Investment Analysis: Portfolio Optimization and Risk Management

This assignment analyzes investment strategies and portfolio optimization across multiple countries. Part 1 focuses on a five-country portfolio, calculating the global minimum variance portfolio (MVS) and an efficient portfolio with a target return. Part 2 expands the analysis to a ten-country portfolio, computing MVS and an efficient portfolio, and comparing risk reduction. Part 3 introduces a risk-free asset, calculating the tangent portfolio and Sharpe Ratio. Finally, Part 4 considers MVS with short sales constraints, determining portfolio weights and the range of expected returns where the short sales constraint is not binding. The analysis includes expected returns, variance-covariance matrices, and parameter calculations to evaluate portfolio performance and risk.

25503 Investment Analysis
Assignment—Part I
Autumn 2018

Part 1:
The vector of expected return of five countries is as follow:
Australia -0.005224061
New Zealand 0.034752496
Canada 0.005008164
United Kingdom 0.007547769
Japan 0.091924797
The variance covariance matrix is as mentioned below:
Australia
New
Zealand Canada
United
Kingdom Japan
Australia 0.000635137 0.00033103 0.000385666 0.00041008
0.00029
5
New Zealand 0.00033103
0.00049466
2 0.000218994
0.00020507
1
0.00020
3
Canada 0.000385666
0.00021899
4 0.000510277
0.00040375
6
0.00023
8
United Kingdom 0.00041008
0.00020507
1 0.000403756 0.00054732
0.00028
8
Japan 0.000294866
0.00020263
3 0.00023771
0.00028807
7
0.00049
3
It has seen that among these five countries, New Zealand and Japan indices are efficient ones and
they dominates indices of Australia, Canada and United Kingdom.
The parameters A, B, C and ∆ are as follows:
Australia
New
Zealand Canada
United
Kingdom Japan
Australia 0.00063758
0.00056267
2 0.000571484
0.00059186
4
0.00056
2
New Zealand 0.000562672
0.00049656
4 0.000504341
0.00052232
7
0.00049
6
Canada 0.000571484
0.00050434
1 0.000512239
0.00053050
7
0.00050
3
United Kingdom 0.000591864
0.00052232
7 0.000530507
0.00054942
5
0.00052
1
Japan 0.000561733
0.00049573
6 0.000503499
0.00052145
5
0.00049
5
Australia
New
Zealand Canada
United
Kingdom Japan
Australia 1.0 0.58831744 0.674850958
0.69286210
5
0.52492
2
New Zealand 0.58831744 1.0 0.434217585
0.39261162
3
0.40875
3
Canada 0.674850958 0.43421758 1.0 0.76107658 0.47211

5 2 5
United Kingdom 0.692862105
0.39261162
3 0.761076582 1.0
0.55244
8
Japan 0.524921576
0.40875267
5 0.472115171
0.55244846
1 1.0
MVS Portfolio:
10.000% 20.000% 30.000% 40.000% 50.000% 60.000% 70.000%
-5.000%
0.000%
5.000%
10.000%
15.000%
20.000%
25.000%
30.000%
35.000%
40.000%
45.000%
MVP
MVS
MVS MVP Australia
New Zealand Canada United Kingdom
Japan
Global minimum variance portfolio weights, return and standard deviation
Country Weight
Australia -12.45%
New Zealand 39.58%
Canada 26.29%
United Kingdom 14.05%
Japan 32.54%
Expected Port Return 4.669%
Annual Port Variance 12.63%
Stdev 36%
Portfolio weights with 14% return
Country Weight
Australia -66.14%
New Zealand 46.01%
Canada 6.03%
United Kingdom -18.20%
Japan 132.31%

Part 2:
Vector of expected return:
Australia -0.00522
New Zealand
0.03475
2
Canada
0.00500
8
United Kingdom
0.00754
8
Japan
0.09192
5
United States
0.11757
5
India
0.05064
7
China
0.08818
8
South Africa -0.01114
Malaysia -0.05399

