Capital Asset Pricing Model (CAPM)
Table of contents
Contents
- Introduction. 2
- CAPM equation. 3
- The security market line. 4
- Efficient frontier. 5
- Assumptions of the Capital Asset Pricing Model 6
- Limitations/Problems with the CAPM model use. 7
- Conclusion. 9
- References. 10
Capital Asset Pricing Model (CAPM)
1. Introduction
Capital Asset Pricing Model (CAPM) is an essential aspect in Finance because it provides a basis for pricing risky securities and generating expected returns of assets as long as there is the provision of the cost of capital and the risk of the assets (Fama et al. 2004). This estimation is essential because it enables financial planners to come up with decisions regarding the addition of assets to a substantially expanded portfolio. The model utilizes Modern Portfolio Theory ideologies for it to decide whether there is a fair valuation of a given security. There are various assumptions that the model relies on. They are going to get an in-depth view in this essay. Therefore, the concepts associated with the model play a vital role to investors as the relationship between the reward and the foreseen risk gets understood. Every critical decision related to given security has a basis on the CAPM. The inventors of the formula include Jack Treynor, Mossin, William Sharpe, and Lintner (Dolgopolov, 2004). The invention made these people receive the award of the Nobel Memorial Prize in Economics in 1990.
It is worth noting that there is a consideration of the market risk and the market expected return. The theorized risk-free asset has a review. According to Bornholt, there have been some fails from some empirical tests, but this has not made the model to get eradicated (Bornholt, 2012). It is still used globally and intensively because it is simple, and it applies in various circumstances. Among the things talked about in the model include the assumption, a thorough explanation of the formula, problems associated with it, the efficient frontier, and an outline of the security market line. Don't use plagiarised sources.Get your custom essay just from $11/page
2. CAPM equation
The model has a use in the determination of the pricing of a portfolio or security. The relationship between the security market line, the systematic risk and the expected return is essential in the resolution of the individual securities. The reward-to-risk ratio has a foundation on a calculation that calls for the use of the security market line (SML). This statement means that in an event where the beta coefficient reduces the expected return rate of a portfolio, the market reward-to-risk ratio is the same as the reward-to-risk ratio for any security.
For us to get the Capital Asset Pricing Model (CAPM), we have to arrange the above equation by making E(Ri) to be the subject of the formula. Therefore, the equation below is the CAPM:
Below are the definitions of each variable in the model:
E(Ri)- The return on the capital asset, Rf- Risk free degree of interest, ß- represents the sensitivity of the predictable extra asset returns to the predictable excess market returns, E (Rm)- the anticipated return of the market, E (Rm) the market premium and E (Ri)-the risk premium (Chen, 2003).
It is also worth noting that beta has another representation as in the formula below:
Where: ρm denotes the standard deviation for the market, ρi denotes the standard deviation for investments, ρ represents the correlation coefficient for the variables mentioned above.
Therefore, it is the expectation of any investor to get compensation for any risk. Apart from this, there is also the consideration of the time value for money. Risk-free-rate that is present in the model takes into account this time value. However, all the other variables represent the instances where the investor decides to take an extra risk. The beta variable, which is the most important in the formula indicates the measure of the amount of risk that the venture will put to a selection which appears like in the marketplace. The result from the CAPM models offers a person who wants to invest the discount rates and the expected returns, which is useful in calculating an asset’s value (Chen, 2003). The fairness of the valuation of the stock is an essential aspect that the formula determines.
3. The security market line
The line is responsible for bringing out a graph from the CAPM. On the y-axis is the expected return, while on the x-axis is the risk. Finding the gradient of the line is the same as finding the market risk premium. This line is beneficial to investors. The ß is a function of the expected return. The risk-free-rate is found by reading the value at the interception. Therefore, the line is vital as it shows a model that has a single factor from the value of an asset. One can use it to see if a given asset gives an expected risk-return that can get consideration in investments. The reason is that the graph contains individual securities. A plot above the security market line means that there is an undervaluation because an investor gets a forecast of a greater return on the risk (Dybvig and Ross, 1985). A plot below the security market line indicates overvaluation because there shall be acceptance of less return on the risk by a shareholder. The perfect equation for the security market line is:
4. Efficient frontier
According to the Capital Asset Pricing Model, there is the assumption that there is the possibility of improving a risk-return outline of a portfolio. The idea is that a portfolio that is at the optimal status shows the lowermost probable level of risk for its reappearance level. An extra asset leads to the diversification of a portfolio. Therefore, a portfolio that is at the optimal status must have all these assets keeping in mind the assumption that there is no incurrence of any trade-related costs. Every asset in the portfolio must have a value. All portfolios in this status make up the efficient frontier (Byrne and Lee, 1994). The entire risk in a collection has a view of beta because of the divided nature of the risk. From the work of the scholars mentioned above, below is the Markowitz efficient frontier graph:
The y-axis represents the expected return, while the x-axis has the standard deviation. The efficient frontier gets a representation of the curved line in the graph.{\displaystyle E(R_{i})=R_{f}+\beta _{i}(E(R_{m})-R_{f})\,}
5. Assumptions of the Capital Asset Pricing Model
Most of the formulas and models across the world adopt some assumptions. By the formulas undergoing development by human beings and machines, they are not one hundred percent perfect. Therefore, the Capital Asset Pricing Model is not an exception. All of the assumptions touch on the investors (Mirza and Shabbir, 2005). Below are the assumptions of the model.
