dynamic portofolio optimization and asset pricing
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7/27/2019 Dynamic Portofolio Optimization and Asset Pricing
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Acknowledgments
I am grateful to my Lord for all his blessings and for having given me the
opportunity to meet my supervisor Mike Sherris who is an example of endless
dynamism and a source of pertinent ideas. Thank you Mike for this great
personality. I would also like to thank Dr. John van der Hoek for his early
directions in this area and my co-supervisor Rob Womersley who is always
happy to meet up and have good discussion. The friendly sta in Actuarial
Studies deserve many thanks for the nice ambiance they created.
Thanks also go to my family, especially to my father Professor Farouk
Hamada for his useful advice and remarkable viewpoints. Thank you my
Lord for this nice environment and for making this intellectual adventure a
success. To You this work is dedicated.
Sydney, November 15, 2001.1
1The research was funded by the International Postgraduate Research Scholarship
(IPRS), the Faculty of Commerce and Economics Scholarship and the Actuarial Stud-
ies Grant A79803988
iv
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Initial Wealth
b Stand Mean
(risk aversion) 1 2 3 4 5 6 7 Deviat
101 3000 108.75% -6.46% -0 .38 % 6.75% -2.16 % -1.11% -5.4 0% 1.3 5% 5.63%
102 6000 106.57% -4.91% -0 .07 % 4.70% -1.53 % -0.79% -3.9 7% 1.0 3% 5.73%
103 9000 104.39% -3.37% 0 .24 % 2.64% -0.90 % -0.46% -2.5 4% 0.7 4% 5.83%
105 2000 102.21% -1.83% 0 .55 % 0.58% -0.27 % -0.14% -1.1 1% 0.5 3% 5.93%
106 5000 100.03% -0.28% 0 .87 % - 1.47% 0.36 % 0 .19% 0.3 2% 0.5 1% 6.04%
1078000 97.85% 1.26% 1 .18% - 3.53% 0.99% 0 .51% 1.75% 0.69% 6.14%
1091000 95.66% 2.81% 1 .49% - 5.59% 1.62% 0 .83% 3.17% 0.96% 6.24%
1104000 93.48% 4.35% 1 .80% - 7.65% 2.25% 1 .16% 4.60% 1.28% 6.34%
1117000 91.30% 5.90% 2 .11% - 9.70% 2.88% 1 .48% 6.03% 1.61% 6.44%
1130000 89.12% 7.44% 2.42% -11.76% 3.52% 1.80% 7.46% 1.94% 6.54%1143000 86.94% 8.99% 2.73% -13.82% 4.15% 2.13% 8.89% 2.28% 6.64%
115 6000 84.76% 10.53% 3 .04 % -1 5.87% 4.78 % 2.45% 10.3 2% 2.6 2% 6.75%
116 9000 82.57% 12.08% 3 .35 % -1 7.93% 5.41 % 2.77% 11.7 5% 2.9 6% 6.85%
118 2000 80.39% 13.62% 3 .66 % -1 9.99% 6.04 % 3.10% 13.1 7% 3.3 1% 6.95%
119 5000 78.21% 15.17% 3 .97 % -2 2.04% 6.67 % 3.42% 14.6 0% 3.6 5% 7.05%
120 8000 76.03% 16.71% 4 .28 % -2 4.10% 7.30 % 3.75% 16.0 3% 4.0 0% 7.15%
