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Price estimation of assets which can be traded in the capital market is considered to be one of the primary aspects in the field of finance and investment. Various economic theories suggest that asset trade is dependent upon the expected cash flow, its timing and the rate of return. Anticipating the future cash flows and its uncertainties can vary for different classes of assets, and it is in the interest of investors to gain this information, which specifically based upon the asset of interest. The relationship between the expected rate of return for an asset, and the risk associated with it is the most fundamental aspect for any investor, and therefore asset evaluations are conducted in terms of both practical as well as theoretical bases. These evaluations reflect upon different asset classes, varying degree of risks and the expectations of the investor to produce an expected pattern of cash flows. The Capital Asset Pricing Model (CAPM) is the most widely used model which provides the relationship between the asset value, rate of expected returns and the risk associated with it.

CAPM, which is the subject topic of this research, is the methodology adopted by various sets of investors to determine the most influential asset evaluation components/parameters. Variations of the basic models have been proposed by researchers in the last many decades. In this research paper, these developed models will be analyzed to determine how adaptation of this methodology can be useful for investment decisions in today’s global and integrated economy.

The CAPM basic model which was developed in the latter half of 19^{th} century takes into account certain assumptions regarding the behaviors of investors as well as capital market, and it derives a linear relationship which was presented in the literature review section of this paper. According to the CAPM model, the derived relationship must hold true for any individual or a group of assets for it to reach equilibrium with capital market. Empirical test and analytical findings have been presented in the various research articles in order to conduct validity of the subject model.

The CAPM is continued to be considered as an introduction to asset pricing and as the fundamental concepts of portfolio theory. It is a theoretical concept, much like its predecessor Markowitz’s (1952, 1959) portfolio model upon which it was built. Its foundation was later derived through models such as Merton’s (1973) ICAPM. Nonetheless, there are several problems related to this model that questions its utilization in various applications, which will also be briefly outlined in the research.

As for this paper, it is important to outline the findings of the CAPM, and analyze the major controversies that surround it. Furthermore, the extensions of the CAPM along with the imperative implications must be analyzed in order to discuss how the concept of rate of investment returns depend upon the risks in the capital market, and how it compensate the investors for risks. Therefore extensive research is conducted to present qualitative explanations of the utilization of CAPM, while using the data available to correlate and examine the regressions in the various variables involve

As discussed in the literature review, the Capital Asset Pricing Model has been extended to present various models. Some of the most widely used models include;

- Lintner, 1969 and Merton, 1987; which incorporated heterogeneous options
- Black, 1972; which eliminated possibilities of risk free borrowing and lending
- Merton, 1973 and Breeden, 1979; which allowed time based investment opportunities
- Solnik,1974, Stulz, 1981 and Adler & Dumas, 1983; which provided models for International investments

For all such models of CAPM, it is important to note that these provide estimated values only, and any single model cannot be considered to be applicable for all investors. The investors distribute the wealth amongst various risky portfolios, which integrates to market portfolio across the accumulated set of investors associated with the market.

In order to analyze the application of such models, a brief example International Asset Pricing Model can be considered. When examining/evaluating the international investments, the economical impacts such as currency fluctuations and local consumption requirements must be analyzed considering the economical conditions of the country of interest.. The international CAPM model takes into account such factors, and therefore incorporates real time variations in currency and inflation. This leads to insight of expected returns through involvement of asset betas against the subject market, along with the asset betas against currency fluctuations and other variants/risks. For any country of interest, the beta values can vary with respect to the variations in investment/market conditions

Analyzing the various CAPM models, it was found that most of the models are integrated with the multiple beta formulations to predict the expected returns on investments. Furthermore, all these variants are derived through the same fundamental notions, which are;

- The investors hold their optimized portfolios in accordance with their specific requirements, preferences of risks and constraints.
- The asset prices reflect the demands (such as specific needs, constraints and risk preferences) when in state of equilibrium.
- Assets which have the potential for higher investment returns are inter-linked with the risks which a group of investors are not able to eliminate

Furthermore, from the research conducted by Fama and French (1992), it was suggested that neither the basic CAPM nor any of its multidimensional / derived models can be considered to be the only correct method of asset pricing; as the CAPM modeling is based upon the empirical assessment. Test have been performed on CAPM by various researchers such as by Black et al., 1972 and Fama, 1973, and it was suggested that lower beta stocks are not as productive as the high beta stock in terms of returns.

Along with the risk factors of the overall market, the inclusion of factors such as ‘value’ and ‘size’ can effectively enhance the performance of CAPM. There is also strong evidence which suggest that often there are multiple risk factors which are processed to determine the asset prices.

