Case 3:Templeton Growth Fund Presented By: Zhu Zhu Mehmet Can

Assignment Analyze Templeton Growth Fund in terms of international diversification, rates of return and determine its risk Construct an internationally diversified optimal portfolio Build an optimal constrained portfolio Compare the performance of construct optimal portfolio and optimal constrained portfolio & with Templeton’s Growth Fund, the MSCI USA,and the MSCI World Index. Use 2010 new data and compare the out-of –sample performance

Constructing the OP weight USD rt rWORLD SD ßWorld RVAR RVOL U.S. 35.48% 24.2% 0.92 15.5% 0.89 1.558 0.271 U.K. 14.77% 37.3% 0.73 22.5% 1.1 1.657 0.339 France 8.99% 27.6% 0.78 22.6% 1.2 1.221 0.230 Switzerland 6.72% 22.9% 0.74 18.5% 0.93 1.237 0.246 Germany 5.77% 21.3% 0.75 21.8% 1.12 0.975 0.190 Netherlands 4.41% 37.9% 0.83 19.1% 1.07 1.980 0.353 South Korea 3.72% 69.4% 0.06 39.4% 1.31 1.761 0.530 Sweden 60.2% 0.67 17.1% 3.516 0.771 Italy 2.77% 0.61 25.4% 1.06 -0.318 0.213 Singapore 1.97% 67.3% 0.58 21.7% 0.95 3.099 0.708 Japan 1.82% 4.4% 0.66 22.0% 0.99 0.199 0.044 Spain 1.62% 36.5% 0.65 1.618 0.303 Hong Kong 0.86% 55.20% 0.48 36.1% 1.18 1.528 0.467 Ireland 0.80% 9.91% 22.7% 1.09 0.434 0.090 Brazil 0.59% 121.25% 0.07 53.7% 1.49 2.257 0.813 Total Equity 99.00 0.315463757 0.1951742 0.974771 1.6137571 0.323 Cash & Notes 1.00

Constructing the OP RVAR RANK RVOL RANK 3.516 Sweden 0.813 Brazil 3.099 Singapore 0.771 2.257 0.708 1.980 Netherlands 0.530 South Korea 1.761 0.467 Hong Kong 1.657 U.K. 0.353 1.618 Spain 0.339 1.558 U.S. 0.303 1.528 0.271 1.237 Switzerland 0.246 1.221 France 0.230 0.975 Germany 0.213 Italy 0.434 Ireland 0.190 0.199 Japan 0.090 -0.318 0.044

Driving the OP Portfolio Variance: sp2 = bp2sm2 + sep2 = (Sjwjbj)2sm2 + Sjwj2sej2 Reward to Market Volatility RVOL = (ri – rf) / b ri = country return rf = risk free return bi = Systematic risk

Driving the OP Unsystematic Risk: sei2 = si2 - bi2sm2 where si2 = Variance of country return sm2 = Variance of market index bi = Systematic risk Cut off ratio: Ci = Cnum / Cden Cnum = sm2Sj=1i(rj – rf) / (bj / sej2) Cden = 1 + sm2 Sj=1i (bj2 / sej2)

Driving the OP Modern Portfolio Theory and Investment Analysis Ranks assets according to RVOL from highest to Lowest The optimal portfolio consists of investing in all stock for which RVOLi > C* C* is the last value of Ci that is less than the RVOL of an individual country. Zi = (bi/sSi2)(RVOLi – C*) This Z is then used to calculate w Where: wi = Zi / SjZj

Constructing the OP Market (rI-rf) ßWorld RVOL si2 (ri-rf)ßi/s2ei s2mßi2/S2e Ci Included Brazil 121.2% 1.49 0.7802 0.241 7.4921 0.196327 0.1963 0.13349 yes Sweden 60.1% 0.78 0.7072 0.016 28.8158 0.796975 36.3079 0.9933 0.38827 Singapore 67.2% 0.95 0.6557 0.028 22.9370 0.690728 59.2449 1.6840 0.47051 South Korea 69.4% 1.31 0.4917 0.119 7.6583 0.308290 66.9032 1.9923 0.47659 Hong Kong 55.2% 1.18 0.4255 0.101 6.4668 0.294915 73.3700 2.2872 0.47577 no Netherlands 37.8% 1.07 0.3071 0.012 33.5027 2.020873 106.8727 4.3081 0.42917 U.K. 37.3% 1.1 0.2940 0.025 16.5189 1.038648 123.3916 5.3468 0.41442 Spain 36.4% 1.2 0.2622 0.020 21.9226 1.540146 145.3142 6.8869 0.39274 U.S. 24.2% 0.89 0.2158 0.007 30.1040 2.364565 175.4182 9.2515 0.36475 Switzerland 22.9% 0.93 0.1928 13.4754 1.167677 188.8936 10.4191 0.35261 France 27.6% 0.1887 16.2469 1.506064 205.1405 11.9252 0.33831 Italy 22.6% 1.06 0.1663 0.041 5.8988 0.590422 211.0393 12.5156 0.33284 Germany 21.3% 1.12 0.1456 0.021 11.4557 1.286434 222.4949 13.8021 0.32041 Ireland 9.9% 1.09 0.0451 0.026 4.1020 0.966496 226.5970 14.7686 0.30631 Japan 4.4% 0.99 -0.0057 1.5785 0.759476 228.175451 15.5280 0.29428

