estimate the
stock market's volatility using equity market call options. This
information will be useful for the Asset Allocation Model.


Here's the mathematics:

E
Po = Ps * N(d1) - --- N(d2)
rt
e

2
ln(Ps/E) + (r+.5*s )*t
where: d1 = ----------------------
s* sqr(t)



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ln(Ps/E) + (r-.5*s )*t
d2 = ----------------------
s* sqr(t)



Legend:

Po = current value of the option
Ps = current value of the stock
E = exercise price of the option
e = 2.71828
t = time remaining before expiration (in years, i.e.
t = .5 equals 6 months)
r = continuously compounded riskless rate of interest
(i.e. r = .09 equals 9% per year)
s = standard deviation of the continuously compounded
annual rate of return of the stock (i.e.
s = .3 equals a standard deviation of 30%)
ln (Ps/E) = natural logarithm of (Ps/E)
Nd = probability that a deviation of less than d will
occur in a normal distribution (use a standard
cumulative normal distribution table)





The mathematics involved is fairly complex, but the formula can
be written in only a few lines of code!





















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P/E MODEL

The P/E Model is derived from the Dividend Discount Model (see
page 9) using a constant growth rate.

By definition, the price of the stock represents the present
value of all future dividends. Assuming a constant growth rate of
earnings and a constant dividend payout ratio, the formula be-
comes very simple:


D * (1 + g) where: P= Price of the stock
P = ----------- D= Dividend
(k - g ) g= Growth rate
k= Discount rate

Dividing both sides by E (Earnings), you will get a simple P/E
Model:

D/E * (1 + g) where: D/E= Payout ratio
P/E = -------------
(k - g )


The discount rate k is the sum of current interest rates (broken
down into real interest rates and inflation) and the risk premium
for being invested in the stock market to begin with (as opposed
to buying a risk-less Treasury issue). Historically, this risk
premium has ranged between 1 and 5% and has averaged about 2.5%,
i.e. the expected return of the stock market must be at least
2.5% higher than the expected return of the risk-free bond in or-
der to be equally attractive on a risk-adjusted basis. In the
early part of 1987, this risk premium has been reduced to his-
torically low levels raising clear warning signals. But many in-
vestors chose not to listen because they believed that, in an en-
vironment of excess liquidity, the risk premium will find a new
equilibrium at a lower level. At the time of this writing
(January 1988), the risk premium has nearly approached its his-
torical norm. This implies that the market's downside risk at
this point is no longer primarily one due a change in investor's
risk preference, but due to an unexpected rise in interest rates.

The growth rate g can be input directly, or you can have INVES-
TOMAT calculate it if you chose to provide the data for the
Dupont formula. This formula goes as follows:

Return on Assets (ROA) = (Profit/Sales) * (Sales/Assets)
Return on Equity (ROE) = ROA / (1 - Leverage) [Leverage=debt
ratio]
Sustainable Growth (g) = ROE * (1 -Dividend Payout Ratio)

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The actual use of the program is very easy and self-explanatory.
A quick glance at the P/E formula helps you understand that the
discount rate always must be higher than the growth rate because
a P/E never can be a negative number. If the growth rate almost
equals the discount rate, the P/E becomes an unreasonably high
number. If the P/E is less than zero or over 100, INVESTOMAT will
reject your assumptions and will flash an error message.












































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DIVIDEND DISCOUNT MODEL / ASSET ALLOCATION MODEL

The basic idea here is that the price of the stock equals the
present value of all the future dividends. The process involves
two major steps: First, the future dividend stream has to be es-
timated. Second, a way must be found to arrive at an appropriate
discount rate in order to discount that dividend stream.

Here's the mathematics:
n P = Price of stock
i Do * (1+g) Do= Initial Dividend
P(stock) =SUM ------------ k = Discount Rate
n=1 n g = Growth Rate
(1+k) i = infinite



In practice, it is neither possible nor desirable to make in-
dividual dividend estimates for an infinite number of periods.
The formula can be significantly simplified by assuming that the
dividend growth rate will be forever constant. We then would get
the formula we have encountered before:


D * (1 + g) where: P= Price of the stock
P = ----------- D= Dividend
(k - g ) g= Growth rate
k= Discount rate

(As an aside, this formula can be regrouped as follows:
k= D(1+g)/P +g which reads, in prose, that the expected return
of a stock equals its dividend yield plus its growth rate. This
can be quite useful when making a rough evaluation of a stock.)

