Portfolio performance measurement using differential evolution

Abstract

The basic problem in finance theory is the selection of an appropriate mix of assets in a portfolio in order to maximize portfolio expected return and subsequently to minimize portfolio risk. Another approach takes into account portfolio performance expressed by various measurement techniques e.g. Sharpe ratio, Treynor ratio, Jensen's alpha, Information ratio, Sortino ratio, Omega function and Sharpe Omega ratio that are focused on determine the allocation of the available resources in the selected group of assets. This paper presents the alternative approach computing the weights of assets in portfolio assets based on the nonlinear measure techniques: Sortino ratio and Omega function. The proposed alternative includes principle of differential evolution from the group of evolutionary techniques. The experiments are set up on assets included in Dow Jones Industrial Average. Presented original approach enables using also other evolutionary algorithms in the area of portfolio selection based on different measurement techniques.

Small versus Large Caps—Empirical Performance Analyses of Stock Market Indices in Germany, EU & US since Global Financial Crisis

“…This means that an investment with a higher Sortino Ratio per additional unit of negative risk taken will generate more return than an investment with a lower Sortino Ratio. It can therefore be concluded that the Sharpe ratio penalises the investor for positive volatility, above the MAR, whereas the Sortino ratio does not (Pekar, Čičková, & Brezina, 2015).…”

Location problem of Osmia cornuta nesting aids for optimum pollination

“…The algorithms’ steps are described in detail, e.g. [ 68 , 69 ], and the principle of the basic version of differential evolution can be characterized by the pseudocode listed in [ 63 , 65 ].…”

“…In the solution procedure, it was necessary to set the values of the differential evolution algorithm’s parameters, and the values were set based on experiments conducted in previous research, according to [ 63 , 74 ]:…”

“…Differential evolution, introduced by Storn and Price [62], is an evolutionary technique, which forms the basis of many nontraditional computing techniques whose common characteristic is they are based on the observation of natural processes. Evolutionary algorithms are practical tools that can be used to search for solutions to a wide range of optimization problems, e.g., [59,[63][64][65][66][67]. The advantage over traditional optimization methods is that they are designed to find global extremes.…”

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“…The algorithms' steps are described in detail, e.g. [68,69], and the principle of the basic version of differential evolution can be characterized by the pseudocode listed in [63,65].…”