St. Petersburg State University
Graduate School of Management
Master in Corporate Finance
NONMARKETABLE ASSETS AND CAPITAL
MARKET EQUILIBRIUM UNDER UNCERTAINTY
Master’s Thesis by the 2nd year student
Concentration – Corporate Finance
Alexander V. Bukhvalov, Professor
ЗАЯВЛЕНИЕ О САМОСТОЯТЕЛЬНОМ ХАРАКТЕРЕ ВЫПОЛНЕНИЯ
ВЫПУСКНОЙ КВАЛИФИКАЦИОННОЙ РАБОТЫ
Я, Бокучава Лаша Зурабович, студент второго курса магистратуры направления
«Менеджмент», заявляю, что в моей магистерской диссертации на тему «Неторгуемые
Активы и Равновесие на Рынках Капитала в Условиях Неопределенности»,
представленной в службу обеспечения программ магистратуры для последующей
передачи в государственную аттестационную комиссию для публичной защиты, не
содержится элементов плагиата.
Все прямые заимствования из печатных и электронных источников, а также из
защищенных ранее выпускных квалификационных работ, кандидатских и докторских
диссертаций имеют соответствующие ссылки.
Мне известно содержание п. 9.7.1 Правил обучения по основным образовательным
программам высшего и среднего профессионального образования в СПбГУ о том, что
«ВКР выполняется индивидуально каждым студентом под руководством назначенного
ему научного руководителя», и п. 51 Устава федерального государственного бюджетного
государственный университет» о том, что «студент подлежит отчислению из СанктПетербургского
квалификационной работы, выполненной другим лицом (лицами)».
_______________________________________________ (Подпись студента)
STATEMENT ABOUT THE INDEPENDENT CHARACTER OF
THE MASTER THESIS
I, Lasha Bokuchava, second year master student, program «Management», state that my
master thesis on the topic «Nonmarketable Assets and Capital Market Equilibrium under
Uncertainty», which is presented to the Master Office to be submitted to the Official Defense
Committee for the public defense, does not contain any elements of plagiarism.
All direct borrowings from printed and electronic sources, as well as from master theses,
PhD and doctorate theses which were defended earlier, have appropriate references.
I am aware that according to paragraph 9.7.1. of Guidelines for instruction in major
curriculum programs of higher and secondary professional education at St.Petersburg University
«A master thesis must be completed by each of the degree candidates individually under the
supervision of his or her advisor», and according to paragraph 51 of Charter of the Federal State
Institution of Higher Education Saint-Petersburg State University «a student can be expelled
from St.Petersburg University for submitting of the course or graduation qualification work
developed by other person (persons)».
_______________________________________________ (Student’s signature)
Название магистерской диссертации
Описание цели, задач и основных
Бокучава Лаша Зурабович
Неторгуемые Активы и Равновесие на
Рынках Капитала в Условиях
Высшая Школа Менеджмента
Бухвалов Александр Васильевич
В данной работе автор обращает особое
расширил модель CAPM путем добавления в
нее эффекта от неторгуемого актива.
доходности человеческого капитала как
Расширенная модель Майерса предполагает,
что, поскольку человеческий капитал
любого индивидуального инвестора является
уникальным, ковариация между рыночным
портфелем и выплатами человеческому
оптимальный вес рыночного портфеля,
таким образом, ковариация объясняет,
почему инвесторы держат различные
портфели в реальности.
Основной целью этого исследования
является проверка значимости модели
CAPM с неторгуемыми активами на
Следующие задачи выполняются для
реализации конечной цели исследования:
эмпирических работ, касающихся CAPM
с неторгуемыми активами
3. Разработка методики расчета разницы
между традиционной мерой риска по
CAPM и мерой риска Майерса
4. Сбор данных о 50 наиболее
различных сегментов экономики, чтобы
точнее оценить влияние доходности на
человеческий капитал по различным
5. Регрессионный анализ для оценки
меры риска для соответствующих
6. Расчет различия между показателями
риска Майерса и традиционной CAPM,
чтобы проверить, приводят ли эти
различия к значительным отклонениям в
окончательных оценках доходности
рискованных активов в России;
В отличие от традиционной модели CAPM,
расширенная модель предполагает, что не
портфель рыночных активов. Это означает,
что каждый инвестор владеет портфелем
активов, который решает его личную (и,
значительную разницу оценок моделей для
сектора Инноваций. Бета предсказанная
расширенной моделью на 9.2% выше, чем
обоснованность модели для других секторов
компаний и для рынка в целом, что может
быть связано с ограничениями, указанными
в работе. Эти ограничения включают в себя:
человеческого капитала, 2) противоречие
использования человеческого капитала в
качестве прокси, и 3) несовершенство
данных на российском фондовом рынке.
Неторгуемые активы, Рынки капитала,
Инвестор, Доходность, Модель оценки
долгосрочных активов, CAPM, ММВБ
Master Student's Name
Master Thesis Title
Main field of study
Academic Advisor's Name
Description of the goal, tasks and main results
Nonmarketable Assets and Capital Market
Equilibrium under Uncertainty
Graduate School of Management
Alexander V. Bukhvalov
In this paper, the author pays special attention to
the model developed by Mayers (1972), who
challenged the assumption of marketability of
all assets by introducing the effect of
nonmarketable assets. Mayers examined the
role of returns to human capital as a proxy for
nonmarketable asset. Mayers’ extended model
suggests that since any individual investor’s
human capital is unique, the covariance between
the market portfolio and payoffs to human
capital will have an impact on the optimal
weight of the market portfolio, therefore, the
covariance explains why investors hold
different portfolios in reality.
This research aims to understand whether the
CAPM with nonmarketable assets has
meaningful implications in the Russian market.
The following objectives are met to realize the
ultimate goal of the paper:
1. Theoretical and empirical background of
the traditional Capital Asset Pricing Model
2. Theoretical and empirical background of
the CAPM model with nonmarketable assets
3. Methodologies for the calculation of
differences between the Mayers and SLM
risk measures are derived;
4. The data on 50 most liquid stocks of
Russia’s largest companies is obtained. The
companies are further segmented into 10
different sectors of economy to precisely
evaluate the effect of returns to human
capital on different classes of assets;
5. Regressions are run to estimate risk
measures for respective classes of assets;
6. Differences between the Mayers and
SLM risk measures are calculated to check
whether this differences lead to significant
deviations in final estimations of the
required returns on risky assets in Russia;
7. Interpretation of results and limitations
of the approach are elaborated.
Contrary to the SLM model, the expanded
model implies that not all maximizing investors
hold the identical (except for scale) portfolio of
marketable assets. It implies that each investor
holds a portfolio of marketable assets that
solves his personal (and possibly unique)
portfolio problem and, therefore, allows
investors to maintain unique portfolios.
Empirical analysis of the CAPM with
nonmarketable assets has shown significant
difference of the estimates of the models for
Innovations sectors. The beta predicted by
extended model is 9.2% higher than the SLM
beta. Unfortunately, the research has failed to
prove the validity of the model for other sectors
of companies and for the market in general,
which may be attributable to the limitations
stated in the paper. These limitations include: 1)
the quarrels about the way to define human
capital, 2) the controversy of using human
capital as a proxy, and 3) the imperfection of
data on Russian stock market.
Nonmarketable assets, Capital markets,
Investor, Return, Capital asset pricing model,
Introduction ................................................................................................................................... 8
Chapter 1. CAPM with nonmarketable assets.......................................................................... 11
1.1 Overview of the traditional CAPM model ........................................................................... 11
Overview of the model and its key assumptions .................................................................... 11
Effect of inflation ................................................................................................................... 13
1.2 Empirical tests of SLM CAPM ............................................................................................ 13
Stationarity of β coefficients .................................................................................................. 14
CAPM tests based on the construction of the SML line ........................................................ 15
Current state of CAPM........................................................................................................... 16
1.3 CAPM with nonmarketable assets ....................................................................................... 17
1.4 Empirical tests of CAPM with nonmarketable assets .......................................................... 21
Fama, Schwert (1977) Human Capital and Capital Market Equilibrium............................... 21
Jagannathan, Wang (1996) Conditional CAPM and Cross-Section of Expected Returns ..... 22
Jagannathan et al (1996) CAPM with human capital: Evidence from Japan ......................... 24
Chapter 2. CAPM with nonmarketable assets in Russia ......................................................... 26
2.1 The data................................................................................................................................ 26
Definitions .............................................................................................................................. 26
Summary statistics ................................................................................................................. 28
2.2 Econometric approach ......................................................................................................... 40
Econometric model ................................................................................................................ 40
Test for statistical significance of results ............................................................................... 42
2.3 Statement of the results ........................................................................................................ 43
2.4 Interpretation of the results .................................................................................................. 45
2.5 Limitations ........................................................................................................................... 46
Ways to define human capital ................................................................................................ 46
Human capital as a proxy for nonmarketable assets .............................................................. 46
Company data......................................................................................................................... 47
Conclusions .................................................................................................................................. 48
References .................................................................................................................................... 49
Appendices ................................................................................................................................... 52
Appendix 1. List of companies by sector .................................................................................. 52
For the fund managers the decision to invest or not is usually based on such factors as
expected return on the security and the risk of the unfavorable deviations. Currently, the Capital
Asset Pricing Model is the most popular model among investors to calculate the returns on
securities. According to CAPM, the total risk of a security can be broken down into systematic
(undiversifiable) and asset-specific (diversifiable) risks. The model suggests that investors
require premium only for systematic risk, since specific risk can be completely eliminated by
diversification, and the systematic risk measure, β, depends on the covariation of asset returns
with market returns. As any other financial theory, CAPM implies a number of assumptions:
Investors are risk-averse maximizers of expected returns;
All investors can give loans and borrow an unlimited amount of money at a certain
risk-free interest rate;
All investors have similar expectations;
All assets are perfectly divisible and liquid;
There are no transaction costs or taxes;
All investors take price as an exogenously given value;
The number of all financial assets is fixed and determined in advance;
All investors have the same fixed holding period;
All information is available to all investors at zero costs.