INVESTOMAT, like many dividend discount models, is making a com-
promise and divides the future life of a stock into 3 phases. In
each of the three phases, you can estimate the growth rate and
the dividend payout rate. Also, you can determine the length of
phase 1 and 2 (phase 3 is indefinite). This way, you can accom-
modate stable rust belt stocks as well as new venture companies
(presumably, phase 1 of an emerging company involves high growth
and low dividend payout, phase 2 experiences a slowdown in growth
and a higher payout, and phase 3, the maturity phase, will have
parameters similar to the S+P's).

Once you have estimated the future dividend stream, you will have
to know at what rate the dividends have to be discounted in order
to arrive at a fair present value (the stock's fair price). This
discount rate is sometimes also referred to as the required rate

9






of return, and the most efficient way of estimating this return
is by using the Capital Asset Pricing Model (CAPM).


The CAPM formula looks as follows:

Ri = Rf + beta*(Rm - Rf) + e

where,
Ri = required return of stock i
Rf = risk-free interest rate
Rm = expected return of the stock market
beta= the systematic risk of stock i
e = error term (assumed to be zero in this context)

Please note that (Rm - Rf) equals the excess return of the stock
market and is usually referred to as the risk premium. Stocks are
riskier than risk-free Treasuries, and their expected return must
be higher. Ex ante, the term (Rm - Rf) is always a positive num-
ber (about 1 to 5% per annum), but ex post it can be negative, of
course (there are times when Treasury bonds outperform stocks).

Beta represents the non-diversifiable risk associated with a par-
ticular stock. Usually, it is estimated by regressing a stock's
monthly return for the past five years against the stock market's
excess return. A beta of 1 means that the company's risk is ex-
actly average, a beta of less than 1 suggests below average, a
beta of greater than 1 above average risk. Most stocks have a
beta between 0.5 and 1.5. An intuitively appealing (but not quite
correct) way of understanding beta is the following notion: Beta
is an indication of the stock's relative volatility. A beta of
1.1 means that, if the market goes up 10%, the stock will go up
1.1 times 10%, or 11%. Similarly, if the market drops 10%, the
stock will drop 11%. A stock with a beta of .5 would only drop
5%. Therefore, you want to own high beta stocks in up markets,
and low beta stocks in down markets.

The CAPM is an extremely important concept in financial theory,
and despite criticism is widely used in corporate and financial
decision making.


Once you know the future dividend stream, and you know the
required return of the stock (the discount rate), the stock's
fair price can be estimated. INVESTOMAT not only tells you the
fair price, it also breaks the stock price down into 3 com-
ponents, i.e. the contribution to the price from the dividends
paid in phase 1, phase 2, and phase 3.
The stock's present price is known, and the Dividend Discount
Formula can also be solved for the discount rate. The result is
the implied (as opposed to the fair) rate of return. If the im-
plied return is higher than the fair return, a stock is under-

10






valued on a risk adjusted basis. This is where the famous alpha
comes in (alpha equals the difference between the implied return
and the fair return). A positive alpha implies undervaluation, a
negative alpha implies overvaluation. Maybe, just maybe, I will
find the energy some day to work on INVESTOMAT v2 where I could
add some graphics in order to make this business with alpha, beta
etc. a bit easier to understand.


The actual data input is self-explanatory. Use the default data
to acquaint yourself with the model. Unreasonable input will not
be accepted (I hope). Always check the function key menu (invoked
by pressing ALT F1) to make sure you do not miss out on any of
the options.







































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ASSET ALLOCATION MODEL

The Asset Allocation Model represents the heart of Modern
Portfolio Theory, and INVESTOMAT is the first program that makes
such an algorithm available to the investing public at no charge.
This topic is fairly complicated, and I apologize if some of the
explanations below sound a bit technical.

The basic idea is to find a portfolio that both maximizes return
and minimizes risk.

Return can be defined as the change in price plus dividends paid
and/or accrued during the holding period.

Risk can be defined as the standard deviation of the security's
return during the holding period. Or, intuitively, risk repre-
sents the confidence we have in the return estimate.

Example 1: A 1-year Treasury Bill yields 8%. Assuming a holding
period of 1 year, the return is 8%, and the risk is 0. The inves-
tor knows for a fact that this investment will yield 8%.

Example 2: An investor believes that the stock market will go up
5% in 1987, but he thinks that it may return anywhere between
minus 10% and plus 20% (i.e. 5% +/- 15%). If the investor
believes that odds are 2 out of 3 that the market will trade
within that range during the next year, the standard deviation,
or the risk, of the market is expected to be 15%.

