The CAPM’s foundation is the Markowitz’s mean-variance method for investment appraisal (Sharifzadeh, 2010). The Capital Asset Pricing Model is widely used by professionals in evaluating the interdependence between risk and return of an asset (Bodie, Kane and Marcus, 2014). This relationship is used when estimating the feasibility of future projects. Other uses are determining the price of stocks in an initial public offering and evaluation of the performance of portfolios (Fama and French, 2003). The CAPM is very popular for practitioners due to its simplicity arising from the fact that it is a one-factor model. Despite this, however, the use of the model may not always bring accurate results (Bodie, Kane and Marcus, 2014). Since the empirical performance of the model is not stable it is criticized for giving unreliable values. One of them being that the model assumes only one measure of risk – the beta which represents the relationship between market portfolio and the asset movement over time (Jagannathan and Meier, 2002).

The Arbitrage Pricing Theory is developed as an alternative to the CAPM by Ross (1976). Similarly to the Capital Asset Pricing Model, the APT considers the relationship between expected return and risk of an asset. The latter, however, presents the rate of return of an instrument as a function of risk with respect to systematic independent risk factors (Bodie, Kane and Marcus, 2014). They may be numerous and they are not pre-specified in the model.

The APT is built around the assumption of the arbitrage opportunity – the ability to profit from securities which are traded at an incorrect price at a specific moment. It also assumes that is such opportunity exists an investor would take infinite short position where the price is high and long position where the price is low until the opportunity is gone (Bodie, Kane and Marcus, 2014).

There are numerous assumptions concerning the CAPM:

1. “Investors are rational, mean-variance optimizers” (Bodie, Kane and Marcus, 2014, p. 303). This assumption implies that market players’ only concerns related to return are the mean and the variance. All the investors are risk-averse and hold identical risky portfolio.

2. The second assumption is that investors’ time horizon is limited to a specific period of time. This is a consequence of the CAPM being a single-period model (Aukea et al., 2017). In the real world, market players have a more complex way of making decisions. In most cases, there are different time horizons to consider (Fabozzi, Neave and Zhou, 2012).

3. Investors have similar outlooks about the returns and variances. According to Bodie et al (2014), this assumption is not that questionable. According to them if all information is publically available stockholders generally tend to reach a consensus. If, however, investors do not have similar expectations, there would be a large number of efficient frontiers so that no frontier would be universally suitable.

4. The existence of one risk-free rate (zero variance) at which every investor could lend or borrow with no limit in volume (Fabozzi, Neave and Zhou, 2012). A risk-free rate implies that investors have the same capital allocation lines and will, therefore, choose an identical portfolio of assets. It is assumed that no matter the risk aversion of market participants they will consider the same portfolio as most feasible to invest in (Sharifzadeh, 2010). This market portfolio lies on the tangency point of the capital allocation line and the efficient frontier. Discrepancies between investors’ risk-free rate would mean different optimal risky portfolios. Criticism by (Fama and French, 2003) states that unlimited investment at the risk-free rate is practically impossible.

5. All information is publicly accessible (Sharifzadeh, 2010).

6. The model ignores taxes and transaction costs. In practice, the difference in taxes can cause serious distortions in the returns market participants acquire (Bodie, Kane and Marcus, 2014). Market participants are usually subject to different taxation due to differences in tax brackets. This may affect their investment prospects.

7. The actions of a particular market participant do not have implications on the price of an asset (Elton, 2003)

Grabowski and Pratt (2013) criticize the CAPM assumptions that investors hold similar assets in a portfolio and that there are similar expectations and no transaction costs. According to them, some market participants are unwilling to diversify their portfolios in search of a bigger profit through risk so they can’t be considered to be mean-variance optimizers. This implies that their expectations are not the same as other investors who are more risk-averse. Moreover, Grabowski and Pratt (2013) state that even large well-diversified portfolios have some idiosyncratic risk left. This presumes that even the most risk-averse portfolio holders will still be exposed to a certain amount of firm-specific risk.

