Understanding Capital Asset Pricing Model

Components of the CAPM

A capital asset refers to the properties that are associated with the business of any kind. The CAPM or the capital asset pricing model is the model that helps in the process of elaboration of the link between the anticipated return of the asset and the systematic risk that is used widely in the context of the stocks. In case of securities that are risk bearing, the CAPM is widely used. This also helps in the generation of return that are expected for the assets and evaluating the cost of capital.

In this context, the security market line refers to the line that is drawn that helps in serving graphically representing the model of capital asset pricing. The SML also known as the characteristics line which is visual capital pricing model that represents both risks and the return.

 On the other hand, the CML stands for capital market line refers to the model that helps in the pricing of asset CAPM mechanism. It represents the trade-off between return for portfolios that are efficient and the various risks that are associated (Bodnar, Mazur and Okhrin 2017). It can be said to be a theoretical concept which elaborates the various portfolios that efficiently collaborate the rate of return that are free from risk as well as the risky assets market portfolio.

Definition:

The SML or the security market line refers to the optical depiction of the model   of capital asset pricing or CAPM. It represents the link between the return from security that is expected and the associated risk. The measurement of risk is done by the beta coefficient (Chow, Kose and Li 2016). It can also be said in this context that, the representation of the SML shows the anticipated return for any beta that is given or highlights the associated risk with any expected return that is given. 

Equation: 

As highlighted in the above definition the SML is on the basis of the CAPM model that is shown below:

E(R_i) = R_F + β_i × (E(R_M) – R_F)

Where, E(R_i) is an expected return of a security, R_F is a risk-free rate, β_i is a security’s beta coefficient, and E(R_M) is an expected market return.

In the SML graph the x-axis is shown by the beta, and expected return is represented in the y-axis. The beginning of the line represents the risk-free rate value:

1. The expected return of the security of zero-beta will be equivalent to the risk-free rate. The zero-beta portfolio anticipated return is equivalent to the risk-free rate as well.
2. The security market line slope is found out by the RP_Mwhich is known as the market risk premium, that is equivalent to the distinction of the rate of risk-free and the expected market return (Maillet, Tokpavi and Vaucher 2015) . It can be hereby said that if the market risk premium is more, the graph becomes steep and vice versa.
3. The security market line can be sad to be not fixed and the slope can vary and over time the y-axis intersection may also vary. It is dependent on the tradeoff between the interest rates changes and risk-return.
4. In case the coefficient of beta of the provided security in due course changes,  there can also be a change in its line position.

The security market line shift may also take place in case there is a change in the key fundamental economical factors, like the change in the GDP, unemployment rate or expected rate of inflation.

The Security Market Line (SML)

It can be observed that in case of security market line there exists the same limitations that is present in the capital asset pricing model since it is consists of the similar assumptions. In this context, it can be said that the conditions of real markets will not be able to be featured by a sound efficiency as the participants of the market consists of variable lending and borrowing ability of money at a rate that is risk-free and costs of transaction are varying. Therefore, in the real world, the given stock position can be below or above the SML. 

Definition:

The CML or the Capital market line refers to the graph that shows the anticipated portfolio return that consists of all the proportions that are possible between a risk-free asset and market portfolio. In case the market portfolio is totally changed and carries the systematic risk only, along with expecting a profit is equivalent to the anticipated return of the market. In simpler terms, the  calculation of the expected return of a specific portfolio (E(R_C)) can be evaluated as shown in te following equation:

E(R_c) = y × E(R_M) + (1 – y) × R_F

Here, the y market portfolio is a proportion, E(R_M) stands for the  expected market return portfolio, the (1-y) refers to the  risk-free asset proportion, and rate that is risk-free stands for RF.

The non leveraged portfolios return can be equal to or less than the market return in case the market portfolio proportion of the is 100% or 1. However, the leveraged return  portfolio can considerably exceed the market return.

As highlighted in the above definition the capital market line is on the basis of the CAPM model that is shown below:

E(Rc) = RF + SDc	E(RM) – RF
SDM

Here, SD_C stands for portfolio of standard deviation of C return; SD_M refers to the a market return standard deviation.

The CML slope is the reward to variability ratio (RVR).

RVR =	E(RM) – RF
SDM

Graphical representation:

The CML model  may be conveniently plotted in the space of risk-return  since the intercept R_f is known and the slope is obtained from the ratio between the vertical distance from P and R_f and their horizontal distance ().

Hence, the CML constructs the frontier line that is made of several combinations or portfolios between the the market portfolio P and the risk-free asset, and  hereby elaborates the relationship between return and return for perfectly broad-based and efficient mixes. In this context, the point arises whether the relationship will still remain linear for single stocks or for broad-based mixes, and what appropriate risk measurement shall be attached with each of the category as mentioned previously. During the creation of the portfolio, It is the interest of the investor to analyse the each security contribution of to the variance mix and to the mix return (He, Kelly and Manela 2017). 

