The Capital Asset Pricing Model (CAPM) was introduced by William Sharpe (1964) and John Linter (1965) and fundamentally highlights the concept that securities are priced so that expected returns will compensate investors for the expected risks (Galagedera, 2007). The model relates the expected rate of return of an individual security to a measure of its systematic risk which is the risk associated with overall movements in the general market or economy (Galagedera, 2007). CAPM states that the expected risk premium on any security equals its beta (a measure of systematic risk) multiplied by the market risk premium (Brealey et al., 2018). CAPM can be graphically represented by the security market line which is shown by Figure 1.
According to CAPM, the expected rates of return for all securities and all portfolios lie on this line (Brealey et al., 2018). Despite its wide use, this model has been highly challenged ever since it was introduced primarily because it is based on very strong assumptions. This essay will explore the assumptions of CAPM with the view of evaluating its usefulness in determining the required rate of return of a security. To aid the evaluation, this essay will also investigate the reasoning behind the rise of additional models that have been formed with the purpose of challenging the traditional CAPM using evidence from global financial markets.
One assumption of CAPM is that investors can borrow or lend any funds at the risk-free rate of return (Naylor and Tapon, 1982). This assumption derives from Markowitz’s portfolio theory which states that investors are risk averse and if given two portfolios that offer the same expected return, they would favour the less risky one. Rossi (2016) states that risk-free borrowing and lending is an unrealistic assumption. This is because, government securities are rarely close to being risk free as for most investors, their own government’s bonds and bills are deemed as having substantial risk (Arnold, 2013). Additionally, it is reasonable to assume that investors can lend any funds at the risk-free rate of return however the same cannot be said for borrowing. Reilly and Brown (2003) as cited in Elbannan (2014), argue that there are restrictions on borrowing unlimited funds at the risk-free rate because investors must pay a higher rate when borrowing money.
These particular flaws have encouraged extensions of the traditional CAPM. One noteworthy extension of the traditional CAPM model is Fischer Black’s zero-beta model developed in 1972. In this model, Black permits the use of the unrestricted short sales of risky assets (Elbannan, 2014). The reasoning behind this is that, if the market portfolio is mean-variance efficient, meaning it has the lowest risk for a given level of return among a possible set of portfolios, then risk-free assets are not required (Reilly and Brown, 2002). Thus, a portfolio whose correlation with market portfolio returns is zero and in turn, whose beta is zero, replaces the risk-free rate (Koseoglu and Mercangoz, 2013). Although this portfolio does not have any systematic risk, it may have some unsystematic risk (Reilly and Brown, 2002). Unsystematic risk can be defined as a specific risk associated with investing in a specific company or industry (Arnold, 2013). In comparison to the traditional CAPM, the zero-beta model has a more linear security market line which is not as steep. The security market line with a zero-beta portfolio can be shown by Figure 2.
The zero-beta model is supported by Stambaugh (1982) who tested the model using portfolios within the United States, using the Langrage multiplier test. This testing resulted in the rejection of the traditional CAPM but acceptance of the zero-beta model as the tests accepted the linear relationship but not the equivalence of the zero-beta return to the risk-free rate. This is emphasised by more recent research by Koseoglu and Mercangoz (2013) who tested the validity of both the traditional CAPM and the zero-beta CAPM using 64 common stocks in the Istanbul Stock Exchange (ISE). They found that the zero-beta CAPM was more valid. These pieces of research show evidence that throughout time, the zero-beta model has succeeded in fixing the flaws of the traditional CAPM model. However, there is also opposition towards the zero-beta model. Rossi (2012) states that the belief that short selling is unrestricted, is as unrealistic as risk-free borrowing and lending. The reasoning behind this is that, if there is no risk-free asset and short sales of risky assets are not allowed, mean-variance investors will still choose efficient portfolios. This is supported by Wakyiku (2010) who tested the zero-beta model using 10 companies listed on the Uganda Stock Exchange (USE) and found that there was insufficient evidence since the zero-beta rate was not statistically significant.
