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An investor has asked you to recommend an optimal portfolio consisting of the 9 risky assets and a risk-free asset. The risk-free asset is a T-Bill with an annual return of 3%. Draft a memo to the investor in your own words. At the very least, the memo should contain the following.

1. Recommend two optimal risky portfolios, one with shorting and one without shorting, to combine with the risk-free asset. Mention the weights of the 9 assets in the portfolios.

2. Include the graphs of the two efficient frontiers with and without shorting, with the optimal risky portfolios marked on them.

3. The investor may wonder why the variance of the portfolio is less than that of some of the risky assets and yet the returns are higher. Explain that in the memo.

B D E F. G H K M N 0 14 12 10 8 With shortsales Standard Deviation Mean 1.63 1 1.32 2 1.16 3 0.96 4 1.00 5 1.20 6 1.81 8 2.55 10 3.32 12 2.05 8.65 6 Investment Opportunity Set 4 2 0 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 Optimal Risky Portfolio Weight of Assets in the Optimal Risky Portfolio SPX 0.265514206 CICO C7CO MXWD RMS HY DLJLTR HEDGNAV 30 Yr Bond 0.814905 -0.229106 -0.342297 0.1095695 0.0182054 0.0331236 0.264838189 0.065247106 14 12 10 Area 8 Without shorts ales Standard Deviation Mean 8.88 1 6.96 2 5.13 3 3.43 4 1.99 5 1.62 6 2.36 8 3.58 10 4.97 12 2.21 7.69 Investment Opportunity Set 6 4 2 0 Optimal Risky Portfolio 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 Weight of Assets in the Optimal Risky Portfolio SPX C7CO MXWD HY 30 Yr Bond CICO 0.7829967 RMS 0.0900861 DLJLTR HEDGNAV 0.0471621 0.079755146 0 0 0 0 0 16.33887126 1.910544776 7.51933077 15.679895 14.047728 9.60975742 2.7235851 5.312292 11.58268 SPX Cico C7CO MXWD RMS HY DULTR HEDGNAV 30-Yr Bond Annual Ret -0.997612923 6.122998663 10.44260588 -2.403352147 22.859292 7.287748187 5.047121782 7.530689971 10.74244394 Annual S.D. 16.33887126 1.910544776 7.519330771 15.67989499 14.04772839 9.609757418 2.723585063 5.312291927 11.5826846 SPX cico c7co MXWD RMS HY DUILTR HEDGNAV 30-Yr Bond SPX 1 -0.228320139 -0.138863746 0.968920583 0.251910843 0.51884168 0.168684992 0.331923279 -0.216626469 Correlation Matrix C1C0 C7CO MXWD RMS HY DLJLTR HEDGNAV 30 Yr Bond -0.228320139 -0.138863746 0.968920583 0.25191084 0.5188417 0.168685 0.33192328 -0.2166265 1 1 0.81888544 -0.209055456 0.08593803 0.1729362 0.0414742 0.21555815 0.614378 0.81888544 1 -0.088014481 0.13550771 0.2174251 0.0711805 0.29533238 0.8506927 -0.209055456 -0.088014481 1 0.31015007 0.5538881 0.2257026 0.44304042 -0.1797137 0.085938025 0.135507708 0.310150074 1 0.2034525 0.3505112 0.07633551 0.0072008 0.17293619 0.217425066 0.553888122 0.20345255 1 0.5725788 0.40490296 0.0642968 0.041474209 0.071180497 0.225702641 0.35051116 0.5725788 1 0.34991907 -0.1684472 0.215558151 0.295332377 0.44304042 0.07633551 0.404903 0.3499191 1 0.1540123 0.614377969 0.850692738 -0.17971371 0.00720083 0.0642968 -0.1684472 -0.1684472 0.15401227 1 SPX c1co c7co MXWD RMS HY DULTR HEDGNAV 30-Yr Bond SPX 266.958714 -7.127274601 - 17.06043566 248.2294944 57.81959089 