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Abstract:In this study, we present a multi-objective approach based on a mean-varianceskewness-entropy portfolio selection model (MVSEM). In this approach, an entropy measure is added to the mean-variance-skewness model (MVSM) to generate a well-diversified portfolio. Through a variety of empirical data sets, we evaluate the performance of the MVSEM in terms of several portfolio performance measures. The obtained results show that the MVSEM performs well out-of sample relative to traditional portfolio selection models.

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Many estimation methods have been proposed for the parameters of statistical distribution. The least squares estimation method, based on a regression model or probability plot, is frequently used by practitioners since its implementation procedure is extremely simple in complete and censoring data cases. However, in the procedure, heteroscedasticity is present in the used regression model and, thus, the weighted least squares estimation or alternative methods should be used. This study proposes an alternative method for the estimation of variance, based on a dependent variable generated via simulation, in order to estimate distributional parameters using the weighted least squares method. In the estimation procedure, the variances or weights are expressed as a function of the rank of the data point in the sample. The considered weighted estimation method is evaluated for the shape parameter of the log-logistic and Weibull distributions via a simulation study. It is found that the considered weighted estimation method shows better performance than the maximum likelihood, least-squares, and certain other alternative estimation approaches in terms of mean square error for most of the considered sample sizes. In addition, a real-life example from hydrology is provided to demonstrate the performance of the considered method.

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