## Introduction

The portfolio management as an investment approach requires in depth analysis of the investment market and the stock levels, represented on the stock markets. Additionally, this analysis requires the consideration of the strength, weakness, opportunities and threats of the marketing situation from the perspectives of threat of choice and debt vs. equity based capital structures of the companies. Moreover, the aspects of domestic and abroad influence of the capital investment are considered. Growth and safety of the invested resources are considered from the perspectives of the tradeoffs and the efforts, aimed at maximizing the return, taking into consideration the particular business risk.

The aim of this paper is to analyze the companies, which are included into the FTSE 250 index, and provide the clear-grounded investment report, considering the aspects and processes of the investment market. The first assignment of the report is the definition of the asset classes, required for the investment processes. Considering the fact, that once these classes are allocated, it should be stated that the effective resource management practices and allocations typically require the realizing of the existing labour and resource commitments, as well as the definition and analysis of skills, available for the resource pool. The investment risks, which are involved into the investment process, depend not only on the market processes, but also on the behaviour of the investors, as some of them are conservative and careful, while the others are aggressive. In addition, these two groups define their behaviour thus changing the marketing standards and investment flows.

## Portfolio Management Process Outline

The key requirements of the investment process report is the definition of the assessment classes for the further performing of the proper and effective resource allocation understanding of existing labour and funding resources. As it is stated by Blake (2000, p. 56):

Resources may be subject to physical constraints. For example, IT hardware may not be readily available to support technology changes associated with ideal implementation timeframe for a project. Thus, a holistic understanding of all project resources and their availability must be conjoined with the decision to make initial investment or else projects may encounter substantial risk during their lifecycle when unplanned resource constraints arise to delay achieving project objectives.

In the light of this statement, it should be emphasized that the understanding of the investment practices for the further allocation of the asset classes will depend on the matters of the expectations and the actual performance of the analyzed companies.

Originally, the key aspect of the asset analysis is the sum of monthly HPR, and the arithmetic mean of this index. These values are the following:

From the position of this analysis, the key aspects of investment should be discussed. These are investment objectives, investment constraints and asset allocation. The objectives of the investment are closely associated with increasing the invested money by offering them to a company, which shows the positive growth and income tendencies. The provided analysis provides the results of the 10 year activity of the ten companies, selected from the FTSE 250 UK Index. The arithmetic mean of the HPR index reveals the average monthly income of the companies for the 10 year period. Thus, Aegis Group, Ashmore Group and Ashtead Group are not reliable for the investments, as the regarded period is sufficient for the detailed and objective analysis of the companyâ€™s performance.

Investment constraints, which should be regarded depend on the aims of the investment, and the most common constraints of the investment market are the following:

**Liquidity needs.**These rates define the process of converting the investments into cash, and providing the favourable price of the market value favourable**Time Horizon.**The time range when the investors will need the access to funds**Tax concerns.**The taxation rules and principles- Legal factors and financial regulation
- Unique requirements of the spheres and industries

The constraints of the analyzed companies are closely associated with the liquidity needs, and requirements of the accurate definition of the time horizon, as the spheres, which the companies mainly represent require the precise time analysis of the incomes and returns.

Asset Allocation principle is associated with the idea that various periods require various assets for the best performance. Considering the particular investment risks, it should be emphasized that the precise allocation plan will be required for the better returns and more effective financial performance of the companies. From the perspective of the offered analysis, the asset allocation will be based on the values of the average monthly return indexes and the variance rates of the companies. In accordance with Cooper, Edgett and Kleinschmidt (2005, p. 129), the following statement should be emphasized:

A fundamental justification for asset allocation is the notion that different asset classes offer returns that are not perfectly correlated, hence diversification reduces the overall risk in terms of the variability of returns for a given level of expected return. Therefore having a mixture of asset classes is more likely to meet the investor’s wishes in terms of amount of risk and possible returns.

## Thus, the allocation

The analysis of the average mean will be required for the definition of the general tendencies of the return rates, and the performance of the companies on the market. Comparing the monthly HPR rates, there is strong necessity to consider the values of the discrete series of returns and variability of the average mean. Thus, these values will be used for revealing the required meaning of the return rates for the further analysis and increasing variability in the series as the price level increases. From the perspective of the investment principles stated by Bodie, Kane and Marcus (2001), it should be emphasized that the original value of the investment assessment, and the consideration of the possible risks is closely associated with the matters of the tension between the analyzed assets. Moreover, the following statement should be emphasized:

While proposals for financial and corporate governance reform strive to eliminate all risk, we need to ask whether artificial limits on all “risk” may actually create the greatest risk of all. Consider for a moment a world in which the tolerance for risk is zero, or at least one in which perceived risk is heavily penalized. In a risk-intolerant environment, markets would require enormous returns on equity investments and significantly higher interest rates on debt for all but the safest “blue chip” borrowers. (Bodie, Kane and Marcus, 2001, p. 341)

Thus, it should be stated that the investment analysis strongly depends on the business environment, associated with the funding practices. The Indexes of the analyzed companies represent the stable business environment, and considering the analyzed numbers, it should be stated that the actual principles of the investment analysis is associated with the development of projects and potential growth of the companies.

