Model Risk Analysis of Multiplier Technology Applied at Stock Valuation of Russian Companies

This work is a new direction in the authors’ previous study on applying the market multipliers in assessing the value of oil and gas companies. The work is based on the findings of statistical studies of multipliers calculated for the industry, as well as their volatility over a 12-year period — from 2006 to 2017 inclusively, as exemplified by 46 companies from nine sectors of the economy of the Russian Federation. The analysis of the risk measures Value-at-Risk (hereinafter VaR) and Expected Shortfall (hereinafter ES) was conducted by means of volatility calculated in different ways. In particular, the multiplier volatility was introduced by V. B. Minasyan. It was established that for all nine sectors of the Russian economy, calculated with conventional stock volatility statistics (when possible), risk valuation measures VaR and ES led to lower calculated risk values compared to those calculated using multiplier volatility. The results of the study are of interest to evaluators, investors and other interested parties, as it allows to analyze the general behavior of the stock value in Russian companies and to compare the change in indicators of various economic sectors in terms of multiplier technology.


INTRODUCTION
Speaking about company valuation, it is important to mention various approaches, models with their own advantages and disadvantages (see, for example, [1]). Today, experts note an increasing number of mergers and acquisitions 1 [2], which emphasizes the additional interest in quick and efficient company valuation with minimum resources.
The data necessary for a qualitative company valuation, especially if they are not public, are 1 M&A market in Russia. Overview by KPMG. February 2019. URL: https://assets.kpmg/content/dam/kpmg/ru/pdf/2019/02/ ru-ru-ma-survey-feb-2018.pdf (accessed on 27.09.2019). not always available. Moreover, required indicators often change due to the high market volatility. What values should be used in a particular valuation model?
To evaluate stocks by the multiplier technology, the expected value estimated statistically often replaces their value.
Based on the example of 46 Russian companies, the results of multiplier behavior study by D. G. Ivko [3][4][5] show that multipliers have very high volatility both in industries and in specific companies. Therefore, the realized multiplier value will not necessarily be close to the expected value or to the value at the selected moment. This may lead to a significant deviation of the real stock value from its valuation results when the multiplier method is applied.
Company valuation is mainly associated with decisions on purchase or sale of an asset, a merger and acquisition transaction. In such cases, incorrect valuation of a company or asset can affect the yield or contribute to loss of a deal for a potential investor.
The subject of this study is the risks associated with using multiplier technology in its various versions.

