Free Sample hgof Portfolio Optimization

8/11/2019 Free Sample hgof Portfolio Optimization

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Opp Set Curve -60.0%






Opp Set Curve 0.0%

Opp Set Curve 10.0%

Opp Set Curve 20.0%

Opp Set Curve 30.0%Opp Set Curve 40.0%

Opp Set Curve 50.0%

Opp Set Curve 60.0%

Opp Set Curve 70.0%

Opp Set Curve 80.0%

Opp Set Curve 90.0%

Opp Set Curve 100.0%





Opt Risky Port

Cap Alloc Line 0.0%

Cap Alloc Line 1000.0%

Indifference CurveIndifference Curve

Indifference Curve

Indifference Curve

Indifference Curve

Indifference Curve

Indifference Curve

Indifference Curve

Indifference Curve

Indifference Curve

Indifference Curve

Indifference Curve

Indifference Curve

1 21E r wE r w E r

2

1 1 2 2 1 2

2 2

1 2 2 1 1 2 1 2 /

w E E

E E E E

s s s

s s s s


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Indifference Curve

Indifference Curve

Indifference Curve

Opt Comp Port

Constant Utility Value


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PORTFOLIOOPTIMIZATION Descriptive Statistics

Returns Stock Stock Stock Stock Stock Stock US Portfolio US Portfolio

Month Barrick Hanson IBM Nokia Telefonos YPF Small-Growth Small-Neutral

Dec 2006 -3.50% -0.24% 2.06% 8.76% 8.63% 0.50% -0.59% 0.83%

Nov 2006 -2.37% 4.88% 5.69% 0.51% 9.01% -0.95% 2.58% 2.66%Oct 2006 1.79% 3.78% -0.12% 1.70% -1.08% 3.49% 5.87% 5.01%

Sep 2006 0.92% -3.49% 12.69% 0.93% 3.14% 7.02% 1.09% 1.11%

Aug 2006 -8.23% 14.36% 1.20% -5.68% 6.76% -3.83% 3.22% 2.74%

Jul 2006 8.68% 3.72% 5.00% 5.20% 3.02% 2.00% -5.76% -2.73%

Jun 2006 4.06% 0.88% 0.78% -2.02% 12.51% 9.98% -0.65% 0.27%

May 2006 -3.30% -0.32% -3.86% -5.67% 6.23% 0.03% -7.71% -4.48%

Apr 2006 0.80% -8.40% -2.61% -5.23% -9.99% -17.69% -0.80% 0.94%

Mar 2006 11.90% 3.92% -0.16% 9.38% -2.17% -3.07% 4.08% 5.49%

Feb 2006 -0.48% 7.12% 2.78% 13.88% 1.21% -2.81% -0.42% -0.36%

Jan 2006 -13.00% 5.15% -1.05% 1.08% -5.72% 0.89% 8.59% 9.37%

Dec 2005 12.90% 5.55% -1.09% 0.46% -3.81% 3.63% -0.18% -0.17%

Nov 2005 4.72% 7.22% -7.54% 7.16% 10.88% -11.58% 4.96% 4.87%

Oct 2005 5.80% 1.22% 8.83% 1.55% 11.10% -0.88% -3.60% -2.86%Sep 2005 -13.06% -2.72% 2.07% -0.56% -5.09% -11.61% 0.52% 0.57%

Aug 2005 10.78% -0.94% -0.49% 7.22% 11.77% 8.89% -2.03% -1.36%

Jul 2005 7.01% 5.52% -3.17% -1.11% -0.33% 12.07% 6.72% 6.86%

Jun 2005 -2.11% 5.30% 12.48% -4.14% 1.97% 1.06% 2.55% 4.20%

May 2005 8.89% 3.30% -1.78% -1.30% 2.18% 8.57% 7.31% 6.21%

Apr 2005 3.48% 0.39% -0.82% 5.49% 10.11% -0.65% -6.42% -5.65%

Mar 2005 -6.82% 0.32% -16.42% 6.55% -1.86% 3.40% -3.98% -2.38%

Feb 2005 -3.78% -3.28% -1.29% -4.39% -11.23% -14.72% 0.39% 2.21%

Jan 2005 13.88% 4.21% -0.72% 5.63% 5.28% 31.78% -5.72% -3.05%

Dec 2004 -9.74% 8.86% -5.23% -2.47% -2.82% 6.38% 4.22% 2.61%

Nov 2004 -1.50% 6.76% 4.61% -3.12% 10.45% 2.83% 8.13% 8.62%

Oct 2004 9.71% 8.98% 5.20% 4.88% 2.23% 6.99% 3.21% 1.17%Sep 2004 7.02% -0.26% 4.68% 12.37% 6.07% 0.00% 5.52% 4.92%

