Erlangga NugrahabharataEileen Chu

Templeton Growth Fund facts: Introduced in November 1954 Goal: LT capital appreciation in global

equities Average return : 12.55% since

inception The last 10 years: 3.66%

1. Determine Optimal Portfolio (OP)Identifying countries and weights

Measure performance

2. Determine Optimal Constrained Portfolio (OCP)With Floor and Cap

Summary measures for Templeton- for the year of 2009 rtemp: 8.82 % βtemp: . 98 RVOLtemp: .0886

Market Weight ri σ β ri* β* RVOL

US 0.3548 0.0734 15.5 0.89 0.026054567 0.3158 0.0808

UK 0.1477 0.0843 22.5 1.1 0.012451617 0.1625  

France 0.0899 0.0944 22.6 1.2 0.008489179 0.1079  

Switzerland 0.0672 0.1076 18.5 0.93 0.007229886 0.0625  

Germany 0.0577 0.0953 21.8 1.12 0.005498676 0.0646  

Netherlands 0.0441 0.0955 19.1 1.07 0.004209702 0.0472  

South Korea 0.0372 0.1273 39.4 1.32 0.004735199 0.0491  

Sweden 0.0672 0.1301 24.19 0.78 0.00874272 0.0524  

Italy 0.0277 0.0647 25.4 1.06 0.001792923 0.0294  

Singapore 0.0197 0.1330 29.4 1.17 0.002619471 0.0230  

Japan 0.0182 0.1020 22 0.99 0.00185554 0.0180  

Spain 0.0162 0.0731 22.5 1.2 0.001183612 0.0194  

Hong Kong 0.0086 0.1703 36.1 1.18 0.001464671 0.0101  

Ireland 0.008 0.0127 22.7 1.09 0.000101991 0.0087  

Brazil 0.0059 0.3114 53.7 1.49 0.001837263 0.0088  

Templeton 0.9701       0.088267018 0.9795 0.088585

*rf2009: .0015

1. Calculate RVOL for individual countries (RVOLi)

2. Rank countries based on RVOLi

3. Calculate C* as the cutoff point4. Calculate each countries weights in OP5. Calculate OP performance

Market ri (ri-rf) σ β RVOLiUS 0.0734 0.0719 15.5 0.89 0.0808

UK 0.0843 0.0828 22.5 1.1 0.0753

France 0.0944 0.0929 22.6 1.2 0.0774

Switzerland 0.1076 0.1061 18.5 0.93 0.1141

Germany 0.0953 0.0938 21.8 1.12 0.0837

Netherlands 0.0955 0.0940 19.1 1.07 0.0878

South Korea 0.1273 0.1258 39.4 1.32 0.0953

Sweden 0.1301 0.1286 24.19 0.78 0.1648

Italy 0.0647 0.0632 25.4 1.06 0.0596

Singapore 0.1330 0.1315 29.4 1.17 0.1124

Japan 0.1020 0.1005 22 0.99 0.1015

Spain 0.0731 0.0716 22.5 1.2 0.0596

Hong Kong 0.1703 0.1688 36.1 1.18 0.1431

Ireland 0.0127 0.0112 22.7 1.09 0.0103

Brazil 0.3114 0.3099 53.7 1.49 0.2080

World 0.080611313 0.0791 14.6948 0.9979052 0.0793

Market ri (ri-rf) σ β RVOLiBrazil 0.3114 0.3099 53.7 1.49 0.2080

Sweden 0.1301 0.1286 24.19 0.78 0.1648

Hong Kong 0.1703 0.1688 36.1 1.18 0.1431

Switzerland 0.1076 0.1061 18.5 0.93 0.1141

Singapore 0.1330 0.1315 29.4 1.17 0.1124

Japan 0.1020 0.1005 22 0.99 0.1015

South Korea 0.1273 0.1258 39.4 1.32 0.0953

Netherlands 0.0955 0.0940 19.1 1.07 0.0878

Germany 0.0953 0.0938 21.8 1.12 0.0837

US 0.0734 0.0719 15.5 0.89 0.0808

France 0.0944 0.0929 22.6 1.2 0.0774

UK 0.0843 0.0828 22.5 1.1 0.0753

Italy 0.0647 0.0632 25.4 1.06 0.0596

Spain 0.0731 0.0716 22.5 1.2 0.0596

Ireland 0.0127 0.0112 22.7 1.09 0.0103

Rank RVOL1 Brazil2 Sweden3 Hong Kong4 Switzerland5 Singapore6 Japan7 South Korea8 Netherlands9 Germany10 US11 France12 UK13 Italy14 Spain15 Ireland

