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.

## Security Market Line (SML) vs Capital Market Line (CML)

Investment appraisal is based on the tradeoff between risk and return. The risk return trade off theory has been of great interest to scholars and practitioners seeking to establish accurate predictive models to be used by investors. The Capital Asset Pricing Model (CAPM) developed by William Sharpe in 1960’s is also based on the risk and return relationship (Al-Afeef, 2017). The model has a wide acceptance in the finance industry and hence has attracted much research from application and practitioners. The capital market line is located on the CAPM graph. Also, the security market line is the main graph that illustrates the CAPM.This study highlights the differences between the Capital Market Line (CML) and the Security Market Line (SML). The paper also goes ahead to explain why CAPM is superior and more acceptable among required rate of return models.

Security and capital market lines are concepts used in portfolio management by investors and financial analysts. They are technical analysis tools that facilitate the selection of worthy investments considering risk and expected return (Turner, 2014). There exist many investment vehicles available in the world today. Stocks, bonds, and real estate are example of investment tools available for individual and corporate investors. To clearly distinguish SML from CML, it is important to briefly discuss the CAPM which is the basic concept underlying the two lines.

The CAPM was developed during the 1960’s as an extension of Markowitz portfolio theory. It describes how rational investors should construct and select efficient portfolios (Chandra, 2017). Portfolio theory develops pricing strategies that work under the assumption that all investors are rational and seek to maximize on their returns. CAPM assumes that risk and return are the two basic important features of every investment that investors should consider while making investment decisions (Hoesli & MacGregor, 2014). Diversification is the basic idea that facilitates building of portfolios. A portfolio that consists of uncorrelated assets is less risky since the loss incurred in one security is compensated by the gain in the other security. The risk of an investment is measured by the variability in returns such that standard deviation and variance are used as measures of risk.

The SML is illustrated below;

SML=E(R_{i})= R_{f}+β_{i}[E(R_{M})-R_{f}]

Where; E(R_{i}) is the expected return of the asset

R_{f }is the risk free return

E(R_{M}) is the expected return of the market

The SML is a straight line that joins risk-free return and the market return in a graph where portfolio beta coefficients are plotted on x- axis while expected returns are plotted on the vertical axis (Kaiser , El Arbi & Ahlemanne, 2015). Beta of a security determines measures the volatility of an investment by comparing its risk with that of the market. From the graph above, it can be deduced that, the beta of a risk-free security is zero. A risk free security is assumed to have zero risk since investors are guaranteed of its expected returns (Klingebiel & Rammer, 2014). In finance, the government bond is regarded as a risk free security since governments of economically stable countries do not default on their financial obligations. The market portfolio consists of all the risky assets in the market. It has a beta of one and expected return of R_{m}. From the illustration, the line labeled as SML is the security market line.

## Importance of Minimum Variance Portfolios

The CML

The capital market line is a graph that denotes expected return of a portfolio consisting of all possible combinations of market portfolio and a risk- free security. The market risk in this scenario is diversified completely such that unsystematic risk is completely eliminated. Portfolio theory assumes that all investors have similar expectations about the market (Stettina & Horz, 2015). The line illustrates capital allocation between risky assets and risk free assets for all investors. A rational investor would only undertake more risk provided return rises proportionally.

The CML illustrates risk-return associations for all efficient portfolios. They are defined as portfolios that either yield the highest expected returns for a certain risk level or that carries the lowest risk for some expected return. Efficient portfolios lie along the CML. The SML shows risk- return relationships between all securities either efficient or inefficient (Rank, Unger & Gemunden, 2015). It indicates expected returns of each individual asset in a portfolio unlike a capital market line that shows only the risk- return relationships between individual assets. Standard deviation measures risk on the CML while beta coefficient quantifies risk on the security market line. These risk measures appear on the x-axis of the risk-return graphs to yield the CML and SML. Measures of market risk estimates the movement of the market. The investor shall then estimate how specific components will move, given the size and direction of the prices in the market. Standard deviation is a statistical measure of dispersion of a distribution obtained by calculating absolute deviation from expected values (Cejnek & Randl, 2016). It assumes that returns of securities conform to normal distribution.

The CML gives the market portfolio and risk free securities whereas the CML determines all factors underlying a security. All capital investments lie on the security market line. The SML assumes that assets are priced efficiently on the basis of the expected return and beta (Wang, Yan & Yu, 2017). Securities that appear below the SML have less expected return and high cost. Companies raising capital would prefer to have their stock lying below the security market line while rational individual and corporate investors would prefer investments with a high return or low risk.

The vertical axis of capital market line features expected return of a security while the X-axis features risk. This is different from the Security market line which presents the required return on individual securities on the Y-axis and beta, the risk measure on the X- axis.

## CAPM Equation and Required Rate of Return

Minimum variance portfolio is a combination of securities that minimize the volatility of the overall portfolio (Cremers, Halling & Weinbaum, 2015). It is worth noting that investments are characterized by risks arising from different factors. Risk is the probability that an expected outcome from an investment will not be realized. Investments are affected by a diverse kinds of risks ranging from those occurring as a result of changes in the political, social, economic, and legal environment. These risk make up both systematic and unsystematic risk. The aim of minimum- variance portfolio theory s to build a portfolio that has the least variance irrespective of the level of return. Diversification is the key concept of the mean- variance portfolio theory. Diversification is the spreading of risk in to different markets with the objective of minimizing the overall risk.

