The design of an automatic portfolio
management system for Borsa Istanbul
Interim Report
Advisors: Asst. Prof. Dr. Kaya TOKMAKÇIOĞLU, Prof. Dr. Burç
ULENGİN
Hayri Aydın ve Yunus Şevli
1
Introduction
2
Literature
a) National Literature
b) International Literature
Portfolio Theory
Diversification of Portfolio
Creating Portfolio with PCA
Identificaion of Crises
Research Questions:
3
3
4
4
5
6
8
9
Data
9
Method
Constructing Portfolios
Measuring degree of diversification
Identifying Bear Markets
10
11
13
13
References
15
2
Introduction
Securities markets are technical markets that require a certain level of knowledge, and developments
in this market need to be closely monitored. Any transaction made without knowledge can result in
great losses in these markets. Knowledgeable investors make their investments in stock market based
on fundamental and technical analysis. This information often saves them from harm and allows them
to turn to potential profits. However, these types of analyzes are known to very few investors who
invest in BIST, and those with expertise in these analyzes are much less. Furthermore implementing
these analyzes consumes a lot of time even for the experts. This leads investors to follow social media
accounts that analyze stocks and to join paid groups set up there. There are 2 drawbacks of following
stock market accounts through social media. Firstly, these accounts, which affect people's investment
considerations, can lead to manipulative movements. Thus, people can remember the BIST as a place
they are deceived, and they may refrain from investing in this market throughout their life. Secondly,
these manipulative movements negatively affecting the investments made based on fundamental and
technical analysis by being obstacle to reaching the target prices of the shares. As a result, this leads to
loss in confidence in the stcok market, causing potential investors, who are willing to invest in equity
markets, to withdraw their savings from BIST after a period of time. Moreover, by transferring their
own experiences to their relatives, BIST is also deprived of potential investments.
The subject of the project is, building a portfolio management decision support system that
automatically allows us; to construct a portfolio that provides higher return than BIST100 index and
other alternatives, for particular time period (daily, weekly and monthly), over all stocks in BIST100.
This decision support system will decrease the need of technical knowledge and cut time cost either
for individuals and portfolio management companies.
In our project, principle component analysis (PCA) will be used to determine the stocks to be
examined in the stock market. PCA is a statistical method of reducing dimensionality and is an
approach that reduces the complexity of the data by creating basic components that are as
uncorrelated as possible so as to preserve the variation in the variables to a large extent (Jolliffe,
1986). Using this method, stocks or stock groups that represent different risk groups will be
determined by analyzing different time periods and amount of data. Then, portfolios will be
constructed according to determined stocks and performance of those portfolios will be measured.
Successful method will be used to identify portfolios that will be proposed to the customer.
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With this project, decision makers will be able to use their time in the most efficient way, as all stocks
in the market will be evaluated automatically. The portfolio that will be created, which has regular
return, will provide new investors with to the market. In addition PCA will be used for the first time to
analyze stocks in Istanbul Stock Exchange.
Literature
a) National Literature
Investments made on the stock market are considered high risk and highly profitable, and thus attract
a large number of investors. However, information about stocks is complex and there are many
uncertainties. Therefore, it is a difficult situation for investors to predict which stocks can get the most
returns with the least risk, and which stocks they should invest. There are many different analytical
and forecasting methods in this regard. The most common ones are fundamental and technical
analysis methods. Fundamental analysis is a valuation method used to measure the instrinsic value of
securities by examining the relevant financial, economic and other quantitative and qualitative factors.
Sevinç, made a price forecast for the future by analyzing a stock market traded on a stock exchange in
four different approaches within the scope of fundamental analysis (2004). Technical analysis is an
analytical method used to forecast the direction of prices by examining past market data, mainly
volume and price (Kirkpatrick & Dahlquist, 2006). As another strategy, momentum investment
strategy is based on the assumption that stocks that have risen in the past will be bought and those that
have been dropped in the past will be sold (Kandır, 2009, 85-92). Kandir and Inan reported that, this
strategy was not successful at 3, 6 and 9 months; but it was successful in the 12-month period (2011).
These methods can be used for stock trading, but their performance have not been fully proven. A
feature of the stock market, however, is that it can fall as well as increase significantly in short and
medium walks. Bear market and many other market declines will be painful for many investors who
are unprepared for such possible declines. Moreover, investors' desire is to have a capital that does not
diminish even if the market is falling. It is not always possible to achieve this with a single investment
in securities. For this reason, an investor should use a diversification strategy such as creating a
portfolio to spread the risk to assets.
