Frederico Silva Valentim Sallum
Fuzzy Consultoria, Brazil
E-mail: frederico.sallum@gmail.com
Luiz Flavio Autran Monteiro Gomes
Ibmec/RJ, Brazil
E-mail: luiz.gomes@ibmec.edu.br
Maria Augusta Soares Machado
Ibmec/RJ, Brazil
E-mail: maria.machado@ibmec.edu.br
Submission: 13/04/2018
Accept: 25/04/2018
ABSTRACT
This
paper analyzes the performance of 20 multimarket investment funds in the
Brazilian market from May/2015 to April/2017 in order to categorize them into 4
performance levels. The cumulative rate and the funds' volatility are
calculated in 2 periods among the total periods studied, in order to generate a
mutual degree of influence among the funds of each group. Next, the WINGS
method is applied. This method splits each group into 2 subgroups, generating
the 4 levels of classification. The use of the methodology classified 5 funds
in each subgroup. The data analysis compared the obtained classification with
the classification established by the cumulative rate of the funds throughout
the entire period and presented 4 ways to prioritize the decision for the funds
ranked higher. These 4 ways of prioritizing the decision aim at assisting
investors with different points of view.
Keywords: classification of investment funds,
DEMATEL method, TOPSIS method, WINGS method
1. INTRODUCTION
The
great offer of investment funds and other financial products in the Brazilian
financial market make the investor inquire which asset better meets his/her
profile and future perspectives. Classifying investment funds consists of
placing the collected sample in different levels or performance categories in
the studied criteria.
A
good classification aims at orienting investors and advisers about the assets' behavior
with regard to their decisions, analysis and evaluations. One of the ways of
obtaining a classification of the many collectively analyzed assets is using
multicriteria methods which support the decision. One of the great advantages
of using these methods is to analyze a set of alternatives in light of a set of
criteria (LONGARAY; ENSSLIN; MACKNESS, 2014). Therefore, a classification made
through these methods allows a comparative evaluation of the studied
alternatives.
According
to Caldeira et al. (2014), the economy's openness in the 90s and the economic
stability achieved by the Plano Real were great allies of the development and
growth of investment funds industries in Brazil. These authors also state that
the first multimarket investment funds emerged in Brazil in the mid-90s and
since then they have been presenting a significant growth.
Thus,
it is seen that the investment funds are an investment modality that has
already been consolidated in the Brazilian market. The offer of this product in
the financial market is also significant and, for that reason, many times it
may generate a conflict in the decision making process when an investor analyzes
a set of funds eligible to his/her investment under the performance of two or more
criteria. With this in mind, a classification of these funds worthy of
investment may facilitate the decision, since it presents which ones are
closest to his/her profile and future perspectives with respect to these
assets.
There
are other types of investment funds in the Brazilian market besides multimarket
investment funds, for example, fixed income funds, currency, international debt
and pension (ANBIMA, 2014). Rovai (2015) emphasizes that it is important to
know these types of investment funds, because the performance rate is charged
according to the funds’ performance, it should be known that the fund's
performance is linked to the type of fund used for investment.
This
author also reinforces that usually fixed income funds have a lower return than
the multimarket investment funds. Multimarket investment funds have investment
policies attached to many risk factors without necessarily concentrating on a
risk factor alone. Because of that, there are multimarket funds that are more
conservative than fixed income funds and others more aggressive than investment
funds in shares.
Hedge
funds are funds that adopt a certain number of investment strategies that
cannot be adopted by traditional investment funds without being more or less
risky than these ones (Infomoney,
2005). Malaquias and Eid (2014) state that funds classified as multimarket use
hedge funds strategies utilized in other countries and, with that, Brazilian
managers can be found using characteristics similar to these ones.
This
paper strives to analyze monthly profitability’s of 20 multimarket investment
funds in the Brazilian market from May/2015 to April/2017, in order to classify
them into 4 performance levels. For this purpose, initially the DEMATEL method
is applied, which will split the studied funds into 2 groups: Group A and Group
B.
It
is necessary for the implementation the DEMATEL method to do the classification
of the funds month by month in a decreasing order and through these
classifications, the degrees of mutual influence will be established. Thereafter,
the WINGS method is applied to each of the groups created previously. However,
it is necessary to define the degree of power of each fund in its group and the
degree of mutual influence between the members of each group.
The
TOPSIS method is applied in order to define the degree of power of each fund in
the group they belong to. Moreover, the degree of mutual influence between the
members of each group is identified by the calculation of the cumulative rate
and the volatility in two periods among the total of periods studied, the last
12 months and the 12 second-to-last months.
After
the degrees of power of each fund in its group and the degree of mutual
influence among the members of each group are established, the WINGS method is
applied in groups A and B. The WINGS method splits group A into two subgroups:
Subgroup A1 and Subgroup A2; and splits Group B into 2
subgroups: Subgroup B1 and Subgroup B2. Subgroup A1,
A2, B1 and B2 are the 4 performance levels
defined in order to classify the 20 analyzed multimarket investment funds.
2. BIBLIOGRAPHIC REVIEW
2.1.