81.46467563 7.506533722 28.80989634 -40.99612444 Covariance Matrix C1CO C7CO MXWD RMS HY DLJLTR HEDGNAV 30 Yr Bond -7.1272 74601 -17.06043566 248.2294944 57.8195909 81.464676 7.5065337 28.8098963 -40.996124 3.650181342 11.76412308 -6.262703859 2.30647469 3.1750863 0.2158123 2.18777977 13.595716 11.76412308 56.54033525 -10.37711121 14.3136137 15.710906 1.4577436 11.7970164 74.090265 -6.262703859 -10.37711121 245.859107 68.3157971 83.459855 9.6387504 36.9035744 -32.638756 2.306474687 14.3136137 68.31579712 197.338673 27.46513 13.410621 5.69658587 1.1716504 3.175086281 15.71090582 83.45985512 27.4651303 92.347438 14.986099 20.6702298 7.1566728 0.215812339 1.457743627 9.638750423 13.4106213 14.986099 7.4179156 5.06279675 -5.3139085 2.187779772 11.79701642 36.90357438 5.69658587 20.67023 5.0627967 28.2204455 9.4764675 13.59571603 74.09026459 -32.63875551 1.17165042 7.1566728 -5.3139085 9.47646746 134.15858 Bordered Covariance Matrix for Target Returns C7CO 0.0000000 Weights 0 0.782996726 0 0 0.090086053 0 0 0.047162087 0.079755146 0 1.000000012 SPX 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 C1CO 0.7829967 0.0000000 2.2378673 0.0000000 0.0000000 0.1626920 0.0000000 0.0079695 0.1366225 0.0000000 2.5451513 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 MXWD 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 RMS HY DLJLTR HEDGNAV 0.0900861 0.0000000 0.0471621 0.0797551 0.0000000 0.0000000 0.0000000 0.0000000 0.1626920 0.0000000 0.0079695 0.1366225 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 1.6015014 0.0000000 0.0569770 0.0409290 0.0000000 0.0000000 0.0000000 0.0000000 0.0569770 0.0000000 0.0164994 0.0190433 0.0409290 0.0000000 0.0190433 0.1795070 0.0000000 0.0000000 0.0000000 0.0000000 1.8620994 0.0000000 0.1004891 0.3761018 30 Yr Bond 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 -0.99761 0 6.122999 4.794288 10.44261 0 -2.40335 0 22.85929 2.059303 7.287748 0 0 5.047122 0.238033 7.53069 0.600611 10.74244 0 B D E F. G H K M N 0 14 12 10 8 With shortsales Standard Deviation Mean 1.63 1 1.32 2 1.16 3 0.96 4 1.00 5 1.20 6 1.81 8 2.55 10 3.32 12 2.05 8.65 6 Investment Opportunity Set 4 2 0 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 Optimal Risky Portfolio Weight of Assets in the Optimal Risky Portfolio SPX 0.265514206 CICO C7CO MXWD RMS HY DLJLTR HEDGNAV 30 Yr Bond 0.814905 -0.229106 -0.342297 0.1095695 0.0182054 0.0331236 0.264838189 0.065247106 14 12 10 Area 8 Without shorts ales Standard Deviation Mean 8.88 1 6.96 2 5.13 3 3.43 4 1.99 5 1.62 6 2.36 8 3.58 10 4.97 12 2.21 7.69 Investment Opportunity Set 6 4 2 0 Optimal Risky Portfolio 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 Weight of Assets in the Optimal Risky Portfolio SPX C7CO MXWD HY 30 Yr Bond CICO 0.7829967 RMS 0.0900861 DLJLTR HEDGNAV 0.0471621 0.079755146 0 0 0 0 0 16.33887126 1.910544776 7.51933077 15.679895 14.047728 9.60975742 2.7235851 5.312292 11.58268 SPX Cico C7CO MXWD RMS HY DULTR HEDGNAV 30-Yr Bond Annual Ret -0.997612923 6.122998663 10.44260588 -2.403352147 22.859292 7.287748187 5.047121782 7.530689971 10.74244394 Annual S.D. 16.33887126 1.910544776 