According to the Capital Asset Pricing Model, investors need to attain the following two factors to ascertain the expected return of a stock;;

- The risk premium of the equity market EM _ rf (considering that the main unsafe assets are the equities)
- The beta value of the stock against the associated market of interest.

The risk premium of the stock is dictated by the component of its return that correlates perfectly with the market, which means the degree to which the stock can be a substitute for putting resources into the market. The part of the stock's return which is uncorrelated with the market might be diversified away and it is not considered to be a risk premium.

There are a number of imperative implications of the Capital Asset Pricing Model. To start with, the most striking part of the CAPM is that the expected return of an asset/stock does not necessarily depend upon its standalone risk. It is a known fact that a part of a stock's stand-alone risk is controlled by its beta, however for a stock to have a high stand-alone risk, it does not has to have a high beta.

Therefore, to a certain extent, a high standalone risk will generate a higher expected rate of return. This limitation is derived from the stock-markets sensitivity to the standalone risk. This reflects the basic principle of CAPM that any project/asset involving higher risks or market beta required a high expected rate of return, for investors to satisfy the market equilibrium

Beta also offers a methodology for calculating the risks associated with an asset. We have already observed that any risk measure for estimating the expected returns should fulfill the condition that; ‘portfolio risk is the mean weighted value of the holdings risks in the portfolio’. Beta fulfills this condition. Consider a situation in which two stocks have market betas of 1.4 and 0.8. If we consider the market beta of a 50/50 portfolio for these stocks, it comes out to be 1.1, the average beta value of the two stocks.

The graphical presentations show that if the risks of an asset as determined by the beta are drawn on the horizontal axis, against the expected returns on vertical axis, it produces a straight line. This is known as the Securities Market line, as shown in the figure 1 below. Te results show that all the assets must lie on this single line in order for the market to be in equilibrium. In case the market is not in equilibrium, the investors will have the opportunity to attain a higher value of Sharpe Ratio, and hence improve the market portfolio.

**Figure 1:** The security Market line (source: Economic Prospective, 2004)

In the Capital Asset Pricing Model, the expected returns of a stock does not rely on the rate of growth of its anticipated future cash flows. To calculate the expected return of the shares of a company, it does not necessarily require completion of detailed financial examinations/analyses and estimating the anticipated cash flows of the company. As per the CAPM, the primary parameter required to predict the expected rate of return for any investment is the beta value of the shares of the company, which is a parameter typically much easier to determine as compared to the firm's expected future cash flows and other financial analyses.

The CAMP is an exquisite theory with significant implications in asset evaluations and determining the behavior of investors. But how useful is this model, given that it has been derived through assuming idealized conditions? There are many approaches to answer this. To begin with, we can analyze whether asset costs and investor portfolios in real world conditions are in line with the predictions generated by the model; not necessarily in a quantitative sense, but at least qualitatively it should be able to support the model predictions. Secondly, regardless of the fact that the model does not depict the on-ground conditions particularly, it may anticipate future behavior of investors. Thirdly, the CAPM can also be used as a ‘standard’ to understand the phenomena of capital market that causes deviations in the investor behavior and asset costs from the model predictions.

In order to understand the diversification of CAPM and its extensions/derivations, consider the prediction by CAPM that all investors will own equal (market) portfolio of risky assets. However, in the real world conditions, the investors do not hold similar portfolios, which is not a surprise since taxes alone will result in a distinctive behavior of investors. For instance, ideal administration of capital-gains taxes includes early acknowledgment of deferral and losses of capital gains, thus investors who can be taxed may respond diversely to any changes in the value of the assets depending upon when they acquired those assets (Constantinides, 1983). However, it will still be in favor of the model if most investors hold diverse portfolios. The question that arises here is why suboptimal diversification is so pervasive? Explanations that are common include that acquiring broad diversification could be unreasonably expensive, as far as taxes and direct expenses are concerned, and that investors have behavioral predispositions and absence of complexity. None of these explanations implies that the CAPM is not advantageous. The CAPM lets us know that investors pay a cost for being undiversified because they are going for risks for which they are not receiving any compensation. Consequently, there exists an opportunity for improving portfolio, which thus creates opportunities for financial innovation and investor training/education. It is a fact that ownership of foreign equities in numerous countries have multiplied throughout the previous two decades, probably because of the expanded accessibility to invest internationally. Today, investors appear to be much more diversified than before, and this pattern seems to continue similarly in the future as well.

As stated by the CAPM, the expected return rate without risk, the beta against the market trend and the market risk premium are primary parameters which determines the suitable discount rate for calculating the value of the expected company or its projected cash flows. These values must be precise/accurate as these play an important role in the decision making process, and any error can increase many times over a long period of time.