Consulted
Studies
Many
scholars have been using different multicriteria analysis methods to evaluate,
sort, classify and select investment funds in their studies. That happens
because these methods are able to evaluate various investment funds as
alternatives in light of their performances in more than one criterion. Since
there are many ways to evaluate investment funds through indicators already
consecrated in literature, a multicriteria approach is able to analyze a set of
investment funds to be studied, considering their performance in the criteria
used in the evaluation.
As it
has been previously said, there are many indicators outlined in the investment
funds' literature. Many of these indicators are used by researchers and market
traders to evaluate investment funds. Elton and Gruber (1995) and Haugen (1997)
mention as an example the Treynor ratio, the Sharpe ratio, the Jensen's alpha,
the Sortino ratio, the Modigliani risk-adjusted performance, among others. However,
it is important to highlight that each indicator has its limitation.
Varga
(2001) reports the difficulty in applying some performance indicators to
Brazilian funds. What occurs is that each return indicator adjusted to risk
takes into consideration only one risk measurement (Melo; Macedo, 2013). In this regard, the use of multicriteria
methods in the performance analysis of investment funds allows the evaluation
of the set of investment funds to be analyzed, considering the performance of
all the indicators seen as relevant by the analyst.
Melo
and Macedo (2013) examined the performance of macro multimarket investment
funds in Brazil from April/2005 to March/2010. In the research, the Data
Envelopment Analysis (DEA) was used. Although it was not part of the
multicriteria analysis, it has allowed a joint analysis of various parameters
considered relevant to the performance evaluation of an investment fund.
Mesrinejad
and Moradi (2015) used the TOPSIS method to classify 20 investment fund offered
in Tehran's, capital of Iran, stock exchange. The use of this method allowed
the classification of the 20 funds studied according to their performance in 3
indicators: Sharpe's ratio, Jensen's
alpha and Treynor's ratio over 12 months.
Duarte
and Medeiros (2016) used the TOPSIS method to select funds of private equity in
Brazil in a case in which 11 private equity investment funds are offered in the
national financial market. The implementation of the TOPSIS method has allowed
the analysis of the 11 offered funds according to the performance of each one
in 22 criteria.
As a
consequence, the classification and selection of possible investments were
possible. Martins (2014) uses the TOPSIS method to evaluate managers, classify
investment funds in shares and classify multimarket investment funds. In this
piece of work, qualitative and quantitative criteria were used for the
classifications. The implementation of the TOPSIS method facilitates the high
complexity described in the work involved in the selection of investment funds
with criteria, which are many times conflicting and should be analyzed
simultaneously.
Gomes,
Rangel and Santos (2016) applied the AHP method in order to classify mutual
funds for a subsequent selection in light of the criteria that identify the
investor's characteristics and aims. This paper seeks to offer diversification
in the portfolio of mutual investment funds placing the assets on the
investor's profile in the appropriate manner.
The
use of the AHP method brought a better comprehension of the problem and the
assets' ordination that entailed a portfolio's selection. Mello (2014) used the
WINGS and AHP methods to classify the credit risk of 14 sectors in the economy
with qualitative and quantitative criteria. This author explains that the use
of the WINGS method was made to measure how sectors of economy influence each
other in the classification model created.
With
a joint implementation of these methods it was possible to obtain a way of classifying
economic sectors considering the degree of influence that exists between them
as well as its strength inside the Brazilian market.
2.2.
The
DEMATEL Method
The
DEMATEL method - Decision Making Trial and Evaluation Laboratory - was
developed by Gabus and Fontela (1972) in order to analyze a set of components,
alternatives or criteria, able to exert influence one over the other, not
always in a reciprocal manner.
The
first step to apply the DEMATEL is to build a crossed relationship matrix A, expressing the degree of influence
that the element i of the matrix line
exerts over the element j in the
matrix's column, where aij
is the influence that element i
exerts over the element j. For that,
a comparative scale of degrees of influence should be established. For example,
in a scale from 0 to 4, 0 means no influence, 1 low influence, 2 medium
influence, 3 high influence and 4 very high influence. If it is necessary, this
scale can be amplified.
The
second step is to build the direct relationship matrix D, calibrating the previous matrix according to Equations 1 and 2.
|
(1) |
where:
|
(2) |
The
third step is to build the total relationship matrix T according to Equation 3.
|
(3) |
In
the Equation 3, I is the identity
matrix and (I-D)-1 an
inverse matrix. From then on, the sum of each line ri of the matrix T
(Equation 4) and sum of each column ci
of the matrix T (Equation 5) are
calculated.
|
(4) |
|
(5) |
The
line's sum of each element ri represents the total impact that each
element has in the set of analyzed elements. The column's sum of each element ci represents the total
impact received by each element in the set of analyzed elements.
The
sum ri+ci
should also be calculated for each element, which represents the total
involvement that each element has in the set of analyzed elements and the
difference ri-ci,
which represents the net effect that each element has in the set of analyzed
elements.
DEMATEL
classifies the analyzed components into 2 groups: the impacted, which have
negative ri-ci
and the impactors, which have positive ri-ci.
This happens because the impactors exert a degree of impact superior to the
degree of impact they receive inside the analyzed set. The impacted receive a
degree of impact superior to the one the exert over the other component inside
the analyzed set.
2.3.
