Using the Regression Model in the Analysis of Financial Instruments Portfolios

Procedia Economics and Finance 10 ( 2014 ) 324 – 329

2212-5671 © 2014 Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).Selection and peer-review under responsibility of the Department of Statistics and Econometrics, Bucharest University of Economic Studies.doi: 10.1016/S2212-5671(14)00308-6

ScienceDirectAvailable online at www.sciencedirect.com

7th International Conference on Applied Statistics

Using the Regression Model in the Analysis of Financial Instruments Portfolios

Constantin Anghelachea,b*, Mădălina Gabriela Anghelb a Bucharest University of Economic Studies, Bucharest, Romania

b “Artifex” University of Bucharest, Romania

Abstract

An especially important aspect in the analysis of performance for financial instruments is the determination of the correlation existing between the evolution of its performance and the overall trend of the capital market. The determination of such econometric model ensures, for capital investors, a series of 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 of a portfolio of financial instruments and the evolution of the corresponding capital market. The portfolio is made of ten financial titles, quoted on the main market of the Bucharest Stock Exchange. The dataset which offers the source data for analysis includes details regarding the daily evolution in 2012 of the selected shares. © 2014 The Authors. Published by Elsevier B.V. Selection and peer-review under responsibility of the Department of Statistics and Econometrics, Bucharest University of Economic Studies.

Keywords: portfolio, performance, EViews, regression, investor

Nomenclature

RAN_PORT value of the performance of the portfolio of shares (dependent variable) RAN_BET value of the performance for BET (independent variable) α, β parameters of the linear regression model ε error of the regression model.

The data analyzed characterize the daily evolution in 2012 (366 calendar days/250 effective transaction sessions)

for ten financial titles, selected from the companies quoted on the main market of 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. Email address: [email protected].

© 2014 Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).Selection and peer-review under responsibility of the Department of Statistics and Econometrics, Bucharest University of Economic Studies.

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325 Constantin Anghelache and Mădălina Gabriela Anghel / Procedia Economics and Finance 10 ( 2014 ) 324 – 329

(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 of the BET index during the considered period. Based on these information, the performance of the portfolio which includes the ten shares in equal quotas (equiponderate portfolio) was determined, and also the performance of the BET index for the one year period analyzed.

In the first stage, the data processed with the help of Microsoft Excel were imported in a new application created in Eviews. Statistical tests were applied for the two data series considered and the evolution of the two indicators was graphically represented. The results are displayed below:

For the data series regarding the performance of the portfolio

0

10

20

30

40

50

-0.0500 -0.0375 -0.0250 -0.0125 0.0000 0.0125 0.0250

Series: RAN_PORTSample 1/04/2012 12/28/2012Observations 250

Mean 0.000642Median -0.000250Maximum 0.031100Minimum -0.047800Std. Dev. 0.010440Skewness -0.592186Kurtosis 6.501837

Jarque-Bera 142.3500Probability 0.000000

Figure 1. Statistical tests for portfolio performance (a)


-.05

-.04

-.03

-.02

-.01

.00

.01

.02

.03

.04

M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12

2012

RAN_PORT

Figure 2. Statistical tests for portfolio performance (b)

For the data series related to the evolution of the BET index:

0

5

10

15

20

25

30

35

40

-0.04 -0.03 -0.02 -0.01 0.00 0.01 0.02 0.03

Series: RAN_BETSample 1/04/2012 12/28/2012Observations 251

Mean 0.000749Median 0.001059Maximum 0.030267Minimum -0.042056Std. Dev. 0.010372Skewness -0.743136Kurtosis 6.064497

Jarque-Bera 121.3182Probability 0.000000

Fig.3. Statistical tests for BET index (a)


-.05

-.04

-.03

-.02

-.01

.00

.01

.02

.03

.04

M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12

2012

RAN_BET

Fig. 4. Statistical tests for BET index (b)

As it can be observed from figures 1-4, the repartition of 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 of the graphical representation of the evolution of the two analyzed indicators:

-5

-4

-3

-2

-1

0

1

2

3

4

25 50 75 100

RAN_BET RAN_PORT

Fig. 5. Data series repartition

Figure 5 reveals that the evolution of the two data sets is highly similar, leading to the conclusion that a


strong dependence exists between the two analyzed indicators. To establish the type of econometric model that is to be used in order to define the relationship existing

between the performance of the portfolio made of the ten described shares (as dependent variable) and the overall evolution of the capital market (reflected through the evolution of the BET index – as explicative parameter), the two data sets were represented in a chart, together with the related regression line.