Aug 2004 5.18% 7.96% 1.24% 15.57% 0.61% 5.71% -2.05% -0.20%

Jul 2004 4.62% -1.00% -2.53% 2.22% 4.84% -2.81% -9.86% -5.22%

Jun 2004 -3.22% 1.37% -1.22% -20.10% -7.14% 3.53% 3.41% 4.33%

May 2004 -4.42% -9.22% -0.50% 5.79% -0.26% 0.31% 1.02% 1.04%

Apr 2004 8.05% -0.35% 0.68% -1.92% -1.43% -1.54% -3.60% -3.37%

Mar 2004 -19.13% 1.67% -3.99% -30.90% -2.22% 6.90% 1.08% 0.57%

Feb 2004 16.30% -4.69% -4.83% -5.08% 3.62% 4.45% 0.44% 0.68%

Jan 2004 3.82% 9.27% -2.59% 5.41% -1.30% 1.86% 3.89% 4.32%

Dec 2003 -13.27% 1.93% 7.07% 21.52% 4.20% 1.03% 0.79% 2.36%

Nov 2003 1.66% 4.11% 2.36% -5.48% 0.68% 10.29% 2.91% 3.87%

Oct 2003 15.28% 2.08% 1.37% 5.87% 2.95% 1.67% 8.13% 8.23%

Sep 2003 3.41% 7.41% 1.31% 8.92% 5.24% 23.16% -1.73% -1.73%

Aug 2003 -6.82% -1.78% 7.70% -4.24% 1.73% 8.96% 4.53% 4.99%

Jul 2003 18.05% 12.95% 1.14% 6.44% -1.77% -4.87% 8.37% 6.22%

Jun 2003 -4.35% 3.25% -1.52% -6.87% -1.74% 0.82% 2.40% 2.51%

May 2003 2.37% -2.30% -6.30% -8.93% 4.63% 7.96% 13.10% 10.68%

Apr 2003 17.66% 3.24% 3.90% 8.86% 0.30% 25.69% 11.21% 9.41%

Mar 2003 -3.89% 18.50% 8.25% 18.30% 1.70% 14.65% 2.06% 0.63%

Feb 2003 -3.50% 4.25% 0.62% 8.02% 3.11% 19.28% -3.54% -2.42%

Jan 2003 -2.03% 6.93% -0.13% -8.00% -2.87% 14.21% -2.28% -2.40%

Dec 2002 6.77% -0.70% 0.90% -7.21% -6.39% 13.27% -9.13% -4.09%


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Nov 2002 5.80% -11.97% -10.84% -19.31% 0.07% 8.24% 13.90% 7.45%

