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Intelligent Optimization of Investment Rules on the Basis of Genetic Scientific Journal of Riga Technical University Computer Science. Information Technology and Management Science 2011 ________________________________________________________________________________________________ Volume 49 Construction of Equity Portfolio on the Basis of Data Envelopment Analysis Approach Tatyana Arshinova, Riga Technical University Abstract. The research focus of the scientific paper is on the theory of investment decision to maximize portfolio expected problem of equity portfolio construction. The author return on interest for an accepted amount of portfolio risk, or recommends applying frontier analysis technique such as Data equivalently minimize risk for an accepted level of expected Envelopment Analysis to the performance measurement of emitters. Using modern computer technologies, the author has return on interest, by thoroughly choosing quantities of calculated efficiency score of twenty Baltic companies which are various assets. So far all efforts to “translate” theoretical quoted at NASDAQ OMX Riga and NASDAQ OMX Tallinn foundations into a viable portfolio step by step construction stock exchanges on the basis of DEA CCR approach and algorithm are in vain due to technical difficulties, trying to elaborated proposals for effective asset allocation. formulate stable original optimization framework within the available data limitations. Keywords: portfolio construction, DEA (Data Envelopment Analysis), Decision Making Units (DMUs), performance The results based on the above-mentioned approaches measurement frequently provide inconsistent conclusions concerning potential investment opportunities and do not grant possibility I. INTRODUCTION to evaluate the enterprise activity of emitters as a single process. Problem of equity performance measurement, Recent macroeconomic events played a major role in estimating performance of production process of each current Eurozone financial crisis. In the last decade of October company could be faced a principally different approach by 2011 European country leaders agreed to reduce bank losses usage of methods of frontier analysis. Such method framework up to 50% of the nominal value of their Greek debt that makes provides an opportunity of complex analysis of company’s around 100 billion euro. European country leaders are also efficiency level for a certain period of time and its comparison very close to settle an agreement for creating Continent's among investigated objects. The objective of the author’s bailout fund. This fund volume could make around 1 trillion research is to improve and supplement the methodology of euro. Such immense sum is necessary to deter similar risk measurement before the equity portfolio construction on speculations (that pushed Greece to need a rescue) around the basis of the Data Envelopment Analysis approach. larger European economies like Portugal, Italy and Spain.[7] In the circumstances of unstable macroeconomic Additional indicators could be news from Standard & Poor’s environment and competition, profitability and market that has downgraded Italy rating from A +/A+1 to A/A-1, capitalization are among the most important indicators of estimating Italy’s economy growth perspectives as “negative”. stability and development of companies for the potential [8] The continuing uncertainty in Europe’s recovery and the investor. Total operating revenue is a measure of the market future of euro puts additional pressure on all economical value of company’s production and the demand for it. Market subjects of European countries, making European companies capitalization is a parameter that reflects market value of all of especially vulnerable and unattractive to potential investors. a company’s outstanding shares. It is a basic determinant of Creation of profitable and effective equity portfolio is asset allocation and risk-return parameters. In this connection, becoming of vital importance for investors nowadays. the author analyzed the performance of a set of Baltic Traditionally the portfolio construction process includes four companies, assuming total operating revenue and market steps: risk profile creation, asset allocation, correction of capitalization value as outputs. The objects of the research are portfolio structure corresponding to the decision maker’s Baltic companies which are quoted at NASDAQ OMX Riga requirements and regular control over portfolio structure to and NASDAQ OMX Tallinn stock exchanges; their efficiency avoid the excessive risk in a particular asset field. At present level is analyzed using data for the second quarter 2011. risk measurement and asset allocation phases of portfolio Evaluating the performance on the basis of the Data construction are set up using Modern Portfolio Theory by Envelopment Analysis approach, the author included into the H.Markovitz, methods of technical and fundamental analysis set of investigated objects companies that are considered to be and Sharpe ratio analysis etc. The assumption that market liquid at the Baltic