It can be seen that the assumption that investors can borrow and lend at the risk-free rate has been a prominent weakness of the traditional CAPM and has spurred extensions of the model to be created such as the zero-beta model. There has been evidence from multiple countries that both support and reject the zero-beta model. Nevertheless, it can be difficult to generalise the evidence to all countries as the size of stock exchanges vary from country to country. For example, the New York Stock Exchange (NYSE) itself is bigger than the world’s 50 smallest major exchanges (Desjardins, 2016).
Assumption two:
Another assumption of CAPM is that all investors in securities are single period expected utility wealth maximisers (Naylor and Tapon, 1982). The major shortcoming of this assumption is that investments usually involve a commitment for many years (Arnold, 2013). Fama and French (2004) as stated in Elbannan (2014) discuss that it is reasonable that investors also focus on how their portfolio return interacts with their income and future investment opportunities, therefore a portfolio’s return variability fails to capture important dimensions of risk. Furthermore, Reilly and Brown (2012) mention that if one investor is using a one-year planning period, their security market line would differ from another investor who is using a one-month planning period. Therefore, in the case that there are multiple periods, additional assumptions are required in order to account for them (Armitage, 2005). Consequently, Armitage (2005) also argues that this reduces confidence in the one-period model as there is doubt over whether the analysis of the relationship between expected return and risk is correct.
In response to that assumption, there have been many developments of multi-period capital asset pricing models. One of these is the Intertermporal Capital Asset Pricing Model (ICAPM) developed by Robert Merton in 1973. Under the assumptions of ICAPM, when choosing a portfolio at time t-1, ICAPM investors consider how their wealth at time t might vary with future variables including labour income, the prices of consumption goods and nature of portfolio opportunities at t (Elbannan, 2014). In addition to this, the ICAPM reflects the fact that expected returns depend both on the covariance of returns with the current return of the market portfolio, and information about future returns (Brosch, 2008). Therefore in essence, the ICAPM predicts that an security’s risk premium will depend not only on the covariance on of its rate of return with the return on the market portfolio but also on covariances with state variables (Machado et al., 2013).
Fama (1996) as cited in Fama and French (2004) discuses that ICAPM generalises the logic of CAPM. If there is risk-free borrowing and lending or if short sales of risky assets are allowed, market clearing prices imply that the market portfolio is multifactor efficient. Furthermore, ICAPM is supported by Machado et al., (2013) who tested the validity of ICAPM using Brazilian market data between 1988 and 2012 using the Bali & Engle (2010) methodology. The results of tests were found to be favourable to the ICAPM for the sample period tested; more specially, that risk aversion co-efficient was highly significant which meant that the risk-return relationship was a positive one. On the other hand, there is also disapproval of ICAPM model. Elton et al., (2014) state that although the model says that there should be additional influences present in pricing securities, it does not give any information about what these influences are or exactly how to form portfolios to minimise whatever risks they represent. This is supported by Fama (1991) as cited in Maio and Santa-Clara (2012) who interprets ICAPM as a “fishing license” because of this reason. The ICAPM approach has also been characterised as difficult to follow because of the continuous-time methods used (Fama, 1996 as summarised by Elbannan, 2014).
It is clear that the ICAPM is an improvement on the traditional CAPM through factoring in multi-periods and acknowledging that most investors have a futuristic mind-set when it comes to investments. However, the model can still be further improved. Fama and French (2004) state that multifactor efficiency implies a relationship between expected return and beta risks, but it requires additional betas along with a market beta to explain expected returns. Therefore, it can be concluded that, the extent to which ICAPM is an improvement on the standard CAPM model is limited because of the ambiguity around what the state variables actually are.