122 1000 73.85% 18.26% 4 .59 % -2 6.16% 7.93 % 4.07% 17.4 6% 4.3 5% 7.25%
123 4000 71.67% 19.80% 4 .90 % -2 8.21% 8.56 % 4.39% 18.8 9% 4.6 9% 7.35%
124 7000 69.48% 21.35% 5 .21 % -3 0.27% 9.20 % 4.72% 20.3 2% 5.0 4% 7.46%
126 0000 67.30% 22.89% 5 .52 % -3 2.33% 9.83 % 5.04% 21.7 5% 5.3 9% 7.56%
1 27 30 00 6 5.12 % 2 4.44 % 5 .8 3% -3 4.39 % 1 0.4 6% 5 .3 6% 2 3.1 7% 5 .7 3% 7 .6 6%
1 28 60 00 6 2.94 % 2 5.98 % 6 .1 4% -3 6.44 % 1 1.0 9% 5 .6 9% 2 4.6 0% 6 .0 8% 7 .7 6%
1 29 90 00 6 0.76 % 2 7.53 % 6 .4 5% -3 8.50 % 1 1.7 2% 6 .0 1% 2 6.0 3% 6 .4 3% 7 .8 6%
1 31 20 00 5 8.58 % 2 9.07 % 6 .7 6% -4 0.56 % 1 2.3 5% 6 .3 4% 2 7.4 6% 6 .7 8% 7 .9 6%
1 32 50 00 5 6.40 % 3 0.62 % 7 .0 7% -4 2.61 % 1 2.9 8% 6 .6 6% 2 8.8 9% 7 .1 2% 8 .0 6%
1 33 80 00 5 4.21 % 3 2.16 % 7 .3 8% -4 4.67 % 1 3.6 1% 6 .9 8% 3 0.3 2% 7 .4 7% 8 .1 7%
1 35 10 00 5 2.03 % 3 3.71 % 7 .6 9% -4 6.73 % 1 4.2 5% 7 .3 1% 3 1.7 4% 7 .8 2% 8 .2 7%
1 36 40 00 4 9.85 % 3 5.25 % 8 .0 0% -4 8.78 % 1 4.8 8% 7 .6 3% 3 3.1 7% 8 .1 7% 8 .3 7%
1 37 70 00 4 7.67 % 3 6.80 % 8 .3 1% -5 0.84 % 1 5.5 1% 7 .9 5% 3 4.6 0% 8 .5 2% 8 .4 7%
1 39 00 00 4 5.49 % 3 8.34 % 8 .6 2% -5 2.90 % 1 6.1 4% 8 .2 8% 3 6.0 3% 8 .8 6% 8 .5 7%
1 40 30 00 4 3.31 % 3 9.88 % 8 .9 4% -5 4.96 % 1 6.7 7% 8 .6 0% 3 7.4 6% 9 .2 1% 8 .6 7%
1 41 60 00 4 1.12 % 4 1.43 % 9 .2 5% -5 7.01 % 1 7.4 0% 8 .9 2% 3 8.8 9% 9 .5 6% 8 .7 7%
1 42 90 00 3 8.94 % 4 2.97 % 9 .5 6% -5 9.07 % 1 8.0 3% 9 .2 5% 4 0.3 2% 9 .9 1% 8 .8 8%
1 44 20 00 3 6.76 % 4 4.52 % 9 .8 7% -6 1.13 % 1 8.6 6% 9 .5 7% 4 1.7 4% 1 0.2 6% 8 .9 8%
1 45 50 00 3 4.58 % 4 6.06 % 1 0.1 8% -6 3.18 % 1 9.2 9% 9 .9 0% 4 3.1 7% 1 0.6 1% 9 .0 8%
1468000 32.40% 47.61% 10.49% -65 .24% 19.93% 10.22% 44.60% 10.95% 9 .18%
1481000 30.22% 49.15% 10.80% -67 .30% 20.56% 10.54% 46.03% 11.30% 9 .28%
1494000 28.03% 50.70% 11.11% -69 .35% 21.19% 10.87% 47.46% 11.65% 9 .38%
1507000 25.85% 52.24% 11.42% -71 .41% 21.82% 11.19% 48.89% 12.00% 9 .48%
1520000 23.67% 53.79% 11.73% -73 .47% 22.45% 11.51% 50.32% 12.35% 9 .59%
1533000 21.49% 55.33% 12.04% -75 .52% 23.08% 11.84% 51.74% 12.70% 9 .69%
1546000 19.31% 56.88% 12.35% -77 .58% 23.71% 12.16% 53.17% 13.04% 9 .79%
1559000 17.13% 58.42% 12.66% -79 .64% 24.34% 12.49% 54.60% 13.39% 9 .89%
1572000 14.94% 59.97% 12.97% -81 .70% 24.97% 12.81% 56.03% 13.74% 9 .99%
1585000 12.76% 61.51% 13.28% -83 .75% 25.61% 13.13% 57.46% 14.09% 10.09%1598000 10.58% 63.06% 13.59% -85 .81% 26.24% 13.46% 58.89% 14.44% 10.19%
1611000 8 .40% 64.60% 13.90% -87 .87% 26.87% 13.78% 60.31% 14.79% 10.30%
