A theoretical approach to quantitative downside risk measurement methods

Evaluating the results of the investment portfolio it is important to take into account not only the expected profitability, but also the risk. Risk measurement is based on the historical data applying various methods. The methods, that take into account the downside volatility, measures risk most effectively. The importance of these methods is emphasized by the empirical research. There are three main downside risk types: downside or asymmetric risk, tail risk, drawdown risk. The paper describes and compares the different risk measurement methodologies and criteria. Market risk measurement methods must meet four basic risk measurement axioms: positive homogeneity, subadditivity, monotonicity, transitional invariance. These axioms represent only a part of evaluating methods for tail risk and drawdown risk. Having conducted empirical studies the scientists have shown that empirical research is becoming more and more popular involving the use of a downside risk measurement methods. This popularity can be explained by the fact that based on the research results the downside risk measurement methodologies help increase the efficiency of investment portfolio