portsolver by ju5Vkd41

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									                                                      Example


Use solver under tools
Data: international portfolio 1980-1993, Clarke and Kritzman
Country/Asset       Average SD                       rate
                                           risk-free Sharpe Excess Ret
sp                           12      4.513     5.00       1.55  7.00   144
agg bond                       8     1.107     5.00       2.71  3.00    96
hy                           10      1.852     5.00       2.70  5.00   120
int                            4     4.241     5.00      -0.24 -1.00    48
reit                         14      3.931     5.00       2.29  9.00   168
t-bill                         5    0.1548     5.00       0.00  0.00    60

Correlation matrix
                 sp            agg bond hy           int           reit           t-bill
sp                         1      -0.028     0.49          0.807     0.254 0.072
agg bond              -0.028            1   0.116          -0.21     0.042 0.151
hy                      0.49        0.116        1         0.494     0.337 -0.14
int                   0.807         -0.21   0.494             1      0.229 0.037
reit                  0.254         0.042    0.337         0.229         1 -0.08
t-bill                0.072         0.151   -0.139         0.037          -0.08            1

Covariance Matrix
                sp             agg bond hy       int       reit       t-bill
sp                    20.37         -0.14   4.10     15.45       4.51     0.05
agg bond              -0.14          1.23   0.24     -0.99       0.18     0.03
hy                     4.10          0.24   3.43      3.88       2.45 -0.04
int                   15.45         -0.99   3.88     17.99       3.82     0.02
reit                   4.51          0.18   2.45      3.82    15.45 -0.05
t-bill                 0.05          0.03  -0.04      0.02      -0.05     0.02

                             Var Columns
                  Pf weights sp        agg bondhy                  int            reit          t-bill
sp                    0.0085      0.00    0.00              0.00          0.00           0.00        0.00
agg bond              0.1628      0.00    0.03              0.00          0.00           0.00        0.00
hy                    0.0754      0.00    0.00              0.02          0.00           0.00        0.00
int                   0.0123      0.00    0.00              0.00          0.00           0.00        0.00
reit                  0.0047      0.00    0.00              0.00          0.00           0.00        0.00
t-bill                0.7364      0.00    0.00              0.00          0.00           0.00        0.01

Variance                0.09      0.01        0.04          0.03          0.01           0.00       0.01
Mean              5.9543033
St dev                 0.303 0.091964
Sum wts                 1.00
Try Mean                   1




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                                               Example


