ECONOMETRIC ASSESSMENT OF THE EFFICIENCY AND VOLATILITY OF THE STOCK MARKET IN UKRAINE

The validity of published research findings is related to their demand from both investors and issuers and from the side of research scientists. The methods used make it possible to determine the general trend of market movement in the direction of increasing or decreasing its efficiency. For investors, such an assessment of the efficiency of the stock and bond markets creates a basis for optimizing the allocation of assets when building portfolio strategies, and for issuers, it is the basis for building a strategy for emission activity. It is necessary to analyze the factors affecting the efficiency of the Ukrainian market and show that the illiquidity of the Ukrainian bond and stock markets has a negative impact on the overall efficiency of the market, and therefore it is necessary to increase liquidity, which is an important factor for improving the efficiency of the market. The analysis of the efficiency of stock and bond markets is presented as an impact on the markets themselves. For research scientists, the predictability of returns, or the lack of such predictability, is critical to creating models that can accurately describe risks and returns in financial markets. The paper proposes a different approach to the study of stock market efficiency, using a time-varying parameter model that can estimate indicators, efficiency and inefficiency as parameters change.


INTRODUCTION
The fundamental basis of the concept of stock market efficiency is the existence of price efficiency, which Y. Fama divided into three levels: weak, semi-strong and strong forms of efficiency.Investigating the performance of the stock market is important for forecasting the prices of financial assets and developing investment strategies.The development of the science of financial markets in connection with the emergence of the stock market efficiency hypothesis led to the construction of pricing models for financial assets based on the price efficiency hypothesis, including the pricing model, and the can allow an investor to predict the behaviour of future returns on securities in such a market.

LITERATURE REVIEW
The riskiness of financial assets is a decisive characteristic that determines their equilibrium price.Volatility, as it is known, is measured by the standard deviation of asset returns and has some important peculiarities.The bottom line is that volatility changes over time depending on trades, the economic cycle, political events and information entering the market.
The model of autoregressive conditional heteroskedasticity (ARCH) [5] is an empirical model of financial data.Its generalization -the GARCH model [6] -is used to estimate the volatility of financial assets, such as bonds, exchange rates, stock returns, and stock indices.The model analyzes time series in which the conditional variance of the series depends on the previous values of the variances of this series [7][8][9][10].
Heavy tails: This means that asset returns usually peak; 2.
Clustering: large changes in the price of financial assets cause large changes in market trends, and small changes follow small changes, which means that there are periods of low volatility and periods of high volatility.
An actual problem of the theory of financial markets is that in order to evaluate the efficiency of the stock and bond market in Ukraine, an effective toolkit for its testing based on modern econometric models is needed [13][14][15][16][17]. Therefore, in order to build an econometric model that allows to answer such a difficult question in economic science, analyses should take into account not only the characteristics of the market but also its qualitative characteristics [18][19][20][21][22][23][24].
Unresolved aspects of the problem.The procedures for verifying the efficiency of the Ukrainian stock market, outlined in the works of contemporary scientists, do not take into account the time-varying parameter models, do not reflect the dynamics of the movement towards market efficiency and are not an efficient approach to assessing the efficiency of the market from the current perspective.Due to the lack of development of theoretical, methodological and empirical aspects of stock market efficiency and volatility assessment, this study is particularly relevant for the development of stock market theory and optimization of investment strategies in the stock market.

AIMS AND OBJECTIVES
The purpose of the article is to evaluate the efficiency and volatility of shares and bonds on the basis of modern methods adapted to the modern Ukrainian stock market, to develop a multifactor strategy for its investment.The objectives of the article are to analyze the effectiveness of the Ukrainian stock market, using the example of the Ukrainian Stock Exchange, to find the main problems in the stock exchange.

METHODS
Non-parametric (series test -normality test) and parametric tests (time series stationarity test -autocorrelation function) are included in the weak form of market efficiency assessment methods.In this paper, traditional methods (tests) are included which can be used to assess the efficiency of the stock market in a weak form for the study of random walk processes.In this paper, a generalized autoregressive model with conditionally varying variance (GARCH) is used to study the efficiency of the market in a weak form and predict the volatility of the Ukrainian stock market.