The
TOPSIS Method
The
TOPSIS method (Technique for Order Preferences by Similarity to Ideal Solution)
was originally proposed by Hwang and Yoon (1981). The main idea is based on the
compromised solution concept, which implies having to make a concession to
reach an agreement.
In
this case, the aim is to choose the closest alternative to the positive ideal
solution (optimal solution) and the farthest from the negative ideal solution
(inferior solution) (Tzeng; Huang,
2011). Each alternative is evaluated according to each attribute defined by the
decision maker. The TOPSIS measures the distance between each alternative and
the positive ideal and negative ideal solutions.
The
basic elements needed for the implementation of the TOPSIS are: a set of
alternatives A = {ak |k=1,…,
n}, where k is the ordinal number of each alternative and n is the
alternatives' total inside the multicriteria matrix; a set of criteria C = {cj |j=1,…,m}, where j is the ordinal number of each
criterion and m is the criteria's
total inside the multicriteria matrix; X
= {xkj |k=1,…,n; j=1,…,m} is a set of performance evaluations of
each alternative k according to each
criterion j; and W = {wj |j=1,…,m} is a set of weights given to each
criterion according to the decision maker's preferences, with wj being the weight of
criterion j.
There
are two types of criteria: cost or benefit. The benefit criteria indicates that
the bigger the value, the more likely it will become an alternative. As for the
cost criteria, the opposite is what counts. The positive ideal solution
maximizes the benefit criteria and minimizes the cost criteria and the negative
ideal solution maximizes cost criteria and minimizes the benefit criteria. For
the negative ideal solution to take place, the opposite happens (Hwang; Yoon, 1981).
The
first step to implement the TOPSIS method consists of calculating the
standardized matrix of the performance evaluations, outlined by rkj (x) (Equation 6), that
is, the standardized performance evaluation of alternative ak in the criterion cj.
Which enables the comparison between attributes of different scales.
|
(6) |
The
second step considers the performance evaluation by the weight of each criterion.
The result is given by vkj (x)
(Equation 7), that is, the result of alternative k's evaluation in the
criterion j.
|
(7) |
Moreover,
the positive ideal solution (PIS) and the negative ideal solution (NIS) must be
identified. The PIS (A+)
and the NIS (A-) are
calculated with the maximum or minimum value of vkj (x) in each criterion (Equation 8 and Equation 10); vj+ (x) to measure
the PIS and vj- (x)
to measure the NIS (Equation 9 and Equation 11) where J1 and J2
are the benefit and cost criteria, respectively.
|
(8) |
where:
|
(9) |
|
(10) |
where:
|
(11) |
The
next step is to calculate the Euclidean distances between A+ and Ak
(dk+) for benefits (Equation 12) and between A- and Ak (dk-) for costs (Equation 13).
|
(12) |
|
(13) |
The
final value generated by the TOPSIS is the calculation of the relative proximity
ξk for each alternative Ak. Through the value of ξk, there's the alternatives' ordination (Equation 14):
|
(14) |
2.4.
The
WINGS Method
The
WINGS method – Weighted Influence Non-linear Gauge System (Michnik, 2013) is derived from the
method DEMATEL – Decision Making Trial and Evaluation Laboratory (Gabus; Fontela, 1972). It is use allows
the indication of the degree of influence among the variables utilized in a
certain multicriteria evaluation context.
From
this point of view, the WINGS method emerged with the assumption that the
influence among the components of the decision-making system – in this case,
alternatives or criteria - is not enough to calculate factors such as impact,
receptivity and the variables' involvement; also, which components should be properly
studied, considering a variable's strength inside the system. This factor is
not used in the DEMATEL method.
The
first step to use the WINGS method is to select two or more components to form
a system, a set of alternatives or criteria studied. Next, the degree of power
that each component possess inside the system should be established in 5
points: (0) no strength; (1) low strength; (2) moderate strength; (3) high
strength and (4) very high strength. The degree of influence that each
component possesses over the other should also be established in 5 points: (0)
no influence; (1) low influence; (2) moderate influence; (3) high influence and
(4) very high influence. If appropriate, the scale should extended in order to
avoid very approximate readings, given the nature of the problem studied, the
user can extend it (Michnik,
2013). The Equation 15 illustrates an example with three components.
|
(15) |
In
the second step, the matrix D should
be calibrated according to Equations 16 and 17, transforming it into matrix C.
|
(16) |
where:
|
(17) |
The
WINGS method's third step follows the DEMATEL method's steps as of equations 3,
4 and 5. Just as in the DEMATEL method, the system of sum and difference ri+ci and ri-ci of each
element inside the system should also be calculated. In such calculations, ri represents the total
impact that a component has in the system, whereas ci represents the total receptivity (received impact)
that an element has inside the system.
The
sum ri+ci
represents the total involvement that a component has inside the system,
because it is the result of the sum of how one component impacts the others and
how the others impact it too. The difference ri-ci, on the other hand, classifies the
system's components as influenced, in case its result is a negative number, or
influencing, in case its result is a positive number, since it expresses the
difference between the total impact that an element has over the others and the
total impact received by the rest.
3. METHODOLOGY AND IMPLEMENTATION
The
monthly profitability of 20 multimarket investment funds currently in the
Brazilian investment funds market from May/2015 to April/2016 will be studied.