Oct 2002 -2.65% 9.99% 10.31% 15.60% 5.68% 24.30% 6.88% 4.24%

Sep 2002 -3.11% -10.94% 35.38% 25.49% 8.31% -4.27% -8.62% -7.66%

Aug 2002 -3.20% -15.58% -22.64% -0.34% -4.07% -14.01% -0.56% 0.48%

Jul 2002 4.87% -1.47% 7.31% 7.21% 2.53% 21.49% -14.61% -14.19%

Jun 2002 -19.31% -12.19% -2.22% -14.43% -9.94% -4.42% -7.63% -2.78%

May 2002 -12.87% -7.43% -10.51% 4.35% -6.92% -4.52% -6.48% -3.67%

Apr 2002 9.10% 5.21% -3.76% -14.64% -8.07% -26.09% -3.56% 2.73%

Mar 2002 8.13% -2.57% -19.47% -21.61% -6.32% -17.48% 8.99% 7.49%

Feb 2002 2.87% 14.66% 5.99% 0.81% 6.21% 5.53% -8.16% -1.28%

Jan 2002 5.56% 1.65% -8.94% -11.41% -0.25% -2.09% -5.15% 1.13%

Dec 2001 7.22% -2.13% -10.81% -4.42% 9.67% -11.52% 6.64% 6.80%

Nov 2001 5.37% 0.33% 4.65% 6.62% 5.27% 23.08% 9.20% 7.15%

Oct 2001 -2.18% -2.12% 7.09% 12.16% -1.63% 8.78% 11.16% 5.04%

Sep 2001 -10.18% -2.32% 17.83% 31.07% 5.55% -0.34% -17.19% -12.93%

Aug 2001 8.30% -9.69% -8.23% -0.57% -10.83% -16.65% -7.64% -2.34%

Jul 2001 7.57% 9.15% -4.87% -27.83% 5.28% -9.18% -9.43% -4.01%

Jun 2001 -1.69% -3.67% -7.31% -1.73% -1.18% -5.23% 6.43% 5.18%

May 2001 -8.19% 5.01% 1.52% -24.11% 1.70% -20.64% 4.06% 4.52%

Apr 2001 1.64% 5.40% -2.78% -14.46% -0.28% 3.51% 10.10% 4.98%

Mar 2001 14.31% 20.00% 19.70% 42.45% 9.67% -2.51% -7.34% -1.49%Feb 2001 -11.76% -11.36% -3.72% 10.21% -1.45% -4.61% -12.22% -0.47%

Jan 2001 4.71% 1.39% -10.70% -35.94% -1.35% 1.94% 12.32% 5.22%

Dec 2000 -5.56% -6.42% 31.76% -21.04% 20.25% 0.19% 2.75% 9.18%

Nov 2000 9.21% 27.73% -9.09% 1.76% -3.15% -3.05% -16.23% -4.26%

Oct 2000 12.98% 2.14% -4.96% 0.00% -13.09% 1.11% -8.11% -1.07%

Sep 2000 -12.31% -5.60% -12.53% 4.57% 1.47% -3.10% -7.08% -0.20%

Aug 2000 -4.39% -5.55% -14.70% -8.66% -1.97% -11.04% 8.45% 5.51%

Jul 2000 0.07% 2.26% 17.74% 1.71% 4.10% -3.34% -7.23% 1.50%

Jun 2000 -12.28% -17.19% 2.46% -12.87% -8.57% -4.37% 17.15% 9.03%

May 2000 0.30% 0.70% 2.10% -2.89% 18.03% 16.06% -7.77% -5.46%

Apr 2000 8.46% -4.28% -3.64% -7.24% -17.18% 4.03% -14.24% -5.46%

Mar 2000 7.12% 5.89% -5.81% 1.01% -11.75% -8.81% -13.62% -3.74%Feb 2000 -3.79% 10.99% 15.20% 12.24% 1.64% -0.16% 28.59% 15.35%