MULTIPLIER TECHNOLOGY FOR STOCK VALUATION AND THE RELEVANT RISKS.
DESCRIPTION OF THE SAMPLE OF COMPANIES In the Russian Federation, a market (comparative) approach is widely used for company stock valuation. The approach is based on the market multiplier method. The valuation considers the information about the company compared to similar companies within the industry by other key performance indicators (see, for example, [1]), or compared to the industry indicators.
This approach suggests that these companies should be quoted at the same multiplier values.
There is a number of studies by European and American companies. However, the Russian stock market is relatively young and a series of minor shock news can increase the volatility of stock value indicators, etc. [6][7][8][9].
The "relative youth" of the mechanisms is an additional factor to be considered when using conclusions based on statistics from Western companies.
It is important that when applying the multiplier calculated for the industry, its real (fair) value for a particular company can deviate greatly from the corresponding estimate, since it is an average indicator for companies in the target industry. When using a multiplier of a public company, similar within the industry or in terms of operating activity, business structure or other key indicators, often they use either a statistical estimate of its expected value, or it is determined at a certain moment of time (for example, at the current moment of valuation). The result of applying the multiplier method described above depends on the choice of a similar company. In particular, the expected value of the multiplier of a similar company, as well as its value at a selected moment, can deviate greatly from the value at the time of the quote or deal. Obviously, the valuation quality is low.
The study examines how significant this deviation can be and how this will affect the valuation risk of companies from nine leading sectors of the Russian economy. Table 1 presents a list of the Russian economic sectors and the result of a sample of industry companies included in the MICEX index as of December 31, 2016. Some works, for example, the one by V. A. Cherkasova [2], explore methods to select the so-called peer companies for valuation and describe the application of certain models to calculate corrective indicators. The approach using corrective indicators requires certain parameters and resources for the calculation. In practice, many evaluators use the multiplier technology due to its simplicity and speed of obtaining the stock valuation to make appropriate decisions.
A lot of research is devoted to this method and its application. A significant work by J. Liu, N. Doron and T. Jacob [10] is one of them. Other authors (S. Seghal, A. Pandey [11], C. Cheng and R. McNamara [6], E. F. Fama, and K. R. French [8]) have studied various aspects of the relationship of company multipliers with their profitability and value indicators. R. Barnes [7] and D. Koutmos [9] have investigated the connection between the volatility of stock prices of companies and their individual indicators.
Following is the work by D. G. Ivko [4,5], that studied the volatility of the multipliers P/E and P/B and their influence on the volatility of stock prices of Russian companies. We provide the volatility calculations for nine sectors of the Russian economy and the selected companies from the respective sectors for 2006-2017 inclusively. Table 2 shows the data from the telecommunications industry and PJSC "ROSTELECOM". Appendix 1 presents the results for the other sectors -the input data, on which only calculation results will be presented below. Table 2 shows the expected values and standard deviations of both absolute and relative values of the multipliers P/E and P/B at the industry and company level. The values of the multipliers and their volatility are quite high. Thus, using the multiplier calculated for the industry as part of valuation of the selected company at the moment, one can make a serious mistake due to the possible deviation of the multiplier calculated for the industry from the multiplier of the selected company and due to the significant volatility of the multiplier calculated for industry.
For example, replacing the multiplier P/B calculated for the industry with a multiplier of a similar company is even worse. Thus, ROST-ELECOM, which is a public company, is the best similar company for itself. However, in this case, the significant volatility of its multiplier is obvious.
Therefore, the value of the company multiplier -both its expected value and the data at any particular moment (for example, during the valuation) -can significantly differ from the real value of the company multiplier at the time of a quote/deal. For non-public companies, there will also be a difference between the selected and the similar company. Obviously, there are significant risks in stock valuation of Russian companies as part of the multiplier method.
Following the study by D. G. Ivko on the presence and significance of the correlation of stock price volatility with the volatility of the considered multipliers [3,4], the current study was   Table 3 presents the values of the correlation coefficients between the volatility of returns and the multipliers calculated for the industry. They show a periodically different, but significant statistical relationship between relative changes in the index calculated for the industry and the corresponding multipliers in seven out of nine industries.
The result makes us think about the quality of the valuations by the multiplier technology as applied to Russian companies.
In general, for the entire period from 2006 to 2017, for the telecommunications industry, the correlation coefficients between the volatility indicators of the portfolio index returns and the P/E portfolio volatility indicators and between the indicators of the portfolio index return volatility and the P/B portfolio volatility returns are

Results of correlation coefficients
Between the volatility of returns on the portfolio's index and the volatility of returns on P/E portfolio close to zero. Now, the "behavior" of the indicators by year within the studied period should be considered in more detail. Table 4 makes it clear that only in two cases out of 12 none of the indicators "showed" a high level of connection (in 2007 and 2013). Over a number of years, the coefficient generally changes the sign from "+" to "-". In this industry, one should consider not only the impact of the financial crisis in the economy in 2008-2010 and in 2014, but also the features of the industry itself, the specifics of the telecommunications company. Thus, in 2006-2011 and 2012-2017, this group does not fully reflect the situation on the market and one should consider the annual calculation results.
The multipliers P/E and P/B were chosen as the most common and basic indicators that evaluators often check first. This study can additionally be conducted for other equally important multipliers: EV/EBITDA (company value / profit before taxes, interest and depreciation), P/ CF (price / cash flow) or P/DIV (price / dividends) and others.
Further, to assess the model risk (multiplier technology), we used the method of model risk analysis in stock valuation proposed by V. B. Minasyan [12].
On the example of the method by V. B. Minasyan, it is expedient to conduct calculations for the telecommunications industry, thereby showing that the method is accessible and requires minimal knowledge of statistics and econometrics to be applied. The results are explained below.

