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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.

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Minimum Variance Portfolio

Identifying the nature of the different corporate financial tools is crucial for the financial analyst, financial managers and the investors. The different tools take the concern on the different aspects of an investment and offer different result. It is necessary for the related parties to identify the necessity and choose the better method accordingly. Such as, minimum variance portfolio method is better when an investor wants to get lower risk, no matter what would be the return from the investment. As well, the SML line is used to represent the related risk position and return on the basis of risk. CAPM method is helpful for the business and the investors to identify the expected rate of return from the business (Damodaran, 2011).

In the report, the SML line, CML line, CAPM model and minimum variance portfolio has been studied and it has been recognized that how an organization could identify the different investment position of a stock with the help of these tools.

Security market line (SML) represents the result of CAPM equation in a graphical manner. It basically represents the relations among the expected return of the stock and risk of the stock which is represented in the beta factors. In different words, it could be said that the security market line of a portfolio and stock represents the expected return which could be expected from a particular stock or the portfolio against the different beta factors of that stock or portfolio (Lee and Lee, 2006). The security line is basically based on the equation of CAPM which is as follows:

E(Ri) = RF + βi × (E(RM) - RF)

 Beta Security Market Line: ri Risk-Free Rate Market Return 0 5.00% 5% 8% 0.5 6.50% 5% 8% 1 8.00% 5% 8% 1.5 9.50% 5% 8% 2 11.00% 5% 8%

Figure 1: Security Market line

(Damodaran, 2011)

It represents that security market line only focuses on the beta factors of the stock and the total expected return on the basis of that stock.

Further, capital market line (CML) represents the risk (in the manner of standards deviation) against the return in a graphical manner. It basically represents the relations among the expected return of an efficient portfolio and risk of the stock which is represented in the standard deviation factors (Lumby  and Jones, 2007). In different words, it could be said that the capital market line of a portfolio represents the return which could be expected from a particular portfolio against the different standard deviation level of that portfolio. The capital line is basically based on the equation below equation:

## Modern Portfolio Theory

(Lumby  and Jones, 2007)

The graphical representation of CML line has been presented on the basis of the below case:

 capital market line risk return 0.00% 6.00% 4.00% 9.16% 8.00% 12.32% 12.00% 15.48% 16.00% 18.64% 20.00% 21.80% 24.00% 24.96% 28.00% 28.13% 32.00% 31.29% 36.00% 34.45% 40.00% 37.61% 44.00% 40.77% 48.00% 43.93% 52.00% 47.09% 56.00% 50.25% 60.00% 53.41% 64.00% 56.57% 68.00% 59.73%

Figure 2: Capital market line

(Lumby and Jones, 2007)

It represents that capital market line only focuses on the standard deviation factors of the portfolio and on the basis of that, the return of the business is calculated.

Through evaluation on both the graphs, it has been found that the SML graphical representation depict about the expected return which could be expected from a particular stock or the portfolio against the different beta factors of that stock or portfolio whereas the CML line graph represents the return which could be expected from a particular portfolio against the different standard deviation level of that portfolio (Damodaran, 2011). The SML focuses on the beta factor to measure the expected return from the portfolio while the CML focuses on the standard deviation factor to measure the expected return from the portfolio.

The CML line is useful to identify the risk free rate of an economy as well as the market portfolio position while the SML line represent about the stock’s beta and the return factor on the basis of which, an investor could make decision about the investment into that particular company (Michaud, 2009). It is the major point among the CML and SML line that CML line only represent about the efficient portfolios while in case of SML line, efficient and non efficient portfolios could be shown in graphical manner.

On the basis of the above definitions of CML and SML and their graphical comparison, it has been found that both of the methods must be followed and applied by the financial analyst, financial manager and the investors to get the same outcome from the different figures on the basis of the needs and nature of investment.

Minimum variance portfolio is basically based on the Modern portfolio theory which has been introduced in the year of 1950 by H. Markowitz (Markowitz, 1959). This is one of the common and most used theory to select the financial portfolio. Mainly, the minimum variance portfolio theory has been introduced to minimize the associated risk of a stock and portfolio along with no sacrifice of return from that stock. The main focus of the theory is on the diversification of the assets portfolio. It forces the risk of assets to be lower through combining the various stock and instrument together in order to lower the average risk of all the portfolios.

## Security Market Line

For instance, two securities are available for the purpose of investment along with 1% standard deviation, if a portfolio s prepared with both of the securities than the volatility of the portfolio would be lower than 10% (Blitz and Vliet, 2007). The theory is basically applied by the analyst and the investors through  applying the different weights to different stock. These portfolios which are basically prepared to reduce the risk of the assets are called minimum variance portfolios. It is very much possible for the financial analyst to prepare a portfolio associated with the lowest risk in the market with the help of the minimum variance portfolio theory. The below is the framework of the MVP:

(Jagannathan & Ma, 2013)

The minimum variance portfolio is just a part if the entire modern portfolio theory which assigns the different weight to the different stock on the basis of various related factors such as the covariance among the stock, correlation of the stock, return and risk of the stock etc. It takes the concern of all these factors and after it assigns the weight in such a way that the associated risk of the stock could be lowest. MVP always focuses on 2 or more assets because the main motto of the theory is to follow the diversification effect to reduce the risk kevel of the stock (Markowitz, 1959).

Further few of the weak point of MVP theory has also been studied in order to critically analyze the theory. Memmel, (2013) has claimed into his study that minimum variance portfolio assigns the different weight to the stocks to reduce the risk factor of the portfolio but in this process, the return factor is ignored in theory. There is no proper estimation system to evaluate the total return from that stock and thus CAPM model is followed to identify the stock return. This is one of the limitations of the modern portfolio theory that it doesn’t add a process to identify the total return from the portfolio.

