Finance

The modern theory of portfolio has clearly conceptualized the notion of optimal portfolio. According to this theory the investors always try to achieve the highest possible return from their investment in any asset or portfolio of assets while they want to minimize the associated risks. Actually the theory tells about the rational behavior of the investors who always intend to maximize the return from their investment with an acceptable level of risk. (Financial Concepts The Optimal Portfolio). In 1952 Harry Markowitz first uses such an approach of optimal portfolio selection. His works has showed us that the investors can invest in different portfolio of assets having varying level of risks and returns. In this case first the investors are required to decide on the risks which they are able to handle and then they should diversify their portfolio based upon their decisions. Such an idea given by Harry Markowitz has brought revolution in the theory of financial economics and modernizes the functionalities of investment practice. All these workings of Harry Markowitz have been recognized by giving him the Nobel Prize in Economics in 1990. According to the basic principle of the economics, in the faade of trade-offs all the economic decisions are taken since the scarcity of resources is always there.  According to Markowitz, the economic behavior of an investor can always be described by the trade-off between the expected return and the associated risk of investment. An investment decision can not merely be explained by the securities which an investor own, rather it is explained by the mechanism of divisions of the wealth of an investor among different securities. Here comes the portfolio selection problem of an investor. In an article published in March 1952 and through all the subsequent workings, Markowitz has established the linier programming method for developing the algorithm of critical line which can be used to identify the possible portfolio of securities that minimize risk when the level of expected return is given and that maximize return when the level of risk is given. Standard deviation of the actual returns from the expected return is used as the measurement of risk. The portfolio graph of standard deviation in relation to the expected return builds the efficient frontier which then can be used as a trade-off between the expected return and the associated risk.  This efficient frontier is a replication of all the diversified portfolios as the portfolio diversification is a tool used to reduce risk. The basic meaning of portfolio diversification is very clear. It tells that a rational investor should not invest all hisher money in a single security, rather the investors must diversify hisher money into different portfolio of securities. To select a portfolio of assets, a mean-variance analysis has been developed by Markowitz. For allocation of assets the technique of mean-variance analysis has been highly applied in the theory of investment over the last decade.  The allocation of assets is nothing but the selection of portfolio of assets where the investors invest in a collection of securities rather than in an individual security.

Portfolio analysis not only requires the formation of expected return and standard deviation of the assets but also the correlation of returns between each pair of assets of a portfolio. (Kaplan, January, 1998). Beta values of shares or beta coeffecients have been used by the investors for measuring the changes in the relative values of a share. When an investor put hisher money into a portfolio of assets, the beta values also help to assess the associated risks of investments. The beta value is calculated with the help of the historical share price of the assets and market index information. We can get an idea about the previous sensitivity of a stock relative to market by analyzing the beta values. (Share Prices - Beta Values, 2010).

Findings
The theory of portfolio investment tells about the risk aversion characteristics of the investors. The investors are required to be compensated for holding more risky securities so that they take an additional amount of risk. If risk is higher, the potential return is also higher. The compensation provided to the investors for holding risky assets is known as risk premium. The risk premium of each share is different. When an investor invests in a particular share, the expected earnings of the investor from that share may be higher than the overall market if heshe perceives that the share is more risky. Similarly the expected earnings from a share may be lower than the overall market is the investor perceives that the share is less risky in comparison with the market. Actually the relationship between the return expected from a share and the return expected from the overall market is described by the beat values. The standard index of beta is 1. This implies that in a trading day, if there is a 1 increase in the Australian Security exchange (ASX), a share price with a beta of 1.5 is expected to increase by 1.5. Similarly the performance of the share would become worse if the market index falls. Therefore, if the beta of a share is greater than 1, it implies that the share is more risky and high sensitive than the market index. If the beta of a share is less than one, it implies that the share is less risky and less sensitive than the market index. If beta is equal to 1, it implies that the share is following the market index. (WOW Fastrack Investment Group Current goal - a share portfolio worth 150,000, n.d.).