The main question of creating a portfolio is which stocks have to be bought. In this regard, studies
have been carried out on the determination of the shares to be portfolioed through many different
methods. Kapusuzoğlu and İbicioğlu (2013) examined the interrelationships between the sectors of
the companies in the national stock market and studied which sectors the investors should form a
portfolio from if they wanted to create a portfolio that fits the modern portfolio theory. In another
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study, securities that are to be taken to the portfolio have been determined by performing a
hierarchical clustering analysis on stocks' risks, financial ratios and returns (Karabayır and Doğanay,
2010). One of the methods used in national literature is the creation of a portfolio by multi-criteria
decision making. Multi-criteria decision making is the modeling of complex situations where the set
of variables and criteria is defined (Moldrik, Gurecky and Paszek, 2008). Şahin and Akkaya (2013)
conducted a study in which they form a portfolio by evaluating the 34 stocks in the national stock
exchange with the PROMETHEE ranking method based on volatility, transaction amount, dividend
payment and transaction volume criterion. In another study on similar area, the stocks in the bank
sector were analyzed based on returns using the Fuzzy AHP and MOORA methods, and a portfolio is
constructed according to results. (Dince, 2015). These studies are thought to be weak with the low
number of stocks included in the studies, the performance of the generated portfolios are not measured
and compared, and the studies are conducted only in one period.
Another important issues in the Modern Portfolio Theory is determining weights of stocks in the
portfolio. Most of the studies on portfolio diversification are based on Markowitz’s (1952)
mean-variance theory. There are a variety of methods for building an optimal portfolio. Kaya and
Kocadağlı (2012) studied a portfolio selection procedure that included beta coefficients using
Markowitz's mean variance, Konno and Yamazaki's mean absolute deviation, and Sharpe's single
index models. Abay (2013), Toraman and Yürük (2014) used quadratic programming based models
for analysis of variance-covariance matrix obtained from the returns of stocks traded in BIST30 and
BIST100 indices, in order to create optimal portfolio. Artificial intelligence methods have also been
used in this area. While Bekci (2001) used fuzzy logic in portfolio optimization; Çelenli, Eğrioğlu and
Soup (2015) used particle swarm optimization. Genel (2004)’s, and Zeren and Bayğin (2015)’s studies
are examples of research conducted in area of genetic algorithms. In addition, game theory approach
was used for the optimization of the portfolio (Demirci, Şahinkul and Eren, 2017). However, there is
no study done with principal component analysis on Borsa Istanbul.
b) International Literature
Portfolio Theory
Markowitz's (1952) mean-variance theory is the basis for modern portfolio theory, offering first proof
that investing in a portfolio of assets rather than a single security could be more beneficial. In
addition, the study by Lowenfeld (1909), in which benefits of diversification are mentioned, is the
first meticulous study of portfolio diversification.
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There are some drawbacks in practice for the mean-variance optimization. By estimating the
parameters such as yield and risk, the mean-variance optimal portfolio is determined. Hence, stocks in
the mean-variance optimal portfolio are highly sensitive to these parameters. However, returns and
risks, especially returns are estimated with large error terms. In this regard, Chopra and William
(1993) note that the error of the expected return is about 10 times more than the error term of the
variance, about 20 times more than the covariance error term. Minor changes in parameters cause
significant changes in portfolio distribution (Jorion, 1985). Working on the limitations of the
mean-variance approach, Michaud (1989) argued that this approach is a method to maximize the error
term. In addition, the mean variance approach tends to concentrate on a few assets that have the most
expected returns if the historical data is used in the portfolio (Bernstein, 2001). This contradicts the
purpose of portfolio diversification. Allen (2010) claimed that the mean-variance approach failed in
the 2008 crisis.
There is a growing need to create more diversified portfolios for both academic researchers and
investors. The new portfolio creation pattern is a risk-based portfolio allocation strategy that creates a
portfolio based solely on the variance-covariance of assets. Examples of risk-based portfolio
allocation strategy include, minimum variance (Behr et al., 2008; Clarke et al., 2006; Haugen and
Baker, 1991), maximum diversified portfolio (Choueifaty and Coignard, 2008), risk parity (Maillard
et al., 2010; Qian, 2006) and diversified risk parity (Kind, 2013; Lohre et al., 2012, 2014).