Jagannathan and Ma, 2013) has further tested the performance of minimum variance portfolio which has been obtained by using different covariance estimation from the stock which offers the different constraints and outcome. On the basis of the overall study, it has been found that the minimum variance portfolio is one of the finest methods in order to reduce the associated risk of a portfolio.

The minimum variance portfolio calculations are given as below in order to understand the process in better way:

 Four assets Correlations Exp ret Std dev Asset 1 Asset 2 Asset 3 Asset 4 Asset 1 0.07 0.15 1 0.30 0.35 0.25 Asset 2 0.08 0.20 0.30 1 0.38 0.10 Asset 3 0.09 0.25 0.35 0.38 1 0.15 Asset 4 0.10 0.30 0.25 0.10 0.15 1 Risk free 0.05 Covariance matrix 0.0225 0.0090 0.0131 0.0113 0.0090 0.0400 0.0190 0.0060 0.0131 0.0190 0.0625 0.0113 0.0113 0.0060 0.0113 0.0900 Minimum variance portfolio Weight 1 0.586 Weight 2 0.260 Weight 3 0.059 Weight 4 0.095 Exp ret 0.077 Std dev 0.132

## Capital Market Line

(Michaud, 2009)

It explains that after applying the theory of minimum variance portfolio, the associate risk of the portfolio has been 0.132 which is lowest in comparison with the individual stock risk position.

CAPM method is an economical theory which is used by the investors and the financial analyst to represent about the relations among the expected return and risk position of an assets or the portfolio of the asset (Memmel, 2013). The CAPM theory explains that only the systematic risk affect the return of an assets and this risk cannot be eliminated even with the diversification of the assets. The theory further represents that the expected return from an assets or a portfolio is always equivalent to the risk free security rate which is added with the market premium of capital market and multiplied by the asset’s beta factor (i.e. the systematic risk of the stock). The equation of the CAPM is as follows:

E(Ri) = RF + βi × (E(RM) - RF)

Where,

E(Ri) stands for the expected return from the stock or the portfolio

RF stands for the risk free rate of the economy

Βi stands for the beta factor of asset or the portfolio

(E(RM) - RF) stands for the market premium (Michaud, 2009)..

The equation of the CAPM represent that it focuses on the individual beta factor of the company which is the systematic risk of the company and impact the return from that particular stock (Ross, Westerfield And Jaffe, 2007). The systematic risk can never be eliminated in the investment position even through using the diversification method and thus it is important for the business to measure the beta factor which is not calculated by the other methods.

Further, the CAPM equation focuses on the risk free rate of the economy. This rate is collected from the Australian government bond rates and it represents the minimum return which could be got by any investor without the association of any kind of risk (Xiao, Faff Gharghori and Min, 2017). Further the market risk premium represent the total return which could be get by an investor through a risky return. All of these factors play crucial role in the expected return from a stock or the portfolio (Mazzola and Gerace, 2015). And CAPM model considers the all. Thus, it could be said that it is one of the best method to calculate the required rate of return from a particular project.

## Comparison between SML and CML

Conclusion:

On the basis of the study on various tools to identify the different corporate financial tools, it has been found that all the methods are quite crucial for the financial analyst, financial managers and the investors to get the different constraints and the outcome from the methods. The different tools focuses on different factors and thus outcome of all the methods are also different. It is necessary for the financial analyst, financial managers and the investors to identify the nature and needs of the investment and must apply the tool accordingly.

On the basis of the study on CML and SML and their graphical comparison, it has been found that both the lines take the different risk factors to identify the return level from the stock. Further, the minimum variance portfolio method is a great method in case of an investor wants to get lower risk along with the ignorance on the risk factor. As well, CAPM method is helpful for the business and the investors to identify the expected rate of return from the business.

References:

Appel, D. 2008. Low volatility, high return strategies get a look. [online]. available at: https://www.pionline.com/apps/pbcs.dll/article?aid=/20081103/reg/811039995/1011/portfoliostrategies [accessed 18/9/18].

Blitz, D., and Vliet, P. 2007. The volatility effect: lower risk without lower return. ERIM Report Series Research in Management. [online]. available at: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=980865 [accessed 18/9/18].

Damodaran, A, 2011, Applied corporate finance. 3rd edition, John Wiley & sons, USA.

Jagannathan, R. and Ma, T. 2013. Risk reduction in large portfolios: Why imposing the wrong constrains helps. The Journal of Finance, 58(4), 1651-1684.

Lee.C.F and Lee, A, C,.2006. Encyclopedia of finance. Springer science, new York.

Lumby,S and Jones,C,.2007, Corporate finance theory & practice, 7th edition, Thomson, London.

Markowitz, H. 1959. Portfolio selection: Efficient diversification of investments. New York: John Wiley & Sons, Inc.

Mazzola, P. and Gerace, D., 2015. A comparison between a dynamic and static approach to asset management using CAPM models on the Australian securities market. Australasian Accounting, Business and Finance Journal, 9(2), pp.43-58.

Memmel, C. 2013. Performance hypothesis testing with the Sharpe ratio. Finance Letters 1, pp. 21-23.

Michaud, R. 2009. Efficient asset management. Boston, MA: Harvard Business School Press.

Michaud, R. 2009. The Markowitz optimization enigma: is “optimized” optimal? Financial Analysts Journal. 25(2), 2013-240.

Ross, S, A,. Westerfield, R, W,. And Jaffe, J,.2007. Corporate Finance. the McGraw-hill, India

Xiao, Y., Faff, R., Gharghori, P. and Min, B.K., 2017. The Financial Performance of Socially Responsible Investments: Insights from the Intertemporal CAPM. Journal of Business Ethics, 146(2), pp.353-364.

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