Markowitz mean-variance optimization is one of the tools to measure the efficient frontier, to find out the maximum return at lower risk. This method is introduced by Harry Markowitz in year 1952.
In the paper write by ZhiDong Bail et al had mentioned that, the function of mean-variance optimization introduced by Markowitz was able to provide investor to incorporate their preferences on risk and expectation of return to figure out best combination of the portfolio or the best combination of two wealth to maximum the return of the portfolio at certain level risk, where the risk is acceptable to the investor. In other word the function of the mean variance optimization is to minimize the variance contains in the portfolio and achieves the expected return of the portfolio.
Other than that, in this research, it also mentioned that mean variance optimization is a very powerful measurement for the investor to allocation their wealth to different investment to achieve the maximum profit at the lowest risk. From the journal can clear see that, the important of the mean variance optimization, without it, the investor hard to allocation their wealth efficient and effective, and without it also the risk for a portfolio will increase due to the unknown risk if the investor make a wrong allocation of the wealth.
This can further explain by the following example, if the make a combination for wealth A and wealth B in his or her portfolio, but in fact combine for those two will only increase the variance but will not increase the return and reduce the variance. However, by using the mean-variance optimization theory the investor able to allocation the wealth at the correct position therefore by helping of the theory investor able to reduce the variance and maximum the return of the portfolio.
In the paper written by John Alexander McNair (2003) had state mean variance optimization is widely used in drawing an efficient frontiers. In this paper it is study by using the excel software to drawn the efficient frontiers by following the theory of mean variance optimization. In the paper, the author had mentioned that the mean variance optimization take in consider the dilemma facing by the investor when their thinking how to allocation the wealth. By using the mean variance optimization, it will help the investor solve the problem.
From here we can find that, there is two advantages to use that the mean variance optimization is suitable to use in draw an efficient frontier. First, by running the mean variance optimization theory, it does not require the high education or any advance software to run it. It can be done by using the excel software. From here, the investor able to save their portfolio cost, because sometime to run other portfolio model, it need some more advance software to support the theory, this will increase the cost of the investor to setting up a portfolio, because some advance software is require to pay before can run it. But with mean variance optimization does not need any additional software; just the Excel is more than enough. Therefore is theory can run easier, at the same time it also saving the investor time.
Another advantages can see from in paper is that, mean variance optimization is widely used by past researcher therefore the investor does not worry about the theory is not work well in the reality. Because if the theory really does not work well, if will not widely used by those past researcher. The most advantages for this theory compare other theory is that, this theory is able the help the investor allocation their wealth to reduce the variance and increase the return of the portfolio.
In the paper written by Ali Argun Karacabey(2007) had mentioned that, Markowitz legendary work about portfolio optimization is accepted to be the pioneer of the modern portfolio theory. From here can clearly know that, the mean variance optimization created by the Markowitz was has a higher reputation in the portfolio area. In this paper it also mentioned that Markowitz's mean variance model accept risk as the deviation that can be positive or negative from the expected return. In other words both of the models punish not only the negative deviations but also the positive deviations.
Based on those past journals had done by those researcher, can figured out that, mean variance optimization theory had been widely used in the past therefore it is proved that the theory is work efficiently and effectively in the reality else if will not had so many past researcher do research on that mean variance optimization theory.
2.1.1 Portfolio Selection
Based on Markowitz's paper (1952)-"Portfolio Selection", there are two stages for the process of selecting a portfolio. The first stage starts with observation and experience, and end with beliefs about the future performance of available securities. Or in other words, the first thing we need to do before we form a portfolio is to select some available securities by observing the growth and value of the companies, the companies' price-to-book (P/B) ratio, price-to-earning) P/E ratio, and dividend yield (Sulagna Chakravarty, How to Select Stocks, 2005).
It is believe that a company with rapidly growing earnings or some stocks that has not yet discovered and hence they quote below their true worth will be given a higher return. These stocks are usually found in mature industries like steel, commodities, and fast-moving consumer goods and so on. Such stocks also show high dividend yields which can considered being evidence that the stock is underpriced.
