Introduction
Methodology for assessing the financial assets appeared in the second half of the 20th century, and the most effective pricing model of financial assets, as practice shows, is the CAPM and its further extentions.
First of all it is necessary to explain what are assets and financial assets in particular: assets of the company is a property that has cash value and is reflected in the asset balance, and financial assets is part of the company's assets in the form of financial resources, such as cash and securities. Financial assets include cash, bank deposits, deposits, checks, insurance policies, investments in securities, obligations of other companies and organizations for the disbursement of funds for products delivered (commercial loan), portfolio investment in shares of other companies, shares in other companies which give the right of control, shares or equity interests in other enterprises.
The purpose of the work is explanation of valuation models of financial assets (CAPM), overview of the main properties of the standard CAPM, including its weaknesses, and explanation of its further extentions which serve the CAMP shortcomings.
Capital Asset Pricing Model (CAPM) and its characteristics
In 60-es of the XX century were published three works, which opened a new milestone in the development of investment theory, devoted to the model of assessment of financial assets. Works by Sharp (1964), Lintner (1965), Mossina (1966) were devoted to the same question: "If all the investors, having the same information, equally assess the risk and expected stock returns. If they form the optimal portfolio according to the theory of Markowitz on the basis of individual risk, what in this case will be the price of shares?". (Fama et al., 2004)
Thus, the CAPM (Capital Assets Pricing Model) can be viewed as a macroeconomic generalization of the theory of Markowitz. The main result of the CAPM was the establishment of the relationship between risk and return of an asset in case of equilibrium in the market. One of the most important things is the fact that while making the choice the investor must take into account not the entire risk of the securities, but only a systematic or non-diversifiable.
This part of the risk of an asset is closely connected with the market in general, and is quantitatively represented by the beta coefficients, introduced by William Sharpe in his one-factor model (as opposed to two-factor Markowitz model, where an investor considers both expected return and standard deviation). The diversifiable part of the risk is limited by choosing the optimal portfolio, and the nature of the relationship between risk and return is a linear dependence.
Assumptions that lie in the base of the model of pricing of financial assets, include some postulates of the theory of capital market of Markowitz, and additional assumptions:
1. The main factors of the evaluation of investment portfolios are the expected return and standard deviation for the period of portfolio ownership.
2. The premise of unsaturation: when making the choice between two equal portfolios, the investor will always prefer the portfolio with higher profitability.
3. The premise of risk aversion: when making the choice between two equal portfolios, investor always chooses a portfolio with the lowest standard deviation.
4. All assets are completely liquid and infinitely divisible, so that they can always be sold at market price, and investors can buy only a portion of the shares.
5. An investor can perform lending and borrowing at the risk-free interest rate.
6. Transaction costs and taxes are infinitesimal.
7. The investment period is the same for all investors.
8. Risk-free interest rate is equal for all investors.
9. Information is instantly available to all investors.
10. Investors' expectations are homogeneous, so that they equally assess the expected returns, standard deviations and covariance of securities.
Situation, given in these assumptions, is perfect: all investors equally assess the parameters of the securities, all the information is available to each investor, there are no obstacles to the transactions. This is done not to consider how the investor makes the choice between shares, but to analyze how the price on market assets will be formed in a perfect market.
There are two main features that characterize the capital assets pricing model:
1) First is a theorem about the separation: from the above assumptions comes the assertion that, after analyzing the characteristics of securities and specifying the effective set, investors choose the same tangent portfolio. This is due to a precondition 10 about the equal expectations of investors.
2) The second feature of CAPM is the fact that each type of securities has a nonzero fraction of the tangent portfolio. This is determined by the market mechanism of supply and demand. If the share of any securities is zero, then its course on the market will fall, respectively, the expected yield will rise, as investors begin to buy this paper and its share in the portfolio will not be different from zero. If, conversely, some asset has too high demand, the brokers will have to raise prices that, therefore, will reduce the yield and reduce the proportion of such share in the tangent portfolio, equating supply and demand. Ultimately, the market should reach equilibrium.
