Financial and institutional determinants of the price dynamics of the Russian stock market

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Financial and institutional determinants of the price dynamics of the Russian stock market

Introduction

The price-earnings (P/E) multiplier is one of the widely used multiple in relative valuation model and in diagnosing overvalued/undervalued stock markets in different countries. The popularity of the multiplier is explained by the simplicity in calculation and the intuitive interpret. The motivation for doing this research is the existence of the huge discount on the Russian P/E multiplier against the other developed and developing countries, which cannot be explained by the existing models.

The diagram of the countries' P/E multiplier and the dynamics of Russian P/E multiplier relative to the world are shown below (Picture 1, Picture 2). The Russian market is taking the last position among the others.

Picture 1. Median P/E for the period 2006-2016 (authors' calculations)

Picture 2. The dynamics of Russian P/E multiplier relative to the world (authors' calculations)

The goal of the research is to explain the position of Russia stock market and create a method of calculating the target P/E multiplier, which could substantiate the existence of the discount relative to the developed and developing markets.

The object is P/E multiplier of the Russian stock market. The subjects are fundamental determinants that influence the value of P/E. To achieve the goal several tasks should be solved:

1. To identify the main fundamental determinants

2. To analyze the existing empirical studies on determining the risk factors of P/E multiplier

3. To define the methodology of estimating the target P/E for the country

4. To estimate target P/E for the Russian stock market

5. To interpret the obtained results.

The practical value of such method lies in the following applications:

1. To diagnose if the Russian stock market is overvalued/undervalued

2. To estimate the country discount in the valuation of the company's peers from the other countries

3. To estimate a target P/E ratio for the company on the basis of regression of the multiplier on the key determinants.

In this research how the structure and specific features of the economy influence on the medium P/E ratio of the country using the indexes of the stock exchange is studied. It means that in this paper the P/E multiplier is examined at the level of the overall market, not considering each local company in the country.

The first chapter contains the theoretical models on the basis of which identifies the fundamental determinants of P/E, discusses the characteristics of this multiplier and analyzed existing empirical studies for developed and developing countries.

The second chapter contains the methodology of the study: the hypotheses, the specification of models, the investigated determinants and the requirements of the sample.

The third chapter is devoted to description of the sample and the regression equations.

In this study database of periodicals, Web of Science and Scopus, information terminals Bloomberg database, World Bank, Inernational Monetary Fund, etc. were used.

Chapter 1. Literature review

In order to identify fundamental determinants the cost of equity estimating models were used. In these models net income is accepted as a proxy indicator of cash flow:

		(1)

· F--model;

· V--estimated cost of equity;

· E--net income;

· {d}--a set of fundamental determinants.

These models allow defining the determinants of the multiplier:

		(2)

1.1 Relevant theoretical models

To identify fundamental determinants it is necessary to analyze relevant models of value estimation. The simplest model is discount dividend model. This model assumes that dividends grow at a constant rate:

		(3)

· --expected earnings per share

· payout ratio;

· g--expected annual growth rate of dividends;

· --discount rate.

This model implies strict assumptions. However, in reality companies go through several life cycle stages: introduction, growth, maturity and decline. As a result, for each stage the value of earnings and the payout ratio are different.

The following model is more applicable - the two stage dividend discount model. The two stage model involves the allocation stages of growth and maturity periods:

(4)

· --expected earnings per share;

· --payout ratio;

· --expected growth rates at growth and maturity stages;

· --discount rates at growth and maturity stages.

Taking into account the relationship between payout ratio and return on equity the following formula will be obtained:

		(5)

Thus, the fundamental determinants of P/E ratio can be defined:

	(6)

There are several relationships between P/E and the determinants Damodaran (2009):

· P/E rises with the increase in the payout ratio and ROE;

· P/E decreases with the increase in the cost of equity;

· P/E increases with the increase in the growth rate, if ROE exceeds cost of equity.

The Olson model associates the value of the company with the future discounted stream of the excess earnings Ohlson and Gao (2006):

		(7)

· book value of the company;

· --forecasted excess returns.

Taking into account the link between excess returns with the return on equity:

		(8)

It can be concluded that both models lead to the following set of determinants:

· The cost of equity

· ROE

· The growth rate

· The payout ratio

Moreover, there is the possible impact of capital structure on the multiplier. In the collective monograph McKinsey Koller, Goedhart and Wessels (2010) shows the multiplier dependence of P/E multiplier on the value of the borrowed capital:

		(9)

· D--debt;

· V--value of the company;

· --cost of debt.

