Application of descriptive statistics methods to Kazakhstan stock market

The article discusses the methods of descriptive statistics and its application for the most liquid shares of the Kazakhstan stock market KASE (trading codes: HSBK, KZTK, CCBN, KZTO, KCEL, KEGC, KZKAK) from 2007 to 2022. Descriptive statistics are calculated for each stock, such as average return, variance, sample range, standard deviation, coefficient of variation, kurtosis, and skewness. The coefficients of the regression equation and the coefficient of determination R2 are estimated, which show the relationship between the market return and the return on an individual stock. The comparative analysis of index growth of stocks was carried out from 2013 to 2022. The histogram of the frequency distribution of KASE market returns based on annual and monthly periods and its empirical distribution function have been constructed. The hypothesis about the normal distribution of returns according to the Pearson criterion was tested. The distributions of returns for many stocks do not fully correspond to the normal distribution and have a positive skewness, i.e. have a long tail on the right side. The market curve has been constructed that characterizes the dependence of stock returns on the level of risk. According to this curve, it is established that HSBK stocks are the most risky of all the considered stocks, undervalued and attractive investments for investors using an aggressive investment strategy. KEGC stocks are less risky and very attractive investments for investors who use a more conservative investment strategy in the Kazakhstani stock market.

1. Ibbotson R.G., Harrington J.P. (2021) Stocks, Bonds, Bills and Inflation. Yearbook. 198 p. URL:https://www.cfainstitute.org/en/research/foundation/2021/sbbi-2021-summary-edition. (In English).

2. Press-reliz KASE po itogam 2020, 2021 i 2022 godov. URL: https://kase.kz/ru/press_releases/. (In Russian).

3. Sharp U., Aleksander G., Bjejli Dzh. (2006) Investicii. M.: INFRA-M, XII, 1028 p. (In Russian).

4. Van Horn D.K., Vahovich D.M. (2008) Osnovy finansovogo menedzhmenta. 12-e izdanie. M.: OOO «I.D. Vil'jams», 1232 p. (In Russian).

5. Pearson K. Contributions to the Mathematical Theory of Evolution. II. Skew Variation in Homogeneous Material // Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 1895. Vol. 186. P. 343–414. (In English).

6. Damodaran A. Historical Returns on Stocks, Bonds and Bills: 1928–2022. URL: https://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/histretSP.html. (In English).

7. Ibbotson R.G., Sinquefield R.A. (1983) Stocks, Bonds, Bills, and Inflation: The Past and the Future. Charlottesville, VA: Financial Analyst Research Foundation. 137 p. (In English).

8. Wilson J.W., Jones C.P. (1987) A Comparison of annual Common Stcok Returns: 1871–1925 and 1926–1985 // Journal of Business, 60, no. 2, pp. 239–258. (In English).

9. Siegel J.J. (1992) The Equity Premium: Stock and Bond Returns Since 1802 // Financial Analyst Journal, 48, no. 1, pp. 28–38. (In English).

10. Schwert G.W. (1989) Why Does Stcok Market Volatility Change Over Time? // Journal of Finance, 44. no. 5, pp. 1115–1153. (In English).

11. Shirjaev A.N. Osnovy stohasticheskoj finansovoj matematiki. Tom 1. Fakty. Modeli. Moskva: FAZIS, 1998. 512 p. (In Russian).

12. Azimli A. Degree and structure of return dependence among commodities, energy stocks and international equity markets during the post-COVID-19 period // The International Journal of Minerals Policy and Economics. 21 March 2022. URL: https://doi.org/10.1016/j.resourpol.2022.102679. (In English).

13. Wolski R. Risk and return in the real estate, bond and stock markets // Conference: 24th Annual European Real Estate Society. January 2017. URL: https://doi.org/10.1016/j.frl.2021.102524. (In English).

14. Patjoshi P. Comparative Risk Return Analysis of Bombay Stock Market with Selected Banking Stocks in India // IRA-International Journal of Management & Social Sciences. 2016, no. 4(1). ISSN 2455-2267 URL: http://dx.doi.org/10.21013/jmss.v4.n1.p18. (In English).

15. Hull J.C. (2011) Options, futures, and other derivatives / Prentice Hall; 8th ed. Edition. 841 p. (In English).

16. Defusco R.A., McLeavey D.W., Pinto J.E., Runkle D.E. (2011) Ethical and Professional Standards and Quantitative Methods CFA PROGRAM CURRICULUM // Statistical concepts and market returns, CFA Institute. Vol. 1. Reading 7. (In English).

17. Jelektronnaja torgovaja ploshhadka «Bloomberg terminal», razdel Security, podrazdel KZ Equity. URL: https://www.bloomberg.com/markets/stocks. (In Russian).