Data
Date         SP500       Agg Bond     High Yld      MSCINUS      Reit            3tbill
   1/31/1986        0.56         0.56             1       0.066            2.6            0.602
   2/28/1986        7.48         3.94           4.2        4.16           2.93               0.6
   3/31/1986        5.58         3.11           3.4      14.093           5.48            0.563
   4/30/1986       -1.13         0.53          1.93       0.362          -0.44            0.517
   5/30/1986        5.32        -1.91          1.36       0.048            0.1            0.523
   6/30/1986        1.69         2.62           0.5       1.115           4.64             0.53
   7/31/1986       -5.59         0.89         -1.95          1.6         -0.85            0.497
   8/29/1986        7.42         2.49           1.7       9.108           5.13            0.475
   9/30/1986       -8.27        -0.99           0.8      -0.762          -3.49            0.442
 10/31/1986        5.761         1.45          1.94      -2.661           3.52            0.442
 11/28/1986        2.438          1.4         -0.39       3.335          -0.48            0.455
 12/31/1986         -2.55         0.38         0.27        3.495         -0.54            0.468
   1/30/1987        13.47         1.41         4.13        6.821         3.88             0.465
   2/27/1987         3.95         0.69         1.28        2.163         4.48             0.477
  3/31/1987          2.89        -0.45         0.59        4.543         -0.67            0.474
  4/30/1987         -0.89        -2.74           -3        6.969         -2.08            0.492
  5/29/1987          0.87        -0.39        -0.36        1.737         -1.43            0.491
  6/30/1987          5.05         1.38         1.97       -1.719          3.89            0.485
  7/31/1987          5.07        -0.08         1.01         2.04         -0.42            0.493
  8/31/1987          3.73        -0.54         1.03         2.99         -1.43            0.512
  9/30/1987         -2.19        -2.13        -2.45        0.402         -1.38             0.54
 10/30/1987        -21.54         3.56        -3.83       -18.77        -15.86            0.547
 11/30/1987         -8.24          0.8         3.87       -3.932          2.32            0.496
 12/31/1987          7.61         1.36         2.46       -3.229          3.68            0.495
  1/29/1988          4.21         3.52         3.42        6.413          5.96            0.503
  2/29/1988          4.66         1.19         2.89        6.843          4.33            0.485
  3/31/1988         -3.09        -0.94        -0.68        2.561          0.44            0.485
  4/29/1988          1.11        -0.54         0.71        1.807          0.49            0.505
  5/31/1988          0.87        -0.67          0.5       -2.594          -0.6            0.535
  6/30/1988          4.59         2.41         2.12        3.573          4.71            0.555
  7/29/1988         -0.38        -0.52         1.14        2.764          1.57            0.575
  8/31/1988          -3.4         0.26        -0.29       -4.364         -0.47               0.6
  9/30/1988          4.26         2.26         0.91        3.142          0.03            0.618
 10/31/1988          2.78         1.88         1.37        1.723         -0.02            0.628
 11/30/1988         -1.43        -1.21         0.22        2.828         -1.41            0.657
 12/30/1988          1.75         0.11         0.64        2.732          1.49            0.693
  1/31/1989          7.32         1.44         2.01        5.432          1.32             0.71
  2/28/1989         -2.49        -0.72         0.46       -1.308         -1.21            0.727
  3/31/1989          2.33         0.43        -0.72        1.872          0.58            0.757
  4/28/1989          5.19         2.09        -0.24        1.049          1.56            0.746
  5/31/1989          4.05         2.63         2.38        1.126          2.05             0.72
  6/30/1989         -0.57         3.04         1.44       -1.783          0.44            0.704
  7/31/1989          9.03         2.13         0.22        7.045           3.2            0.678
  8/31/1989          1.96        -1.48        -0.01         0.33         -0.27            0.677
  9/29/1989         -0.41         0.51        -2.27        0.894         -0.43            0.661
 10/31/1989         -2.32         2.46        -2.51       -2.734         -3.84             0.65
 11/30/1989          2.04         0.95          0.2        4.401          -0.1            0.655
 12/29/1989           2.4         0.27        -0.45        2.558         -0.44            0.654
  1/31/1990         -6.71        -1.19        -3.52       -4.344         -3.82            0.654