Jan 2000 -0.40% -11.46% -8.37% 7.30% 23.48% 1.87% 0.65% -0.25%

Dec 1999 -7.42% -10.69% 4.06% -3.16% -5.32% -4.91% 17.97% 8.43%

Nov 1999 -1.75% -2.60% 4.67% 36.48% 21.98% -4.06% 12.78% 6.11%

Oct 1999 -0.66% 7.14% 5.04% 21.15% 8.29% -0.25% 1.13% -0.58%

Sep 1999 -15.78% -0.17% -18.80% 28.56% 19.88% -0.30% 0.82% -0.80%

Aug 1999 12.22% -8.64% -2.86% 7.50% -3.61% -0.79% -2.88% -3.06%

Jul 1999 4.37% -4.57% -0.80% -1.72% -1.44% -2.69% -1.24% -0.86%

Jun 1999 -4.19% 1.39% -2.76% -7.10% -6.54% 6.73% 6.47% 6.00%

May 1999 12.33% -2.05% 11.42% 28.52% 1.58% -9.82% 1.34% 1.57%

Apr 1999 -13.24% -6.93% 11.03% -3.95% 5.57% 1.31% 10.03% 9.77%

Mar 1999 17.88% 12.46% 18.02% -4.76% 14.69% 32.44% 0.03% 0.20%

Feb 1999 -3.51% 8.31% 4.41% 15.55% 16.17% 8.86% -9.31% -6.93%

Jan 1999 -7.22% 24.04% -7.24% -5.88% 11.77% -8.31% 4.63% 1.26%

Dec 1998 -2.22% -16.02% -0.61% 19.65% 5.05% 14.08% 6.77% 3.30%

Nov 1998 -2.50% 5.04% 11.66% 22.93% 5.51% -6.11% 9.07% 5.48%

Oct 1998 -5.65% 5.15% 11.36% 5.35% -11.69% 3.58% 4.85% 3.58%

Sep 1998 6.88% 13.89% 15.56% 18.82% 19.84% 11.26% 8.69% 5.57%

Aug 1998 53.92% 27.70% 14.10% 17.24% 24.46% 17.55% -24.12% -18.73%

Jul 1998 -20.64% -4.41% -14.86% -23.44% -28.42% -23.59% -7.67% -7.79%

Jun 1998 -14.94% -15.04% 15.41% 19.87% 3.59% -2.74% 0.74% -0.90%

May 1998 0.00% 2.53% -2.28% 12.06% 2.20% -3.36% -7.44% -4.64%


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Apr 1998 -13.39% -0.61% 1.59% -2.89% -16.15% -10.21% 0.78% 1.50%

Mar 1998 3.76% 0.66% 11.54% 23.89% 0.46% 2.62% 4.45% 4.54%

Feb 1998 12.00% 19.98% -0.53% 8.52% 11.94% 7.49% 8.29% 7.07%

Jan 1998 -0.35% 13.76% 5.97% 32.68% 3.03% 4.62% -0.32% -1.52%

Dec 1997 4.00% -3.28% -5.62% 9.12% -12.21% -10.97% -2.16% 1.08%

Nov 1997 12.48% -11.51% -4.46% -16.37% 14.11% 1.70% -3.05% -0.83%

Oct 1997 -18.69% 1.96% 11.39% -5.71% 14.75% 5.77% -6.09% -3.39%

Sep 1997 -16.72% 5.73% -7.06% -5.96% -16.44% -13.10% 8.97% 7.87%

Aug 1997 8.52% 2.17% 4.55% 21.20% 13.84% 13.04% 3.85% 3.23%

Jul 1997 -0.30% -5.15% -3.96% -9.59% -17.26% 1.47% 4.93% 5.46%

Jun 1997 4.33% 1.22% 17.19% 16.20% 15.67% 5.11% 3.82% 5.72%

May 1997 -13.37% -2.43% 4.32% 11.58% 9.16% 2.90% 15.37% 9.76%

Apr 1997 13.54% 5.68% 7.78% 2.31% 7.44% 8.97% -3.10% 0.59%

Mar 1997 -5.80% 6.56% 16.94% 10.90% 7.03% 4.24% -8.42% -3.23%

Feb 1997 -15.92% 2.28% -4.51% -0.32% -0.93% -0.47% -6.13% -0.28%

Jan 1997 5.12% -58.44% -8.15% -12.57% 3.36% -3.76% 4.23% 2.83%


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US Portfolio US Portfolio US Portfolio US Portfolio Country Port Country Port Country Port Country Port

Small-Value Big-Growth Big-Neutral Big-Value Australia Hong Kong Italy Japan

2.08% 0.43% 1.79% 2.79% 3.59% 6.23% 2.72% 2.40%

3.08% 1.42% 2.83% 1.94% 3.38% 6.04% 5.74% 0.45%5.17% 3.14% 3.08% 4.78% 8.65% 1.10% 4.27% 1.94%

0.87% 2.69% 2.16% 1.86% -1.53% 0.79% 0.67% -1.88%

2.38% 3.45% 1.58% 0.81% 2.23% 2.71% 3.98% 1.68%

-1.75% -1.18% 1.26% 1.41% 1.74% 2.44% 1.03% -0.83%

0.24% -0.37% 0.05% 1.67% 0.71% 0.73% -0.20% -1.10%

-4.00% -3.12% -2.71% -1.37% -5.49% -6.27% -2.14% -6.28%

1.51% -0.31% 2.34% 3.44% 9.33% 5.08% 4.15% 2.75%

4.95% 1.57% 1.66% 0.84% 0.43% 1.19% 3.08% 2.27%

-0.65% 0.33% 0.40% -1.00% -2.05% 0.69% 1.52% -1.02%

7.61% 1.26% 3.87% 4.45% 7.49% 5.80% 6.14% 4.34%

-0.32% -0.65% 1.02% 0.43% 2.47% 1.20% 4.39% 8.91%

3.54% 4.26% 3.88% 2.21% 2.64% 3.30% 1.86% 3.64%

-2.50% -0.26% -2.81% -2.92% -5.19% -6.91% -6.41% -0.74%0.39% -0.23% 1.82% 2.20% 5.35% 2.39% 1.46% 8.99%

