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a. Explain and graphically depict how Security Market Line (SML) is different from Capital Market Line (CML).

b. Identify and discuss the importance of mininnun variance portfolios?

c. Why CAPM equation might be more relevant than other equations when calculating required rate of return.

## Capital Market Line

a. The Capital Market Line (CML) establishes a relation between the risk and return of an efficient portfolio. The risk in Capital Market Line is calculated using variance or standard deviation. Whereas the Security Market Line (SML) depicts a relation between the expected returns and beta of any portfolio. In the Security Market Line beta is basically the volatility of the portfolio. The major differences arising in the Capital Market Line and Security Market Line is that the Capital Market Line takes into account only the efficient portfolios on the other hand the security Market Line takes into account the individual as well as the inefficient portfolios which are not included in the efficient portfolios. Further, Security Market Line is the major concept that is used in the Capital Asset Pricing Model (CAPM). Both the concepts of Capital Market Line and Security Market Line are discussed in details in the following part along with the graphical analysis.

In the financial market there are basically two types of securities that are available to the investors namely the risky securities and the risk free securities. The portfolio of all the risky securities that are available to investors is called the market portfolio denoted by M. The investors who are willing to invest in the market will hold a combination of both the risky and the risk free securities. The above said combinations of the risk free and the market portfolios will lie along the tangent drawn against the efficient frontier. Therefore, the Capital Market Line is the line formed by taking into account the combination of the risk free and risk less securities of all the investors in the security market (Brooks and Mukherjee 2013). The relation that exists between the risk and return of the efficient portfolios is depicted using the following equation,

The slope of the Capital Market Line is the term . The slope measures the increase in return due to one unit increase in the risk. This term also shows the risk premium associated with the portfolio. The graphical analysis provided below.

Now the Security Market Line depicts all the inefficient as well as the individual securities which do not lie in the efficient frontier (Jordan 2014). The Capital Market Line does not include all these inefficient points. The relation between the returns and volatility of the portfolio is depicted using the following equation,

## Security Market Line

Here in the Security Market Line β depicts the slope of the line. The sensitivity of the portfolio with respect to the changes in the market returns is measured by this term β. When the value of β is zero then the expected return from a portfolio will be similar to the risk free rate (Pandya 2013). However if the value of β is greater than one then the prices of the stocks are more sensitive as compared to the market. The stocks with higher values of β are considered as more risky as compared to the stocks with low β. The SML depicts a cross sectional analysis of different stocks. The mean return on the two stocks is proportional to the β values. The graphical representation of the Security Market Line is provided below.

The above diagram shows the Security Market Line with beta portfolio. The major difference between the SML and the CML is the term beta. The risks associated with a portfolio is depicted by using standard deviation in case of CML and that by beta in case if SML.

b. Consider two assets X and Y that are available in the market for investment. Further, consider that both of these two assets have the same variance of 10 percent. Somehow, if the assets are correlated then the portfolio consisting of these two assets will have a standard deviation more than 10 percent. However, if the assets are uncorrelated then the risks associated with the portfolio will have a standard deviation lower than 10 percent. The primary aim is to minimize the risks associated with a portfolio by varying the weights associated these assets. Thus, the Modern Portfolio Theory (MPT) tries to minimize the standard deviation or the variance of a portfolio without reducing the expected returns associated with that portfolio. Another important fact is that the because of the correlation that exists between various portfolios the securities cannot be chosen as per individual characteristics. Lower the level of correlation between the assets will lead to a stronger diversification effect. There exists a unique portfolio which can be can be derived for each level of expected return which has lowest risk. These portfolios are called the mean variance portfolios. Any other combination of portfolios does not possess such low risks and the high level of expected returns. The set of all such mean variance portfolios plotted in a graph gives the efficient frontier.

## Modern Portfolio Theory

From the above figure the efficient frontier can be depicted clearly. A rational investor will always choose appoint on the efficient frontier (Gupta, Varga and Bodnar 2013). The darker circles in the above graph represents all the individual securities and the darker point on the efficient frontier represents the minimum variance portfolio. In the modern portfolio theory the minimum variance portfolio is an important part. The minimum variance portfolio (MVP) has the lowest variance that is the lowest risk among all the available efficient portfolios (Jacquier 2013). The minimum variance portfolio does not consist of a single unique stock rather it is made up of all the stocks that are available for investment. The risks associated with these portfolios are minimised by assigning different weights to the corresponding assets (Lee 2013). From the figure it can be seen that the risk associated with the minimum variance is R1, which is the lowest as compared to the corresponding efficient portfolios whose risks associated are R2, R3 respectively.  Thus, the minimum variance portfolio is set of all efficient portfolios that have the lowest risk associated with it. Thus, the minimum variance portfolio has been identified.