There are different point of view about the models for evaluation of capital assets. With the time have developed some typical views favoring and criticizing this model.
First of all, it is necessary to say that the concept of CAPM, which is based on the priority of market risk over the general, is very useful and is fundamental in the conceptual plan. In theory, CAPM provides a unique and well-interpreted results on the relationship between risk and required return, but it suggests that to build a connection must be used a priori expected values of variables, whereas analytics have only posteriori factual values. Therefore, the estimates of profitability found with this model can potentially contain errors. Also some studies on the empirical validation of the model showed significant variations between actual and calculated data, that is the reason for serious criticism.
The main weaknesses of the theory are:
- CAPM does not account all factors affecting the yield, and moreover does not allow to analyze them , because it is a single-factor model - and this is its main drawback.
- The model is conditional enough, because is limited by a number of unrealistic assumptions (it does not account taxes, transaction costs, lack of transparency of the financial market, etc.)
- Static, inability to use the new investment opportunities.
- Normal distribution of returns and market efficiency is observed only on a limited list of markets.
Criticism of the CAPM and its modifications
Several empirical studies of 1970s proved benefits of the CAPM in predicting stock returns. The classical works include: Black, Jensen, Scholes (1972), Fama and MacBeth (1973) and others. However, criticism of CAPM in the academic community began almost immediately after the publication of works devoted to the model. For example, the work of Richard Rolle (Roll, 1977) focuses on the problems associated with the definition of the market portfolio. In practice, the market portfolio is replaced by some as a diversified portfolio, which is not only available to investors in the market, but also amenable to analysis (for example, stock index). The problem with such a proxy portfolio lies in the fact that his choice can significantly affect the results of the calculations (for example, the beta value).
CAPM is also criticized by E. Fama and K.French (1988), who have studied the relationship between the beta coefficients and yield of a few thousand shares on data for 50 years. They wrote that "the empirical record of the model is poor to invalidate the way it is used in applications". Even though the CAPM's empirical problems may come from "theoretical failings, simplifying assumptions, anyway they may also be caused by difficulties in implementing valid tests of the model." (Fama, 2004)
Brigham recalled that CAPM described the relationship between just the expected values, and therefore any conclusions based on empirical tests of statistical data are hardly right, and can not oppose the theory. And Roll (1977) pointed that the CAPM can not be tested , because it is based on the market portfolio which is theoretically and empirically elusive. That is why tests of the CAPM use proxies for the market portfolio, that are not the true market portfolio, the results of such tests have no value. (Roll, 1977)
the CAPM.
R. Levy [Levy, 1971], M. Blum [Blume, 1975] and Scholes-Villimsa [Scholes, Williams, 1977] focuse on the problem of stability of a key parameter of CAPM - the beta coefficient, which is traditionally estimated by linear regression based on historical data using the method of least squares (Ordinary Least Squares, OLS). Based on the calculations and analysis of the dynamics of beta coefficient of a number of individual stocks and portfolios of securities, R. Levy came to the conclusion that, for any share its beta coefficient is not stable over time, and therefore can not serve as an accurate assessment of future risk. On the other hand, beta portfolio consisting even of 10 randomly selected stocks, is stable enough and, therefore, can be regarded as an acceptable measure of risk portfolio. (Levy, 1971)
Blum, M. studies have shown that over time the beta coefficient of portfolio is close to one, and the inherent risk of the company is close to industry average, or average in the market. As a practical recommendation of this study appeared corrective variations of the beta, derived from the regression equation connecting the dynamics of market returns and the observed risk premium of the selected stocks (OSL beta). M. Blum correction:
beta = 0,67 x (beta OSL) + 0,33 x 1 (this type is used by Bloomberg, ValueLine).
Also an alternative solution to the problem of stability of the model parameters of CAPM are estimates obtained on the futures market, where for basis are taken expectations for prices of financial assets. This approach is MSRM - Market-Derived Capital Pricing Model.