Two important characteristics of securities investment are the uncertainties of the returns and the
correlations between the returns. Low or negative correlations between securities provide
diversification. At the same time, this situation leads to the complexity of the portfolio distribution
analysis. For example, if there is only a few securities, say five stocks, it is easy and intuitive to look
at five variances and 10 correlations or covariances. However, if the number of securities is large, for
example 400, then simply looking at 400 variances and 79800 correlations or covariances would not
be very useful. PCA is a statistical method of reducing dimensionality and is an approach that reduces
the complexity of the data by creating basic components that are as uncorrelated as possible so as to
preserve the variation in the variables to a large extent (Jolliffe, 1986). This method, even if it is
widely used in many areas, is very rarely used in the financial sector, especially in the context of
portfolio management.
Diversification of Portfolio
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In context of the number of shares to be selected to diversify a portfolio, Evans and Archer (1968)
stated that ten randomly selected stocks would be sufficient for diversification. In addition, he also
observed that the diversification benefits have decreased as the number of stocks on the portfolio
increases. Newbould and Poon (1993, 1996) suggested that only 8 to 20 stocks would be sufficient to
obtain the benefit of diversification as much as possible, following Evans and Archer's (1968)
approach. Statman (1987), on the other hand, compared the cost and benefit of portfolio
diversification and stated that at least 30 stocks should be randomly selected to generate a well
diversified portfolio using data obtained mid-1980s. In 2004, Statman used the same approach more
data and stated that the break-even point, which is equal to the marginal cost of marginal benefit,
exceeded 300 stocks. However, considering number of stocks in the portfolio as a measure of
diversification is a questionable case.
Frahm and Wiechers (2011) stated that the number of stocks in the portfolio would be an important
parameter if all stocks in the market had equal average variance and covariance. In addition, if the
randomly selected stocks show high correlation between them, the desired diversification will not be
achieved. The problem with randomly selected stocks is solved by PCA. If stocks are selected through
the stock correlation matrix, the selected stocks will be able to define the market and represent the risk
sources in the market. Rudin and Morgan (2006) used PCA to measure the diversification
quantitatively and by testing equally weighted portfolios of stocks in the S&P100 index, found that
the diversification of the portfolio generated by the 40 randomly selected stocks approximatly the
same with the diversification of independent 20 principal components generated by the PCA. The
PCA ensures that risk sources that are not correlated with each other in the market are identified and
stocks are selected over these different risk sources. In this respect, the number of stocks to be
selected is determined from the risk sources. In addition, market connectedness does not remain
constant over time. While market connectedness is increasing, assuming that assets in the portfolio do
not change, the diversification of the portfolio is reduced (Billioand et al., 2012; Fenn et al., 2011;
Kritzman et al., 2011; Zheng et al., 2012). Campbell et al. (2001) stated that the number of stocks
required to reach a certain level of diversification was not the same in 1963-85 and 1986-97. For this
reason, it is necessary to regularly perform PCA for different time periods.
Creating Portfolio with PCA
PCA is one of the best known techniques in multivariate data analysis. In the last 50 years, with the
spread of computers, it has been used in many different areas (Jolliffe, 1986). This method of
determining patterns in multidimensional data is a very attractive tool for examining complicated
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structures in the financial markets, since it creates non-correlated components from correlated
variables. It was used by Feeney and Hester in 1967 to create a market index. There are also studies
used PCA to identify similar factors in the bond returns (Driesson et al., 2003; Pérignon et al., 2007).
Recently, there is a developing literature in the use of principal component analysis on market
cross-correlation studies and systemic risk measurement studies (Billioand et al., 2012; Kritzman et
al., 2011; Zheng et al., 2012). Most studies have focused solely on the theoretical suitability of the
implementation of the princpial component analysis in portfolio management, and several studies
highlighted the performance of this method.
First, in 2004, Partovi and Caputo introduced the idea of using PCA for efficient portfolio creation.
The main idea is based on a dramatic reduction in the complexity of the portfolio selection if there is
no correlation between the assets. They stated that every asset group with short-term trading
characteristics could be transformed into uncorrelated principal components.