                                                Page 6
                               Example


 2/28/1990     1.29     0.32   -1.85     -5.288   -1.68   0.664
 3/30/1990     2.65     0.07    2.88     -7.012   -0.11   0.674
 4/30/1990      -2.5   -0.92    0.42     -1.371    -2.1   0.666
 5/31/1990     9.75     2.96    2.08      8.422   -1.65   0.666
 6/29/1990    -0.68      1.6    3.15     -2.356    1.18   0.663
 7/31/1990    -0.32     1.38    3.23     -2.588   -2.54   0.656
 8/31/1990    -9.04    -1.33   -4.62     -11.01   -8.99   0.637
 9/28/1990    -4.87     0.83   -7.62     -15.25   -8.13   0.631
10/31/1990    -0.43     1.27   -2.52      9.855   -4.39   0.615
11/30/1990     6.46     2.15    2.01     -4.587    6.76   0.605
12/31/1990     2.79     1.56    0.48      2.665    0.02   0.582
 1/31/1991     4.36     1.24    2.74      0.733    9.48   0.538
 2/28/1991     7.15     0.85    8.62     11.755    3.88   0.508
 3/28/1991     2.42     0.69     6.2      0.964    9.04   0.504
 4/30/1991     0.24     1.08    4.15       0.38    0.39   0.484
 5/31/1991     4.32     0.58     0.5      1.561    0.74    0.47
 6/28/1991    -4.58    -0.05    2.62     -5.371   -3.03   0.478
 7/31/1991     4.66     1.39    3.38      3.013      -1   0.476
 8/30/1991     2.37     2.16    1.82     -2.407   -1.41    0.46
 9/30/1991    -1.67     2.03    2.27      1.631    1.55   0.448
10/31/1991     1.34     1.11    3.31      1.247   -1.58   0.429
11/29/1991    -4.03     0.92     0.8      -5.94   -0.34   0.392
12/31/1991    11.44     2.97    0.73      0.174    4.74   0.351
 1/31/1992    -1.86    -1.36    4.07      0.341    4.95   0.327
 2/28/1992       1.3    0.65    2.43     -1.514    0.23   0.327
 3/31/1992    -1.95    -0.56    1.49     -5.155   -0.84   0.345
 4/30/1992     2.94     0.72    0.09      0.113   -0.77   0.324
 5/29/1992     0.49     1.89    1.36      2.834     1.2   0.311
 6/30/1992    -1.49     1.38    0.99     -7.379   -2.23   0.315
 7/31/1992     4.09     2.04    1.54     -3.391    3.31   0.279
 8/31/1992    -2.05     1.01    1.38      2.363    0.58   0.267
 9/30/1992     1.18     1.19    0.65     -0.836    3.55   0.252
10/30/1992    0.343    -1.33   -1.04      0.925   -0.03   0.241
11/30/1992    3.396     0.02     1.5      3.226    1.98   0.267
12/31/1992    1.227     1.59    1.13      0.781    2.62   0.276
 1/29/1993    0.835     1.92    2.73      0.064    6.66    0.26
 2/26/1993    1.362     1.75    1.98      2.272    6.51    0.25
 3/31/1993    2.109     0.42    2.11       5.46     6.9   0.252
 4/30/1993   -2.417      0.7    0.57      5.847   -6.03   0.245
 5/28/1993    2.668     0.13    1.46      1.331   -1.84   0.251
 6/30/1993    0.292     1.81    1.81     -0.912    3.79   0.263
 7/30/1993   -0.403     0.57    1.04       4.12    1.08   0.259
 8/31/1993    3.786     1.75    0.85      4.287    2.36   0.259
 9/30/1993   -0.767     0.27    0.57     -2.691    4.01   0.251
10/29/1993    2.067     0.37    1.83      5.083   -2.82   0.258
11/30/1993   -0.953    -0.85    1.26     -7.836    -5.1   0.265
12/31/1993    1.209     0.54    1.26       8.31    0.06   0.262
 1/31/1994    3.397     1.35    1.78      6.675    2.42   0.256
 2/28/1994   -2.712    -1.74    0.15     -2.747    4.44   0.273
 3/31/1994   -4.351    -2.46   -2.94     -5.443   -4.06   0.299
 4/29/1994    1.281     -0.8   -1.34      2.743    1.37   0.318
 5/31/1994    1.635    -0.01    0.57       0.46    2.07   0.357