These assumptions, which are rather strict and unrealistic, have caused many doubts
around the validity of the model. Vast amount of research has been done to prove insufficiency
of CAPM – various authors claimed that actual returns differ significantly from those predicted
by the Sharpe-Lintner-Mossin CAPM, and tried to improve the model by extending it through
inclusion of new factors.
In this paper, the author pays special attention to the model developed by Mayers (1972),
who challenged the assumption of marketability of all assets by introducing the effect of
nonmarketable assets. Mayers examined the role of returns to human capital as a proxy for
nonmarketable asset. Mayers’ extended model suggests that since any individual investor’s
human capital is unique, the covariance between the market portfolio and payoffs to human
capital will have an impact on the optimal weight of the market portfolio, therefore, the
covariance explains why investors hold different portfolios in reality. In his work Mayers
derived and suggested extended formula for calculating the measure of risk:
𝑉𝑀 𝑐𝑜𝑣(𝑅𝑗 ,𝑅𝑀 )+𝑐𝑜𝑣(𝑅𝑗 ,𝐷𝐻 )
2 +𝑐𝑜𝑣(𝑅 ,𝐷 )
is the return on asset j,
is the return on market portfolio,
is the total payoff to human capital in the economy,
is the total value of marketable assets in the economy,
is the variation of the returns of market portfolio.
There were several research papers in which Mayers model was considered and
empirically tested for validity. The most famous was the paper of Fama and Schwert (1977), who
analyzed the effect of human capital on the returns of the US assets over the period of 1950s –
1970s. Jagannathan and Wang (1996) introduced the model with conditional returns, and
observed that human capital forms a substantial part of the aggregate capital stock in the US. The
key findings of these papers will be further presented in the coming chapters.
As stated earlier, Russian market is currently one of the riskiest. Now, it is extremely
important for investors to be as precise as possible in estimations of risk and return on their
portfolio or potential investments, and CAPM with nonmarketable assets can be a possible
solution at this point.
To the best of my knowledge, there are no major researches in this field for the Russian
market. Therefore, the topic is extremely urgent and relevant. Even though it has been more than
40 years since Mayers first published his work on nonmarketable assets and capital market
equilibrium, the author of this paper believes that the theory developed by Mayers is meaningful
from economic point of view and can contribute to explaining the relationship between risk and
return in the contemporary Russian market.
This research aims to understand whether the CAPM with nonmarketable assets has
meaningful implications1 in the Russian market.
The following objectives are met to realize the ultimate goal of the paper:
1. Theoretical and empirical background of the traditional Capital Asset Pricing Model are
By meaningful implications the author means that the model will yield the results significantly different from those
produced by SLM CAPM.
2. Theoretical and empirical background of the CAPM model with nonmarketable assets are
3. Methodologies for the calculation of differences between the Mayers and SLM risk measures
4. The data on 50 most liquid stocks of Russia’s largest companies is obtained. The companies
are further segmented into 10 different sectors of economy to precisely evaluate the effect of
returns to human capital on different classes of assets;
5. Regressions are run to estimate risk measures for respective classes of assets;
6. Differences between the Mayers and SLM risk measures are calculated to check whether this
differences lead to significant deviations in final estimations of the required returns on risky
assets in Russia;
7. Interpretation of results and limitations of the approach are elaborated.
The rest of the paper is organized as follows. In Chapter 1, the author covers main
theoretical background of the problem and provides the relevant methodology for the calculation
of the risk measure. Chapter 2 describes the data and states the results of the empirical research.
After that, the author presents the interpretation of the obtained results and explains some
Chapter 1. CAPM with nonmarketable assets
1.1 Overview of the traditional CAPM model
Overview of the model and its key assumptions
The debates about which factors best explain the return on securities are still in place.
One of the first and still the most popular works in this area is the Capital Asset Pricing Model,
or CAPM. It was developed in early 1960’s by Jack Trainor (1962), William Sharpe (1964),
John Lintner (1965) and Jan Mossin (1966) independently.
In his work, W. Sharpe2 (Sharpe 1964) developed a theory according to which the return
on any marketable asset depends on three factors. The first is the risk-free rate of return – a
significant factor in determining the profitability of the portfolio, which represents the investor’s
price of time. The author believed that any investor can get a risk-free rate of return on their
investments, regardless of the circumstances, so if money is not invested, they create opportunity
costs. The second factor is the excess return of the market portfolio over the risk-free rate – it
represents a reference point (benchmark) for the investor. This means that on markets with a
higher excess return over the risk-free rate, the investor is entitled to a higher portfolio returns.
Finally, the third factor – the risk (sensitivity of asset returns to fluctuations in market yields)
also determines the return on a security, as investors require higher returns from riskier assets
(price of risk), otherwise, all other things being equal, it would be preferable to invest in less
As any other financial theory, CAPM also implies a number of assumptions, including
the assumption of market efficiency. They are as follows:
The main goal of every investor is to maximize the returns on their assets at the end of
the planning period by estimating the expected returns and standard deviation of
alternative investment portfolios;
Investors are risk-averse, meaning they require additional returns for additional risk;
All investors can give loans and borrow an unlimited amount of money at a certain
risk-free interest rate;
There are no restrictions on the short selling of any assets3;
William F. Sharpe, ‘Capital Asset Prices – A Theory of Market Equilibrium under Conditions of Risk’. The
Journal of Finance, Vol. XIX (Issue 3) 1964, pp. 425–442.
The term ‘short selling’ means that the investor sells securities, which he or she does not possess, expecting to buy
them back at a lower price. If the price of a short-sold security rises, the investor is in loss, and if the price goes
down the investor makes profit.
All investors have the same expectations about future returns, variation and covariance
of returns of all assets. This implies that investors are in equal conditions regarding the
prediction of parameters;
All assets are perfectly divisible and liquid (i.e., they can always be traded on the
market at the current price);
There are no transaction costs;
There are no taxes;
All investors take price as an exogenously given value (i.e., all investors assume that
their activity of buying and selling securities does not affect the level of prices).
The number of all financial assets is fixed and determined in advance;
All investors have the same fixed holding period;
All information is available to all investors at zero costs.
The subsequent development of theoretical CAPM made many of these assumptions less
stringent and generally led to results that are consistent with the basic theory. Nevertheless, even
the more recent studies contain assumptions, which are very strict and unrealistic. Therefore, the
validity of this model can be confirmed only by means of empirical research. Further in this
chapter the author provides an overview of the studies on empirical validity of CAPM, but first it
is necessary to give a description of the model.
Despite its high value, CAPM is quite easy to comprehend. It carries out the connection
between the return on the asset and the market on which it is listed. Thus, it assumes that the
returns on assets that belong to the same market are interconnected and have a common
component. It is also important to note that the CAPM model is an equilibrium model. It can
mathematically be presented by the following formula:
𝐸[𝑅̃𝑗 ] = 𝑅𝑓 + 𝛽𝑗 × (𝐸[𝑅̃𝑀 ] − 𝑅𝑓 )
𝑐𝑜𝑣(𝑅̃𝑗 ;𝑅̃𝑀 )
𝜎 2 (𝑅̃𝑀 )
𝐸[𝑅̃𝑗 ] is the expected return on a long-term asset,
𝑅𝑓 is the risk-free rate,
𝛽𝑗 is the risk coefficient,
𝐸[𝑅̃𝑀 ] is the expected return on the market portfolio.