Theoretical work by Partovi and Caputo (2004) on creation of portfolio through principal componetns
has increased the number of academic works in this area. Particularly, after the 2008 crisis, it has
become a priority to reduce the risk. Meucci (2009), through Partovi and Caputo (2004)'s work,
presented a tool called diversification distribution to analyze the concentration profile of the portfolio.
The diversification distribution is described as the ratio of the variance of each principal component to
the total variance. When the diversification distribution is near the uniform, maximum diversification
is achieved. That is, it occurs when the variances of the principal components are equal to each other.
Lohre et al. (2012) and Lohre et al. (2014) adopted the work of Meucci (2009) to provide maximum
portfolio diversification. The general idea is to distribute the risk evenly by investing equally in the
basic components. This strategy is called "diversified risk parity". Moreover, as the well-diversified
risk parity, they studied 1 / N, the minimum variance and risk parity strategies. Lohre et al. (2012) and
Lohre et al. (2014) reported that the diversified risk parity provides more risk-adjusted performance
than other alternatives and is the best portfolio diversification approach.
The basic idea of the risk parity, also known as equal risk contribution strategy, is to provide an equal
risk contribution for every asset in the portfolio. Qian (2011) argued that the risk parity provided
better diversification and higher returns. The risk parity and diversified risk parity strategies are
similar, as they both create a portfolio by diversifying the risk. However, while the risk parity
distributes the risk over the assets, the diversified risk parity risk is distributed over the uncorrelated
principal components. In the risk parity strategy, if the correlation between assets is high, portfolio
diversification will be less. However, since there is no correlation between the principal components
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in the diversified risk parity, this is not the case. If we assume that correlations between assets are
significantly positive, the risk parity will include many assets with the same risk in the portfolio, while
all variation in the diversified risk parity will be explained on the first principal component.
Kind (2013) stated that the 1/N strategy is the best performing strategy by comparing the risk parity
and the diversified risk parity with the 1/N strategy. Also, DeMiguel et al. (2009) and Lee (2011)
suggest that 1/N strategies are superior to other strategies in their research.
Identificaion of Crises
Risks that can lead to financial crises, which are related to the whole financial system, rather than the
individiual risk of each entitiy in the system, are called systemic risk (Zhen et al., 2012). After the
2008 financial crisis, the literature on systemic crisis became more important. The empirical studies
on this subject are examined in three different groups. The first group focused on the joint crashes,
spillover effects and contagion in financial markets (Adrian, 2007; Billioand et al., 2012; Kritzman et
al., 2011; Wang et al., 2011). These studies are focused on analyzing the interconnectedness between
the returns of securities on the market, and the steps in these studies will also be applied in our work
on systemic risk.
The greater the connectedness of the market, the greater the systemic risk, since the effect of negative
shocks spreads faster and wider. For this reason, monitoring the change in correlation over time is of
great importance. In addition, the low correlation between assets increases the possibility of
diversification. Therefore, examining the correlations between securities is important for portfolio
management.
Some studies have shown that correlations between securities vary according to different time periods.
Butler and Joaquin (2001) and Campbell et al. (2002) emphasizes that market correlations increase in
falling markets. In recent studies, a sliding window approach has been used instead of comparing
different time periods to examine correlation changes. Fenn et al. (2011), by using the PCA to
examine the correlation change, pointed out that the increase in variance explained in the first
component means that the common variance in the market is high. Moreover, they have emphasized
that the variance explained by the first component may be the result of increasing correlations
between several entities or a correlation of the overall market. In the first case, the low correlation
between the assets increases the possibility of diversification, so it will be less effective on
diversification of the portfolio. Unlike the first case, if there is a market-wide increase in correlation,
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it will become much more difficult to reduce risk by diversifying different assets. Fenn et al. (2011)
stated that when Brother Brother filed for bankruptcy, the variance explained by the first component
increased rapidly, and when Merrill Lynch was taken over by Bank of America on September 15,
2008 there was an increase in market-wide correlation.
Kritzman et al. (2011) presented a systemic risk measure called the absorption ratio. This ratio is
based on the ratio of the variance explained by a certain number of components obtained in the PCA
result to the total variance. They reported that most global financial crises correspond to a shift in the
absorption rate in the positive direction. Asian Financial Crisis in 1997, Russian default and LTCM
collapse in 1998, Housing bubble in mid-2006 and Lehman Brothers default in 2008 are among these
crises. Another interesting finding in this article is that stock prices change significantly in many cases
where the rate of absorption reaches the highest or lowest level.
