Differences between capital market line (CML) and security market line (SML) with the help of graphical illustration
The report is prepared for demonstrating different aspect of the corporate financial management with particular emphasis on portfolio management, capital market theory and security market analysis. The objective studying investment management and portfolio analysis is to gain an understanding in the field of investment for understanding the concept of sound investment decision making. Investors relies on the concept of capital market line, capital asset pricing model, minimum variance portfolios and security market line to have an understanding of the portfolios of stocks and making feasible investment. In the first section, the graphical illustrations of the difference between security market and capital market line has been demonstrated. The second part of report emphasises on the importance of minimum variance portfolios that helps in explaining the relationship between risk and return. The last section of report deals with the evaluation of the equation of Capital asset pricing model (CAPM) that helps investors in finding the optimum portfolio.
The concept of efficient frontier can be taking into account for explaining the difference between capital market line and security market line. Efficient frontier is depicted graphically in the diagram show below which outlines three investment point of investors such as either A or B and B or C. However, investor would prefer making investment at point B or C as it provides higher level of return compared to A. Here, C would of offering higher return along with higher risk compared to point A or B with lower level of risk. Therefore, investor would prefer to opt for investment decision C compared to A.
Graph 1: Efficient frontier curve
(Source: Christensen et al. 2016)
Graph 2: Graph depicting Capital market line
(Source: Yang et al. 2015)
The above graph presents the efficient and feasible set of portfolios and the optimal set of investment portfolio would be the one lying between A and B on the assumption of risk aversion and non satiation. All the portfolios within the feasible set are not the optimal investment made by investors. The optimum portfolio is prepared by the combination of risk free and risky stocks. The efficient frontier becomes a tangent line if the risk free assets is introduced into the whole set of assets. That particular line containing the combination of risky and risk free assets is known as capital market line which is indicated by point M. Such line depicts a linear relationship between the efficient portfolios combination with their standard deviation and required rate of return. The risk price is represented by the portfolio on capital market line in the form of slope and the return that is in excess of risk free rate (Becker et al. 2015). Such return generated by portfolio would be in the proportion of standard deviation of portfolio which is generated by market.
Graph 3: Security Market Line
(Source: Bodnar et al. 2018)
It has been found that the capital market line does not represent the risk associated with the inefficient portfolio and there is failure on its part to make the identification of relationship between risk and return. The characteristic of risk and return of various securities is represented by Security market line by making the assumption of having liner relationship between return and risk. There is gauging of individual securities on part of security market line irrespective of whether the portfolios are efficient or not. Furthermore, the expected return on the security is ascertained by such line which is provided by value beta. Such value helps in capturing the overall systematic risk associated with the given security. However, there is possibility to make the diversification of unsystematic risks associated with the security whereas the systematic risks represented by value of beta cannot be diversified. The specific security market line helps in providing description of each security risk and the difference in securities are attributed to difference in value of their beta that is a reflection of different level of market risk.
Importance of minimum variance portfolios
Graph 4: Evaluation of stock using SML
(Source: Kim and Kim 2016)
The overpricing and underpricing of stocks can be evaluated with the help of application of security market line. Buying the under prices stocks is the efficient decision made by investors and they intend to make investment in such stocks. The under priced securities are those which are above the line SML and therefore points X, Y and Z represents three underpriced stocks. On other hand, over priced stocks are those lying below the SML and it is represented by the points U, V and W on above graph. The difference between these stocks is because of difference in the level of return provided to investors whereas the level of risks remaining same.
The formula depicted in the above diagram can be used for validation of underpriced stocks that is X, Y and Z. The formula contains three variables that is P1, P0 and the amount of dividend. The current price is represented by P1 and the purchase price represented by P0 and the amount of dividend is represented by Div. Therefore, the optimal level of stocks is the one that is lying on security market line indicated by the points A, B and C. Such stocks are neither underpriced nor over priced and they depict the appropriate combination of return and risks. Portfolio of beta is simple weighted average of betas of different securities. Therefore, the relationship between beta and expected return of stocks gives the security market line. The coefficient beta is the undiversified systematic risks that are indicated by security prices that depend upon the market force.
