Available online at ScienceDirect. Procedia Economics and Finance 10 ( 2014 )

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1 Available online at ScienceDirect Procedia Economics and Finance 1 ( 214 ) th International Conference on Applied Statistics Using the Regression Model in the Analysis Financial Instruments Portfolios Constantin Anghelache a,b*, Mădălina Gabriela Anghel b a Bucharest University Economic Studies, Bucharest, Romania b Artifex University Bucharest, Romania Abstract An especially important aspect in the analysis performance for financial instruments is the determination the correlation existing between the evolution its performance and the overall trend the capital market. The determination such econometric model ensures, for capital investors, a series information necessary in order to establish their behaviour in the subsequent periods. Within the research, the regression econometric model was used with the aim to evaluate the relation between the performance a portfolio financial instruments and the evolution the corresponding capital market. The portfolio is made ten financial titles, quoted on the main market the Bucharest Stock Exchange. The dataset which fers the source data for analysis includes details regarding the daily evolution in 212 the selected shares. 214 Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license ( 214 The Authors. Published by Elsevier B.V. Selection Selection and and peer-review peer-review under under responsibility responsibility the the Department Department Statistics Statistics and and Econometrics, Econometrics, Bucharest Bucharest University University Economic Studies. Keywords: portfolio, performance, EViews, regression, investor Nomenclature RAN_PORT value the performance the portfolio shares (dependent variable) RAN_BET value the performance for BET (independent variable) α, β parameters the linear regression model ε error the regression model. The data analyzed characterize the daily evolution in 212 (366 calendar days/25 effective transaction sessions) for ten financial titles, selected from the companies quoted on the main market the Bucharest Stock Exchange (S.C. Electromagnetica S.A. Bucharest (symbol ELMA), OMV PETROM S.A. (symbol SNP), S.C. BERMAS S.A. * Corresponding author. address: actincon@yahoo.com Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license ( Selection and peer-review under responsibility the Department Statistics and Econometrics, Bucharest University Economic Studies. doi:1.116/s (14)38-6

2 Constantin Anghelache and Mădălina Gabriela Anghel / Procedia Economics and Finance 1 ( 214 ) (symbol BRM), S.N.T.G.N. TRANSGAZ S.A. (symbol TGN), S.C. TURISM FELIX S.A. BĂILE FELIX (symbol TUFE), SIF OLTENIA S.A. (symbol SIF5), SIF MUNTENIA S.A. (symbol SIF4), C.N.T.E.E. TRANSELECTRICA (symbol TEL), S.C. BIOFARM S.A. (symbol BIO) and Transilvania Bank (symbol TLV), as well as the dataset for the evolution the BET index during the considered period. Based on these information, the performance the portfolio which includes the ten shares in equal quotas (equiponderate portfolio) was determined, and also the performance the BET index for the one year period analyzed. In the first stage, the data processed with the help Microst Excel were imported in a new application created in Eviews. Statistical tests were applied for the two data series considered and the evolution the two indicators was graphically represented. The results are displayed below: For the data series regarding the performance the portfolio 5 4 Series: RAN_PORT Sample 1/4/212 12/28/212 Observations Mean.642 Median -.25 Maximum.311 Minimum Std. Dev..144 Skewness Kurtosis Jarque-Bera Probability. Figure 1. Statistical tests for portfolio performance (a)

3 326 Constantin Anghelache and Mădălina Gabriela Anghel / Procedia Economics and Finance 1 ( 214 ) RAN_PORT M1 M2 M3 M4 M5 M6 M7 M8 M9 M1 M11 M Figure 2. Statistical tests for portfolio performance (b) For the data series related to the evolution the BET index: Series: RAN_BET Sample 1/4/212 12/28/212 Observations 251 Mean.749 Median.159 Maximum.3267 Minimum Std. Dev Skewness Kurtosis Jarque-Bera Probability. Fig.3. Statistical tests for BET index (a)

