Evaluation of assets portfolio VAR on the base of parametric models

Yuzv'yak Oleh
Postgraduate Student at the Institute of Physics, Mathematics, Economics and Innovative Technologies, Drogobych State Pedagogical University named after Ivan Franko, e-mail:courage539@mail.ru

Cite this article:

Yuzv'yak, O. (2016). Evaluation of assets portfolio VAR on the base of parametric models. Ed.: М.D. Baldzhy (ed.-in-ch.) and others [Systema pensiinoho zabezpechennia Ukrainy ta yevrointehratsiini protsesy; za red.: М. D. Baldzhy (gol. red.)], Scientific Bulletin of the Odessa National Economic University (ISSN 2313-4569), Odessa National Economics University, Odessa, No. 7 (239), pp. 160-172.

Abstract

The article analyzes the existing parametric VaR models of portfolio assessment concerning their sensitivity to the type of portfolio assets and the volatility of its characteristics. It is shown that parametric VaR approach is quite informative and flexible because it allows you to evaluate the portfolio as a whole and its individual assets. It is noted that VaR methodology presents information in an easy and intuitive format and, in addition, parametric models do not require a large number of assumptions about the type of parameters distribution. This makes the need for choosing a particular restrictions imposed on the variable P / L. The article shows that if the distribution has heavy tails, then use the normal distribution is not appropriate. In the normal distribution of P / L or return may take any value and as a result there can be losses bigger than on available capital you can lose more than our total investments. It was shown that the return in most cases have excess kurtosis and fatter tails than at normal distribution. As a result VaR of the asset or portfolio for normal distribution is seriously undervalued in the case of heavy tails and using a normal distribution. The author recognizes that the use of normal distribution based on the central limit theorem is valid only for quantile or probability close to the center. Instead of the normal distribution in this case, it is reasonable to use one of the distributions with fat tails and we need to consider asset position - long or short. It is noted in the article that in case we need to estimate VaR at very high levels of confidence necessary it is advisable to use the theory of extreme values and prefer GEV or EV approaches.

Keywords

Portfolio VaR, parametric model, Gumbrl distribution, lognormal distribution, t-Student distribution, geometric return.

JEL classification: R400

UD classification: 330.4:336

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