Explain and graphically depict how Security Market Line (SML) is different from Capital Market Line (CML). Identify and discuss the importance of minimum variance portfolios? Why CAPM equation might be more relevant than other equations when calculating required rate of return.

## What is Capital Market Line (CML)?

The Capital Market Line (CML) depicts a risk- return relationship as well as a measure of risk for the efficient portfolios. On the other hand the Security Market Line (SML) shows a relationship between the expected return and beta of a portfolio. The Capital Market Line takes into account only the efficient portfolios that are available whereas the Security Market Line depicts the individual as well as the inefficient portfolios that are not included in the Capital Market Line. In the Capital Asset Pricing Model the concept of SML is used. The risk associated with a portfolio is measured in terms of variance or standard deviation in case of CML and that with volatility in case of SML. Both the concepts of CML and SML are discussed thoroughly in the answer along with the graphical analysis.

There are two types of securities namely the risky securities and the risk free securities. The portfolio of all the risky securities is called the market portfolio M. All the investors who are investing will hold combinations of the two assets namely the riskless securities and the market portfolio. All the above said combinations will always lie along the straight line which represents the efficient frontier. The line drawn or formed by the action of all the investors mixing the risk free asset with the market portfolio is known as Capital Market Line (Brooks and Mukherjee 2013). All the efficient portfolios of every investor will lie in this Capital Market Line. The relation between the risk and return associated with a portfolio is shown in the following equation,

Where, = the expected return on the efficient profile

= rate of return on the risk free assets

= expected return on market portfolio

= variance of the market portfolio

= variance of the efficient portfolio

The term is the slope of the Capital Market Line as well as the risk premium. The slope measures the increase in return due to one unit increase in the risk.

Whereas the Security Market Line is valid for all the inefficient as well as the individual portfolios which do not lie in the efficient frontier. These points are not included in the Capital Market Line. The equation of the SML is provided below,

Where, = expected return of stock i

= rate of return on the risk free assets

= expected return on market portfolio

= volatility of asset

## What is Security Market Line (SML)?

The slope of the SML is β which represents a measure of the security sensitivity with respect to the fluctuations in market returns (Antoniou, Doukas and Subrahmanyam 2015). β is represented in numeric terms. The main difference between CML and SML is this term β. The risk in case of CML is represented by variance and that for SML it is represented by volatility that is β. The graphical representation of both the markets are provided below.

In order to identify the minimum variance portfolio the Modern Portfolio Theory need to be understood. The Modern Portfolio Theory (MPT) is an investment theory that is based upon the idea that the risk averse investors can maximize or optimize the expected returns on the basis of the given level of the market risks in order to construct portfolios (Swamy 2013). Risk is always associated with higher rewards. The MVT is one of the most influential theories.Consider that there are two assets namely A and B. Consider that both of these have a variance of 5 percent. A portfolio consisting of both these assets will have a lower risk than 5 percent if these assets are uncorrelated. However, if these assets are correlated then the risk associated with the portfolio will be higher than 5 percent. Therefore it is very important to choose portfolios with minimum amount of risk associated with respect to the expected returns. The main aim of minimising the risks is attained by allocating varying weights to the corresponding portfolios. These portfolios are called mean variance portfolios as any other combination of such portfolios do not have such low risks and level of expected returns. When plotted in a graph these mean variance efficient portfolios gives the efficient frontier (Gupta, Varga and Bodnar 2013). The graphical explanation can be provided as follows,

In the diagram drawn above the brown points represents the individual securities that are available. The green curve represents the efficient frontier that is the combination of all the mean variance efficient securities. The dark point on the extreme left on the graph represents the minimum variance portfolio (MVP). The minimum variance portfolio has the least standard deviation or minimum risk associated with it (Clarke, De Silva and Thorley 2013). The MVP consists of a number of stock that is available for investment and not only a single stock. Thus, the minimum variance portfolio is the set of portfolios that have the minimum risk associated with it provided that they are efficient. From the diagram the dark point has R1 amount of risk associated with it which is minimum as compared to the other points that have risks of R2 and R3.

## Importance of minimum variance portfolios

The main reasons for the importance of minimum variance portfolio is described as follows. Firstly, in most of the empirical studies it has been observed that the minimum variance theory has performed relatively well as compared to other indexes. Secondly, the expected returns forecast are the major source errors that arise while estimating. The MVP does not consider such expected returns forecast and the process of optimization is independent of such forecasts. Thirdly, in real life the investor I the marker are primarily risk averse in nature. Therefore the theory fits in well with the real life scenario.This phenomenon stimulates the creation of the financial products with a managed volatility.Finally, the MVP has also drawn attention of the market of stock exchange. The stock market index providers are benefited from the minimum variance theory. Therefore the importance of the minimum variance portfoliocan be observed clearly

The relationship between risk and return that is established by Security Market Line is called the Capital Asset Pricing Model. The relationship is basically a linear relationship and the higher the value of βhigher is the risk of the security and thus larger would be the value of the returns that the investors will gain. However, the relationship is meant for an individual as well as the inefficient portfolios associated.The general equation of the CAPM model is similar to that of the SML.

- …………………………….(1)

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

= risk free rate of return

= volatility of the individual asset

= average return on capital market

Another model that can be used to calculate the required rate of return is the Dividend Growth Model (DGM). The value of the stock or the returns 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 general equation of the model for calculating the rates of return isas follows:

………………………………… (2)

Where, P = value of stock, is the next year’s dividends, k = rate of return and gis the constant rate of growth.

Comparing equation (1) and (2) the superiority of the CAPM equation over the DGM can easily be identified. 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 rate of the growth of dividends is constant in case of the Dividend Growth Model. Moreover, the volatility factor is also missing in context of the DGM which is a primary factor as in case of the CAPM. Therefore CAPM equation is far more relevant as compared to the DGM.

Further the Weighted Average Cost of Capital (WACC) model is also used tocalculate the rate of returns to an asset. The equation to this WACC model is represented by the following equation.

WACC = {Cost of Equity * percentage of Equity} + {Cost of debt * percentage of debt * (1 – Tax Rate)} + {Cost of preferred stock * percentage of preferred stock}………… (3)

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 difference and the superiority of the CAPM model with respect to that of the WACC model can be shown graphically in more details.

Consider the point a in the above diagram. Point A is not feasible as per WACC as the internal rate of return is which is less than that of the WACC rate of return which is fixed at M. however, considering the CAPM model, point A is feasible as the internal rate of returns is more. Further considering the point B, it is not feasible in case of CAPM but is an option for the WACC model. This cannot be a feasible point as the point gives insufficient compensations for the level of systematic risks.The importance of the CAPM model 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 and the equation has a great impact on the real life scenario.

**References**

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.

Swamy, M.K., 2013. Modern Portfolio Theory. Journal of Financial Management & Analysis, 26(2), p.84.

Clarke, R., De Silva, H. and Thorley, S., 2013. Minimum Variance, Maximum Diversification and Risk Parity: An Analytic Perspective. Journal of Portfolio Management, 39(3), pp.39-53.

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

Lee, W., 2013. Risk Based Asset Allocation

Antoniou, C., Doukas, J.A. and Subrahmanyam, A., 2015. Investor sentiment, beta, and the cost of equity capital. Management Science, 62(2), pp.347-367.

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

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