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Portfolio Optimization Portfolio Selection Problem Description Initial Data Computational Results Divided Portfolio Problem Description Initial Data Computational Results Asset Allocation   Conclusions

Divided Portfolio/Computational Results For our example we selected the subset of divided portfolios of 14 funds ranged in performance from 8 to 12 % and corresponding standard deviation as low as from 2.43 to 3.06 %. Selected portfolios are optimal in terms of performance (annual return) and risk (average standard deviation). They can be selected in any range of minimum and maximum performance and include any number of funds (FIGURE 2.2).   TABLE 2.7: The subset of optimal divided portfolios (14 funds) return % std dev % A85/C56/C66/C71/C72/I06/I14/L41/L49/L50/M06/N56/N60/N67/ 8.04 2.43 A85/C56/C66/C71/C72/I06/I14/L41/L49/L50/M06/N56/N60/N93/ 8.09 2.44 A85/C56/C66/C71/C72/I06/I14/L41/L49/L50/M06/N60/N67/N93/ 8.09 2.44 A85/C56/C66/C71/C72/I06/I14/L41/L49/L50/M06/N56/N67/N93/ 8.09 2.44 A85/C56/C66/C71/C72/I06/I14/L49/L50/L67/M06/N56/N67/N93/ 8.14 2.45 A85/C56/C66/C71/C72/I06/I14/L49/L50/L67/M06/N41/N56/N93/ 8.16 2.46 A85/C56/C66/C71/C72/I06/I14/L49/L50/L67/M06/N41/N67/N93/ 8.16 2.46 A85/C56/C66/C71/C72/I06/I14/L19/L41/L50/M06/N56/N67/N93/ 8.27 2.47 A85/C56/C66/C71/C72/I06/I14/L19/L49/L50/M06/N56/N60/N67/ 8.31 2.48 A85/C56/C66/C71/C72/I06/I14/L19/L49/L50/M06/N56/N67/N93/ 8.37 2.49 A85/C56/C66/C71/C72/I06/I14/L19/L49/L50/M06/N41/N60/N93/ 8.39 2.50 A85/C56/C66/C71/C72/I06/I14/L19/L49/L50/M06/N41/N67/N93/ 8.39 2.50 A85/C56/C66/C71/C72/I06/I14/L19/L49/L50/M06/N41/N56/N93/ 8.39 2.50 C45/C56/C66/C71/C72/I06/I24/L41/L49/L50/L67/N60/N67/N93/ 8.59 2.51 C45/C56/C66/C71/C72/I06/I24/L41/L49/L50/L67/N56/N60/N93/ 8.59 2.51 C45/C56/C66/C71/C72/I06/I24/L41/L49/L50/L67/N56/N67/N93/ 8.59 2.51 C45/C56/C66/C71/C72/I06/I24/L41/L49/L50/L67/N41/N60/N93/ 8.61 2.52 C45/C56/C66/C71/C72/I06/I24/L41/L49/L50/L67/N41/N67/N93/ 8.61 2.52 C45/C56/C66/C71/C72/I06/I24/L41/L49/L50/L67/N41/N56/N93/ 8.61 2.52 A85/C45/C56/C66/C72/I06/I24/L41/L49/L50/L67/N60/N72/N93/ 9.30 2.53 A85/C45/C56/C66/C72/I06/I24/L41/L49/L50/L67/N60/N87/N93/ 9.30 2.53 A85/C56/C66/C71/C72/I06/I24/L41/L49/L50/L67/N56/N67/N93/ 9.55 2.54 A85/C45/C56/C66/C72/I06/I24/L41/L49/L50/M06/N56/N60/N67/ 9.82 2.55 A85/C56/C66/C71/C72/I06/I24/L41/L49/L50/M06/N56/N67/N93/ 10.11 2.56 A85/C56/C66/C71/C72/I06/I24/L41/L49/L50/M06/N41/N56/N93/ 10.13 2.57 A85/C56/C66/C71/C72/I06/I24/L41/L49/L50/M06/N41/N67/N93/ 