Although, academic research studies have majored on modern portfolio theory, Minimum variance optimization procedures are widely used in practice. Many investment firms and investors prepare their investment strategies basing on minimum variance techniques. Studies have established that mean variance optimization performs better on out of –sample procedures compared to other techniques. Also, most modern portfolio theory critics do not criticize minimum variance techniques since it is independent of forecasts of expected returns, a common cause of estimation errors. Minimum variance portfolio estimation is only dependent on risk parameters that can be modelled and estimated using econometric techniques (Bjork, Murgoci & Zhou, 2014). The estimates of returns are not required while predicting minimum variance portfolios.

Mean-variance portfolios have less risk since they are highly diversified. The variance is the measure of risk. Therefore, when the variance is minimized, the overall risk of the portfolio declines. Unsystematic risk is uncertainty occurring as a result of the characteristics of a specific firm or industry. Selecting investments from a single market increases the overall risk of the investment. The concept of diversification enables investors to create portfolios from combining assets from different industries such that a loss from one asset is offset by a profit in the other investment (Pedersen & Peskir, 2017). Correlation is used to measure the degree of relationship between two securities such that assets which are least correlated are preferred. Normally, minimum variance portfolios rest near the efficient frontier. Sharpe ratio is the quotient of excess return and standard deviation. It gives the risk-adjusted return of a portfolio. Portfolios with higher Sharpe’s ratio is more desirable to investors because it has higher excess return. The benefit of optimized portfolio diversification is lower volatility and relatively lower losses in case of market corrections. They are therefore attractive to many risk averse market participants.

## Conclusion

Minimum-variance portfolios yield high returns. The risk-return trade off theory states that risk and return are directly proportional. Also, according to modern portfolio theory, securities with lower volatilities yield higher average returns. Higher returns are associated with higher risk although, the creation of a minimum-variance portfolio ensures that higher returns are obtained at relatively lower risk levels. Investors select investments depending on their risk tolerance levels such that investors with high risk appetite invest in highly risky ventures with the expectation of securing high returns.

The SML basically illustrates association between risk and return of securities. The CAPM equation calculates expected return from investments. Higher beta value demotes a higher risk which results to a higher expected return. The CAPM relationship is not only true for individual assets but also, for portfolio of assets. The CAPM formula for required return of an investment is represent;

E (r_{i}) = R_{f }+ βi (E (r_{m})- (R_{f })

Where;

E (r_{i}) is the required return of the asset i

R_{f} is the risk- free rate of return

βi is the beta of asset i

r_{m }is the return of the market

CAPM assumes that, investors eliminate unsystematic risk of their holdings through diversification. The theory also assumes that, investors have a standardized holding period for their assets. Also, market participants can borrow and lend capital at the prevailing risk free rate of interest determined by interest on government bonds. Most finance scholars and practitioners believe that CAPM is one of the most notable discoveries in the finance industry. In the CAPM model, expected return is the dependent variable that is predicted by the security beta and risk of the market. The market is assumed to be efficient such that, all market participants have full information on available security market prices. The theory argues that, systematic risk is the major determinant of expected return.

The required portfolio return of an individual security can be obtained from the CAPM formula. However, the dividend discount approach, and Weighted Average Cost of Capital techniques can also be used to calculate required rate of return. CAPM takes in to consideration systematic risk and disregards unsystematic risk. This conforms to the reality in practice where investors create diversified portfolios from which unsystematic risk has been eliminated (Sharpe & Litterman, 2014). The dividend capitalization model considers systematic risk in relation to the market unlike CAPM which explicitly considers systematic risk.

Many empirical studies have theoretically derived and tested the association between required return and market risk. In practice, it is common for investors to consider the impact of risk on their investments. The risk tolerance of investors determine the investments they undertake such that risk averse investors would select an investment with less risk provided two investments with different risk profiles and similar expected returns. Investors with high risk appetite would select highly risky stocks in expectation of huge returns.

When compared to WACC, CAPM is more superior in calculating discount rates used in project appraisal. The discounting rate obtained through CAPM assumes that investment risk is equal to company business risk (Al-Afeef, 2017). WACC also assumes an optimal capital structure not realistic in practice. The WACC is determined by the capital values of the market which are dynamic although assumed constant. The use of past information might render a model inefficient. The capital asset pricing model asset does not rely on past information and thus is superior to other formulas such as the WACC which is based on past information.

Although capital asset pricing model has features that make it more relevant in calculating the required cost of capital, it also has its weaknesses mainly arising from its assumptions. The implementation of CAPM requires assigning values to risk free rate, market return, and equity beta. Inputting unrealistic or wrong values would lead to the poor results and hence making the model defective (Joo & Durri, 2015). The assumption of a single time period among investors is also not realistic since investors have independent investment plans.

Conclusion

The SML and CML are essential features of CAPM. The SML is the main line that depicts CAPM since it is a plot of beta on the X-axis and expected return of the security on the Y-axis. The Capital market line on the other hand, presents a visual representation of securities that form the efficient frontier and the efficient portfolio. Its vertical axis features the expected return while the horizontal axis has the risk. CAPM is more superior compared to the WACC model and the dividend discount method since it is more accurate in estimating the rate of discount. CAPM also takes in to account the systematic risk while assuming that unsystematic risk is insignificant as it is the norm in practice

References

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Cejnek, G. & Randl, O., 2016. Risk and return of short-duration equity investments. Journal of Empirical Finance,36(1), pp. 181-198.

Chandra, P., 2017. Investment analysis and portfolio management. 6^{th} ed. New York: McGraw-Hill Education.

Cremers, M., Halling, M. & Weinbaum, D., 2015. Aggregate jump and volatility risk in the cross?section of stock returns. The Journal of Finance, 3(1) pp. 577-614.

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Sharpe, W. F. & Litterman, R., 2014. Past, present, and future financial thinking. Financial Analysts Journal. 70(6), pp. 16-22.

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