Assumption: An investor likes high return and dislikes high risk.
In the above example, the investor has the choice between a cer-
tain return of 8% and an uncertain, but most likely return of 5%
(+/- 15%). What will he prefer? Portfolio theory assumes that the
investor will prefer the certain 8% over the uncertain 5%, even
though in the latter case he would have a chance of earning 15 to
20%. This assumption is absolutely crucial, and if you don't buy
it, read no further....

A more interesting case is the following one, however. Assume the
market return is not 5%, but 15%, +/- 15%. What does a rational
investor prefer now? A certain 8% or an uncertain 15%? The answer
is:it depends. Stay tuned....

From now on, let's assume that an investor has a choice between
only 3 securities: Cash, stocks, and gold. The investor wants to
be fully invested in those 3 securities, but now he needs to know
how to allocate among the three (INVESTOMAT comes with one
default file: DEFAULT.INV which helps you to decide how to allo-
cate your money to the global equity markets).


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The investor makes the following assumptions for the next 12-
month period:

Expected Expected Range of
Return Risk expected Return
--------- --------- --------------------------
Cash 6.19% 0.05% 6.19% +/- 0.05%
Stocks 10.58% 13.83% 10.58% +/- 13.83%
Gold 3.29% 16.08% 3.29% +/- 16.08%

If the investor is completely risk-averse, he will chose to be
fully invested in cash. If he is strictly return-oriented and
does not care about risk, he will be 100% invested in stocks. But
how about the rest of us who want to maximize return and minimize
risk at the same time?

Portfolio Theory adds an important new concept to portfolio risk:
the correlation of returns of each security. The less one
security correlates with another, the greater the risk reduction
(diversification) benefit becomes. A correlation coefficient can
have a value between -1 and +1. A correlation coefficient of +1
implies that, if security A goes up by, say, 10%, security B will
go up by 10% as well. So there is no diversification benefit in
holding both security A and B. If the correlation coefficient is
-1, security B will go up by 1% for each 1% security A goes down
in value and vice versa. If the correlation coefficient is be-
tween 0 and 1, the two securities tend to move in the same direc-
tion, but in a more or less unpredictable way. If the coefficient
is between 0 and -1, the securities tend to move in the opposite
direction. -1 offers the greatest possible diversification
benefit, while +1 offers no benefit at all.

Assume now that the investor believes that the following correla-
tion coefficients will hold true:

Cash Stocks Gold
Cash 1.00 0.62 -0.13
Stock 1.00 -0.43
Gold 1.00


A security has a correlation coefficient of 1 with itself, by
definition ('If stocks go up 10%, stocks go up 10%). If a
security has a zero standard deviation (such as cash), its cor-
relation coefficient with other securities must be zero as well.
In reality, however, even cash investments have a slight risk be-
cause the short term interest rate will change frequently. Roll-
ing over 3 month Treasury Bills is riskless as far as repayment
of principal is concerned, but the expected return for a 12 month
period cannot exactly be determined.


13






Our investor assumes that stocks and gold have a negative cor-
relation coefficient of -.43. This suggests that the gold and
stock market tend to move in the opposite direction (high infla-
tion, general uncertainty, may be bullish for gold and bearish
for stocks).

Now, our investor has all the information available to construct
an efficient portfolio. Before he runs the Asset Allocation
Model, he will have to understand the return and risk charac-
teristics of his portfolio, though.

The return part is simple. The return of the portfolio equals the
weighted return contribution of each security held in the
portfolio:

i=1 where:Rp = Return of the portfolio
Rp = SUM Ri * x(i) Ri = Return of security i
n x(i)= Weight of security i
n = Number of security types available


If our investor wants to hold 1/3 each in cash, bonds, and
stocks, the expected return of his portfolio would be
(1/3) * 7% + (1/3) * 10% + (1/3) * 13% = 10%


The risk part is more complex, I'm afraid. The portfolio risk
equals the sum of the weighted covariances:

i=1,j=1 where: Vp = Risk of the portfolio
Vp =SUM si*sj*ci,j*xi*xj si = Risk of security i
n,n sj = Risk of security j
ci,j= Correlation between i and j
x(i)= Weight of security i
x(j)= Weight of security j
n = Number of security types




So we are left with a problem where we have to maximize Rp and
minimize Vp at the same time. There are a few, but not many algo-
rithms, that can solve such a problem. Minimizing Vp is the same
as maximizing -Vp, and INVESTOMAT is using a quadratic program-
ming algorithm to maximize both Rp and -Vp.

