Capital Assets Pricing Model

Capital is the main economic basis for the creation and development of a company. In the course of functioning, the capital represents the interests of the state, owners, and personnel. From the position of the financial management, the capital of the company characterises the total cost of means in the monetary, material and non-material forms invested in the formation of its assets. The cost model of the capital market, often indicated as “Capital Assets Pricing Model” (CAPM), is the cornerstone of the modern financial theory. The CAPM is the theory of pricing of risky financial assets in the conditions of marketing balance (Da, Guo, & Jagannathan, 2012, p. 205). It is grounded on the principles of the formation of the investment portfolio. CAPM is the theoretical model developed for the explanation of the dynamics of the securities’ rates and provision of the mechanism by means of which investors could estimate the impact of investments in estimated securities on the risk and profitability of their portfolio. The required standard of profitability (discount rate) for any kind of investments is dependent on the risk connected with these investments.
According to Da, Guo, and Jagannathan (2012), CAPM allows foreseeing the interconnection with the risk of any financial assets and the expected profitability, which can be used for the assessment of potential investments. This interconnection fulfils two vital functions. Firstly, it allows receiving the benchmark rate of return used for the assessment of the expected investments. For example, a financial analyst can be interested whether the expected rate will be more or less than its objective value in correspondence with the existing level of risk. Secondly, this model allows doing well-grounded presumptions concerning the expected profitability of assets, which were not traded in the market (Da, Guo, & Jagannathan, 2012, p. 207).
CAPM is grounded on the assumption that the corresponding bonus for the risk of any asset will be determined by its contribution to the total portfolio risk. A market portfolio risk represents the biggest interest for investors as it determines the value of the bonus for the risk demanded by investors (Choudhari, K. & Choudhari, 2010, p. 128). However, CAPM has two limitations. It is guided by the existence of the theoretical market portfolio, which includes all assets (shares, real estate, and others), and considers the expected rates of return instead of the factual ones.
At the investment calculations, the discount rate is defined as the weighted average cost of capital (WACC), including the equity cost of capital and the cost of borrowed funds. In fact, it is the most objective method of the determination of a discount rate. At the same time, CAPM is applied for the determination of the equity cost of capital. Kruger, Landier, and Thesmar (2011) state that the determination of a discount rate for investments is connected with the calculation of the current cost of the so-called “debt-free” cash flow (Kruger, Landier, & Thesmar, 2011). The value of the capital cost used by the company for the financing of its activity is applied for the calculation of the “debt-free” cash flows. Owning to the idea that both the equity cost of capital and the borrowed funds participate in such financing, the WACC acts as the size of the “general” cost of the capital (Mitra, S. (2011, p. 89).
The profitability of a new investment project has to be higher than the WACC size. Otherwise, it is unreasonable to realise it as it will lower the total cost of the company. Therefore, it is logical to use WACC as a discount rate. There are two main problems arising when using WACC as a discount rate. The first one is connected with the fact that WACC reflects the current cost of the set of sources used for the financing of capital investments usual for this company (Kruger, Landier, & Thesmar, 2011; Mitra, 2011, p. 90). The second one states that in case the company starts the unusual activity, the investments are exposed to absolutely other risks than the “normal” ones. Thus, WACC cannot be used as the required standard of profitability as does not consider the distinction in the risks of different investments.
The security of the ownership rights of shareholders is dependent on such factors as the ownership structure, concentration of property, the conflicts between various owners and groups of owners, the relation of owners to the corporation, and others. There is positive dependence of the company’s profit on the concentration of ownership in the hands of administrative personnel (Pindado & La Torre, 2011, p. 213). A careful selection of new capital owners is the practical expression of the importance of a company’s ownership structure for the increase in the business efficiency and the cost of equity capital. For example, according to Driffield, Mahambare, and Pal (2007), many owners worry when direct investments or hedge funds enter the company’s equity capital. It is caused by possible essential divergence of time periods of obtaining benefits. If owners of capital are often interested in the long-term successful functioning of the company in the market, then the interests of direct investment funds can be limited to 5-7 years (Driffield, Mahambare, & Pal, 2007, p. 537).
While analysing the cost of equity capital, Margaritis and Psillaki (2010) try to answer the following questions. Firstly, it is necessary to determine whether there is an optimum ownership structure (the size of large equity shares concentrated in one person, the volumes of shares possessed by managers, board members, the presence of institutional investors, and others) which allows maximising the cost of equity capital at the equal involvement of the fundamental factors. Secondly, it is vital to understand how the changes in the ownership structure will affect the company’s cost of equity capital. For example, one has to determine how market investors will assess the inclusion of the state in the number of owners or, on the contrary, the sale of the state package (Margaritis & Psillaki, 2010, p. 624).
The empirical researches in developed and emerging markets allow finding the answers to these questions. The institutional environment and the sphere of activity render a significant effect on the optimum ownership structure. For example, if in the USA the controlling stake in large companies does not exceed 10%, for the European countries, the control is characterised by the capital share at the level of 40%, and in the emerging markets, it totals around 51% (Margaritis & Psillaki, 2010, p. 629; Lin, Mab, & Xuan, 2011, p. 417).
Traditionally, the efficiency of the change of the ownership structure is checked either by the cost indexes (for example, on the basis of the ratio of the market assessment and the balance one, the “price/revenue” multiplication), or by balance (on the basis of the ROCE indicator). The holder of more than 5% is considered to be the major shareholder by the standard methodology (bloc holders) (Driffield, Mahambare, & Pal, 2007, p. 539). It is connected with the fact that in the world practice, 5% is the threshold for the disclosure of information on the company’s ownership structure.