C*=CJapan= 0.09594

Market (ri-rf) β RVOL σ σ2εi (ri-rf)βi/σ2

εiσ2mβi/σ2εi Ci

Brazil 0.3114 1.49 0.2080 53.7 2,404.29 0.000193 0.19940 0.03474

Sweden 0.1301 0.78 0.1648 24.19 453.74 0.000224 0.28954 0.06042

Hong Kong 0.1703 1.18 0.1431 36.1 1,002.54 0.000200 0.29991 0.07448

Switzerland 0.1076 0.93 0.1141 18.5 155.48 0.000644 1.20118 0.09104

Singapore 0.1330 1.17 0.1124 29.4 568.76 0.000274 0.51972 0.09438

Japan 0.1020 0.99 0.1015 22 272.36 0.000371 0.77707 0.09594

South Korea 0.1273 1.32 0.0953 39.4 1,176.11 0.000143 0.31991 0.09598

Netherlands 0.0955 1.07 0.0878 19.1 117.58 0.000869 2.10260 0.09386

Germany 0.0953 1.12 0.0837 21.8 204.37 0.000522 1.32543 0.09241

US 0.0734 0.89 0.0808 15.5 69.21 0.000944 2.47156 0.09008

France 0.0944 1.2 0.0774 22.6 199.81 0.000567 1.55625 0.08861

UK 0.0843 1.1 0.0753 22.5 244.96 0.000379 1.06663 0.08764

Italy 0.0647 1.06 0.0596 25.4 402.53 0.000170 0.60276 0.08647

Spain 0.0731 1.2 0.0596 22.5 195.30 0.000449 1.59218 0.08381

Ireland 0.0127 1.09 0.0103 22.7 258.73 0.00005 0.99159 0.07943

Market β σ2εi RVOL C* Zi Wi

Brazil 1.49 2,404.29 0.2080 0.09594 0.000069 0.17119

Sweden 0.78 453.74 0.1648 0.09594 0.000118 0.29196

Hong Kong 1.18 1,002.54 0.1431 0.09594 0.000055 0.13672

Switzerland 0.93 155.48 0.1141 0.09594 0.000108 0.26734

Singapore 1.17 568.76 0.1124 0.09594 0.000034 0.08329

Japan 0.99 272.36 0.1015 0.09594 0.000020 0.04950

0.000406 1.00000

Market Weight% ri (ri-rf) σ β ri* β*Weight RVOLop

Brazil 0.17119 0.3114 0.3099 53.7 1.49 0.0533 0.2551  

Sweden 0.29196 0.1301 0.1286 36.1 1.14 0.0380 0.3328  

Hong Kong 0.13672 0.1703 0.1688 17.1 1.18 0.0233 0.1613  

Switzerland 0.26734 0.1076 0.1061 18.5 0.93 0.0288 0.2486  

Singapore 0.08329 0.1330 0.1315 29.4 1.17 0.0111 0.0974  

Japan 0.04950 0.1020 0.1005 22 0.99 0.0050 0.0490  

OP 1.00000 0.15946 1.1443 0.13804

Summary measures for Optimal Portfolio (OP) rop: 15.94% βop: . 98 RVOLop: .1380

OCPANGGA

OCPCHU

Maximize floor for US Apply cap 6.5% to RVOL-ranked

countries up to US

Floor 35% for US Apply cap 6.5% to RVOL-ranked

countries up to Japan International Diversification (keep all

countries in the portfolio) An Art not Science

Summary measures for Optimal Portfolio (OP) rohu: 10.93% βchu: 1.0316 RVOLchu: .1380