The assumptions of the CAPM make it difficult to apply the model in practice (Frake, 2017). It appears that they are made for the purpose to oversimplify the complex real-world situations. What is crucial when applying the model is the evaluation of how consistent are these assumptions with the current conditions in the real world (Sharifzadeh, 2010).

The Arbitrage Pricing Theory is based on the theory that riskless profit could be made by the discrepancies of assets’ prices at a given moment (Bodie, Kane and Marcus, 2014). The one that investors are mean-variance optimizers is not present. Instead, it is presumed that arbitrage opportunity will last until the prices at the respectful markets are driven up or down in order to be equal. The APT has a smaller number of assumptions than the CAPM. The most significant ones are (Bodie, Kane and Marcus, 2014):

1. The return of assets can be determined by a model that comprises several systematic risk factors.

2. In a highly diversified portfolio, the non-systematic risk is negligible.

3. If markets are efficient arbitrage conditions are not possible.

The assumption that well-diversified portfolios have negligible non-systematic risk similarly to CAPM is relevant for portfolios with many securities with each weight being small enough to not have an impact on the overall non-systematic risk of the portfolio (Bodie, Kane and Marcus, 2014). Unlike the CAPM, however, APT there is more than one factor that impacts the return on different assets. Each factor contributes to a risk premium with beta in the equation (Aukea et al., 2017). Examples of such factors are inflation rate, the spread between short-term and long-term interest rates, etc.

The Arbitrage Pricing Theory and the Capital Asset Pricing Model have similar functions. Both models are linear and consider that the returns are affected only by the systematic risk since the non-systematic can be eliminated through diversification. Maybe the biggest difference is the number of systematic risk factors (Hossain, n.d.). Another difference is that the CAPM is used only for a single period whereas the APT is not. The CAPM assumes that all investors possess the market portfolio whereas the APT does not consider any specific portfolio (Bodie, Kane and Marcus, 2014).

The Capital Asset Pricing Model is a one-factor model. In the basic equation, the leading factor is the ? which measures the sensitivity of an asset to the market (systematic) risk. This is the portion of risk that is not diversifiable and the investors require a risk premium for. The risk premium on an asset according to the CAPM depends on the portion of additional risk that the asset brings to the overall portfolio risk (Bodie, Kane and Marcus, 2014).

It appears that the market risk premium is an important input in the equation (Jagannathan and Meier, 2002). However, constructing the market portfolio with all available stocks is virtually impossible in reality. For the purpose of the model approximations of the market portfolios are used. Examples of such proxies are the S 500 and other market indexes. In the equation, ? depends on the covariance of the market return and the asset’s return. In order to calculate it the prevailing assumption is that historical returns for a past period need to be taken. This, however, would not be entirely correct since the premium is subject to changes over time (Jagannathan and Meier, 2002). The non-systematic risk is considered not to bring any premium since it is possible to be minimized even eliminated through diversification (Robert, 2017). It is therefore excluded from the equation.

Another challenging aspect of the beta is that it may not capture all of the systematic risk. The APT tries to solve this challenge by introducing several sources of risk in the equation. The presumption is that the systematic risk can be influenced by several factors (Huberman, 2005). These factors are chosen based on the specific situation – they may be macroeconomic or related to the industry. Although several such as inflation, interest, GDP growth and industrial production are empirically tested they are not pre-specified in the equation. Similarly to the CAPM, the sensitivity of the asset to the factor is marked by ? (Robert, 2017). In the APT, contrary to the CAPM, there are several ? coefficients that measure the exposure to every risk factor (Aukea et al., 2017).

The formula is:

E(Ri) = rf + ?i1xRP1 + ?i2xRP2 + … +?knxRPn (Investopedia.com)

“Rf” represents the risk-free rate. “?” is the sensitivity to the specific factor. “RP” is the risk premium to the specific factor.

This makes the APT more flexible but also makes the application of APT more complex. An essential part of applying the model and estimating the excess return is the careful analysis and selection of the risk factors and establishing the betas (Tambakis, 2018). Using irrelevant ones may lead to misleading results.