Therefore, the list of determinants could be expanded by the cost of debt and the financial leverage.

The multiplier, despite the simplicity of the calculation, is exposed to as characteristics of the financial architecture of the company and the environment. In comparative analysis these features should be taken into account by using the adjustments, leveling the differences. This approach is reasonable to use in the diagnosis of overvalued/undervalued markets.

1.2 Empirical studies

A large number of papers were published due to popularity of the P/E multiplier.

Growth rate

There are many researches devoted to the influence of the growth rate on the P/E multiplier. According to the Gordon model, there is a positive relationship between the growth rate and the P/E multiplier. The results of the empirical analysis are consistent with the common sense: the higher growth rate provides the higher equity multiples. An increase in growth rate is to be associated with an increase in a share price. Thus, this leads to a higher P/E multiple.

The growth forecast was used in most of the researches and this factor was shown to be significant in papers Fairfield (1994), Huang, Tsai, Chen (2007), Afza, Tahir (2012), Huang, Wirjanto (2012), Deaves et al. (2008), White (2000), Malkiel, Cragg (1970), Zarowin (1990), Dudney et al. (2008), Loughlin (1996), Jain, Rosett (2006), Shamsuddin, Hillier (2004). According to these researches, the past behavior of the growth rate is inappropriateness in predictions of the future growth rate. Allen and Cho (1999) examined the ex-post and the ex-ante values of growth. The results show that the forecasted growth rate rather than the historical one is a significant risk factor of the P/E multiplier. In order to conduct cross-country analysis of the P/E multiplier the projected GDP growth rates were used in Jain, Rosett (2006), Ramcharran (2002), White (2000), Shamsuddin, Hillier (2004). As the same way the forecasted GDP growth rate were used in this article as the proxy of the expected growth rate.

Financial Leverage

The effect of the financial leverage and the cost of debt also were studied. The higher value of the debt is associated with the greater risks. Thus, a negative influence of the financial leverage on the P/E multiplier is expected. The empirical researches Huange et al. (2007), Kumar, Warne (2009), Taliento (2013), Malkiel, Cragg (1970) show that the financial leverage and the cost of debt are significant and results are consistent with the claim of negative correlation. However, in the research Afza and Tahir (2012) the financial leverage was not significant. This result can be explained by the peculiarity of the sample - chemical sector of Pakistan. In general, for specific industries financial leverage tends to the optimal level Agliardi and Luk'yanova (2011) and has low variability.

The cost of equity

The most popular risk factor, which was considered in numerous empirical studies, is the cost of equity. According to the theoretical models, the negative correlation between discount rate and P/E multiplier is expected. This claim has been confirmed in the researches Azam (2010), Shamsuddin, Hillier (2004). The majority of the researches used the volatility of returns as a proxy of the cost of equity. The results of the studies Hunt et al. (2005), Huang, Wirjanto (2012), White (2010), Shamsuddin, Hillier (2004), Thomas, Zhang (2006) Constand et al. (1991) show the negative relationship between the volatility of returns and the equity multipliers which are consistent with the theoretical models.

Payout rate

There is a positive relationship between the payout rate and the P/E multiplier in the Gordon model. According to the signal theory, companies' announces of an increase of the dividends payout are the indicators of the positive future prospects of the company. The empirical results confirmed this claim in developed and developing countries (Loughlin (1996), Dudney, Zorn (2004), Reilly et al. (1983), White (2000), Azam (2010)). However, Faezinia et al. (2012) obtained the negative relationship. The reason of this result is that investors can receive more money from their investments. This situation illustrates that if the company pays more dividends it does not provide funds to the future development.

The average size of the listed firms on the stock market

One of the widely used proxies of the risk of investing is a size of the company. The larger companies provide the lower risks. However, the results of the researches are quite different for both developed and developing countries. One more specific of measuring the size is that companies' size could be measured as natural logarithm of market capitalization, total assets or revenue.

In the papers King and Segal (2008) and Liu (2002) were examined the dependence of P/E multiplier on the size of the firm in the developed markets, such as USA and Canada. The result is unexpected. The interpretation of this finding is the following: the increase in assets provides faster growth in profit, so the multiplier decreases. However, for UK and Europe markets the size has a positive influence on the P/E multiplier. In both researches Anderson, Brooks (2005) and Harbula (2009) were used the natural logarithm of market capitalization as a size measure. These results illustrates that large companies are less risky.

