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Construction of optimal portfolios using Python
(2021) Velli, Anastasia; Βελλή, Αναστασία; Athens University of Economics and Business, Department of Accounting and Finance; Episcopos, Athanasios; Georgoutsos, Dimitrios; Chalamandaris, George
Asset managers target to choose investment portfolios, whose returns are the maximum possible, ensuring though that the risk exposure is at acceptable levels given the risk preferences per investor.The very first theory for optimal portfolios’ selection was introduced by Markowitz in 1950’s. Through his paper, formalized the portfolio selection principles, winning thus the 1990 Noble Prize in the field of economics.It is worth mention though, that 1950 and onwards mathematical programming techniques have been broadly used and have become essential tools in financial management, resulting though in their increasingly application in practice. The most important element that mainly boosted the adoption of more sophisticated methods in financial management procedure, which focus on portfolio optimization, is fully aligned with the continuously increasing diversity of complex financial instruments and the multiple factors in need of capturing the effect of risk and performance measures.Financial management studies the economic resources allocation and deployment across time throughout an uncertain environment. To capture and influence the various risk factors in an effective manner, the implication of the said, sophisticated analytical ways, is required.Mathematical programming techniques as the Principal Component Analysis combined with the Python coding language. Over the past years, the use of mathematical programming techniques has proven able to reduce financial risks, which affect the portfolios’ performance, by diversifying away the non-systematic risk of these portfolios.The diversification principle of Principal Component Analysis stated that an investment should be distributed across various assets, to limit the risk exposure of any particular asset in the number of principal that the asset manager has selected.The goal of this thesis is the optimal portfolios constructions using the concepts of Principal Component Analysis based on paper “Directed Principal Component Analysis” (2017) by Yi-Hao Kao, Benjamin Van Roy and their rebalancing using different windows of twelve, eighteen and twenty-four months as introduced by Meihua Wang, Fengmin Xu and Yu-Hong Dai in their research paper “An index tracking model with stratified sampling andoptimal allocation”. Our aim was the construction of two different portfolios, the Sharpe Ratio portfolio, as proposed by Taras Bodnar and Taras Zaboloskyy (2017) in their paper “How risky is the optimal portfolio which maximizesthe Sharpe ratio?” and the Global Minimum Variance portfolio, as proposed by Alexander Kempf and Christoph Memmel (2006) in their paper “Estimating the Global Minimum Variance Portfolio”. We formulated two scenarios based on these portfolios, using different rebalancing participation percentages per portfolio.The financial instruments used to attain our said goal are the Exchange Traded Funds (ETFs), “The sidedness and informativeness of ETF trading and the marketefficiency of their underlying indexes” (2019) by Liao Xua, Xiangkang Yinb, Jing ZhaoThe whole procedure was implemented in Python programming language.Finally, to compare and conclude with the performance of our portfolios, we conducted the evaluation of these portfolios with the calculation of various performance measures such as the total return, the standard deviation, the Sharpe ratio, the Sortino ratio and the Maximum drawdown. Given these measures and specific thresholds for each of them we made our final choices given our optimal portfolios.