Figure 2 illustrate that the line DEF is the efficient frontier.

For any combination along BC, we can achieve a higher return for the same risk by moving to the combination vertically above it on DEF (Lumby and Jones, 2000). As a result, the investor should select any portfolio along DEF, depending on his degree of risk aversion (Pike and Neale, 2006). However, if the portfolio combines with the risk-free asset, the CML which is line rf G becomes the new efficient frontier.Portfolio G (SDP=3.26%, ERP=19%) which 62% of fund investing in Touchstone, 37% in Gladstone Plc and 2% in ICM computer appears to be the only one portfolio of risky investment the investors will be interesting.

As Arnold (2002) said, the more negative between the returns of the different share, the better degree of risk reduction. Table 2 shows that the correlations between the three companies in portfolio G are significant smaller than others which proved that portfolio G is the most optimal portfolio.Furthermore, investor can adjust the riskiness of his own portfolio, not by changing portfolio G, but by changing the proportions of their fund between G and the risk free asset Medium risk sector The UK retail sector is undergoing a sustained period growth- the level of consumer confidence is holding up. Nevertheless, retail is the sector that is affected by many of the drivers of change in modern economy. The companies need to keep pace with the changes constantly. (www. prospects. ac.

uk). A large number of companies in this sector also make high competition.Consequently, it can be argued that the general retailer sector in UK is the medium risk sector. The six companies within the sector are: JJB Sports plc, Marks and Spencer Group PLC, Blooms of Bressingham Holdings PLC, W H Smith PLC, Beale PLC and Moss Bros Group PLC. The efficient frontier-line AB in Figure 3 suggests that investor should choose any portfolio between A and B because they are more attractive than any other portfolios for a given risk. Moreover, comparing with line CD, the line rfH describes the best possible risk-return combinations if the portfolio combines with the risk-free rate asset.Investors will be best served by choosing to invest in portfolio H (SDP =3.

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53%, ERP=64%) which 51% of fund invest in MKS-LN, 60% in BBR-LN and 8% in SMWH-LN. Investors can selecting an optimum risk-return combination by allocating appropriate proportions of a fund between H and the risk free asset, rf (Arnold, 2002). Looking at table 3, although the correlations among those three companies is not the most negative one; the good performances of risk/ return of the three companies still make portfolio H to be the best optimal portfolio in the sector.UK portfolio& comparison between the results for each of the UK sector portfolio and the combined UK portfolio The combined portfolio of UK equities is created by merging the top four companies from each of the high, medium and low risk sector in UK. The 12 companies are: Royal Bank of Scotland Group plc, Barclays, Halifax Bank of Scotland, Lloyds TSB, Marks and Spencer Group PLC, Blooms Of Bressingham Holdings PLC, W H Smith PLC, Moss Bros Group PLC, ICM Computer Group plc, Touchstone Group PLC, Gladstone PLC and Innovation Group plc (TIG).

Figure 4 Illustration of 12 assets UK portfolioFigure 5 Illustration of guardians of 3 UK sectors and UK portfolio From efficient frontier ABC in Figure 4, we can see that a highly risk-averse invest should choose the portfolio lying on AB, which gives a relatively low return with a low risk. Conversely, the less risk-averse investor should select the portfolio displaying in the curves BC, which gives a high return with a high risk. Under circumstances where risk-free lending is possible, the original efficiency frontier is significantly altered to line rf M (Arnold, 2002).

Portfolio M (SDP=1.6%, ERP=22%) which 5% of fund invested in Barclays, 10% in Halifax bank of Scotland, 26% in Marks and Spencer Group PLC, 36% in Blooms Of Bressingham Holdings PLC, 4. 5% in W H Smith Plc, 4. 3% in Moss Bros Group PLC, 5. 9% in Touchstone Group PLC and 4. 5% in Innovation Group plc comes to the most attractive portfolio to investors. Efficiency frontiers and CMLs in Figure 1, 2, 3, 4 all apply the theory that the higher the risk of a particular investment in each of the three sectors, the higher the expected return would have to be, to compensate the investor for bearing such a level of risk.On the other hand, the lower the risk of an investment, the lower the likely return.

Moreover, Comparing with the gradient of bank sector and computer sector, the general retailer sector has the highest gradient which indicates that for a given level of risk, a given proportion in risk free asset and in most optimal portfolio, the efficient combined portfolio in general retailer sector must offer the higher level of return than the efficient combined portfolios in bank sector and computer sector.According to Arnold (2002), the grater the number of securities is, the lower the risk. Furthermore, to achieve a low risk, the fundamental requirement is to construct a portfolio in which the securities have low covariance between them. Thus to invest in the shares of different firms in the same sector will not bring about as many benefits of diversification as the same sized portfolio spread between different sector. This is evidenced by the gradient of UK combined portfolio.Looking at figure 5, the gradient of UK combined portfolio M (line 1) yields the highest slope comparing with 3 UK sectors(line 2, line 3, line 4) and thus provides the largest return per unit of risk or the lowest risk per unit of return. International portfolio& comparison between the results of 12 assets UK portfolio and 12 assets international portfolio We have seen that diversifying fund into different share and different sector can make investment more efficiency.

Furthermore, further risk reduction is probably available by investing internationally (Arnold, 2002).Risk reduction effect of investment internationally is caused by the correlation coefficient between the national stock market and the further away from +1, the greater the effect. Therefore, I choose four companies from Australia, four from Hong Kong and the best four equities from 12 assets UK portfolio to create an international equities combined portfolio because the correlations among the three areas economic have a low level with each other which indicate that the economies among those three areas are not closely linked (see Table 4).The 12 companies with the international portfolio are: Barclays PLC, Marks and Spencer Group PLC, Blooms of Bressingham Holdings PLC and Touchstone Group PLC from UK, Bank of East Asia Limited, Cheung Kong Holdings Limited, Cathay Pacific Airways Limited and Henderson Land Development Company from Hong Kong, Coca-Cola Amatil Limited, Bendigo Bank Limited, Anglo Australian Resources NL and First Capital Group Limited from Australia.