**Introduction**

The Capital Asset Pricing Model (CAPM) of John linter and William Sharpe introduced the asset pricing theory. The CAPM focuses on portfolio theory and market model where the only important thing is the co-movement with the market also known as Beta. Additionally, the CAPM is an alternative to valuation theory for single firms. The model is mostly famous for cost of capital estimation and evaluation of managed portfolios hence it is the core of MBA investment courses (Naylor & Tapon, 1982). The advantage behind the CAPM is that provides powerful and impressive predictions on the methods used in measuring risks and determining the association between risk and expected return. However, in as much as there are advantages in the model, there are also disadvantages (ACCA, 2008). Unluckily, the empirical record of the model is inappropriate to the extent of invalidating its practicality in applications. Most of the failures in the theoretical model trace back to its simplifying assumptions.

In an attempt to counter the anomalies derived from Capital Asset Pricing Model, the Multi-Factor Approach model devised by Fama and French explains how the new theory incorporates these anomalies in their asset pricing formula (Fama & French, 1996). Although the CAPM’s usage is famous in developed markets due to its popular purposes, it has limitations of not accommodating the less developed and liquid emerging markets. Therefore, there was a proposal to come up with several factor models aimed at overcoming the shortcomings of CAPM. These macroeconomic models vary in their abilities of explaining average stock returns. Moreover, it becomes necessary to observe abnormal market returns as being the basis for market inefficiencies. The Efficient Market hypothesis contributes significantly to defining a suitable asset-pricing model applicable in the ideal world (Malkiel, 2005).

Further reviewing of the shortcomings of the CAPM inspired the establishment of an alternative pricing theory such as the Arbitrage Pricing Theory. APT is also an extension of asset pricing theory and depends on a factor model of asset returns. The core aim of this paper is to provide an explain the shortcomings associated with Capital Asset Pricing Model and the contribution made by the multifactor approach in countering the limitations of CAPM. The paper also reviews the role of Arbitrage Pricing theory and efficient market hypothesis in eliminating the anomalies of Capital Asset Pricing Model (Connor & KorajczyK, 1993).

**The Capital Asset Pricing Model**

The capital asset pricing model (CAPM) represent a model which which provides its user with an expected rate of return otherwise referred to as cost of capital for each project on the condition that you give it the project’s appropriate risk features. The model presents that the cost of capital for an investor is lower upon preferable diversification advantages for that investor having the overall market portfolio. Market beta is a unit measurement for risk contribution. Projects characterised with more risk that is the market beta require a higher expected rate of return for you to want them. however, those projects providing a smaller amount risk require a lesser probable rate of return for you to develop an interest towards them. The CAPM gives this precise relationship (Fama & French, 2004).

The capital asset pricing model measures both risk and return by dividing the price of a stock into two variables: risk of the stock and the time value of money. The CAPM enables investors compute their return by using a formula that explains the correlation between risk and expected return.

Expected rate of return (r) = rf + B (rm-rf)

Where rf = risk-free interest rate

B = a stock beta

Rm = the expected market return

The formula shows that the expected return of a stock is equal to the risk-free interest rate, and the risk associated with all common stocks, adjusted for the risk of the common stock under consideration In other words, it presents an expression that compares the expected return to stock’s systematic risk. The evaluation of systematic risk in the CAPM is the Beta.

The CAPM is an imperative model that used to determine the cost of capital. It is applicable in the computation of cost of equity (ke) of the firm, which is, therefore, applicable in calculating the value of equity and weighted equity. In overall, these two elements are used to compute weighted average cost of capital. However, most managers have difficulties in applying it in their decision making because it is based on unrealistic. These assumptions include; single-period transaction horizon, perfect capital market and investors hold a diversified portfolio.

The CAPM is a development of the portfolio model formerly introduced by Harry Markowitz in 1959. In Markowitz’s model, he holds the assumption that an investor selects a portfolio at a certain time, which gives him a certain return. In an assumption, investors are risk averse people and therefore use variance when choosing among portfolios (Carhart, 1997). The portfolio model offers an algebraic condition on assets where the CAPM converts this algebraic statement into an examinable prediction in association to risk and expected return

**Limitations of CAPM**

** **The innovation of the Capital Asset Pricing Model is a great scientific advancement in the area of finance where it describes the determination of asset prices in an equilibrium framework. However, there have been several modifications made in CAPM; to represents a shift from the traditional approaches to the modern approaches. In the classical approach, presentation of the structure of the capital market equilibrium is in such a manner relating the equilibrium asset returns to an individual factor. This approach forecasted the CAPM into becoming one of the dominant standards of modern finance (Roll, 1997).