In a first step, INVESTOMAT calculates the portfolio with the
least possible risk, taking the following constraints into
consideration:
1) The portfolio must be 100% invested (if this constraint was
relaxed, the program would simply tell you "don't invest at all
when you are trying to minimize risk"). This constraint is an ab-

14






solute requirement.
2) Short positions are not allowed. This constraint has been
hardcoded into the program, even though neither theory nor logic
suggest that this must be a binding constraint at all times. But
since I felt that institutional investors very rarely go short
when making long term asset allocation decisions, I include this
constraint to get clean results. Relaxing this constraint is pos-
sible, but I think it will require a substantial programming ef-
fort in order to ensure that the program will never bomb. (I have
never seriously tested INVESTOMAT without the short constraint,
so I cannot be quite sure about that).
3) The exposure to a specific security or security class cannot
exceed 100%. This constraint, of course, is related to constraint
#2. Exposure of over 100% to one security implies a short posi-
tion of another.

The default constraints thus are:
minimum exposure 0%, maximum exposure 100% to each security.
You will be given the option to modify these defaults, however,
and both the minimum as well as the maximum exposure can be a
positive percentage number between 0 and 100. For example, our
investor may believe that a normal cash ratio is 0 to 30%, a nor-
mal equity ratio is 25 to 75%, and a normal bond ratio is also 25
to 75%. The more restricting the constraints become, the less ef-
ficient the portfolio becomes, however. To give an extreme ex-
ample, using a minimum constraint of 90% and a maximum constraint
of 95% for your equity ratio will make it difficult for INVES-
TOMAT to propose an efficient portfolio. You will get a result,
but it will be vastly different from the result you would get if
you did not impose any constraints. The ability to use con-
straints is important, however, because many institutional inves-
tors are measured against some index they have to beat, and they
have to control their bets. For example, a global investor who is
measured against the Morgan Stanley Capital International Index
(where both the U.S. and Japan have a weigthing of about 35%)
will want to have a minimum constraint for the major markets.
Also, if the investor is bullish on, say, the Spanish stock
market (with a weighting of about 1%), he will want to impose a
maximum constraint on Spain.

At any rate, the first portfolio that INVESTOMAT will calculate
is the one with the least risk. Minimum risk is the objective,
portfolio return is the result. There will be no portfolio, that
offers that same return at a lower risk than portfolio #1. Also,
there will be no portfolio that offers a higher return at the
same risk than portfolio #1. The efficient, minimum risk
portfolio has been found.

In step number 2, INVESTOMAT will calculate the portfolio with
the highest possible return. The purpose of that exercise is to
define the steps at which the minimum return is supposed to in-
crease. INVESTOMAT wants to find the minimum risk portfolio, the

15






maximum return portfolio, and (usually) 9 portfolios in between.

In steps number 3 to 11, INVESTOMAT finds 9 additional efficient
portfolios along the efficient frontier. All of these portfolios
have the same characteristics: There is no portfolio offering a
higher return at the same risk than the proposed portfolio, or
there is no portfolio that offers the same return at a lower risk
than the proposed proposed portfolio.

Typically, you will end up with 11 portfolios, where portfolio #1
is the low risk, low return portfolio, and where #11 is the high
risk, high return portfolio. The choice of your portfolio is
simply a function of your risk preference (which can be quan-
tified, too, but which is beyond the scope of INVESTOMAT because
my programming interest now has shifted elsewhere).

INVESTOMAT provides you with a tool which, until now, has been
available only to America's large pension funds and investment
managers. To the best of my knowledge, the algorithm (maybe not
the input error check) is bug-free, and the only significant con-
straint may be that INVESTOMAT is limited to seven different
security types. The reasons for that are simple: First, the
screen design becomes much more complicated when adding more
securities due to the 80 character width of the IBM monitor, and
secondly, the performance of the algorithm deteriorates exponen-
tially with each security added. Also, most practical applica-
tions do not require a decision between more than seven distinct
asset classes.


How to use the Asset Allocation Model

I am not going to explain each keystroke and function key you
should use when working with the Asset Allocation Model. Use your
common sense, get help (F1), and make sure you know of all the
options available to you (ALT F1).