The software ECONOMÁTICA® was used to obtain the monthly
profitability. The funds analyzed are presented in Table 1 as well as the
abbreviation of each fund's name to be mentioned throughout this paper.
Table 1: Multimarket investment funds and abbreviation
This
paper seeks to classify multimarket investment funds into 4 performance levels:
A1, A2, B1 and B2. By splitting the
funds into 2 groups, A and B, and each group into 2 subgroups. With A's subgroups being: A1 and A2;
and B's subgroups being: B1 and B2, according to the
performance reached throughout the analyzed period. Initially, the DEMATEL
method will be applied, which will split the 20 analyzed funds into 2 groups.
Next,
the TOPSIS method is used to establish the degree of power of each alternative
inside the group it was designated by the DEMATEL method. This degree of power
will be utilized during the implementation of the WINGS method. The TOPSIS'
methodology uses the difference between the alternative with the best
performance and the others in each criterion and the difference between the
alternative with the worst performance and the others in each criterion. Thus,
the best fund will be the closest to have achieved the best return in all
criteria and the farthest from obtaining the worst performance in all criteria.
The profitability’s
are analyzed by the TOPSIS method as grades or scores acquired by the funds
being studied each month and note as a rate properly speaking, because the
difference will be calculated according to Equation 12 and Equation 13 and not
by the calculation commonly used to obtain the difference between to rates
(Equation 18). Equation 18 presents the calculation to obtain the difference
between rates i1 and i2.
|
(18) |
A
degree of power for each alternative is given through the value of the relative
proximity of each alternative calculated by the TOPSIS method. After that, the
WINGS method should be applied. Besides the degree of power, the degree of
influence between alternatives should also be established. For that, 4 other
criteria will be analyzed for the alternatives in both groups, which are able
to establish a degree of influence between alternatives: each fund's cumulative
rate in the last 12 months (May/2016 to April/2017) and in the 12
second-to-last months (May/2015 to April/2016) as well as the volatility in the
last 12 months and the volatility in the 12 second-to-last months.
After
establishing the degree of influence between the alternatives of each group by
the 4 criteria mentioned above, the WINGS method is applied, which will split
the alternatives from each group into 2 subgroups based on the degree of power
each alternative has inside their group and on the degree of mutual influence
in the 4 criteria mentioned above. Tables 2, 3, 4 and 5 present the monthly
profitability of the analyzed multimarket investment funds from April/2017 to
November/2016, October/2016 to May/2016, April/2016 to November/2015 and
October/2015 to May/2015, respectively.
Table 2: Monthly profitability of the analyzed funds
from April/2017 to November/2016
Table 3: Monthly profitability of the analyzed funds
from October/2016 to May/2016
Table 4: Monthly profitability of the analyzed funds
from April/2016 to November/2015
Table 5: Monthly profitability of the analyzed funds
from October/2015 to May/2015
3.1.
DEMATEL
Method Implementation
Initially
the DEMATEL method is used to split the set of multimarket investment funds
into two groups. The DEMATEL method makes use of the mutual influence between
the components of a studied system, being able to classify these components as
impacted, if the offered influence of a given component is inferior to the
influence received by the others or as impactors, if the offered influence of a
given component is superior to the influence received by the others in the analyzed
system.
The
funds classified as impactors belong to Group A and the funds classified as
impacted belong to Group B. The degree of influence each fund has over the
other should be established so that the DEMATEL method is implemented. A scale
from 0 to 8 will be chosen to establish this degree. This article, assumes that
an alternative a1 is able
to exert influence over an alternative a2
when a1 finds itself on a
superior position from a2.
That is, if the alternative a1
has a better performance than alternative a2
in a given criterion, then alternative a1
is able to exert influence over alternative a2.
Therefore,
the influence between alternatives will be established under the following
principle: the influence exerted by an alternative a1 inside a set of 2 or more alternatives is established
when the first occupies a best position in the studied criteria. In case it
occupies its best position in more than one criterion, the influence exerted
will be established by the most important criterion.
Furthermore,
the influence received by an alternative a1
in the same set of analysis depends on its performance in moments which the
other alternatives occupy their best positions in the studied criteria. In
order to define the degree of influence between alternatives demanded by the
DEMATEL method, the alternatives should be classified in each criterion
according to their performances, analyzing their position criterion by
criterion starting with the most important criterion and ending with the least
important one.
In
this article, the analyzed criteria will be the monthly profitability of the 20
multimarket investment funds, with the most recent month being the most
important criterion. This order of importance is done successively until the
least recent month.
Thus,
every time a given alternative reaches a position superior than another one in
a given criterion, it will be able to obtain influence over the one in an
inferior position. If an alternative has the same position in two criteria, the
preference will be given to the degree of influence in the most important
criterion.
It is
essential to emphasize that if an alternative has a superior position over the
others in only 1 criterion, it does not mean that its influence is exerted in a
biased way, because this will be compensated with the impact received by the
other alternatives. In this way, the influence that an alternative exerts in
the system will be given when this alternative finds itself in its best
position in the studied criteria. Preference will be given to the most
important criterion if the alternative has the same position in more than one
criterion.