The researches which were devoted to study the relationship between the size and the P/E multiplier in the developing countries also provides mixed results. A positive influence of the firms' size on P/E multiplier for the Tehran and Indian companies was revealed (Faezinia (2012) and Sehgal, Pandey (2009)). However, negative relationship between size and company's value was found by Premkanth (2013) and Afza,Tahir (2012) for Sri Lanka and Pakistan respectively.

The same results were obtained in the researches Lorie Zorn (2007) for United States and Canada. The authors claim that for larger companies there are more information regarding the management and potential earnings. The same logic is used in the article Zaini Embong (2012) where the impact of size found to be negatively correlated with the cost of equity in the developing country Malaysia.

Therefore, the results of the papers considered are varies from each other. There is no solid statement about dependence of the size of the firm on the P/E multiplier. In this research the average size of the listed firms in the different stock markets is considered.

Return on equity

Profitability is also considered as a fundamental factor. It is usually measured as the ratio of company's net income to its total assets (ROA) or equity (ROE). These multipliers provides information about investment attractiveness of company's shares. The higher is ROE the more profit can be obtained from the unit of equity capital. The researches Faezinia et al. (2012), King and Segal (2008) confirmed the positive correlation between the values of ROA, ROE multipliers and P/E multiplier.

Illiquidity of the stock market

The next fundamental factor, which is used in this research, is the illiquidity of the stock markets. Illiquidity is a measure of the degree to which an asset or security might be quickly bought or sold on the market without affecting the asset's price. The numerous empirical studies confirmed the negative correlation between the stock market liquidity and expected returns (Chordia et al (2000), Huberman, Halka (2001), Pastor, Stambaugh (2003), Martinez et al. (2005)). There are several methods of measuring liquidity: bid-ask spread, trading volume, free float and illiquidity ratio. The most appropriate method is illiquidity ratio, which was proposed by Amihud (2002). It is calculated as the ratio of stock's total return to dollar trading volume scaled to the number of trading days in a year. Amihud confirmed a negative stock price-illiquidity relationship. The result is consistent with the idea that illiquidity raises stock expected returns and lowers stock prices. In this paper illiquidity ratio is defined in the same way: the annual average of the daily absolute return to the (dollar) trading volume on that day. The return on stock is estimated as the ratio of subtraction of the previous days' closing price from the current days' close to the previous days' close. Thus, the illiquidity defined as the ratio of absolute price change to absolute excess demand for trading:

 (10)

· --the number of days;

· --return on stock i on day d of year y;

· --daily traded volume in dollars.

This method was considered by other researches Hasbrouck (2004) and Brennan and Subrahmanyam (1996) and showed its efficiency. Moreover, in the article Hernan (2010) the relationship between liquidity and the cost of capital were investigated. The authors claim that a more liquid assets reduces a firm's cost of unwinding its capital stock and it increases its ability to raise cash which means that the firm is more flexible to a changing business environment especially in a financial crisis. In the more recent research Mohsen (2017) the authors investigated the relationship between the asset's liquidity and the cost of equity for 14808 companies in 52 countries. They found that there is negative correlation between liquidity and the cost of equity as in the previous paper.

In the Table 1 the significance of the commonly used risk factors such as the cost of equity, the cost of debt, ROE, the expected growth rate, the payout rate and the financial leverage on the P/E multiplier is shown.

Table 1. Literature review of the commonly used risk factors

Authors	Sample	Cost of equity	Cost of debt	ROE	Expected growth rate	Payout rate	Financial Leverage
Fairfield, 1994	S&P 500, 1970-1984				Percentage Earings Change
Ramcharran, 2002	21 emerging markets, 1992-1999	Euromoney score on credit risk indicator for each country		Euromoney score on economic performance for each country
Anderson, Brooks, 2006	United Kingdom,1975-2003	Size (MV)
Huang, Tsai, Chen, 2007	USA, 1982-2002	standart deviation of stock returns			analysts' growth rate forecast	Dividend payout ration	financial leverage
		yiled of Baa-rates bonds
		Size (MV)
Afza, Tahir, 2012	Pakistan, 2005 - 2009	Market returns			Tobin's Q	Dividend Payout	financial leverage
		Variability in market price
		Size (Sales)
Huang, Wirjanto, 2012	USA, China, 1997 -2007	Earnings Volatility			EPS growth rate over the past three years
Dudney , Jirasakuldech , Zorn, 2004	S&P 500, 1963-2003	T-Note Yield			Dividend payout ration
		Fama-French SMB Factor	Default Spread		Forecasted Growth S&P500 Index
		Fama-French HML Factor
Faezinia, 2012	Iran, 2005-2011	systematic risk (в)	interest rate	return on equity	expected growth rate	dividend yield	financial leverage

