Browsing by Author "Bodnar, Taras"
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Item Determination and estimation of risk aversion coefficients(Springer-Verlag GmbH, 2018-05) Bodnar, Taras; Okhrin, Yarema; Vitlinskiy, Valdemar; Вітлінський, Вальдемар Володимирович; Витлинский, Вальдемар Владимирович; Zabolotskyy, TarasIn the paper we consider two types of utility functions often used in portfolio allocation problems, i.e. the exponential utility and the quadratic utility. We link the resulting optimal portfolios obtained by maximizing these utility functions to the corresponding optimal portfolios based on the minimum value-at-risk (VaR) approach. This allows us to provide analytic expressions for the risk aversion coefficients as functions of the VaR level. The results are initially derived under the assumption that the vector of asset returns is multivariate normally distributed and they are generalized to the class of elliptically contoured distributions thereafter. We find that the choice of the coefficients of risk aversion depends on the stochastic model used for the data generating process. Finally, we take the parameter uncertainty into account and present confidence intervals for the risk aversion coefficients of the considered utility functions. The theoretical results are validated in an empirical study.Item Statistical Inference for the Beta Coefficient(MDPI AG, 2019-06) Bodnar, Taras; Hupta, Arjun; Vitlinskyi, Valdemar; Вітлінський, Вальдемар Володимирович; Витлинский, Вальдемар Владимирович; Zabolotskyy, TarasThe beta coefficient plays a crucial role in finance as a risk measure of a portfolio in comparison to the benchmark portfolio. In the paper, we investigate statistical properties of the sample estimator for the beta coefficient. Assuming that both the holding portfolio and the benchmark portfolio consist of the same assets whose returns are multivariate normally distributed, we provide the finite sample and the asymptotic distributions of the sample estimator for the beta coefficient. These findings are used to derive a statistical test for the beta coefficient and to construct a confidence interval for the beta coefficient. Moreover, we show that the sample estimator is an unbiased estimator for the beta coefficient. The theoretical results are implemented in an empirical study.