‘The Capital asset pricing model (CAPM) is a very useful model and it is used widely in the industry even though it is based on very strong assumptions. Discuss in the light of recent developments in the area.’
The Capital asset pricing model (CAPM) is a beneficial model, and it is used widely in the industry even though it is based on extreme assumptions. In line with this statement, this paper seeks to investigate on the issues surrounding CAPM as a financial/ investment concept heavily relied upon by the investors in the economic and investment markets. Specifically, the study seeks to address the specific issues surrounding CAPM such as its definition, key assumptions, criticisms and limitations, other alternative financial models that can be used in place of CAPM and the application of CAPM.
Description of CAPM
The Capital Asset Pricing Model (CAPM) is a financial/ investment model used by to evaluate the relationship between expected returns and risks associated with an investment. In the real world, investors take up investment risks with a hope of higher returns (Fama & French, 2004, p. 27). The CAPM model demonstrates that the expected return should be equivalent to the risk premium plus risk-free returns based of the beta of a given investment.
R = Expected return
Rf = Risk-free rate
β = Beta of the investment
Rm = Expected return on the market
Note: (Rm – Rf) refers to the Risk Premium of the investment.
The CAPM formula is applied when calculating the return associated with an investment. The method is based on the proposition that investors accept systematic/ market risk hence they should be compensated using risk premium. In simple terms, investors expect higher returns for taking additional risks after investing in an asset (Graham & Harvey, 2001, p. 190).
The CAPM variables cab be defined as below:
- Expected return (R): The notation "R" stands for the expected return from a capital investment over time. The expected return is dependent on the other three variables. According to the CAPM model, the expected return is measured using a long-term period, for example, the entire life of the capital asset (Ang, et al., 2006, p. 261).
- Risk-free rate (Rf): The notation "Rf" represent risk-free rate which is equivalent to the return from a 10-year government bond. A 10-year bond is mostly used to measure the risk-free rate associated with a capital investment because it is most liquid and heavily quoted in the investment market (Lewellen & Nagel, 2006, p. 300).
- Beta (β): The notation "β" represents beta which measures the degree of risks associated with a stock. Beta can be obtained by establishing the degree at which the price of a stock fluctuates relative to the market price. For example, if the beta of a company is 1.5 relative to the market's 1, therefore the company has a volatility rate of 150%. In other words, beta measures the sensitivity of an investment to the market risks.
- Premium market risk (Rm): The notation "Rm" represents the premium market risk which is obtained by subtracting the risk-free rate from the expected return. The variable represents the excess return that an investor would realize by accepting additional investment risk (Banz, 1981, p. 12).
Suppose you have been provided with the following information:
- A stock trades in the Singapore stock exchange market.
- Its current yield based on a ten year Singapore bond is 3.5%.
- Historically the stock has an annual return of 6.5%.
- The stock has a beta of 1.26.
Calculate the expected return on the investment using the CAPM formula.
Expected return = [Risk Free Rate + (Beta x Market Return Premium)]
R= [Rf + β (Rm – Rf)]
R= [Rf + β (Rm – Rf)]
R= 3.5% + [1.26 x 6.5%]
Therefore, the expected return on the investment is 11.9%.
The CAPM model has received criticism from different quarters because of its unrealistic assumptions. This section discusses the four main assumptions of CAPM and their applicability in the real world. The premises are:
First, Investors hold diversified portfolios. The assumption states that investors should rely on systematic risk when choosing an investment portfolio. The unsystematic risk is ignored because it is diversified (Sharpe, 1964, p. 427).
In the real world, it is impossible for investors to hold an entire market portfolio. However, it is inexpensive and more manageable for investors to diversify unsystematic risk which offers an opportunity for an expected return to relying entirely on the systematic risk. Therefore the assumption is reasonable where investors only focus on acquiring systematic risk for financial compensation (Kellerhals, 2013, p. 76).
Second, single-period transaction horizon. CAPM model prefers to apply a standardized period for different investments for comparability purposes. In other words, returns realized from a six-month investment cannot be compared to returns realized from a twelve-month investment. CAPM usually uses a one year as a universally acceptable holding period (Fama & French, 2006, p. 2172).
In the real world, a single period transaction horizon is reasonable. Although investors hold investment portfolio for at least one year, the returns are disclosed on an annual basis. Therefore, using a one year horizon period realistic in the investment market.