In the Table 2 the significance of the relatively new risk factors such as the average size of the listed firms in the country and the liquidity of the stock markets on the P/E multiplier is shown.

Table 2. Literature review of the relatively new risk factors

Authors	Sample	Size	Liquidity
King and Segal, (2008)	Canada, USA, 1989-2004	Total assets
Liu et al., (2002)	USA, 1982-1999	Market capitalization
Anderson and Brooks, (2006)	UK, 1975-2003	Market capitalization
Harbula, (2009)	Europe, 1986-2006	Market capitalization
Faezinia et al., (2012)	Iran, 2005-2011	Market capitalization
Sehgal and Pandey, (2009)	India, 1990-2007	Market capitalization
Premkanth, (2013)	Sri Lanka, 2007-2011	Market capitalization
Afza and Tahir, (2012)	Pakistan, 2005-2009	Market capitalization
King and Segal , (2006)	Canada, USA, 1989-2004		Free float
Brounen et al., (2009)	Australia, Europe, U.K., USA, 1990-2007		Trading volume Free float Illiquidity ratio
Amihud and Mendelson, (1986)	USA, 1960-1979		Bid-ask spread
Benveniste et al., (2001)	REITs listed in the NAREIT, 1985-1992		Trading volume
Amihud, (2002)	USA, 1964-1997		Illiquidity ratio

According to these papers such fundamental factors as the growth rate, the cost of equity, the debt ratio, the cost of debt, ROE, the size of the firm and the illiquidity of company's shares were defined as the factors which have significant influence on the P/E multiplier. It is worth noting that these articles could be derived into two groups:

· Researches devoted to determine factors that influence on the P/E among the local firm's within one country. In this article samples contain local firms and the authors make regression analysis of the fundamental factors on the multiplier.

· Researches determine how the structure and specific features of the economy influence on the medium P/E ratio of the country using several indexes of the market. The authors make regression of these indexes on the P/E multiplier.

This research is conducted by using the second methodology. It means that we examine the P/E multiplier at the level of the overall markets by using the information for stock exchanges, not considering the local companies for each country.

The authors Harvey, Liu and Zhu, (2015) present approximately 400 factors, of whom 65 macro factors, that may defined as the risk factors for the cost of capital at the level of the market index. In the research the investment climate and economic structure indexes in order to estimate the cost of equity were used.

Based on the foregoing it is reasonable to conclude that analyzed determinants could be considered as the factors of P/E multiplier.

Overall, the investment climate indexes, economic structure indicators, the average firm's size and stock's illiquidity are proved by the previous researches to be significant in estimations of the P/E multiplier.

The hypothesis tested in this study:

H1. The indicators of the investment climate in the country have significant influence on the price dynamics of the Russian stock market.

H2. The structure of the country economy has influence on the price dynamics of the Russian stock market.

H3. The average size and the illiquidity of the market also have influence on the price dynamics of the Russian stock market.

Chapter 2. Research methodology

The main objective of this study is to identify those characteristics that cause an existing discount among different geographical markets. Such determination should be universal. So the sample includes the markets of developed and emerging countries.

It is logical to conduct the analysis in the context of the fundamental determinants considered below, which can be divided into two groups.

The measurable (observable) indicators are:

· The return on equity;

· The payout ratio;

· The cost of debt;

· The size of listed firms;

· The illiquidity level;

· The financial leverage.

The estimated indicators are:

· The equity risk premium;

· The forecasted income growth rate.

The first group includes indicators that are observed and can be measured.

The second group includes indicators, the assessment of which is subjective. The growth forecasts are estimated for the needed period of time by analysts. The data is taken from the International Monetary Fund source. Assessment of the equity risk premium may be formed as the sum of the risk-free rate and risk premiums. In this paper, risk factors of the cost of equity and their impact are researched.

