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cannot be realized in practice. To resolve this problem, we choose to invest 100% into the active portfolio. Hence, the final composition of the optimal portfolio, together with its risk return profile and sharp ratio are given in table 9.

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 (RB, p.1114). 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 (RB, P.1115).

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.

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 (RB, p.1117).

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.