Therefore,
the 20 investment funds were classified in a decreasing order according to the
monthly profitability’s presented in Tables 6, 7 and 8.
Table 6: Classification of monthly profitability’s
from April/2017 to September/2016
Table 7: Classification of monthly profitability’s
from August/2016 to January/2016
Table 8: Classification of monthly profitability’s
from December/2015 to May/2015
Initially,
it is observed that the fund better positioned in the most important criterion
(Table 6) takes into account a scale from 0 to 8 to establish a degree of influence
between the alternatives. In this manner, the Safra fund has influence 1 over
the Mauá fund, degree of influence 2 over the Bradesco funds, degree of
influence 3 over the ARX fund, degree of influence 4 over the Itaú fund, degree
of influence 5 over the Apex fund, degree of influence 6 over the Sul fund,
degree of influence 7 over the Citifirst fund and degree of influence 8 over
the other funds.
Nest,
the degree of influence of the SPX fund (fund in the best position according to
the second most important criterion) should be established in the same way
demonstrated previously. After that, the degree of influence of Bradesco fund
should be established and so on, until the degree of influence of all the funds
is established in Tables 6, 7 and 8. Alternatives do not have influence over
the ones in the same position and they do not have influence over the ones in
superior positions. After the degree of influence each alternative has over the
others is established, a crossed relationship matrix A should be created
(Equation 19).
|
(19) |
The
position of each fund in the lines and columns of matrix A is given
alphabetically according to the data presented on Table 1. Thus, the Apex fund
occupies the first line and first column and the XP fund occupies the last line
and column. After the crossed relationship matrix A is created, the DEMATEL
method's calculations should start.
Table 9 presents the results found with the implementation of the
DEMATEL method.
Table 9: The DEMATEL method's results
After
the implementation of the DEMATEL method, the funds should be split into 2
groups: Group A and Group B. The ones classified as impactors, that is, funds
that have a positive r-c, belong to
Group A and the funds classified as impacted belong to Group B. In this way,
the Apex, BB, BTG, Growler, ARX, Mauá, Opp., SPX, Sul and XP funds are members
of Group A and the Bradesco, Brasil, Citifirst, Fator, Itaú, Modal, Safra,
Santander, Sicredi and Vinci funds are members of Group B (Table 10).
Table 10: Funds' division in Groups A and B
3.2.
WINGS
Method Implementation to the Group A
At
this stage, the WINGS method should be applied in Group A's members. For that,
the degree of power of each fund in Group A and the degree of mutual influence
between its members should be established with the use of the TOPSIS method.
3.2.1. Establishment
of the degree of power to the Group A’s members
The TOPSIS method is applied on the
members of Group A after they were selected using the DEMATEL framework, as it
was presented on column 1 of Table 10. The TOPSIS method is used in this moment
in the decision-making process in order to establish the degree of power that
each member of Group A has in Group A, according to the value of the relative
proximity attributed to each fund (Table 11). This degree of influence will be
used during the implementation of the WINGS method.
Table 11: Degree of Power established by the TOPSIS
method
The degree of power consists of analyzing
the performance of the investment funds reached throughout the studied period,
comparing the fund with the best performance in each criterion with all the
other funds and comparing the fund with the worst performance in each criterion
with all the other funds. Based on these grounds, the TOPSIS method will
classify the funds, the best fund will be the one closest to the best
performance in every criteria, at the same time it will be the one that
distances itself from the worst performance in every criteria.
The TOPSIS method will be applied at
this stage considering the funds members of Group A as alternatives and all the
months analyzed in the period as criteria. These data are available in Tables
2, 3, 4 and 5. Table 12 presents the results of the TOPSIS method applied in
the funds belonging to Group A.
Table 12: The TOPSIS method’s results
3.2.2. Establishment
of the Degree of Mutual Influence Between Group A's Members
Besides establishing the degree of
power of each alternative in the studied group, the WINGS method also requires
the degree of mutual influence between the alternatives. This degree will be
established according to the performance of Group A's members in the following
criteria: cumulative rate from May/2016 to April/2017 (C1), volatility
from May/2016 to April/2017 (C2), cumulative rate from May/2015 to
April/2016 (C3) and volatility from May/2015 to April/2016 (C4).
It is important to emphasize that the profitability’s' standard deviation was
calculated in order to obtain the volatility in the given period.
This paper takes into account that
in order to split a group into two subgroups, a degree of mutual influence
between the funds should be established in the same way it is done with the
DEMATEL framework. Nevertheless, now other criteria will be analyzed to
establish this degree of influence. To establish a degree of influence in the
DEMATEL method, months were used as criteria, whereas the performance in two
cumulative periods among the months are now used as criteria to split 1 group
into 2 subgroups.
The criteria used to establish a degree of mutual
influence can be calculated according to the data presented in Tables 2, 3, 4
and 5. The order of importance of the criteria used to obtain the degree of
mutual influence is given in decreasing order following the sequence they are
mentioned above. Table 13 presents the classification of performances of Group
A's members in the 4 criteria mentioned above.
Table 13: Position of Group A's members in criteria
C1, C2, C3 and C4
After
the performance classification of Group A's members in criterias C1,
C2, C3 and C4 is known, the degree of mutual
influence between the members of Group A should be established using the same
procedure in the DEMATEL method, that is, initially, the degree of influence
the XP fund exert over the others is established and so on and so forth, as it
was explained previously. method.