2.1 Research approach

All reviewed researches studies the dependence of P/E multiplier on its determinants without taking into account the functional form of relationship. The reason of taking this approach according to Danilov (2013) is a different goal of the studies, namely: the identification of the determinants to select the most suitable peers for comparative analysis. It is sufficient to determine the existence of dependence of the multiplier on the determinants. Therefore, this methodology ignores the functional dependence of the P/E multiplier on determinants, which lead to incorrect estimation of their impact.

It is reasonable to make our study in two stages:

· To calculate the cost of equity for the country from the observed indicators;

· To determine the risk factors affecting the estimate obtained in the first stage.

2.2 Estimating the cost of capital

The following formula is based on the two-stage model of cash flows discounting:

	(11)

So, the cost of equity could be defined as .

It is worth noting that in the equitation P/E with the zero debt (unlevered) is used, which is obtained from the observed P/E (levered) and the early presented relation.

As the growth rate in the forecast period it is proposed to use the IMF forecast of GDP growth, which published twice a year.

It is proposed to value the forecasted return on equity by taking with the coefficient the current observed value.

The valuation of the forecast return on equity is proposed according to the current observed value.

In terms of parameters of the terminal period, it is assumed that the return on equity and the growth rate converge to the global:

		(12)
		(13)

· --coefficient characterizing the degree of convergence of the forecasted growth to the world growth of GDP; the range of values from 0 to 1;

· --coefficient characterizing the degree of convergence of the forecasted return on equity to the global figures; the range of values from 0 to 1.

To determine the parameters of convergence and duration of the forecast period it is expected to calibrate the model to minimize the differences in the estimates obtained using the model and values of P/E multiplier for the countries which are calculated using Damodaran's cost of equity. By changing three variables (, it is possible to estimate P/E multiplier. To account for the possible influence of differences in the degree of integration of markets of the studied countries into the world economy it is proposed to estimate the parameters for developed and developing countries separately. Considering developed and developing markets separately, the variables ( are chosen in such a way as to minimize the difference between factual P/E values and estimated P/E multiplier using Damodaran's cost of equity. As the calibration is conducted on the large sample of the countries, the calculated values of the variables can be used in this research.

2.3 Specification of the model

Many practitioners have developed various models using different risk factors and different linking these factors.

In this paper, the functional dependence of P/E multiplier on the risk factors ( is considered. In order to estimate the equity risk premium we propose to use the most basic form of the model - multifactor model:

	,	(14)

· --value of the i risk factor.

· coefficient of the sensitivity to the i factor risk.

This form is widely used in identification of risks. In the research we consider MRP along with other risk factors.

The model involves the preliminary estimation of beta for each market. The beta for each market could be estimated:

	,	(15)

· --return of the considered index.

· --return of MSCI World index;

· --covariance;

· --variance of the return of MSCI World index.

The following formula determines the market risk premium (MRP):

	,	(16)

· --risk-free rate.

In this study, the weighted yields on government bonds were used as the risk-free rate. In order to obtain the weighted yields on government bonds 42 countries were considered. Return of MSCI World index is considered as the market return.

Since в is equal to 1 for the global index:

		(17)

In the model MRP is considered along with the other risk factors:

	.	(18)

2.4 Determination of risk factors

The following list demonstrates all risk factors which used in the model.

Dependent variable:

1. The equity risk premium of the stock market.

Control variables:

1. The market risk premium multiplied by the beta calculated for the stock market of the country

2. The indicators of the investment climate

· Doing Business Index

· Economic Freedom Index

· Corruption Perception Index

· Control of Corruption Index

· International Property Rights Index

3. The indicators of the economic structure

· Export Concentration Index

· Export Diversification Index

· Economic Complexity Index

4. The average size of the listed firms on the stock market of the country

5. The illiquidity of the stock market of the country

Market risk premium is considered one of the risk factors in the model. The market risk premium multiplied by the beta estimated for one-year period is denoted as MRP*Beta1 and could be estimated:

		(19)

--beta for i country considering the one-year period;

The more complex risk factors are shown in the following article. Harvey, Liu and Zhu, (2015) present approximately 400 factors, of whom 65 macro factors, that may defined as the risk factors for the cost of capital at the level of the market index. However, in this paper we propose to focus on those factors, which can be reached in the analysis of our main case--Russia's investment climate and economic structure. Each factor is presented in several variants, which reflect different aspects of the problem.

