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Introduction

This report is aimed to draw a vivid picture regarding the basic needs and expertise that a qualified portfolio manager has to possess in the process of portfolio management.

Preparation before the portfolio construction

As a qualified portfolio manager, before processing any concrete portfolio construction and modification, it is rather essential to have a comprehensive understanding concerning the portfolio management process. Theoretically, investment process can be divided into four stages: specifying objectives, identifying constraints, formulating policies and later monitoring and updating the portfolio as needed (Bodie et al. 2005).

First and foremost, portfolio objectives focus on the trade-off between return requirements and risk tolerance of investors. In other words, investment managers must figure out clients’ willingness as well as ability to accept risk in the pursuit of higher rates of return. (Bodie et al. 2005).

Besides, both individual and institutional investors would limit their investments within the boundaries arising from their specific restrictions. Generally, main constraints for investors can be summarized into five common categories. That is, liquidity needs, time horizon, tax considerations, regulations and unique needs and preference (Bodie et al. 2005).

Having considered various objectives and constraints for different investors, the third step of portfolio management — asset allocation — is able to advance in an effort to satisfy investors’ needs in compliance with their specific restrictions. In detail, asset allocation refers to the procedure of making decision regarding the proportion of wealth invested in each major asset categories. (Bodie et al. 2005).

In short, each stage in the process of portfolio management is not in isolation. After indentifying clients’ risk and return objectives for investment, a qualified portfolio manager has to take serious consideration regarding the constraints that the clients are facing. Then tailored asset allocation is ready to be made in accordance with those objectives and constraints obtained previously, ensuring the investment policy relevant to the investor’s specific situation and desires.

In practice, as far as I am concerned, as a young investor, capital appreciation will be my priority for investing. In terms of risk tolerance, according to the questionnaire offered by Dow Jones & Company, I am a moderate investor with a risk aversion of 6 (Bodie et al. 2005).Thus, my investment objectives would be to bear moderate risk in the pursuit of high return.

As to investment constrains, I have little needs for liquidity since the possibility of unemployment is rather low for me. Other substantial expenses are not foreseeable at present. Besides, given the fact that I am a young investor, long investment horizon generally enable me to tolerate greater risk while requiring less liquidity. Tax concerns and regulatory factors will not be an issue for me in the near future.

Therefore, considering the objectives and constraints presented above, I would be better off if investing in risky assets in pursuit of higher returns. With a risk aversion of 6, I would invest my wealth in stocks while allocating remainders to treasury bills.

Data and methodology

This following report will introduce essential concepts and methodologies in use, together with relative data applied, as groundwork of the subsequent portfolio construction and evaluation.

Portfolio diversification

The concept of diversification should be kept in mind at all time by a portfolio manager since it is the most fundamental notion that can facilitate an efficient portfolio.

In theory, stocks in a portfolio are facing two broad sources of uncertainty. One arises from macroecomomic factors which will exert influences on all stocks. The other one concentrates on firm-specific situations, which would only affect a particular firm or industry without noticeably impacting other companies (Bodie et al. 2005).

A diversification strategy attempts to reduce the portfolio deviation by adding more stocks into the portfolio until all firm-specific risk (unsystematic risk) is eliminated and only risks that are attributable to marketwide risk sources (systematic risk)remains.

Treynor/Black (TB) method

Treynor and Black offer an optimizing model that strikes a balance between diversification motives and aggressive exploitation of security mispricing for active portfolio managers (Bodie et al. 2005).

Theoretically, the model has several underlying assumptions. First of all, only a limited number of stocks can be analyzed. Then, Mispricing is the guidance of the composition of the active portfolio and the market index portfolio is treated as the passive portfolio. Besides, macro forecasting provides information concerning expected return and variance of the passive portfolio. Lastly, a combination of the active and passive portfolio is the ultimate optimal risky portfolio (Bodie et al. 2005).