## Assuming Investment in Stocks and Treasury Bills

The portfolio diversification is generally presupposed by the particular processes and tendencies on the market. The fact is that, the strategies, required for the proper diversification are defined by the accurate measures of the monthly returns of the companies, and by calculating the deviation rate of the returns.

In accordance with Cooper, Edgett and Kleinschmidt (2001, p. 561), the diversification strategies, that may be applied for this case are the following:

- The portfolio may be spread among the investment vehicles applied on the market, such as Management Futures Account, mutual funds, bonds, stocks and cash. This strategy is applicable if all the vehicles are available and provide the positive forecast. Considering the analysis of monthly returns, the companies with negative numbers will require Management Futures Accounting, while the other companies will be more effectively invested using the stock tool.
- Vary the risk securities. Originally, the portfolio in general may be diversified into different mutual funds and investment strategies, thus, the growth funds of the analyzed companies involve the varied risks, and,. it should be stated that the actual value of these variation is explained by the necessity to analyze and consider the losses in one area are offset by other areas (Cooper, Edgett and Kleinschmidt, 2003, p. 125)
- The securities should be inevitably varied in accordance with the industrial principle, as the impact of the related industries should be minimized. The analyzed companiesâ€™ portfolio should be diversified by investing both industrial and consultancy (management) companies, which are not related
- Verification of investment managers will be required in accordance with the strategies, used by managers, and in accordance with the profiles and successes of the companies.

As it is stated by CÃ¡Ã±ez and Garfias (2006, p. 78):

Diversification reduces the risk of a portfolio, and consequently it can reduce the returns. However, since diversification reduces the risk of an entire portfolio being diminished by a single investment’s loss, it is referred to as “the only free lunch in finance.” Statistical analysis shows that there may be some validity to this claim.

## Treynor / Black Method

The theoretical concept of the Treynor-Black method presupposes the consideration of the scenario, when the mean-variance criterion is used, and applied by investors. (Hutchinson, 2002) This criterion is also regarded as the Sharpe ratio. The passive strategy is aimed at defining the specified market index, then the security analysis covers the restricted amount of securities. The securities, which are not included into consideration are regarded as effectively priced by default. On the other hand, the covered securities can not be regarded as efficient. As Rose (2001, p. 67) emphasized in the research, this analysis model is not effective, as even if the companies and the market share residuals are associated with the securities, it is unknown, whether the generalized analysis model will be profitable.

The calculation formula of the Risk-Adjustment performance is the following:

Where:

- Rp = return of portfolio
- R
_{f}= risk free rate - R
_{m}= Return of market portfolio - Ïƒ
_{m}= Standard deviation of the Return of market portfolio - Ïƒ
_{p}= Standard deviation of the Return of portfolio

The x axis of the analysis shows the standard deviation rates, and the y axis is for the return rates. Pm point represents the market portfolio with teh actual rates of deviation, represented by Ïƒ_{M} and the total return â€“ r_{M}. The riskless deviation and marketing investment, represented by P_{0} point on the graph, which stands for the zero deviation in the performance. Considering the fact, that this statement represents also minimal return deviation, the effectiveness of the risk free analysis method, offered by Treynor Black can not be regarded as the effective tool.

From the perspective of this analysis, the mispriced stocks of the FTSE 250 Index are Bodycote, Brewin Dolphin and British Assets, as the analysis of the total index of these companies originates the negative standard deviation, which means the high risk assets, thus, the average price of the market shares should be changed in accordance with the risk rates.

## Risk Return Profile Analysis

Risk return profile may be calculated in accordance with the following formula:

Where:

- M = (k
_{m }– k_{f}) - K = (k
_{i }– k_{f}) - n = number of years (months)
- Â = average of M
- Â = average of k
- k
_{m}= expected market return - k
_{f }= risk-free rate (treasury bond)

Thus, the numbers of the risk analysis are the following:

In accordance with the risk portfolio analysis the beta index is low, and the investment may be performed from the perspectives of the effective diversification of the risks. In general, the represented index is risk low. In accordance with Larr (2003, p. 55). The following statement should be emphasized:

Rather than lauding this as evidence of a healthy market phenomenon, we should consider whether a truly healthy financial sector should depend on such lightly capitalized, speculative vehicles for “risk management.” On the other hand, funds are a source of risk and even recklessness that threaten our financial system. These vehicles are unsuitable for the vast majority of investors and justly deserve additional oversight and regulation by financial authorities.

From the perspective of this consideration, the risk return profiles of the stocks require the analysis of the derived rates, associated with the monthly return analysis, and the analysis of the joint returns, represented by the index in general.

## Optimal and Complete Portfolios

### Markowitz methodology

Total Stock of the selected companies is 10,98%. The average means of the analyzed returns are represented in the following table.