Beta is generally calculated through the use of the linear regression analysis, for which data is obtained form the stock exchange returns. Beta can be measured using this method even for a moderately brief time interval, given that there is enough high-frequency data. For companies and/or projects which have not traded in the open market, or there is no applicable return history, the beta values of the practically identical entities can be used. However, various measurement issues can occur regardless of the accessibility of market returns data, for instance when covariance with the market is time dependent and when regional stock exchange lists are utilized as proxies in the broad market portfolio in light of the fact that the latter is not specified in detail.

One of the most difficult parameter to determine is the market risk premium. The risk premium is assessed from the mean of past returns and unlike measures related to variance such as beta, average returns are exceptionally sensitive to the starting and ending values of stock. Consequently, it is advisable to measure the risk premium over long intervals of time, and even then this may not be sufficient, especially if the risk premium changes considerably with time. However, none of these estimation issues represents a problem for the CAPM fundamentally. All cash flow evaluation models have the market risk premium common between them, and it is unavoidable to estimate it without considering the difficulty of performing this task. Given that CAPM is the "right" choice of model, beta also needs to be evaluated, no matter how difficult it is.

Acquiring significant returns by owning high beta stocks does not necessarily require great levels of complexity. Investors can simply make use of a leveraged place in the market portfolio to establish a high beta portfolio. However, attaining higher yields with low beta stocks is much more difficult, because such activity cannot be recreated with a passive approach.

CAPM and its extensions provide an essential perspective regarding asset prices to understand the dynamics of different factors involved, which contributes towards asset prices. It gives an understanding of how ownership of assets by diverse investors results in a decline of their expected returns and an increase in their prices. Whereas the less diverse investors who have less extravagant portfolios have the tendency to waste their efforts in taking risks where there isn’t much reward involved. The model has the potential to provide support in a way that broadens our understanding of the relationship between risk and its expected outcomes. The CAPM gives a reasonable scheme with respect to investment decisions and validity in today’s economy.

CAPM has been subject to change over the years and the earlier versions developed by Sharpe (1964) and Lintner (1965) hardly received the expected empirical success. The Black (1972) version however, which was one of the earlier empirical works that had some success, is well known for its accommodation of a flatter tradeoff of average return for market beta. But the boom in research in the late 1970’s has helped in adding explanation to the beta provided average returns by revealing various variables like size, momentum and different ratios of price. However, most uses and applications of the CAPM are nullified by some serious problems that are henceforth explained.

One such example is how the cost of equity capital is estimated using the Sharpe-Lintner CAPM risk-return relation. It does this by estimating the stock’s market beta entwined with the average risk premium in market and the risk-free interest rate. Only the U.S common stocks were included in the typical market portfolio exercises. However, latest trends and work has showed that the prediction made by the Sharpe-Lintner version of the CAPM regarding the relation between average return and beta is more flat. Hence CAPM gives a low estimated value for low beta stocks (Friend and Blume, 1970) and a far too high value of the cost of equity for high beta stocks.

The CAPM also provides us with several other description of how mutual funds can be measured. Jensen (1968) lays out its approach for measuring abnormal performance by estimating the CAPM time-series regression for a portfolio and hence using Jensen’s alpha (intercept). There is a problem with this model, which is due to the CAPM’s empirical failings. As the investment strategies turns towards CAPM problems; even well managed stock portfolios produce abnormal returns (Eltonet al., 1993).

One such instance is how the funds that focus upon low profile stocks such as, low beta stocks, small value stocks etc are likely to provide positive abnormal returns relative to the predictions stated by the Sharpe-Lintner CAPM, even though the people behind the funds have no special or outstanding skills.

The international professional financial community has opened up to portfolio analysis and the usefulness brought by CAPM in practical investment in the past 3 decades. CAPM is well known for its simplicity, and its potential testability. It caters to numerous problems that are somehow related to the relation between risk and returns, such as cost benefit analysis, portfolio selection, capital budgeting and cost benefit analysis.

All the above arguments make it hard to pin a conclusion to the model presented. Whereas there is strong evidence that empirically invalidates the pricing model on one hand, however, on the other hand, there is not sufficient evidence in terms of empirical findings to completely invalidate the model. However, it is nearly impossible to reject the theoretical aspect of CAPM, according to researchers including Fama and French, who believe that due to the uncertainty in the market portfolio, the empirical tests are of no use.

The problems with CAPM are evident by the fact that there have been number of theories that are inter-related but different. These theories challenge the concepts provided by CAPM, such as Merton (1973) and Ball (1978). However, CAPM holds a prestigious place in the minds of portfolios managers and investment advisors.

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