Model of Portfolios Analysis

Transcription

1 Model of Portfolios Analysis Lecturer Mădălina - Gabriela Anghel PhD The Bucharest University of Economic Studies/ ARTIFEX University of Bucharest madalinagabriela_anghel@yahoo.com Abstract The valuation of the transactions on financial instruments implies a thorough analysis of the ratio between the potential gains and the joint risks to a capital investment emphasizing thus the maximization of the profit function under the conditions of minimizing the risks connected to the analyzed transactions. The activity of the portfolio management aims to optimize the holding of financial instruments. But, the optimum has a different significance depending on each and every investor given as known the fact that these ones bear different degrees of tolerance and adversity as regards the exposure to risk. The investor is the one deciding on that particular combination to be considered as optimum, taking into account the attitude he has as regards the risk. Key words: portfolio investment, yield, adversity against risk, portfolio management, optimum portfolio. General aspects concerning the financial instruments portfolio The portfolio represents the combination of financial instruments achieved depending on the investor s behavior against risk as well as on the capital which he is willing to invest over a certain interval of time. The construction of portfolio aims to diversify the made investments so that the final outcome consists of diminishing the related overall risk. Thus, in the case of a mixed portfolio consisting of shares and bonds when there is a decrease of the price for the shares being held- the loss being recorded can be partially or totally compensated by the gain achieved through the interest cashed on the bonds making part of the portfolio.. The construction of any portfolio implies as a first stage the identification of the financial instruments meant for transaction, as well as the proper moment for entering the capital market (respectively, the optimum moment for transacting). This is the stage where the market analysis is accomplished with the purpose to gather the necessary information for the process to take the investment decision. In this respect it is recommended that the investment activity is based on a profound valuation for both the individual performances of the instruments to be acquired and the general evolution of the capital market on which the investment is going to be made. The decision on fixing the number of the composing financial equities is taken by the investor but it is recommended to take into consideration also the Revista Română de Statistică Trim IV/2013- Supliment 39

2 opinion of the specialists in the domain who declare that this number has to be minimum 7 in order to compensate the opposite variations of the yield of these equities and maximum equities in order to have lasting results out of the applied models. Based on these aspects, it has been decided that the portfolio to be analyzed is composed of 10 equities. Table nr. 1 The selected companies which shares are considered as components of the portfolio Crt. nr. Company s name Activity domain Symbol Category 1. AEROSTAR Aircraft and spacecraft manufacturing ARS II 2. ALRO Aluminum metallurgy ALR I 3. Antibiotice Basic pharmaceutical products manufacturing ATB I 4. Banca Comercială Monetary intermediation Carpatica S.A. activities BCC I 5. Boromir Prod Buzau Bread, fresh cakes and pastry (Spicul) products manu- facturing SPCU II 6. BRD - Groupe Societe Monetary intermediation Generale activities BRD I 7. Calipso Oradea Pubs and other beverage serving activities CAOR II 8. Farmaceutica Remedia Wholesale trade with pharmaceutical products RMAH II 9. Prodplast Plastic material items production PPL II 10. SIF Banat Crişana Other financial c.a. intermediations SIF 1 I Source: self-systematization The analysis of the yield and risk of the portfolio built up by ten equities issued by companies listed on the București Stock Exchange market. Once the financial instrument matching with the investors requirements are identified and acquired, the need to continuously administrate the portfolio thus built up becomes a must. In this respect it is to underline the fact that the portfolios management is in fact an extremely complex activity, grounded on a series of scientific models through which it is possible to permanently evaluate the financial performances of the assets as well as the risks at which the investors are exposed. Farther on, we shall calculate the yield and risk relating to the portfolio composed by the equities issued by the 10 considered companies. The yield of the portfolio built up by the 10 equities is the weighted average of the equities composing it and is established on the basis of the following formula: 40 Revista Română de Statistică Trim. IV/ Supliment

3 where: E i represents the average yields of the equities X i represents the weights allocated to the equities In order to establish the portfolio risk we must consider both the risk relating to each equity belonging to the portfolio and the interdependence degree of the equities variations between each other. The risk of the 10 equities portfolio is given by the sum of the possible combinations between the profitableness variations of the component equities (including their own dispersions) as against the participation weights of the equities to the portfolio construction. The portfolio risk comes out the matrix of the dispersions and profitableness covariance of the component equities. In order to set up the yield and risk relating to the portfolio built up by the 10 equities, it is necessary to know the yield and volatility of each equity as well as the covariance between the yields of the equities making subject of the analysis. The daily yields of the equities issued by the analyzed companies have been established on the basis of the daily prices recorded on their account, excepting the week-end days and legal holidays. Table nr. 2 The average daily yield and volatility for he analyzed equities Equity Daily yield Volatility ARS ALR ATB BCC SPCU BRD CAOR RMAH PPL SIF Source: self-calculations Revista Română de Statistică Trim IV/2013- Supliment 41

4 The covariance between the equity i and the equity j ( established on the basis of the relation: ) is t = 1...T (number of observations over the time on the rarmahor R it = the yield of the equity i by the moment t = the average yield of the equity i R jt = the yield of the equity j by the moment t = the average yield of the equity j Table nr. 3 The matrix of covariance between the yields of the analyzed equities Source: self-calculation Based on these elements, the portfolio yield and risk are calculated, considering that the ten financial assets hold various weights of participation in the portfolio frame and simulating thus more variants of them. The results are submitted in the following table: Table nr. 4 The profitableness and risk for the portfolio built of 10 equities (holding different weights of participation) Source: self-calculations 42 Revista Română de Statistică Trim. IV/ Supliment

5 Out of the out coming data, it is obvious that diversifying the portfolio by including into its structure more equities generates an increase of its yield simultaneously with the decrease of the corresponding risk. Conclusions The portfolio yield is directly proportional with the individual yields of the assets but also with the weight allocated to each one within its structure. Thus, in order to increase the portfolio profitableness it is necessary only to increase the weight of the equities of the highest profitableness in the frame of portfolio structure. Meanwhile, it must be underlined that any increase of the portfolio profitableness is generating an increase of the relating risk. The portfolio structure bears a particular significance since anytime the equities hold a weight relatively equal within its composition, the relating risk is smaller as comparatively with the case when an equity holds 90% of the portfolio while the rest of them are holding the balance of 10% only. Bibliography Anghel, M.G. (2013). Modele de gestiune şi analiză a portofoliilor, Editura Economică, Bucureşti, ISBN Anghelache, G.V.; Marinescu, R.T., Anghel, M.G. (2013). Specific concept for the financial instruments portfolios, Revista Română de Statistică Supliment, Trim. III, pg , ISSN x CNCSIS, Categoria B+ Dragotă, V. (coordonator) (2009). Gestiunea portofoliului de valori mobiliare - ediţia a doua, Editura Economică, Bucureşti Roman, M (2003) Statistica financiar - bancară şi bursieră, Editura ASE, Bucureşti Stancu, I. (2007). Finanţe. Vol I. Pieţe financiare şi gestiunea portofoliului, Editura Economică, Bucureşti Revista Română de Statistică Trim IV/2013- Supliment 43