Firstly, we need to define the word of portfolio in order to get more understanding about the portfolio theory and portfolio development. Portfolio is refers to a group of financial assets such as stocks, bonds and cash. The portfolios are mostly hold by investors according to their risk tolerance, time taken and investment objectives and/or will be controlled by financial professionals, banks and other financial institutions to get the better allocation of risk-return portfolio. Besides, there are two types of risk that involved: diversified and undiversified risk. Diversified risk also called as unsystematic risk which the risks cannot be fully predicted and avoided, the examples are interest rates and wars. The undiversified risk is known as systematic risk and this kind of risk can be reduced through suitable diversification and it is more specific to individual stock.

## The History of Portfolio Management

Portfolio Theory is also known as Modern Portfolio Theory (MPT). It was first developed and discovered by Harry Max Markowitz. He is an American economist, born on 24th August 1927. He is also a professor of finance at the Rady School of Management at the University of California, San Diego.

Portfolio Theory was introduced in his paper 'Portfolio Selection' which was published in the Journal of Finance in 1952. In 1990, he won the Nobel Prize in Economic Sciences for the Theory, shared with Merton Miller and William Sharpe.

Markowitz is not only known for his pioneering work in Portfolio Theory. He is also very known for the study of the effects of asset risk, return, correlation and diversification related to investment portfolio returns.

## The Benefits of Portfolio Management

The main advantage of portfolio management is to help companies manage all their processes as well as set objectives. Small businesses may not have a structure for portfolio management, but most companies often employ someone to handle their projects.

A portfolio management benefits the investors in making decisions especially risk matters. It is very important for investors to know how to control risk in their business portfolios. Besides that, it improves business performances. Portfolio management improves business performances by setting the priorities for better project delivery.

Business projects are often achieved by resources which are evenly shared alongside with other projects. Many projects may end up competing for resources. This is where portfolio management is much needed. It helps in planning so that resources are equally distributed in all the business processes. This involves measuring, comparing, and prioritizing the most valuable projects only. The conflicts between the projects for resources are resolved by the high level management. The skill sets required for each project and ideal source of these resources are determined by incorporating formal sourcing strategies.

The performance problems are corrected earlier to their development in major issues. Although, portfolio management cannot completely eliminate performance failures, it helps in identifying the performance issues early. The portfolio management involves steps such as identify, growth and deal with any issues related to implementation. The portfolio also helps in keeping the progress of projects or work on track.

## Traditional and Modern Portfolio

From the evolution of mankind, people are trying to get rich. Hence, many investments have been made. Countless method has been introduced to manage portfolio. In this page, we will compare Markowitz Modern Portfolio Theory and Altman Z-score theory.

## Modern Portfolio Theory

Also called modern investment theory, this theory states that investors will only bear excessive rate if they are compensated sufficiently. This theory is developed by Harry Markowitz in year 1950th. Modern Portfolio Theory seeks to construct an optimal portfolio by looking at the relationship between risk and return by measuring alpha, beta and R-squared. Investors can construct an optimal portfolio by maximizing the expected return for that level of risk. The formula for Markowitz's theory is as below.

E(R_i) = R_f + beta_{i}(E(R_m) - R_f),

Where

E(R_i)~~is the expected return on the capital asset

R_f~is the risk-free rate of interest such as interest arising from government bonds

beta_{i}~~(theÂ beta) is theÂ sensitivityÂ of the expected excess asset returns to the expected excess market returns, or alsoÂ beta_{i} = frac {mathrm{Cov}(R_i,R_m)}{mathrm{Var}(R_m)},

E(R_m)~is the expected return of the market

E(R_m)-R_f~is sometimes known as theÂ market premiumÂ (the difference between the expected market rate of return and the risk-free rate of return).

E(R_i)-R_f~is also known as theÂ risk premium

According to Markowitz, there is a formulation, efficient market frontier that used to measures and calculates the portfolio in the level of ideal return and risk. Graph below shows the efficient frontier for two stocks (Google and Coca Cola) in year 2006 where the Google has high risk -return and Coca Cola has low risk-return.

http://i.investopedia.com/inv/articles/site/CT_MPT_2r.gif

The Efficient Frontier along with the portfolios would expect a higher on returns than its typical on the average for the level of risk the portfolio assumes. We would notice the Efficient Frontier line will starts lower at first and then slowly the expected risks and return will move higher. Investors having different investing profiles can find a suitable portfolio at any place within The Efficient Frontier. As the Efficient Frontier flattens, it goes higher due to the peak limit the investors can already expect.