The logic behind the Asset Allocation is as follows:
In order to run the model, you will need an estimate of the
return, risk, and correlation of each security. Mathematically
speaking, this is nothing but a multiple regression problem. As-
sume our investor observed the following historical returns (in
%):

Cash Stocks Gold

January .50 2.20 -6.70
February .48 -3.20 4.50
March .52 6.80 1.02
April .50 1.40 2.80
May .51 -3.45 3.40
June .50 1.30 -3.40

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Input this data to INVESTOMAT (submenu selection: "Input new
data"). When all done, press to invoke the calculations, and
you will get the following results:

Cash Stocks Gold

Mean .50 .84 .27
Standard Deviation .01 3.81 4.40

Correlation Coefficient 1.00 .62 -.13
1.00 -.43
1.00


Make sure to save the file (F2 key) before modifying the data or
proceeding to the model.

This historical data can serve as an unbiased input for the Asset
Allocation Model. INVESTOMAT gives you the option to accept the
historical data as input for the Model (which works with
expectations) or to change the expected returns, risks, or cor-
relations. Experience has shown that correlations tend to be
stable over short time periods. So you must have a good reason if
you want to change the historical relationships. Similarly, risk
(standard deviation) is fairly stable, and I advise you not to
change the historical data. Returns is a different matter,
though. Past return data cannot be simply extrapolated into the
future, and I urge you to modify the past return data.
Academicians have tried to extrapolate efficient frontiers. They
have found that minimum risk portfolios can successfully be ex-
trapolated, while the same is not the case for maximum return
portfolios. This is strong evidence for the assertion that risk
is more stable over time than return (I think this makes sense
intuitively).

In short, then, INVESTOMAT first calculates what it terms
'original' data (mean return, standard deviation, and correlation
based on the historical return data you have input). This
'original' data defaults to the 'modified' data. The 'modified'
data can be overwritten by you, if you disagree with the sug-
gested expected return, risk or correlation. The model always
works with the modified data, not the original data.

INVESTOMAT has an elegant feature that allows you to change the
time period of the observed data. Let's assume that you have in-
put monthly return data on cash, stocks, and bonds, and INVES-
TOMAT has calculated the monthly mean returns, risks, and cor-
relations. A simple key stroke will allow you annualize this
data. As a matter of fact, you can convert the observed returns
and risks to daily, monthly, quarterly, or annual. In order for

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this conversion to work, INVESTOMAT has to assume that returns
are not autocorrelated. Random walk theory suggests that this as-
sumption is reasonable. Even if this assumption is wrong,
however, the resulting error would be negligible in most cases.
In investment situations of high autocorrelations (an investor's
delight...because he can extrapolate past return data into the
future), an asset allocation should not be used to begin with.
The current version of INVESTOMAT does not calculate the autocor-
relations and thus lets you annualize data even when such a con-
version may not be appropriate. So please be careful.


All data must be saved (F2 key) before proceeding to the Model.


The use of the Model is fairly simple. After having chosen the
desired file, you will be prompted for the minimum and maximum
constraints for each security type. When done, press 'PgUp' for
the model to start. INVESTOMAT will calculate the low risk
portfolio and time itself to get an idea how long it will take to
calculate the entire efficient frontier. You will be constantly
kept up to date on the progress. Each portfolio will be plotted
on a chart with Return as the Y-Axis and Risk as the X-Axis. In
order for INVESTOMAT to be able to run on Monochrome systems as
well, no graphics commands were used. If 2 or more portfolios lie
on the same X,Y coordinated, the symbol 'X' will appear instead
of the portfolio number.

When done, the efficient frontier will be plotted on the right
side of the screen. Use the 'TAB' key to move along the frontier,
On the left side of the screen you can see the portfolio struc-
ture required in order to get a portfolio with the risk/return
characteristics shown on the right. INVESTOMAT will also high-
light which of the constraints were binding (relax those con-
straints in order to get an even more efficient portfolio).


The results can be printed either to the printer or to a disk
file by pressing the appropriate function keys.














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Concluding Remarks

If you are an individual investor, INVESTOMAT will not make money
for you. But hopefully you will get an idea on how institutional,
quantitative approaches are designed.

If you are an institutional investor, you are familiar with the
concepts described here and I am surprised that you have read so
far...

If you are not an investor, I hope that INVESTOMAT has made you a
bit curious about the market and that you want to learn more
about investing. If INVESTOMAT has been able to contribute to

your decision to become an investor and to put some of your
savings to work in the stock market, then the countless hours I
have spent writing this program were not wasted.


Peter Morant
New York, N.Y.
March 1, 1988





























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