Stanovení míry rizika pro eliptická rozdělení pravděpodobnosti akciového portfolia

Abstract

Risk management has been, for a long time, a part of corporate finance and financial institutions. The standard for measuring and risk management is the value indicator Value at Risk (VaR) and Conditional Value at Risk (CVaR). This work provides a research in what way the amount of risk differ under the assumption of normal distribution, Student and Laplace distribution of probability, which belong to the group of elliptic distribution. Aim of the doctoral dissertation thesis is the verification of estimating Value at Risk and Conditional Value at Risk for known composition of assets portfolio under the assumption of elliptical distribution and also portfolio optimization by Mean-VaR and Mean-CVaR models under the assumption of elliptical distribution on a share market. The structure of the work is as following: firstly the share market is defined, then the theoretical-methodological backgrounds, which serve as a base for empirical part, are described. The last chapter shows the results of estimating the VaR and CVaR under the assumption of above mentioned probability distribution for known portfolios for three various time periods. The most appropriate distribution type will be verified by back testing. It has been proven that for period I, the most appropriate is to use VaR and CVaR under the assumption of normal distribution, for period II the Student distribution and for period III the most suitable is Laplace distribution. Further, the work presents the portfolio optimization by the VaR and CVaR criteria under the assumption of all elliptical distributions executed only for the shortest periods. It is assumed that, in the case of normal distribution the portfolio will not be as diversified as under the assumption of Student or Laplace probability distribution.