                                Page 7
                               Example


 6/30/1994   -2.447    -0.22   -0.67     -2.735       -2   0.356
 7/29/1994    3.281     1.99    0.47      1.679   -0.55    0.374
 8/31/1994     4.09     0.12    0.72      2.105    0.02    0.383
 9/30/1994   -2.443    -1.47     0.4      -4.57   -1.42    0.395
10/31/1994    2.243    -0.09    0.07       0.84   -4.09    0.423
11/30/1994   -3.637    -0.22   -1.16     -2.361   -3.43    0.448
12/30/1994     1.48     0.69    1.06      0.651    8.62    0.481
 1/31/1995    2.591     1.98    1.05      -5.02   -3.43    0.496
 2/28/1995    3.893     2.38    2.46     -1.766    1.63    0.495
 3/31/1995    2.946     0.61    1.13     -1.189   -0.14    0.489
 4/28/1995    2.942      1.4    2.22      2.655   -0.68    0.484
 5/31/1995    3.991     3.87    2.82     -0.161    4.14    0.486
 6/30/1995    2.319     0.73    0.66     -2.182    2.01    0.469
 7/31/1995    3.315    -0.22    1.55      6.902    1.38    0.466
 8/31/1995     0.25     1.21    0.28      2.504    0.92     0.46
 9/29/1995    4.218     0.97    1.15       0.63    1.96     0.45
10/31/1995   -0.357      1.3    1.11     -1.679   -3.07     0.45
11/30/1995    4.385      1.5    0.47       3.67    1.18    0.457
12/29/1995    1.926      1.4    1.27      3.824    6.09    0.438
 1/31/1996       3.4    0.66     1.9      3.641    1.23    0.426
 2/29/1996     0.93    -1.74    0.53     -1.199    1.41    0.412
 3/29/1996    0.963     -0.7   -0.27      2.538    0.04    0.423
 4/30/1996    1.473    -0.56    0.54      3.325   -0.23    0.425
 5/31/1996    2.575     -0.2    0.81     -1.188    2.39    0.428
 6/28/1996    0.381     1.34    0.22       0.68      1.9   0.435
 7/31/1996   -4.416     0.27     0.9     -4.938    0.14     0.44
 8/30/1996    2.113    -0.17    1.09      0.812    4.03    0.434
 9/30/1996    5.623     1.74    1.72       4.44    2.46    0.439
10/31/1996    2.757     2.22    0.84     -1.045    2.65    0.427
11/29/1996    7.552     1.71    1.56      4.031    4.78    0.429
12/31/1996   -1.981    -0.93    1.95     -0.871   11.66    0.419
 1/31/1997    6.244     0.31    0.73      1.393      0.6   0.429
 2/28/1997    0.785     0.25    1.88      2.174   -0.35    0.426
 3/31/1997   -4.101    -1.11   -1.12      0.105    0.76    0.439
 4/30/1997    5.965      1.5    0.89      2.855   -3.66    0.442
 5/30/1997    6.084     0.95    2.01      2.966   2.997    0.436
 6/30/1997    4.478     1.19    1.36      5.104      5.5   0.423
 7/31/1997    7.952      2.7    2.12      5.123    2.71    0.431
 8/29/1997   -5.598    -0.85    0.54     -7.303   -0.57    0.437
 9/30/1997    5.474     1.47    1.98      4.992    9.65    0.423
10/31/1997   -3.336     1.45   -0.01     -9.244   -3.19    0.423
11/28/1997    4.625     0.46    0.71      1.413    2.06    0.439
12/31/1997    1.716     1.01    0.91      3.028    2.29    0.442
 1/30/1998    1.105     1.28     1.7      4.392   -1.19    0.432
 2/27/1998    7.208    -0.08    0.78       5.55   -2.04    0.435
 3/31/1998    5.117     0.34     0.5      5.083    2.28    0.429
 4/30/1998    1.006     0.52    0.75     -0.751   -3.43    0.424
 5/29/1998   -1.716     0.95     0.3      0.777   -0.74    0.428
 6/30/1998    4.059     0.85    0.21      0.802   -0.02    0.425
 7/31/1998   -1.062     0.21     0.7       1.16   -7.06    0.422
 8/31/1998   -14.44     1.63   -6.79     -13.83   -9.39    0.418
 9/30/1998    6.406     2.34   -0.01     -6.505    6.11    0.396


