Nonmarketable Assets Version of the CAPM: The Case of the Russian Stock Market 173 Российский журнал менеджмента Russian Management Journal 16 (2): 173–186 (2018) 16 (2): 173–186 (2018)

теоретические и эмпирические исследования

Nonmarketable Assets Version of the CAPM: The Case of the Russian Stock Market

A. V. Bukhvalov Graduate School of Management, St. Petersburg University, Russia L. Z. Bokuchava Master Program Graduate, St. Petersburg University, Russia

The paper deals with a modification of the CAPM, being called the Mayers model, which takes into account the existence of nonmarketable assets. Human capital is the classic example of such assets though we present and discuss some other important examples. This ap- proach, as well as more advanced conditional CAPM, gives a correction to traditional CAPM beta coefficient as a measure of market risk. In this paper we present two attempts to test CAPM with nonmarketable assets. First, we start from analysis of the small size effect of the Russian stock market. We show that in this case the Mayers model gives the possibility of substantial improvement of risk exposure estimate. Second, empirical analysis in the case of human capital shows no impact of the Mayers model in all sectors of the Moscow Stock Exchange other than Innovation. Keywords: nonmarketable assets, CAPM, the Mayers model, Russian stock market, human capital. JEL: G11, G12, G32, J24.

Capital Asset Pricing Model (CAPM) is cen- survey [Bukhvalov, 2016] the author char- tral for the discipline of corporate finance. acterized the current status of the model as During her more than half-of-the-century the foundation of the modern managerial history it has been many times criticizing, theory of the firm. CAPM has transformed rejecting, modifying and reviving. Modern from the tool aimed for asset traders to standing of CAPM, of course, shows tremen- really universal model. Now it is reflecting dous qualitative transformations. In recent and guiding every firm’s managers’ efforts

Research of the first author was conducted with financial support from the grant provided by St. Petersburg University (project No. 16.23.1460.2017). Postal Address: 3 Volkhovskiy per., Graduate School of Management, St. Petersburg University, St. Petersburg, 199004, Russian Federation. © A. V. Bukhvalov, L. Z. Bokuchava, 2018 https://doi.org/10.21638/spbu18.2018.201 174 A. V. Bukhvalov, L. Z. Bokuchava through the modified concept of systematic some principle issues we still need to return risk (cf. [Babenko, Bo­guth, Tserlukevich, back to not very technical versions of clas- 2016]). On the other hand, new model is sical CAPM and its modifications. It is even consistent with modern empirical trends in more reasonable because new theorists still asset pricing and trading. keep the place for application of CAPM for In this paper we will return back to the WACC evaluation and, hence, for investment early days of CAPM’s modification, i. e., to projects appraisal (see [Bukhvalov, 2016, the CAPM with nonmarketable assets. This Section 5]). That’s why we devoted this paper model appeared in the beginning of 1970s to the Mayers model. in the stream of M. Jensen’s research, which The notion of nonmarketable asset should treated CAPM as a particular case of general not been treated literally. Any nonmarket- equilibrium model [Jensen, 1972]. It was able asset can be “a little bit” traded. It invented by David Mayers, his student (see means that in a certain sense it can be sold [Mayers, 1972; 1973]). and bought with higher transaction costs, CAPM with nonmarketable assets allows or unusual efforts are needed to maintain assets owned by investors who obtain uncer- trade, or its liquidity is very low and price is tain income from this ownership but public uncertain, or institutional barriers for trade trades in such assets is impossible due to exist (but still workaround in possible), and institutional or technological issues. Mayers so on. This issue was discussed for the case himself saw the main interpretation of such of human capital as early as [Fama, Schwert, assets as a form of human capital.1 For that 1977] paper has appeared. It is very difficult reason he used sub/superscipt H for them. to model such “a little bit” feature. This Classical CAPM and the Mayers model notice was a starting for [Bukhvalov, 2008] as its extension until very recently were where the Mayers model was expanded to the only theoretical models in asset pricing include new areas of applications. theory, which had solid economic foundation Main contributions of [Bukhvalov, 2008] in the equilibrium theory. Multifactor asset are the following. First of all, a new manage- pricing models that followed the appearance rial model of the firm was invented. It was of the Fama–French three-factor model had assumed that the firm has two types of inves- applied econometrics origins. They obviously tors: most interested investors (key owners, were better fit into reality but three factors top managers, activist members of the corpo- in few years became four- and then five- rate board) and outsiders (all other sharehold- factor models. Further it became clear that, ers and speculators). This is an institutional for example, any factor related to asymme- and rather stable division. Its importance is try of returns can be associated with econo- explained by institutional asymmetry, which metrically sound risk premium, i. e., a new is caused by ability for the most interested factor. Fortunately, from the beginning of investors to implement their strategic deci- 2000s the approach from corporate finance sions, rather than informational asymmetry, and real options theory (with its stochas- which is also present. Modern strategic man- tic differential equations techniques) has agement states that each company lives in shown another perspective. Many new great uncertain and unpredictable business environ- names have appeared. The story of these ment and real options are the main tool of contributions was presented in some detail creating company’s value [Grant, 2016, Ch. 2]. in [Bukhvalov, 2016]. This modern theory Real options are designed and exercised (or is still in the shape of development. So, for not) by the most interested investors. So it is reasonable to treat real options as strate- 1 Of course, there are numerous studies on hu- gically important nonmarketable asset. Now man capital impact but they are not about the risk two values for two above mentioned classes (betas). We will not consider such researches here. of investors should be assigned to the com-