Zheng et al. (2012) calculated the change in variance explained for capturing the systemic risk as well
as looking at the variance explained by the first component. They acquired similar findings with
Kritzman et al. (2011), stating that both the variance value and the variance change increased during
the financial crisis. On the other hand, time length and the moving window size used for calculating
the change in variance has an impact on spike date of crisis. When the moving window size is bigger,
and saturated roughly after 20 month, the spike of variance explained by first principal component
appeared later. Thus, longer the time lenght used to calculate change, later the change appears. Even
though many researchers choose the size of moving window randomly, Zheng et al. (2012), reported
that it may affect the results. From this point of view, our project will measure the performance of PC
in both long-term and short-term using 5-minute, hourly and daily data.
Research Questions:
1.
Are the stocks selected by the system sufficiently diversified portfolio?
2.
Are the portfolios constructed based on different allocation strategies substantially provide
higher returns than BIST index and other alternatives in certain period (daily, weekly or monthly)?
3.
Data
Can the system be used as an indicator for financial crisis and bear market?
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The project is based on the Turkish stock market. The examination is done on the constituents of the
XUTUM index from January 2013 to October 2017. The XUTUM index is a measure of the joint
performance of all shares which are traded in Istanbul Stock Exchange.
In the period of analysis, there are a number of stocks that were added or deleted from index. Only the
stocks which do not have enough data are deleted for the examination. After deletion, 271 are
remained from 351 stocks.
Trading is done on years 2015, as decreasing year, 2016 as flat year, and 2017 as increasing year of
index. Analysis will be done on a weekly basis and forecasting will only be done on the weeks that
contains 5 full work days, because it will make the analysis much easier . In other words, if there is a
holiday in a week, that week is excluded for forecasting. For the years 2015, 2016 and 2017 there are
131 full weeks in total.
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Daily closing and opening prices for each stock are obtained from the Thomson Reuters database.
The blanks in the data are filled with the previous available data. The PCA will be performed on the
correlation matrix of the return series.
The returns are calculated as:
Method
For the project, a rolling window approach will be applied. In the literature, it is stated that the size of
the window matters. Thus, in the project, different sizes will be examined in order to find the one
gives best results. Formation period -which is the window size of training data- will change between 1
month and 24 months, and the trading period -size of test data- is 5 days.
So, it is assumed that PCA is applied at every weekend in 2015 to 2017 based on moving window
approach, and also, it is assumed that stocks are bought at every monday’s open price and sold at close
prices of each weekday.
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Scilicet, at each weekend, there will be 24 portfolios to compare, coming from 24 different formation
period.
PCA can be applied to both correlation and covariance matrix however there are some issues related
with using covariance matrix. Because, number of principal components will be fewer and will be
dominated by variables which have large variance, if the difference of variances are large between
variables. This situation may prevent creating convenient information for diversification by applying
PCA (Jolliffe, 1986). So, the correlation matrix of return series will be used on PCA.
Constructing Portfolios
The principal components that are created with PCA can be described as uncorrelated risk sources that
are in the original stock set.
Eigenvalue of a principal component means how much variance that principal component carries, and
for the stock market, it means how much risk that component carries. The eigenvalues generally
decrease rapidly, and the principal components that are higher numbered, have relatively smaller
eigenvalues. In theory it is possible to construct portfolios with all principal components to catch all
the risk sources. However, it seems irrational to allocate any budget on higher numbered principal
components that are not major risk sources.
Kim and Jeong (2005) decomposed the correlation matrix and organized the principal components as;
the marketwide effect with the largest eigenvalue, the group part with intermediate discrete
eigenvalues, and the random part with small eigenvalues. By following Kim and Jeong (2005),
principal components are decomposed into three parts that correspond to the three kinds of fluctuation
of stock price changes:
1. The first principal component which has the largest eigenvalue stands for a marketwide
effect that affects all stocks.
2. A portion of principal components following the market component stands for
synchronized fluctuations that only affects a group of stocks.
3. And the other principal components stands for random fluctuations.
Thus, in the project only the components that identify structure within the stock market will be
retained, which are the market and group components. In order to eliminate the principal components
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that represent random fluctuations, in other words, that are not major risk sources, there are two rules.
The first one is Kaiser’s rule (Kaiser, 1960), keeping the principal components which have eigenvalue
greater than 1. The idea behind that is, all principal components would have unit variance if all the
stocks were uncorrelated. As second, Jolliffe (1986) considered a more conservative break point, 0.7.
