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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.

## Understanding Capital Market Line (CML)

In the world of technology and advancements, the share market is one of the most dynamic fields affected by the forces of demand and supply  (Adelaja, 2015).

For the fruitful investment decisions to be made in the market, it is important that one should have a clear idea about the forces of market. There is a much known concept called portfolio analysis. Analysis of stocks on an individual basis and analysis of the entire portfolio is important for the investor's decision making as investors expect returns and returns are possible only when the market is rising or the economy is growing and a complete idea is available to the investors. However, the analysis of the market is a broad concept that makes use of various other concepts such as CAPM, CML, CAL and SML discussed in details below.

From here comes into the picture, the concept of “security market line”. Security market line is the representation of the CAPM model graphically for risks or betas at different levels. The graphical representation shows different levels of risks of marketable securities whether systematic risk or market risk pointed against the expected rate of return at a particular time of the entire market. We also consider SML line as the characteristic line as it visualizes the CAPM where the x-axis of the graph is beta and the y-axis shows us the return to be expected. And this is when market risk premium is calculated by where it is plotted on the graph related to a particular security  (Atkinson, 2012).

SML is more like an investment tool that evaluates the relationship between risks and returns for securities and follows the concept that the investors should be compensated for both value of money in terms of time and the risk premium which represents level of risk involved in an investment. The concept of beta is of prime importance for CAPM and SML concepts. The beta of the asset is measuring systematic risk which diversification cannot eliminate. The beta is a reflection of overall average market  (Bierman & Smidt, 2010). When this value is higher than one, it shows that the level of risk is higher than the average market rate while the beta less than one shows the level of risk less than average of market. The security market line's formula for the purpose of plotting is

Required Return = Risk Free Rate of Return + Beta (Market Return - Risk Free Rate of Return)

## Understanding Security Market Line (SML)

We use SML concept for analyzing a security whether to include it in the portfolio of investment in terms of whether expected favourable return is received or not against its risk level. When the security is plotted above the SML, the security is considered to be undervalued because that means that the security offers a return which is way greater than its risk  (Dayananda, Irons, Harrison, Herbohn, & Rowland, 2008). On the other hand, in case of vice - versa, the stock is considered as overvalued in terms of price because in that case, the expected return doesn't exceed the risks involved. The frequent use of SML is in comparing the two securities of similar nature that offers almost same return in order ro estimate that which security involves the minimum level of risk involved in relation to expected return. In a similar way, two stocks are compared with equal risk that which security offers highest expected return.

We shall now have an understanding about the capital market line (CML) under the CAPM concept that is used to identify the tradeoffs between return and risk for efficient portfolios. The concept is a representation of portfolios that combines the risk free return rate in an optimal manner and the market portfolio of assets with allot of risks. All the investors under the CAPM concept choose a point in equilibrium on the CML, by the tools of lending and borrowing at the freely risky rate, as this would be maximizing the return given the risk level. The CML is the line that connects the rate of return free of risk with the tangent point on the efficient frontier of portfolios at optimum level that for a particular risk level offers the maximum expected return or for a given expected return offers the lowest risk level. The portfolios with most favorable trade off between the risks or variances and expected return lies on the line. The tangent point is known as the market portfolio which is considered as optimal one for risky securities. Following the assumption of mean variance analysis, the potential investors look for maximizing their  return expected for a given level of risk and that there is a freely risky return - meaning all investors will choose the portfolios that lies on the CML  (Donohue, 2015).

Taking references from Tobin's separation theory, identification of market portfolio is one thing while combining the risk free assets and that market portfolio is another thing. An investor would consider investing in either risk free assets or some sort of combination of it with the portfolio of the market depending on the risk fear  (Girard, 2014)

## Importance of Minimum Variance Portfolios

When an investor goes along the CML upwards, the portfolio on the overall basis returns as well as risks will increase. Investors concerned about risk aversion will choose portfolios that are close to the risk free assets that prefer high returns with low variances. However, investors concerned less with risk averse would like to go upwards on the CML for higher expected returns with more risks or variances.

The equation of Capital Market Line Equation is :

In the following equation,

Rp = return on portfolio;

RT and σT = tangency portfolio T's return and standard deviation;

Rf = Risk Free return including the tradeoff between return and risk.

(RT- rf)/σT is also known as the Sharpe ratio multiplied by the standard deviation of portfolio p.

One of the major reasons for differentiating CML and SML is how the risk factors are measured. While CML uses standard deviation for measuring risk , SML make use of beta coefficient for determining the risk factors. On being represented graphically, CML shows fruitful portfolios while SML defines both effective and non effective portfolios. On a graph, the y-axis in case of CML shows the expected return of the portfolio and in case of SML, it shows the return of the securities  (Holtzman, 2013). The x-axis in case of CML represents the standard deviation of the portfolio whereas in case of SML, beta of the security is shown.

CML shows the risk free assets and market portfolio while SML determines the other factors of security. SML shows the expected returns on an individual basis in case of all securities unlike CML. While CML determines the return or risks for efficient portfolios, SML determines the return or risks associated with individual stocks. However, SML can be a tool valued enough for valuation of equity and comparison purposes; it shouldn't be use for isolation purposes as the expected return rate over risk free return rate is not considered as the only reason for decision making related to investment. That is why, capital market line is considered better when it comes to measurement of risk factors  (McLaney & Adril, 2016).