4 Constantin Anghelache and Mădălina Gabriela Anghel / Procedia Economics and Finance 1 ( 214 ) RAN_BET M1 M2 M3 M4 M5 M6 M7 M8 M9 M1 M11 M Fig. 4. Statistical tests for BET index (b) As it can be observed from figures 1-4, the repartition the two data series is very similar, indicating that a pronounced dependence exists between the two measures. This idea can be further justified with the help the graphical representation the evolution the two analyzed indicators: RAN_BET RAN_PORT Fig. 5. Data series repartition Figure 5 reveals that the evolution the two data sets is highly similar, leading to the conclusion that a

5 328 Constantin Anghelache and Mădălina Gabriela Anghel / Procedia Economics and Finance 1 ( 214 ) strong dependence exists between the two analyzed indicators. To establish the type econometric model that is to be used in order to define the relationship existing between the performance the portfolio made the ten described shares (as dependent variable) and the overall evolution the capital market (reflected through the evolution the BET index as explicative parameter), the two data sets were represented in a chart, together with the related regression line RAN_PORT RAN_BET Fig. 6. Data sets and the regression line Based on the observations made, the linear simple regression model was defined as: RAN_PORT = α + β * RAN_BET + ε In Eviews, by using for estimation the least squares method, the parameters the model identified above were estimated. Subsequently, the model was tested for validity by using specific tests: Dependent Variable: RAN_PORT Method: Least Squares Date: 7/3/13 Time: 18:41 Sample (adjusted): 1/4/212 12/18/212 Included observations: 25 after adjustments Variable Coefficient Std. Error t-statistic Prob. C 6.61E RAN_BET R-squared.6839 Mean dependent var Adjusted R-squared S.D. dependent var S.E. regression.6549 Akaike info criterion Sum squared resid.1637 Schwarz criterion

6 Constantin Anghelache and Mădălina Gabriela Anghel / Procedia Economics and Finance 1 ( 214 ) Log likelihood Hannan-Quinn criter. F-statistic Durbin-Watson stat Prob(F-statistic) Estimation Command: ========================= LS RAN_PORT C RAN_BET Estimation Equation: ========================= RAN_PORT = C(1) + C(2)*RAN_BET Substituted Coefficients: ========================= RAN_PORT = e *RAN_BET According to the results the previous stage, the regression model that describes the linear dependence between the performance the ten shares portfolio and the evolution the BET index can be written as: Conclusions RAN_PORT = * RAN_BET + ε. The influence the general evolution the Romanian capital market on the performance the portfolio is significant. The free term the model has a very low value, fering the image a relatively reduced influence the factors not connected to the dynamics the stock exchange market on the performance the analyzed portfolio. Regarding the validity this econometric model, it is confirmed by the tests performed by default in Eviews. It is appropriate to observe the values R 2, F-statistic (384,7167) or Prob(F-statistic) (,) tests. All these fully confirm the strength the model and also the possibility to be used in future analyses, to estimate the performance the portfolio depending on the evolution the main index the Bucharest Stock Exchange. The model justifies, based on ficial data recorded on the Romanian capital market, the idea, outlined in economic literature, that such econometric model can be successfully used to define and systematize, under a mathematic form, the relationships existing between various indicators specific to the stock exchange system. Also, it can be stated that the performance a portfolio financial instruments can be estimated starting from the values stock exchange indexes. References Andrei, T., Stancu, S., Iacob, A.I..Introducere în econometrie utulizând Eviews, Economica Publishing House, Bucharest, 28 Anghelache, G. Piaţa de capital în context european, Economica Publishing House, Bucharest, 29 Anghelache, G.V. Piaţa de capital din România evoluţii actuale in Romanian Statistical Review Supplement, 28, ISSN x; Anghelache, C., Mitruţ, C., Deatcu, C., Bugudui, E. Econometrie: studii teoretice şi practice, Artifex Publishing House, Bucureşti, 21 Bade, Al., Frahm, G., Jaekel, U. A general approach to Bayesian portfolio optimization, in Mathematical Methods Operations Research, v. 7, iss. 2 Codirlaşu, A., Chidesciuc, N.Al.. Econometrie bancară. Econometrie aplicată utilizând EViews 5.1. Note de curs, 28 Dougherty, C. Introduction to econometrics. Fourth edition, Oxford University Press, 28 Hagstromer, B., Binner, J.M. Stock portfolio selection with full-scale optimization and differential evolution in Applied Financial Economics, ISSN print/issn ,