Calculate the performance of OCP chu

Market Weight% ri (ri-rf) β ri* β* RVOL*

US 0.35000 0.0734 0.0719 0.89 0.0257 0.3115

Brazil 0.06500 0.3114 0.3099 1.49 0.0202 0.0969

Sweden 0.06500 0.1703 0.1688 1.18 0.0111 0.0767

Hong Kong 0.06500 0.1076 0.1061 0.78 0.0070 0.0507

Switzerland 0.06500 0.1076 0.1061 0.93 0.0070 0.0605

Singapore 0.06500 0.1330 0.1315 1.17 0.0086 0.0761

Japan 0.06500 0.1020 0.1005 0.99 0.0066 0.0644

South Korea 0.01077 0.1273 0.1258 1.32 0.0014 0.0142

Netherlands 0.06500 0.0955 0.0940 1.07 0.0062 0.0696

Germany 0.04623 0.0953 0.0938 1.12 0.0044 0.0518

France 0.04685 0.0944 0.0929 1.2 0.0044 0.0562

UK 0.03405 0.0843 0.0828 1.1 0.0029 0.0375

Italy 0.01582 0.0647 0.0632 1.06 0.0010 0.0168

Spain 0.03691 0.0731 0.0716 1.2 0.0027 0.0443

Ireland 0.00438 0.0127 0.0112 1.09 0.00006 0.0048

OCPCHU 1       0.1093 1.0316 0.10450

Portfolio rp β RVOL

Temple Growth 0.08827 0.98 0.0886

OP 0.15946 1.14 0.1380

OCP Angga 0.11318 1.04 0.1068

OCP Chu 0.10931 1.03 0.1045

MSCI USA 0.07343 0.89 0.0808

MSCI World 0.08061 1.00 0.0793

Rank rp Beta RVOL

1 OP OP OP

2 OCP Angga OCP Angga OCP Angga

3 OCP Chu OCP Chu OCP Chu

4 Templeton G World Templeton G

5 MSCI World Templeton G MSCI USA

6 MSCI USA MSCI USA MSCI World

Gather 2010 data www.msci.com/products/indices/country_and_regional/all_country/performance.html

Run the out of sample calculation for each country’s return, beta

Use the same weight of 2009 Calculate the portfolio performance

(Templeton, OP, OCP, USA & World)

Index Level : Price

Currency : USD

Date/Country FranceGermany

Netherland

SWITZERLANd UK USA

HONG KONG ITALY JAPAN

SINGAPORE SPAIN

SWEDEN BRAZIL

IRELAND KOREA

AC WORLD

2009-12-31 102.240 101.210 103.730 101.640 102.560 101.900 102.030 101.070 100.700 105.070 97.490 99.070 101.230 105.140 108.330 101.960

2010-1-29 94.680 92.240 100.060 98.240 97.560 98.230 95.310 92.520 102.610 98.720 85.970 96.600 90.110 100.490 103.060 97.500

2010-2-26 92.480 90.180 95.340 100.090 95.620 101.030 98.970 87.350 103.720 99.430 79.500 99.380 94.090 96.540 101.900 98.580

2010-3-31 98.230 98.340 102.140 104.950 100.920 106.920 104.170 93.710 108.060 103.610 82.270 106.240 100.710 103.290 111.340 104.680

2010-4-30 93.160 95.750 100.590 98.840 99.550 108.520 101.190 87.180 107.850 108.850 78.190 109.870 99.360 111.560 117.600 104.660

2010-5-31 79.530 84.260 88.230 87.910 88.270 99.550 94.000 72.830 99.120 98.560 64.280 94.360 88.540 89.430 101.890 94.380

2010-6-30 78.050 84.010 87.630 91.660 86.090 94.100 96.700 71.800 97.100 102.120 63.960 97.070 84.570 82.750 102.830 91.340

2010-7-30 87.650 91.990 97.060 96.070 96.410 100.560 102.310 83.170 100.520 110.140 77.660 108.420 96.150 88.460 110.550 98.670

2010-8-31 82.210 86.530 89.610 98.470 94.020 95.870 103.070 76.980 98.190 108.570 73.160 102.130 92.700 74.820 107.560 95.030

2010-9-30 94.110 98.000 101.380 103.840 102.280 104.420 117.070 85.620 101.910 117.170 80.890 121.050 102.370 79.360 120.310 103.910

2010-10-29 98.900 105.650 103.080 106.210 106.150 108.410 119.500 91.070 103.990 120.960 84.320 121.640 103.640 80.940 122.140 107.590

2010-11-30 87.730 100.280 92.970 102.380 100.600 108.270 121.430 76.530 106.160 118.870 66.540 118.270 98.530 74.320 122.190 105.010

2010-12-31 95.350 107.300 103.080 111.640 107.860 115.330 122.100 83.260 114.150 124.450 72.740 130.050 105.050 84.420 135.720 112.590

Monthly Ri

2010-1-29 -7.394 -8.863 -3.538 -3.345 -4.875 -3.602 -6.586 -8.459 1.897 -6.044 -11.817 -2.493 -10.985 -4.423 -4.865 -4.374

2010-2-26 -2.324 -2.233 -4.717 1.883 -1.989 2.850 3.840 -5.588 1.082 0.719 -7.526 2.878 4.417 -3.931 -1.126 1.108

2010-3-31 6.218 9.049 7.132 4.856 5.543 5.830 5.254 7.281 4.184 4.204 3.484 6.903 7.036 6.992 9.264 6.188

2010-4-30 -5.161 -2.634 -1.518 -5.822 -1.358 1.496 -2.861 -6.968 -0.194 5.057 -4.959 3.417 -1.340 8.007 5.622 -0.019