Analysis
In our analysis we have taken ten companies listed on the ASX. We have considered a time period of six years (1999 to 2004). The historical share price of these 10 companies is taken. We take weekly data for our analysis. Beside these 10 companies we have also considered another company ( Westpack Banking)as standard with which we will measure the movement share prices of these 10 companies. The starting date of the data is 4th January 1999 and the end date of the data is 14th June 2004. Since we have considered weekly data as available, to calculate return of each asset, we transformed the returns into the 52 week average value. Finally we take the 6 years average return of those 52 week average value as the asset means of those 10 shares. We have shown this by the table 1 as follows.

In our analysis we have seen that the average return of the company, namely, BHP Billion is highest among all the 10 companies whereas the return of the company, namely, Brambles Industries is lowest relative to the other 9 companies. The associated risk is highest for the company, namely, QBE Insurance group whereas it is lowest for the Fosters group. It is seen that for those companies whose average returns are relatively higher, the associated risks are also higher whereas the companies whose average returns are relatively lower, the associated risks are also lower. Obviously in our example, we have seen a little different case for the company, namely, Brambles Industries for which though the return is very low, the risk is relatively higher. In such cases, one can undoubtedly say that rational investors will never invest on such companies. This is why the mean-variance analysis is utmost important for an investors to get an clear idea which will tell himher that whether heshe should invest hisher money in a particular share. However, there is no doubt that if the return is higher, the associated risk is also higher. But the modern theory of investment tells that an investor will always try to invest hisher money for getting the maximum return by bearing minimum possible risks. The selection of optimum portfolio has enabled an investor to pursue hisher target. In our case we have constructed 10 portfolios. The first portfolio has taken only one asset, namely, Australian and New Zealand Banking group. The second portfolio consists of two companies. Here another companys share is added with the first company. Similarly for the third portfolio we have considered three company shares and thus in a subsequent way we get 10 portfolios. The 10th portfolio consists of all the 10 selected companies shares. We have calculated all the associated portfolio means, variances and betas. The calculated portfolio average return and the portfolio standard deviations are shown by the table 4 and 5.
                                   
We have seen that as the investors diversify, the associated risks falls, i.e, as the number of assets increase in a portfolio the portfolio risk falls. However, the associated returns also fall. Then what is the justification of diversification Regarding this issue we can say that diversification helps the investors to find out a way through which heshe will be guaranteed to draw a risk reluctant return when the investor is not sure where heshe should invest hisher capital. One thing should be noted here. In our case we have given equal weights to all the shares. We have calculated the average beta of all the 10 portfolios by multiplying the beta of each share by the respective portfolio weights. This is shown by the table 6 as follows.

As the sensitivity of the beat of a portfolio is different from the market, so the beta of a portfolio will help the investors against any downfall of hisher shares. In our analysis we have seen that as the number of shares increases in a portfolio, the beta of that of that portfolio falls. This is understandable. As the number of assets increase the risks of a portfolio falls, but the return also falls. This is the reason why the beta value of a portfolio falls if the number of shares increases.  

Conclusion
The investors invest in assets to earn some tangible benefits. But for achieving such return the investors also have to bear some specified amount of risks. The risk is nothing but the dispersion of actual return from the expected return over a period of investment. If the risk is low then the return is also low. On the other hand, if the risk of investment is high then the potential return is also high. (Risk and Return Analysis, n.d.). Our analysis also supports this behavior of the assets. To reduce the associated risks of investment the investors can diversify their investments into more than one asset in the form of portfolio investment. In our analysis we have also seen this behavior of the risk and return of assets. However, the selection of optimum portfolio is another issue.

Limitation and Recommendation
There are many limitations in our study. First we have taken weekly information of shares of 10 companies over a period of 6 years. We know that the share prices are very volatile in nature and overtime movement of the share prices cannot be easily estimated. Second, in our case we have considered that there is no correlation between two assets for constructing the portfolio risks. In practice this is not the case. So, further research regarding this case is important to get a clear picture over the issue.