7.519330771 15.67989499 14.04772839 9.609757418 2.723585063 5.312291927 11.5826846 SPX cico c7co MXWD RMS HY DUILTR HEDGNAV 30-Yr Bond SPX 1 -0.228320139 -0.138863746 0.968920583 0.251910843 0.51884168 0.168684992 0.331923279 -0.216626469 Correlation Matrix C1C0 C7CO MXWD RMS HY DLJLTR HEDGNAV 30 Yr Bond -0.228320139 -0.138863746 0.968920583 0.25191084 0.5188417 0.168685 0.33192328 -0.2166265 1 1 0.81888544 -0.209055456 0.08593803 0.1729362 0.0414742 0.21555815 0.614378 0.81888544 1 -0.088014481 0.13550771 0.2174251 0.0711805 0.29533238 0.8506927 -0.209055456 -0.088014481 1 0.31015007 0.5538881 0.2257026 0.44304042 -0.1797137 0.085938025 0.135507708 0.310150074 1 0.2034525 0.3505112 0.07633551 0.0072008 0.17293619 0.217425066 0.553888122 0.20345255 1 0.5725788 0.40490296 0.0642968 0.041474209 0.071180497 0.225702641 0.35051116 0.5725788 1 0.34991907 -0.1684472 0.215558151 0.295332377 0.44304042 0.07633551 0.404903 0.3499191 1 0.1540123 0.614377969 0.850692738 -0.17971371 0.00720083 0.0642968 -0.1684472 -0.1684472 0.15401227 1 SPX c1co c7co MXWD RMS HY DULTR HEDGNAV 30-Yr Bond SPX 266.958714 -7.127274601 - 17.06043566 248.2294944 57.81959089 81.46467563 7.506533722 28.80989634 -40.99612444 Covariance Matrix C1CO C7CO MXWD RMS HY DLJLTR HEDGNAV 30 Yr Bond -7.1272 74601 -17.06043566 248.2294944 57.8195909 81.464676 7.5065337 28.8098963 -40.996124 3.650181342 11.76412308 -6.262703859 2.30647469 3.1750863 0.2158123 2.18777977 13.595716 11.76412308 56.54033525 -10.37711121 14.3136137 15.710906 1.4577436 11.7970164 74.090265 -6.262703859 -10.37711121 245.859107 68.3157971 83.459855 9.6387504 36.9035744 -32.638756 2.306474687 14.3136137 68.31579712 197.338673 27.46513 13.410621 5.69658587 1.1716504 3.175086281 15.71090582 83.45985512 27.4651303 92.347438 14.986099 20.6702298 7.1566728 0.215812339 1.457743627 9.638750423 13.4106213 14.986099 7.4179156 5.06279675 -5.3139085 2.187779772 11.79701642 36.90357438 5.69658587 20.67023 5.0627967 28.2204455 9.4764675 13.59571603 74.09026459 -32.63875551 1.17165042 7.1566728 -5.3139085 9.47646746 134.15858 Bordered Covariance Matrix for Target Returns C7CO 0.0000000 Weights 0 0.782996726 0 0 0.090086053 0 0 0.047162087 0.079755146 0 1.000000012 SPX 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 C1CO 0.7829967 0.0000000 2.2378673 0.0000000 0.0000000 0.1626920 0.0000000 0.0079695 0.1366225 0.0000000 2.5451513 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 MXWD 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 RMS HY DLJLTR HEDGNAV 0.0900861 0.0000000 0.0471621 0.0797551 0.0000000 0.0000000 0.0000000 0.0000000 0.1626920 0.0000000 0.0079695 0.1366225 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 1.6015014 0.0000000 0.0569770 0.0409290 0.0000000 0.0000000 0.0000000 0.0000000 0.0569770 0.0000000 0.0164994 0.0190433 0.0409290 0.0000000 0.0190433 0.1795070 0.0000000 0.0000000 0.0000000 0.0000000 1.8620994 0.0000000 0.1004891 0.3761018 30 Yr Bond 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 -0.99761 0 6.122999 4.794288 10.44261 0 -2.40335 0 22.85929 2.059303 7.287748 0 0 5.047122 0.238033 7.53069 0.600611 10.74244 0