Formula (1), also called the Security Market Line or SML, allows for the calculation of
return on a risky asset (certainty equivalent).
The main conclusions one can draw from SML are: 1) the interpretation of beta
coefficient, and 2) the breakdown of the total risk of an asset by systematic (undiversifiable) and
asset-specific (diversifiable) risks:
βj measures the sensitivity of asset j returns to the market portfolio returns;
Total risk can be expressed by the formula: 𝜎 2 (𝑅𝑗 ) = 𝛽𝑗2 𝜎 2 (𝑅𝑀 ) + 𝜎𝑗,𝑠𝑝𝑒𝑐
Moreover, SML assumes that the estimation in (1) is made in terms of a fully diversified
portfolio, which completely eliminates the specific risk of every single security due to
covariation effects. This is reasonable because a rational investor sees no point in paying for the
risk that can be eliminated by diversification, i.e. investors only pay for the risk, which is not
possible to get rid of.
Effect of inflation
The risk-free rate of return, measured by the interest rate on treasury bonds, is the
nominal rate is composed of two elements: 1) the real, non-inflated return, 𝑅𝑓𝑟 , and 2) the
inflation premium, IP, equal to the expected rate of inflation4.
Thus, 𝑅𝑓 = 𝑅𝑓𝑟 + 𝐼𝑃, meaning if inflation takes place, then a premium should be added to
the real risk-free yield to compensate investors for the loss of purchasing power, which occurs as
a result of inflation. Note that in CAPM, the increase in Rf by a certain amount also leads to an
increase in the yield of all risky assets by the same amount, due to the fact that the inflation
premium is included in the returns of both risk-free and risky assets.
1.2 Empirical tests of SLM CAPM
As noted earlier, the CAPM model was developed based on a series of partly unrealistic
assumptions. If all these conditions were fair, the CAPM would represent an ideal, true model.
But due to the conditional nature of key prerequisites of the model, the SML equation (1) is not
quite adequate to the real attitude of investors to the process of defining required returns on
Inflation premium for each asset is equal to the average expected inflation rate over the life of the asset. Thus, it is
assumed that all securities on the SML graph have the same lifetime, and the expected rate of inflation is constant. It
should also be noted that the risk-free rate in CAPM can be expressed as either a long-term (e.g., in the U.S. –
Treasury bonds) or a short-term (Treasury bills) interest rate. In recent years, there has been a tendency to use the
interest rate of long-term Treasury bonds, as they are more closely correlated with stock returns.
individual stocks in the market. Thus, assuming that a large number of investors has stock
portfolios undiversified, in this situation, first, beta cannot be regarded as adequate risk criterion;
second, it is unreasonable to use SML as a tool to explain the logic of calculation of the required
return. In addition, the relationship described by CAPM is obviously distorted by the presence of
tax payments and expenses on operations with securities.
These arguments indicate that the CAPM is likely to not fully reflect the actual situation;
SML, in turn, does not give an accurate estimation of the required return. Therefore, empirical
testing of CAPM, which could confirm its validity and suitability for practical application, is
necessary. The literature on empirical testing of CAPM is very extensive; therefore, the author
only gives a brief overview of some key works in this area.
Stationarity of β coefficients
According to CAPM, beta coefficient (used to measure the market risk of the stock)
should reflect investors estimate of the future sensitivity of the share prices in relation to changes
in the market situation. Obviously, it is not known in advance how exactly the future stock
performance will be associated with the average of their values, and how the average investor
will assess the relative future variability of the price. There are only statistical data on the
dynamics of shares that can be used for the construction of the characteristic line and for the
calculation of actual beta. If the value of the beta coefficient has not changed for some time, it
may seem that there are grounds for investors to use the current trend for the evaluation and
calculation of future sensitivity of the stocks to market. But how valid such assumption is?
Robert Levy (1971)5, Marshall Bloom (1975)6 and other researchers considered the
problem of stationarity of beta coefficients in their works. Levi, in particular, has come to the
following conclusions, based on the results of calculations and the analysis of the dynamics of
betas for a number of individual stocks and securities portfolios:
beta of any particular security is not stable over time and therefore cannot serve as an
accurate assessment of future risk;
beta of a portfolio, consisting of 10 or more randomly selected stocks, is stationary
and can therefore be considered a good estimate of future portfolio risk. This
Levy R. A. ‘On the Short-Term Stationarity of Beta Coefficients’. Financial Analysts Journal, issue November
1971, pp. 55-62.
Blume M.E. ‘Betas and Their Regression Tendencies’. The Journal of Finance, issue June 1975, pp. 785-796.
conclusion is quite reasonable, because the errors in the estimates of beta values for
randomly selected stocks mutually cancel each other in the portfolio.
Works of Blum and other researchers confirmed the results of Levi.
These tests for the stationarity of beta lead to the following conclusion – CAPM is a
concept more suitable for explaining the structure of investment portfolios rather than for the
assessment of individual financial assets.
CAPM tests based on the construction of the SML line
According to the Capital asset pricing model concept, there is a linear relationship
between the required return on the security and its beta coefficient. Moreover, SML line crosses
the y-axis at the point 𝑅𝑓 , and the required rate of return on a security (or a portfolio) with beta
of 1.0 is the average market yield.
Many researchers have tried to verify the viability of this model on the actual material.
Typically, such an analysis uses historical data on monthly stock returns, and the YTM of longterm treasury bonds as a risk-free rate. Additionally, the majority of studies is devoted to the
analysis of portfolio investment, rather than individual securities, due to the instability of beta
Before presenting the key findings of the aforementioned studies, it is necessary to stress
once again that, although the CAPM is an ex ante model (estimation model), it can only be
checked for adequacy based on the factual material, i.e. historical data, and there is no reason to
believe that the historical data on the returns will necessarily coincide with the expected yields,
with which the model is dealing. In addition, the historical beta can both reflect and not reflect
the current and expected risk. This quite understandable lack of a future state of the market data
makes it incredibly difficult to test for the validity of CAPM.
The key findings are as follows:
The results generally confirm the hypothesis of a close direct relationship between the
actual returns and systematic risk. However, the slope of the SML line that reflects this
dependence is usually less steep than the slope predicted by the CAPM.
The assumption of linearity of relationship between risk and return is quite reasonable.
Empirical studies have not produced any significant evidence to abandon this premise.
Studies, which aimed to establish the relative importance of the systematic
(undiversifiable) and specific (diversifiable) risk, did not yield any definite results.
CAPM theory assumes that diversifiable risk is not relevant; yet it turned out that both
types of risk are positively correlated with the returns on the securities, i.e. it turns out
that the higher rate of return is expected to compensate for a diversifiable risk as well
as market risk. However, it is possible that this relationship is only partly true,
meaning that it may reflect the statistical relationship, but not the true nature of the
Richard Roll (1977)7 questioned the possibility of precise conceptual test of CAPM.
Roll showed that a linear relationship, which the previous researchers observed, was
the result of mathematical characteristics of the tested model, so the discovery of
linear relationship does not prove that CAPM is true. Roll’s work did not refute the
theory of CAPM, but showed that in fact it is impossible to be absolutely sure that the
behavior of investors in the future will be identical to their intentions.
If the CAPM model was absolutely correct, it would have been applicable to all
financial assets, including bonds. Experience shows that when bonds are introduced in
the analysis, the points, reflecting their characteristics, do not lie on the SML. This is
at least a cause for concern.
Current state of CAPM
CAPM concept is extremely attractive for theorists – it is logical and rational; specialists
with sufficient mathematical education, usually accept it unconditionally. However, when given
a thought, the assumptions underlying the model, raise some doubts, often reinforced by
empirical tests of the model. Brigham and Gapenski (1990)8 have the following point of view on
the current state of CAPM:
The concept of CAPM, which is based on the priority of the market risk over the
general risk is undoubtedly useful in providing the overall understanding of riskiness
of assets in general, therefore, conceptually model has a truly fundamental value.
Despite the fact that the CAPM at first glance gives clear and precise answers to
questions about the relationship of risk and required rate of return, in reality it does
not. The issue is that it is not known exactly how to estimate parameters included in
Richard Roll ‘A Critique of the Asset Pricing Theory’s Tests’. The Journal of Financial Economics, issue March
1977, pp. 129-176.
Brigham E.F., Gapenski L.C. ‘Financial Management: Theory and Practice’. Thomson Learning, 2nd Edition
(November 1993), pp. 92-94.
the model. It is assumed that a priori expected data (ex ante data) should be used,
while only a posteriori actual values (ex post data) are available. In addition, the data
on the market return, risk-free rate and beta vary considerably depending on the time
periods observed and the methods used to evaluate them. Thus, although CAPM
model seems adequate, its parameters cannot be measured accurately, so the estimates
of returns using the CAPM potentially include significant errors.
