SPSS analysis on modern portfolio theory-optimal portfolio strategies in today’s capital market

go upThis opus provides information on detail ideas embedded in virtuoso advocate pattern/construction of optimum portfolios compargond to the classic Markowitz stumper. Important arguments ar redeemed regarding the validity of these deuce molds. The interrogationer utilises SPSS analysis to demonstrate important research visitings. This type of analysis is conducted to seek the presence of both world-shaking statistical difference among the variance of the mavin big businessman object lesson and the Markowitz gravel. The paper also includes implications for investors.IntroductionIn the contemporary environment involving business enthronisations, selecting distinguish investments is a relevant task of most organisations. Rational investors try to down put-on guesss as well as maximise returns on their investments (Better, 2006). The ultimate culture is to reach a level identified as best portfolios. The snap in this process is on initiating the portfolio c hoice models, which are essential for optimising the grow of investors. Research learns that the Markowitz model is the most sui defer model for conducting stock selection, as this is facilitated finished the function of a full covariance matrix (Bergh and Rensburg, 2008).The importance of this moot reflects in the application of different models so as to develop adapted portfolios in organisations. It is essential to compare certain models because investors whitethorn be provided with competent knowledge about how they can best construct their portfolios. In this context, the finespun variance of the portfolio selection model is important, as it reflects portfolio risk (Bergh and Rensburg, 2008). Information on the parameters of different models is meaning(a) to make the most appropriate decisions regarding portfolio creation. Markowitz is a introduce in the research on portfolio analysis, as his works have contributed to enhancing investors perspectives on the available options regarding particular proposition models of constructing optimum portfolios (Fernandez and Gomez, 2007).Research MethodologyThe research gesture presented in this study referred to the exploration of ideas embedded in wiz index number model/construction of optimal portfolios and comparing them with the classic Markowitz model. The focus was on the construction of optimal portfolios, as the researcher was concerned with the evaluation of constructed portfolios with specific marketplace parameters (Better, 2006). Moreoer, the researcher paid attention to the stock market charge index, including stocks of organisations distributed in three major sectors services, financial, and industrial (Fernandez and Gomez, 2007). The behaviour of this index was explored through the implementation of SPSS analysis. The data covered a period of seven course of studys, head start on January 1, 2000 and ending on December 31, 2006. It was essential to evaluate the persuasiveness parame ters of the single index model/construction of optimal portfolios and the Markowitz model. The criteria for the selection of companies include that all organisations shared the same fiscal year (ending each year on December 31) as well as they have not demonstrated any change in position.Results and Data AnalysisThe research methodology utilised in the study is based on the model of single index/optimal portfolios and the Markowitz model. The exploration of the relationship amid these twain models required the selection of 35 equally weighted optimal portfolios, as two sizes of portfolio were outlined. An approximate number of 10 optimal portfolios delineated the first-year size, which further turn ind 12 portfolios. In addition, the researcher considered the option of simulating of optimal portfolios represented at second sizes (Bergh and Rensburg, 2008). The criterion of queuing randomise portfolio selection has been apply to generate approximate 23 portfolios from the secon d size category. The researcher selected five and 10 stocks to analyse the data. The portfolio size split allowed the researcher to explore how the portfolio size could be used to affect the relationship between the single index model/optimal portfolios and the Markowitz model (Fernandez and Gomez, 2007). Results of testing the data are provided in the table below optimum portfolio numberVariance of Single king sampleVariance of the Markowitz lesson best portfolio numberVariance of the Single Index deterrent exampleVariance of the Markowitz forge 100.00370.003950.00210.0023 100.00140.001750.00280.0038 100.00210.002850.00420.0051 100.00200.002150.00250.0030 100.00310.003550.00260.0024 100.00190.001950.00330.0038 100.00880.008650.00670.0071 100.00280.003750.00370.0053 100.00250.002450.00380.0043 100.00220.002350.00210.0020 100.00190.002050.00630.0061 100.00230.002650.02120.0202 card 1 Variance of Five and 10 Optimal Portfolios found on the results provided in the table, it can be conclude that the variance between the single index model/construction of optimal portfolios and the Markowitz model is similar. For instance, value of 0.0020 and 0.0019 for the variance of the two models are similar. This stand fors that the results do not show substantial statistical differences between the two models. The tables below contain a descriptive summary of the results presented in the previous table MeasureSingle Index ModelMarkowitz Model Mean0.00440.0047 Minimal0.00210.0020 Maximum0.02120.0202 Standard Deviation0.00370.0035Table 2 Descriptive Summary of 10 Optimal PortfoliosThe results in Table 2 were derived from testing the performance of 10 optimal portfolios. It has been indicated that the mean for the single index model of 10 portfolios is 0.0044, turn the mean for the Markowitz model is 0.0047, implying an insignificant statistical difference. The minimal value of the single index model is inform at 0.0021, while the minimal value of the Markowitz model is 0.0020. The difference is insignificant. The maximum value of the single index model is 0.0212, while the same value of the Markowitz model is 0.0202. Based on these values, it can be argued that there is a slight difference existing between the two models. The exemplification deviation of the single index model is 0.0037, while the hackneyed deviation of the Markowitz model is 0.0035, which also reflects an insignificant statistical difference. MeasureSingle Index ModelMarkowitz Model Mean0.00280.0031 Minimal0.00140.0017 Maximum0.00880.0086 Standard Deviation0.00200.0019Table 3 Descriptive Summary of 5 Optimal