Variance covariance matrix
Australia
New
Zealand Canada
United
Kingdom Japan
United
States India China South Africa Malaysia
Australia 0.000635 0.00033103 0.000386 0.00041008 0.000294866 0.000197716 0.000322 0.000384 0.000559202 0.000285
New
Zealand 0.000331 0.000494662 0.000219 0.000205071 0.000202633 0.000122285 0.000208 0.000191 0.000304678 0.000179
Canada 0.000386 0.000218994 0.00051 0.000403756 0.00023771 0.00025336 0.000218 0.000312 0.000520275 0.00022
United
Kingdom 0.00041 0.000205071 0.000404 0.00054732 0.000288077 0.00024552 0.000293 0.000363 0.00057759 0.000246
Japan 0.000295 0.000202633 0.000238 0.000288077 0.000493012 0.000168795 0.000258 0.000278 0.000338082 0.000173
United
States 0.000198 0.000122285 0.000253 0.00024552 0.000168795 0.000240463 0.000156 0.000205 0.000272748 0.000124
India 0.000322 0.000208257 0.000218 0.000292706 0.000257568 0.000156222 0.000712 0.000378 0.00044806 0.000272
China 0.000384 0.000190929 0.000312 0.000363499 0.00027815 0.000204764 0.000378 0.000735 0.0005353 0.000274
South
Africa 0.000559 0.000304678 0.00052 0.00057759 0.000338082 0.000272748 0.000448 0.000535 0.00119985 0.000437
Malaysia 0.000285 0.000179128 0.00022 0.000246156 0.000173453 0.000124125 0.000272 0.000274 0.000437431 0.00043
The parameters A, B, C and ∆ are as follows:
Australi
a
New
Zealand Canada
United
Kingdom Japan
United
States India China
South
Africa Malaysia
Australia 0.000638
0.00056267
2
0.00057
1
0.00059186
4
0.00056173
3
0.00039230
6
0.00067
5 0.000686
0.00087632
3 0.000525
New Zealand 0.000563
0.00049656
4
0.00050
4
0.00052232
7
0.00049573
6
0.00034621
4
0.00059
6 0.000605
0.00077336
6 0.000463
Canada 0.000571
0.00050434
1
0.00051
2
0.00053050
7
0.00050349
9
0.00035163
6
0.00060
5 0.000615
0.00078547
7 0.00047
United
Kingdom 0.000592
0.00052232
7
0.00053
1
0.00054942
5
0.00052145
5
0.00036417
6
0.00062
7 0.000637
0.00081348
8 0.000487
Japan 0.000562
0.00049573
6
0.00050
3
0.00052145
5
0.00049490
8
0.00034563
7
0.00059
5 0.000604
0.00077207
5 0.000462
United States 0.000392
0.00034621
4
0.00035
2
0.00036417
6
0.00034563
7
0.00024138
8
0.00041
5 0.000422
0.00053920
6 0.000323
India 0.000675
0.00059569
4
0.00060
5
0.00062659
9 0.0005947 0.00041533
0.00071
5 0.000726
0.00092775
3 0.000556
China 0.000686
0.00060529
7
0.00061
5 0.0006367
0.00060428
7
0.00042202
5
0.00072
6 0.000738
0.00094270
9 0.000564
South Africa 0.000876
0.00077336
6
0.00078
5
0.00081348
8
0.00077207
5
0.00053920
6
0.00092
8 0.000943
0.00120446
5 0.000721
Malaysia 0.000525
0.00046308
4 0.00047
0.00048710
9
0.00046231
1
0.00032287
1
0.00055
6 0.000564
0.00072122
2 0.000432