Graph 5: Imperfect market and Security market line
(Source: Evstigneev et al. 2015)
The pricing of the stocks would be considerably affected when there is lack of availability of perfect information’s about market. This is due to the fact that all the stocks would lie on the security market line where the investors are provided with the complete information available in the perfect market (Zabarankin et al. 2015). Nevertheless, security market line becomes a band as depicted in the above graph instead of a single line in a market where incomplete information is available that is in an imperfect market.
The differences between CML and SML can be explained in the table below after in depth discussion of all the concepts associated with investment portfolio and different market lines.
|
Capital market line (CML) |
Security Market Line (SML) |
|
The combination of risk free assets and market portfolio forms the basis of capital market line. Compared to any points on efficient frontier, all the portfolios lying on the CML have superior profiles in terms of return and risks (Berk and Van Binsbergen 2016). |
The graphical representation of capital asset pricing model is given by the security market line. Using this line, the individual security expected return is represented as a function of no diversifiable and systematic risks. |
|
The risks associated with the securities under CML are gauged by the standard deviation. |
Risks under SML on other hand are gauged by the value of beta that cannot be diversified. |
|
The rate of return relating to efficient portfolios is represented by the line in capital asset pricing model. |
It is a line reflecting the risks of investment versus risk associated with the given value of investment. |
|
The CML accounts only for efficient portfolios. |
SML take into account both the efficient and inefficient portfolios. |
The optimization of minimum variance portfolios relies on the modern portfolio theory which takes into account the formation of portfolio by considering the risk and expected returns of individual stocks. Such interrelationship between the return and risk is explained by the correlation and using the concept of correlation, investor has the possibility of bettering the simplistic portfolios. Such method makes use of indifference curve for choosing the most desirable portfolios. According to this approach of modern portfolio, the mar jet risk for investors is high if the investment volatility is higher (Yang et al. 2015). Therefore, investors to make a movement up or down in terms of investment return if they seek to minimize the risks associated with their investment. However, efficient portfolios are those providing higher return for the same level of risks associated with inefficient portfolios.
Evaluation of the equation of Capital Asset Pricing Model (CAPM)
The portfolios having minimum variance are the one that lies on the efficient portfolios where the risk parameter can be modified according to the market and investors preferences. Method of econometrics can be used to make estimations from time to time.
It has been found that stocks generate average returns if they have lower fluctuations to market and such return is in excess of the expected return offered by the stocks. Over the past forty years, the low volatility premium has been documented. Such low volatility premium can be implemented optimally using the concept of minimum variance portfolio (Varga et al. 2016).
Minimum variance portfolio incorporates the assets that are risky on individual basis and when they are combined for forming the portfolio would generate lower level of risks for the expected return. Using such portfolio would help investors to hedge their investment by offsetting the level of risks (Mackaya and Haque 2016).
Capital assets pricing model helps in identifying linear relationship between the systematic risks and return generated by investment. Such model takes into account unsystematic and systematic risks whereas it is possible to diversify the unsystematic risk compared to systematic. It is identified by the model that an investor would be provided with greater expected return the investment carries higher systematic risks (Hornuf and Schwienbacher 2018).
Graph 5: Capital asset pricing model
(Source: Qin 2015)
Investors can measure the expected return generated from their investment using the above graph. In addition to this, they can also compute the weighted average cost of capital linked to their investment. The technique of capital budgeting employs the concept of weighted average rate of return that is used as discounting rate (Pedersen and Peskir 2017).
The equation explaining the risk and return using the model of CAPM is depicted in the above diagram. Rf is the risk free rate of return offered by the risk free assets, βs is the coefficient beta that measures the unsystematic risk associated with the individual security and kM measures the expected return generated by market (Christensen et al. 2016). Some of the assumptions of CAPM are identified below:
- The market can be influenced by individual investor and they act as price taker (Liu 2016).
