Security Market Line and Capital Market Line

The Security Market Line (SML) is a tool that is used to evaluate the portfolios which is based on the Capital Asset Pricing Model. The Security Market Line establishes a relationship between the volatility of risk and the expected returns that are associated with a portfolio for an individual as well as the inefficient portfolios. The Security Market Line is the main concept that is used in the Capital Asset Pricing Model. The risk that is associated with the Security Market Line is presented in terms of beta. Beta is nothing but the security sensitivity with regards to fluctuations in the market returns. On the other hand, Capital Market Line is used to represent the risk free rate of return corresponding to an efficient portfolio. The risk in case of the Capital Market Model is presented in terms of variance or standard deviation. By standard deviation, it is meant the deviation from the mean value. The mathematical and graphical representation of the models are provided for a better understanding of the matter.

Let (  be the point corresponding to the market portfolio M and ( be the point on the capital market line. The equation of the capital market line is denoted by,

Where,  = rate of return of the efficient portfolio and  = variance of the expected portfolio,   is the price of risk as well as the slope of the Capital Market Line.

For any ith individual,

Where,  = required rate of return on the ith individual financial asset

= risk free rate of return

 = volatility of the ith individual asset

= average return on capital market

From the two diagrams provided below it can be seen that the Capital Market Line is the locus of the point of the most efficient portfolio and the risk free rate of returns associated with that portfolio. The tangent that passes through the efficient portfolio is the Capital Asset Line.  By efficient portfolio it is meant by the combination of the risky and risk free assets that a person can buy which will maximize the sharp ratio. In Figure 1 the tangent passing through the most efficient portfolio is the Capital Market Line. In contrast to that the slope of the Security Market Line shows the volatility of the risk associated to an individual assets or of all the portfolios which include inefficient ones. The β that is said in the above equation of the Security Market Line is the major concern. Beta represents the measure of the changes in security’s sensitivity with respect to that of the market returns and also the slope of the Security Market Line. Often beta is considered as a more appropriate measure for the security risk.

Modern Portfolio Theory

The Modern Portfolio Theory (MPT) tries to minimize the risks (which can be also termed as the variance, standard deviation or volatility) that is associated with a portfolio or an asset without reducing the mean or the expected returns form that asset. Consider that there are two assets P and Q. Consider that they have equal variance of 10 percent. Now, a portfolio that consists of both of the above said articles will tend to have a standard deviation or volatility lower than then original 10 percent. Somehow if the assets are correlated then the volatility may be greater than 10 percent. The main aim or the main goal of minimizing the risks is attained by varying the weights of the corresponding portfolios. Further, another important fact is that the securities cannot be selected as per the individual characteristics, as the correlation between these securities also needs to be taken into account as lower the level of correlation between the assets the stronger is the level of diversification. A unique portfolio can be derived for each level of expected return which has lowest risk. These portfolios are called mean-variance efficient portfolios as any other combination of such portfolios do not possess such low risks and the level of expected returns. There the set of all such mean variance efficient portfolios when plotted in a graph gives the efficient frontier. The graphical diagram is provided below.

Figure 2

shows the efficient frontier curve. Any rational consumer will choose a point on the on the above drawn efficient frontier. The dark point in the above diagram represents the minimum variance portfolio. The minimum variance portfolio (MVP) has the lowest risk or standard deviation among all the availableefficient portfolios. The minimum variance portfolio is an important part of the modern portfolio theory. The main feature of this is that the risks of the portfolios are minimized by assigning weights to the assets. The minimum variance portfolio is not made up of a single or unique stock but it may consist of all the stocks that are available in the investment universe. Therefore the minimum variance portfolio is the set of all the efficient portfolios that have the lowest risk associated with it.As shown in the Diagram-2, the minimum variance portfolio is positions at the extreme left tip of the efficient frontier. The risk associated at this point is R1 which is the lowest as compared to the other points whose risks are R2, R3 and so on.Therefore the minimum variance portfolio is identified.