-0.92% -1.63% 0.06% 0.06% 0.95% -0.99% 1.82% 7.46%

6.12% 4.61% 2.66% 4.22% 2.42% 6.19% 4.62% 1.02%

4.60% -0.98% 1.97% 2.63% 5.26% 3.70% 0.79% 0.70%

5.61% 3.92% 2.96% 3.26% -0.10% -0.39% -1.79% -1.93%

-6.39% -1.33% -2.95% -2.33% -1.44% 3.73% -4.89% -2.15%

-1.84% -1.23% -2.81% -0.06% -3.87% -3.42% -0.62% -2.24%

3.60% 0.81% 4.35% 3.22% 4.90% 3.72% 2.92% 1.62%

-2.28% -2.95% -1.78% -1.40% 0.74% -3.62% -1.70% -1.67%

3.87% 4.04% 2.58% 3.63% 4.35% 2.13% 8.06% 5.29%

9.82% 3.45% 5.23% 5.59% 8.33% 9.70% 7.85% 4.80%

1.39% 1.76% 0.89% 1.60% 6.13% -0.65% 5.91% 2.41%3.82% 0.54% 2.28% 2.95% 5.89% 1.41% 5.95% -2.80%

-0.82% -0.18% 0.91% 0.54% 1.20% 6.34% -0.55% 0.67%

-4.34% -4.91% -1.67% -1.55% 0.43% 1.76% -2.35% -6.10%

5.21% 1.20% 2.22% 2.99% -0.18% 0.31% 2.88% 4.50%

0.72% 1.40% 0.81% 1.23% 0.86% -0.69% -0.54% -2.90%

-6.10% -0.69% -3.17% -1.77% -4.91% -5.04% 1.35% -4.96%

0.36% -1.84% -0.54% -1.08% 0.41% -6.05% -2.78% 14.24%

0.66% 1.20% 2.44% 1.82% 4.26% 3.16% 1.64% 0.06%

6.06% 1.57% 2.12% 2.74% 0.49% 9.62% 2.02% 1.69%

3.96% 4.28% 4.93% 6.53% 7.91% 2.26% 5.00% 6.73%

4.47% 0.86% 1.69% 2.08% -0.38% -0.19% 8.08% -3.23%

10.80% 5.11% 7.42% 6.00% 8.60% 4.79% 5.09% 4.16%

0.90% -0.81% -1.95% -1.49% 3.26% 5.94% 4.25% 6.14%

6.10% 1.80% 2.25% 3.77% 3.11% 11.32% -2.38% 10.47%

6.35% 2.33% 1.72% 0.24% 0.27% 6.50% -0.03% 4.06%

3.41% 1.20% 1.36% 1.32% 3.48% 1.18% -2.77% 7.86%

10.40% 4.97% 7.11% 8.05% 4.82% 8.64% 10.57% 4.68%

9.17% 7.59% 8.95% 9.74% 8.47% -0.96% 13.73% 0.62%

0.89% 1.71% -0.01% -0.62% 2.98% -5.08% -5.59% -4.36%

-3.46% -1.03% -3.22% -4.22% -2.38% -1.04% 1.98% 1.05%

-1.35% -2.66% -2.32% -5.29% 2.78% 1.35% -1.44% -3.65%

-3.45% -6.27% -4.52% -4.28% -1.59% -6.45% -3.18% -2.40%


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7.72% 5.07% 6.42% 8.11% 2.54% 6.00% 9.71% 3.97%

-0.28% 9.62% 6.51% 3.65% 5.29% 3.70% 9.26% -6.59%

-6.63% -10.56% -10.32% -10.21% -5.65% -7.49% -13.83% -4.94%

-0.86% 0.25% 0.79% 4.80% 2.43% -4.68% 1.91% -1.37%

-14.87% -6.01% -9.37% -12.97% -6.33% -3.83% -9.17% -5.93%

-2.35% -7.35% -6.43% -9.59% -5.23% -5.52% -1.38% -5.35%

-2.53% -1.37% 0.13% -0.27% 6.20% -3.19% -2.30% 7.15%

3.93% -6.92% -1.38% -5.99% -1.19% 5.57% 0.51% 5.45%

10.03% 3.63% 5.18% 4.85% 4.08% 5.50% 6.92% 6.32%

-0.45% -2.60% 0.17% -2.39% 0.48% -3.33% 0.10% 4.21%

2.71% -0.87% -1.85% -1.74% 0.23% -1.50% -3.37% -7.64%

6.87% 0.76% 2.93% 1.30% 1.21% 5.11% 1.18% -8.17%

8.96% 8.25% 5.89% 10.00% 6.69% 10.53% 3.76% 0.30%

4.44% 3.30% 0.86% -3.99% 8.38% 3.75% 4.09% 0.54%

-14.38% -8.29% -9.04% -7.73% -11.53% -13.47% -15.17% -7.28%

-1.19% -6.94% -3.98% -6.70% 2.15% -6.05% -1.40% -3.08%

-1.09% -1.68% -1.25% 1.06% -4.98% -1.97% 2.06% -8.50%

2.16% -1.90% -2.01% -1.79% 2.81% -3.24% -4.83% -5.70%

6.30% 0.41% 1.81% 3.78% 0.88% -0.85% -8.59% -0.38%

5.04% 8.91% 5.47% 5.03% 10.77% 1.80% 5.38% 8.59%

-1.20% -8.17% -1.76% -1.85% -10.95% -10.95% -6.96% -3.49%0.40% -11.61% -0.37% 3.18% -5.55% -1.81% -10.80% -5.49%

6.38% 3.73% 1.09% -1.57% 3.93% 3.04% 2.40% -0.34%

8.14% -0.27% 9.10% 6.50% 3.98% 11.39% 1.69% -8.61%

-2.53% -10.91% -3.08% 0.37% 1.97% -1.94% 1.32% -2.68%

-1.87% -2.19% 0.66% 1.29% -5.12% -4.63% 1.03% -6.77%

-0.98% -6.19% 1.87% 1.43% -5.75% -4.13% -5.65% -4.29%

6.26% 7.55% 8.94% 7.06% -0.12% 5.84% -0.47% 6.36%

2.22% -2.97% 3.67% 4.37% -4.31% 6.61% -3.55% -11.26%

7.86% 4.93% -5.87% -5.40% 12.77% 8.67% 5.68% 6.73%

-3.64% -3.39% 0.88% -0.03% -3.16% -10.03% 2.84% -7.09%

-4.47% -4.27% -1.14% 4.10% -3.17% -9.23% -6.44% -8.02%

-1.02% 8.70% 10.66% 11.98% -1.13% 4.13% -7.22% 7.87%11.44% 1.21% -4.48% -6.97% -2.54% 3.06% 17.04% -2.27%

0.24% -4.78% -3.80% -3.94% -4.14% -7.53% -5.15% -5.53%

5.75% 7.82% 1.97% 1.86% 5.59% 9.70% 20.44% 5.08%

3.32% 4.14% -2.50% -1.97% 6.57% 11.43% 3.71% 7.63%

-3.02% 7.01% 5.70% 4.84% -2.18% 3.62% -2.80% 6.89%

-2.55% -1.96% -5.66% -4.78% 0.95% -4.62% 1.74% 6.77%

-2.84% -0.26% -2.62% -2.16% -5.04% 0.49% 1.86% 2.38%

-0.52% -3.13% -3.52% -2.72% -0.36% -2.78% -2.40% 10.35%

5.97% 6.80% 2.66% -0.86% 5.42% 10.27% -2.11% 9.62%

4.45% -2.56% -0.90% -0.23% -7.62% -7.63% -4.15% -4.41%

8.66% 1.78% 8.80% 8.19% 9.82% 21.88% -2.34% 4.93%

-2.74% 4.20% 3.69% 1.06% 5.32% 12.74% 3.64% 14.64%

-8.12% -4.48% -0.66% -2.15% -2.88% 0.58% -1.55% -2.82%

0.45% 5.66% -0.34% -1.07% 7.17% -8.25% -4.36% 0.73%

2.77% 8.81% 1.83% 2.74% -0.01% -2.02% 7.53% 3.55%

5.40% 7.00% 5.74% 3.89% 6.67% 0.07% 10.98% 4.23%

2.84% 8.23% 7.79% 4.85% 8.54% 32.18% 6.27% 16.74%

2.80% 7.78% 3.95% 5.62% 8.56% 17.11% -5.08% -2.05%

-17.13% -14.32% -17.71% -11.19% -13.18% -7.41% -13.97% -10.72%

-6.61% -0.50% -3.04% -3.91% -0.15% -7.72% 9.75% -1.02%

0.32% 5.84% 1.57% 2.43% -0.12% -6.88% -5.74% 0.69%

-2.57% -2.58% -2.36% 1.02% -4.55% -14.25% 4.96% -4.81%


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6.31% 6.13% 0.12%

4.43% 7.50% 0.14%

-12.05% -10.00% 0.14%

0.17% 0.80% 0.14%

-8.87% -8.11% 0.15%

-1.58% -7.02% 0.13%

1.21% -1.05% 0.14%

1.41% -4.96% 0.15%

8.89% 4.47% 0.13%

5.59% -2.17% 0.13%

-4.22% -1.61% 0.14%

5.13% 1.78% 0.15%

5.97% 7.87% 0.17%

1.49% 2.80% 0.22%

-13.85% -9.15% 0.28%

-3.06% -5.91% 0.31%

0.13% -1.83% 0.30%

-3.44% -1.75% 0.28%

-2.47% 1.06% 0.32%

7.38% 8.39% 0.39%

-8.08% -7.03% 0.44%-2.75% -9.93% 0.39%

3.80% 3.95% 0.54%

6.60% 2.03% 0.50%

-3.56% -10.25% 0.51%

-2.83% -2.46% 0.56%

-2.29% -5.11% 0.51%

6.50% 7.64% 0.50%

-1.74% -1.71% 0.48%

10.10% 5.16% 0.40%

3.89% -3.90% 0.50%

-7.38% -5.95% 0.46%

1.08% 5.35% 0.47%0.67% 3.17% 0.43%

-7.59% -3.98% 0.41%

11.34% 8.39% 0.44%

4.05% 3.69% 0.36%

-4.62% 6.20% 0.39%

1.16% -2.28% 0.39%

2.88% -1.00% 0.39%

4.07% -3.06% 0.38%

-1.41% 5.10% 0.40%

-2.56% -2.07% 0.34%

7.46% 4.90% 0.37%

10.39% 3.79% 0.43%

-9.16% -3.81% 0.35%

11.65% 3.83% 0.35%

-5.87% 6.31% 0.38%

-7.86% 6.20% 0.31%

15.17% 7.44% 0.32%

-1.99% 6.38% 0.46%

-28.23% -15.77% 0.43%

1.39% -2.33% 0.40%

-3.36% 3.20% 0.41%

-8.49% -2.58% 0.40%


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5.37% 1.09% 0.43%

8.73% 5.13% 0.39%

3.93% 7.32% 0.39%

-7.05% 0.45% 0.43%

-0.56% 1.78% 0.48%

-6.76% 3.05% 0.39%

-3.18% -3.45% 0.42%

10.59% 5.84% 0.44%

0.60% -3.63% 0.41%

1.95% 7.65% 0.43%

1.76% 4.41% 0.37%

5.39% 7.16% 0.49%

-5.15% 4.23% 0.43%

2.59% -4.48% 0.43%

-4.53% -0.11% 0.39%

7.86% 5.34% 0.45%


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Stock Stock Stock Stock

Covariances Barrick Hanson IBM Nokia

0.0000 0.0000

0.0000 0.0000

0.0000 0.0000

0.0000 0.0000

0.0000 0.0000

0.0000 0.0000

0.0000 0.0000

0.0000 0.0000

0.0000 0.0000

0.0000 0.0000

0.0000 0.0000

0.0000 0.0000

0.0000 0.0000

0.0000 0.0000

0.0000 0.0000

0.0000 0.0000

0.0000 0.00000.0000 0.0000


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Stock Stock US Portfolio US Portfolio US Portfolio US Portfolio US Portfolio US Portfolio

Telefonos YPF Small-GrowthSmall-Neutral Small-Value Big-Growth Big-Neutral Big-Value


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Country Port Country Port Country Port Country Port Country Port Country Port

Australia Hong Kong Italy Japan Norway US


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Country Port Country Port Country Port Country Port Country Port Country Port

Australia Hong Kong Italy Japan Norway US


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PORTFOLIOOPTIMIZATION Many Risky Assets and a

Inputs

Asset Type 1

Method to

Forecast

Expected

Return 4

Risk Aversion 2.8 28

Expected

Return/Mon

Standard

Deviation

US Riskfree 0.00% 50 0.00%

0 1.70% 50 0.00% 50

0 2.11% 50 0.00% 50

0 1.55% 50 0.00% 50

0 2.01% 50 0.00% 50

0 1.77% 50 0.00% 50

0 1.41% 50 0.00% 50

0 0 0 0 0 0

0 100.0% 0.0% 0.0% 0.0% 0.0% 0.0%

0 0.0% 100.0% 0.0% 0.0% 0.0% 0.0%

0 0.0% 0.0% 100.0% 0.0% 0.0% 0.0%

0 0.0% 0.0% 0.0% 100.0% 0.0% 0.0%

0 0.0% 0.0% 0.0% 0.0% 100.0% 0.0%

0 0.0% 0.0% 0.0% 0.0% 0.0% 100.0%

10

10 10

Correlations

0.00%

0.50%

1.00%

1.50%

2.00%

2.50%

3.00%

0.00% 5.00%

Expe

ctedReturn/Month

Standard

Risky Opportunity S

Indi

0%

20%

40%

60%

80%

100%

120%

US Riskfree 0

Po

rtfolioWeights

Portfolio W

and t

Stock US Port Country Port

AssetType

Average Past Return

Static CAPM

Fama-French 3 Factor

Forecast Expected Ret.

Macro 3 Factor


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10 10 10

10 10 10 10

10 10 10 10 10

0 0 0 0 0 0One plus

Exp Ret

[1 + E(ri)]

0 0 0 0 0 0 US Riskfree

0 0

0 0

0 0

0 0

0 0

0 0

Outputs

A

B

C

Delta

Gamma

Risky Asst Capital Optimal Optimal

Opp Set Allocation Individual Risky Indifference Complete

Proportion Curve Line Asset (Tangent) Curve Portfolio

in Optimal Standard Expected Expected Expected Portfolio Expected Expected

Risky Port Deviation Ret / Mon Ret / Mon Ret / Mon Weights Ret / Mon Ret / Mon

US Riskfree

0 0.0%

0 0.0%

0 0.0%

0 0.0%

0 0.0%

Variance-Covariance Matrix

Standard Deviations


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0 0.0%

Opp Set Curve 0.00%

Opp Set Curve 0.10%

Opp Set Curve 0.20%

Opp Set Curve 0.30%

Opp Set Curve 0.40%


Opp Set Curve 0.70%

Opp Set Curve 0.80%

Opp Set Curve 0.90%

Opp Set Curve 1.00%

Opp Set Curve 1.10%

Opp Set Curve 1.20%

Opp Set Curve 1.30%

Opp Set Curve 1.40%

Opp Set Curve 1.50%

Opp Set Curve 1.60%


Opp Set Curve 1.90%

Opp Set Curve 2.00%

Opp Set Curve 2.10%

Opp Set Curve 2.20%

Opp Set Curve 2.30%

Opp Set Curve 2.40%

Opp Set Curve 2.50%

Opp Set Curve 2.60%

Opp Set Curve 2.70%

Opp Set Curve 2.80%

Opp Set Curve 2.90%

Opp Set Curve 3.00%

Opt Risky Port

Cap Alloc Line 0.0%

Cap Alloc Line 1000.0%

Indiffer Curve 0.0%

Indiffer Curve 0.5%

Indiffer Curve 1.0%

Indiffer Curve 1.5%

Indiffer Curve 2.0%

Indiffer Curve 2.5%

Indiffer Curve 3.0%

Indiffer Curve 3.5%

Indiffer Curve 4.0%Indiffer Curve 4.5%

Indiffer Curve 5.0%

Indiffer Curve 6.0%

Indiffer Curve 7.0%

Indiffer Curve 8.0%

Indiffer Curve 9.0%

Indiffer Curve 10.0%

Indiffer Curve 11.0%


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iskfree Asset

10.00% 15.00%

eviation (s)

t, Capital Allocation Line, and

ference Curve

0 0 0 0 0

eights of the Optimal Risky Portfolio

e Optimal Complete Portfolio

Optimal Risky Portfolio

Optimal Complete Portfolio


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Ones

Optimal

Complete

Portfolio

Weights


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Documents

Free Sample hgof Portfolio Optimization