Since CAPM is logical in the sense that it reflects the behavior of investors seeking to
maximize returns at a given level of risk and availability of all the necessary data, it
provides a useful conceptual method. Of course, further attempts will be made to
improve it and make it of a more practical significance.
A major criticism of the CAPM has been made by Eugene Fama and Kenneth French
from the University of Chicago. Fama and French (1992)9 have studied the
relationship between beta coefficients and asset returns for a few thousand shares on
the time period of 50 years. According to CAPM, on average, stocks with high beta
should generate higher returns than stocks with low beta. Nevertheless, the study
found no relationship between the actual data – stocks with low beta had about the
same yield as the stocks with high beta.
Many of the problems related to the financial side of the CAPM concept require
detailed study. For the practical application of the model it is also important to be
aware of its limitations.
1.3 CAPM with nonmarketable assets
One of the main prerequisites of CAPM is the homogeneity of investors’ market
portfolio. Mayers (1972)10 suggested that these portfolios are not identical for different investors.
He extended CAPM to include nonmarketable assets. As such he considered assets that
possessed high value but with uncertain return, and which could not be traded according to the
current legislation. Mayers introduced human capital as the main nonmarketable asset. He
claimed that the covariance between the market portfolio and human capital explains the optimal
weight of the market portfolio that different investors hold. In this paper, the author briefly
covers the main aspects of Mayers model, its mathematical derivation and conclusions.
Fama E., French K. ‘The Cross Section of Expected Stock Returns’. The Journal of Finance, issue June 1992, pp.
David Mayers ‘Nonmarketable Assets and Capital Market Equilibrium under Uncertainty’. Studies in the theory
of capital markets, pp. 223-248, Praeger, New York, 1972.
The CAPM mean-variance assumptions are in place. It means, that every investor (single
period) is assumed to be risk-averse, and have their own preferences on risk and return,
mathematically described by the utility function: 𝐺𝑖 (𝐸𝑖 , 𝑉𝑖 ), where Ei is the one-period expected
return and Vi is the variance of the ith investor’s portfolio. Obviously, the function is upwardsloping by E and downward-sloping by V. To derive an equilibrium model the author solves the
problem of maximization of the function G with appropriate constraints. It is assumed that assets
are infinitely divisible, transactions are costless, and investors can lend and borrow funds at the
risk-free rate. Function G and its derivatives will not be a part of the final return calculations.
However, they will define the variable that shows the allocation of funds between the risky and
risk-free assets – the balance of risk and return for a particular investor11.
𝐸𝑖 = ∑𝑛𝑗=1 𝑋𝑖𝑗 𝐸(𝐷𝑗 ) + 𝐸(𝐷𝑖𝐻 ) − (1 + 𝑅𝑓 )𝑑𝑖
𝑉𝑖 = ∑𝑛𝑗=1 ∑𝑛𝑘=1 𝑋𝑖𝑗 𝑋𝑖𝑘 𝜎𝑗𝑘 + 𝜎 2 (𝑅𝑖𝐻 ) + ∑𝑛𝑗=1 𝑋𝑖𝑗 𝑐𝑜𝑣(𝑅𝑖𝐻 , 𝑅𝑗 )
𝑊𝑖 = ∑𝑛𝑗=1 𝑋𝑖𝑗 𝑃𝑗 − 𝑑𝑖
Xij is the share of company j held by investor i,
Dj is the total (random) cash flow paid to the shareholders of company j at the end of the
DiH is the total (random) cash flow paid to the investor i on nonmarketable assets (human
capital) at the end of the period,
σjk is the covariance/variance of the returns of the two assets j and k,
Rf is the risk-free rate of return,
di is the net debt of investor i,
Pj is the total value of company j at the beginning of the period,
Wi is the total wealth of investor i in the form of marketable assets at the beginning of the
n is the total number of firms in the economy.
Alexander Bukhvalov ‘Asymmetry between Insiders and Outsiders: the Problem of Duality of Companies’ Assets
Valuation’, Russian Journal of Management, Vol. 6, No. 4 (2008), pp. 17-48.
Each investor solves the problem of maximization of 𝐺𝑖 (𝐸𝑖 , 𝑉𝑖 ) with the variables Xij, di,
under the constraints described above. This classical problem is solved with the help of
Lagrangian equation. As a result, we arrive at the following equations for the expected return of
a marketable asset:
𝐸(𝑅𝑗 ) = 𝑅𝑓 + 𝜆[𝑉𝑀 𝑐𝑜𝑣(𝑅𝑗 , 𝑅𝑀 ) + 𝑐𝑜𝑣(𝑅𝑗 , 𝐷𝐻 )]
2 +𝑐𝑜𝑣(𝑅 ,𝐷 )
Where λ is the market price paid for the unit of risk, DH is the total payoff to all nonmarketable
assets in economy, 𝑅𝑗 is the return on asset j, 𝜎𝑀2 is the standard deviation of the market returns,
and 𝑉𝑀 is the total value of marketable assets.
The key features of Mayers model can be summarized as follows12:
3. Unlike CAPM, investors hold different portfolios of risky assets as their
nonmarketable asset has its own risk;
a. If an investor does not hold a nonmarketable asset, his portfolio of risky
assets matches the market portfolio as in CAPM, but anyway this investor
will also have a different beta now, because beta does not depend on
b. If the return on nonmarketable assets is certain for every investor, the model
will simply resemble traditional CAPM;
c. Investors with nonmarketable assets modify market premiums in such a way
so that the higher priority is given to the market assets, which have the lowest
covariation with the nonmarketable assets;
4. Just like in CAPM, market prices do not depend on the indifference curves of
investors. The formula (5) does not even contain the i index, which is representative
of an investor;
5. Just like in CAPM, the risk is measured in terms of covariation, although now with
two portfolios – of marketable and nonmarketable assets.
The first property basically means that in the Mayers model the Capital Market Line13
(CML) does not exist. Nevertheless, an analogue of SML exists and the risk premium is either
Copeland T.E., Weston J.F., Shastri K. ‘Financial Theory and Corporate Policy’, Pearson Addison Wesley
(Boston, MA), 2005.
higher or lower than for the traditional CAPM, depending on the sign of cov (Rj, DH). The 1c
property plays a key role as a base for the decisions on diversification.
Let β* denote the following coefficient:
𝑉𝑀 𝑐𝑜𝑣(𝑅𝑗 ,𝑅𝑀 )+𝑐𝑜𝑣(𝑅𝑗 ,𝐷𝐻 )
2 +𝑐𝑜𝑣(𝑅 ,𝐷 )
Then Mayers model can be rewritten in the form of CAPM as:
𝐸(𝑅𝑖 ) = 𝑅𝑓 + 𝛽𝑗∗ [𝐸(𝑅𝑀 ) − 𝑅𝑓 ]
β* – the measure of sensitivity to the market – represents the key element of the model. It
is reasonable to compare the β* in (9) against the traditional CAPM β in (2). The main difference
is that the β* in (9) contains additional component which represents covariation between the
market portfolio and the nonmarketable asset in the denominator. Intuitively, this covariation
should be positive, i.e. the value of the nonmarketable asset should grow as the market grows
and vice versa. Moreover, (9) incorporates two types of measures with different dimensions: R,
which is measured in fractions of a unit, and DH, which is measured in monetary units. Thus,
knowing the aggregate value of nonmarketable assets, VH, we can rearrange 𝑐𝑜𝑣(𝑅𝑀 , 𝐷𝐻 ) =
𝑉𝐻 𝑐𝑜𝑣(𝑅𝑀 , 𝑅𝐻 ).
