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Modern Portfolio Theory Combined with Magic Formula

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Modern Portfolio Theory Combined with Magic Formula Bachelor Thesis Modern Portfolio Theory combined with Magic Formula A study on how Modern Portfolio Theory can improve an established investment strategy. Authors: Axel Ljungberg & Anton Högstedt Supervisor: Maziar Sahamkhadam Examiner: Håkan Locking Term: Spring 21 Subject Finance Level: Bachelor Course code: 2FE32E Abstract This study examines whether modern portfolio theory can be used to improve the Magic Formula investment strategy. With the assets picked by the investment strategy we modify the portfolios by weighting the portfolios in accordance with modern portfolio theory. Through the process of creating efficient frontiers and weighting the portfolios differently we will create two alternative portfolios each year. One portfolio that aims for maximum Sharpe ratio and one that aims for minimum variance. These weighted portfolios produce higher risk-adjusted returns consistently during the examined period of 2010-2020. We conclude that the Magic Formula can be improved by using modern portfolio theory. Keywords Magic Formula, Modern portfolio theory, efficient frontier, Efficient market hypothesis, Sharpe ratio, risk-adjusted returns, Jensen’s alpha, beta, CAPM, OMXSPI Acknowledgements We want to thank our supervisor Maziar Sahamkhadam for his highly appreciated help throughout the development of this thesis as well as our examiner Håkan Locking for constructive discussions. i Table of Contents Introduction _________________________________________________________ 3 Background ______________________________________________________ 3 Problem definition ________________________________________________ 5 Research question _________________________________________________ 6 Limitations ______________________________________________________ 6 Theory ______________________________________________________________ 7 Modern Portfolio Theory ___________________________________________ 7 Efficient Market Hypothesis ________________________________________ 10 The Magic Formula ______________________________________________ 11 Measures of risk _________________________________________________ 13 Methodology ________________________________________________________ 15 Study approach __________________________________________________ 15 Data collection __________________________________________________ 15 Significance testing ______________________________________________ 17 Risk-free rate ___________________________________________________ 18 Empirical Results ____________________________________________________ 19 Efficient frontier and illustration of results ____________________________ 19 EQW, Optimal and GMV portfolio results ____________________________ 20 Cumulative returns and Measures of risk ______________________________ 22 Significance tests ________________________________________________ 24 Analysis ____________________________________________________________ 27 Efficient market hypothesis ________________________________________ 27 Comparing empirical results ________________________________________ 28 Risk measures ___________________________________________________ 30 Conclusion _________________________________________________________ 32 Future research _____________________________________________________ 33 References__________________________________________________________ 34 Literature ______________________________________________________ 34 Articles ________________________________________________________ 34 Appendices ___________________________________________________________ I ii Introduction Background The stock market provides an opportunity for individuals to get an increased value of assets over time. By allocating resources on the stock market individuals can acquire both positive and negative returns. To assist investors with allocating their resources several investment strategies has been developed to support individuals when investing on the stock market. The investment strategies are there to support individuals with making strategic and wise investment decisions. A popular value-based strategy is the “Magic Formula”. The Magic Formula was first described by Joel Greenblatt in the book “The little book that beats the market” which was published in 1980. The purpose of the strategy is to help investors find undervalued stocks and beat the market. The Magic Formula does this with the two key figures Return on Capital (ROC) and Earnings Yield (EY). The strategy helps both unexperienced and experienced investors with building their individual portfolios and only needs a small amount of effort from the investor. According to Joel Greenblatt the Magic Formula presents an easy way to make money for any individual investor, with or without any knowledge of the stock market. Recent research of the Magic Formula proved that by using certain adjustments and improvements to the formula an investor can increase their returns (Sjöbäck & Verngren, 2019). However, this research does not always consider the amount of risk the investors are exposed to when using the method. Joel Greenblatt’s research uses the 30 highest ranked companies to decide for the investor which companies the investor should invest in. The investor is asked to weigh the stocks equally, meaning the investor should invest the same amount of money into each company the investor buys (Greenblatt, 2006, p. 131-132). When reading previous studies about investment strategies, several discuss that it would be interesting to weigh the companies based on their performance (Eriksson & Svensson, 2020; Sjöbäck & Verngren, 2019). The value investing strategy Magic Formula could easily be weighted based on each stocks rank. Since the method involves ranking each stock based on RoC and EY, an investor could decide to weight the 3 highest ranked stock the highest, the second highest ranked stock the second highest etc. A big disadvantage of this weighting based on ranks would be the amount of risk the investor is exposed to. Since the Magic Formula strategy does not take any measure of risk into account, there would be nothing that would keep the investor from losing most or all his/her money if the highest ranked stocks would decrease in value. Since the Magic Formula is directed towards individuals who are both experienced and inexperienced it is simplified and there should be room for improvement. If we weight the stocks that are picked by the Magic Formula strategy with a method that includes risk in its calculations, the performance of the strategy should be improved. By using Harry M. Markowitz “Modern Portfolio theory” (MPT) we can narrow down the number of companies used, include a measure of risk, and calculate the expected returns. MPT is used by analysing historical data and looking at its historical returns and volatility. It can be used to visualize and describe different portfolio options available to an investor and provide estimations of how much risk as well as returns that are expected of the different portfolios. The study will be conducted by constructing three portfolios each year. The three portfolios will have the same stocks available for investment but the method for their construction will differ. One of the portfolios will be constructed by dividing the available capital equally between the assets selected. This portfolio will be referred to as the equally weighted portfolio (EQW). The second and third portfolio will share the stocks available for investment with the EQW portfolio each year but will not split the capital equally and will instead be weighted differently each year. These portfolios will be referred to as the optimal portfolio and the Global Minimum Variance portfolio (GMV). Our contribution is to combine MPT, the ideas first proposed by Markowitz with a well- established investment strategy such as Joel Greenblatt’s Magic Formula. The investment strategy suggests investing in an arbitrary number of stocks, but why not use well established theories to reduce the risk for similar return, or increase return for similar risk. To our knowledge, there is little to no research that combines MPT with any investing strategy. By combining MPT with Magic Formula, we discuss a possible 4 way MPT can be used in practice and whether the theory can contribute to an improved strategy on the stock market. Problem definition Joel Greenblatt claims that the Magic Formula strategy can make anyone a master on the stock market (2011, p.39). He claims that anyone can beat the market, beat professional investors and most trustees with the help of two simple rules. This claim is also supported by historical data . However, the efficient market hypothesis (EMH) states that investors cannot consistently beat the market since share prices already reflects all information. For this paper to be viable and contribute to research, the market cannot be completely effective. The Magic Formula strategy ranks companies based on RoC and EY and suggests investors should buy the highest 20-30 ranked stocks, and weight the stocks equally. Harry M. Markowitz, the father of MPT claims that there is (at least in theory) a possibility to create an optimal portfolio which maximizes the amount of return in relation to the amount of exposed risk. The theory suggests that in every portfolio, there is an optimal way of weighting the stocks. In our essay the foundation of the Magic Formula is used together with MPT where the stocks found by Greenblatt’s strategy is weighted with Markowitz’s theory to create optimally weighted portfolios, with the highest
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