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The impact of the ownership structure on the company’s cost of equity capital

The received dependences often have nonlinear character. The cost of equity capital differs taking into account the property share of the board members in the American market. The analysis was grounded on the study of 371 companies of the non-financial sector which enter the Fortune 500 Index (Pindado & La Torre, 2011, p. 221). At the same time, the presence of the family member of the business owner or a top manager of the company as an owner significantly influences the cost of equity capital. This impact has a negative character with regard to mature companies working for a long time on the market. For young companies, on the contrary, the presence of the founder is positively significant.
A big concentration of property in the hands of managers, while allowing aligning the interests of managers and owners, is characterised by the high cost of equity capital. On the other hand, empirical results of researchers on the identification of the interrelation between the ownership structure and the cost of equity capital state that there are negative relations (Pindado & La Torre, 2011, p. 226; Lin, Mab, & Xuan, 2011, p. 418). The sign of dependence of the equity capital on the ownership structure is dependent on various external factors.
The number of the company’s owners and the rates of changes in the number of owners compose quantitative indices of the uncertainty degree of the ownership structure. With poor quality of protection of the property rights, the company will aspire to have the less complex ownership structure. It can cause the decreased rates of the number of owners and a new optimum trajectory both for the financial leverage and the cumulative cost of the company (Driffield, Mahambare, & Pal, 2007, p. 546). Thus, empirical researches show that the dependence on the growth rate of the number of owners is not monotonous as it varies in different companies. The concentration of property is generally inversely proportional to the number of owners. It allows making a conclusion about the dependence of the cost of equity capital on the ownership structure.

Capital Market Line (CML)