10.13 2.57 A85/C56/C66/C71/C72/I06/I24/L49/L50/L67/M06/N41/N56/N93/ 10.17 2.58 A85/C56/C66/C71/C72/I06/I24/L49/L50/L67/M06/N41/N67/N93/ 10.17 2.58 A85/C56/C66/C71/C72/I06/I24/L19/L41/L50/M06/N56/N60/N67/ 10.23 2.59 A85/C56/C66/C71/C72/I06/I24/L19/L49/L50/M06/N56/N60/N67/ 10.33 2.60 A85/C56/C66/C71/C72/I06/I24/L19/L49/L50/M06/N56/N67/N93/ 10.39 2.61 A85/C56/C66/C71/C72/I06/I24/L19/L49/L50/M06/N41/N67/N93/ 10.41 2.62 A85/C56/C66/C71/C72/I06/I24/L19/L49/L50/M06/N41/N56/N93/ 10.41 2.62 A85/C56/C66/C71/C72/I06/I24/L19/L47/L49/M06/N60/N67/N93/ 10.46 2.63 A85/C56/C66/C71/C72/I06/I24/L19/L47/L49/M06/N56/N60/N93/ 10.46 2.63 A85/C56/C66/C71/C72/I06/I24/L19/L47/L49/M06/N56/N67/N93/ 10.46 2.63 A14/A85/C66/C71/C72/I06/I24/L19/L41/L49/M06/N60/N87/N93/ 10.51 2.64 A14/A85/C66/C71/C72/I06/I24/L19/L41/L49/M06/N60/N72/N93/ 10.51 2.64 A14/A85/C66/C71/C72/I06/I24/L19/L49/L50/M06/N56/N67/N93/ 10.60 2.65 A14/A85/C66/C71/C72/I06/I24/L19/L49/L50/M06/N41/N67/N93/ 10.62 2.66 A14/A85/C66/C71/C72/I06/I24/L19/L49/L50/M06/N41/N56/N93/ 10.62 2.66 A85/C56/C66/C71/C72/I14/I24/L41/L49/L50/M06/N56/N60/N93/ 10.71 2.67 A85/C56/C66/C71/C72/I14/I24/L41/L49/L50/M06/N60/N67/N93/ 10.71 2.67 A85/C56/C66/C71/C72/I14/I24/L41/L49/L50/M06/N41/N56/N93/ 10.74 2.68 A85/C56/C66/C71/C72/I14/I24/L49/L50/L67/M06/N56/N67/N93/ 10.76 2.69 A85/C56/C66/C71/C72/I14/I24/L19/L41/L50/M06/N56/N60/N67/ 10.84 2.70 A85/C56/C66/C71/C72/I14/I24/L19/L49/L50/M06/N56/N60/N67/ 10.94 2.71 A85/C56/C66/C71/C72/I14/I24/L19/L49/L50/M06/N60/N67/N93/ 10.99 2.72 A85/C56/C66/C71/C72/I14/I24/L19/L49/L50/M06/N56/N60/N93/ 10.99 2.72 A85/C56/C66/C71/C72/I14/I24/L19/L49/L50/M06/N56/N67/N93/ 10.99 2.72 A85/C56/C66/C71/C72/I14/I24/L19/L49/L50/M06/N41/N60/N93/ 11.01 2.73 A85/C56/C66/C71/C72/I14/I24/L19/L49/L50/M06/N41/N67/N93/ 11.01 2.73 A85/C56/C66/C71/C72/I14/I24/L19/L49/L50/M06/N41/N56/N93/ 11.01 2.73 A85/C56/C66/C71/C72/I14/I24/L19/L47/L49/M06/N56/N67/N93/ 11.07 2.74 A14/A85/C66/C71/C72/I14/I24/L19/L41/L49/M06/N56/N67/N93/ 11.14 2.75 A14/A85/C66/C71/C72/I14/I24/L19/L49/L50/M06/N56/N67/N93/ 11.21 2.76 A14/A85/C66/C71/C72/I14/I24/L19/L49/L50/M06/N41/N67/N93/ 11.23 2.77 A14/A85/C66/C71/C72/I14/I24/L19/L49/L50/M06/N41/N56/N93/ 11.23 2.77 A14/A85/C66/C71/C72/I14/I24/L19/L47/L50/M06/N56/N67/N93/ 11.26 2.78 A14/A85/C66/C71/C72/I14/I24/L19/L47/L49/M06/N60/N72/N93/ 11.26 2.78 A14/A85/C66/C71/C72/I14/I24/L19/L47/L49/M06/N60/N87/N93/ 11.26 2.78 A14/A85/C66/C71/C72/I14/I24/L19/L47/L49/M06/N41/N67/N93/ 11.31 2.79 