-.05

-.04

-.03

-.02

-.01

.00

.01

.02

.03

.04

-.05 -.04 -.03 -.02 -.01 .00 .01 .02 .03 .04

RAN_BET

RA

N_P

OR

T

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 of 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: 07/30/13 Time: 18:41 Sample (adjusted): 1/04/2012 12/18/2012 Included observations: 250 after adjustments

Variable Coefficient Std. Error t-Statistic Prob.

C 6.61E-05 0.000415 0.159076 0.8737RAN_BET 0.783438 0.039942 19.61420 0.0000

R-squared 0.608039 Mean dependent var 0.00064

2

Adjusted R-squared 0.606459 S.D. dependent var 0.01044

0

S.E. of regression 0.006549 Akaike info criterion -

7.210973

Sum squared resid 0.010637 Schwarz criterion -

7.182802


Log likelihood 903.3717 Hannan-Quinn criter. -

7.199635

F-statistic 384.7167 Durbin-Watson stat 2.10434

5Prob(F-statistic) 0.000000

Estimation Command: ========================= LS RAN_PORT C RAN_BET Estimation Equation: ========================= RAN_PORT = C(1) + C(2)*RAN_BET Substituted Coefficients: ========================= RAN_PORT = 6.60561413185e-05 + 0.783437809153*RAN_BET According to the results of the previous stage, the regression model that describes the linear dependence between

the performance of the ten shares portfolio and the evolution of the BET index can be written as: RAN_PORT = 0.0000660561413 + 0.783438 * RAN_BET + ε.

Conclusions The influence of the general evolution of the Romanian capital market on the performance of the portfolio is

significant. The free term of the model has a very low value, offering the image of a relatively reduced influence of the factors not connected to the dynamics of the stock exchange market on the performance of the analyzed portfolio.

Regarding the validity of this econometric model, it is confirmed by the tests performed by default in Eviews. It is appropriate to observe the values of R2, F-statistic (384,7167) or Prob(F-statistic) (0,00) tests. All these fully confirm the strength of the model and also the possibility to be used in future analyses, to estimate the performance of the portfolio depending on the evolution of the main index of the Bucharest Stock Exchange.

The model justifies, based on official 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 of a portfolio of financial instruments can be estimated starting from the values of stock exchange indexes.

References Andrei, T., Stancu, S., Iacob, A.I. .Introducere în econometrie utulizând Eviews, Economica Publishing House, Bucharest, 2008 Anghelache, G. Piaţa de capital în context european, Economica Publishing House, Bucharest, 2009 Anghelache, G.V. Piaţa de capital din România – evoluţii actuale in Romanian Statistical Review – Supplement, 2008, ISSN 1018-046x; Anghelache, C., Mitruţ, C., Deatcu, C., Bugudui, E. Econometrie: studii teoretice şi practice, Artifex Publishing House, Bucureşti, 2010 Bade, Al., Frahm, G., Jaekel, U. A general approach to Bayesian portfolio optimization, in Mathematical Methods of Operations Research, v. 70, iss. 2 Codirlaşu, A., Chidesciuc, N.Al.. Econometrie bancară. Econometrie aplicată utilizând EViews 5.1. Note de curs, www.dofin.ase.ro, 2008 Dougherty, C. Introduction to econometrics. Fourth edition, Oxford University Press, 2008 Hagstromer, B., Binner, J.M. Stock portfolio selection with full-scale optimization and differential evolution in Applied Financial Economics, ISSN 0960–3107 print/ISSN 1466–4305, 2009 www.bvb.ro www.cnvm.ro www.kmarket.ro www.bnro.ro

Using the Regression Model in the Analysis of Financial Instruments Portfolios

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