Omega-optimized portfolios: applying stochastic dominance criterion for the selection of the threshold return

Abstract

Purpose of the article: While using asymmetric risk-return measures an important role is played by selection of the investor's required or threshold rate of return. The scientific literature usually states that every investor should define this rate according to their degree of risk aversion. In this paper, it is attempted to look at the problem from a different perspective -empirical research is aimed at determining the influence of the threshold rate of return on the portfolio characteristics. Methodology/methods: In order to determine the threshold rate of return a stochastic dominance criterion was used. The results are verified using the commonly applied method of backtesting. Scientific aim: The aim of this paper is to propose a method allowing selecting the threshold rate of return reliably and objectively. Findings: Empirical research confirms that stochastic dominance criteria can be successfully applied to determine the rate of return preferred by the investor. Conclusions: A risk-free investment rate or simply a zero rate of return commonly used in practice is often justified neither by theoretical nor empirical studies. This work suggests determining the threshold rate of return by applying the stochastic dominance criterion.

An omega portfolio model with dynamic return thresholds

“…The Omega function is strictly descending when the return threshold increases since the possibility for the portfolio yield to achieve it decreases (Vilkancas, 2016). The value of τ typically can be the risk‐free rate, the market return, or simply a constant, such as zero (Kapsos et al., 2014a; 2014b; Vilkancas, 2014).…”

“…The value of τ typically can be the risk‐free rate, the market return, or simply a constant, such as zero (Kapsos et al., 2014a; 2014b; Vilkancas, 2014). However, Vilkancas (2016) suggests that a fixed threshold is not suitable for use in the Omega model optimization; instead, a specific point return threshold is needed in portfolio rebalancing. Therefore, we retain the return threshold as an endogenous variable instead of a given parameter.…”

“…However, how to appropriately determine return thresholds in the Omega portfolio has not yet been addressed. Vilkancas (2014, 2016) documents that floating thresholds may enhance portfolio performance, as they better reflect market dynamics than fixed thresholds. Sharma and Mehra (2017) synthesize the features of the Omega ratio optimization and mean‐risk models by incorporating various risk measures, such as semi‐MAD, CVaR, and the minimax criterion.…”

“…Sharma and Mehra (2017) synthesize the features of the Omega ratio optimization and mean‐risk models by incorporating various risk measures, such as semi‐MAD, CVaR, and the minimax criterion. Vilkancas (2016) suggests that the Omega function should be assessed within a range of τ values to obtain full information about the return‐risk distribution. This is because the outcome of a single threshold can be misleading due to a lack of market information.…”

“…This is because the outcome of a single threshold can be misleading due to a lack of market information. However, investors must choose one specific point of the return threshold while rebalancing portfolios (Vilkancas, 2016). The empirical results by Vilkancas (2016) show that a rate threshold of zero or close to zero, which are widely used as return thresholds, is not the best option.…”