An Empirical Study of Stock Market Efficiency and Volatility
To analyze the efficiency of the Ukrainian market, the UX index is used, which is traditionally weighted by market capitalization.The most liquid shares of the largest dynamically developing Ukrainian issuers whose types of economic activity belong to the main sectors of the economy were also used.
Stock indices of the Ukrainian Stock Exchange are key indicators of the organized securities market of Ukraine.They belong to the type of capitalization-weighted, taking into account Free-Float stock indices.
For analysis, the UX index provides daily closing prices.As a measure of efficiency and volatility, the absolute values of logarithmic returns on indices, calculated on the basis of consecutive price observations are used.To calculate a stock's daily return, the closing prices derived from the index are adjusted for non-trading days.
If a stock market follows a random walk pattern, it is considered to have the characteristics and effects of a weak market, that is, prices fully reflect the information contained in historical price movements, and stock prices should change only after new information about the market appears.In these circumstances, historical price information does not allow for profit.An efficient market follows a random walk and is therefore unpredictable.An efficient market is unpredictable, but it can be tested using the random walk hypothesis.
The selection of this index is based on its general characteristics, which guarantee a sufficiently long time series.To do this, the daily return of the UX index from January 1, 2020, to December 31, 2022, will be analyzed, giving a general observation (U = 1234).
The analysis of the profitability of the UX index was made to check the efficiency of the stock market in Ukraine and to study the presence of volatility clustering in the Ukrainian stock market.Data normality was assessed by the Harke-Behr test and stationarity by the Dickey-Fuller (ADF) test, ARCH and GARCH models were used to study the behavior of bond yields and to estimate the volatility model [25][26][27][28].
The normality test rejects the null hypothesis, the kurtosis is clearly greater than 3, especially in the case of the higher kurtosis (14.07>3) for the UX stock index and the negative skewness.Figure 1 presents a histogram of the UX index yield.Thus, we reject the normal distribution of returns due to the high value of the Harke-Behr statistic and conclude that the daily stock market returns do not follow a normal distribution, so stock markets are not efficient in the weak form.
On the basis of the random walk hypothesis, an empirical weak-form test of market efficiency was conducted using the Dickey-Fuller augmented test.The Dickey-Fuller test is a statistical and econometric method used to test for stationarity in financial time series.Figure 2. presents a graph of returns over the entire study period for the UX index.The Y-axis represents returns (or index changes), and the X-axis represents days.From the graph, the returns appear to be constant over this period for the index.We will use the unit root test to test whether the underlying series is truly a stationary process-a precondition for a random walk process (Table 1).
The ADF statistic of the UX index is minus 33.36337 and the p-value is less than 0.000.In addition, the result shows critical values at the 1%, 5%, and 10% levels.The absolute value of the t-statistic is significant, so we reject the null hypothesis and conclude that there is no unit root and the data series is stationary.In addition, the studied data do not follow the random walk process, and the dynamics of the stock market index are inefficient in the weak form [25,26,29]. Before estimating a GARCH model for a financial time series, it is necessary to check for ARCH effects in the residuals.If there is no ARCH effect in the residuals, a GARCH model is not required and is not specified.For Gaussian residuals, it is equivalent to uncorrelated independent.The residuals will not be Gaussian.The ARCH-LM test was used to test ARCH effects.As part of the ARCH-LM test, the null and alternative hypotheses for both bond indices are as follows: H0: there is no ARCH effect, H1: there is an ARCH effect.Table 2 shows that Prob.Chi-Square is responsible for the null hypothesis that there is no ARCH effect in the residuals tested.The test results reject the null hypothesis and therefore conclude that there is an ARCH effect in the financial data series on the profitability of shares of the UX index.We continue testing the weak form of the efficiency of the Ukrainian stock market using the GARCH model.ARCH model and GARCH model were used to test the null hypothesis.Data on parameter estimates are given in Table 3.  (2) The coefficients for both the lagged squared residual (r) and the lagged conditional variance (β) in the variance equation are statistically significant.In addition, the sum of the ARCH and GARCH coefficients (α + β) of the UX stock index is very close to one, which indicates the high persistence of volatility clusters during the sample period in the market.Large sums of coefficients mean that larger positive and negative returns will lead to the fact that the future variance forecast will be high for a long period (Figure 3).
It is possible to estimate the daily volatility of the return of the UX index based on historical data and say that the Ukrainian stock market is not efficient in a weak form [25,30]. Table 3 shows that most of the information based on forecasts of previous days is about 92% for the UX index (a fact that contradicts the hypothesis of the efficiency of financial markets), and when new information arrives, there is a minimal change, which has little effect on the long-term average variance.Thus, the results of the analysis allow stating that the Ukrainian stock market is inefficient in a weak form and shows high volatility and the absence of a stable trend.

