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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, Kane and Marcus, 2004,p.317).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, Kane and Marcus, 2004,p.378). Additionally, high transaction costs incurred from Markowitz diversification may be reduced to a large extent by “naÏve” diversification (RB. P.657).

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 (RB, p. 657). 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) (RB, p. 657).

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.

The input and computation for constructing the active portfolio are shown in the Appendix. 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%.

积极的投资组合-ACTIVE PORTFOLIO

However, due to the restriction for short selling, weights achieved above