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

2. 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

3. 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
0.323
Cash & Notes
1.00

4. 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

5. 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

6. 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)

7. 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

8. 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
0.1963
yes
Sweden
60.1%
0.78
0.7072
0.016
0.9933
Singapore
67.2%
0.95
0.6557
0.028
1.6840
South Korea
69.4%
1.31
0.4917
0.119
7.6583
1.9923
Hong Kong
55.2%
1.18
0.4255
0.101
6.4668
2.2872 no
Netherlands
37.8%
1.07
0.3071
0.012
4.3081
U.K.
37.3%
1.1
0.2940
0.025
5.3468
Spain
36.4%
1.2
0.2622
0.020
6.8869
U.S.
24.2%
0.89
0.2158
0.007
9.2515
Switzerland
22.9%
0.93
0.1928
France
27.6%
0.1887
Italy
22.6%
1.06
0.1663
0.041
5.8988
Germany
21.3%
1.12
0.1456
0.021
Ireland
9.9%
1.09
0.0451
0.026
4.1020
Japan
4.4%
0.99
1.5785

9. 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%

10. Optimal Portfolio Optimal Portfolio Zi wi MSCI USD ri SD rf
Weighted ri
Weighted Bi
RVAR
RVOL
Brazil
121.25%
0.537
0.1%
Sweden
60.17%
0.171
Singapore
67.29%
0.217
South Korea
69.42%
0.394
Hong Kong
55.20%
0.361
Total

11. 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

12. Optimal Portfolio Zi wi MSCI USD ri SD rf Weighted ri Weighted Bi SD RVAR RVOL Brazil % % Sweden % % Singapore % % South Korea % % Hong Kong % % Total 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
0.0847
0.3115
Brazil
0.065
1.49
0.0788
0.0969
Sweden
0.78
0.0391
0.0507
Singapore
0.95
0.0437
0.0618
South Korea
1.31
0.0451
0.0852
Hong Kong
1.18
0.0359
0.0767
Netherlands
1.07
0.0246
0.0696
U.K.
1.1
0.0243
0.0715
Spain
1.2
0.0237
0.0780
Switzerland
0.93
0.0149
0.0605
France
0.0180 1
0.4328
1.0402
0.2318

13. 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

14. Comparison of Various Portfolios
2009
2010
Return B
RVOL
RVAR
Templeton
32%
0.97
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

15. 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.