Because it would be undesirable to delete the princpal components that have eigenvalue close to 1.
After elimination of components, dimensionality will be reduced. However, even though
dimensionality was reduced, there will still be 99 stocks in the portfolio. It is known that, when the
number of variables in a data set is large, it is frequent that some variables contain repeated
information. Thus, variable selection must be done.
Based on the variable selection method of Jolliffe (1986), the selection procedure is described as:
1. Apply PCA to the correlation matrix of BIST100 data set.
2. Associate one variable with the highest coefficient in absolute value with each of the principal
components that have eigenvalue less than a certain level which is called the deletion criteria, then
those variables will be deleted. For this point, Kaiser’s rule will be used, which a principal component
with eigenvalues smaller than 1 contains less information than one of the original variables (Kaiser,
1960). Therefore, the deletion criteria will be 1. In addition, if the variables which have highest
coefficient in absolute value with each of the principal components that have eigenvalue less than
deletion criteria also have highest coefficient in absolute value with each of the principal components
that have eigenvalue more than deletion criteria, those variables will not be deleted because those
variables can contains much information.
3. A second PCA is performed on remaining variables. The same procedure was applied that
associates one variable with each principal components that have an eigenvalue less than l, and delete
those variables.
4. The procedure is repeated until no further deletions are considered necessary based on a stopping
criteria which be determined based on the eigenvalue of the last principal component. Jolliffe
suggested that deleting principal components that have eigenvalue less than 1 is too aggressive and
likely to result in a loss of useful information, a more conservative level is 0.7 (1986). Therefore, the
stopping criteria can be deleting variables until the retaining variables all have eigenvalue not less
than 0.7.
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As a result of implementing the selection procedure with a deletion criteria 1 and a stopping criteria
0.7, we will obtain few stocks which are representing uncorrelated risk sources in the Bist100 for each
study period ,which will make easier to construct the portfolios.
After obtaining the stocks based on the selection method, with using 1/N allocation strategy, the
portfolios will be constructed for 24 different formation (Kind, 2013).
After all, portfolios’ returns will be compared with BIST100 index for whole trading periods.
Measuring degree of diversification
The degree of diversificaion in portfolios will be measured with diversification ratio introduced by
Choueifaty and Coignard (2008).
𝑁
𝐷𝑅(𝑃) =
𝐶𝑜𝑚𝑏𝑖𝑛𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑡ℎ𝑒 𝑟𝑖𝑠𝑘𝑠
𝑅𝑖𝑠𝑘 𝑜𝑓 𝑡ℎ𝑒 𝑐𝑜𝑚𝑏𝑖𝑛𝑎𝑡𝑖𝑜𝑛
=
∑ σ𝑘ω𝑘
𝑘=1
σ𝑝
where σ𝑘 is the volatility of each asset’s returns and ω𝑘 is the weight of each asset in the portfolio for
N assets and σ𝑝 is the volatility of portfolio’s returns.
The weighted average volatility of the
individual stocks is indicated by the numerator of the diversification ratio and the portfolio standard
deviation is indicated by denominator. In this way, the higher the diversification ratio means better the
degree of diversification . If a portfolio only contains one stock, then the diversification will achieved
its lower bound of 1.
Identifying Bear Markets
To investigate whether the system can be used as an indicator for bear market, the absorption ratio
will be calculated and the performances will be measured across years. This ratio is based on the ratio
of the variance explained by a certain number of components obtained in the PCA result to the total
variance (Kritzman et al., 2011). A reseach done by Fenn et al. indicates that using the variance
explained by more than one principal component can be misleading, thus, the variance explained by
first compenent will be used (2011).
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While applying PCA to daily returns of Bist100 stocks for different formation periods changing
between 1 month and 24 months, we will measure the performances of absorption ratio for incoming
weekdays.
It is assumed that higher absorption ratio means higher systemic risk. Therefore, for the formation
periods that the absorption ratio is high, then, the market return for incoming trading periods will be
low. For that, the correlation coefficient between market returns and absorption ratios will be
calculated. Negative and high correlation coefficient will show that the system can be used as an
indicator for bear market.
Design
Based on the analysis, the results of the M12 , M24 and combined portolio are found
as satisfying, therefore, these portfolios will be used for the design of the proposed system.
16
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