RMJ 16 (2): 173–186 (2018) Nonmarketable Assets Version of the CAPM: The Case of the Russian Stock Market 175 pany. Outsiders get capitalization and usual This is related to the small size of Russian CAPM beta whereas most interested inves- stock market and sanctions, which affect tors get strategic value of the company (to the activities of Russian investors. be defined) and the Mayers beta as a measure Second, significant difference between of risk. More detailed presentation and other traditional CAPM beta and the Mayers beta applications (e. g., corporate governance) are for the Russian stock market has led to idea given in [Bukhvalov, 2008]. of analyzing for the same market the old It was also suggested that empirical iden- problem of human capital impact on mar- tification of such model can be done by means ket risks. As in [Fama, Schwert, 1977] for of analyzing M&A deals where strategic US we found impact of human capital not value appears (in the form of goodwill). The being significant for entire Russian mar- techniques from [Fama, Schwert, 1977] re- ket and most sectors but for some sectors, viewed below here seems to be appropriate primarily for Innovations, we observed its in doing so using M&A activities indices. influence. A simplified version of [Fama, It is possible to do it only for the markets Schwert, 1977] techniques was used. with a good disclosure practices like the The structure of the paper is as follows. USA. Nevertheless, all time series machin- Section 1 provides a brief introduction to ery should be checked carefully for the rel- the Mayers model and a review of [Fama, evant data. What is the source of a hope Schwert, 1977] techniques of empirical test- that techniques that has shown no impact ing. Section 2 is devoted to new applications for human capital will work with M&A. Such of the Mayers model to the Russian stock a hope exists because of high share of M&A market. Section 3 deals with the problem market in the stock market. of human capital impact. The second contribution is related with the size effect, which exists in the Mayers model. Its importance was, as far as we 1. CAPM with nonmarketable know, noticed in [Bukhvalov, 2008] for the assets first time. Namely we speak about the ratio of nonmarketable assets to marketable ones. 1.1. Brief overview Human capital, being measured as wages and salaries, is much less than the stock market The Mayers model, or Mayers CAPM, was in the USA. So, the direct use of the static invented in [Mayers, 1972; 1973] (see [Gold­ Mayers model has not shown any impact. But enberg,­ Chiang, 1983] for further develop- sometimes nonmarketable assets are much ment). In [Copeland, Weston, Shastri, 2005, bigger than marketable ones. It happens with p. 162] a reader can find basic features and derivative securities where (broadly treated) peculiarities of the Mayers model (unfortu- open interest is much greater than the mar- nately without derivation). In Russian the ket of underlying assets and (if we will take Mayers model (including its construction, into account swaps and other advanced de- main properties, and generalization) is giv- rivative instruments) it is much greater than en in [Bukhvalov, 2008, p. 25–31]. all spot markets together. Using this idea Mayers model is one-period model with and basic formulas of the Mayers model (see usual assumptions from mean-variance analy- Section 1 below) an explanations of world sis [Copeland, Weston, Shastri, 2005, Ch. 5–6]. financial crisis of 2007–2009 was provided. To formulate main equations related to the The original contribution of this paper model we use the following notation: is the following. First, we exploit the idea Rj — return of the firmj ; of the size effect to show that the Mayers DH — stochastic cash flow paid to all in- model provides a significant correction to vestors at the end of the period on the market risk of the Russian companies. nonmarketable asset;

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Rm — return of the market portfolio; If Vm is much less than VH then we can σm — risk of the market portfolio; assume that their ratio is equal to 0. Using Vm — total market capitalization; the formula for the traditional beta we get Rf — risk free rate. that for any company Equations for expected return E(Rj) and cov RR, market value of unit risk λ are provided below * ()jH β j = . (2) cov()RRmH,

ER( j) = R f +λ V mcov( R jm , R ) +  Formula (2) presents the size effect in this + cov(RDjH ,) ; case (see [Bukhvalov, 2008, p. 28, proposi- tion (B)]).