3.2.3. WINGS
Method Application to the Group A
After the degree of power of Group
A's members and the degree of mutual influence between the funds in Group A is
known by the criteria C1, C2, C3 and C4,
a force-influence matrix D should be built to initiate the implementation of
the WINGS method. Equation 20 presents the force-influence matrix D of Group
A's members.
|
(20) |
The position of each fund in the
lines and columns of the force-influence matrix D is given alphabetically
according to the data presented in the first column of Table 9. Thus, the Apex
fund occupies this matrix's first line and first column and the Sul fund
occupies this matrix's last line and column. Table 14 presents the WINGS
method's results.
Table 14: The WINGS method's results
After the implementation of the
WINGS method, the funds should be split into 2 subgroups: A1 and A2.
The ones classified as impactors, that is, funds that have a positive r-c, will
belong to Subgroup A1 and the funds classified as impacted will
belong to Subgroup A2. Therefore, the BTG, Mauá, SPX, Sul and XP
funds are members of Subgroup A1 and the Apex, BB, Growler, ARX and
Opp. funds are members of Subgroup A2 (Table 15).
Table 15: Subgroups A1 and A2
3.3.
WINGS
Method Implementation to the Group B
As it
was done previously with the funds that belong to Group A, at this point, the
WINGS method should be applied to the funds belonging to Group B after defining
the degree of power with the implementation of the TOPSIS method and
establishing a degree of mutual influence between the funds through their
positions in the criteria C1, C2, C3 and C4.
3.3.1. Establishment
of the degree of power to the Group B's members
The
funds that belong to Group B are presented in the second column of Table 10.
The TOPSIS method should be applied to these funds in order to establish the
degree of power each one has in Group B. The implementation of the TOPSIS
method will evaluated the performance of this group's funds in the months from
May/2015 to April/2017 (Tables 2, 3, 4 and 5), that is, these months are the
criteria. Table 16 presents the results of the TOPSIS method applied to the
Group B's funds, as well as the degree of power each one has in the group,
established according to Table 11.
Table 16: Results of the TOPSIS method in Group B's
members
3.3.2. Establishment
of the degree of mutual influence between Group B's members
As it
was done previously with the funds that belong to Group A, at this point, the
degree of mutual influence between the Group B's members should be established
through the position of each one in the criteria C1, C2,
C3 and C4. Table 17 presents the classification of the
performance of Group B's members in these criteria.
Table 17: Position of Group B's members in criteria
C1, C2, C3 and C4
Now, the
degree of mutual influence between Group B's members should be established
according to these funds' positions in Table 17 in the same way it was done in
this paper's sections 3.1. and 3.2.2. In this way, initially, the degree of
mutual influence of Citifirst fund over the others inside Group B and so on.
3.3.3. WINGS
method application to the Group B's members
After
the degree of power of each Group B's funds and the degree of mutual influence
between the funds in Group B is known, a force-influence matrix D should be
built to initiate the implementation of the WINGS method. Equation 21 presents
the force-influence matrix D between Group B's members.
|
(21) |
The
position of each fund in the lines and columns of the force-influence matrix D is given
alphabetically according to the data presented in the second column of Table
10. Thus, the Bradesco fund occupies this matrix's first line and first column
and the Vinci fund occupies this matrix's last line and column. Table 18
presents the WINGS method's results.
Table 18: The WINGS method's results
After
the implementation of the WINGS method, the funds should be split into 2
subgroups: B1 and B2. The ones classified as impactors,
that is, funds that have a positive r-c,
will belong to Subgroup B1 and the funds classified as impacted will
belong to Subgroup B2. Therefore, the Brasil, Itaú, Modal, Sicredi
and Vinci funds are members of Subgroup B1 and the Bradesco,
Citifirst, Fator, Safra and Santander funds are members of Subgroup B2
(Table 19).
Table 19 - Subgroups B1 and B2
4. DATA ANALYSIS
This
data analysis seeks to investigate 2 evaluation points. The first one analyzes
the cumulative rate in the studied period and forms 4 levels of classification
in order to see the funds with higher profitability throughout the period that
were best evaluated by the methodology. The second one seeks to present 4 ways
prioritizing the decision inside the best subgroup, that is, Subgroup A1.
These 4 ways of prioritizing the decision are established through the results
of the WINGS method, they are 4 ordinations done based on the foundations of
power and mutual influence of this method's framework. This allows a support
among investors' decision with different points of view.
4.1.
Comparison
between the Subgroups Established by the Methodology and the Subgroups
Established by the Cumulative Rate
Since
the multimarket investment funds are already split into 4 subgroups, that is,
in 4 levels of classification, subgroups: A1, A2, B1
and B2; at this point, a comparison of this classification with the
classification done by the funds' cumulative rate throughout the studied period
should be made.
Based
on the results obtained with implementation of the methodology presented in
this paper, each subgroup has 5 funds in its level of classification. Therefore,
the 20 funds will be divided into 4 groups (A, B C and D) with 5 funds in each
one of them according to the classification in decreasing order established by
the calculation of the funds' cumulative rate in the studied period. This
calculation will be made with the data of Tables 2, 3, 4 and 5. Table 20 presents the 4 subgroups formed by
the methodology proposed here.