Constructing the OP Calculation of Weights Zi = (bi/sSi2)(RVOLi – C*) wi = Zi / SjZj Zi wi Brazil 1.5689 0.8639 Sweden 0.0368 0.0202 Singapore 0.1989 0.1095 South Korea 0.0114 0.0063 Hong Kong Total 1.816 100%

Optimal Portfolio Optimal Portfolio Zi wi MSCI USD ri SD rf Weighted ri Weighted Bi RVAR RVOL Brazil 1.56890 0.86394 121.25% 0.537 0.1% 1.04757 1.28728 0.46394 Sweden 0.03677 0.02025 60.17% 0.171 0.01218 0.01579 0.00346 Singapore 0.19890 0.10953 67.29% 0.217 0.07371 0.10405 0.02377 South Korea 0.01140 0.00628 69.42% 0.394 0.00436 0.00822 0.00247 Hong Kong 0.00000 55.20% 0.361 Total 1.00000 1.13782 1.41535 0.49364 2.30393 0.80356

Deriving the weights of the Constrained Optimal Portfolio Countries with weights above the cap are reduced to the cap limit of 6.5% and a floor of 35% for the US

Optimal Portfolio Zi wi MSCI USD ri SD rf Weighted ri Weighted Bi SD RVAR RVOL Brazil 1.568901016 0.863943659 121.25% 0.537 0.1% 1.047567292 1.2872761 0.4639377 Sweden 0.036770163 0.020248154 60.17% 0.171 0.1% 0.012182391 0.0157936 0.0034624 Singapore 0.198904969 0.109530611 67.29% 0.217 0.1% 0.073708446 0.1040541 0.0237681 South Korea 0.011399928 0.006277576 69.42% 0.394 0.1% 0.004357678 0.0082236 0.0024734 Hong Kong 0 55.20% 0.361 0.1% 0 0 0 Total 1 1.137815807 1.4153473 0.4936417 2.30393 0.80356 Constrained Optimal Portfolio Optimal Constrained Portfolio RVARi = (ri - rf) / si RVOLi = (ri - rf) / ßi. Weight Beta Return Weighted ri Weighted Bi RVAR RVOL sd U.S. 0.35 0.89 0.242028763 0.0847 0.3115 0.05425 Brazil 0.065 1.49 1.212541212 0.0788 0.0969 0.034905 Sweden 0.78 0.60165439 0.0391 0.0507 0.011115 Singapore 0.95 0.67294837 0.0437 0.0618 0.014105 South Korea 1.31 0.694165782 0.0451 0.0852 0.02561 Hong Kong 1.18 0.552042433 0.0359 0.0767 0.023465 Netherlands 1.07 0.378620829 0.0246 0.0696 0.012415 U.K. 1.1 0.373415986 0.0243 0.0715 0.014625 Spain 1.2 0.364596483 0.0237 0.0780 Switzerland 0.93 0.229274561 0.0149 0.0605 0.012025 France 0.27643982 0.0180 0.01469 1 0.4328 1.0402 1.864860278 0.4156425 0.2318

Comparison of Various Portfolios Portfolios under comparison: Optimal portfolio Constrained optimal portfolio - Floor for US weights: 35% - Caps for other country indexes: 6.5% MSCI world index MSCI USA

Comparison of Various Portfolios   2009 2010 Return B RVOL RVAR Templeton 32% 0.97 0.323116 1.6137571 0.012714 0.974771 0.011915 0.059508 Optimal 114% 1.42 0.80 2.304 6.67% 0.79 0.08 0.382 Constrained Optimal 43% 1.04 0.42 1.865 1.13% 0.01 0.049 MSCI World Index 27% 1.00 0.27 1.845 2.75% 0.03 0.181 EAFE 28% 0.28 1.799 -0.02% 0.00 -0.008 MSCI USA Index 29.68% 0.30 1.840 5.23% 0.05 0.318

Conclusion: Even though the optimal portfolio worked very well in 2009, the year when it was constructed. However, the superior performance is not guaranteed for the future years. The composition of the optimal portfolio should be continuously re – adjusted over the investment horizon to reap better returns with lower risks.