ER( mf) − R λ = 2 . Vmσm + cov( RDmH , ) 1.2. Empirical tests of CAPM with nonmarketable assets Let us rewrite the Mayers model in full Thus far only the version with human cap- analogy with CAPM introducing b* coeffi- ital was empirically tested. The first paper cient as a new measure of risk, the Mayers on this topic [Fama, Schwert, 1977] made beta: two important contributions. First of all econometric techniques has been devel- cov , cov , * Vm( RR jm) + ( RDj H) oped. We will provide below all necessary β=j 2 . Vmmσ + cov( RDm , H) details because it is either used directly in our study or important for comparison. Using simple algebra we can derive a re- Second, the conclusion of the paper is neg- * lation between βj and βj: ative for the perspectives of the model. Namely, the difference between traditional

cov(RDjH , ) and Mayers betas was proved to be negli- 1 + gible for US market (even after adding to Vmcov( RR jm , ) β* =β . (1) the stock market that of government bonds jj cov , (RDmH) of any maturity to represent more com- 1 + 2 Vmmσ pletely the whole financial market). This was a shock, and further development of Let us assume that total value of nonmar­ studies devoted to influence of human cap- ketable assets is equal to VH and RH is re- ital on CAPM has been suspended for al- turn on these assets. Then cov = (Rm, DH) = most two decades. = VH cov(Rm, RH) and, hence, we can rewrite In the middle of 1990s a dynamic ver- (1) as sion of CAPM, named conditional CAPM, was introduced, to a large extent, for cap- turing influence of human capital on the  V cov()RRjH,  1 + H  market risk. In [Jagannathan, Wang, 1996], Vm cov()RR, as opposed to [Fama, Schwert, 1977], the ββ* =  jm = jj V cov()RR,  confirmation of importance of human cap- + H mH 1 2  ital for US market has been empirically  Vm σ  m (1′) validated. Though the techniques do not V cov()RR,  rely on the Mayers model but the authors m + jH V  give credit to Mayers’ contribution to the  H cov()RRjm,  = β . problem. j V cov(()RR,  m + mH In [Jagannathan, Wang, 1996] authors V σ2   H m  considered the return on human capital

RMJ 16 (2): 173–186 (2018) Nonmarketable Assets Version of the CAPM: The Case of the Russian Stock Market 177 in the context of the return on aggregate bor force to measure the variation through wealth. Following Mayers’ assumption that time in the payoff to a unit of human cap- human capital contributes a significant ital. The measure of the labor force, Lt, is portion of the total capital in the economy the seasonally adjusted total civilian labor the authors also made a notice that in the force collected by the Bureau of the Census structure of total monthly per capita per- of the Department of Commerce. To estimate sonal income in the US during the period covariance between income and returns from of 1959–1992 the share of dividend income time series data, one assumes that the bi- was less than 3%, while at the same time variate distributions of the income and re- the share of wages and salaries was more turn variables are stationary through time, than 60%. Growth rate of the per capita which implies that the marginal distribu- payoff to human capital in the economy tions of the variables are stationary. How­ was taken as a proxy for return on human ever, the distribution of per capita income capital, similar to the measure suggested is not stationary — income has an upward by [Fama, Schwert, 1977] research. Even trend, and the autocorrelations of per cap- though [Jagannathan, Wang, 1996] arrive at ita income are close to one for many lags. this measure being based on different lines The standard cure for this type of mean non- of reasoning, the calculation is the same as stationarity suggested by Fama and Schwert in formula (3) below. is to work with a differenced form of the In [Jagannathan, Kubota, Takehara, 1998] variable: the importance of human capital is con- firmed for the case of Japan. As in the Lt−1 Ht  previous paper the authors follow [Fama, Lt ht =−1. Schwert, 1977] approach to return on hu- Ht−1 man capital, taking growth rate in per capita labor income in economy as a proxy. In new notation Mayers’ equation (1) can The theoretical difference of this paper be rewritten as follows from [Jagannathan, Wang, 1996] is that it compares the results obtained from es- cov(RHjt , t ) timating the model with human capital to 1 + the ones obtained from [Fama, French, Vm,1 t− cov( RRjt , mt ) β* =β . (3) 1992] three-factor model, instead of tra- jj cov(RHmt , t ) 1 + ditional CAPM. VRσ2 ( ) Let us review now some important tech- m,1 t− mt nical details from [Fama, Schwert, 1977], which will be used further for Russia. An To work with the percentage change in obvious way to test whether the Mayers per capita income ht, the parameters Rmt and model improves the pricing of marketable cov(Rmt, Ht) in (3) must be restated in terms * assets is to estimate the differences βj – βj of ht. Obviously, Ht = Ht – 1(1 + ht). So (3) can between the Mayers and CAPM risk measures be rewritten as of marketable assets. One of the main contributions of [Fa­ma,    Schwert, 1977] is the restatement of Mayers’ Ht−1 cov(Rhjt , t ) risk measure. To estimate the betas it is Vmt,1− 1 +  necessary to consider appropriate time se- covRR , * ( jt mt ) ries. So, instead of the authors introduce βjj =β DH H  . (4) H as the aggregate income received at the t−1 covRh , t V ( mt t ) time t by the labor force employed from mt,1− 1 + 2 t – 1. They use income per capita of the la- σ (Rmt )