Table 20: Subgroups A1, A2, B1 and B2
Now,
the funds will be split into 4 groups: Group A, Group B, Group C and Group D
according to the calculation of the cumulative rate from May/2015 to
April/2017. The 5 funds with higher cumulative profitability in this period
will belong to Group A and so on until the 4 Groups are formed (Table 21).
Table 21: Groups A, B, C and D
Initially,
it is important to emphasize that the proposed methodology used indicators in
its implementation, such as, volatility and cumulative rate in two of the
studied periods established in the total studied period (the last 12 months and
the 12 second-to-last months), which is significantly different from using the
cumulative rate of the entire period. The main motivation for this comparison
is to see if the funds that obtained higher profitability in the entire period,
that is, the funds which enabled higher returns to their investors, are the
ones best classified in the proposed methodology.
It is
also important to highlight that the way the mutual influence between funds was
established in 3 parts of the methodology's implementation does not correspond
to the way the cumulative rate is calculated. Therefore, the proposed
methodology intends to evaluate the funds' behavior according to the precepts
following its implementation.
The
calculation of the cumulative rate will classify the funds according to the
best performance throughout the period, it does not matter the path outlined by
each fund to reach its final return in this period. A fund that at some point
obtains a very high profitability in order to be taken to a better position
compared to the others, but that in other moments obtained a bad profitability
if compared to others, is considered the best alternative, because the
calculation of the cumulative rate in influenced by spikes.
The
proposed methodology intends to evaluate a fund's profitability’s in comparison
to the others and many times without taking into account how a fund is superior
to the other, only if it is superior or not, except for the moment when the
degree of power is generated during the implementation of the TOPSIS method.
The
motivation behind such analysis is that there is no guarantee that moments with
high profitability’s will repeat in other moments, but there is a behavior that
many times is superior and demonstrated a better management and expertise. For
that, the behavior of the funds' profitability’s should be analyzed according
to this paper's Section 3, based on the assumption that the best funds for
future investments are the ones that behaved better in comparison to the others
in each studied point and did not obtain high profitability in the entire
period.
Comparing
Tables 20 and 21, it is noted that the XP, Mauá and SPX funds find themselves
in the best level of classification in both tables, that is, these funds
behaved better in comparison to the others in the studied points and they have
also the higher profitability in this period.
The
BTG and Sul funds find themselves in the best level of classification in Table
20 while they are classified as Group C in Table 21. That happens because, although
they did not obtain the best profitability’s in the studied period, they
behaved better compared to the others in the period. That is, they are the best
options for a future investment that the Modal (Group A in Table 21 and
Subgroup B1 in Table 20) and Growler funds (Group A in Table 21 and
Subgroup A2 in Table 20).
4.2.
Prioritization
of funds in Subgroup A1
With
the implementation of the WINGS method it is possible to obtain the 4
classifications for the analyzed funds in order to create different ways of
prioritizing the decision inside Subgroup A1. The results of Group
A's members generated by the WINGS method (Table 14) present the following
interpretation: the values in column r represent the impact of each alternative
on the others it does not matter how much impact it receives or how much it
impacts the others.
The
results of column r+c represent the
total involvement of a funds in the analyzed subgroup, because this result is
the sum of the offered with the received impact. The results of column r-c classify the funds as impacted or
impactors. The impacted have a negative result of r-c, since they represent funds that obtained inferior offered
impact to the impact received in this analyzed subgroup.
The
impactors have a negative result of r-c,
since they represent funds that obtained superior offered impact to the impact
received in this analyzed subgroup. Thus, the 4 classifications were formed
with the funds belonging to Subgroup A1 (Table 22) with the results
of the WINGS method (Table 14).
Table 22: Prioritization of the funds members of
Subgroup A1
The
classification formed by column r was
established in decreasing order. In this classification, the best fund is the
one that impacts the others in the analyzed points it does not matter how much
impact it receives. The way that this prioritization was established seeks to
assist an investor who prioritizes how a given fund is found more superior than
the others in the analyzed points, without taking into account how this funds
behaved when the others obtains a better performance when compared to it.
The
classification formed by column c was
established in increasing order. In this classification, the best fund is the
one that receives less impact from the others it does not matter how much it is
able to impact the others. In other words, it is the fund the better defends
itself. The way that this prioritization was established seeks to assist an
investor who prioritizes how a given fund behaves when the others find
themselves in their best positions.
The
classification formed by column r+c
was established in decreasing order. In this classification, the best fund is
the one that has a bigger involvement inside the system, because its result is
the sum of the offered impact with the received impact.
The
way that this prioritization was established seeks to assist an investor who
prioritizes the alternative that impacts the others, that is, how a fund is
found in the best positions of the studied points compared to the others summed
in some level of risk. This level of risk is used in this classification
because it takes into consideration the received impact by an alternative in
the analyzed subgroup.
The
classification formed by column r-c
was established in decreasing order. This classification is formed by the
difference between the offered impact and the received impact by an alternative
in the analyzed subgroup, that is, is it the offered impact discounted from the
received impact. It can be said that this classification is more conservative
than the others, because it discounts from the offered impact the received
impact by a fund in the analyzed subgroup.
