International Portfolio Optimization with Higher Moments

Abstract

We analyze the international portfolio optimization problem by introducing the higher moments of the main financial index returns. We take especially account of their skewness and kurtosis. We introduce various decision criteria, based on these moments. In this framework, we solve different optimization problems: skewness maximization, kurtosis minimization, Polynomial Goal Programming (PGP), and finally, truncated utility maximization. For all of these objective functions, we determine, analyze and compare the optimal solutions, especially their degree of diversification.We illustrate our results on monthly returns of eighteen major international stock market

Portfolio optimisation with higher moments of risk at the Pakistan Stock Exchange

“…However, finance literature is now enriched with various methods to solve this complex task (Smimou & Thulasiram, 2010). Although there are approaches like shortage function developed by Briec, Kerstens, and Jokung (2007) that uses non-parametric efficiency measurements or the evolutionary algorithm approach in an experimental setting by Chiam, Tan, and Al Mamum (2008), but in line with Lai et al (2006) and Mhiri and Prigent (2010), we decided to use PGP with a multi-objective approach, to incorporate higher moments of risks while selecting an optimal portfolio. PGP, according to the existing literature is considered as highly effective and efficient to solve such problems with multiple conflicting risk preferences.…”

“…Lai et al (2006) also augmented the dimension of portfolio selection from mean-variance-skewness to mean-variance-skewness-kurtosis using the multi-objective method. Similarly, Mhiri and Prigent (2010) incorporated higher moments of skewness and kurtosis and also Davies, Kat, and Lu (2009), who focused on selection of efficient funds from hedge funds.…”

“…Finally, to consolidate multiple objectives, we use the PGP approach used by (Aracioglu et al, 2011;Lai et al, 2006;Mhiri & Prigent, 2010). With the intention to maximise portfolio return and skewness and minimise variance and kurtosis:…”

On 2-moment completeness of non pre-emptive, non anticipative work conserving scheduling policies in some single class queues

“…We consider an extension of this model and minimize the third moment of waiting time subject to constraint on second moment over all non pre-emptive, non anticipative and work conserving scheduling policies which span entire feasible space. Some similar problems of minimizing skewness (related to 3rd moment) under mean and variance constraints are solved in finance literature (See [39] Subject to E(W 2 ) ≤ β By the above result, the parametrized queue discipline discussed in section II-B is 2-moment complete class and hence spans the entire feasible space of this optimization problem.…”

“…Study of higher moments is quiet popular in queueing systems as well as other application areas (see [38], [39], [40]). …”