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2 LITERATURE REVIEW
2.1 Investment Portfolio
The concept behind investment portfolio is to com-
bine different investment targets to avoid concentrat-
ing too much risk on any one target with the aim of
dispersing overall investment risk. Any combination
of two or more securities or assets can be termed an
investment portfolio.
On the other hand efficient-markethypothesis is an
idea partly developed in the 1960s by Eugene Fama
and defended by Burton G. Malkiel (Malkiel, 1973)
which asserts that financial markets are “information-
ally efficient”, or that prices on traded assets (e.g.,
stocks, bonds, or property) already reflect all known
information, and instantly change to reflect new in-
formation. Therefore, according to theory, it is im-
possible to consistently outperform the market by us-
ing any information that the market already knows,
except through luck.
2.2 Fuzzy Inference Systems
A fuzzy inference system is a computer paradigm
based on fuzzy set theory, fuzzy if-then-rules and
fuzzy reasoning.
Fuzzy inference systems have been successfully
applied in fields such as automatic control, data clas-
sification, decision analysis, expert systems, and com-
puter vision. Because of its multidisciplinary nature,
fuzzy inference systems are associated with a number
of names, such as fuzzy-rule-basedsystems, fuzzy ex-
pert systems, fuzzy modeling, fuzzy associative mem-
ory, fuzzy logic controllers, and simply (and ambigu-
ously) fuzzy systems.
In the field of financial market analysis, we have
for example, (Dourra and Siy, 2002), which uses
three technical indicators (rate of change, stochastic
momentum and resistance indicator) in a fuzzy con-
trol system with the following modules: convergence
(maps the technical indicators into new inputs), fuzzi-
fication, fuzzy processing and defuzzification (using
the center of area method to map the output universe
with four membership functions -low, medium, big
and large- into a nonfuzzy action). Also in (Che-
ung and Kaymak, 2007) the fuzzy trading system
is based on four technical indicators (Moving Av-
erage Convergence/Divergence, Commodity Channel
Index, Relative Strength Index and Bollinger Bands)
and the output of the fuzzy system is a signal on a nor-
malized domain, on which four different fuzzy sets
(strong sell, sell, buy and strong buy) are defined.
On the other hand in (Atsalakis and Valavanis,
2009) use a neuro-fuzzy based methodology to fore-
cast the next day’s trend of chosen stocks. The fore-
casting is based on the rate of change of three-day
stock price moving average.
3 RESEARCH FRAMEWORK
3.1 Intelligent System for Tactical Asset
Allocation
The proposed system for decision making is based on
a policy of buying and selling the stocks that make up
any stock market over a period of time.
This policy of buying and selling is based on that
if we assume a stock market quoted from a start date
(date
start
) until an end date (date
end
), each one of
those days, all their stocks have had an opening price
(p
open
), a maximum price (p
max
), a minimum price
(p
min
) and a closing price (p
close
).
If we take a day d between date
start
and date
end
in
which you have no shares purchased (there is no order
of sale or purchase pending), then we will be able to
select a set of m stocks (S
b
), using technical analysis
or any other technique, which would be most recom-
mendable to buy, because it expects them to give a
good return.
The technique for selecting stocks should calcu-
late a value for each one of the stocks that make up the
market on that day d, quantifying if it would be advis-
able to buy the shares. Stocks are ordered from most
to least according to this value, and the system will
have to choose the best set of stocks, defining which
minimum value is considered for a stock to belong
to this set of the better stocks, existing the possibility
that one day any stock is not recommended (m = 0),
or that many are recommended because its analysis
has been the sufficiently satisfactory for all them.
Once we have this set S
b
with the selection of the
best stocks for a day d, we might try to buy all or some
of these stocks. To simplify the algorithm we will try
to buy only one of the selected stocks every day, so
that after several days, we could have a portfolio of
n stocks (S
a
). Thus, to choose the stock to buy we
would have two possibilities, to select the best or well
to select any randomly.
Once we have chosen a stock, we will have to give
the purchase order for the next day. We will limit the
purchase price to any of the prices that has had the
stock during that same day ([p
min
, p
max
]), or choose
the opening p
open
or closing p
close
price of the next
day. If we use a low purchase price, there are fewer
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