1624000 6 .22% 66.15% 14.21% -89 .92% 27.50% 14.10% 61.74% 15.14% 10.40%
1637000 4 .04% 67.69% 14.52% -91 .98% 28.13% 14.43% 63.17% 15.48% 10.50%
1650000 1 .85% 69.24% 14.83% -94 .04% 28.76% 14.75% 64.60% 15.83% 10.60%
Asset Allocation
1,000,000
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Comparison of Efficiency Frontiers
0
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Standard Deviation
Mean Unconstrained
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13.94 -200.3 13.94 -200.04
13.92 -22.01 13.92 -22.02
13.9 -200 13.9 -200.01
13.88 -199.8 13.88 -200
13.86 -199.5 13.86 -199.9
13.84 -199.3 13.84 -199.7
13.82 -199 13.82 -199.5
Value Function
Wealthat t=10.000
Value Function
Wealthat t=10.002
One-step backwards
recursion
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71 Vwrfkdvwlf G|qdplf Surjudpplqj yv1 Pduwlqjdoh Phwkrgv 458
wealth value consum- proportion wealth value consum- proportion wealth value consum- proportion
function ption in risky function ption in risky function ption in risky
10.20 2.87 6.93 1.2482 10.20 2.79 7.32 1.2483 10.20 2.43 9.44 1.2487
10.18 2.86 6.92 1.2482 10.18 2.78 7.30 1.2483 10.18 2.42 9.42 1.2487
10.16 2.86 6.91 1.2482 10.16 2.78 7.29 1.2483 10.16 2.42 9.41 1.2487
10.14 2.86 6.89 1.2482 10.14 2.78 7.28 1.2483 10.14 2.42 9.39 1.2487
10.12 2.85 6.88 1.2482 10.12 2.78 7.26 1.2483 10.12 2.42 9.37 1.2487
10.10 2.85 6.87 1.2482 10.10 2.77 7.25 1.2483 10.10 2.42 9.35 1.2487
10.08 2.85 6.85 1.2482 10.08 2.77 7.23 1.2483 10.08 2.41 9.33 1.2486
10.06 2.84 6.84 1.2482 10.06 2.77 7.22 1.2483 10.06 2.41 9.31 1.2486
10.04 2.84 6.82 1.2482 10.04 2.77 7.20 1.2483 10.04 2.41 9.29 1.2486
10.02 2.84 6.81 1.2482 10.02 2.76 7.19 1.2483 10.02 2.41 9.28 1.2486
10.00 2.84 6.80 1.2482 10.00 2.76 7.18 1.2483 10.00 2.41 9.26 1.2486
9.98 2.83 6.78 1.2482 9.98 2.76 7.16 1.2483 9.98 2.40 9.24 1.2486
9.96 2.83 6.77 1.2482 9.96 2.75 7.15 1.2482 9.96 2.40 9.22 1.2486
9.94 2.83 6.76 1.2482 9.94 2.75 7.13 1.2482 9.94 2.40 9.20 1.2486
9.92 2.82 6.74 1.2482 9.92 2.75 7.12 1.2482 9.92 2.40 9.18 1.2486
9.90 2.82 6.73 1.2482 9.90 2.75 7.10 1.2482 9.90 2.39 9.17 1.2486
9.88 2.82 6.72 1.2482 9.88 2.74 7.09 1.2482 9.88 2.39 9.15 1.24869.86 2.82 6.70 1.2481 9.86 2.74 7.07 1.2482 9.86 2.39 9.13 1.2486
9.84 2.81 6.69 1.2481 9.84 2.74 7.06 1.2482 9.84 2.39 9.11 1.2486
9.82 2.81 6.67 1.2481 9.82 2.73 7.05 1.2482 9.82 2.39 9.09 1.2486
9.80 2.81 6.66 1.2481 9.80 2.73 7.03 1.2482 9.80 2.38 9.07 1.2486
t = 0 t =1 month t = 5 month
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