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The ratio Ht – 1/Vm, t – 1 in (4) is estimated Russian investors to US market was always as the average of the monthly values of this not easy. In the period after the world finan- ratio for the indicated period. Covariances cial crisis, 2010–2017 two circumstances may be calculated directly using standard were important for them: (1) unpredictable formulas or on the base of time series es- declines of national currency (RUB), which timation (the latter was done in [Fama, made very difficult to form rational expecta- Schwert, 1977]). Anyway, we wish to clar- tions about stock prices and returns; (2) in- ify formula (4) where t is present at the ternational sanctions and counter-sanctions right side. In the case of direct calculation appeared since 2014. It became possible to t is running across the entire sample (from treat US stock market as the market of non- t = 2 up to final value oft ). In the case of marketable assets for Russian investors. time series the estimates are used. Formally, index m stands for Russian Here the key point lies in stationarity stock market represented by (USD denomi- through time of parameters (variances and nated) RTSI index and its return, H stands covariances) of distributions of Rjt, Rmt and for US stock market represented by S&P500 ht that appear in usual definition of beta index and its return. We show that in the and in formula (3) for the Mayers beta. It case of Gazprom, one of leading Russian gives a possibility to estimate both betas companies, traditional CAPM beta is signifi- from time series. cantly different from the Mayers beta (see So, using the techniques described abo­ Table 1). We use USD-denominated Gazprom­ * ve Fama and Schwert estimate βj – βj for ADR prices, which exactly follow Russian portfolios of New York Stock Exchange RUB prices converted into USD in accordance (NYSE) common stocks and for portfolios to official exchange rate. Data are collected of U.S. Treasury Bills and bonds. Their from Bloomberg. As it was already said we study covers the 1953–1972 period and can assume that ratio of the size of Russian both monthly and annual estimates are market to US market is zero. So, we can use provided. They find that the differences formula (2) to calculate the Mayers beta. between the Mayers and CAPM risk mea- There is no unique prescription what sures are very small. The authors attribute should be the length of the period to calculate this finding to the fact that the relation- beta. Also different financial agencies use ships between the payoff to human capital their proprietor algorithms to adjust betas and the returns on bonds and stocks are for their practical needs. We start our study weak, so that any existence of nonmarket- from 2010 when the major period of the world able human capital does not have substan- financial crisis has ended almost everywhere. tial effects on risk for these two important All estimates are based on monthly data. The classes of marketable assets. As we already Mayers beta is calculated directly on the base know the last conclusion was corrected in of sample covariations. We treat it as a usu- [Jagannathan, Wang, 1996]. al number without taking into account its statistical nature because if too many assump- tions being involved. For traditional beta we 2. CAPM WITH NONMARKETABLE calculated regressions for 2017 using the ASSETS IN RUSSIA: data from periods shown. EFFECT OF SIZE IMPACT Now let us move to interpretation of Table 1. One year with monthly estimates In accordance to the World Bank data for is too short period. So the beta of CAPM 2017 (see World Development Indicators, regression for 2017 is only 5% significant 2017) US stock market capitalization is whereas others are 1% significant. The es- $32.121 trln whereas Russian stock market timate is so poor that though the difference capitalization is $623.425 bln. Access of between betas is huge it is not significant