In terms of the investment climate were proposed the following indicators:

Rating “Doing Business Index” (World Bank)--a comprehensive assessment of legal acts regulating business activity and ensuring compliance with them;

The ranking of “Economic Freedom Index” (Heritage Foundation)--a comprehensive assessment of the absence of government interference or obstruction of production and the distribution and consumption of goods and services, except as necessary for the citizens to protect and support freedom as such;

The “Corruption Perceptions Index” (Transparency International)--an assessment of the analysts and entrepreneurs of the corruption level;

The “Control of Corruption Index” (The Millennium Challenge Corporation)--an assessment of the extent to which public power is exercised for private grain, including both petty and grand forms of corruption.

The “International Property Rights Index” is a measure of the legal and political environment, physical and intellectual property rights.

In terms of the economic structure, the indicators that may show low competitiveness of the economy were considered:

The “Export Concentration Index” presents the range of goods exported by the country:

	,	(20)

· i--index of the item (from 1 to 239);

· 239--number of product types classified by the UN;

· x_i--value of exports of i good in the country;

· x--total value of exports of the country.

If ConcenEx tends to 0, there is a positive trend (a wide range of exported products); if ConcenEx tends to 1--the trend is negative (a narrow range of exported products).

The “Export Diversification Index” shows the deviation of the export structure from the structure of world exports:

	,	(21)

· --share of i commodity in total exports of the country;

· --share of i commodity in total world exports.

If DiversEx tends to 1, the export structure of the country is close to the average; if DiversEx tends to 0, the export structure of the country is significantly different from the world.

The “Economic Complexity Index” shows the relationship between the degree of diversity and complexity, the country produced industrial goods and its level of well-being and development potential. Hartmann et. al. (2017) documented a strong and robust correlation between the economic complexity index and income inequality. The authors confirmed that this relationship is robust to controlling for measures of income, education, and institutions. Their findings show that economic complexity captures information about an economy's level of development that is relevant to the ways an economy generates and distributes its income. The data of their research contains 150 countries for the period 1963-2008.

The natural logarithm of market capitalization is used as the proxy of size. Thus, the risk factor “Size” is the natural logarithm of average market capitalization of the listed firms in the stock market of the country. The coefficients of the stock exchanges' average sizes are weighted by the number of the listed firms.

		(22)

· i

· j

· nnumber of the listed firms in the stock exchange j of the country i

· weighted natural logarithm of the average market capitalization of the listed firms in the stock market of the country i

· natural logarithm of the average market capitalization of the listed firms in the stock exchange j of the country i

· number of the listed firms in the stock exchange j of the country i

The illiquidity of the stock exchange, which was described in the Chapter 1, is also considered as the risk factor of the cost of equity:

		(23)

· the number of days;

· --return on index i on day d on year y;

· --daily traded volume in dollars.

2.5 Description of the risk factors

In the model market risk premium multiplied by beta, economic structure and investment climate indexes, average firm's size and stock's illiquidity are used. The beta is calculated for one, two and five historical years.

Table 3. The list of MRP multiplied by betas estimated for different periods

Variable	Description
MRP*Beta1	MRP multiplied by the one-year beta of the country
MRP*Beta2	MRP multiplied by the two-year beta of the country
MRP*Beta5	MRP multiplied by the five-year beta of the country

In the model five investment climate indexes are used. There is a high correlation between each other as they determine one problem from different sides. The indicators of the investment climate are published for the year by the World Bank. Thus, the indicators take the same numbers within the year.

Table 4. The list of the indicators of investment climate:

Variable	Description
DoingBusin	Index «Doing business»
EconFreed	Index «Economic freedom»
CorrPer	Index «Corruption Perceptions»
ContCorr	Index «Control of Corruption»
PropRights	International Property Rights Index

The indicators of the economic structure are published also for the year by the World Bank. Thus, the indicators take the same numbers within the year.

Table 5. The list of the indicators of the economic structure:

Variable	Description
ExpConc	Index of export concentration
ExpDiver	Index of export diversification
ECI	Index of economic complexity

According to literature review (Table 2) average firm's size and illiquidity ratio are expected to have an influence on the P/E multiplier.

Table 6. The list of the other risk factors:

Variable	Description
AverSize	Natural logarithm of the average market capitalization of the listed firms in the stock market
IlliqRatio	Illiquidity ratio

The variable R_e-R_f is the difference between the return on the i country stock market and the risk-free rate of return:

		(24)

The risk factor “AverSize” is the natural logarithm of average market capitalization of the listed firms in the stock market of the i country. The coefficients of the stock exchanges' average sizes are weighted by the number of the listed firms.