Plugging the aforementioned rearrangement into (6), we arrive at the following formula
𝑉𝑀 𝑐𝑜𝑣(𝑅𝑗 ,𝑅𝑀 )+𝑉𝐻 𝑐𝑜𝑣(𝑅𝑗 ,𝑅𝐻 )
2 +𝑉 𝑐𝑜𝑣(𝑅 ,𝑅 )
𝑐𝑜𝑣(𝑅𝑗 ,𝑅𝑀 )+𝑉 𝐻 𝑐𝑜𝑣(𝑅𝑗 ,𝑅𝐻 )
2 + 𝐻 𝑐𝑜𝑣(𝑅 ,𝑅 )
𝑐𝑜𝑣(𝑅𝑗 ,𝑅𝑀 )+𝑐𝑜𝑣(𝑅𝑗 ,𝑅𝐻 )
𝜎 +𝑐𝑜𝑣(𝑅𝑀 ,𝑅𝐻 )
Capital Market Line, or CML, is the graphical representation of all possible combinations of a market portfolio
and a risk-free asset, which can mathematically be described by the formula: 𝑅𝑖 = 𝑅𝑓 + 𝜎𝑖
, where Ri is the
expected return on asset i, Rf is the risk-free rate, RM is the return on the market portfolio, σi is the standard deviation
of asset i, and σM is the standard deviation of the market portfolio
1.4 Empirical tests of CAPM with nonmarketable assets
Fama, Schwert (1977) Human Capital and Capital Market Equilibrium
The purpose of this paper is to determine whether, as an empirical matter, the Mayers
model improves on the description of the pricing of marketable assets provided by the SharpeLintner-Black (SLB) model
Since the interpretation of the risk-free rate 𝑅𝑓 , and the premium per unit of risk
[𝐸(𝑅𝑀 ) − 𝑅𝑓 ] is the same in equations (7) and (1), the only difference between the expected
return-risk equations of the Sharpe-Lintner-Black and Mayers models is in the measure of the
risk of a marketable asset. Thus, one way to test whether the Mayers model improves on the
description of the pricing of marketable assets is to estimate the differences 𝛽𝑗∗ − 𝛽𝑗 between the
Mayers and SLB risk measures for different classes of marketable assets.
One of the main contributions of Fama and Schwert (1977)14 is the restatement of Mayers
risk measure. In the Mayers model, 𝐻𝑡 is the aggregate income received at t by the labor force
employed from t – 1. To get appropriate measures of the covariances of income with returns, the
authors suggested that one must first abstract from any variation through time in aggregate
income that just reflects changes in the size of the labor force. Fama and Schwert solve this
problem by using income per capita of the labor force to measure the variation through time in
the payoff to a unit of human capital. The measure of the labor force (Lt) is the seasonally
adjusted total civilian labor force collected by the Bureau of the Census of the Department of
Commerce. To estimate covariance between income and returns from time series data, one
assumes that the bivariate distributions of the income and return variables are stationary through
time, which implies that the marginal distributions of the variables are stationary. However, the
distribution of per capita income is not stationary – income has an upward trend, and the
autocorrelations of per capita income are close to one for many lags. The standard cure for this
type of mean nonstationarity suggested by Fama and Schwert is to work with a differenced form
of the variable15:
𝐻𝑡 ( 𝑡−1
Eugene F. Fama, G. William Schwert ‘Human Capital and Capital Market Equilibrium’. Journal of
Financial Economics 4 (1977), pp. 95-125, North-Holland Publishing Company.
Income per capita is 𝑡. Therefore, the differenced form is obtained as ℎ𝑡 = ( 𝑡) ÷ ( 𝑡−1) − 1, which can be
rewritten as (9).
Before going further with Fama and Schwert restatement of the beta, let us note that
Mayers equation (8) can be rewritten in terms of 𝛽𝑗 as:
𝑉𝑀,𝑡−1 𝑐𝑜𝑣(𝑅̃𝑗 ;𝑅̃𝑀𝑡 )+𝑐𝑜𝑣(𝑅̃𝑗𝑡 ;𝐻
𝑉𝑀,𝑡−1 𝜎 2 (𝑅̃𝑀𝑡 )+𝑐𝑜𝑣(𝑅̃𝑀𝑡 ;𝐻
̃𝑡 )/(𝑉𝑀,𝑡−1 𝑐𝑜𝑣(𝑅̃𝑗 ;𝑅̃𝑀𝑡 ))]
̃𝑡 ))/(𝑉𝑀,𝑡−1 𝜎 2 (𝑅̃𝑀𝑡 ))]
To work with the percentage change in per capita income ℎ̃𝑡 , the parameters
̃𝑡 ) and 𝑐𝑜𝑣(𝑅̃𝑀𝑡 ; 𝐻
̃𝑡 ) in (10) must be restated in terms of ℎ̃𝑡 . Interpret 𝐻𝑡−1 and 𝐻
𝑐𝑜𝑣(𝑅̃𝑀𝑡 ; 𝐻
aggregate income earned at t – 1 and t by Lt-1 the total labor force at t – 1. Looking forward from
t – 1, which is the perspective of equations (1) and (7),
̃𝑡 = 𝐻𝑡−1 (1 + ℎ̃𝑡 ),
and (10) can be rewritten as
𝛽𝑗∗ = 𝛽𝑗
(𝑉 𝑡−1 )𝑐𝑜𝑣(𝑅
𝑗𝑡 𝑡 )
𝑗 𝑀𝑡 )
̃ 𝑀𝑡 ;ℎ
(𝑉 𝑡−1 )𝑐𝑜𝑣(𝑅
̃ 𝑀𝑡 )
Taking nonmarketable assets to be synonymous with human capital, Fama and Schwert
estimate 𝛽𝑗∗ − 𝛽𝑗 for portfolios of New York Stock Exchange (NYSE) common stocks and for
portfolios of U.S. Treasury Bills and bonds. They find that the differences between the Mayers
and SLB risk measures are small, at best. The authors attribute this finding to the fact that the
relationships between the payoff to human capital and the returns on bonds and stocks are weak,
so that any existence of nonmarketable human capital does not have important effects on risk for
these two important classes of marketable assets. Fama and Schwert conclude that for bonds and
common stocks, the extensions of two-parameter theory provided by the Mayers model are not
of much consequence for describing the relationship between expected return and risk.
Jagannathan, Wang (1996) Conditional CAPM and Cross-Section of Expected Returns
Another important paper to consider is the research of Jagannathan and Wang (1996)16, in
which the authors used conditional model as opposed to static one. As claimed by Jagannathan
and Wang, the researchers who have previously examined the conditional version of CAPM
have not studied directly the ability of conditional model to explain the cross-sectional variation
Jagannathan R., Wang Zh. ‘Conditional CAPM and Cross-Section of Expected Returns’. The Journal of Finance,
vol. LI, No. 1 (1996), pp. 3-53.
in average returns on a large collection of stock portfolios. For the purpose of their paper,
Jagannathan and Wang derived both conditional model and the implied unconditional model of
CAPM, and have shown that when conditional model holds, a two-factor model applies
unconditionally – average returns on assets are jointly linear in the average beta and in the
measure of beta instability over time.
It is important to mention that Jagannathan and Wang considered the return on human
capital in the context of the return on aggregate wealth. They have noted that stock only form a
small part of the total economy wealth and, therefore, other assets should be considered for
assessing the systematic risk. Following Mayers assumption that human capital contributes a
significant portion of the total capital in the economy, Jagannathan and Wang included human
capital in their model. The authors also took a notice that in the structure of total monthly per
capita personal income in the US during the period of 1959 – 1992 the share of dividend income
was less than 3%, while at the same time the share of wages and salaries was more than 60%.
This further proved the validity of considering payoff to human capital to measure returns on
aggregate wealth more accurately.
Jagannathan and Wang pointed out that even though securities like mortgage loans are
issued against future income and active insurance markets exist for hedging the risk of human
capital (life and medical insurance, unemployment insurance), there is a significant difference
between human capital and other physical assets owned by corporations. The idea is that, unlike
other physical assets, from the use of which the entire cash flow is usually promised away by
issuing financial securities, it is not the case for human capital, where only a portion of income is
secured by mortgages. Therefore, the authors concluded that factors affecting return on human
capital cannot be identified precisely by examining returns on such securities as mortgages.
Growth rate of the per capita payoff to human capital in the economy was taken as a proxy for
return on human capital, similar to the measure suggested by Fama and Schwert (1977) research.
Even though Jagannathan and Wang arrive at this measure based on different lines of reasoning,
the calculation is the same as in (9).
Further the measure of labor-beta is defined by the authors as:
𝜎 2 (ℎ)
Finally, Jagannathan and Wang introduced the so-called Premium-Labor (PL) model,
which is assumed to hold for every asset i:
𝐸[𝑅𝑖𝑡 ] = 𝑐0 + 𝑐𝑀 𝛽𝑖𝑀 + 𝑐𝑝𝑟𝑒𝑚 𝛽𝑖
+ 𝑐𝑙𝑎𝑏𝑜𝑟 𝛽𝑖𝑙𝑎𝑏𝑜𝑟
Where 𝑐𝑀 , 𝑐𝑀 , 𝑐𝑝𝑟𝑒𝑚 , and 𝑐𝑙𝑎𝑏𝑜𝑟 are some constants;
𝑅𝑝𝑟𝑒𝑚 denotes yield spread between BAA- and AAA-rated bonds;
𝑐𝑜𝑣(𝑅𝑖 ,𝑅𝑀 )
𝜎 2 (𝑅𝑀 )
𝑐𝑜𝑣(𝑅𝑖 ,𝑅𝑝𝑟𝑒𝑚 )
𝜎 2 (𝑅𝑝𝑟𝑒𝑚 )
In their empirica1 research, authors use the returns on 100 portfolios created using the
same methodology as in Fama and French (1992) paper. For each calendar year starting 1963,
they first break down the firms into size groups (deciles) based on market value at the mid of the
year. After that for each size group, the authors calculated beta coefficients of companies using
24 to 60 months of historic returns and CRSP value-weighted index as proxy for market index.
