Case 3 Templeton Growth Fund Shane Helmle Steve

Case 3 – Templeton Growth Fund Shane Helmle Steve Potter

Our Assignment Look at Templeton Growth Fund and determine its risk Construct an internationally diversified optimal portfolio Construct a constrained Optimal Portfolio Compare portfolios using both in-sample and out-of-sample performance

Templeton Growth Fund Geographical Breakdown (as of August 31, 2004) Europe 45. 90% North America 26. 30% Asia 16. 00% Latin America/Caribbean 1. 00% Mid-East/Africa 0. 40% 1. Shell Transport & Trading Company PLC 2. 10% 2. AT&T Wireless Services Inc. 1. 90% 3. Glaxo. Smith. Kline PLC 1. 90% 4. BP PLC 1. 80% 5. E. ON AG 1. 80% 6. Aventis SA 1. 70% 7. Nestle SA 1. 60% 8. ENI Sp. A 1. 50% 9. BCE Inc. 1. 40% 10. Nippon Telegraph & Telephone Corp. 1. 40%

Templeton Growth Fund

Templeton Growth Fund Some facts as of 08/31/04: Inception date: 11/29/54 Total assets $15, 766, 000 Expense ratio 1. 11% Benchmark : MSCI World Index

Constructing the OP Reward to Market Volatility RVOL = (ri – rf) / bi ri = country return rf = risk free return bi = Systematic risk Portfolio Variance: sp 2 = bp 2 sm 2 + sep 2

Constructing the OP Market ri St Dev i weight Beta world RVAR RVOL U. S. 0. 1494 0. 155 0. 203 0. 97 0. 88 0. 140618557 U. K. 0. 172 0. 144 0. 17 0. 79 1. 104166667 0. 201265823 Japan 0. 177 0. 217 0. 053 0. 95 0. 755760369 0. 172631579 Hong Kong 0. 1971 0. 301 0. 049 1. 22 0. 611627907 0. 150901639 Switzerland 0. 0921 0. 171 0. 045 0. 78 0. 462573099 0. 101410256 South Korea 0. 2395 0. 441 0. 044 1. 4 0. 513605442 0. 161785714 Germany 0. 2289 0. 225 0. 037 1. 2 0. 959555556 0. 179916667 Canada 0. 2988 0. 197 0. 033 1. 09 1. 450761421 0. 262201835 Netherlands 0. 0543 0. 19 0. 032 1. 08 0. 217368421 0. 038240741 France 0. 1201 0. 19 0. 027 1. 05 0. 563684211 0. 102 Spain 0. 2318 0. 226 0. 021 1. 15 0. 968141593 0. 19026087 0. 064 0. 259 0. 02 0. 34 0. 196911197 0. 15 Italy 0. 0953 0. 242 0. 018 0. 94 0. 340082645 0. 087553191 Sweden 0. 2817 0. 374 0. 014 1. 46 0. 718449198 0. 184041096 Denmark 0. 2512 0. 181 0. 012 0. 79 1. 316022099 0. 301518987 Belgium 0. 0411 0. 18 0. 01 0. 76 0. 156111111 0. 036973684 Brazil 0. 4737 0. 441 0. 009 1. 74 1. 044671202 0. 264770115 Australia 0. 2063 0. 182 0. 009 0. 9 1. 062087912 0. 214777778 China 0. 3477 0. 4 0. 008 0. 97 0. 83675 0. 345051546 Israel 0. 4373 0. 28 0. 007 1. 03 1. 515357143 0. 411941748 Mexico 0. 1635 0. 357 0. 007 1. 38 0. 421568627 0. 109057971 Finland

Contructing the OP Rank the Indexes by RVOL: RVAR rank RVOL RANK 1 Israel 2 Canada China 3 Denmark 4 U. K. Brazil 5 Australia Canada 6 Brazil Australia 7 Spain U. K. 8 Germany Spain 9 U. S. Sweden 10 China Germany 11 Japan 12 Sweden South Korea 13 Hong Kong 14 France Finland 15 South Korea U. S. 16 Switzerland Mexico 17 Mexico France 18 Italy Switzerland 19 Netherlands Italy 20 Finland Netherlands 21 Belgium