To begin with, the active portfolio is constructed by running a series regression and identifying securities with significant nonzero alpha values. The weights of each mispriced securities can be obtained by maximizing the sharp ratio of the overall active portfolio. As mentioned previously, the passive portfolio is assumed to be the market index portfolio with its forecasting being made already.

The essence of Treynor/ Black method lies in the optimization process with the active and passive portfolios. By definition, the market index (passive portfolio) is the tangency point of the capital market line (CML) with the efficient frontier representing the universe of all securities assumed to be fairly priced. However, in practice, the market-index portfolio has been proved to be inefficient as a result of superior analysis identifying mispricing. Therefore, the active portfolio, with its positive alpha value, must lie above the CML. So far, the optimization problem has become a simple application of the construction of optimal risky portfolio from two component assets: active portfolio constructed at first and the passive portfolio represented by market index portfolio.

Considering that the active portfolio is not perfectly correlated with market index portfolio, the efficient frontier consisting of these two components would be a curve as well, similarly to but above the one from the universe of all securities. The optimal capital allocation line (CAL), passing through the risk-free rate and tangent to the new efficient frontier can be obtained by now. The optimal risky portfolio, which combines the active and passive portfolio, locates at the tangency point of the CAL to the efficient frontier. Hence, TB method has successfully exploited mispriced opportunities, while achieving optimal diversification.

Data analysis

To achieve diversification, I have selected 10 stocks from the constituents of the FTSE 250 UK index from 1999 to 2008 and collected monthly returns for this 10-year period. Furthermore, to conduct TB methodology, 3 mispriced stocks from the FTSE 250 are identified. Table 1 reveals the t stat and p-value for the alpha (constant) of each stock, indicating mispricing. Due to short-selling restriction, it can be seen that these stocks are all underpriced, represented by positive alphas.

With the purpose of obtaining an overall understanding of those stocks we are about to use in the portfolio construction, I have implemented an exploratory data analysis, including descriptive statistics, autocorrelation and correlation analysis.

Descriptive statistics

From table 2, it can be seen that all the 13 stocks have a relatively high average return in this 10-year period, accompanied by low or median risks, with most figures for the standard deviation below 0.1.

Autocorrelation

Correlation analysis

The table for the overall correlation coefficients can be found in Appendix 2. It can be seen that only ULTRA ELECTRONICS HDG and JARDINE LLOYD THOMPSON are negatively correlated.

Portfolio construction and comparison

In the following report, I am going to construct optimal and complete portfolios based on different methodologies using data in section 3, while comparing them from several aspects.

Markowitz VS. Market value-weighted strategy

The Markowitz portfolio

To construct optimal portfolios based on Markowitz methodology, the first stage is to construct efficient frontier from the set of risky assets by minimizing the portfolio variance for any given returns. The universe of stocks for our portfolio comprises 10 stocks selected previously for diversification. Due to the restriction of short selling, the lowest and highest returns of the efficient frontier depend on the extreme historical returns of the 10 stocks. The efficient frontier obtained from the 10 stocks is shown in the graph 1.

Graph 1

Then, by maximizing the sharp ratio of the portfolio, the optimal portfolio can be achieved. It is noteworthy that because risk free rate was not constant over the analysing period, the sample average is taken for measurement (0.0038). The weights for each stock and risk return profile of the optimal portfolio are shown in table 4 and 5, respectively. Graph 2 presents the optimal risky portfolio on the efficient frontier.

Graph 2

The complete portfolio relies on the risk aversion of the investor. In my case, A is designated as 6. Thus, to maximise my utility, I can choose the best allocation between the risky and risk-free assets based on the equation:

It is advisable for me to allocate 15.79% of my total wealth to risk-free asset and the remaining to optimal risky portfolio. In all, the weights for the complete portfolio are presented in table 6, together with the risk return profile and sharp ratio for the ultimate complete portfolio. Graph 3 shows the best allocation on the CAL.