They denoted these betas as pre-ranking beta estimates. Thus, authors arrived at 100 portfolios
by sorting firms within each size group into beta deciles according to pre-ranking beta
The empirical test of Jagannathan and Wang model has shown that the unconditional
model implied by conditional CAPM explains around 55% of the cross-sectional variation in
average returns of 100 stock portfolios, when human capital is included, as compared to 1%
explained by traditional static CAPM.
Jagannathan et al (1996) CAPM with human capital: Evidence from Japan
Ravi Jagannathan, Keiichi Kubota & Hitoshi Takehara (1996) also suggested that human
capital is particularly important to consider in CAPM model. The claimed that payoffs to human
capital form more than one third of the total wealth in developed countries.
The authors follow Fama and Schwert (1977) approach to return on human capital, taking
growth rate in per capita labor income in economy as a proxy. Two betas were estimated in the
model – one based on covariation of asset returns with stock index portfolio and the other based
on covariation of asset returns with per capita labor income.
The difference of this paper from other papers discussed is that it compares the results
obtained from estimating the model with human capital to the ones obtained from Fama and
French (1992) three-factor model, instead of traditional SLM CAPM.
In their empirical analysis Jagannathan, Kubota and Takehara used data for Japanese
market because they thought that human capital played a crucial role in its economic
development. The authors have shown that human capital forms a crucial part of the total wealth
in economy. Wages and salaries comprised more than 70% (¥251,996 billion) of the national
income (¥355,799 billion) in Japan in 1991, while income from dividends contributed less than
3% (¥9,993 billion). These results are similar to those obtained by Jagannathan and Wang (1996)
for the US market.
In their methodology, Jagannathan, Kubota and Takehara followed the approach by
Jagannathan and Wang (1996). They applied the model with labor-beta to Japanese market,
which yielded coefficient of determination of more than 60%. Thus, the authors concluded that
including human capital in the standard CAPM substantially improves the performance of the
Chapter 2. CAPM with nonmarketable assets in Russia
2.1 The data
The income per capita of the labor force, henceforth called income, is defined as the
average wage and salary disbursements to the unit of labor force in the economy, as computed by
the Federal State Statistics Service of the Russian Federation. Monthly data for the years 2009 –
2015 are used.
The empirical task of this paper is to compare estimates of 𝛽𝑗 and 𝛽𝑗∗ of (2) and (11) for
different marketable assets j. Estimates of 𝛽𝑗 and 𝛽𝑗∗ require time series of:
the total value of marketable assets,
the return on the market portfolio of marketable assets, and
returns for different classes of marketable assets.
MICEX value-weighted index17 is considered as a proxy for the market portfolio, and the
aggregate capitalization of all securities traded on Moscow Exchange also comprise the total
value of marketable assets in economy. Portfolios of subsets of MICEX stocks provide the
different classes of marketable assets for comparing estimates of 𝛽𝑗 and 𝛽𝑗∗ .
In more detail, data on the end-of-month total market capitalization of MICEX stocks and
values for MICEX index were obtained from ‘Investfunds’ database.
Estimates of 𝛽𝑗 and 𝛽𝑗∗ of (2) and (11) are eventually compared for companies of ten
major sectors of economy18:
Oil & Gas,
MICEX index is the value-weighted index of 50 most liquid stocks of Russia’s largest public companies.
Only securities of the largest most liquid public companies were considered in the analysis. For the list of
companies, refer Appendix 1.
Metal & Mining,
To calculate the returns on securities a return index (RI) is used. It shows a theoretical
growth in value of a share for a defined period of time. Dividends are assumed to be re-invested
for the purpose of purchasing additional shares at a closing price applicable on the ex-dividend
Return index is calculated using the measure called annualized dividend yield. This
method adds an increment of 1/260th part of the dividend yield to the price each weekday.
Ignoring market holidays, it is assumed that there are 260 weekdays in a year. The base date
value of RI is 100, and is further adjusted in subsequent time periods using the formula:
𝑅𝐼𝑡 = 𝑅𝐼𝑡−1 ×
× (1 +
is the return index on day t
𝑅𝐼𝑡−1 is the return index on previous day
is the price index on day t
𝑃𝐼𝑡−1 is the price index on previous day
is the dividend yield % on day t
is the number of working days in the year (taken to be 260).
The calculation ignores reinvestment charges as well as any taxes. Gross dividends are
used for calculations where available. Closing prices for the respective periods are used to
calculate return index.
Returns are calculated based on return index, using the traditional formula:
In the two-parameter portfolio model, which is the foundation of both the Mayers and
SLB models, people invest in order eventually to consume. They evaluate investment payoffs in
units of consumption goods and services. This implies that variables should be measured in real
rather than nominal units. All of the results below are reported for real versions of the variables,
where the real variables are the nominal variables deflated by the Consumer Price Index (CPI).
Summary statistics section is divided into two parts: 1) market statistics, and 2) sectorspecific statistics. The former describes economy-wide parameters such as market return, market
capitalization, total payoff to human capital in the economy, count of labor force and wage per
capita. The latter focuses on sector companies’ performance.
Market returns at the end of each month in the observed period were calculated19 as
𝑅𝑀 𝑡 =
Where 𝑀𝐼𝐶𝐸𝑋𝑡 and 𝑀𝐼𝐶𝐸𝑋𝑡−1 are the values of MICEX index at t and (t-1) respectively, t ∈
31.12.2008 … 31.12.2015.
The mean value for market returns is 0.015, and median 0.018 (1.5% and 1.8%), while
standard deviation is more than x4 times higher than the mean (6.5%). The same can be observed
for ht, with the same mean of 0.015, it has standard deviation of more than x7 times higher than
mean (11.9%). Thus, one can say that these two measures are very volatile and the data should
be checked for outliers.
Table 2.1.1 Summary statistics for market data
market cap, m
wage per capita
total payoff to H, m
24 936 094
70 844 062
1 899 321
25 195 296
71 229 715
1 902 658
4 259 753
21 269 847
2 134 958
1 890 958
10 643 790
69 410 458
1 209 472
31 913 636
71 545 416
3 100 430
Source: Investfunds.ru, fedstat.ru, author’s calculations
Recall that the data was gathered on a monthly basis.
Pic. 2.1.1 Market returns, monthly data
As for other variables, the level of volatility is lower and standard deviations are much
less than x1 mean. Market capitalization has the mean and median of around RUB 25 trillion,
with a standard deviation of only RUB 4.26 trillion. Total payoff to human capital has the mean
and median of RUB 1.9 trillion, with a standard deviation of 0.45 trillion. The lowest relative
standard deviation is that of a labor force – with mean and median of 71 million, it has standard
deviation of only 0.73 million.
Table 2.1.2 Summary statistics for sector-specific data
Source: Investfunds.ru, author’s calculations
Graphical representation of returns time series for all ten sectors is given on Pic. 2.1.2.
Besides high volatility, one can see that returns have similar patterns and, more importantly,
resemble the behavior of market returns, which proves the validity of the chosen benchmark
Pic. 2.1.2 Sector companies’ returns, monthly data
No sector breakdown can be complete without Oil & Gas industry, which represents the
key sector of the Russian economy. Most liquid companies that fell into the category of Oil &
Gas are as follows:
These companies are also constituents of MICEX Oil & Gas index, and attribute to more
than 90% of the Russian Oil & Gas sector turnover. They are considered to be highly
representative of the sector.
With the mean return of 1.9% per month, standard deviation of the returns of companies
in Oil & Gas sector reaches 6.4%, which makes it one of the least volatile sectors of the Russian
Pic. 2.1.3 O&G sector returns, monthly data
Financial sector is made up of such companies as:
Sberbank of Russia
Although not numerous, these companies represent the lion part of the Financial sector.
Sberbank and VTB alone control more than 50% of the commercial banking activities in Russia,
and AFK Sistema is the largest financial conglomerate in Russia with the turnover of more than
USD 35 billion. Thus, the sample can be treated as representative of the sector.
Mean monthly return level of the sector companies is at 1.6% with the standard deviation
of 8.8%, showing the average volatility as compared to other sectors.
