Case 3:Templeton Growth Fund

Presented By: Zhu Zhu Mehmet Can

AssignmentAnalyze 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 OPweight 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 6.72% 60.2% 0.67 17.1% 0.78 3.516 0.771

Italy 2.77% 22.6% 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 22.5% 1.2 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% 0.73 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 99.000.31546375

7 0.1951742 0.974771 1.6137571 0.323

Cash & Notes 1.00

Constructing the OPRVAR RANK RVOL RANK

3.516Sweden 0.813Brazil

3.099Singapore 0.771Sweden

2.257Brazil 0.708Singapore

1.980Netherlands 0.530South Korea

1.761South Korea 0.467Hong Kong

1.657U.K. 0.353Netherlands

1.618Spain 0.339U.K.

1.558U.S. 0.303Spain

1.528Hong Kong 0.271U.S.

1.237Switzerland 0.246Switzerland

1.221France 0.230France

0.975Germany 0.213Italy

0.434Ireland 0.190Germany

0.199Japan 0.090Ireland

-0.318Italy 0.044Japan

Driving the OP

Portfolio Variance:sp

2 = bp2sm

2 + sep2

= (Sjwjbj)2sm2 + Sjwj

2sej2

Reward to Market VolatilityRVOL = (ri – rf) / bri = country returnrf = risk free returnbi = Systematic risk

Driving the OPUnsystematic Risk:

sei2 = si2 - bi2sm2 where

si2 = Variance of country returnsm

2 = Variance of market indexbi = Systematic risk

Cut off ratio:Ci = Cnum / Cden

Cnum = sm2Sj=1

i(rj – rf) / (bj / sej2)Cden = 1 + sm

2 Sj=1i (bj

2 / sej2)

Driving the OPModern Portfolio Theory and Investment

AnalysisRanks assets according to RVOL from

highest to LowestThe 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 wWhere: 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 7.4921 0.1963 0.13349yes

Sweden 60.1% 0.78 0.7072 0.016 28.8158 0.796975 36.3079 0.9933 0.38827yes

Singapore 67.2% 0.95 0.6557 0.028 22.9370 0.690728 59.2449 1.6840 0.47051yes

South Korea 69.4% 1.31 0.4917 0.119 7.6583 0.308290 66.9032 1.9923 0.47659yes

Hong Kong 55.2% 1.18 0.4255 0.101 6.4668 0.294915 73.3700 2.2872 0.47577no

Netherlands 37.8% 1.07 0.3071 0.012 33.5027 2.020873 106.8727 4.3081 0.42917no

U.K. 37.3% 1.1 0.2940 0.025 16.5189 1.038648 123.3916 5.3468 0.41442no

Spain 36.4% 1.2 0.2622 0.020 21.9226 1.540146 145.3142 6.8869 0.39274no

U.S. 24.2% 0.89 0.2158 0.007 30.1040 2.364565 175.4182 9.2515 0.36475no

Switzerland 22.9% 0.93 0.1928 0.016 13.4754 1.167677 188.8936 10.4191 0.35261no

France 27.6% 1.2 0.1887 0.020 16.2469 1.506064 205.1405 11.9252 0.33831no

Italy 22.6% 1.06 0.1663 0.041 5.8988 0.590422 211.0393 12.5156 0.33284no

Germany 21.3% 1.12 0.1456 0.021 11.4557 1.286434 222.4949 13.8021 0.32041no

Ireland 9.9% 1.09 0.0451 0.026 4.1020 0.966496 226.5970 14.7686 0.30631no

Japan 4.4% 0.99 -0.0057 0.028 1.5785 0.759476228.1754

51 15.5280 0.29428no

Constructing the OPCalculation 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 PortfolioOptimal Portfolio

Zi wi MSCI USD ri SD rf Weighted ri Weighted Bi SD 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 0.1% 0.01218 0.01579 0.00346

Singapore 0.19890 0.10953 67.29% 0.217 0.1% 0.07371 0.10405 0.02377

South Korea 0.01140 0.00628 69.42% 0.394 0.1% 0.00436 0.00822 0.00247

Hong Kong 0.00000 55.20% 0.361 0.1% 0.00000 0.00000 0.00000

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

Ziwi MSCI USD riSD rfWeighted riWeighted BiSDRVARRVOLBrazil 1.5689010160.863943659121.25%0.5370.1%1.0475672921.28727610.4639377

Sweden0.0367701630.02024815460.17%0.1710.1%0.0121823910.01579360.0034624

Singapore 0.1989049690.10953061167.29%0.2170.1%0.0737084460.10405410.0237681

South Korea0.0113999280.00627757669.42%0.3940.1%0.0043576780.00822360.0024734

Hong Kong 0

55.20%0.3610.1%000

Total

1

1.1378158071.41534730.49364172.303930.80356

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 0.065 0.78 0.60165439 0.0391 0.0507 0.011115

Singapore 0.065 0.95 0.67294837 0.0437 0.0618 0.014105

South Korea 0.065 1.31 0.694165782 0.0451 0.0852 0.02561

Hong Kong 0.065 1.18 0.552042433 0.0359 0.0767 0.023465

Netherlands 0.065 1.07 0.378620829 0.0246 0.0696 0.012415

U.K. 0.065 1.1 0.373415986 0.0243 0.0715 0.014625

Spain 0.065 1.2 0.364596483 0.0237 0.0780 0.014625

Switzerland 0.065 0.93 0.229274561 0.0149 0.0605 0.012025

France 0.065 1.2 0.27643982 0.0180 0.0780 0.01469

1 0.4328 1.0402 1.864860278 0.4156425 0.2318

Comparison of Various PortfoliosPortfolios 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     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   Optimal 6.67% 0.79 0.08 0.382

Constrained Optimal 43% 1.04 0.42 1.865  

Constrained Optimal 1.13% 1.04 0.01 0.049

MSCI World Index 27% 1.00 0.27 1.845   MSCI World Index 2.75% 1.00 0.03 0.181

EAFE 28% 1.00 0.28 1.799   EAFE -0.02% 1.00 0.00 -0.008

MSCI USA Index 29.68% 1.00 0.30 1.840   MSCI USA Index 5.23% 1.00 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.