A14/A85/C66/C71/C72/I14/I24/L19/L47/L49/M06/N41/N56/N93/ 11.31 2.79 A85/C56/C66/C71/C72/I14/I24/L19/L49/M06/M14/N56/N67/N93/ 11.37 2.81 A14/A85/C66/C71/C72/I14/I24/L18/L19/L50/M06/N56/N67/N93/ 11.43 2.82 A14/A85/C66/C71/C72/I14/I24/L18/L19/L49/M06/N56/N67/N93/ 11.46 2.83 A14/A85/C66/C71/C72/I14/I24/L19/L50/M06/M14/N56/N60/N67/ 11.50 2.84 A14/A85/C66/C71/C72/I14/I24/L19/L49/M06/M14/N56/N67/N93/ 11.59 2.85 A14/A85/C66/C71/C72/I14/I24/L19/L49/M06/M14/N41/N56/N93/ 11.61 2.86 A14/A85/C66/C71/C72/I14/I24/L19/L49/M06/M14/N41/N67/N93/ 11.61 2.86 A14/A85/C66/C71/C72/I14/I24/L19/L47/M06/M14/N56/N67/N93/ 11.64 2.87 A14/A85/C66/C71/C72/I14/I24/L19/L47/M06/M14/N41/N67/N93/ 11.66 2.88 A14/A85/C66/C71/C72/I14/I24/L19/L47/M06/M14/N41/N56/N93/ 11.66 2.88 A14/A85/C66/C71/C72/I14/I24/L18/L47/M06/M14/N56/N67/N93/ 11.68 2.90 A14/A85/C66/C71/C72/I14/I24/L18/L19/M06/M14/N56/N67/N93/ 11.81 2.91 A14/A85/C66/C71/C72/I14/I24/L18/L19/M06/M14/N41/N67/N93/ 11.83 2.92 A14/A85/C66/C71/C72/I14/I24/L18/L19/M06/M14/N41/N56/N93/ 11.83 2.92 A14/A85/C66/C71/C72/I14/I24/L18/L90/M06/M14/N41/N56/N93/ 11.84 2.95 A14/A85/C66/C71/C72/I14/I24/L18/L90/M06/M14/N41/N67/N93/ 11.84 2.95 A72/A85/C66/C71/C72/I14/I24/L18/L19/M06/M14/N56/N60/N93/ 11.89 2.97 A72/A85/C66/C71/C72/I14/I24/L18/L19/M06/M14/N60/N67/N93/ 11.89 2.97 A72/A85/C66/C71/C72/I14/I24/L18/L19/M06/M14/N56/N67/N93/ 11.89 2.97 A72/A85/C66/C71/C72/I14/I24/L18/L19/M06/M14/N41/N60/N93/ 11.91 2.98 A72/A85/C66/C71/C72/I14/I24/L18/L19/M06/M14/N41/N56/N93/ 11.91 2.98 A72/A85/C66/C71/C72/I14/I24/L18/L19/M06/M14/N41/N67/N93/ 11.91 2.98 A14/A72/A85/C66/C72/I14/I24/L18/L19/M06/M14/N56/N67/N93/ 11.96 3.00 A14/A72/A85/C66/C72/I14/I24/L18/L19/M06/M14/N41/N56/N93/ 11.98 3.01 A14/A72/A85/C66/C72/I14/I24/L18/L19/M06/M14/N41/N67/N93/ 11.98 3.01 A14/A72/A85/C66/C72/I14/I24/L18/L90/M06/M14/N41/N67/N93/ 11.99 3.04 A14/A72/A85/C66/C72/I14/I24/L18/L90/M06/M14/N41/N56/N93/ 11.99 3.04 A72/A73/A85/C66/C72/I14/I24/L18/L19/M06/M14/N41/N56/N93/ 12.04 3.06 A72/A73/A85/C66/C72/I14/I24/L18/L19/M06/M14/N41/N67/N93/ 12.04 3.06 (FIGURE 2.2) Range of minimum and maximum return (%) and risk (average standard deviation) for divided portfolios of 14 funds This diagram shows that selected portfolios have practically the same level of the risk in the range of the annual return from 6 to 10%. It means that better performers not necessarily have to be riskier. You can increase the return of your portfolio, and not at the cost of the higher risk! Top In-Stream Hydrokinetic Technology www.optimpower.com