Mean - extended gini approach to estimating systematic risk-an empirical analysis

Markowitz Approach to optimum portfolio construction determines the optimal portfolio for the investor through three important variable i.e., return, standard deviation and correlation coefficient as a measure of inter-relationship between the return on assets considered. But this model is extremely demanding in its data needs and computational requirements. This indicates operational necessity to simplify this process to use a common "index” for looking at the correlation of each stock rather than the correlation of each stock to all other stocks. This was done by William Sharpe (1963). But Sharpe's Mean Variance Approach does not take into consideration the case of the investors with differentiated risk aversion levels. Mean-Gini approach to analyze risky prospects and construct optimum portfolios has proved to be more adequate than the mean-variance approach for evaluating the variability of a prospect since mean-Gini is consistent with investors' behavior under uncertainty for a wide class of probability distributions. Gini's mean difference may be extended into a family of coefficients of variability differing from each other in the decision-makers degree of risk aversion.

This paper is an empirical evaluation of Mean Variance (MV), Mean-Gini (MG) and Mean Extended Gini (MEG) approaches to an optimum portfolio selection. Initially these approaches have been reviewed describing their econometric analysis and the difficulties which they raise while making an optimum portfolio selection. Initially, we have constructed an optimum portfolio out of 20 selected companies from the two leading sectors of the Indian Economy: pharmaceutical and Information Technology sectors, using Sharpe's methodology. Then we have attempted to estimate the MG and MEG Betas for these selected companies comprising the optimum portfolio. The significance of the difference between MV Betas and MEG Betas and also the validity of normality assumption has been tested for these securities using Haussman's test and D'Agostino's normality test. Further, these securities have been ranked according to their Betas obtained for various risk aversion levels. Significance of the difference in the rankings of securities according to the various systematic risks has also been examined. To arrive at an optimal portfolio for various risk-aversion levels Excess Return to Beta ratios have been computed. Lastly, the paper concludes by ranking the securities according to their Excess Return to Beta Ratios at various risk-aversion levels, thus suggesting the preference order of the securities for the investors at various risk-aversion levels.