Transformation of Various Measures of Financial Risks with their Limitation on Outcomes Associated with Losses

Abstract

In assessing the risk of investing in various financial assets, risk management focuses on the analysis of the worst possible losses (the right tail of the loss distribution). At the same time, most often, when speaking about losses, it is assumed that losses can, in principle, take on negative values (which corresponds to receiving positive profits). However, there are many theoretical studies suggesting that losses take only positive values. Many risk managers use only a portion of the sample of data that corresponds to positive losses when assessing the relevant risk measures using the statistical method or the Monte Carlo method. The purpose of this paper is to study the transformation of risk estimates of various levels of catastrophicity with such a change in the space of elementary events, and hence the law of loss distribution. The paper uses methods of analysis of financial risks of various levels of catastrophicity, including methods developed in the author’s previous papers. As a result of the study, it turned out that with such a transformation of the random value of losses, all the most important estimates are significantly transformed with the help of risk measures of various catastrophicity. The author concludes that the theoretical conclusions of the work will also contribute to a more conscious understanding of the theoretical results and the results of practical risk assessments, depending on the basis on which this assessment was made: allowing losses to accept negative values or focusing only on their positive values.