There is substantial criticism towards the practical use and validity of Capital Asset Pricing Model due to its empirical testing. According to Fama and French (2003), part of them are a result of the underlying assumptions that the CAPM is based on. Jagannathan and Meier (2002) outline the main empirical findings related to the model. Firstly, the initial success of the CAPM when using its forecast for the New York Stock Exchange until the mid-1960s is given credit to. In addition to that Fama and MacBeth (1973) cited in Jagannathan and Meier (2002) conclude that for the same period the ? coefficient was a good measure to find expected return. However, Banz (1981) cited in Jagannathan and Meier (2002) states that the CAPM based on empirical evidence is not appropriate for small-sized enterprises’ stocks since the model predicts lower returns than the actual. Another criticism outlined is by Fama and French (1992) who state that there are better measures than ? to account for systematic risk such as the market to book value of stocks and the company size. Roll (1977) as cited in Fama and French (2003) presents another weakness of the CAPM. As mentioned above one of the most defining assumptions of the model is the market portfolio. In practical use, however, there is uncertainty on which assets are to be included in it. Fama and French (2003) conclude that the “relation between beta and average return is flatter than predicted by the Sharpe-Lintner version of the CAPM” (p. 43). This causes distortion as the results for stocks with high ? are higher than expected and stocks with low ? are lower than expected.

The APT’s purpose is to explain systematic risk with more than one factor. According to Chen, Roll and Ross (1986), there are several that arise from the macroeconomic variables: inflation, Treasury-bill rate, return on long-term government bonds, industrial production, return on junk bonds, GDP growth and oil prices. Their conclusion is that these factors affected returns in the US at that time. In addition to that Fama and French (1996) used firm-specific factors to develop their Three-factor model. Their contribution to the model is empirical evidence that the specific factors coming not only from the macroeconomic environment but from the companies themselves. Those are factors affect the non-diversifiable risk – the difference between returns on a small-capitalized stocks portfolio and large-capitalized stocks portfolio, the difference between the returns of a high book-to-market ratio portfolio and low book-to-market ratio portfolio and the difference between market return and the risk-free rate. Their study concludes that small-capitalised companies’ stock portfolios tend to have higher returns than large-capitalized companies’ stock portfolios. Another finding is that stocks of companies with a higher book to market value tend to have higher returns than lower book to market value companies (Fama and French, 1996).

If I had to use one of the models:

The Capital Asset Pricing model is the most popular model among practitioners for determining the expected return on assets (Aukea et al., 2017). It is attractive due to its simplicity and the fact that it takes into account non-diversifiable risk. Despite that, as seen before in the analysis the CAPM does not hold well in the empirical tests. The model possesses too many unrealistic assumptions that oversimplify the reality (Aukea et al., 2017). It assumes only one source of risk – the beta which represents the relation between the returns of the stock to the return of the market portfolio. Moreover, the CAPM is built on the presumption of a perfect market where there are possibilities for unlimited exploitation of the risk-free rate, no taxes or transaction costs. Another inconsistent with reality notion of the CAPM is that all market participants are mean-variance optimisers. These inconsistencies with the reality distort the results generated by the CAPM. In the same line of taught, the ? is not always easy to predict (mostly historical data is used) since it is prone to changes (Hossain, n.d.). The same goes for the market risk premium which is subject to controversy (Jagannathan and Meier, 2002).

The unsatisfying empirical results of the CAPM led to the emergence of new models (Jagannathan and Meier, 2002) such as the Arbitrage Pricing Theory. It tries to free the users from some of the restricting assumptions. Although being more complex, the Arbitrage Pricing Theory should be more reliable since it does not specify which sources of risk or how many to use in the calculations. It holds better with the reality and allows more of a tailor-made approach to the specific conditions than the one-size-fits-all approach of the CAPM.

Still, no model will ever tell the whole story. Both the APT and the CAPM receive thorough and well-justified empirical criticism. What makes the Arbitrage Pricing Theory more favorable to be developed in future is its ability to be adapted to newly found sources of risk.