The Capital Market Line (CML)

As per the CAPM market model, in any case the investor will make the choice of the market portfolio P, by the consideration of the risk and its return (Fama and French 2017). With respect to the return, it is easy to observe the input that is given proportionally to E(R_m) by the single asset regarding the own E(R_i).By  ignoring the analytic derivation the quilibrium point can be observed from the diagram given above that the contribution of asset should be compensated in terms of E(R_p). Therefore, if there are two securities, and they have similar , it is advisable that they must produce the same return. Opssosite to the case,there may be reduction of amount that has the  less lewcrative asset for incresing to a more profitab;e one. Therfore, it can bew said  tht thre assets that has the same expected return must have similar `

Limitation

In real markets conditions, the key issues that is faced by the capital market line is that the it is on the basis of similar assumptions as the model of CAPM.

1. There exist transaction costs and taxes, that may considerably differ in case of  various investors.
2. It can be assumed that the investor may ether borrow or lend the amount that is unlimited at the rate that is risk-free. In case of the conditions for real market the investors may lend at a rate that is lower than the amount of borrowing, this leads to the bend in the CML curve..
3. The real markets don’t have a sound efficiency form; therefore, investor possesses information unequal.
4. It can be said that all the investors are not risk-averse and rational.
5. Standard deviation is not the single unit for risk measurement, since the real markets are expose to reinvestment risk, inflation risk, currency risk and so on (Barillas and Shanken 2018).
6. There exist no risk-free assets.

Therefore, in real market condition the CML looks like a area that is fuzzy rather than a line that is precise. 

Differences between CML and SML

Following represents the fundamental differences between SML and CML:

1.The Capital market line is the line that represents the return rate, it depends on rates of return that are risk-free and risk level for a particular portfolio. The SML, that is known as the Characteristic Line,  refers to the graphical representation of the risk of the market and at a given time risk(Bao, Diks and Li 2018).

2.In case of SML the risk factors  are determined by the Beta coefficient and in case of CML the standard deviation measures the risk.

3.The Security Market Line graphs define both non-efficient and efficient portfolios. However in case of the CML the graphs define efficient portfolios

4.Hence it can be concluded that the CML is more superior at the time of measurement the factors of risk.

The portfolio for minimum variance is the securities portfolio that minimizes the risk of price for the overall portfolio. The volatility refers to the term that is more used commonly instead of a variance in the community of investment; it is a statistical measure of a specific price of the security movement that can be ups or downs.

The investment volatility can also be said to be interchangeable in meaning with its risk of market. Hence, the more the investment volatility the up and down in price has wider swings that results in higher risk in market. Therefore, in case an investor opts for risk minimization, they need to reduce the upasa and down in the market simultaneously.

Minimum Variance Portfolios

The benefit of the minimum variance is that, there is a determination of the lower bond of the efficient frontier. When there exists portfolios on the investment opportunity  set to the right and below the minimum variance portfolio, they are  not efficient. That is, there is a portfolio with the same level of a higher return and risk. None of the investor who is rational would ever  make an investment in a portfolio below the minimum variance portfolio.

The capital asset pricing model or the CAPM  is the model that helps in the process of elaboration of the relationship between the expected return of the asset and the systematic risk that is used widely in the context of the stocks. In case of securities that are risk bearing, the CAPM is widely used (Goh, Li, Ng and Yong 2015). This also helps in the generation of return that are expected for the assets and evaluating the cost of capital. On the other hand the rate of return refers to the loss or gain of investment over a time period that is specified, and is expressed in terms of cost of investment percentage. The Investments gains are the income that is received added with the capital gains that is realized on the sale of investment. 

There are several advantages of the capital asset pricing model over other processes of evaluating the needed return that explains the reason for it being popular for 40 years or more:

• The CML only considers the systematic risk that reflects a reality where most of the investors have portfolios that have been diversified from which unsystematic risk has been eliminated essentially.
• It refers to a relationship that is derived theoretically between the needed systematic risk and return that is subject to frequent empirical testing and research.
• It is seen generally as a a method that more efficient in calculating the cost of equity than the growth model of dividend (DGM) in that it considers explicitly the  level of the company of systematic risk  that is relative to the stock market on the whole (Barberis, Greenwood, Jin and Shleifer 2015).
• It can be identified that the CML is clearly superior to the WACC in giving rates of discount that can be used for appraisal of investment.

However, the CAPM suffers from various limitations and disadvantages that can be noted in a balanced discussion of this vital theoretical model. In addition to this values need to be assigned to the risk-free rate of return for using the model of CAPM that includes the the equity beta, market return and the equity risk premium.

Conclusion

As per various researches it can be seen that the CAPM stands up fine to the various criticism, even though the criticism against are increasing in present times. However, the model of CAPM still remains a quite helpful item in the toolkit of financial management. In case of securities that are risk bearing, the CAPM is widely used. This also helps in the generation of return that are expected for the assets and evaluating the cost of capital. Hence from the above discussion, it can be concluded that the CML is more superior at the time of measurement the factors of risk. 

References

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Barillas, F. and Shanken, J., 2018. Comparing asset pricing models. The Journal of Finance, 73(2), pp.715-754.

Bodnar, T., Mazur, S. and Okhrin, Y., 2017. Bayesian estimation of the global minimum variance portfolio. European Journal of Operational Research, 256(1), pp.292-307.

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