As the name suggests, minimum variance portfolio is a portfolio with diversified securities that consists of risky assets on an individual basis, which are hedged in case they are traded together which in return results in the lowest possible risk for the expected rate of return. This refers to the leveraging of the risk in each asset with an offsetting investment which, thus, hedges the total risk of the portfolio for the level of accepted risk in relation to the expected rate of return of the portfolio. Putting the money in a minimum variance portfolio would be risky if it is traded individually (Menifield, 2014). However, when traded through a portfolio, the risk is hedged. The name has been originated from the Markowitz Portfolio Theory which shows us that the risk can be replaced or eliminated by the volatility and therefore, less risk in investment correlates with less volatility variance.

## CAPM Equation for Required Rate of Return

To construct a minimum variance portfolio, an investor should consider a pairing of low volatile money investments or a combination of money investments that are volatile and have a low link between each other. The second case of portfolio is preferred more while building minimum variance portfolios  (Peterson & Fabozzi, 2012).

Talking about minimum variance portfolio model, we can consider categories of mutual funds that have a low link with each other. This can be explained through an example: 40 percent S&P 500 index fund, 20 percent emerging markets stock fund, 10 percent small cap stock fund and 30 percent bond index fund. While the first three are volatile in nature, all the four are correlated with each other on a lower level. Except for bond index fund, all the four when combined together gives lower volatility than what it gives on an individual basis.

Investments having a Lower correlation are headed under those investments that perform differently given the market conditions and the political environment is constant. This is one of the examples of diversification. When an investor wants to expand his portfolio through diversification, their prime motive is to deduct volatility and this forms the basis of the minimum variance portfolio  (Rivenbark, Vogt, & Marlowe, 2009). One of the most common examples of minimum variance portfolio is a combination of a bond mutual fund and a stock mutual fund. In that case, when prices of stock rises, bond prices may show a slight negativity whereas when stock prices fell, bond prices usually rise. This is because usually stocks and bonds moves in the same direction but they have a low correlation when it comes to performance. With minimum variance portfolio, an investor can efficiently combine the investments together that are risky and can still manage to achieve high returns without bearing the high risk level  (Robinson, 2014).

The 'Capital Asset Pricing Model' or CAPM is a relationship between the expected return and systematic risk for assets and most particularly, stocks. CAPM has wide use in the field of finance for deciding the price for risky securities and expected returns for assets are generated provided the risk associated with the assets are given and cost of capital is calculated  (Seitz & Ellison, 2009). The expected return of an asset is calculated as follow provided the risk is known

The reason for adopting CAPM is that there are two kinds of concerns for investors, that is, time value of money and risk. The risk free rate above represents the time value of money and let the investors knows about whether to invest their money over time. It is usually the yield obtained on government bonds such as US Treasuries. The other half of the formula shows the risk and calculates the amount so as to let investors know whether they are capable of taking additional risk. This is calculated by using beta of the security that compares asset returns with the market over a period of time and to the market premium which is considered as the market return over the risk free return. The beta calculates the risk associated with an asset in comparison to market risk and therefore, shows the volatility in case of both the asset and the market and the relationship between the two  (Taillard, 2013).

Thus, the above model calculates the return expected on the portfolio or the security and equals to the risk premium and rate on a risk free security. In the nutshell, if this doesn’t exceed the required rate of return, the investors do not make an investment.

"The CAPM is an important area of financial management. In fact, it has even been suggested that finance only became ‘a fully-fledged, scientific discipline’ when William Sharpe published his derivation of the CAPM in 1986” (Shapiro, 2007).

Being a popular concept for more than 40 years, the reasons of choosing CAPM formulas over other formulas can be explained as below:

• A single systematic risk is considered which reflects the reality of the diversified portfolios in which investors have an interest and an unsystematic risk is significantly eliminated (Siciliano, 2015).
• It has derived from the relationship between systematic risk and required return through a theoretical approach which is frequently researched about and tested on a regular basis.
• Generally, for the calculation of cost of equity, the CAPM approach is better than the dividend growth model (DGM) as it considers a company’s systematic risk level in relation to the stock market wholly.
• For the use of it in investment appraisal, it is justifiably better than WACC approach in providing discount rates.

Conclusion

The researchers have always found that CAPM has been able to stand up well against the criticisms although such critics a have been increasing since last few years. Until and unless a better concept is coming into existence, the CAPM remains one of the most useful formulas in the field of financial management.

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Atkinson, A. A. (2012). Management accounting. Upper Saddle River, N.J.: Paerson.

Bierman, H., & Smidt, S. (2010). The Capital Budgeting Decision. Boston: Routledge.

Dayananda, D., Irons, R., Harrison, S., Herbohn, J., & Rowland, P. (2008). Capital Budgeting: Financial Appraisal of Investment Projects. Cambridge: Cambridge University Press.

Donohue, R. (2015). An introduction to-- cashflow analysis. Mission Viejo, CA: Regent School Press.

Girard, S. L. (2014). Business finance basics. Pompton Plains, NJ: Career Press.

Holtzman, M. (2013). Managerial Accounting For Dummies. Hoboken, NJ: Wiley.

McLaney, E., & Adril, D. P. (2016). Accounting and Finance: An Introduction. United Kingdom: Pearson.

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Rivenbark, W. C., Vogt, J., & Marlowe, J. (2009). Capital Budgeting and Finance: A Guide for Local Governments. Washington, D.C.: ICMA Press.

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Seitz, N., & Ellison, M. (2009). Capital Budgeting and Long-Term Financing Decisions. New York: Thomson Learning.

Shapiro, A. C. (2007). Capital Budgeting and Investment Analysis. New Jersey: Wiley.

Siciliano, G. (2015). Finance for Nonfinancial Managers. New York: McGraw-Hill.

Taillard, M. (2013). Corporate finance for dummies. Hoboken, N.J.: Wiley.

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