Dead or Alive: Modern Portfolio Theory Based on Financial Analysis

Currently, there are a lot of criticisms on Modern Portfolio Theory (MPT). Black Swan argument claims that in the event of a financial turmoil, the stock prices move beyond what is expected by normal distribution. This study empirically investigates whether it is possible to apply MPT by using additional criteria. The criteria used in this research are related to financial analysis, a well-known field in corporate finance. The ratios used are debt-to-equity and return on equity. According to the analysis, Modern portfolio theory can be applied by the use of these additional criteria. The analysis with debt-to-equity criterion reveals that Portfolios 3 and 5 which have lower debt-to-equity ratios performed better in the period. The analysis with return on equity reveals that only Portfolio 8 which has 9 companies with ratios larger than 0.2 has positive return whereas the other portfolios have negative returns. The results further show that, while applying MPT with these criteria is perfectly possible and sound, the investor could diversify further by selecting portfolios with higher number of securities and still have better financial ratios. This research to the authors’ knowledge brings a novelty by proposing these selection criteria in MPT. The suggested method could be applied by practitioners in this field. This study also targets to bring a new direction to the ongoing debate whether the theory of Markowitz (commonly known as father of Modern Portfolio Theory) is dead or alive.


Introduction
A wise investor doesn't will to risk all of his/her wealth by investing all his and wealth in single asset class. Portfolio theory has application in various assets such as bonds, equity, gold, oil and real estate. As Bernstein (1997) points out the roots of portfolio theory could be seen in Shakespeare's play or more specifically in the words of Antonio, merchant of Venice. However, mathematical foundations of what we today call modern portfolio theory are given by Markowitz (1952). Some of these computations are also available in the methodology section of this study. Accordingly, it is possible to determine an efficient portfolio given previous returns, variances, and covariances of different asset clases.
Later, Sharpe (1966) comes up with what we call Sharpe ratio to measure the performance of a portfolio. Actually, what we do by adding different assets to a portfolio is to try to increase Sharpe ratio as much as possible. Sharpe Ratio could be computed as follows. The motivation of this paper is to find a selection criteria between a set of portfolios. The selected portfolio should be more efficient in terms of risk and return. An efficient portfolio should have more return for a given level of risk or less risk for a given level of return. These expectations could be set by the investor.
The criteria chosen in this paper comes from financial analysis. In other words, knowledge on portfolio theory and financial analysis are combined in this study.
In financial analysis, a ratio is computed by using the data from various financial statements of a company such as balance sheet (also referred as statement of financial position in IFRS-international financial reporting standards), statement of cash flows and income statement. These ratios represent different quantities such as liquidity, solvency, turnover, profitability and market based indicators. Debt-to-equity and return on equity ratios are used in this research.
In the balance sheet, liabilities and shareholders' equity are used to obtain a company's assets. However, it is up to the company to determine how this is divided between liabilities and shareholders' equity. This is a well-known financial decision in corporate finance and often referred as capital structure. Yang et al. (2017) point out that trade off theory, pecking order and market timing hypothesis are important in this decision. Trade off theory indicates that one should consider bankruptcy and tax shield effects when holding debt. Pecking order suggest to use internal finance and debt before they issue equity. According to market timing hypothesis, a decline in the price of stock is likely after a stock issue.
As indicated by Fabozzi and Peterson (2003), Debt-to-equity ratio is a quantified representation of capital structure. Debt-to-equity ratio is obtained by the formula below.
Alawneh (2019) another form of leverage which is known as operating leverage is also important in stock selection. According to this study, buying stocks on Amman Stock Exchange based on net investment cash flows is recommended.
Return on equity (ROE) is the other criteria used in this study. As stated by Ross et. al. (1990), this ratio is a representation of the unit profitability of capital provided by shareholders. This also indicates the performance of the management of that specific company. Return on equity is computed by the formula below.
The rest of the study is organized as follows. The next section is a collection of some works related to this study. In the section main focus of the paper, scope of the research and methodology is given. In the solutions and recommendations, solutions for both debt-to-equity and return on equity and investment decision are available. In the discussion section, the results of the research is elaborated. The conclusion section includes the final remarks.