stock markets (according to the amount of price of an asset reflects impact of all influencing factors operations): JSC “Latvijas Balzāms”, JSC “Grindeks”, JSC information is the main principle of technical analysis. “Latvijas gāze”, JSC “Liepājas metalurgs”, JSC “Latvijas Technical analysis does not take into consideration either the Kuģniecība”, JSC “Olainfarm”, JSC “Rīgas kuģu būvētava”, growth strategy of the company and perspectives, or balance JSC “SAF Tehnika”, JSC “Ventspils nafta”, JSC “Valmieras sheet data. Fundamental analysis in its turn is based on the stikla šķiedra”, JSC “Arco Vara”, JSC “Baltika”, JSC estimation of financial statements and figures, and relative “Ekspress Grupp”, JSC “Harju Elekter”, JSC “Olympic competitive advantages. Modern Portfolio Theory is the 104 Scientific Journal of Riga Technical University Computer Science. Information Technology and Management Science 2011 ________________________________________________________________________________________________ Volume 49 Entertainment Group”, JSC “Silvano Fashion Group”, JSC vi – the input multiplier of DMU0; “Tallink Grupp”, JSC “Tallina Kaubamaja”, JSC “Tallina yr0 – the output of DMU0; Vesi”, JSC “Viisnurk”. xi0 – the input of DMU0; yrj – outputs of 1,2…n DMUs; xij – inputs of 1,2…n DMUs. II. THE CCR DEA MODEL The CCR DEA model was proposed by Charnes, Cooper The above-mentioned fractional form of the model has an and Rhodes in 1978 for the performance evaluation of infinite number of solutions; if (u*, v*) is optimal, (αu*, αv*) Decision Making Units (DMUs). The notion of Decision is also optimal for α > 0. The transformation which was Making Unit might be applied to refer to any organization that proposed by Charnes and Cooper in 1962 for linear fractional m programming selects a solution (u, v) for which v x 1 is to be evaluated in terms of its efficiency to convert inputs i1 i io into outputs. These evaluations can involve different types of and yields the multiplicative linear programming problem in entities profit and non-profit organizations as well as which variables from (u, v) are changed to (μ, ν). The educational and medical institutions. Charnes-Cooper transformation is expressed in (2): The process of production might be concentrated either at s minimization of inputs or maximization of output volumes. max z r yro The model’s orientation should be concentrated on variables r1 which are over control. Volumes of inputs are usually subject to controlled by management; therefore only input-oriented s m y v x 0 models will be introduced in the research. r rj i ij r1 i1 The comparative performance estimation is based on the m concept that the efficiency of each Decision Making Unit is vi xio 1 calculated, comparing its performance to n investigated i1 DMUs. Each Decision Making Unit uses different amounts of r ,vi 0, (2) m variable inputs in the production process of s different where outputs. DMUj uses volume xij of input i and produces volume z – the CCR input-oriented function of DMU (multiplier yrj of output r. The assumption xij ≥ 0 and yrj ≥ 0 shall be 0 maintained and each investigated entity has at least one input form); and output having positive value. Firstly the DEA CCR model μr – the output multiplier of DMU0; was formulated in fractional form. Using this formulation of νi – the input multiplier of DMU0; the model, the ratio of outputs/inputs is considered to measure yr0 – the output of DMU0; x – the input of DMU ; the relative performance of the specific DMUj = DMU0 to be i0 0 estimated in comparison to the ratios of all of the j = 1,2, ..., n yrj – outputs of 1,2…n DMUs; x – inputs of 1,2…n DMUs; DMUj. The CCR model construction might be formulated as ij the minimization of the output/input ratio for each analyzed DMU to that of a single optimal (i.e. 'virtual') output and The model in Formula 2 can be solved using its dual input. For an investigated DMU the fraction of this single problem (3): optimal output to single optimal input provides a measure of * min performance that is a function that might be expressed in multiplier form. According to the mathematical programming subject to methodology, this ratio is the objective function for the n investigated DMU. Normalizing constraints ensure the xij j xio i 1,2,..., m; execution of the condition that the optimal output to optimal j1 n input ratio of each analyzed Decision Making Unit, including y y r 1,2,..., s; DMU = DMU , must be lower than or equal to 100%. [4] The rj j ro j 0 j1 mathematical programming problem will be formulated in (1): j 0 j 1,2,..., n, (3) max h (u,v) u y / v x 0 r r ro i i io where * subject to θ – the optimal value of dual variable θ of DMU ; u y / v x 1 for j 1,..., n, 0 r r rj i i ij θ, λj – dual variables of DMU0; yr0 – the output of DMU0; ur , vi 0 for all i and r, (1) x – the input of DMU ; where i0 0 yrj – outputs of 1,2…n DMUs; h0 – the function of virtual output and virtual input ratio of xij – inputs of 1,2…n DMUs. DMU0; ur – the output multiplier of DMU0; 105 Scientific Journal of Riga Technical University Computer Science.
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