Assumption three:
The final assumption to be addressed is the one that the CAPM only uses a single risk factor which is the market risk represented by beta. Ball (1978) as cited in Elbannan (2014) states that a major limitation of the traditional CAPM is that market betas are imperfect and insufficient to explain the change in expected returns. Hsia et al., (2000) explain that if the market is imperfect, this means that the arbitrage process is hindered, meaning that the explanatory power of beta is weakened and thus, beta needs other factors to supplement it. This is supported by Lu (2014) who discusses that additional factors may be required to characterise the behaviour of expected returns which is also supported by theoretical arguments. An additional issue with beta is the measurement. Arnold (2013) says that although obtaining historical beta is straightforward, difficulty comes when deciding on whether to use daily, weekly or monthly data and the duration of the observation period.
To better explain the returns of a portfolio, Fama and French proposed a three-factor model in 1993 (Elbannan, 2014). In this model, in addition to market risk, they added the factors of size and book-to-market ratio. Their reasoning for adding these factors were; small stocks and stocks with high book to market ratio as proxy for firm value reflect risks that are not explained by beta (the market systematic risk) and market return (Elbannan, 2014). Additionally, Fama and French (1993) justify that size and book-to-market equity are connected to economic fundamentals. In calculating the rate of the return, Fama and French use the risk-free rate and market risk premium with the addition of Small Minus Big (SMB) and High Minus Low (HML). SMB captures the historic excess returns of small-cap companies over large-cap companies and HML represents the historic excess returns of value stocks (high book-to-price ratio) over growth stocks (low book-to-price ratio).
Iqbal and Brooks (2007) tested the three-factor model against the traditional CAPM model using 87 stocks traded on the Karachi Stock Exchange (KSE) and found that the risk factors in the three-factor model were more significant. Support for the three-factor model also comes from Al-Mwalla and Karasneh (2011) who tested the model using stocks from the Amman Stock Exchange (ASE) for the period between 1999-2010. They observed strong size and value effects on the stocks tested. Therefore, this shows convincing evidence of the case for the three-factor model, especially in emerging markets such as Pakistan and Jordan. One drawback of the three-factor model has been noted to be the complexity of it in comparison to the traditional CAPM. Sattar (2017) states that investors may not find it cost effective to collect the additional information required by the three-factor model and in the case of the Dhaka Stock Exchange (DSE) many investors lack in depth financial knowledge and prefer simpler methods in determining required return. Additionally, there has been criticism around the interpretation of the risk factors. Size and book-to-market ratio effects are due to investor overreaction rather than compensation for risk bearing (Griffin, 2002). Due to this, investor overreaction makes value stocks appear under-priced and growth stocks appear overpriced.
The objective of Fama and French’s three factor model was to broaden the traditional CAPM model to include more factors than just market risk. Evidence has shown that in the case of explaining expected returns, the three-factor model has prevailed over the traditional CAPM. However as mentioned, the three-factor model is more complex than the traditional CAPM. Therefore, it can be argued that the choice to use the three-factor model over the traditional CAPM depends on the type of investor. Sattar (2017) states that investors who want to use the three-factor model instead of CAPM must evaluate the time and effort required to use the model beforehand.
Conclusion:
This essay has explored the strong assumptions of CAPM and investigated the reasons for the development of extension models over the years including; zero-beta model, ICAPM and the three-factor model. The main weakness of CAPM has been highlighted as the model being based on unrealistic assumptions. Despite the growing evidence which showcases the weaknesses of the traditional CAPM, it still remains a useful tool for estimating the cost of capital (Elbannan, 2014). In particular, large firms rely heavily on CAPM which is shown by Graham and Harvey (2001) who surveyed 392 CFOs on what methods they use to calculate cost of capital and over 70% used CAPM. This essay has also considered the weaknesses of the extension models. This demonstrates that all models have limitations, but they are useful for explaining basic relationships between variables such as risk and return. In the case of future developments of the model, one factor that hasn’t been accounted for is, transaction costs. Vayanos (1997) states that although transactions costs are often mentioned in asset pricing debates, they are non-existent in asset pricing models. Transaction costs include: brokerage commissions, market impact costs and transaction taxes which are imperative to financial markets (Vayanos, 1997). Therefore, although the traditional CAPM model assumes that are no transaction costs, transactions costs should be accounted for as they play an important role in financial markets and thus will have an impact on the expected return of a security.