The illiquidity ratio is ratio of stock market return to number of days and volume traded denominated in dollar currency. The illiquidity of the stock exchange is estimated for each month.

2.6 Regression equations

The novelty of this research is using two stage discount model to estimate P/E multiplier target values. In order to estimate the cost of equity the average firm's size, stock's illiquidity and the indexes which describe the investment environment and economic structure of the country were used. Proposed risk factors are proved to be significant in explaining the P/E multiplier in the previous researches as has been shown in section 1.2.

According to correlation matrix (Table 13) there is a high correlation among MRP multiplied by betas estimated for different periods, correlation among the indicators of investment climate, correlation among the indicators of the economic structure. Is means that all the indicators cannot be used simultaneously in the regression equations due to the problem of multicollinearity. The solution of this problem is the following: all the possible combinations of the risk factors should be constructed in order to avoid multicollinearity and then the best one should be chosen. Thus, highly correlated variables are distributed into three groups:

· MRP multiplied by betas estimated for different periods;

· The indicators of the investment climate. Despite the fact that they measure different aspects of the investment climate, these indicators are systemically linked;

· The indicators of the economic structure are also highly correlated.

The index of economic complexity correlated with the indicators of economic structure and the investment climate. This can be explained by the fact that the investment climate has a significant impact on the innovativeness of the economy, which also determines the economic structure.

Taking into account that there are three identified groups of the correlated indicators, the risk factors from each group are considered separately in order to avoid the multicollinearity. All possible equations will be formed, and regression analysis will be provided.

In the research were used two specifications (MRP along with the other risk factors).

The first specification is considered with all indexes except ECI due to high correlation (Table 13):

The second specification is considered with alone ECI index:	(25)
	(26)

Overall, for the used specification model there are 27 equations. Adjusted R² will be calculated for all equations. The most appropriate equation will be chosen according to the highest value of adjusted R². Then the target P/E multiplier for the Russian stock market will be estimated, and the interpretation of the obtained results will be provided.

3. Empirical research

3.1 The sample

The data were collected on markets (and respective countries) for the period 2006-2016, which according to the classification of the MSCI index includes developed and developing markets, and for which information is available on the testing risk factors. The main reason of dividing all countries into two baskets is that the factors n, g and ROE in post-forecast period of the two stage discount model which is used for estimating P/E multiplier should be determined individually for developed and developing countries. The growth rate and ROE for developed markets are expect to be more converge to the global values.

Table 7. Considered countries in the research

Developed countries	Developing countries
Australia	Argentina
Austria	Brazil
Belgium	Bulgaria
Canada	Chile
Czech Republic	China
Denmark	Egypt
Finland	Greece
France	India
Germany	Indonesia
Hong Kong	Mexico
Ireland	Peru
Italy	Philippines
Japan	Poland
Netherlands	Qatar
New Zealand	Romania
Norway	Russia
Portugal	South Africa
Singapore	South Korea
Spain	Thailand
Sweden	Turkey
Switzerland
United Kingdom
United States

The data were collected using the following sources:

Table 8. Data sources

Indicator	Source
The stock market index The average size of the listed firms The average P/E multiplier for the stock market Financial leverage Return on equity Volume traded	Bloomberg
The GDP growth forecast	The World Economic Outlook (IMF)
Doing Business Index Economic Freedom Index Corruption Perceptions Index Control of Corruption Index International Property Rights Index Export Diversification Index Export Concentration Index	The World Bank
Economic Complexity Index	The Observatory of Economic Complexity

The data were collected monthly. However, the data on the ratings and indexes of risk factors are published for a year, so within one year have the same value. The GDP forecast is published twice a year. The Damodaran cost of equity estimation values for the countries which were published annually were used to calibrate coefficient in the two stage discount model.

3.2 Results

In the research the main task is to obtain the P/E multiplier by using two stage discount model and the regression equation of the cost of equity to fundamental factors. On the first stage the two stage discount model (equation 11) were calibrated to factual P/E multiplier values. In the following table the coefficient for the developed and developing markets are provided.