However, due to emerging issues in the modern economy, CAPM seems to be diminishing in its appeals because of firstly it testability. According to Roll (1977), there are doubts in the testability of CAPM. Roll noted that it was only possible to test the mean-variance efficiency of the market assets only with the knowledge of the market portfolio. Roll’s critiques branded the CAPM model as one lacking clear observational consequences. The second doubt centred on various asset pricing anomalies missing credible explanations from the CAPM. Moreover, researchers discovered that the Jensen’s alpha, which was a risk-adjusted performance measure, had an indirect affiliation to the level of beta risk. Nevertheless, further studies indicated that stock returns had a negative association to firm size even after controlling the effect of beta risk (Roll, 1997).

Roll’s critiques triggered many researchers to devise alternatives of testing the CAPM factoring the unobservability of the market portfolio. Kandel and stambaugh (1987) developed a joint hypothesis that the true market portfolio is mean variance efficient and that the proxy and true market portfolios are highly correlated this research only favoured hypothesis that had correlations of seven and below. However, these researcher’s attempts were inconclusive as it is possible to associate closely the testability of CAPM and asset pricing anomalies (Eun, 1994). Although the market portfolio may be unobservable, certainly some parts of it are observable.

Among those who settle that the empirical disappointments of the CAPM are lethal, two stories materialize (Lehmann & Modest, 1998). One story centres on the behavioralists whose view depends on proof that stocks with great ratios of book value to market price are characteristically firms that existed during unfortunate times. The behavioralists contend that sorting firms on book-to-market ratios discloses investor overreaction to good and bad times. Investors over extrapolate previous performance, resultant in stock prices that are excessively high for progression firms and too low for troubled firms. Upon eventual rectification, the outcome is low returns for growth stocks and high returns for value stocks.

The second story focuses on explaining the empirical contradictions of the CAPM and debate on the need for a more complicated asset-pricing model. The CAPM dwells on several unrealistic assumptions. For example, the assumption that investors show biased concerns to only the mean and variance of one-period portfolio returns is extreme (Banz, 1981). It is rational that investors also care about how their portfolio return covaries with future investment and labour income opportunities, so a portfolio’s return variance omissions vital dimensions of risk. If so, market beta does not comprise a full description of an asset’s risk (CERGE-EI, 2011). Therefore, it should be no surprise to lack the complete explanation in a different beta of the differences in expected return. In this view, the exploration should try to asset pricing models that do an improved job explaining average returns.

**Assigning of values to CAPM variables**

So as to use the CAPM, there must be values allocated to the equity beta, the equity risk premium (ERP), the risk-free rate of return, and the return on the market. The yield on short-term Government debt, used as an alternative for the risk-free rate of return, is flexible on a daily basis depending on economic circumstances. There can be application of the short-term average value to flat out this volatility. Finding a rate for the ERP is more demanding. The proceeds found in the stock market represent the summation of gain the average dividend yield and the average capital. During the short term, the stock market can deliver a negative rather than a positive return if the consequence of falling share prices overshadows the dividend yield. It is normal to use a long-term average worth for the ERP, booked from empirical research, but it true that the ERP is not stable over time (ACCA, 2008).

**Application of the CAPM in investment appraisal**

Challenges can arise in the application of CAPM while calculating a project-specific discount rate. For instance, one popular challenge is determining favourable proxy betas, since proxy companies very rarely engage in single business activities. The proxy beta for a suggested investment project compulsorily needs disentanglement from the company’s equity beta (ACCA, 2008). An alternative to this is to use the equity beta as the mean of the betas of a number of diverse areas of proxy company activity, weighted by the comparative share of the proxy company market value rising from each activity

Moreover, some companies may incur debts not traded, or use multifaceted sources of finance such as convertible bonds (The economist, 2013). The simple assumption that the beta of debt is nill will result to inaccuracy in the intended value of the discount rate in the (The economist, 2008). One demerit of applying the CAPM in investment assessment is poor the assumption of a single-period time horizon being at odds with the multi-period nature of investment appraisal. Whereas CAPM variables assumptions are constant in succeeding future periods, experience specifies that this is not true in reality.

**The Efficient Market Hypothesis**

Efficient markets function smoothly whereby the possession of new information causes no benefit. Nevertheless, there must be assumptions in financial models that more information should feature at no additional cost since it already features in prices. It is much probable to have transparent pricing for financial instruments exchanged on stock markets e.g. Bonds, commodities, stocks (Markiel, 2003). However, the efficient market hypothesis might fail in practice. Investments on trade in the stock market by far do not have a representation of a full investment portfolio available to investors. Other financial products appear on varied stages, out of which the majority are less transparent than stock markets.

However, the efficient market hypothesis (EMH), derives assumptions that bound its validity within a theoretical market. Inclusive of these assumptions is their transparency, which makes pricing fair (unbiased), as they include all available information. This information is essential for fulfilling the expectations of the market participants of the future and in adjusting the market. Information attains a definition in the theory as being anything that influences prices in a manner unknown in the present and appearing randomly in the future. Due to this reason, it is practically challenging to outstrip the market by taking advantage of news available to the market. (Malkiel, 2005).