ASSESSMENT OF RISK MEASURES VAR AND ES USING MULTIPLIER VOLATILITY FROM VARIOUS SECTORS OF THE RUSSIAN ECONOMY
The stock price in the next time period depends not only on factors such as the current level of development and the situation in the company, industry, sector and region, but also on the perception of information about the company  by its external consumers: investors, regulatory authorities and other market participants. Thus, the price behaves as a random variable. Of course, the stock price volatility is also significantly affected by speculative operations, sometimes not related to the fundamental characteristics of a company's financial performance, but more related to the ability to use specific information that has a short-term effect or its specific perception. Following assessment risks are of particular interest for the study. The importance of stock price volatility is increasing for potential investors.

Results of the calculated values of the correlation coefficients by years in the telecommunications
In his work [12], V. B. Minasyan first introduced the term "multiplier" stock volatility, i. e. proposed a method to express stock price volatility through the volatility of company multipliers. This interpretation of stock volatility became possible due to the dependence of stock volatility on the volatility of the multipliers P/E and P/B for Russian companies.
The "multiplier" volatility of stocks is a new method to estimate their volatility based on the volatility of the multipliers P/E and P/B considered in the study. In this paper, the multiplier estimates of expected prices and their volatility will be denoted by (P), respectively, depending on whether the multipliers P/E and P/B were used. In our opinion, this method will be especially relevant for non-public companies for which there is no available stock price quotation data.
Thus, the following statements are true for the multipliers P/E and P/B [12]: (For details related to the idea of multiplier volatility and the derivation of formulas, see [12]).
VaR p (Value at Risk) indicator is often used to determine the risk of stock investment. VaR p is the maximum possible deviation for the worse from the company's stock price from its expected value in a set time period T with a given confidence probability p [12][13][14][15].
The formula to calculate Value at Risk is: -is the price volatility (here, calculated as its standard deviation for the period τ (days); T -is the investment horizon (days); 0.1 p k -is the quantile of standardized stock price distribution with the confidence probability p [12][13][14][15].
In addition to VaR, it is necessary to calculate the Expected Shortfall with the confidence probability p, , p ES reflecting the average value of price deviations from its expected value, which could potentially occur in the worst-case scenarios implemented with a probability of 1 -p [12][13][14][15].
The formula to calculate the Expected Shortfall is: where π ≈ 3.14, and the standard notation for the exponential function is applied exp(x) = e x , where e ≈ 2.71.
In these VaR and ES formulas, volatility values are usually provided by the statistical estimates from a sample of the company's stock price quotations. Since it is now possibile to determine multiplier estimates of the stock price volatility σ M (P) and σ B (P), we will calculate the VaR and ES multiplier values, which we denote by In the example below, these risk measures will be calculated with the confidence probabilities of 0.95. However, depending on the mission, another confidence probability, different from 0.95, may be chosen.
In terms of the proposed technology, we will now provide the detailed calculations of ROST-ELECOM's stocks valuation and the risks of investing in it in three ways: 1. Risk assessment of investing in the company's stocks by usual stock volatility values.
2. Risk assessment of investing in the company's stocks by values of the multiplier P/E and the multiplier valuation of stock volatility.
3. Risk assessment of investing in the company's stocks by values of the multiplier P/B and the multiplier valuation of stock volatility.
Suppose, the management of the company that invested in ROSTELECOM's stocks knows that this company will face serious financial difficulties if the stock price falls below 15 rubles in a year (in 2018). The investor wants to be sure that a probability of difficulties is no more than 5%. It is important to understand whether this scenario is reliable. What will the average stock price be after 5% of the worst-case scenarios are implemented? We expect normal distribution of the stock price within the calculations provided below.

Risk assessment of investing in the company's stocks by usual stock volatility values.
Statistical Despite the fact that at the end of 2018, the company expects the stock price to be143.93 rubles, in the worst-case scenarios, implemented with a probability of 5%, the average expected price can be 143.93 -135.66 = 8.26 rubles <15 rubles. On average, in 5% of the worst-case scenarios, the investors in ROSTELECOM expect serious financial difficulties.

