UDC 519.213: 5177
DOI: 10.36871/2618-9976.2022.04.002
Authors
Krivolapov S.Ya.
Candidate of Physical and Mathematical Sciences, Assistant Professor Department of Mathematics,
Financial University under Govenment of Russian Federation, Moscow, Russia
Abstract
Data on daily stock quotations of 216 Russian companies for the period from 2004 to 2021 are considered. The subject of the study is the law of distribution of the logarithmic profitability of shares. Out of the total number of companies, a part of the companies is left for the subsequent testing of the model. For each of the remaining companies, using the methods of the Python language, a law is selected (out of 40 available candidates), in the "best" way (in the sense of the KulbackLeibler distance), approximating the law of sample distribution. One of the most frequently appearing as the "best" is the generalized normal law (gennorm). The law has heavier tails compared to the normal one, and is given by three parameters (shape, position and scale). For 178 samples (remaining after removal of outliers) a regression model is constructed for the dependences of the parameters of the generalized normal distribution law on the first four initial moments estimated from the sample. Graphical tools have shown a good approximation of the empirical and hypothetical laws of profitability distribution. The goodness of fit rejected the hypothesis of the consent of laws at the 5% level for two companies out of nine. For seven companies, the goodness of fit showed that there were no grounds for rejecting the hypothesis of consent at the 20% level.
Keywords
Fitting distributions, Logarithmic returns, Conditional optimization