Graph 3

The market value-weighted portfolio (naÏve diversification)

The market value-weighted strategy is a typical passive strategy in practice. For the 10 stocks selected previously, I employ the market value of each stock, divided by the total market value of all stocks as the weight of each security. Given the fact that the weights will change every year, I apply the market value of last year to rebalance funds at the beginning of each year. Table 7 reveals the risk return profile and sharp ratio of the optimal portfolio based on the market value-weighted strategy for the 10-year period.

With regard to the complete portfolio, considering the risk aversion (A=6), I would be better off if invest 59.76% of my total wealth into risk-free asset and 40.24% into risky assets.

Comparison between diversification achieved by naÏve strategy and Markowitz methodology.

Given the portfolios constructed above based on the same database, it is worthwhile to compare the two methodologies in this report while discussing the benefits and costs of each strategy.

Firstly, the implication of Markowitz methodology is confronted with unavoidable complication in terms of data preparing and processing. Specifically, the procedure calls for a great number of estimates as data input, together with mathematical optimization programs to facilitate the performance of necessary calculations, which requires vast computer capacity. By contrast, naÏve diversification eases the computational burden relative to Markowitz methodology (Bodie et al. 2005).Besides, the naÏve diversification is capable of obtaining broad diversification with comparatively low management fees, since the assessment for stock prospects by analysts is no longer in necessity (Bodie et al. 2005). Additionally, high transaction costs incurred from Markowitz diversification may be reduced to a large extent by naÏve diversification (Reilly and Brown, 2003).

Nevertheless, diversification achieved by naÏve strategy does not work perfectly well without costs, and that is why Markowitz methodology is still in popularity in practice. In detail, with the purpose of minimizing tracking error relative to the index that naÏve diversification attempts to replicate, extra time and expense would be necessary to create and maintain the portfolio (Reilly and Brown, 2003). Hence, the essential of managing a portfolio based on naÏve diversification lies in the trade-off between the costs (low tracking error) and benefits (ease of monitoring, lower trading commissions) (Reilly and Brown, 2003).

Treynor/Black VS. Markowitz methodology

Considering that both TB and Markowitz methodologies are wildly utilized in practice, it is valuable for this report to construct another portfolio based on TB method, compare the two techniques from both active and passive investors, and evaluate them using appropriate techniques.

Treynor/Black portfolio

Applying the three mispriced stocks identified previously, the optimal portfolio based on TB methodology can be constructed. Specifically, sharp ratio for the active portfolio consisting of the 3 mispriced stocks is 0.4, whereas the one for market portfolio is only 0.014, suggesting dramatic increase in portfolio performance through the exploitation of mispricing, in other words, market inefficiency.

Weight for each stock in the active portfolio is presented in table 8. Subsequently, portion of funds invested in the active portfolio (W*) can be obtained (336.85%). As the total weight for the sum of active and passive portfolio subject to 1, the percentage for passive portfolio is equivalent to -236.85%.

The procedure for constructing the complete portfolio is identical regardless of methodologies applied for the optimal portfolio. Percentage of funds invested in the optimal portfolio from TB methodology should be 72.14%, whereas the remainder (27.86%) would be allocated to the risk free asset. Table 10 presents the allocation for the complete portfolio, along with relative performance indicators.

Comparison from active and passive investor perspective

The difference between the two methodologies lies in the construction of optimal portfolios. Theoretically, Markowitz portfolio selection model focuses on diversifying risky assets by means of minimising variance for any given returns. With respect to the choice of alternative risky assets for inclusion, there is no specific processing method. Hence, both active and passive investors are capable of implementing Markowitz method to find their complete portfolio, since no attitudes towards the Efficient Market Hypothesis are involved in the model.

By contrast, TB methodology attempts to identify and include mispriced stocks when constructing optimal portfolios. Thus, only active investors, who are opponents of the EMH and believe stock prices in the market are not at fair levels, would utilize this model. Passive investors believing in EMH would follow strategies such as index funds as their optimal risky portfolio.