- The investors have an objective of exploiting the economic utilities.
- There is rationality among all the investors.
- The expectations of the investors are homogenous.
- All the data and information needed by the investors is available to all of them and at the right times.
- There are no costs of taxation and transactions, while the investors engage in trade activities.
- All investors do not influence prices.
- There is a wide diversity among investors in terms of investment variations.
- The securities that the investors handle small portions of divisions.
- All the investors can borrow and lend money without limits considering the risk-free interest ratios.
- The standard deviation calculated from the previous returns is a perfect representation of the imminent risk that that particular security has.
Therefore, these assumptions are essential because if any one of them avoids consideration, then it would mean that the model has a lot of faults. It will be subject to a lot of questioning and criticism.
6. Limitations/Problems with the CAPM model use
There are various problems associated with the Capital Asset Pricing Model. There has been an argument by Kenneth French and Eugen Fama, which states that there is an implication of very many problems of the model by the failures that it has had in various empirical tests (Fama and French, 2006). Therefore, there is no validity in the application of the model.
The first problem is that the traditional Capital Asset Pricing Model puts into use historical information with a primary objective of predicting the future returns of specific assets. There is a lot of insufficiency in historical data, and therefore, the model would be more valid if there was the use of present data. Secondly, there is the problem of the variation in risks, according to various scholars. There is a constant risk measure used in the model. However, according to some recent research, there is variation in the betas with time, and this has helped in improving the accuracy in forecasts (Berglund and Knif, 1999).
The homogenous expectation is an assumption that is a problem in nature. The reasoning behind this is that there is no way that all the shareholders and investors will get the same information and the same time because of the variation in the locations and the changes in the characteristics of the market (Abbas et al., 2011). Another problem is that there is an assumption by the model that the variation in returns is a good measure of risk. All the returns undergo a normal distribution. It is wise to point out that the difference in investments is a loss probability even though it is not a variance. Therefore, its nature is irregular. The model does not give an in-depth explanation of the differences in the stock returns. According to recent research, there is an indication that low beta stocks can, to some point, yield higher returns as compared to the forecasting of the model (Andor et al. 1999).
The assumption of the similarity in the returns distribution and the likelihood views of active investors is also a problem. The problem exists because of the inefficiency in the market data from some biased investors. Therefore, there can never be a similarity. Another problem is that there is an assumption that there is a lack of transaction costs as well as taxes, which is not the case in the real world. Another problem is that the model excludes all the assets that are in possession of a person investing. It only focuses on a few assets. This exclusion puts to question the validity of the model. The model also puts into consideration only two dates. The idea does not offer space for the consumption of portfolios over repeated timelines. Another problem with the assumptions is that the model does not put into consideration the difference in the optimization of individual investor’s assets into one collection (Abbas et al. 2011). It is a well-known fact that human beings have various groups, each with a different goal.
7. Conclusion
From the above analysis, it is clear that the Capital Asset Model is an essential tool in the finance sector of any economy. The vital functions that it performs despite its associated problems cannot lack consideration. Various empirical tests have tried to prove the invalid nature of this tool. However, they do not propose a tool that can replace the model, thereby leaving us with no other option other than adopting CAPM. For its perfection, there is room for more research which shall try to solve the associated problems.
{\displaystyle \mathrm {SML} :E(R_{i})=R_{f}+\beta _{i}(E(R_{M})-R_{f}).~}
8. References
Abbas, Q., Ayub, U. and Saeed, S.K., 2011. CAPM-Exclusive Problems Exclusively Dealt. Interdisciplinary Journal of Contemporary Research in Business, 2(12), pp.947-960.
Andor, G., Ormos, M. and Szabó, B., 1999. Empirical tests of Capital Asset Pricing Model (CAPM) in the Hungarian capital market. Periodica Polytechnica Social and Management Sciences, 7(1), pp.47-64.
Berglund, T. and Knif, J., 1999. Accounting for the accuracy of beta estimates in CAPM tests on assets with time‐varying risks. European Financial Management, 5(1), pp.29-42.
Bornholt, G.N., 2012. The failure of the capital asset pricing model (CAPM): An update and discussion. Available at SSRN 2224400.
Byrne, P. and Lee, S., 1994. Computing Markowitz efficient frontiers using a spreadsheet optimizer. Journal of Property Finance, 5(1), pp.58-66.
Chen, M.H., 2003. Risk and return: CAPM and CCAPM. The Quarterly Review of Economics and Finance, 43(2), pp.369-393.
Dolgopolov, S., 2004. Insider trading and the bid-ask spread: A critical evaluation of adverse selection in market making. Cap. UL Rev., 33, p.83.
Dybvig, P.H. and Ross, S.A., 1985. The analytics of performance measurement using a security market line. The Journal of finance, 40(2), pp.401-416.
Fama, E.F. and French, K.R., 2004. The capital asset pricing model: Theory and evidence. Journal of economic perspectives, 18(3), pp.25-46.
Fama, E. F., & French, K. R. (2006). The value premium and the CAPM. The Journal of Finance, 61(5), 2163-2185.
Mirza, N. and Shabbir, G., 2005. The death of CAPM: A critical review.