RMJ 16 (2): 173–186 (2018) Nonmarketable Assets Version of the CAPM: The Case of the Russian Stock Market 179

Table 1 Difference between betas: Gazprom case

Covariance between Covariance between Significance returns on RTSI Gazprom and S&P500 Gazprom, Gazprom, of difference Periods * and S&P500 index, index returns, bj bj between betas, cov(Rm, RH) cov(Rj, RH) level 2017 –0.00174 –0.00271 1.556315 0.92 No 2016–2017 0.002997 0.002585 0.862416 1.32 5% 2015–2017 0.010875 0.009367 0.861350 1.19 1% 2014–2017 0.010337 0.008248 0.797888 1.14 1% 2013–2017 0.009550 0.008916 0.933674 1.14 5% 2012–2017 0.012492 0.012491 0.999939 1.20 10% 2011–2017 0.017058 0.018619 1.091478 1.12 No 2010–2017 0.019939 0.021601 1.083388 1.12 10% S o u r c e: authors’ calculation. even at 10% level. Another case of failure Mayers beta from (4). This is done for each is calculation for the 2011–2017 period. observation (monthly). Then we apply the In all other cases the Mayers beta is sig- paired difference test to decide about the * nificantly less than traditional one. In two size of βj – βj. cases we have even 1% significance level. We consider the 2009–2015 period and This methodology can be used for any Rus­ monthly data both for human capital and sian company. stock market. So we have 84 observations The Mayers beta is the measure of risk in and 83 pairs of betas (notice that (t – 1) its traditional sense. So, we have improvement and t are present in (3)). for the risk estimation. In this case the Mayers The income per capita of the labor force, beta, not traditional one, should be used for henceforth called income, is defined as the investment projects appraisal and WACC. average wage and salary disbursements to the unit of labor force in the economy as computed by the Federal State Statistics 3. CAPM with nonmarketable Service of the Russian Federation (https:// assets in Russia: fedstat.ru). MICEX value-weighted index (of 50 most human capital case liquid stocks of Russia’s largest public com- 3.1. Research design and data panies) is considered as a proxy for the mar- ket portfolio, and the aggregate capitaliza- Since the history of Russian market is very tion of all securities traded on Moscow Ex­ short it is not possible to use advanced time change also comprise the total value of series econometrics mentioned in subsec- marketable assets in the economy. Portfolios tion 1.2 (and described in detail in [Fama, of subsets of MICEX stocks provide the dif- Schwert, 1977, p. 99–102] to see stationar- ferent classes of marketable assets for com- * ity in reality. Nevertheless, we use the same paring estimates of bj and βj . Data on the methodology of proxy and formula (4). The end-of-month total market capitalization of last formula already assumes stationarity. MICEX stocks and values for MICEX index We obtaining CAPM beta from cross section were obtained from “Investfunds” database at the monthly basis and then calculate the (http://investfunds.ru).

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Estimates for both betas are eventually As in [Fama, Schwert, 1977] we measure compared for companies of ten major sectors human capital and market in real rather of economy, i. e. Oil & Gas, Finance, Tele­ than nominal terms. All of the results below communications, Energy, Consumer Goods, are reported for real versions of the vari- Transportation, Chemicals, Metal & Mining, ables, where the real variables are the nom- Automotive, and Innovations. These sectors inal variables (in RUB) deflated by the Con­ and representing companies have been cho- sumer Price Index (CPI). sen on the base of Moscow Exchange clas- sification (see Appendix and additional in- 3.2. Summary statistics formation on the site https://www.moex.com/ en/index/MICEXO%26G/constituents). It Table 2 presents economy-wide parame­ters should be noticed that the sector lists refer for the sample of Russian companies in- to January 2016 information. cluded in MICEX index. This list of parame­ To calculate the returns on securities a ters contains market return, market capi- return index (RI) is used. It shows a theo- talization, total payoff to human capital in retical growth in value of a share for a de- the economy, count of labor force and wage fined period of time. Dividends are assumed per capita. to be reinvested for the purpose of purchas- Market returns at the end of each month ing additional shares at a closing price ap- in the observed period were calculated as plicable on the ex-dividend date. follows: Return index is calculated using the mea- sure called annualized dividend yield. This MICEX− MICEX R = tt−1 , method adds an increment of 1/260th part mt MICEX of the dividend yield to the price each week- t−1 day. Ignoring market holidays, it is assumed that there are 260 weekdays in a year. The where MICEXt and MICEXt – 1 are the values base date value of RI is 100, and is further of MICEX index at t and (t – 1) respective- adjusted in subsequent time periods using ly, t is the last trading day of the month the formula: between in the 2009–2015 period. So our study includes 84 months.