Pic. 2.1.4 Financial sector returns, monthly data
Telecommunications sector is represented by the following companies:
These include two of the three major mobile operators (MTS and Megafon) and the
monopolist national long-distance service network (Rostelecom). Mean monthly return of the
companies comprising this sector is 1.5% with the standard deviation of 8.1%.
Pic. 2.1.5 Telecom sector returns, monthly data
Energy sector includes numerous entities, which appropriately represent the market:
T Plus Group
This sector is highly volatile with standard deviation of 9.9%, which is x20 times higher
than the mean monthly return of 0.5%.
Pic. 2.1.6 Energy sector returns, monthly data
Consumer goods is represented by the following companies, including major food and
white goods retailers:
Consumer goods sector is characterized with one of the highest mean monthly returns of
2.6%, and with high standard deviation of 8%.
Pic. 2.1.7 Consumer goods sector returns, monthly data
For Transportation sector, the data is quite scarce. Only four liquid companies from
different industries are traded on MICEX, including two airline and two transport operator
Novorossiysk Commercial Sea Port
The returns are extremely volatile, with monthly mean return of 0.2% and standard
deviation of x44 times higher (8.8%).
Pic. 2.1.8 Transportation sector returns, monthly data
Chemicals sector includes Russian largest chemical companies:
The sector shows the highest average monthly returns of 3% with a standard deviation of
Pic. 2.1.9 Chemical sector returns, monthly data
Metal & Mining includes numerous largest representatives of the sector:
GMK Norilsk Nikel
Kuzbasskaya Toplivnaya Company
Chelyabinsk Metallurgicheskiy K
Mean monthly return of the sector companies is 1.8% with a standard deviation of 8.8%.
Pic. 2.1.10 Metals and Mining sector returns, monthly data
Only a few companies of Automotive sector are liquidly traded on MICEX, including:
Mean monthly returns of these companies is 1.6%, while standard deviation amounts
Pic. 2.1.11 Automotive sector returns, monthly data
Innovations sector is extremely versatile and includes companies of a number of different
Human Stem Cells Institute
United Aircraft Corporation
Donskoi Zavod Radiodetalei
These companies have shown negative average monthly return of -1.5% with a standard
deviation of 6.9%.
Pic. 2.1.12 Innovation sector returns, monthly data
2.2 Econometric approach
One of the first stages of the econometric study is the classification of a model that uses
panel data. Following types of models are known:
1. Pooled regression model:
𝑦𝑘𝑡 = 𝛽0 + 𝛽1 𝑥1𝑘𝑡 + ⋯ + 𝛽𝑚−1 𝑥(𝑚−1)𝑘𝑡 + 𝜀𝑘𝑡
All unknown parameters are constant for all groups of panel data at each point of
The random component is assumed to satisfy Gauss-Markov conditions.
2. Fixed effect model:
𝑦𝑘𝑡 = 𝛼𝑘0 + 𝛽0 + 𝛽1 𝑥1𝑘𝑡 + ⋯ + 𝛽𝑚−1 𝑥(𝑚−1)𝑘𝑡 + 𝜀𝑘𝑡
It is assumed that there are deterministic individual effects for panel groups, modeled
through 𝛼𝑘0 , i.e. the value of this ratio is different for each group. Thus, the model allows
us to reflect the effects of variables that are not included in the study but characterize the
features of the observed objects.
The main assumptions of the model ensure unbiasedness and consistency of estimates:
Errors 𝜀𝑘𝑡 are not correlated with each other, 𝐸[𝜀𝑘𝑡 ] = 0 and 𝑉[𝜀𝑘𝑡 ] = 𝜎𝑘2
Errors 𝜀𝑘𝑡 are not correlated with 𝑥𝑖𝑘𝑡 for all 𝑖 = 1 … 𝑚, 𝑘 = 1 … 𝑛 and 𝑡 = 1 … 𝑧
The main disadvantage of this model is that it is not possible to identify the coefficients
corresponding to the independent variables that do not change over time for each object
(binary variables). Formally, this is because in such case in the equation for finding the
fixed effect estimators of the parameters of the model20, one or more regressors are equal
to zero, and therefore, the ordinary least squares method (OLS) cannot be used.
3. Random effect model:
Equation for the calculation of fixed effect estimators using OLS:
𝛽̂ = [∑ ∑(𝑥𝑖𝑡 − 𝑥̅𝑖 )(𝑥𝑖𝑡 − 𝑥̅𝑖 )′ ]
× ∑ ∑(𝑥𝑖𝑡 − 𝑥̅𝑖 )(𝑦𝑖𝑡 − 𝑦̅)
𝑦𝑘𝑡 = 𝛽1 𝑥1𝑘𝑡 + ⋯ + 𝛽𝑚−1 𝑥(𝑚−1)𝑘𝑡 + 𝜀̃𝑘𝑡
This model has random individual effects, 𝜀̃𝑘𝑡 = 𝛼𝑘0 + 𝜀𝑘𝑡 . 𝛼𝑘0 still reflects the impact
of variables that are not included in the model, but it is now assumed that this effect is
random with zero mean and equal variances for all sampling objects, wherein 𝛼𝑘0 and 𝜀𝑘𝑡
The selection of the most adequate model is done through pairwise comparison of the
estimated models for each of the types mentioned above. The characteristics of these tests
are presented in Table 2.2.
Table 2.2 Model selection tests
Types of models
𝐻𝑎 : at least one of
FE / pooled
𝐻𝑜 : 𝑢𝑖 = 0
the equations does
Breusch – Pagan
RE / pooled
𝐻𝑜 : 𝑉[𝑢𝑖 ] = 0
𝐻𝑎 : 𝑉[𝑢𝑖 ] ≠ 0
RE / FE
𝐻𝑜 : 𝜌𝑥𝑢 = 0
𝐻𝑎 : 𝜌𝑥𝑢 ≠ 0
Source: Magnus J.R. Econometrics. Book – 5th Edition, 2001 – 400 p.
Following results were obtained for the observed data:
P-value for Wald test is less than the level of significance, therefore, the main
hypothesis 𝐻𝑜 : 𝑢𝑖 = 0 is rejected, preference is given to the model with fixed effect;
P-value for Breusch–Pagan test is less than the significance level, the main hypothesis
𝐻𝑜 : 𝑉[𝑢𝑖 ] = 0 is also rejected, therefore, the random effects model is preferred to
Using Hausman test to choose between the models with random effects and fixed
effects, we accept the alternative hypothesis 𝐻𝑎 : 𝜌𝑥𝑢 ≠ 0. Thus, using the Wald test,
Breusch-Pagan and Hausman the model with fixed effects was chosen.
Test for statistical significance of results
Although Fama and Schwert could not come up with any tests for statistical significance
of the differences 𝛽𝑗∗ − 𝛽𝑗 , the author of this paper considers the introduction of such a test
crucial for interpretation of the obtained results.
There are two types of tests in econometrics that are useful to consider in this case:
1. Test of the equality of the population means of two at least approximately normally
distributed populations based on independent random samples with a) equal assumed
variances, or b) unequal assumed variances.
2. Test of the mean difference of two populations based on dependent samples, or
‘paired comparisons’ test, assuming normal distribution.
Therefore, first it is important to identify whether there are grounds to suspect the
dependence of samples of two betas. This dependence may stem from a factor that affects both
sets of observations. At this point, the author considers the samples to be dependent because a
substantial part of the calculation of the two betas is the same, and they both depend on market
returns and asset returns, or more precisely their covariation. Based on this evidence, the author
chooses to use the test for dependent samples.
Second, obviously there is a need to obtain samples of betas, which is achieved through
running cross section regressions for each month of the observed period to obtain monthly betas
and then calculate Mayers betas. Thus, the author gets 11 pairs of samples (for 10 sectors and
market in general), each containing 83 observations.
After that, the author calculates t-statistic using formula (20) and compares it with critical
value (from Student’s t-distribution) based on (𝑛 − 1) degrees of freedom and 5% level of
significance. The following hypothesis are set:
𝐻𝑜 : 𝜇𝑑 = 𝜇𝑑𝑧
𝐻𝑜 : 𝜇𝑑 ≠ 𝜇𝑑𝑧
where 𝜇𝑑 = mean of the population of paired differences
𝜇𝑑𝑧 = hypothesized mean of paired differences, which is zero for our case
𝑑̅ = sample mean difference = ∑𝑛𝑖=1 𝑑𝑖
𝑑𝑖 = difference between i-th pair of observations
𝑠𝑑̅ = standard error of the mean difference =
̅ 2 1/2
𝑖=1(𝑑𝑖 −𝑑 )
𝑠𝑑 = sample standard deviation = [
𝑛 = number of paired observations
Finally, the obtained t-test should be compared to t-critical for a two-tailed test at 5%
level of significance and with (83 − 1) = 82 degrees of freedom, which equals 1.99. For the
null hypothesis to be rejected the t-test should be greater than t-critical in absolute value, i.e. the
following inequality must hold: |𝑡𝑛−1 | > 1.99
2.3 Statement of the results
The main part of the work is devoted to the calculation of two types of betas – regular
and the one with human capital – and their difference. The statistically significant difference of
the two risk measures would prove the validity and necessity of including nonmarketable assets
in the traditional CAPM model, or vice versa. For the purpose of calculation of betas with human
capital, equation (11) is used.