Table 9. The converge coefficients for two stage discount model

	Developed countries	Developing countries
	1	0.2
	0.4	0
n	7.5	10

On the calibrate stage we obtained the convergence coefficients for the growth rates and ROE by using Damodaran's cost of equity estimations. Solving the problem |PEdamodaran - PEactual| = min the convergence coefficients were obtained. The coefficient n determines the number of years of forecasted period in the two stage discount model. Higher coefficients of a_g and a_roe shows that the developed markets are more converge into the world economy comparing with the developing ones. The less value of coefficient n shows that for the developed countries it will take less time to come to stable growth.

In order to determine relevance of the coefficients the sensitivity test is provided. In the modelling for the sensitivity value is taken the ratio

.

The results are shown in the following table.

Table 10. The cost of equity sensitivity test

	Sensitivity value
	0.017
	0.03
n	-0.08

The sensitivity value shows the low dependence of the cost of equity on a_g, a_roe and n coefficients. Thus, the obtained solutions of the PE multiplier are not in dependence with these parameters.

In all regressions market risk premium (MRP) was used. MPR is calculated by the equation (17). Based on the MSCI World index the MRP was estimated and the values are provided in the Picture 3.

Picture 3. Estimated market risk premium global

The most of the period MRP is taking values between 4% and 6% what is corresponds with the previous research (Fernandez, 2013). In the 2009 year MSCI World index reached the minimal value due to world crisis in 2008-2009 years.

In the model weighted risk-free rate is used (Picture 4). Stock exchange market capitalization is considered as a weight for the countries risk-free rate.

	(27)

· SE market cap_i - stock exchange of i country market capitalization;

· Countries risk free rate_i - risk free rate for i country;

· Total market cap - sum of all stock exchange market capitalization.



Picture 4. Weighted risk-free rate

Weighted risk-free rate takes values close to United States risk-free rate which is the yield on 10-year US government bond.

Since the two stage discount model was specified we could turn to regressions of the cost of equity upon fundamental factors. The descriptive statistics of the factors is provided.

Table 11. Descriptive statistics of the risk factors

Variable	Mean	Std. Dev.	Min	Max
MRP*Beta1	0,10	0,05	0,00	0,21
MRP*Beta2	0,10	0,04	0,00	0,19
MRP*Beta5	0,10	0,04	0,00	0,18
ECI	0,93	0,71	-0,85	2,60
DoingBusin	0,86	0,09	0,61	1,00
EconFreed	0,69	0,09	0,50	0,90
ContCorr	0,76	0,25	0,11	1,00
CorPerc	0,65	0,09	0,05	0,95
PropRights	0,69	0,12	0,32	0,87
ExpConc	0,44	0,11	0,24	0,69
ExpDiver	0,64	0,22	0,10	0,95
AverSize	9,90	1,54	7,15	14,18
IlliquidRatio	12,91	20,94	0,03	101,40

The first 1% and the last 1% percentiles were dropped as outlying observation. Overall, there are more than 4800 observations. From the table we could conclude that the equity risk premium varies from 0% to 21% with standard deviation around 4%. The values of indexes are in range of 0 and 1, except ECI. The average size is calculated by taking the logarithm of the size and it's taking values between 7 and 15. Illiquidity ratio is calculated by dividing module returns to volume traded in the period in dollar currency and number of the days, then normalized by multiplying 10⁹. Developed countries taking values of illiquidity ratio in a range of 0 and 102.

Table 12. Comparison of the standard deviations between and within group regressions

Variable	Std. Dev. between	Std. Dev. within
MRP*Beta1	1,12149	0,03062
MRP*Beta2	1,61755	0,05030
MRP*Beta5	0,76952	0,04503
ECI	0,00578	0,00290
DoingBusin	0,05803	0,01341
EconFreed	0,07095	0,03707
ContCorr	0,05778	0,01773
CorPerc	0,06390	0,01073
PropRights	0,05612	0,01023
ExpConc	0,04722	0,02683
ExpDiver	0,06171	0,02403
AverSize	0,00226	0,00133
IlliquidRatio	0,00019	0,00003

In the Table 12 the statistics is shown in the context of varying time (within) and countries (between). The fluctuations of risk factors across the countries (between) take higher values comparing with one country over the period (within) because for structural improvement in the country huge reorganization are needed.

The correlation matrix is provided for the risk factors is shown in the Table 13.

Table 13. Correlation matrix

	eci	doingbus	econfree	contcorr	corper	proprights	expconc	expdiv

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