PItt DY 1 The mean value for market returns is RItt= RI −1 ⋅ ⋅+1 ⋅, PIt−1  100 N  0.015, and median 0.018 (1.5% and 1.8%), while standard deviation is more than where RIt — return index on day t; RIt – 1 — 4 times higher than the mean (6.5%). The return index on previous day; PIt — price same can be observed for ht, with the same index on day t; PIt – 1 — price index on pre- mean of 0.015, it has standard deviation of vious day; DYt — dividend yield % on day more than 7 times higher than the mean t; N — number of working days in the year (11.9%). (taken to be 260). As for other variables, the level of vo­ The calculation ignores reinvestment charg- latility is lower and standard deviations es as well as any taxes. Gross dividends are are much less than one mean. Market ca­ used for calculations where available. Closing pitalization has the mean and median of prices for the respective periods are used to around RUB 25 trillion, with a standard calculate return index. Returns are calcu- deviation of only RUB 4.26 trillion. Total lated based on return index, using the tra- payoff to human capital has the mean and ditional formula: median of RUB 1.9 trillion, with a stan- dard deviation of 0.45 trillion. It is worth RI jt to mention that the lowest relative stan- Rjt =−1. RI jt,1− dard deviation is that of a labor force. With

RMJ 16 (2): 173–186 (2018) Nonmarketable Assets Version of the CAPM: The Case of the Russian Stock Market 181

Table 2 Summary statistics for market data and wages

Standard Standard Parameters Mean Median Interval Minimum Maximum error deviation

Rm 0.015 0.007 0.018 0.065 0.356 –0.135 0.221

Market cap, mln 24 936 094 464 777 25 195 296 4 259 753 21 269 847 10 643 790 31 913 636

Wage per capita 26 761 666 26 652 6101 26 310 17 098 43 408 ht 0.015 0.013 0.011 0.119 0.627 –0.276 0.350

Labor force 70 844 062 79 358 71 229 715 727 324 2 134 958 69 410 458 71 545 416

Total payoff to H, mln 1 899 321 48 838 1 902 658 447 604 1 890 958 1 209 472 3 100 430

S o u r c e: http://investfunds.ru, https://fedstat.ru, authors’ calculations. the sample mean and median of 71 million, dard error of the mean difference. If n is the it has standard deviation of only 0.73 mil- number of paired observations then (n – 1) lion. is equal to degrees of freedom and t-statistics is defined by the formula 3.3. Empirical analysis and results d tn−1 = . Our goal is to test whether the differences sd * βj – βj are significantly different from zero. We will use the test of the mean difference In our case the value of t-statistic should of two populations based on dependent sam- be compared with critical value (from Stu­ ples, or ‘paired difference’ test, assuming dent’s t-distribution) based on n – 1 = 83 – 1 = normal distributions [Wooldridge, 2016, = 82 degrees of freedom and 5% level of Appendix C] (there are no extreme outliers significance. In this case critical value is so we can conclude that distributions are equal 1.99. So, for the null hypothesis to approximately normal). be rejected the t-test should be greater than Formula (4) is valid for any portfolio, so t-critical in absolute value, i. e. the follow- we can estimate both betas indices for all ing inequality must hold: |tn – 1| > 1.99. * 10 sectors. We have 83 observations in each To estimate the differences βj – βj we case. Let µd is the mean of the population need to calculate both betas. The estimate * of paired differences βj – βj for companies of βj are the slope coefficients from market included in the sample. model regressions of Rjt on Rmt where m We specify the null and alternative hy- is the value-weighted MICEX index. All potheses (two-tailed test) as beta coefficients are significant at 5% lev- * el. The estimates βj of the Mayers risk Ho : µd = 0; Ha : µd ≠ 0. measure use the market model estimates for βj and the standard formulas for sam- If null hypothesis is accepted then human ple covariances and variances for the re- capital is not important for this sample. If maining parameters in (4). Covariances null hypothesis is rejected then human cap- technically may be also estimated from suit- ital is important for this sample. Let d be able regressions as it is mentioned in paper the mean and sd be the standard deviation [Fama, Schwert, 1977; see formula (8) and table 7]. of sample difference; sd = sd n is the stan-