Background
There are many studies which used mean variance optimization (MVO) in Istanbul Stock Exchange. The method of Markowitz is mean variance optimization. This means, he used mean for return and variance for risk. In this study standard Modern Portfolio Theory procedure is followed but it is perfectly possible to use other measurements for risk such as Value at Risk.
Kucukkocaoglu (2002) also applied the standard procedure. By the use of MVO, efficient portfolios are obtained. The research period is 1999. Closing prices of stocks in ISE30 and ISE100 (these are the bluechip indices in Istanbul Stock exchange) indices are used in this study.
In the universe of assets, there are many risky assets and an assumed risk-free asset. If a straight line is drawn (this is called capital market line-CML) from risk free asset to efficient frontier so that it barely touches (tangent) the efficient frontier (it is a set of portfolios where there is maximum return for a given level of risk and minimum risk for a given level of return), a tangent portfolio (optimal) is obtained.
Topal and Ilarslan (2009) applied this technique in ISE30 index. They formed an equally weighted portfolio by the use of MVO. They geometrically showed the tangent portfolio and proved that it is optimal.
The number of securities in a portfolio has always been a concern. If too few assets are used, then there is probably not enough diversification. And if the number is too high, then the costs increase. Tosun and Oruc (2010) wanted to test what is the ideal number of securities for an investor to hold in ISE30 index. They assumed rational investors who seek minimum risk and maximum return only. The result shows that 6 securities provide adequate diversification.
As mentioned previously MVO is a commonly used technique in asset management, however, it is not the only technique. There are many ways to measure return and risk so there are several other techniques.
Particle swarm optimization (PSO) is an alternative technique. Alagoz and Kutlu (2012) used PSO in ISE. They also tried MVO and compared the results. The results interestingly generated asset weights similar in both studies.
Artificial neural networks (ANN) is also an alternative technique. This technique is also applied with a high frequency in capital markets. Yavuz et al. (2015) used 140 securities listed in ISE. The research period is 2010. They used asset size, market capitalization, shareholders' equity and volume of trade. By the use of ANN, they computed the optimal portfolio. The results of the analysis show that shareholders' equity criteria gave the best result.
Sharpe performance indicator (Sharpe ratio) is as explained very important in portfolio theory and practice. Portfolios with higher Sharpe ratios are superior to others.
Kandemir and Aytekin (2017) used Sharpe Performance indicator in ISE Industry Index. They used 45 stocks. The research period is between 2009 and 2014. Mean variance optimization technique is applied in this study. Standard Markowitz procedure was proven to be accurate in this study.

Main Focus of the Study Presentation of the Scope of the Research
This study analyzes two different criteria to effectively set up and compute different portfolios. The selected criteria are debt-to-equity ratio and return on equity. Both of these are well known computations in financial analysis. The details of the computation of these ratios are given in the following section.
The data is taken from ISE 30 Index (locally known as BIST 30) which covers 30 bluechip stocks in Istanbul Stock Exchange (ISE). Daily closing prices of the stocks are used for the year 2018. There are however some stocks which were traded less than 251 days or were traded in other indices of ISE during the period. For the sake of validity of the study, these stocks were excluded. As a result, 27 stocks which meet the criteria are used in the study.
The goal of the research is to investigate whether the portfolios with minimum risk and maximum return could be obtained by using these criteria.

Methodology
Modern portfolio theory is used in this research. For a portfolio of N assets, the return of the portfolio is calculated by the formula below.
Return on the Portfolio invested, : Expected Return on security(asset) i. Risk is measured by variance or standard deviation. Portfolio variance of a portfolio with N assets is calculated by the formula below.

Debt/Equity Based Portfolios
Debt to equity ratios of the selected companies listed on Istanbul Stock Exchange (ISE 30 index) are computed with the data available in financial statements. The debt to equity ratios for the companies are given in Table 1. Based on literature review, the following portfolios are used for debt/equity criterion in the study.  5 companies with the highest ratios,  5 companies with ratios between 1,5 and 2,  5 companies with the lowest ratios,  17 companies with ratios higher than 2,  10 companies with ratios lower than 2.
According to this criteria, the portfolios are prepared. 5 different portfolios are given below in Table 2.  Table 3.

Return on Equity Based Portfolios
Return on Equity ratios are calculated using the financial statements of the companies in this research. The results are available in Table 4. Based on knowledge in corporate finance literature, the following portfolios are used for return on equity criteria in this research.

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5 companies with the highest ratios,  5 companies with the lowest ratios,  9 companies with ratios higher than 0,2,  18 companies with ratios lower than 0,2.
Following this criteria, the portfolios are determined. Calculation results and the four portfolios are given in Table 5.  Finally, the expected returns and risks of these portfolios are calculated based on Modern Portfolio Theory. The results of these computations are given in Table 6.

