Abstract
In this paper we introduce a new rank dependent utility approach, which unlike existing models, provides an SSD efficient portfolio as a function of the investors’ quantified risk aversion degrees. A parametric family of distortion functions is considered to model various levels of risk aversion. Under assumptions of equally probable scenarios, for any distortion function the corresponding optimization models can be expressed as linear program and easily solved. An empirical study is performed to compare the performance of our proposed model to the previously proposed portfolio selection models in the literature.
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Notes
There exist a number of different ways to consider the case of unequal probabilities. For example, as suggested by others (Roman et al. 2006), unequal probabilities can be handled by multiple replications of certain selected scenarios to achieve the desired probabilities. Another way to address this issue is to introduce a grid of level \(j\) that contain possible break points of the Lorenz curves. For instance, we may assume that the cumulative probability of returns for the bottom 10 % of the return distributions is 0.22, for the bottom 30 % of return is 0.40 and for 100 % of returns is 1.00.
Some of the descriptive statistics of the stocks are presented in Table 6 of Appendix.
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Appendix
Appendix
Table 6 shows some of the descriptive statistics of 15 stocks, S1–S15, for the sample period. The Jarque–Bera test at 95 % confidence level confirms that majority of stocks have non-normal and asymmetric return distributions.
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Javanmardi, L., Lawryshyn, Y. A new rank dependent utility approach to model risk averse preferences in portfolio optimization. Ann Oper Res 237, 161–176 (2016). https://doi.org/10.1007/s10479-014-1761-9
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DOI: https://doi.org/10.1007/s10479-014-1761-9