2010-5-31 -14.631 -12.000 -12.288 -11.058 -11.331 -8.266 -7.105 -16.460 -8.095 -9.453 -17.790 -14.117 -10.890 -19.837 -13.359 -9.822

2010-6-30 -1.861 -0.297 -0.680 4.266 -2.470 -5.475 2.872 -1.414 -2.038 3.612 -0.498 2.872 -4.484 -7.470 0.923 -3.221

2010-7-30 12.300 9.499 10.761 4.811 11.987 6.865 5.801 15.836 3.522 7.854 21.420 11.693 13.693 6.900 7.508 8.025

2010-8-31 -6.207 -5.935 -7.676 2.498 -2.479 -4.664 0.743 -7.443 -2.318 -1.425 -5.794 -5.802 -3.588 -15.419 -2.705 -3.689

2010-9-30 14.475 13.256 13.135 5.453 8.785 8.918 13.583 11.224 3.789 7.921 10.566 18.525 10.431 6.068 11.854 9.344

2010-10-29 5.090 7.806 1.677 2.282 3.784 3.821 2.076 6.365 2.041 3.235 4.240 0.487 1.241 1.991 1.521 3.542

2010-11-30 -11.294 -5.083 -9.808 -3.606 -5.228 -0.129 1.615 -15.966 2.087 -1.728 -21.086 -2.770 -4.931 -8.179 0.041 -2.398

2010-12-31 8.686 7.000 10.874 9.045 7.217 6.521 0.552 8.794 7.526 4.694 9.318 9.960 6.617 13.590 11.073 7.218

r T = (V t+T -Vt) / Vt

2009 2010

Market Weight ri β Market Weight ri β

US 0.3548 0.073 0.89 US 0.3548 0.075 0.91 *

UK 0.1477 0.084 1.1 UK 0.1477 0.084 1.13

France 0.0899 0.094 1.2 France 0.0899 0.092 1.24

Switzerland 0.0672 0.108 0.93 Switzerland 0.0672 0.108 0.94

Germany 0.0577 0.095 1.12 Germany 0.0577 0.095 1.16

Netherlands 0.0441 0.095 1.07 Netherlands 0.0441 0.094 1.10

South Korea 0.0372 0.127 1.32 South Korea 0.0372 0.133 1.35 *

Sweden 0.0672 0.130 1.14 Sweden 0.0672 0.135 1.17 *

Italy 0.0277 0.065 1.06 Italy 0.0277 0.060 1.11

Singapore 0.0197 0.133 1.17 Singapore 0.0197 0.134 1.18 *

Japan 0.0182 0.102 0.99 Japan 0.0182 0.103 0.99 *

Spain 0.0162 0.073 1.2 Spain 0.0162 0.066 1.06

Hong Kong 0.0086 0.170 1.18 Hong Kong 0.0086 0.171 1.19 *

Ireland 0.008 0.013 1.09 Ireland 0.008 0.005 1.15

Brazil 0.0059 0.311 1.49 Brazil 0.0059 0.301 1.52

World   0.08061 1.00 World   0.0815 1.02

Market Weight ri β ri* β* RVOLUS,2010

US 0.3548 0.075 0.91 0.0266 0.3222 0.0812

UK 0.1477 0.084 1.13 0.0124 0.1662  

France 0.0899 0.092 1.24 0.0082 0.1112  

Switzerland 0.0672 0.108 0.94 0.0072 0.0632  

Germany 0.0577 0.095 1.16 0.0055 0.0667  

Netherlands 0.0441 0.094 1.10 0.0041 0.0486  

South Korea 0.0372 0.133 1.35 0.0049 0.0501  

Sweden 0.0672 0.135 1.17 0.0090 0.0788  

Italy 0.0277 0.060 1.11 0.0017 0.0307  

Singapore 0.0197 0.134 1.18 0.0026 0.0232  

Japan 0.0182 0.103 0.99 0.0019 0.0180  

Spain 0.0162 0.066 1.06 0.0011 0.0171  

Hong Kong 0.0086 0.171 1.19 0.0015 0.0102  

Ireland 0.008 0.005 1.15 0.0000 0.0092  

Brazil 0.0059 0.301 1.52 0.0018 0.0090  

Templeton 0.9701     0.0887 1.0244 0.0853

 