The standard deviation values vary depending on the factors, considered in the analysis, nevertheless, independently on the rates, the objectives and constraints, defined earlier presuppose the existence of the risks in the industry. In accordance with the Markowitz methodology, which is often found unrealistically extreme, the allocations, required for the effective investments should be standardised from the perspective of risk premium changes from positive to negative. Additionally, the massive reallocation of the resources will be needed from the perspective of the hypothesis of the transaction costs adding.

### Naive Diversification

Consideration of possible risks from the perspective of naive diversification should be performed in accordance with the analysis of the general tendencies on the market. The fact is that, the additional funds of the offered stocks require the diversification of the manager performance risk. In accordance with El-Hassan and Kofman (2003, p. 45):

The benefits of such diversification are small, while the fact of diversification are generally revealed in the results of risk portfolio analysis. Anyway only two funds are required for the beginning. Thus, a large-cap actively managed fund and an intermediate-term government bond fund. Then we add another actively managed large-cap fund. In this case, an investor who selected a 50-percent equity exposure when offered just one equity fund increases his equity exposure to 54 percent with two funds.

The naive diversification investment preferred strategy is calculated in accordance with the following formula:

Where:

- Ïƒ
^{2}_{p}= variance of portfolio returns - n = number of stocks in portfolio
- Ïƒ
^{2}_{i}= average variance of returns on stock*i* - Ïƒ
_{ij}= average covariance between returns in stocks*i*and*j*

In accordance with this formula, the covariance returns, the risks of the investment strategies should provide the allocation on the investment funds proportionally to the stocks of the funds. Additionally, the plan of the particularly troubling financial decisions, required for the effective investment should be regarded from diversifying the sub-optimal stocks, which are featured with minimal risks and with the low to medium standard deviation.

The following graph represents the 10 share portfolio comparison with the average returns in the industry (calculated on the basis of the FTSE 250 index in average).

The selection of this portfolio for the analysis may be explained by the simplicity of the output data, and the reliability of the calculation methods. The fact is that, these analysis tools offer the objective recommendation data, considering the aspects of the returns and the deviation of the numbers, achieved from the perspectives of averages and industry risk / return analyses. The analysis from the perspective of Treynor / Black Methodology (optimal portfolio), provides the actual analysis of the risks and values of the stock investment. Nevertheless, the aspects of the investment portfolio should be analyzed from the complete portfolio. Beta analysis of the industry reveals the effective analysis tool, thus, these numbers may be regarded as the required aspects for the further analysis and the estimation from the positions of active and passive investor perspectives.

The active perspective presupposes the accurate and sometimes aggressive investment, thus, the beta index may be regarded as the effective tool for defining the measures of the stock and investment. As Campbell and Viceira (2002, p. 182) stated in their research:

The objective is beating the market, as measured by a benchmark or index (or the returns of peer funds). An investment manager or team of investment professionals hand-picks investments that meet the fundâ€™s objective, such as long-term growth or capital preservation, and that support their fundâ€™s specific charter or mandate (for example, the degree to which the fund will be exposed to a given market sector or industry or the amount of assets that will be held in cash at any given time).

On the other hand, the passively managed funds are less costly and risky, and the fees, involved in their management are lower in comparison with active funds. Additionally, they are fully invested, as the revealed index represents the average values of the active and passive management.

## Performance of the Portfolios for the Next Year

The actual performance is offered in the following table.

These are the average indexes of the entire industry (FTSE 250).

The analysis of this performance is the following:

Beta value is 0,15.

Thus, the analysis of the further performance industry revealed the lower risks and the more favourable conditions for the further investment.

## Reference List

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Bodie, Z., Kane, A. and Marcus, A.J. (2001), *Investment*, fifth Edition, New York McGraw-Hill.

Campbell, J. Y., & Viceira, L. M. 2002. *Strategic Asset Allocation: Portfolio Choice for Long-Term Investors*. New York: Oxford University Press

Cooper, R. G., Edgett, S. J., & Kleinschmidt, E. J. 2005. Portfolio Management in New Product Development: Lessons from the Leaders–i. *Research Technology Management, 40*(5), 16

Cooper, R. G., Edgett, S. J., & Kleinschmidt, E. J. 2003. *Portfolio Management for New Products*. Cambridge, MA: Perseus Publishing.

Cooper, R. G., Edgett, S. J., & Kleinschmidt, E. J. 2001. New Problems, New Solutions: Making Portfolio Management More Effective. *Research Technology Management, 43*(2), 18.

CÃ¡Ã±ez, L., & Garfias, M. 2006. Portfolio Management at the Mexican Petroleum Institute. *Research Technology Management, 49*(4), 46

El-Hassan, N., & Kofman, P. 2003. Tracking Error and Active Portfolio Management. *Australian Journal of Management, 28*(2), 183

Hutchinson, H. 2002. *Portfolio Indexing: Theory and Practice*. New York: John Wiley & Sons.

Larr, P. 2003. Make Portfolio Management Four-Dimensional. *ABA Banking Journal, 84*(7), 55

Rose, J. T. 2001. Portfolio Management in Academia. *Baylor Business Review*, *19*, 6