Risk assessment of investing in the company's stocks by values of the multiplier P/E and the multiplier valuation of stock volatility.
To calculate the expected value of ROSTELE-COM at the end of 2018, we first apply industry estimates of the expected value and volatility of the multiplier P/E and the expected profits and profit volatility of ROSTELECOM, provided in  With a probability of 5%, the company's stock price may become less than expected by 756.37 rubles compared to the expected value. Thus, when using the multiplier P/E with a probability of 95%, we can expect the stock price to be no less than 143.77 -756.37 = -612.60 rubles. Given that the stock liability is limited by the stock price, we understand that the stock price cannot be negative. The model claims that in the worst-case scenario, the expected stock price will be zero with a probability of 95%. According to the multiplier model, the company's stock will cost nothing with a probability of more than 5%.
To estimate the average stock price, which may occur in 5% of the worst-case scenarios, we will calculate Despite the fact that the company expects the stock price to be 143.77 rubles by the end of 2018, in the worst-case scenarios, implemented with a probability of 5%, the average expected price can be 143.77-937.58 = -793.80 rubles. On average, in 5% of the worst-case scenarios, the investors in ROSTELECOM expect serious financial difficulties associated with a complete loss of the value of the acquired stocks.
In some cases, using the multiplier valuation of a specific stock in calculations, the comparative method does not use the expected value of the multiplier calculated for the industry, but the expected value of the multiplier of a similar company.
ROSTELECOM is a public company and may act as a similar company itself. Let us recalculate, applying the expected value and standard deviation of ROSTELECOM's multiplier P/E. We get the following results: With a probability of 5%, the company's stock price may become 333.47 rubles less than expected. Thus, when using the multiplier P/E with a probability of 95%, we expect the stock price to be no less than 136.88 -333.47 = = -196.59 rubles. Given that the stock liability is limited by the stock price, we understand that the stock price cannot be negative. The model claims that in the worst-case scenario, the expected stock price will be zero with a probability of 95%. According to the multiplier model, the company's stock will cost nothing with a probability of more than 5%.
To estimate the average stock price, which may occur in 5% of the worst-case scenarios, we will calculate Despite the fact that the company expects the stock price to be 136.88 rubles by the end of the next year, in the worst-case scenarios, implemented with a probability of 5%, the average expected price can be 136.88 -413.36 = -276.48 rubles. On average, in 5% of the worst-case scenarios, the investors in ROSTELECOM expect serious financial difficulties associated with a complete loss of the value of the acquired stocks.