The minimum variance of portfolio is the prime focus of study in the modern portfolio theory as the importance of the minimum variance portfolio is beyond words. There are a large number of companies that solely rely on this theory. These companies form their investment strategies based on the MVP. The three main reasons for the importance of the minimum variance theory can be described as follows. Firstly, the empirical studies that are conducted shows that the minimum variance portfolio has performed efficiently as compared to any other such indicators. Secondly, when the optimization is conducted for the finding the minimum variance portfolio then expected returns forecast is not considered. These expected returns forecast causes errors in the estimation procedure. The optimization is independent of the expected returns forecast thus very efficient in nature. Lastly, most of the participants in the market are risk averse in nature, thus, the theory of minimum variance portfolio fits in well. In the recent times, the stock exchange has also started implement the minimum variance portfolio theory. Therefore, the importance and uses of the minimum variance portfolio theory is much diversified in nature and also growing in the recent times.

c. The linear relationship that exists between the return rates and the systematic risks associated with an investment is depicted in the Capital Asset Pricing Model (CAPM). Investments that are done might be in the form of business operation or in the form of stock market securities (Pigou 2013). The concept of the SML is used in the CAPM model. The general equation of the CAPM model can be described as follows,

## CAPM

The advantage of using CAPM is that the model establishes a theoretical relationship between required rates of return and the systematic risks involved with the portfolios which is a topic of frequent discussion. Another important factor that can be related to the superiority of the CAPM is that the model considers only the systematic risks. These systematic risks are those risks which cannot be diversified (Fan, Liao and Shi 2015). The external factors that are occurring to a firm is the main reason for these systematic risks. These are cannot be controlled and are natural. In the CAPM equation the beta used takes into account these systematic risks. Any other model that tries to establish such a relation does not include this beta factor. The assumption of systematic risks is quite realistic as in the real life scenario investors develop a diversified portfolio and the unsystematic risks associated with the portfolios are essentially eliminated. When the equation is implied in real life it has great relevance.

Consider another model namely the Dividend Growth Model (DGM), which also tries to calculate the rates of return like that of the CAPM. In the DGM the rate of growth of dividends is assumed to be constant in perpetuity. The value of the stock is equal to the following year’s dividends divided by difference between the required rate of return and the constant growth rate in dividends that is assumed (McKenzie and Partington 2013).  There are two versions of the model namely the stable model and the multistage growth model. The mathematical form of the stable model is as follows,

The multistage growth model assumes that investors calculate dividends of each year separately when the rate of growth of the dividends is not constant. Thus, the investors will have to incorporate the expected dividend growth rate of each year separately. The main assumption of the model is that the growth of the dividends become constant in due course of time. The volatility factor that is the main concern for every investor is typically missing in this model which is the main concern in the CAPM model.

Another Model is the Weighted Average Cost of Capital (WACC). The weighted average cost of capital of the firm shows the cost of capital of all the sources. The equation of this model is represented by,

WACC = {Cost of Equity * percentage of Equity} + {Cost of debt * percentage of debt * (1 – Tax Rate)} + {Cost of preferred stock * percentage of preferred stock}

In this model the investing companies do not change the financial risk or the business risk occurring to the investing organisation when the discount rate is given (Pricing and Tribunal 2013). The superiority of the CAPM model can be depicted using the following diagram in details,

From the diagram it can be seen that the point G is not feasible in case of the WACC model as the internal return rates is lower than the WACC rates. However, this point is feasible in the CAPM. Again when the point H is considered then, the point is not feasible in case of CAPM but the rate being higher than the WACC rate the point is feasible for WACC model. Thus, it can be clearly seen that CAPM is far superior to the WACC model.

References

Brooks, R. and Mukherjee, A.K., 2013. Financial management: core concepts. Pearson.

Fan, J., Liao, Y. and Shi, X., 2015. Risks of large portfolios. Journal of econometrics, 186(2), pp.367-387.

Gupta, A.K., Varga, T. and Bodnar, T., 2013. Elliptically contoured models in statistics and portfolio theory. New York: Springer.

Jacquier, E., 2013. Modern Portfolio Theory. Portfolio Theory and Management, p.23.

Jordan, B., 2014. Fundamentals of investments. McGraw-Hill Higher Education.

Lee, W., 2013. Risk Based Asset Allocation

McKenzie, M. and Partington, G., 2013. The dividend growth model (DGM). Report to the AER.

Pandya, F.H., 2013. Security Analysis and Portfolio Management. Jaico Publishing House.

Pigou, A.C., 2013. A study in public finance. Read Books Ltd.

Pricing, I. and Tribunal, R., 2013. Review of WACC methodology. Research–Final report.

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