| Abstract [eng] |
One of the most important problems in emerging financial markets is that these markets in financial data often do not meet the conditions of normality. Many securities markets research carried out on the assumption that financial data is distributed according to Gauss's law and therefore not all of these research findings and the results can be applied to developing the financial markets. To solve the zero returns problem was suggested stable patterns change mixed - continous and discrete models mixture. One of the tasks in this work was to investigate distribution of the dependent mixed-normal sequences. The results showed that when the number of sequences is less than 5 (as well as for independent sequences) mixed-normal distribution describes the sequence of sums better than the normal distribution. When increasing the number of summands, number of sequence that are distributed by normal law is increasing, while compatibility with mixed-normal distribution seem no longer justified. In this we introduce new stock portfolio model, which is based on a mixed-normal distribution. This is a modification of the Markowitz model, adding stock returns mean and variance without 0, and evaluating the effect of no change in stock prices, i.e. stock price change probability p. For analysis were selected Lithuania stock data. For all sampled stock returns, Kolmogorov-Smirnov and Kountruvelis tests, verified by normality and compatibility with mixed-normal laws. The results showed that none of the selected stock satisfy the conditions of normality. Selected stock returns are better described by mixed-normal law. To show efficiency of model developed, we have compared it to Markowitz, MAD and Minmax model portfolios. For all portfolios were calculated portfolio behavioral rations: Sharpe, Sortino, Var, Starr, Rachev. Sharpe, Sortino, VaR and Starr ratios sugests to choose MixNormal portfolio. However Rachev R-ratio predicted to be the best Markowitz portfolio. Historical estimation of possible profit showed that the maximum yield was obtained by a new method consisting MixNormal portfolio. |