An Empirical Study of Bond Market Efficiency and Volatility
A bond is a debt instrument that requires the issuer to repay the lender/investor receives the amount borrowed plus interest for a fixed period.As an instrument, the bond has market indicators that give the investor the property of liquidity of this instrument.The effective functioning of the bond market allows the inclusion of market mechanisms for managing debt and, therefore, the financial structure of capital [31,32].Therefore, the evaluation of the efficiency and volatility of the bond market is necessary for the implementation of management mechanisms embedded in the financial management system.
Long-term dependence on debt markets has important implications for market efficiency in the pricing of fixed-income securities.The efficient market hypothesis provides a standard framework for analyzing and interpreting informational efficiency in the bond market.
Changes in the volume and structure of public debt and the interest rate can affect the dynamics of the bond market, as this is an important factor affecting the efficiency of this market.Therefore, when government debt is issued for investment purposes, it is expected to affect bond prices, as the investment is expected to bring future profits, and when the Ministry of Finance issues debt instruments to finance existing debt, it can affect the stock market, as it indicates that the budget does not generate enough funds to repay the previously issued debt.
Therefore, two indices were used to analyze the efficiency of the Ukrainian bond market.The first is domestic government loan bonds -government securities placed on the domestic stock market.The domestic government loan bonds confirm the obligations of Ukraine to compensate the bearers of these bonds for their nominal value with the payment of income in accordance with the terms of placement of bonds [3].If a bond market follows a random walk pattern, it is said to have the characteristics and effects of a weak-form market, meaning that prices fully reflect the information contained in historical price movements.In these circumstances, historical price information does not allow for profit.An efficient market follows a random walk and is therefore unpredictable.An efficient market is unpredictable, but it can be tested under the random walk hypothesis [4].
The selection of these bonds is based on their general characteristics, which guarantee a fairly long time series.For our analysis, we take daily bond index returns from 2020 to 2022, giving a total observation (U = 1234) for government bonds and corporate bonds (U = 1587).
Two historical data sets of time series of government bonds, and corporate bond index were analyzed to check the efficiency of the bond market in Ukraine and the presence of volatility clustering in the Ukrainian bond market was investigated.Data normality was assessed by the Harke-Behr test and stationarity was assessed by the Dickey-Fuller (ADF) test, ARCH and GARCH models were used to study the behaviour of bond yields and to estimate the volatility model [25,26].
Figure 4 and Figure 5 present the yield histograms of government bonds and corporate bonds.The Harke-Behr test rejects the null hypothesis and the kurtosis is clearly greater than 3, especially in the case of higher kurtosis (97.85>3 for government bonds; 53.41260 for corporate bonds) and negative skewness for both, which means the residuals are not distributed correctly.
Thus, the normal distribution of returns is rejected due to the high value of the Harke-Behr statistic, and we conclude that the Ukrainian bond market is not efficient in the weak form, since the daily returns of the government and corporate bond market do not correspond to a normal distribution.
Below are graphs constructed from the logarithmic form of returns over the entire study period for the two bonds (Figure 6 and Figure 7).From the graph, the yield is constant for this period of both bonds.We will use the unit root test to check whether the underlying series is truly a stationary process, a precondition for a random walk process.
In Table 4 the ADF statistic for bonds is -10,387 and the p-value is less than 0.0001.It also shows critical values at the 2%, 5% and 10% levels; the absolute value of the o-statistic is significant and rejects the null hypothesis.This means that there is no unit root and the data series is stationary; furthermore, the data do not follow a random walk process and government bonds are weakly inefficient.In Table 5 the statistical value of the ADF of corporate bonds rejects the null hypothesis of the existence of a unit root in corporate bond yields, in addition, the studied data do not follow a random walk process, and corporate bonds are inefficient in the weak form.To estimate a GARCH model for a financial time series, it is necessary to check whether there is an ARCH effect [5] in the residuals.If there is no ARCH effect in the residuals, a GARCH model is not required and is not specified.For Gaussian residuals, uncorrelated means independent.Therefore, the residuals are not Gaussian.
In Tables 6 and 7 Prb.Chi-Square is responsible for testing the null hypothesis that there is no ARCH effect in the residuals.Government bonds and corporate bonds gave similar results.According to the results of the testing, it was concluded that the null hypothesis is rejected, therefore, the ARCH effect is present in the series of financial data on bond yields of both indices.To test the weak form of efficiency of the domestic bond market the GARCH model [6] was used.ARCH model and GARCH model were used to test the null hypothesis.
Table 8 shows the conditional mean and conditional variance model for government bonds that best fits the observed data: The α and β parameters of the GARCH model are positive and statistically significant for government bonds.This means that the GARCH model represents well the behaviour of daily government bond returns, as it successfully shows the time dependence of the index yield volatility.As a result, the value of (α + β) is very close to 1 for government bonds, indicating a high persistence of cluster volatility in the market over the sample period.As we can estimate the daily volatility of the bond's yield, we can find an investment strategy in the market and get excess returns.Thus, the Ukrainian government bond market is inefficient in the weak form [25,26].
The lagged squared residual (α) and lagged conditional variance (β) coefficients in the variance equation are both statistically significant.In addition, the sum of the ARCH and GARCH coefficients (α + β) of corporate bonds is very close to unity.Large coefficient sums mean that larger positive and negative returns will cause the future variance forecast to be high over a longer period.It is possible to estimate the daily volatility of bond yields based on the data and say that the Ukrainian corporate bond market is inefficient in its weak form.Thus, from Tables 8 and 9 information based on the previous day's forecasts shows that about 65% of the information is for corporate bonds and 85% for government bonds, which is contrary to the fact that the assumed efficiency of financial markets changes little with new information and has little impact on the long-run mean variance.