                                Page 8
                                  Example


10/30/1998    8.127   -0.53       -1.99      6.393   -1.93    0.34
11/30/1998    6.058    0.57        5.07       7.56    1.64   0.378
12/31/1998    5.759     0.3       -0.23      1.123   -1.79   0.376
 1/29/1999     4.18    0.71        0.94      2.172   -2.64   0.369
 2/26/1999   -3.107   -1.75       -0.21     -0.062   -1.48   0.379
 3/31/1999        4    0.55        0.91      4.574   -0.02    0.38
 4/30/1999    3.872    0.32        2.21      5.109    9.64   0.362
 5/28/1999   -2.358   -0.88       -1.08     -4.279    2.66   0.384
 6/30/1999    5.545   -0.32        0.05      4.867   -1.77   0.394
 7/30/1999   -3.119   -0.43        0.05     -0.692    -3.4   0.388
 8/31/1999   -0.495   -0.05       -0.89     -0.158   -0.72   0.407
 9/30/1999   -2.738    1.16       -0.77     -0.795   -4.35   0.403
10/29/1999    6.325    0.37       -0.49      3.882    -2.1   0.415
11/30/1999    2.033   -0.01        1.36      5.318   -1.41   0.431
12/31/1999    5.886   -0.48        1.21      8.974    3.78   0.452
 1/31/2000   -5.024   -0.33        -0.4     -3.944    0.63   0.469
 2/29/2000   -1.891    1.21        0.62      4.736   -1.55   0.474
 3/31/2000    9.777    1.32        -1.5      2.184    3.96   0.502
 4/28/2000   -3.008   -0.29       -0.15     -1.414    7.09   0.497
 5/31/2000   -2.053   -0.05        -1.6     -2.336    1.28   0.517
 6/30/2000    2.466    2.08        2.24      1.743    2.53   0.503
 7/31/2000   -1.562    0.91        0.94     -1.264    9.41   0.521
 8/31/2000    6.208    1.45        0.67      2.926   -3.75   0.537
 9/29/2000   -5.278    0.63       -0.92     -4.693    3.84   0.527
10/31/2000   -0.424    0.66       -3.11     -0.321   -4.28   0.536
11/30/2000   -7.878    1.64       -3.94     -4.488    2.08   0.544
12/29/2000    0.491    1.86        2.01     -0.721    7.08   0.512
 1/31/2001    3.546    1.64        5.99      1.523   -0.02   0.461
 2/28/2001   -9.112    0.87        1.01     -6.778   -1.65   0.431
 3/30/2001   -6.332     0.5       -1.99     -3.327    0.66   0.393
 4/30/2001    7.765   -0.41       -1.04      5.959     2.2   0.341
 5/31/2001    0.671     0.6           2     -2.352    2.44   0.319
 6/29/2001   -2.433    0.38       -1.55     -2.937    5.92   0.302
 7/31/2001   -0.985    2.24        1.07     -3.498   -2.01   0.308
 8/31/2001   -6.254    1.15         1.4      -5.88    3.98   0.295
 9/28/2001   -8.075    1.17       -6.31     -10.43   -4.21   0.249
10/31/2001    1.908    2.09   2.28           3.749   -3.56   0.192
11/30/2001    7.669   -1.38        3.23      4.589    6.04   0.167
12/31/2001    0.877   -0.63        0.06      1.722    2.56   0.148
 1/31/2002   -1.459    0.81        0.93     -2.654   -0.39   0.143
 2/28/2002   -1.929    0.97       -0.71      0.195    2.19   0.149
 3/28/2002    3.761   -1.66        2.29      4.522    6.46   0.156
 4/30/2002    -6.06    1.94        1.59     -2.781    0.58   0.148
 5/31/2002   -0.734    0.85       -0.35     -1.769    1.34    0.15
 6/28/2002   -7.121    0.86       -3.49     -8.037    2.66   0.147
 7/31/2002   -7.793    1.21       -2.86     -10.04   -5.41   0.145
 8/30/2002    0.655    1.69         1.3     -0.431    0.09   0.141
 9/30/2002   -10.86    1.62       -1.23     -10.82   -3.97   0.141
10/31/2002    8.792   -0.46       -0.61      5.225   -5.37   0.137
11/29/2002     5.88   -0.03        5.29      4.434    4.77   0.107
12/31/2002   -5.872    2.07        1.22      -6.94    1.36   0.103
 1/31/2003   -2.615    0.09        2.72     -5.266   -2.95   0.101


                                   Page 9
                              Example


 2/28/2003   -1.503    1.38    1.48      -1.885     1.82      0.1
 3/31/2003    0.968   -0.08    2.56      -2.785     2.43   0.097
 4/30/2003    8.233    0.83     5.1       7.801     3.85   0.098
 5/30/2003    5.264    1.86    1.45       2.474     5.66   0.093
 6/30/2003    1.277    -0.2    2.92       3.083     2.16   0.081
 7/31/2003    1.764   -3.36   -0.81       4.144     5.32   0.078
 8/30/2003    1.946    0.66    1.12       2.984     0.83   0.082
 9/30/2003   -1.059    2.65    2.73      -2.166     3.52   0.081
10/31/2003    5.654   -0.93    2.04       5.071     1.48    0.08
11/29/2003    0.879    0.24    1.37       0.183     4.36    0.08
12/31/2003    5.241    1.02    2.31       3.661        3   0.077
 1/31/2004    1.835     0.8    1.94       1.547        4   0.077
 2/28/2004     1.39    1.08    0.05       2.381     1.65    0.08
 3/31/2004   -1.508    0.75    0.67      -0.432     6.01    0.08
 4/30/2004   -1.568    -2.6   -0.14       0.731   -14.64    0.08
 5/30/2004     1.37    -0.4   -1.58      -1.734     7.63   0.089
 6/30/2004    1.944    0.57    1.55       2.432     2.94   0.109
 7/31/2004   -3.309    0.99    1.28      -2.297     0.43   0.116
 8/30/2004    0.402    1.91    1.63      -0.426     8.25   0.128
 9/30/2004    1.082    0.27    1.52       1.425    -0.47   0.142
10/31/2004     1.51    0.84    1.72       0.901     5.55   0.151
11/29/2004    4.063    -0.8    1.27        2.31     4.48   0.178
12/31/2004    3.402    0.92     1.5       3.161     5.81   0.191




