The distribution of the characteristics of the maximum expected utility portfolio based on VaR: the impact of investor’s risk aversion coefficient

Анотація

Purpose and subject of research This study investigates the problem of rational choice of portfolio structure using the expected utility based on Value-at-Risk. Research methodology The study used formal mathematical methods, the method of economic and mathematical modeling, methods of portfolio construction, analytical methods of research. Value results We discuss the correctness of sample estimator of rational structure weights. Specifically, we define densities of the sample estimators for main portfolio characteristics and elaborate how the densities depend on investors' risk aversion coefficient. Our empirical tests allow us to give some recommendations about the rational choice of the coefficient based on the data from PFTS Ukrainian stock exchange market. It is shown that the high values (larger than 4) of this coefficient should be avoided as well as the low values (in the neighborhood of one). Conclusions The paper examines properties of portfolio characteristics with maximum expected utility based on Value-at-Risk. The use of this risk measure in portfolio theory is fully consistent with recommendations of the main banking documents. From the theoretical point of view application of expected utility function for portfolio constructing is a generalization of the portfolio constructing problem with minimum risk and given level of portfolio return. Key words: portfolio construction, Value-at-Risk, rational structure weights, portfolio characteristics

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