PortfoliosTable 3 provides the results for five optimal portfolios. These results are similar to the ones reported antecedently (10 optimal portfolios). The mean for the single index model of 5 optimal portfolios is 0.0028, while the mean for the Markowitz model is 0.0031, implying an insignificant statistical difference. there are insignificant differences between the tw o models regarding other values, such as minimal and maximum value as well as standard deviation.Furthermore, the researcher performed an analysis of variance analysis of 10 optimal portfolios, which are presented in the table below. It has been indicated that the effective score for the single index model and the Markowitz model is nearly the same. Yet, an insignificant difference was reported between the two bureau and standard deviations for both models. ANOVA AnalysisSum of squaresDfConditionMeanStandard DeviationStandard Error MeanFSig. Between Groups.00011.000.003125.0018704.0005399.089.768 Within Groups.000222.000.002892.0019589.0005655 Total.00023Table 4 ANOVA Analysis for the Variance between the Single Index Model and the Markowitz Model of 10 PortfoliosFrom the conducted analysis, it can be also concluded that the F-test presents an insignificant statistical value, implying that the researcher rejected the hypothesis of a significant difference existing between portfoli o selections with regards to risk in both models used in the study (Fernandez and Gomez, 2007). Hence, the hypothesis of a significant difference between the variance of the single index model and the Markowitz model was rejected (Lediot and Wolf, 2003). In the table below, the researcher provided the results of an ANOVA analysis conducted on five optimal portfolios ANOVA AnalysisSum of SquaresDfConditionMeanStandard DeviationStandard Error MeanFSig. Between Groups.00011.000.004852.0036535.0007618.096.758 Within Groups.001442.000.004509.0038595.0008048 Total.00145Table 5 ANOVA Analysis for the Variance between the Single Index Model and the Markowitz Model of 5 PortfoliosThe results from Table 5 show that the variance between the single index model and the Markowitz model of five optimal portfolios is almost the same. no matter of the stock number in the selected optimal portfolios, there is no significant statistical difference between the single index model and the Markowitz mode l.The main(prenominal) finding based on the reported data is that the single index model/construction of optimal portfolios is similar to the Markowitz model with regards to the formation of specific portfolios (Bergh and Rensburg, 2008). As indicated in this study, the precise number of stocks in the constructed optimal portfolios does not impact the final result of comparing the two analysed models. The fact that these models are not significantly different from each other can actuate investors to use the most practical approach in constructing optimal portfolios (Haugen, 2001). Placing an idiom on efficient frontiers is an important part of investors work, as they are cogitate on generating the most efficient portfolios at the lowest risk. As a result, optimally selected portfolios would be able to generate positive returns for organisations. This applies to both the single index model and the Markowitz model (Fernandez and Gomez, 2007).Conclusion and Implications of Research FindingsThe results obtained in the present study are important for various parties. Such results may be of concern to policy makers, investors as well as financial market participants. In addition, the findings generated in the study are similar to findings reported by other researchers in the field (Bergh and Rensburg, 2008). It cannot be claimed that either of the approaches has certain advantages over the other one. Even if the number of stocks is altered, this does not reflect in any changes of the results provided by the researcher in this study. Yet, the major limitation of the study is associated with the use of monthly data. It can be argued that the use of daily data would be a more viable option to ensure accuracy, objectivity as well as adherence to strict professional standards in harm of investment (Better, 2006).In conclusion, the similarity of the single index model and the Markowitz model encourage researchers to use both models equally because of their potential to generate optimal portfolios. Moreover, the lack of significant statistical differences between the variance of the single index model and the Markowitz model can serve as an adequate stern for investors to demonstrate greater flexibility in the process of making portfolio selection decisions (Haugen, 2001). The results obtained in the study were used to reject the hypotheses that were initially presented. As previously mentioned, the conducted F-test additionally indicates that the single index model and the Markowitz model are almost similar in scope and impact (Fernandez and Gomez, 2007).Investors should consider that portfolio selection models play an important role in determining the exact amount of risk taking while constructing optimal portfolios. Hence, investors are expected to thoroughly explore those models while they select their portfolios (Garlappi et al., 2007). Both individual and institutional investors can find the results generated in this study useful to facil itate their professional practice. A likely application of the research findings should be considered in the process of embracing raw(a) investment policies in the flexible organisational context (Bergh and Rensburg, 2008). Future research may extensively focus on the development of new portfolio selection models that may further expand the capacity of organisations to improve their performance on investment risk taking indicators.ReferencesBergh, G. and Rensburg, V. (2008). Hedge Funds and Higher Moment Portfolio execution of instrument Appraisals A General Approach. Omega, vol. 37, pp. 50-62.Better, M. (2006). Selecting Project Portfolios by Optimizing Simulations. The Engineering Economist, vol. 51, pp. 81-97.Fernandez, A. and Gomez, S. (2007). Portfolio extract Using Neutral Networks. Computers & Operations Research, vol. 34, pp. 1177-1191.Garlappi, L., Uppal, R., and Wang, T. (2007). Portfolio Selection with Parameter and Model unbelief A Multi-Prior Approach. The Review o f Financial Studies, vol. 20, pp. 41-81.Haugen, R. (2001). Modern Investment Theory. bleak Jersey Prentice Hall.Lediot, O. and Wolf, M. (2003). Improved Estimation of the Covariance Matrix of Stock Returns with an finish to Portfolio Selection. Journal of Finance, vol. 10, pp. 603-621.