**An Alternative Theory: Arbitrage Pricing Theory**

A substitute and parallel theory to the CAPM is one that integrates multiple factors in explaining the movement of asset prices (Helena, 2009). Contrary, The Arbitrage Pricing model (APT) presents a varied approach to asset pricing. It is often problematic to draw portfolio analyses using the weighted sum of its components. Equity portfolios are far more different and considerably large for distinct component assessment, and the correlation existing between the elements would nullify such calculations. Rather, the portfolio’s risk should possess the view of a single product’s innate risk (Connor & KorajczyK, 1993). The APT represents portfolio risk by a linear factor model, in which returns are the total of factor returns. There may be a variation in factors ranging from the macroeconomic to the fundamental market indices which are weighted by sensitivities to variations in each factor. These sensitivities are factor-specific beta coefficients or more commonly, factor loadings (The economist, 2012). This final part is important as provides explanations on what was missing in the original factors especially for all econometric models.

In contrast with the CAPM, APT is not an equilibrium model, as it does not hold any concerns with the efficient portfolio of the investor. Rather, the APT model makes calculations of asset pricing using varied factors and makes assumptions that in case market pricing strays from the price under suggestion by the model, arbitrageurs will utilise the imbalance and swerve pricing back to equilibrium levels. At its basic form, the arbitrage-pricing model can have one factor only, which is the market portfolio factor. This form will provide similar outcomes to the CAPM (Lehmann & Modest, 1998).

**Relationship between the CAPM and APT**

Both APT and CAPM approach asset pricing differently. The APT is more lenient in assumptions as compared to the CAPM. Moreover, the CAPM is statistical while the APT is more of a theoretical model. The APT model holds the assumption that each investor will have a unique portfolio linked to their risk receptiveness and with a unique beta, contrary to the identical market portfolio presumed by the CAPM (Jewczyn, 2014). Additionally, APT undertakes on numerous investments, which resultantly culminates to the disappearance of firm-specific risk. APT is a form of as a supply-side model, whose beta coefficients’ signify the sensitivity underlying the asset to the different factors. In this sense, factor changes will result in sizable shifts in the assets probable returns. Alternatively, the CAPM is a form of demand-side model. Its outcomes originate from the investors’ utility function enlargement problem, and from the subsequent market equilibrium. If investors can have the consideration of being asset consumers, then the demand approach is rational.

**When Theories Fail, Anomalies Prevail**

The popularity of studying anomalies among researchers came about from the recognition bestowed upon the existence of asset mispricing. The reason behind these studies was that it became easier to determine the causes of occurrences and provide solutions to them. However, it becomes challenging identifying them when they are taking place let alone include them in pricing models. For this reason, speculators benefit from their efforts in identifying anomalies (Fama & French, 1996). Upon detection of an anomaly, it is usual that the trend disappears after arbitrages make enough money for themselves. However, the end of the trend is the beginning of the public introduction, which will resultantly provide intense analysis in financial journals. Normally anomalies result from window-dressing of portfolio managers, tax evasion, or expected premium for trading contrasting positions to insiders.

**Causes of the Anomalies**

Due to the increased number of anomalies, researchers set to investigate the causes that would explain the behaviour of asset mispricing. The most prevalent cause explaining the year-end effect was tax-loss selling. This situation related to those states whose income from trading is not exempt from taxation (The economist, 2012). Therefore, investors in these countries would save themselves by closing on their positions to realise their losses before the tax year hence saving on their compulsory tax. At the beginning of the calendar year, calendar year, they would retrieve their cheaper assets and thereby reopen their positions. The success of this activity made the selling power at the close of the year fall even more especially since the number of investors was more. Nevertheless, the purchase rally in the initial days of the year accounted for the extra profits.

Another cause is window-dressing, which is the result of managers rushing to make the best appearance of the performance of their portfolios before publishing their reports. The rush is due to the premium and living up to the manger’s expectations being dependent on the fund’s performance. However, this sudden rush of things provides a window for face-painting portfolios, which is so far the most lenient method used to distress stocks and obtain in “star” instruments regardless of which industry they belong. Moreover, it would be difficult for investors to notice any changes as they will view the best composition of portfolios made by the manager (Fama & French, 1996).

Another explanation related to the causes of anomalies is the poor distribution of the information, information is necessary if investors are to make sound decisions regarding their investments. Traders can make advancements on information declared by firms, and only then, they are at a position to make decisions contrary to those having a close association with such information also referred to as trading against insiders. Since obtaining trading against insiders is a risky affair, it requires a risk premium. This idea also implies that insiders sell at the end of the year and later repurchase the opening of the following year. For those investors lacking insider knowledge, they result to taking up opposite positions. Hence, the January affects results to higher and better rewards.

Finally, inclusive of the causes behind anomalies is joint hypothesis problem. The joint hypothesis signifies that the market efficiency hypothesis joins with the market equilibrium model that is the price setting mechanism. There cannot be a rejection of the notion behind market efficiency a consequent rejection of the model of market equilibrium. It is because of this reason that much discontent arose amongst researcher. However, CAPM can continue in its efficiency while using other factors such as APT.

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