Slides20-2010 - Portfolio and Risk Analysis Lecture XX...

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Portfolio and Risk Analysis: Lecture XX Charles B. Moss October 9, 2010 Charles B. Moss () Portfolio and Risk Analysis October 9, 2010 1 / 17
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1 An Overview of Portfolio Optimal Portfolio 2 Expected Value-Variance Frontier Assuming Normality 3 Portfolio Selection by Utility Maximization Charles B. Moss () Portfolio and Risk Analysis October 9, 2010 2 / 17
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An Overview of Portfolio The beneft to holding a portFolio oF assets appears to Follow the old adage: Dont put all of your eggs in one basket . I However, what are the mathematics? I Data on the returns For Archer-Daniels-Midland, 3M, Hewlett Packard, and John Deere are taken From the WRDS (Wharton Business School) database is presented in Table 1. Charles B. Moss () Portfolio and Risk Analysis October 9, 2010 3 / 17
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Table: Portfolio Example Date ADM 3M HP Deere Portfolio 1/31/2003 -0.0282 0.0101 0.0029 -0.0796 -0.0030 2/28/2003 -0.0905 0.0119 -0.0896 -0.0194 -0.0061 3/31/2003 -0.0092 0.0372 -0.0139 -0.0459 0.0195 4/30/2003 0.0259 -0.0307 0.0482 0.1215 -0.0006 5/30/2003 0.0857 0.0086 0.1963 -0.0082 0.0301 6/30/2003 0.0752 0.0198 0.0964 0.0515 0.0340 7/31/2003 0.0210 0.0870 -0.0061 0.1112 0.0779 8/29/2003 0.0601 0.0209 -0.0586 0.1128 0.0241 9/30/2003 -0.0548 -0.0304 -0.0246 -0.0527 -0.0330 10/31/2003 0.0946 0.1419 0.1524 0.1371 0.1417 11/28/2003 0.0000 0.0063 -0.0255 0.0101 0.0029 12/31/2003 0.0651 0.0758 0.0603 0.0660 0.0725 Average 0.0204 0.0299 0.0282 0.0337 0.0300 Variance 0.0035 0.0025 0.0073 0.0058 0.0023 Portfolio 0.0178 0.7339 0.1188 0.1295 1.0000 Charles B. Moss () Portfolio and Risk Analysis October 9, 2010 4 / 17
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Optimal Portfolio Defne the ”optimal portFolio” as min z V 12 X i =1 z i r i ! s . t . 12 X i =1 z i ¯ r i =0 . 03 12 X i =1 z i =1 . 00 (1) where V 12 X i =1 z i r i ! = 12 X t =1 4 X i =1 z i r it 4 X i =1 z i ¯ r i !
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Slides20-2010 - Portfolio and Risk Analysis Lecture XX...

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