The market portfolio is the portfolio comprising all securities, in which the specific weight of each share corresponds to its relative market value. The relative market value of an asset equals its cumulative market value divided into the sum of the cumulative market costs of all assets. The CML and SML are the main indicators of the portfolio’s efficiency. In CAPM, the dependence of the risk and the expected profitability of assets can be graphically described by means of the capital market line (CML) (Reilly & Brown, 2011). The M graphics represents a market portfolio where rf is an asset without the risk with the rf profitability, rfL is the capital market line, and E(rm) is the expected profitability in the market portfolio. All possible effective portfolios, which include the L market portfolio, are located on the rfL line. It lies between two points, namely rf and M (Reilly & Brown, 2011). Thus, the capital market line (CML) represents an effective border of portfolios at the possibility of loan and crediting. CML received its name because the portfolios composing it are formed with the help of the borrowing means or granting the loans under the rate without a risk in the capital market.
Evidently, all other portfolios, which do not include the market portfolio, are located lower than the rfL line.
CML rises up from left to right, and it says that if a portfolio has a higher risk, it should also possess the higher expected profitability. Similarly, if investors wish to receive higher expected profitability, they should agree to higher risks. The CML inclination should be considered as remuneration for each additional unit of risk undertaken by the investor (Lee & Su, 2014, p. 69).
When investors get assets without a risk, they insure the profitability at the level of the rate without the rf risk. If they seek to receive higher expected profitability, they should agree to some risk. The rate without a risk represents remuneration for the time, within the frameworks of which money have a value. The additional profitability received by the investor over the rate without a risk composes remuneration for the risk. Thus, remuneration for people investing the means in a market portfolio comprises the rf rate, which is remuneration for the time, and remunerations for the risk E(rm)-rf. In other words, the participants of the financial market trade the price of time and the price of risk. Thus, CML describes the ratio of the risk and expected profitability only for widely diversified portfolios, including a market portfolio (Li, 2012, p. 22). However, it is not applied for less diversified portfolios or separate assets.

Security Market Line (SML)

At the state of the market equilibrium, the expected profitability of each asset and a portfolio should be placed on the security market line (SML), irrespective of whether it is effective or not. Security Market Line (SML) is a graphic interpretation of the dependence of the risk of a separate security measured by the beta coefficient and the standard of profitability which will be demanded by investors for its acceptance (Hodbett & Hsieh, 2012, p. 853). At the same time, the higher the level of the accepted risk is, the higher compensation should be offered to the investor. According to Lee and Su (2014), SML reflects the dependence “risk – profitability” for separate actions. The required profitability of any action is equal to the risk-free norm put with the work of an award for the market risk. The absence of the risk on the risk-free securities also involves the minimum level of profit. Therefore, the risk-free securities compose the main regulator of profits and risks (Lee & Su, 2014, p. 71).
SML demonstrates that the expected profitability of assets is equal to the rate without the risk in equilibrium together with remuneration for the market risk measured by the beta variable. It represents a straight line which passes through two points, namely f0 and E(rm); M is a market portfolio. SML can be built knowing the rate without the risk and the expected profitability of a market portfolio (Hodbett & Hsieh, 2012, p. 867).