Risk assessment of investing in the company's stocks by values of the multiplier P/B and the multiplier valuation of stock volatility.
To calculate the expected value of ROSTELE-COM at the end of 2018, we first apply industry estimates of the expected value and the multiplier P/B volatility and the expected profits and profit volatility of ROSTELECOM, provided in With a probability of 5%, the company's stock price may become less than expected by 306.54 rubles compared to the expected value. Thus, when using the multiplier P/B with a probability of 95%, we can expect the stock price value to be no less than 241.73 -306.54 = -64.80 rubles < 15 rubles. Thus, a probability of serious difficulties is more than 5%.
To estimate the average stock price, which may occur in 5% of the worst-case scenarios, we will calculate Despite the fact that the company expects the stock price to be 241.73 rubles at the end of 2018, in the worst-case scenarios, implemented with a probability of 5%, the average expected price can be 241.73-379.97= -138.24 rubles. On average, in 5% of the worst-case scenarios, the investors expect serious financial difficulties associated with a complete loss of the value of the acquired stocks.
We apply the expected value and ROSTELE-COM's multiplier volatility:  With a probability of 5%, the company's stock price may become less than expected by 234.49 rubles compared to the expected value. Thus, when using the multiplier P/B for company valuation with a probability of 95%, we can expect the stock price to be no less than 112.14 -234.49 = -122.35 rubles.
Given that the stock liability is limited by the stock price, we understand that the stock price cannot be negative. The model claims that in the worst-case scenario, the expected stock price will be zero with a probability of 95%. According to the multiplier model, the company's stock will cost nothing with a probability of more than 5%.
To estimate the average stock price, which may occur in 5% of the worst-case scenarios, we will calculate Despite the fact that the company expects the stock price to be 112.14 rubles at the end of the next year, in the worst-case scenarios, implemented with a probability of 5%, the average expected price can be 112.14-290.67= -178.53 rubles. On average, in 5% of the worst-case scenarios, the investors expect serious financial difficulties associated with a complete loss of the value of the acquired stocks.
This example shows the huge risks for the counterparty in the stock valuation by a comparative method using multipliers that can be applied by the evaluator.
It should be noted that the valuation method using multipliers is most frequently applied in equity valuation of non-public companies. For public companies, market valuation is considered the best. At the same time, it is not possible for non-public companies to obtain an estimate of the expected stock price at the end of the next period based on quotes. Therefore, the estimates obtained by using multipliers have nothing to compare.
It should be noted that only 16 of the 46 companies represented in this study did not have serious problems with indicators of net profit and book value, i. e. these indicators had a positive value from 2006 to 2017. This fact further emphasizes the risks of obtaining high-quality estimates by multiplier technology using P/E and P/B. The example of the public company ROSTE-LECOM is interesting as it provides estimates of the company's expected stock prices applying quotes and the expected values of the industry multipliers P/E and P/B. Also, the risks of investing in ROSTELECOM stocks were assessed based on risk measures VaR and ES calculated on normal distribution applying the usual statistical estimation of volatility and of the P/E and P/B multiplier volatility. Table 5 provides the results. Appendix 2 presents the data on the other sectors where one company, the industry representative, was selected.
The above example makes it clear that the company's expected stock valuation by the multiplier method significantly deviate from its statistical estimation.
The difference in estimating the multiplier volatility of the company's stocks using both multipliers is much altered from the usual statistical volatility estimation. This leads to the fact that both the risk measure VaR and the risk measure for catastrophe ("tail"), calculated using multiplier volatility, ultimately provide higher estimates of the corresponding risks compared to the statistical estimation of volatility. These significant differences in assessing the risks of stock investment are associated both with a high risk of valuation using the multiplier method, as well as with the fact that the usual, historical volatility estimation assumes that the future will be an average repetition of the stock history of a particular company. The multiplier volatil-V. B. Minasyan, D. G. Ivko Table 5 Calculation ity estimation may contain information about "fundamental" changes in the industry that may not have happened in the company yet, but may affect it in the future. This may be the added value of a multiplicative estimation of the company's stock volatility.

results of the expected value of investments in ROSTELECOM stocks and the risks of these investments based on risk measures VaR and ES
It is worth noting that the normal distribution of stock prices was expected in the example above, which is not quite realistic. As a rule, in a real situation, the distribution has a thicker left tail. For this reason, risks can only be greater than the estimates obtained in our example. Moreover, the purpose of this study was to compare relative values of risk assessments using various assessment methods and constant assumptions about the distribution law.

CONCLUSIONS
The work studied the multiplier method, a classic and commonly used assessment method. The authors calculated the risks of the method use in stock valuation of Russian companies from nine industries. The expected industry average value was used to estimate the multipliers. It is worth revealing how significant the volatility of the applied multipliers is within the industries, i. e. location, distribution by companies within the industry and distribution over time, and how it affects our valuation. The original method of multiplier estimation of stock volatility was used [12]. It clears the estimation of the short-term background and brings it closer to the fundamental industry related to the nature of the business. The risk measures VaR and ES were assessed based on the multiplier volatility estimation. It makes it possible to obtain a different assessment of risk measures to be considered when deciding on long-term investments.
The paper emphasizes the general behavior of the stock value of Russian companies in 2006-2017 depending on the industry. This will help in making decision on the purchase/ sale of stocks. It will also provide an opportunity to compare the behavior of indicators between the economic sectors in terms of the multiplier technology for Russian companies' stocks.
The model risk analysis in stock valuation proposed by V. B. Minasyan [12] can be used by any market participant to check estimates of the stock value of Russian companies, both public and non-public, from any industry and any country.
The Russian stock market is relatively young compared to the Western ones (officially, the New York Stock Exchange was founded in 1817, the London Stock Exchange -in 1801, the modern Russian stock market was formed in 1991-1992). Therefore, it is important to apply Western approaches in the stock valuation of Russian companies very carefully.