Third, investors can borrow and lend at the risk-free rate of return. The assumption was developed from the portfolio theory which was used to establish the CAPM model as well. In other words, investors can borrow and lend freely without worrying about additional risk (Bailey, 2005, p. 132).
However, the assumption cannot hold in the real world. In the investment market, the risk associated with individual investments is higher compared to the risk associated with the government investments. Therefore, in the real world, there is no possibility of borrowing and lending at a risk-free rate. The inability to borrow and lend at a risk-free rate makes the assumption unrealistic.
Fourth the capital market is perfect. The assumption means that investments in the market are valued correctly. An ideal market is associated with the following attributes. First, there are no transaction costs and taxes related to investments. Second, information can be freely accessed by all investors at the same time. Third, all investors in the market are well informed about the risk. Fourth, all investors are rational decision-makers and possess the desire to maximize the return from their securities. And fifth, the market has many sellers and buyers (Economou, et al., 2017).
The perfect capital market assumption allows the CAPM model to present a relationship between expected return and systematic risk. Although the assumption work in an idealized world, it does not give the same results in the real world.
In the real-world capital markets are not perfect. In developed investment markets, information is not freely available to the investment. Realistically, information is sold to the highest buyers. Likewise, capital markets are characterized by transaction costs and taxes. Lastly, the price of securities, as well as the revenues associated with such securities, cannot be estimated accurately making it challenging to present a relationship between expected return and systematic risk (Levy, 2012, p. 45).
Overall while some assumptions are unrealistic, some are realistic. Although most of the assumptions make sense when applied in the idealized world, there is a possibility of implementing them in the real world to obtain a linear relationship between expected return and systematic risk (Kothari Et Al., 1995, p. 197).
Critique of CAPM
The CAPM's assumptions make the model unrealistic and difficult to apply in the real world. The real capital market does not comprise of assumptions. For instance, free capital markets do not exist; risk-free lending and borrowing is not realistic; different securities have different taxes; not all investors are rational when it comes to decision making, and the information is not free. The assumptions have been used as the basis for criticizing the CAPM model.
According to Roll (1977), the CAPM is incorrect, and the model cannot be tested when the real market portfolio is unknown. Roll used a proxy market (S&P 500) to justify the problems associated with the CAPM model. First, when the S&P 500 proved to be efficient, the market portfolio was not. And second, there was no explanation for the market portfolio is efficient when S&P 500 was inefficient.
The attempt by CAPM to measure the relationship between the expected revenue and beta values as single equity is unrealistic. Market index (S&P 500) comprises of the index of all securities and not a single entity. A market index should comprise of bonds, foreign assets, tangible or intangible human capital and property. Unless the market portfolio is known, the accuracy and efficiency of the CAPM model cannot be ascertained (Fama & French, 1993, p. 34).
According to Jeng (2018, p. 178), CAPM model is affected by the statistical deficiency. By ignoring risks such as P/E ratio, book-to-market equity value and company size make it difficult to prove the accuracy of the model.
The findings by Roll (1977) was also supported by Jagannathan and McGrattan (1995). The study found out that the CAPM model is inappropriate as a result of its assumptions. A real market should comprise of all factors in the economy. CAPM does not capture intangible assets like human capital which profoundly influence the performance of an investment in a capital market.
New directions to resolve challenges
Two models were developed to address the challenges experienced under CAPM. The models are the Intertemporal Capital Asset Pricing Model (ICAPM) and the Consumption Capital Asset Pricing Model (CCAPM).
- Intertemporal Capital Asset Pricing Model (ICAPM)
Merton developed ICAPM in 1973 as an improved version of CAPM. ICPAM takes into account the time-varying factors. The model assumes that investors take into account the current and future risk factors like inflation, unemployment rate and future returns (Riley, 2009).