The SML inclination depending on the expectations of the future market state

The widely diversified and inefficient portfolios and separate assets are located at the SML line. The inclination of the SML line is defined by the attitude of investors towards the risk in the different market conditions. If investors have the optimistic forecasts for the future, the SML inclination will be less abrupt because in the conditions of a good market state, the investors agree for the higher risks at the lower values of the expected profitability(Li, 2012, p. 28).
On the contrary, if there are unfavourable market conditions, SML will be more abruptly inclined as in this case, investors will demand the highest expected profitability on the acquired assets for the same values of risk. If the investors’ expectations concerning the rates without the risk change, it will lead to SML shifts (Lee & Su, 2014, p. 72). The indicators of the portfolio effective management have an identical structure. The SML is applicable for the assessment of the profitability of both separate shares and other portfolios. Therefore, the covariance of the profitability of shares as the risk measure serves the covariance of the profitability of the security or a portfolio with the profitability of securities in a market portfolio.
The existing complex investment strategies allow achieving the desirable result. However, the effect of their application sometimes stresses the need for the use of the complex differentiated approach to the question, thereby increasing the risk component of the process in general. For the realisation of the complex effective strategy, it is necessary to share the funds among the leaders in the growing market and the leaders in the falling market. At the same time, the identification of the leaders requires the compilation of the funds rating allowing conducting the effective analysis of the current market situation. The classical compilation of the rating is made on the basis of the calculation and the analysis of the mathematical indicators, namely coefficients. There are several coefficients showing the degree of dependence of indicators of assets on the benchmark indicators. The alpha (α) and beta (β) coefficients are the quantitative characteristics of the dependence of the separate security price change on the change of an index value (Gorman & Weigand, 2007, p. 3).
It is very important to separate alpha and beta coefficients in the portfolio analysis. The alpha coefficient is rather closely connected with the beta coefficient. If beta estimates the influence of the market on the profitability of fund, alpha shows which part of this profitability was created not by the market growth but by the skills of the managing director or the strategy used in the fund. The negative value of the alpha coefficient shows that the average profitability of a portfolio was lower than the profitability of the benchmark portfolio and the management was inefficient.
The alpha coefficient is the parameter assessing the precisely effective management of the capital, taking the risk component into consideration. The alpha coefficient reflects the way the results of work in the market are dependent on the quality of the trade system but not on the market fluctuations (Gorman & Weigand, 2007, p. 5). Alpha allows estimating the average level of the income brought by the investment portfolio. Moreover, it shows the level of the growth (decrease) of the security’s price independent of the index changes. Alpha represents the difference between the real profitability of the mutual fund for the period and profitability which it had to show, taking into account the extent of the market growth or falling.
The Sharpe ratio as well as the alpha coefficient, compares the profitability of the investment portfolio to the fluctuation of the portfolio profitability for the analysed period, thereby giving the “internal” quality assessment data on the portfolio profitability. According to Pav (2016), the Sharpe ratio has an advantage compared to the alpha coefficient. The standard deviation measures the volatility of the fund in the absolute value but not the relative one as alpha. Therefore, if there has to be a high correlation coefficient for the usefulness of alpha, the Sharpe ratio always has a full-fledged value, irrespective of other indicators (Pav, 2016, p.7).
Sharpe invented the indicator for the efficiency assessment which shows the relation of the average awards for the risk to the average portfolio deviation. The standard deviation acts as the measure of a risk. In other words, the indicator allows understanding how big the investor’s award will be, at the inclusion of assets with high volatility into the portfolio. Similarly, the more value there is, the more the player will receive for the assumed risk.
The alpha “cost-profit” coefficient of Warren Buffett is the main indicator of the market portfolio. According to Frazzini, Kabiller, and Pedersen (2013), the Buffet’s alpha is calculated on the basis of the market cost of shares and annual company’s revenues. The lower the alpha coefficient is, the more reliable is the investment. It provides safety of the investment activity (Frazzini, Kabiller, & Pedersen, 2013, p. 3). Moreover, the Buffet’s portfolio was substantially diversified. The closer the sum to the stock price is, the more reliable is the investment. Buffett always sought to invest in the companies with the high level of the sales profitability. He conducted more careful analysis, tracing the dynamics of the change of this indicator for a certain period and comparing it to the indicators of the similar enterprises. Proceeding from it, Buffet chose the most attractive options (Frazzini, Kabiller, & Pedersen, 2013, p. 5). Thus, the alpha coefficient and its correct application allowed Warren Buffet make successful investment projects.
The beta coefficient is the unit of the measure, which gives the quantitative ratio between the rate movement of this stock and the movement of the stock market in general. Beta is the risk level indicator of the investment portfolio. Also, it reflects the degree of stability of the stocks in comparison with the other stock market. Moreover, it establishes the quantitative ratio between fluctuations of the price of the share and dynamics of market prices in general. If this coefficient is more than 1, the share is unstable; if beta is less than 1, the share is considered to be stable (Bali, Cakici, & Tang, 2009, p. 112).
The alpha coefficient is dependent on the beta coefficient, whose shortcomings affect the general result of the market portfolio. The beta coefficient is dependent on the index, being the basis for the correlation calculation. Being the measure of the market risk, the indicator reflects the risks of an investment. Thus, the more beta is, the more aggressive is the strategy of the investor (Bali, Cakici, & Tang, 2009, p. 105). Thus, the portfolio investors are interested in the beta coefficient and prefer shares with the low beta level.

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