Minimum Variance Portfolio

Various theoretical as well as empirical studies have been conducted in the modern portfolio theory, however the prime focus have been on the minimum variance theory. The importance of the minimum variance portfolio can be described as follows. There exists a large number of companies who are running their investment funds strategy that are solely based on the minimum variance optimization. Further, the minimum variance theory has also drawn attention of the stock exchange. The index providers are also benefited from the minimum variance theory. There exists three reasons for the prevalence of the minimum variance portfolio. Firstly most of the empirical studies that has been conducted till date shows that the minimum variance portfolio has performed relatively well than any other indexes. Secondly, when the optimization is conducted, the optimization of minimum variance portfolio does not require considering the expected returns forecasts. In other words the optimization is independent from the expected returns forecast. These expected returns forecast are the major source of errors that arise due to estimation. Lastly, it has been seen that the participant in the market are primarily risk averse in nature. This phenomenon stimulates the creation of the financial products with a managed volatility. In this case the minimum variance theory serves to the needs of the investors.

The Capital Asset Pricing Model (CAPM) establishes a linear relationship between the required rates of return and the systematic risk associated with that investment. This investment might be in the form stock market securities or in the form of business operation. The Capital Asset Pricing Model incorporates the Security Market Line concept. The general equation of the model is,

 = risk free rate of return

 = volatility of the ith individual asset

= average return on capital market

The Capital Asset Model has an upper advantage and is more relevant than any other equation while calculating the required rate of return. While calculating the rate of return the Capital Asset Pricing Model model considers only the systematic risk. The systematic risks are those risks that cannot be diversified. These systematic risks are caused due to external factors occurring to an organisation. These risks cannot be controlled by nature. The beta that is used in the Capital Asset Pricing Model takes into account these systematic risks. In any other model these are not included. This fact is quite realistic as most of the investors have a diversified portfolio and the unsystematic risks associated with these portfolios are essentially eliminated. Another factor that can be stated relating to the relevance of the Capital Asset Pricing Model equation is that the model generates a theoretical relationship between the required return rates and the systematic risks associated with the assets which is a matter of frequent discussion. The equation when implied in real life scenario has a great relevance. The Dividend Growth Model (DGM) that also tries to calculate the return rates but, the Capital Asset Pricing Model is far more superior. The Dividend Growth Model assumes that the rate of growth of dividends is 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).the model is further divided into two categories the stable model and the multistage growth model. The equation for the stable model can be represented as follows:

Capital Asset Pricing Model

where, P = value of stock,  is the next year’s dividends, k = rate of return and g is the constant rate of growth. The Dividend Growth Model explicitly takes into account the company’s level of the systematic risks relative to that of the stock as a whole. The multistage growth model assumes that when the dividends do not grow at a constant rate then the investors must evaluate the dividends of each year separately. 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 becomes constant in due course of time. In the above model, the volatility factor is missing which is incorporated in the Capital Asset Pricing Model. Further, there is another model that is called 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. These also include common shares. 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}

The Weighted Average Cost of Capital model is primarily used as discount rate given that the investment companies does not change the financial risk or the business risk occurring to the investing organisation (Pricing and Tribunal 2013). However, the Capital Asset Pricing Model model leads to a better investment decision than Weighted Average Cost of Capital. Graphically, the above said can be shown as,

From the diagram, point A is not feasible in case of Weighted Average Cost of Capital as the internal rate of return is less than the Weighted Average Cost of Capital intercept C whereas if Capital Asset Pricing Model would have been considered then, A would have been a feasible option. Similarly, for point B, it would have been feasible for Weighted Average Cost of Capital. The point B is has a rate of return much higher than the internal rate of return. Thus, considering the Weighted Average Cost of Capital model this point B would have been feasible. However, when Capital Asset Pricing Model is considered then this point is not all a feasible point. Point B provides insufficient compensations for the level of systematic risks. There it can be clearly how the Capital Asset Pricing Model is far superior than any of the existing theories.

Reference

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

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