Australi
a
New
Zealand Canada
United
Kingdom Japan
United
States India China
South
Africa Malaysia
Australia 1.00 0.58831744
0.67485
1
0.69286210
5
0.52492157
6
0.50398483
7
0.47685
8 0.559695
0.63812249
8 0.542937
New Zealand 0.588317 1.00
0.43421
8
0.39261162
3
0.40875267
5
0.35320693
5
0.34960
4 0.315431
0.39396357
5 0.386816
Canada 0.674851
0.43421758
5 1.00
0.76107658
2
0.47211517
1
0.72051550
4 0.36075 0.506703
0.66236843
3 0.468094
United
Kingdom 0.692862
0.39261162
3
0.76107
7 1.00
0.55244846
1
0.67417761
9
0.46713
4 0.570911 0.71001673 0.50534
Japan 0.524922
0.40875267
5
0.47211
5
0.55244846
1 1.00
0.48835868
1
0.43310
7 0.460295
0.43788714
2 0.375186
United States 0.503985
0.35320693
5
0.72051
6
0.67417761
9
0.48835868
1 1.00 0.37614 0.485194
0.50583324
5 0.384442
India 0.476858
0.34960417
9 0.36075
0.46713391
9
0.43310653
2
0.37613992
1 1.00 0.520502
0.48295213
8 0.48932
China 0.559695
0.31543075
8
0.50670
3
0.57091145
4
0.46029490
2
0.48519366
3
0.52050
2 1.00
0.56783138
6 0.486232
South Africa 0.638122
0.39396357
5
0.66236
8 0.71001673
0.43788714
2
0.50583324
5
0.48295
2 0.567831 1.00 0.606514
Malaysia 0.542937
0.38681588
7
0.46809
4
0.50534017
5 0.37518608
0.38444198
6 0.48932 0.486232
0.60651374
2 1.00
MVS for expected return

8.000% 10.000% 12.000% 14.000% 16.000% 18.000% 20.000% 22.000% 24.000% 26.000%
-20.000%
-10.000%
0.000%
10.000%
20.000%
30.000%
40.000%
50.000%
MVP
MVS
MVP MVP Australia New Zealand
Canada United Kingdom Japan United States
India China South Africa Malaysia
Minimum Variance portfolio
Country Weight
Australia -4.82%
New Zealand 17.86%
Canada -5.62%
United Kingdom -2.79%
Japan 9.19%
United States 67.23%
India 3.49%
China 0.56%
South Africa -14.15%
Malaysia 29.03%
Expected Port Return 8.163%
Annual Port Variance 9.47%
Stdev
0.30773
9

Efficient portfolio with 14% return
Country Weight
Australia -5.65%
New Zealand 17.32%
Canada -21.87%
United Kingdom -14.73%
Japan 14.34%
United States 100.39%
India 3.96%
China 6.99%
South Africa -9.11%
Malaysia 8.35%
Expected Port Return 14.000%
Annual Port Variance 10.23%
Stdev
0.31976
6
Reduction of risk:
5 countries portfolio risk 19.49%
10 countries portfolio risk 10.23%
Risk Reduction 9.26%
Part 3:
MVS with risk free asset

0.000% 5.000% 10.000% 15.000% 20.000% 25.000% 30.000%
-20.000%
-10.000%
0.000%
10.000%
20.000%
30.000%
40.000%
50.000%
MVP
MVS
MVP MVP Australia New Zealand
Canada United Kingdom Japan United States
India China South Africa Malaysia
Tangent Portfolio
Tangent portfolio
Country Weight Weekly Avg
Australia -5.65% -0.52%
New Zealand 17.32% 3.48%
Canada -21.87% 0.50%
United Kingdom -14.73% 0.75%
Japan 14.34% 9.19%
United States 100.39% 11.76%
India 3.96% 5.06%
China 6.99% 8.82%
South Africa -9.11% -1.11%
Malaysia 8.35% -5.40%
Expected Port Return 14.000% 1%
Annual Port Varience 10.23%
Sharpe Ratio 0.406547
Linear Combo of two
EFF portfolios
Weight in rF 50.000%

Mean 7.5000%
Stdev 5.113%
Reduction of risk:
10 countries portfolio risk 10.23%
Risk free adjusted
portfolio 5.11%
Risk Reduction 5.12%
Part 4:
MVS with short sale
8.000% 10.000% 12.000% 14.000% 16.000% 18.000% 20.000% 22.000% 24.000% 26.000%
-10.000%
-5.000%
0.000%
5.000%
10.000%
15.000%
MVP
MVS
MVP MVP Australia New Zealand
Canada United Kingdom Japan United States
India China South Africa Malaysia
Portfolio weights
Country Weight
Australia 0.00%
New Zealand 15.20%

Canada 0.00%
United Kingdom 0.00%
Japan 6.16%
United States 58.88%
India 0.47%
China 0.00%
South Africa 0.00%
Malaysia 19.29%
Range of expected returns for which the short sales constraint is not binding:
The portfolio with short sale has shown that, if return is less than -5.399% or above 11.758% then it can be said that the LP will be unbounded.