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Table 3 3.4. Interpretation of the results t-statistics for the betas differences and limitations (2009–2015) Due to the nature of Russian economy, which β* – β Sector j j, t-statistic is infrastructure-intensive and resource ori- sector ented, human capital plays in general a less Oil & Gas 0.0048 0.14 significant role, than in more developed and innovation-oriented countries. Therefore, it Innovation –0.0620 –2.83 is not surprising that the effect from inclu- Telecom –0.0049 –0.17 sion of human capital is negligible for the Energy 0.0034 0.23 market in general and for the most sectors. As for Innovation sector, the results that Consumer Goods 0.0100 0.09 were obtained are meaningful, since this type Trans­por­ta­tion –0.0600 –2.27 of corporations usually is very dependent on personnel. Human capital plays a key role Finance 0.0019 0.03 as a driver for innovations. The founders of Chemicals –0.0010 –0.11 the theory of human capital, H. Becker and Automotive –0.0062 –0.25 T. Schultz, proved productive nature of the investments in people, providing a significant Metals & Mining –0.0235 0.48 and lasting effect. For example, [Schultz, N o t e: gray cells indicate significance of the betas’ 1960] identified the formation of human difference for the sector. capital with investments in education. S o u r c e: authors’ calculations. There are some doubts interpreting the results for Transportation sector. Generally Table 3 shows the t-statistics calculated speaking this sector is related to high end for each sample of pairs of the beta’s dif- technologies and innovations but, given a ferences as it is described earlier. The ques- more detailed look at the companies, com- tion posed for Table 3 is whether there are prising the sector, one can see that they are important differences between the Mayers neither numerous nor representative of the and CAPM risk measures for the marketable sector, and operate in different segments of assets in general. The answer seems to be transportation. "no". The difference is very small in absolute Now we add some comments on limita- value. However, even though one can infer tions of the study. First of all information on * from Table 3 that the values of βj – βj are salaries and wages in Russia is incomplete. close to zero for MICEX stocks in general, Second, one can argue that the companies there may be subclasses of stocks for which comprising sectors in this paper are not rep- there are important differences between the resentative of the sector or scarce to make two risk measures. general conclusions. We consider this point For this reason, the stocks were divided quite valid. However, the following points (in according to their MICEX sectors) into must be taken into account: 10 major classes of assets (see Appendix), • The decision on assigning the stocks to * and differences βj – βj were calculated for certain sectors was based on the meth- each group, which has yielded some positive odology of MICEX/Moscow Exchange for results. Yet, although for most classes the choosing companies for sector indices. differences between the Mayers and CAPM • The most comprehensive data on the Rus­ betas are close to zero and statistically in- sian stock market was used. significant, for Innovation and Trans­porta­ • With the current state of market itself tion sectors the differences are as large as and market data, it is difficult to collect 8.5% and 9.2%. better data.

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Conclusion company in 2018 with Price-to-Sales ratio of about 0.2. In this paper we presented two attempts to In [Teoh, Welch, Wazzan, 1999] authors test CAPM with nonmarketable assets. In the show with rigorous econometric analysis that case of analysis of the small size effect in in the case of South Africa under sanctions the Russian stock market we have shown the the following claim is true: both US com- possibility of substantial improvement of risk panies made business in this country and exposure estimate. Let us continue the discus- South African financial markets themselves sion of this case. We provided the general have not been visibly affected. methodology explaining it for the Gazprom This means that our model captures some case. Of course, a more detailed study for all elements of reality. Of course further devel- liquid stocks is welcome. Since CAPM, de- opment is needed. spite of its critics in the case of asset pricing, Empirical analysis in the case of human is still recommended for WACC calculation capital has shown significant difference of the [Berk, Binsbergen, 2017] then the use of the estimates of two models for Innovation sectors. Mayers beta may occur perspective. The beta predicted by the Mayers model is 9.2% There is a huge stream of literature devot- higher than the CAPM beta. The research has ed to comparison between the global CAPM failed to find any impact of the model for oth- (GCAPM), where the only risk factor is the er sectors of the market. Taking into account global market index, and the international negative experience of [Fama, Schwert, 1977] CAPM (ICAPM) with two risk factors, the we conclude that the original Mayers model global market index and a wealth-weighted for human capital is not suitable for studying foreign currency index (the most recent ref- influence of human capital on market risk. erence for 46 countries including Russia The most recent paper [Berk, Walden, is [Ejara et al., 2018], added in proof). 2013] on human capital risk moves the focus Obviously this approach is relevant for the from companies to employees. The paper is topic but it will never explain how Gazprom, technically based on analysis of stochastic with top three capitalization in 2006 and processes. It analyses the issue of “limited which still is the world's largest energy capital market participation”, which can be major in terms of natural gas reserves and relevant to our idea of duality of companies' production (as of 2017), became a troubled assets valuation.