World   0.0815 1.02 0.0788

Summary measures for Optimal Portfolio

rtemp: 8.87%

βtemp: 1.0244

RVOLtemp: .0853

Market Weight% ri β ri* β* RVOLop,2010

Brazil 0.17119 0.301 1.52 0.0515274 0.2605  

Sweden 0.29196 0.135 1.17 0.039299 0.3422  

Hong Kong 0.13672 0.171 1.19 0.0233771 0.1623  

Switzerland 0.26734 0.108 0.94 0.0287952 0.2516  

Singapore 0.08329 0.134 1.18 0.0111836 0.0980  

Japan 0.04950 0.103 0.99 0.0050869 0.0490  

1.00000 0.1593 1.1636 0.1357

Summary measures for Optimal Portfolio

rop: 15.93%

βop: 1.1636

RVOLop: .1357

Market Weight% ri β ri* β* RVOLocp1,2010

US 0.3500 0.075 0.91 0.0263 0.3178  

Brazil 0.0650 0.301 1.52 0.0196 0.0989  

Sweden 0.0650 0.135 1.17 0.0087 0.0762  

Hong Kong 0.0650 0.171 1.19 0.0111 0.0772  

Switzerland 0.0650 0.108 0.94 0.0070 0.0612  

Singapore 0.0650 0.134 1.18 0.0087 0.0765  

Japan 0.0650 0.103 0.99 0.0067 0.0643  

South Korea 0.0108 0.133 1.35 0.0014 0.0145  

Netherlands 0.0650 0.094 1.10 0.0061 0.0717  

Germany 0.0462 0.095 1.16 0.0044 0.0534  

France 0.0468 0.092 1.24 0.0043 0.0579  

UK 0.0340 0.084 1.13 0.0029 0.0383  

Italy 0.0158 0.060 1.11 0.0009 0.0176  

Spain 0.0369 0.066 1.06 0.0024 0.0390  

Ireland 0.0044 0.005 1.15 0.0000 0.0051  

1.0000 0.1106 1.0695 0.1022

Summary measures for Optimal Portfolio

rchu: 11.06%

βchu: 1.0695

RVOLchu: .1022

Market Weight% ri β ri* β* RVOLocp2,2010

US 0.415 0.075 0.91 0.0312 0.3768  

Brazil 0.065 0.301 1.52 0.0196 0.0989  

Sweden 0.065 0.135 1.17 0.0087 0.0762  

Hong Kong 0.065 0.171 1.19 0.0111 0.0772  

Switzerland 0.065 0.108 0.94 0.0070 0.0612  

Singapore 0.065 0.134 1.18 0.0087 0.0765  

Japan 0.065 0.103 0.99 0.0067 0.0643  

South Korea 0.065 0.133 1.35 0.0086 0.0876  

Netherlands 0.065 0.094 1.10 0.0061 0.0717  

Germany 0.065 0.095 1.16 0.0062 0.0751  

1.0000 0.1139 1.0654 0.1057

Summary measures for Optimal Portfolio

rangga: 11.39%

βangga: 1.0654

RVOLangga: .1057

Portfoli o rp β RVOLp,2010

Temple Growth 0.0887 1.024 0.0853OP 0.1593 1.164 0.1357

OCP Chu 0.1106 1.069 0.1022OCP Angga 0.1139 1.065 0.1057MSCI USA 0.0751 0.908 0.0812

MSCI World 0.0815 1.018 0.0788

Rank rp Beta RVOL1 OP OP OP2 OCP Angga OCP Chu OCP Angga3 OCP Chu OCP Angga OCP Chu4 Templeton G Templeton G Templeton G5 MSCI World MSCI World MSCI USA6 MSCI USA MSCI USA MSCI World

Op performs the best.

2009 2010

Portfolio rp β RVOLp,2009 Portfolio rp β RVOLp,2010

Temple Growth 0.0883 0.97 0.0896

Temple Growth 0.0887 1.024 0.0853

OP 0.1595 1.14 0.1380 OP 0.1593 1.16 0.1357

OCP Chu 0.1093 1.03 0.1045 OCP Chu 0.1106 1.069 0.1022

OCP Angga 0.1117 1.02 0.1078 OCP Angga 0.1139 1.065 0.1057

MSCI USA 0.0734 0.89 0.0808 MSCI USA 0.0751 0.91 0.0812

MSCI World 0.0806 0.01 0.0054 MSCI World 0.0815 1.018 0.0788

   

Rank rp Beta RVOL Rank rp Beta RVOL

1 OP OP OP 1 OP OP OP

2 OCP A OCP A OCP A 2 OCP A OCP C OCP A

3 OCP C OCP C OCP C 3 OCP C OCP A OCP C

4 Templeton G World Templeton G 4 Templeton G Templeton G Templeton G

5 World Templeton G USA 5 World World USA

6 USA USA World 6 USA USA World