Another area of criticism are time periods for calculating of parameters of CAPM (so-called problem of the investment horizon). Since in most cases, the CAPM is used to analyze the investment horizon of more than one year, the calculations are based on annual stimates are dependent on the state of the capital market. If the capital market is efficient (the future is predetermined by past performance is no dynamics, stock prices are characterized by a random rise), the investment horizon is not significant and calculations based on annual rates are justified. If the capital market can not be considered effective, the investment time can not be ignored.
DCAMP model
This model of the interdependence of profitability of the asset and the asset market is the so-called semi-variation , which is analogous to the covariance of the standard model. Semi-variation is unlimited and independent, but it also can be normalized. Similarly, by dividing the covariance with semi-variation of market portfolio, it is possible to get a modified beta - coefficient, and a modified beta factor is used in an alternative pricing model. The model proposed was named D-CAPM (Downside Capital Asset Pricing Model)
Thus, the beta coefficient in the traditional CAPM model is proposed to be replaced with the modified beta coefficient, which is a measure of the risk of an asset in a new behavioral model, in which investors' behavior is determined by the expectation and the semi-variance of return. Modified beta coefficient can be found as the ratio of semi-variation of asset and market portfolio, and semi-variation of the market portfolio. In addition, the modified beta coefficient can be found using regression analysis.
It is necessary to point out that D-CAPM is one of the most common extention of the standard pricing model, and is based on the use semi-variation as a measure of risk assessment. In the classical theory, following Markowitz, for such a measure is taken the variance of profitability, which equally explains the deviations up or down from the expected value. In contrast to the dispersion, a semi-variation "punishes" only the downside risk.
It should be noted that this measure has its advantages and disadvantages. The use of semi-variation in portfolio theory allows to weaken some of the assumptions of traditional models of pricing of financial assets: the assumption of normal distribution of returns; and the assumption that investors' behavior is determined by the expected return and variance of return on assets.
Estrada (2002) notes that, firstly, that the standard deviation can be used only in the case of symmetric distribution of returns. Secondly, the standard deviation can be directly used as a measure of risk only if the distribution of returns is normal. These conditions are not supported by empirical data. In addition, the use of beta coefficients, which are displayed in the traditional behavioral model, as a measure of risk in emerging markets is disputed by many researchers, the use of semi-variation, by contrast, is confirmed by empirical data.
Among the shortcomings, it is necessary ty note that ejected the positive side of risk associated with excess of expectations. In addition, such "risk" can not be used as a volatility, and then for pricing derivatives.
Estrada (2002) considered that one of the possible imperfections in emerging markets is a strong asymmetry of the return on assets, which is taken into account in the model D-CAPM. It was found that the modified beta-factor model of D-CAPM is better suited to describe the average yield on the emerging stock market, compared to the standard beta coefficient. Model DCAPM partially solves the problem of underestimating of the required return on emerging markets while using the standard model CAPM. Therefore, the use of model D-CAPM in emerging markets seems to be preferable. There are also theoretical reasons for this, since the model D-CAPM has less stringent assumptions than the standard model CAPM. (Estrada, 2002)
Conclusion
The capital assets pricing model (CAPM) is made to help determine the selection of shares in the investment portfolio. This model demonstrates a direct connection between the risk of a security and its yield, which allows to show a fair return relative to the risks and vice versa. By itself, CAPM is a scientific theory which has a strong mathematical justification. In order to make it "work" it is necessary to observe the obviously unrealistic conditions such as: the presence of an absolutely efficient market, no transaction costs and taxes, all investors must have equal access to credit, etc. However, such an abstract theory has achieved almost universal acceptance in the world of real finances.
Testing of the CAPM shows that the model has many shortcomings and weaknesses, for example, does not apply to emerging markets. One of the possible imperfections in emerging markets - a strong asymmetry of return on assets is taken into account in the model D-CAPM. It was found that the modified beta-factor model of D-CAPM is better suited to describe the average yield on emerging market securities, compared with a standard beta coefficient. Model DCAPM partially solves the problem of underestimating the required return on emerging markets with the standard model, CAPM. Therefore the use of model D-CAPM in emerging markets seems to be preferable.