Investment Decision
The results based on debt-to-equity criterion show that Portfolios 3 and 5 have positive return. (0,0472 and 0,0276 respectively), whereas Portfolios 1, 2 and 4 have negative returns. (-0,1254, -0,0210, and -0,1023 respectively) Portfolio 1 has negative return and also the highest risk. Portfolio 5 has lower risk and return (still positive) when compared to Portfolio 3. It could be recalled that Portfolio 3 includes 5 companies with lowest debt-to-equity and Portfolio 5 has 10 companies with the ratio lower than 2. While both portfolios are investable a risk averse investor could well chose the more diversified but still low debt-to equity Portfolio 5.
According to the results based on return on equity; Portfolio 8 has a positive return(0.0250) ; whereas Portfolios 6, 7 and 9 has negative returns (-0.0188,-0.0796, -0.0938 respectively). Portfolios 7 and 9 which have negative returns also have higher risks than that of Portfolio 8 which has positive return. Despite having 5 highest ratios of Return on Equity, Portfolio 6 has negative return. However Portfolio 8 which has 9 companies with ratios larger than 0,2 has positive return. Therefore Portfolio 8 can be selected for investment purpose.

Discussion
This study has an empirical analysis on Istanbul Stock Exchange, ISE 30 which is an index on 30 bluechip stocks. The research period is 2018. The research to authors knowledge brings a novelty to the MPT literature by proposing financial analysis based selection criteria. The ratios used are debt-to-equity and return on equity.
According to the results, efficient portfolios could be selected when financial analysis based selection criteria is added to MPT. Therefore it is possible to say minimum risks and maximum return portfolios could be selected even when these criteria is added. Further benefits is discussed in the conclusion section of the study.
Returning to the results, the first part of the analysis is debt-to-equity. Both Portfolios 3 and 5 generate positive returns. It is important to note that both of these portfolios are low debt-to-equity (D/E) portfolios. Therefore during the period, low D/E portfolios (lower risk) performed better. The difference between these portfolios are D/E ratios are lower in average in Portfolio 3 but there are fewer companies. The not so low D/E portfolio 5, has lower risk due to the fact that it has more assets with low correlations.
So risk averse investor should go for Portfolio 5, even Portfolio 3 has better D/E ratios, due to the fact that Portfolio 5 is more diversified.
The other analysis is MPT applied with return on equity(ROE) criterion. It is important to note that only Portfolio 8 generated positive return during the period. This is due to the fact that it has high ROE, and is more diversified. It should be emphasized that investor should be cautious even when using financial analysis based criteria on MPT. Blindly picking stocks that have best ratios does not generate best returns. Investors should go for diversified portfolios which should yet have better ratios. Again, in the analysis Portfolio 6 had best ratios but had negative return.

Conclusions
All theories in economics come with assumptions. Modern portfolio theory also has many assumptions and seemingly works in an ideal word. However, applications over years show that the theory is pretty sound and is still part of corporate finance and investment books.
There are however ongoing and increasing number of criticisms on MPT. Some even say that the theory is dead. One of the popular criticisms is black swan argument. One of the assumptions of the MPT is that it assumes the returns of the assets are normally distributed. But in times of a financial turmoil, say 2008, the correlations between asset classes increase, and the assets lose value more than what is expected by the normal distribution.
The motivation of this paper is to bring another dimension to the ongoing discussions. Is it possible to generate efficient (high return / low risk) portfolios by adding selection criteria to the theory? The proposed criteria is financial analysis based, more specifically debt-to-equity and return on equity ratios.
For the selected data, it could be said that these criteria could well generate efficient portfolios. Moreover, in authors' opinion, it is also preferable to standard MPT. Since if you are risk averse investor who try to minimize losses in times of a financial turmoil, you can add fundamental criteria which is not subject to normal distribution. This study brings a new alternative technique to the investor, and adds a new dimension to the ongoing debates whether the MPT is dead or alive.
The portfolios are all selected from the same index. Therefore it can be said that the alternate portfolios are benchmarks. The stocks are different based on risk and return characteristics although they are in the same index. A different analysis may include international comparisons to these stocks in an attempt to find international benchmarks with similar risk and return characteristics.
Like every novelty, for this to be universally accepted, it should be tested hundreds of times in different markets and time horizons. Different time period comparisons couldn't be included due to space limitations. The suggested portfolios vary based on volatility of the market during the period.