Appendix

List of studied companies by sector

Sector Company 1 2 Oil & Gas Gazprom, Rosneft, Lukoil, NOVATEK, Transneft, Tatneft, Surgutneftegaz, Bashneft, Slavneft-Megionneftegaz Energy FSK EES, Interrao, Polus Gold, MMK, Eon Russia, Rus Hydro, Rosseti, Mosenergo, OGK‑2, Irkutskenergo, T Plus Group, Enel Russia, MOESK, TGK-1, MRSK-1, TNS Energo, MRSK CP, VTORRESURSY, Nauka-Svyaz, MRSK Ural, MRSK Volgi, DVEC, Quadra, MRSK Yuga, MRSK Sevzap, Lenenergo

RMJ 16 (2): 173–186 (2018) 184 A. V. Bukhvalov, L. Z. Bokuchava

Appendix (continued)

1 2

Metals & Mining Severstal, ALROSA, GMK Norilsk Nikel, NLMK, Polymetal International, PhosAgro, Uralkali, RUSAL, VSMPO, TMK, Mechel, Zinc, Raspadskaya, Kuzbasskaya Toplivnaya Co, LenZoloto, Chelyabinsky Metallurgicheskiy Kombinat, Amet Innovation Qiwi, Human Stem Cells Institute, Pharmsynthez, United Aircraft Corporation, Donskoi Zavod Radiodetalei, Multisistema, Diod, CZPSN-Profnastil, Rollman Group, Levenhuk Consumer Goods M.video, Lenta, Magnit, Dixy Group, RosAgro, Cherkizovo Group, Pharmstandard, Protek, Otcpharm, Razgulyai Group, Russaquaculture Telecom MTS, Rostelecom, Megafon, MGTS, Central Telegraph Chemicals Acron, Nizhnekamskneftekhim, Kazanorgsintez Transportation Aeroflot, Novorossiysk Commercial Sea Port, Fesco, Utair Finance Moscow Exchange, Sberbank of Russia, VTB, AFK Sistema, Bank Saint Petersburg, Vozrozhdenie Bank Automotive Uniwagon, Sollers, AutoVaz, GAZ

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Initial Submission: May 10, 2018 Final Version Accepted: May 29, 2018

Модель CAPM с не торгуемыми активами на российском фондовом рынке А. В. Бухвалов Профессор, Институт «Высшая школа менеджмента» Санкт-Петербургского государственного университета, Россия E-mail: [email protected] Л. З. Бокучава Выпускник программы магистратуры «Корпоративные финансы» Санкт-Петербургского государственного университета, Россия E-mail: [email protected]

В работе рассматривается модификация модели CAPM, носящая имя «модель Майерса», которая учитывает существование не торгуемых активов. Человеческий капитал является классическим примером таких активов, хотя мы приводим и рассматриваем некоторые другие важные интерпретации. В данной работе предприняты две попытки тестирования полезно- сти CAPM с не торгуемым активом. Мы начали с анализа влияния эффекта малого размера российского фондового рынка. Оказалось, что модель Майерса позволяет значимо уточнить модель оценки риска. Далее, эмпирический анализ показал, что в случае человеческого капи- тала модель Майерса не дает никакой существенной информации ни для одного из секторов Московской фондовой биржи за исключением сектора инноваций.

RMJ 16 (2): 173–186 (2018) 186 A. V. Bukhvalov, L. Z. Bokuchava

Ключевые слова: не торгуемые активы, CAPM, модель Майерса, российский фондовый рынок, человеческий капитал. JEL: G11, G12, G32, J24. Исследование проводилось первым автором при финансовой поддержке гранта Санкт-Пе­ тер­бургского государственного университета (проект № 16.23.1460.2017). For citation: Bukhvalov A. V., Bokuchava L. Z. 2018. Nonmarketable assets version of the CAPM: The case of the Russian stock market. Russian Management Journal 16 (2): 173–186. https:// doi.org/10.21638/spbu18.2018.201

https://doi.org/10.21638/spbu18.2018.201

Статья поступила в редакцию 10 мая 2018 г. Принята к публикации 29 мая 2018 г.

RMJ 16 (2): 173–186 (2018)