Constructing the OP (ri. Market ri ri-rf Beta world σ^2 ei rf)βi/(σ ^2 ei) σ^2 m*βi^2/ σ^2 ei Ci RVOL Yes/No Israel 0. 4373 0. 4243 1. 03 0. 05578586 7. 834046736 0. 405374161 0. 118822834 0. 411941748 yes China 0. 3477 0. 3347 0. 97 0. 13994378 2. 319924545 0. 143316302 0. 13975811 0. 345051546 yes Denmark 0. 2512 0. 2382 0. 79 0. 01945768 9. 671140519 0. 683704974 0. 189299833 0. 301518987 yes Brazil 0. 4737 0. 4607 1. 74 0. 12994468 6. 168917495 0. 496644591 0. 203034299 0. 264770115 yes Canada 0. 2988 0. 2858 1. 09 0. 0639559 4. 870887566 0. 395984412 0. 210531655 0. 262201835 yes Australia 0. 2063 0. 1933 0. 9 0. 01585804 10. 97046041 1. 088782725 0. 211628788 0. 214777778 yes 0. 172 0. 159 0. 79 0. 00743268 16. 89968163 1. 789839967 0. 208539324 0. 201265823 no Spain 0. 2318 0. 2188 1. 15 0. 02288559 10. 99469142 1. 231797389 0. 205427511 0. 19026087 no Sweden 0. 2817 0. 2687 1. 46 0. 09443881 4. 154033514 0. 481128293 0. 204094068 0. 184041096 no Germany 0. 2289 0. 2159 1. 2 0. 01992996 12. 99952433 1. 54014559 0. 200071399 0. 179916667 no U. K.

Calculate the weights Zi = (bi/s. Si 2)(RVOLi – C*) wi = Zi / Sj. Zj Zi wi Israel 3. 69847063 0. 3405421 China 0. 96778377 0. 08911011 3. 9014029 0. 35922739 Brazil 0. 79461608 0. 07316544 Canada 0. 96760444 0. 0890936 Australia 0. 5306608 0. 04886137 10. 8605386 100. 00% Denmark total

The 2003 OP 2003 Optimal weighted Countries MSCI USD ri Zi wi ri weighted Bi σei^2 Israel 0. 4373 3. 698470632 0. 3405421 0. 14891906 0. 350758 0. 055786 China 0. 3477 0. 967783768 0. 08911011 0. 03098358 0. 086437 0. 139944 Denmark 0. 2512 3. 901402902 0. 35922739 0. 09023792 0. 28379 0. 019458 Brazil 0. 4737 0. 794616081 0. 07316544 0. 03465847 0. 127308 0. 129945 Canada 0. 2988 0. 967604439 0. 0890936 0. 02662117 0. 097112 0. 063956 Australia 0. 2063 0. 5306608 0. 04886137 0. 0100801 0. 043975 0. 015858 100. 00% 0. 3415003 0. 98938 totals

Constrained Portfolio Constraints US Returns 20022003 Beta Returns 2003 -2004 Variance 0. 35 0. 3395 0. 05229 0. 032072378 0. 05425 Israel 0. 065 0. 06695 0. 0284245 0. 005080645 0. 0182 China 0. 065 0. 06305 0. 0226005 0. 012206831 0. 026 Denmark 0. 065 0. 05135 0. 016328 0. 018396065 0. 011765 Brazil 0. 065 0. 1131 0. 0307905 0. 02294283 0. 028665 Canada 0. 065 0. 07085 0. 019422 0. 01119073 0. 012805 Australia 0. 065 0. 0585 0. 0134095 0. 013364153 0. 01183 U. K. 0. 065 0. 05135 0. 01118 0. 014061107 0. 00936 Spain 0. 065 0. 07475 0. 015067 0. 013885757 0. 01469 Sweden 0. 065 0. 0949 0. 0183105 0. 008924932 0. 02431 Germany 0. 065 0. 078 0. 0148785 0. 012098085 0. 014625 Total 1 1. 0623 0. 242701 0. 164223514 0. 2265 Std. Dev 0. 15049917

Portfolio Comparisons Return Comparison Beta Std Dev RVOL RVAR 2002 -2003 -2004 0. 3415003 0. 196229714 0. 98938 0. 12813642 0. 332026447 2. 563676283 0. 0824 0. 1857 0. 95 0. 177 0. 073052632 0. 392090395 0. 242701 0. 164223514 1. 0623 0. 150499169 0. 216229879 1. 526260915 MSCI World Index 0. 187 0. 137306644 1 0. 146 0. 174 1. 191780822 S&P 500 0. 125 0. 114 1 0. 1603 0. 112 0. 698689956 Optimal Portfolio Templeton Global Growth (Equity only) Constrained Portfolio

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