5. CONCLUSION
This
paper sought to develop a methodology able to classify the 20 analyzed
multimarket investment funds in 4 performance levels, the subgroups A1,
A2, B1 and B2. For that, DEMATEL, TOPSIS and
WINGS methods were used. It is essential to reinforce that the classification
obtained by the proposed methodology is not influenced by spikes as some performance
indicators are, like the cumulative rate, according to the data analysis.
With
the comparison between the established methodology and the classification
established by the cumulative rate of the entire period, it was possible to
notice how two forms of analysis diverge in some points since they evaluate the
performance differently as well as it was possible to notice that some funds
were well classified in both methodologies. This was important to point out
that the fund with the highest cumulative profitability in a given period may
not be the one with the best performance classification.
The
data analysis presents 4 ways of prioritizing the decision between the best
classified funds, because the results generated by the WINGS method take
different paths because of the way the methodology is founded. This paper is
intended to be used for the classification of other sets of investment funds in
order to facilitate the reading of the funds' performance behavior when analyzed
jointly. The combined implementation of the DEMATEL, TOPSIS and WINGS methods
may also be applied to other sets of financial products, in which a
classification of these products on different performance levels is required.
REFERENCES
ANBIMA.
(2017) http://www.anbima.com.br/data/files/B4/B2/98/EF/642085106351AF7569A80AC2/Cartilha_da_Nova_Classificacao_de_Fundos_1_.pdf.
Access: 20 July 2017.
Caldeira, J. F.; Moura, G. V.; Santos, A. A. P.; Tessari,
C. (2014) Seleção de carteiras com modelos fatoriais heterocedásticos:
aplicação para fundos multimercados. Revista
de Administração Mackenzie, v. 15, n. 2, p. 127-161.
DUARTE JUNIOR,
A. M.; MEDEIROS, L. C. B. (2016) Investing in private equity in Brazil. Brazilian Business Review, v. 15, n. 3,
p. 51-84.
Elton, E. J.; Gruber, M. J. (1995) Modern
portfolio theory and investment analysis, 5 ed. New York: John Wiley &
Sons.
Gabus, A.; Fontela, E. (1972) World problems, an invitation to further
thought within the framework of DEMATEL. Battelle
Geneva Research Centre.
Gomes, L. F. A. M.; Rangel, L. A. D.; Santos, G. (2016) An AHP-based asset
allocation model. International Journal
of Business and Systems Research, v. 10, n. 1, p. 78 – 99.
Haugen, R.A. (1997) Modern investment theory, 4 ed. New Jersey: Prentice-Hall.
Hwang, C. L.; Yoon, K. (1981) Multiple
attribute decision making: methods and applications. Berlin: Springer-Verlag.
Infomoney. (2005)
http://www.infomoney.com.br/noticias/noticia/412945/hedge-funds-sem-misterios-entenda-que-sao-como-funcionam.
Access: 13 June 2017.
LONGARAY,
A. A.; ENSSLIN, L.; MACKNESS, J. R. (2014) Multicriteria decision analysis to
lead about messes problems: an illustrated case. Independent
Journal of Management & Production, v. 5, n. 3, p. 677-692.
Malaquias, R. F.; EID JUNIOR, W. (2014) Fundos
multimercados: desempenho, determinantes do desempenho e efeito moderador. Revista de Administração Mackenzie, v.
15, n. 4, p. 135-163.
Martins, A. S. S. (2014) Seleção de fundos de investimentos no
Brasil: aplicação do método multicritério TOPSIS. Dissertation
(Master in Business Administration). Rio de Janeiro: Ibmec Business
School.
Melo, R. A.; Macedo, M. A. S. (2013) Análise multicriterial do desempenho
de longo prazo das carteiras de ações de fundos de investimento multimercado
macro no Brasil no período de 2005 a 2010. Revista
de Evidenciação Contábil & Finanças, v. 1, n. 2, p. 69-89.
Mello, B. B. R. (2014) Classificação de risco setorial com base
nos métodos Weighted Influence Non-Linear Gauge System and Analytic Hierarchy
Process. Dissertation (Master in Business Administration). Rio
de Janeiro: Ibmec Business School.
Mesrinejad, S.; Moradi, A. (2015) Ranking of investment funds of Tehran
Exchange by using TOPSIS method. Journal
UMP Social Sciences and Technology Management, v. 3, n. 1, p. 157-164.
Michnik, J. (2013) Weighted influence
non-linear gauge system (WINGS) – an analysis method for the system of
interrelated components. European Journal
of Operational Research, v. 228, n. 3, p. 536 – 544.
Rovai, R. L. (2015) Estratégias de
fundos multimercado no Brasil e a influência da taxa de performance no seu
desempenho. Revista de
Finanças Aplicadas, v. 3, p. 1-30.
Tzeng, G.; Huang, J. (2011) Multiple
attribute decision making: methods and applications. Boca Raton: CRC
Press.
Varga, G. (2001) Índice de Sharpe e
outros indicadores de performance aplicados a fundos de ações brasileiros. Revista de Administração Contemporânea,
v. 3, n. 5, p. 215 – 245.