Considering that investors' appetite for risk varies, the ICAPM model a men variance analysis to mitigate projected risk from one investor to another. The mean-variance analysis makes it easier to arrive at a normal distribution of risk over time. Lastly, ICAPM formula comprises of several beta coefficients representing different hedging portfolios (Berk, 1995, p. 281). The ICAPM formula is:
Ri = Rf + β*(Rm-Rf) + βj*(Rn – Rf)
Ri = Expected return
Rf = Risk-free rate
Rm = Return on the market portfolio and
Rn = Expected return on the hedging
β = Measure of systematic risk concerning the market portfolio
βj= Represents the measure of volatility concerning the hedging security
- Consumption Capital Asset Pricing Model (CCAPM)
Breeden created the CCAPM in 1979 as an improved version of the CAPM model. Unlike CAPM that uses a market beta, CCAPM uses consumption beta to determine the expected return premiums over the risk-free rate. According to CCAPM security premiums are determined by consumption betas. CCAPM is useful because it allows measurement of risks associated with stock based on the consumption growth. The higher the consumption beta, the higher the expected return on a security.
The formula for CCAPM is:
?=rf + βo (rm –rf)
?= Expected Return
rf = Risk-free rate
βo = Consumption beta
rm = Market return
Discussion of alternative models
The two commonly used asset pricing models besides CAPM are Arbitrage pricing theory (APT) and Three-Factor Model.
- Arbitrage pricing theory (APT)
According to the APT model return on security depends on both macroeconomic factors and noise. Unlike CAPM, the number of macroeconomic factors that influence expected return is unspecified under APT. The APT formula is;
Expected return = a+hx + r factor: +b2 + r factor 2 +K +bn-r factor n + noise
b, b2,…, bn refer to risk sensitivity associated with each macroeconomic factor. Some of the factors that can be included when calculating the expected rerun are a market portfolio, oil prices, interest rate, exchange rates, and GDP.
APT is based on two assumptions. First, a diversified portfolio is risk-free and should then be designed to provide a risk-free rate as the interest. Second, a diversified portfolio aimed at exposing a given factor offers varying risk premium depending on the sensitivity level associated with each factor (Bailey, 2005, p. 157).
- Three-factor model
Fama and French developed the model. According to the three-factor model, the expected risk premium is determined by three factor namely size factor, a book to market factor and market factor (Kellerhals, 2013, p. 190).
The three-factor model can be represented mathematically as;
R= rf +β1 (rm-rf) + β2 (SMB) + β3 (HML) +ε
r = Expected return
rf = Risk-free rate
ß = Factor’s sensitivity
(rm – rf) = Market risk premium
SMB (Small Minus Big)
HML (High Minus Low)
ε = Risk
Generally, the three-factor model is an expanded CAPM model which has been adjusted to accommodate the outperformance tendency of an investment asset. The inclusion of two additional risk factor makes the three-factor model more realistic and flexible compared to CAPM. Currently, the three-factor model has been expanded further to include the four-factor model and the five-factor model.
Uses of CAPM
CAPM has several applications; some of the common uses have been mentioned below:
- Investment Comparison: CAPM is used by investors to compare and contrast different securities. For instance, securities such as equities, bonds and stocks can be analyzed using CAPM to help in generating an investment portfolio that maximizes expected return and reduced associated risk (Banz, 1981, p. 18).
- Pricing of Assets and Portfolio: CAPM is used to calculate the value of a portfolio or an asset as a way to determine its worth. Investors use CAPM to determine whether or not an asset or portfolio is likely to uphold its value in the long run.
- Calculate the Intrinsic value of an asset: Financial analysts and investors use CAPM to determine the adjacent between the book and market value of a security. An investor should only invest in security when it is trading below its intrinsic value.
- Calculating NPV: CAPM diversifies all the risks associated with an asset. Therefore, it can be relied upon when calculating NPV for an investment (Levy, 2012, p. 57).
CAPM model as a financial/ investment concept is heavily relied upon by the investors when making investment decisions. However, the model has been criticized by many because of its overreliance on several assumptions. Critics argue that without the assumptions (most of which are unrealistic) the CAPM model cannot hold. The study found out that while some assumptions are unrealistic, some are realistic. Even though most of the assumptions make sense when applied in the idealized world, there is a possibility of applying them in the real world to obtain a linear relationship between expected return and systematic risk.
To address the limitations under the CAPM, two models were developed. In 1973 Merton developed the ICAPM model which takes into account the time-varying factors. Likewise, The CCAPM was created by Breeden in 1979. The CCAPM uses consumption beta to determine the expected return premiums over the risk-free rate.
Besides, ICAPM and CCAPM. Other alternative models that can be used in asset pricing are the Arbitrage pricing theory (APT) and the Three-Factor Model. Irrespective of heavy criticisms on CAPM, the model is relied upon by investors when making investment decisions.
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