The second stage starts with the relevant beliefs about future performances and ends with the choice of portfolio. The first rule that need to consider is that the investor should maximize the expected return. This rule is rejected both as a hypothesis to explain, and as a maximum to guide investment behavior. The next rule that need to consider is the investor should consider expected return a desirable thing and variance of return an undesirable thing. It is beliefs that the choice of portfolio according to the "expected returns-variance of returns" rule. (H.Markowitz, 1952)
In selecting the securities, the risk and return measures most commonly used by MPT applications are means or averages, and standard deviations of historical annual or quarterly returns, monthly returns interpolated from quarterly returns, or annualized average quarterly returns and standard deviations. Such measures are within the tradition of the application of MPT theory to stocks and bonds, which are highly liquid investment vehicles.
2.2 Risk Management-Value-at-Risk by using Monte Carlo Simulation
Before go into past journal, here would like to give some brief about VaR. VaR was first developed and introduced in 1993 as part as J.P.Morgan Risk Metrics. And it had gained wide acceptance and is also used by regulators to set reserve requirements for the financial institution, like banks and insurance companies. In the journal written by Gregory P.Malfast had stated that, the advantages of the VaR is that VaR measure of risk is better than the traditional metrics of variance is that VaR only consider the losses as part of risk but the traditional metrics of variance will consider the weights losses and gains equally.
In the same journal, the author also had mentioned that Monte Carlo Method was used to find the value at risk measurement for the portfolio. And the author had figured out that the method can accurately figured out the VaR measurement for all financial instruments linear and nonlinear. Therefore in this journal had proved the important for a VaR, because to figure out the accurate VaR, the less loss will occur in a portfolio or project. In other word mean that, the more accurate VaR can generate the less loss the investor can avoid. Therefore the method using to figure must be trustable and the acceptance. In this journal also had provided evidence to support that the Morte Carlo is suitable to use in calculation VaR.
In the journal written by John W.Hayse and Argonne National Laboratory in the paper the author has do the research by using Monte Carlo Analysis in Ecological Risk Assessments. In this paper, the author had explained that, Monte Carlo Analysis could be very important because it able to evaluate the uncertainty and variability associated with risk assessments for contaminated sites. After the author had run through that test, and conclude that Morte Carlo is potentially a powerful tool for examining the effects of variability and uncertainly on the outcome of modeling calculations used in ERAs. Beside that this the journal also mention that the method able to provide the researcher probability of information for the uncertainly condition.
Again, there was another journal had run the research on Morte Carlo method to calculating or analysis the risk for certain project or area. It also proved that, Morte Carlo method has been widely used and has been acceptance by other researcher. Therefore those journal had provide that the reliable of Morte Carlo method. If the method is unreliable, it would be widely used for that researcher. As a result, Morte Carlo able to provide a good results in running risk analysis.
In the paper written by Susan R. Poulter, the paper had study about monte carlo simulation in environmental risk assessment. In the paper, it had mentioned that Morte Carlo has widely been used in environmental health and safety assessment. And the method has been promoted as part of a larger movement to incorporate "quantitative uncertainly analysis" into risk estimates that form the basisbfgvfd of environmental health and safety standards. In the paper the author also got mentioned about the Morte Carlo able to bring more information and more sophisticated uncertainty analysis into risk assessment.
From the paper, can clearly know that the Monte Carlo method had one important advantage where that traditional method unable to provide there is the Monte Carlo able to bringing information at uncertainly condition. Therefore it is very suitable to use in portfolio to calculate the VaR. Because, as a commonsense, when running a portfolio there is many uncertainly in the market like market risk, inflation risk, interest risk and also exchange risk. Those risks are come from uncertainly condition, and the Monte Carlo had fulfilled the requirement, that was the reason for why this paper will choose Monte Carlo as a method to calculate the VaR.
In the journal written by Dr. Ing Tilo Nemuth and Bilfinger Berger Nigeria GmbH and Wiesbaden had mention in their journal that Morte carlo method is much more significant compare with other traditional risk analysis method. Other than that, in the paper written by Pavel Veretennikov, the paper is study about acceleration of Monte Carlo methods when calculating VAR, ES and PFE. In the paper it mention that Monte Carlo methods can provide the result for researcher in a more efficient and affectivity way.
Therefore had proved that, Monte Carlo method is much better than other risk analysis method, but not to mentioned that it is the best method however it is one of the affectivity and efficient method. The word efficient is very important when we doing any portfolio, because with the efficient attitude able release there is any risk occur in the portfolio and able to avoid or know about it. From there, investor can try to reduce the loss. As a result, based on those evidence provide by those past researcher, had state that Monte Carlo is one of the trustable and reliable method to calculating out the VaR value.