Table 2.3 shows comparisons of estimates of 𝛽𝑗 and 𝛽𝑗∗ for the constituents of MICEX
index21, mentioned above (refer 2.1 The Data, Definitions). The SLB risk estimates 𝛽𝑗 are the
slope coefficients from market model regressions of Rjt and RMt, where M is the value-weighted
MICEX index. The estimates 𝛽𝑗∗ of the Mayers risk measure use the market model estimates for
𝛽𝑗 and the standard formulas for sample covariances and variances for the remaining parameters
in (11). The ratio
in (11) is estimated as the average of the monthly values of this ratio for
the indicated period. Table 2.3 gives the sample standard errors of the SLB risk estimates as well
as t-statistics calculated for each pair of beta differences.
The question posed for Table 2.3 is whether there are important differences between the
Mayers and SLB risk measures for the marketable assets in general. The answer seems to be
‘no’. The difference is only as large as 0.0058 in absolute value.
50 most liquid stocks of Russia’s largest public companies. Refer 2.1 The Data, Definitions.
However, even though one can infer from Table 2.2 that the values of 𝛽𝑗 − 𝛽𝑗∗ are close
to zero for MICEX stocks in general, there may be subclasses of stocks for which there are
important differences between the two risk measures.
For this reason, the stocks were divided into 10 major classes of assets (refer 2.1 The
Data. Definitions), and differences 𝛽𝑗 − 𝛽𝑗∗ were calculated for each group, which has yielded
some positive results. Yet, although for most classes the differences between the Mayers and
SLB risk measures are close to zero and statistically insignificant, for Transportation and
Innovation sectors the differences are as large as 8.5% and 9.2%.
Table 2.3 Statement of the results
𝜷𝒋 − 𝜷𝒋∗
Oil & Gas
Metals & Mining
Source: Stata regressions, author’s calculations
2.4 Interpretation of the results
Due to the nature of Russian economy, which is infrastructure-intensive and resource
oriented, human capital plays in general a less significant role, than in more developed and
Therefore, it is not surprising that the effect from inclusion of human capital is negligible
for the market in general and for the most sectors.
As for Innovation sector, the results that were obtained are meaningful, since this type of
corporations usually is very dependent on personnel. Human capital plays a key role as a driver
for innovations. The founders of the theory of human capital – H. Becker and T. Schultz –
proved productive nature of the investments in people, providing a significant and lasting effect.
For example, T. Schultz identified the formation of human capital with investments in education,
which are realized in the enhanced production abilities and skills of employees, ensuring the
growth of salary and employee satisfaction. At the micro-economic level, the formation of
human capital is associated with the investment in personnel through the costs of education and
training of the workforce, health care expenses, professional and geographical mobility.
Price of labor, emerging on the market, is an economic evaluation of human resources.
The level of this estimate depends on the income of workers and employers costs. Economic
evaluation, in turn, depends on the economic effect of the use of highly skilled human resources,
determined by the level of their use. In the framework of the theory of human capital, efficiency
of investments in the human resources is defined as the value of the additional returns resulting
from the productive use of human resources.
As for Transportation sector, the author could not find any valid economic justification to
explain why the results for this sector are significantly different from those of other eight sectors.
In addition, given a more detailed look at the companies, comprising the sector, one can see that
they are neither numerous nor representative of the sector, and operate in different segments of
transportation. For this reason, Transportation sector was dropped from the analysis, and the
results obtained were considered invalid.
Ways to define human capital
There are many legitimate quarrels about the ways to measure the return to human
capital. For example, in this paper the author uses gross income per capita as the measure of the
payoff to a unit of human capital, while net income, that is, gross income less the maintenance
costs that must be incurred to keep a unit of human capital in working order, is probably more
appropriate. Implicit assumption made in the paper is that such maintenance costs are not highly
related to the returns on marketable assets so that net income, is likely to be more or less
unrelated to the returns on marketable assets [Fama and Schwert, 1977].
Another valid criticism is that working with per capita income corrects for changes in
aggregate income that result from changes in the size of the labor force but it leaves any
problems created by changes through time in the quality of the labor force. One of the ways of
measuring the quality of the labor force is by median school years completed. Thus it seems
reasonable to presume that the effects of quality change show up primarily in the mean rate of
change of per capita income ℎ̃𝑡 , and that the variation through time of ℎ̃𝑡 , which is what is
critical in the tests, is relatively free of the effects of quality changes.
Nevertheless, the rigor of the paper would be improved if all appropriate adjustments of
aggregate income were made. Unfortunately, with the current state of data in Russia it is
impossible to obtain such information.
Human capital as a proxy for nonmarketable assets
Prohibitions against slavery may not be sufficient to justify the assumption that human
capital is nonmarketable. For example, athletic contracts and book publishing contracts involving
bonuses or advances for future services can be regarded as partial sales of human capital. The
same is true of borrowing with future income as the specific collateral. The Mayers model is
quite clear on this point. The model allows unrestricted short selling of marketable assets,
whether riskless or risky, but one cannot borrow specifically against future income. Such
borrowing is in fact possible, although the amount that can be borrowed is usually less than oneor two-year income. Likewise, bonuses and other advances that amount to partial sales of human
capital are not typical of the way payments are made to human capital. The extent to which
human capital is marketable, then, is an open question [Fama and Schwert, 1977].
One can argue that the companies comprising sectors in this paper are not representative
of the sector or scarce to make general conclusions. The author considers this point quite valid.
However, the following points must be taken into account:
The decision on assigning the stocks to certain sectors was based on the methodology
of MICEX for choosing companies for sector indices;
The most comprehensive data on the Russian stock market was used;
With the current state of market data, it is not feasible to collect better data.
Considering the abovementioned, one can see that the limitation is rather caused by the market
conditions than by the methods used in this research paper.
Nevertheless, increasing the number of companies for the study could be a good
extension for further studies in this field in the future.
In this paper, the author has presented and empirically tested the Capital asset pricing
model with nonmarketable assets, namely human capital. The postulated relation between risk
and expected return is of the same linear form as that of the Sharpe-Lintner-Mossin model. Thus,
the structure of asset prices remains essentially the same even when nonmarketable assets are
included in the investor’s portfolio problem. However, the results differ from those of the SLM
model in that the expanded measures of the firm’s systematic risk and the market risk include the
risk attributable to the existence of nonmarketable assets.
The formulation of the modified model is identical to the missing assets formulation of
the SLM model – that is, ignoring the existence of nonmarketable assets in the expanded model
leads to the same form of misspecification of the measure of relative systematic risk as does
excluding portions of the universe of marketable assets in the SLM model.
Contrary to the SLM model, the expanded model implies that not all maximizing
investors hold the identical (except for scale) portfolio of marketable assets. It implies that each
investor holds a portfolio of marketable assets that solves his personal (and possibly unique)
portfolio problem and, therefore, allows investors to maintain unique portfolios.
Empirical analysis of the CAPM with nonmarketable assets has shown significant
difference of the estimates of the models for Innovations sectors. The beta predicted by extended
model is 9.2% higher than the SLM beta. Unfortunately, the research has failed to prove the
validity of the model for other sectors of companies and for the market in general, which may be
attributable to the limitations stated in the paper. These limitations include: 1) the quarrels about
the way to define human capital, 2) the controversy of using human capital as a proxy, and 3) the
imperfection of data on Russian stock market.
For further researches on the topic, one could consider extending the definition of human
capital by including other payments such as corporate trainings, social package, workplace
infrastructure maintenance and other factors that comprise costs of maintaining a unit of human
capital in the working order.
Finally, other types of nonmarketable asset may be elaborated. At this point, the work of
Alexander Bukhvalov (2008) could be considered. Specifically, Professor Bukhvalov has
suggested M&A volumes as a proxy for nonmarketable asset.
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Appendix 1. List of companies by sector
Oil & Gas
Human Stem Cells Institute
United Aircraft Corporation
Donskoi Zavod Radiodetalei
T Plus Group
Metals & Mining
GMK Norilsk Nikel
Kuzbasskaya Toplivnaya Company
Chelyabinsk Metallurgicheskiy K
Novorossiysk Commercial Sea Port
Sberbank of Russia