DISCUSSION
Considering certain aspects of the current state of the Ukrainian stock market and investment portfolios, it should be noted:  most Ukrainian companies do not use the stock market to attract long-term investments;  despite the significant impact of negative factors (high volatility, lack of a stable trend), the Ukrainian stock market remains very attractive for Ukrainian and foreign investors.
The bond market in Ukraine has been growing steadily as the lower inflation environment leads to enhanced planning by investors and borrowers due to the provision of some government support [8,[11][12][13].
Government bonds play a significant role in the debt market, accounting for approximately half of issued debt securities [9,10,[16][17][18].Their yield is widely used as a benchmark for private bonds of companies with low credit risk.Oil and gas, construction and development companies accounted for 75% of bonds issued by non-financial companies.
Systemic financial risk can be assessed and forecast using econometric models.Volatility risk and uncertainty in financial systems are interrelated and may contribute to more frequent defaults on payments to agents in other markets [19][20][21][22][23].
Large-scale risks of this kind (financial crises) can lead to crises in economic activity in the real sector (initially due to liquidity), which makes them the main point of consideration in the Ukrainian market.

CONCLUSIONS
Based on the theoretical analysis, the characteristics of the stock market efficiency hypothesis and the approach to efficiency testing were considered -simultaneously on two markets: shares and bonds.
Factors affecting market efficiency in Ukraine were considered.The main indicators and factors of the stock market in Ukraine, which have the greatest influence on the efficiency/inefficiency of the market, are analyzed, including liquidity, trading volume, capitalization size, transparency and global factors in the international stock market.Based on the analysis, evidence is provided that low liquidity in the Ukrainian bond and stock market negatively affects market efficiency, therefore increasing liquidity is an important factor in increasing market efficiency.
The effectiveness of the stock and bond markets in Ukraine was tested and the results of its practical approbation on the stock and bond market were displayed.An additional GARCH model for volatility modelling is also built and substantiated, which shows high volatility and no stable trend.

Figure 1 .
Figure 1.Histogram of the yield of the UX index.

Figure 2 .
Figure 2. UX index yield minimum and maximum chart.Note: the period from 03.01.2020 to 30.12.2022.

Figure 3 .
Figure 3. Volatility of the UX index.(Sources: [3]) bonds.They are the main indicator of the Ukrainian corporate debt market.It includes the most liquid bonds of Ukrainian borrowers, admitted to trading on the Ukrainian Stock Exchange, with a duration of more than one year, calculated in real-time using the methods of aggregate income and net prices.

Figure 4 .Figure 5 .
Figure 4. Histogram of the yield of government bonds.Figure 5.Corporate bond yield histogram.

Table 1 . The results of the advanced Dickey-Fuller test
. Note: *MacKinnon (1996) One-sided p-value

Table 3
(1)ws the conditional mean and conditional variance (volatility) model for the UX government stock index that best fits the observed data: ℎ  = 0,000161 +  (1)

Table 4 . Results of the extended Dickey-Fuller test of government bonds
. Note: *MacKinnon (1996) One-sided p-value Null Hypothesis: OBDL has a root

Table 9
shows the conditional mean and conditional variance model for corporate bonds that best fits the data: