4) Given a risk free rate of 2% and a market portfolio with a return of 8% and s of 12%, what combination of assets would a risk averse investor hold if he wanted to have no more than 7% volatility?

5) Given a risk free rate of 3% and a market portfolio with a return of 10% and s of 14%, what combination of assets would a less risk averse investor hold if she wanted to have no more than 18% volatility?

6) Given a risk free rate of 1% and a market portfolio with a return of 7% and s of 11%, what combination of assets would a risk averse investor hold if she wanted to have no more than 9% volatility?

Month 1 2 C(Variance) 0.0068 0.0011 0.0138 0.0018 0.0060 C(Variance) 0.0150 0.0105 0.0189 0.0086 3 A&B(Covariance) -0.0056 0.0001 0.0032 0.0027 -0.0010 -0.0046 4 5 0.0333 Asset A Return -5% 2% - 1% 8% 3% 6% -2% 3% 5% 2% -4% 4% 6 Asset B Return 12% 7% -8% 8% -4% -7% 14% 10% 8% 12% -5% -2% Asset C Return 16% 14% -10% 13% 22% -12% 20% 19% -25% 14% 18% -16% A&C(Covariance) -0.0067 0.0002 0.0044 0.0043 0.0020 -0.0077 -0.0052 0.0016 -0.0101 0.0002 -0.0069 -0.0050 B&C(Covariance) 0.0082 0.0026 0.0189 0.0029 -0.0123 0.0194 0.0143 0.0081 -0.0132 0.0065 -0.0104 0.0127 A(Variance) 0.0046 0.0000 0.0008 0.0039 0.0002 0.0018 0.0014 0.0002 0.0011 0.0000 0.0033 0.0005 7 -0.0038 0.0116 0.0105 0.0039 8 0.0248 0.0264 0.0233 0.0827 0.0105 0.0203 9 0.0018 0.0008 0.0014 0.0002 0.0050 -0.0013 10 11 0.0068 0.0077 0.0033 12 0.0390 1.75% 3.75% 6.08% Average Covariance Sdabderd Deviation -0.0240% -0.2398% 0.4802% 0.0383 0.0791 0.1616 Month 1 2 C(Variance) 0.0068 0.0011 0.0138 0.0018 0.0060 C(Variance) 0.0150 0.0105 0.0189 0.0086 3 A&B(Covariance) -0.0056 0.0001 0.0032 0.0027 -0.0010 -0.0046 4 5 0.0333 Asset A Return -5% 2% - 1% 8% 3% 6% -2% 3% 5% 2% -4% 4% 6 Asset B Return 12% 7% -8% 8% -4% -7% 14% 10% 8% 12% -5% -2% Asset C Return 16% 14% -10% 13% 22% -12% 20% 19% -25% 14% 18% -16% A&C(Covariance) -0.0067 0.0002 0.0044 0.0043 0.0020 -0.0077 -0.0052 0.0016 -0.0101 0.0002 -0.0069 -0.0050 B&C(Covariance) 0.0082 0.0026 0.0189 0.0029 -0.0123 0.0194 0.0143 0.0081 -0.0132 0.0065 -0.0104 0.0127 A(Variance) 0.0046 0.0000 0.0008 0.0039 0.0002 0.0018 0.0014 0.0002 0.0011 0.0000 0.0033 0.0005 7 -0.0038 0.0116 0.0105 0.0039 8 0.0248 0.0264 0.0233 0.0827 0.0105 0.0203 9 0.0018 0.0008 0.0014 0.0002 0.0050 -0.0013 10 11 0.0068 0.0077 0.0033 12 0.0390 1.75% 3.75% 6.08% Average Covariance Sdabderd Deviation -0.0240% -0.2398% 0.4802% 0.0383 0.0791 0.1616