Portfolio evaluation

Portfolio evaluation is conducted in the following report, with the purpose of understanding the relative advantage of the portfolios constructed using both Markowitz and TB methodologies.

Sharp ratio measurement

Sharp ratio measures the risk premium return earned per unit of total risk. It evaluates the portfolio on the basis of both rate of return performance and diversification (Reilly and Brown, 2003). Considering that sharp performance is an appropriate measurement when the investment represents the entire wealth of investor’s funds, I would imply this method to evaluate our portfolios from both Markowitz and TB methodology. This measure is not without drawbacks, though. It merely presents relative but not absolute rankings of portfolio performance, and whether the difference between two portfolios regarding the value of sharp ratio is statistically significant cannot be concluded with certainty (Reilly and Brown, 2003).

Table 11 shows the sharp ratio of the complete portfolio from both methodologies. It can be clearly seen that Markowitz portfolio has superior performance compared with TB. However, as indicated previously, whether the difference between the two figures is statistically significant cannot be judged.

Jensen measure

The Jensen measure is based on CAPM. The intercept value indicates whether the portfolio has superior or inferior performance. This measure has several advantages relative to sharp ratio. Firstly, it is easier to interpret with regard to the comparison of actual and expected performance. Secondly, it enables statistical significance statements to be made. And it is possible to be extended to account for various factors that may proxy for risk (Reilly and Brown, 2003).

Table 12 shows the regression results for the complete portfolio based on Markowitz and TB methodologies. It can be seen that all the Jensen’s alpha are statistically significant and above zero, indicating that the portfolio performed better than expected. In the comparison of the two methodologies, the complete portfolio of Markowitz is slightly better that its counterpart, consistent with the result of sharp ratio.

Evaluation of performance in 2009

It is significative for this report to evaluate the performance of portfolios for the subsequent year — 2009—so as to see the validity and application of those methodologies.

After allocating funds according to the weights obtained above, we will have 3 portfolios at the beginning of the year 2009. Until the end of the year, the 3 complete portfolios generated from value-weighted, Markowitz and TB strategies have been witnessed different performances. The risk return profile, sharp ratio and Jensen’s alpha measurement data for the 3 portfolios in 2009 are presented in table 13.

In general, all three portfolios have positive returns in 2009. The Markowitz portfolio has the lowest sharp ratio whereas TB and Value-weighted portfolios are quite similar to each other. This result contradicts to the conclusion obtained in the last section using historical data as the measurement of portfolio performance.

From the perspective of Jensen measure, all three alphas are statistically insignificant, indicating that no superior returns are realized in the portfolios. Hence, although the evaluation based on historical data in the last section has detected superior performance for all three portfolios, when applying the weights to the following year, the portfolios will perform just as expected.

The contradiction of conclusions regarding the performance of different portfolios can be attributed to the use of historical data as approximation of market expectancy. Specifically, applying historical data as estimates of future may exert risk to the portfolios. To illustrate, returns obtained from historical data may be upward biased by the survivorship bias. Moreover, changing nature of the environment prevent estimates from historical data fully reflecting market expectancy towards future. Conditioning information also cannot be captured by historical returns, leading to imprecise estimation.

Conclusion

So far, the process and expertise of portfolio management has been presented in the report, accompanied by an in-depth analysis regarding different portfolio construction methodologies. I believe that a portfolio manager, who is capable of understanding the portfolio management process, taking advantage of all the relative techniques while keeping in mind all the potential risks, is prepared to succeed in his career.

References:

1. Bodie, Z. Kane, A. and Marcus, A. J. (2005) Investments, 6th edn, Singapore: Mc Graw Hill
2. Reilly, F.K. and Brown, K.C. (2003) Investment Analysis and Portfolio Management. 7th edn. Ohio: Thomson South-Western