- There is one period expectation on part of investors concerning future.
- Investors can borrow money and lend at the risk free rate.
- All the information is instantly and freely available to investors.
- The cost of transactions and taxes are not relevant.
However, such assumptions seem not to be realistic. Nevertheless, investors could rely on the model for making better investment decision. The literature in financial management provides the alternative to the CAPM such as Gordon growth model, Fama French model and dividend discount model that helps in enhancement of investment decision by required rate of return computation (Björk et al. 2014). Despite this, many investors prefer CAMP over all these models because of several advantages in terms of discount rate, cost of equity and diversification.
Conclusion:
From the analysis conducted relating to the investment portfolio, it can be inferred that the level of measurements is represented by CML, SML and minimum variance portfolio that would help investors in undertaking sound investment decision. Any portfolio that is below the minimum level of variance would not be opted by any rationale investor. Diversification and efficiency of investment is enhanced by the optimization of systematic portfolio. In addition to this, it has been found that investor can compute the return rate of returns in an effective way by the application of CAPM compared to other methods available. Therefore, investors can maximize their wealth by undertaking investment using assets pricing model.
References:
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Berk, J.B. and Van Binsbergen, J.H., 2016. Assessing asset pricing models using revealed preference. Journal of Financial Economics, 119(1), pp.1-23.
Björk, T., Murgoci, A. and Zhou, X.Y., 2014. Mean–variance portfolio optimization with state?dependent risk aversion. Mathematical Finance: An International Journal of Mathematics, Statistics and Financial Economics, 24(1), pp.1-24.
Bodnar, T., Parolya, N. and Schmid, W., 2018. Estimation of the global minimum variance portfolio in high dimensions. European Journal of Operational Research, 266(1), pp.371-390.
Christensen, H.B., Hail, L. and Leuz, C., 2016. Capital-market effects of securities regulation: Prior conditions, implementation, and enforcement. The Review of Financial Studies, 29(11), pp.2885-2924.
Evstigneev, I.V., Hens, T. and Schenk-Hoppé, K.R., 2015. Capital Asset Pricing Model (CAPM). In Mathematical Financial Economics (pp. 53-59). Springer, Cham.
Hornuf, L. and Schwienbacher, A., 2018. Market mechanisms and funding dynamics in equity crowdfunding. Journal of Corporate Finance, 50, pp.556-574.
Kim, K.H. and Kim, T., 2016. Capital asset pricing model: A time-varying volatility approach. Journal of Empirical Finance, 37, pp.268-281.
Korinek, A., 2018. Regulating capital flows to emerging markets: An externality view. Journal of International Economics, 111, pp.61-80.
Liu, E.X., 2016. Portfolio diversification and international corporate bonds. Journal of Financial and Quantitative Analysis, 51(3), pp.959-983.
Mackaya, W. and Haque, T., 2016. A study of industry cost of equity in Australia using the Fama and French 5 Factor model and the Capital Asset Pricing Model (CAPM): A pitch. Accounting and Management Information Systems, 15(3), p.618.
Pedersen, J.L. and Peskir, G., 2017. Optimal mean-variance portfolio selection. Mathematics and Financial Economics, 11(2), pp.137-160.
Qin, Z., 2015. Mean-variance model for portfolio optimization problem in the simultaneous presence of random and uncertain returns. European Journal of Operational Research, 245(2), pp.480-488.
Varga-Haszonits, I., Caccioli, F. and Kondor, I., 2016. Replica approach to mean-variance portfolio optimization. Journal of Statistical Mechanics: Theory and Experiment, 2016(12), p.123404.
Yang, L., Couillet, R. and McKay, M.R., 2015. A robust statistics approach to minimum variance portfolio optimization. IEEE Transactions on Signal Processing, 63(24), pp.6684-6697.
Zabarankin, M., Pavlikov, K. and Uryasev, S., 2014. Capital asset pricing model (CAPM) with drawdown measure. European Journal of Operational Research, 234(2), pp.508-517.
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