By using the Monte Carlo simulation, we can use the percentage of standard deviation and average return, types of chosen investment and time horizon to compute and comparing the annualized return rate of different investments. The formula is Ã¢Ë†Å¡(ÃŽÂ£Wa2ÃÆ’a2 + ÃŽÂ£ÃŽÂ£WaWbCovab), where w is the size of portfolio in a security, ÃÆ’ is the standard deviation of the expected return in the security and Cov is the covariance of the expected return in the security. According to the graph below, when the number of portfolio is increasing, the percentage of average portfolio standard deviation and risk to a one-stock portfolio will also decreasing at the same time.

In Modern Portfolio Theory, the Sharpe Ratio is use to find the best proportion of the possible securities used and also a measurement for return to risk. The formula for Sharpe Ratio is:

S(x) = ( rx Â -Â Rf ) / StdDev(x)

where

x is some investment

rx is the average annual rate of return of x

Rf is the best available rate of return of a "risk-free" security (i.e. cash)

StdDev(x) is the standard deviation of rx

The Sharpe Ratio of X is the slope of the line joining cash with X

There is another calculation method to calculate the expected return for two assets portfolio, which is ERP = Ã¢Ë†â€˜wiERi

## Portfolio Strategies

According to Mr. Markowitz, there are two types of portfolio strategies which are passive portfolio strategies and active portfolio strategies. The passive portfolio strategy is a strategy that will relies more on the minimum of input in order to have better performances in some of the market index. The other one, active portfolio strategy is a strategy that uses all the market information or available information and evaluating techniques to get a better portfolio performance.

In addition, there are 3 types of portfolio, which are patient, aggressive and conservative portfolio. The patient portfolio is mostly the famous taken stock and has the most holders and buyers for longer time period. Those also reflect of the high growth companies and having the higher profit of income. The aggressive portfolio is those having higher return, higher risk and also has the most potential of future development stock. However, the aggressive portfolio would experience unexpected turnovers over time. The conservative portfolios have a stable and trustable earnings growth and history of dividend.

## Argument of Modern Portfolio Theory

When Markowitz and Sharpe first created this theory, they define "risk" and volatility. This theory concept is the greater the volatility, the higher the beta, the greater the risk. Yet, there are no proof that measuring "volatility" as "risk" is a good measurement. In (J. Michael Murphy, "Efficient Markets, Index Funds, Illusion, and Reality",Â Journal of Portfolio ManagementÂ (Fall 1977), pp. 5-20.), it states that "I realized returns appear to be higher than expected low low-risk securities and lower than expected for high-risk securities ... or that the [risk-reward] relationship was far weaker than expected." He also stated that "Other important studies have concluded that there is not necessarily anyÂ stableÂ relationship between risk and return; that there often may be virtually no relationship between return achieved and risk taken; and that high volatility unit trusts were not compensated by greater returns". In Haugen and Heins, "Risk and the Rate of Return on Financial Assets: Some Old Wine in New Bottles,"Â Journal of Financial and Quantitative AnalysisÂ (December 1975), pp 775-84) concluded that "The results of our empirical effort do not support the conventional hypothesis that risk - systematic or otherwise - generates a special reward." These papers were published in the mid to late 70s, just as EMH and MPT were really taking off and "revolutionizing" the way Wall Street invested money.

In year 2008 economy meltdown, lots of stocks were losing money. Yet, only a few assets classes performed well, namely gold, oil, gasses and Treasury bond. These assets classes have very low risk or "volatility". Moreover, calculating beta is practically very difficult.

http://www.smart401k.com/Content/Education/Smart401k/Home/advanced-retirement-investing/Modern-Portfolio-Theory.aspx

http://www.efficientfrontier.com/ef/996/basics.htm

http://www.investopedia.com/walkthrough/corporate-finance/4/return-risk/portfolios.aspx