                               Page 10
                     Variance           Standard Deviation     Frontier Mean
             Unrestricted Restricted Unrestricted Restricted    Mean     US Germany UK Japan Australia Canada France
      2.62     489.39910    547.02070   22.12237    23.38847       10.51
         3     467.79211    508.86282   21.62850    22.55799       10.89
         4     417.03816    433.03827   20.42151    20.80957       11.89
         5     375.13331    379.95873   19.36836    19.49253       12.89
         6     342.07776    342.45869   18.49534    18.50564       13.89
         7     317.87149    317.87215   17.82895    17.82897       14.89
         8     302.51452    302.51451   17.39294    17.39294       15.89
       8.5     298.15450    298.15450   17.26715    17.26715       16.39
         9     296.00681    296.00681   17.20485    17.20485       16.89
    9.125      295.81557    295.81557   17.19929    17.19929       17.02
   9.1875      295.77293    295.77293   17.19805    17.19805       17.08
 9.21875       295.76315    295.76541   17.19777    17.19783       17.11
9.234375       295.76172    295.76510   17.19772    17.19782       17.12
      9.25     295.76259    295.76493   17.19775    17.19782       17.14
    9.375      295.84788    295.76960   17.20023    17.19795       17.27
       9.5     296.07145    296.10495   17.20673    17.20770       17.39
        10     298.34841    300.83400   17.27276    17.34457       17.89
        11     309.53944    331.76857   17.59373    18.21452       18.89
        12     329.57944    393.35613   18.15432    19.83321       19.89
        13     358.46888    492.14538   18.93327    22.18435       20.89
   13.815      388.55883    624.99887   19.71190    24.99998       21.71
        14     396.20816                19.90498                   21.89
        15     442.79564                21.04271                   22.89
        16     498.23294                21.10000                   22.93 15.7
                                        22.32113                   23.89
                                        23.40000                   24.66                                  10.5
                                        23.50000                   24.73             18
                                        25.04000                   25.67        21.7
                                        26.60000                   26.76                 17.3                    17.2
                                        27.60000                   27.38                          14.8


                                           Figure 8.13
                             Efficient frontier with seven countries
                       Efficient frontier with seven countries
Expected Return
      (%)
    28                                                                  Unrestricted
                                                                        efficient frontier
    26                 Restricted
                       efficient frontier:
                       NO short
    24
                       sales
    22                                                  Germany

    20

    18                                                               Japan
                       Equally                    U.K
                       weighted                                      France
    16
                       portfolio
                                      U.S
    14                                                            Australia

    12
                                                  Canada
    10

     8
         15       17      19        21       23          25        27         29
                                                              Standard deviation (%)
Equally Wtd
 Portfolio




       16.5
             A              B              C                D              E           F               G          H        I
 1   Table 8.4 (A)     Annualized Standard Deviation, Average Return
 2                     and Correlation Coefficients of International Stocks, 1980-1993
 3
 4                       Standard     Average
 5       Country       Deviation (%) Return (%)
 6      US                 21.1         15.7
 7      Germany            25.0         21.7
 8      UK                 23.5         18.3
 9      Japan              26.6         17.3
10      Australia          27.6         14.8
11      Canada             23.4         10.5
12      France             26.6         17.2
13
14                     Correlation matrix
15                          US        Germany            UK           Japan        Australia      Canada       France
16      US                 1.00           0.37           0.53          0.26          0.43          0.73         0.44
17      Germany            0.37           1.00           0.47          0.36          0.29          0.36         0.63
18      UK                 0.53           0.47           1.00          0.43          0.50          0.54         0.51
19      Japan              0.26           0.36           0.43          1.00          0.26          0.29         0.42
20      Australia          0.43           0.29           0.50          0.26          1.00          0.56         0.34
21      Canada             0.73           0.36           0.54          0.29          0.56          1.00         0.39
22      France             0.44           0.63           0.51          0.42          0.34          0.39         1.00
23
24   Source: Roger G. Clarke and Mark P. Kritzman, Currency Management: Concepts and Practice ,
25   Charlottesville, VA, Research Foundation of the Institute of Chartered Financial Analysts, 1996
26
27   Table 8.4 (B)     Covariance Matrix: Cell Formulas
28
29                          US         Germany           UK          Japan         Australia     Canada         France
30      US             b6*b6*b16     b7*b6*c16      b8*b6*d16     b9*b6*e16      b10*b6*f16    b11*b6*g16    b12*b6*h16
31      Germany        b6*b7*b17     b7*b7*c17      b8*b7*d17     b9*b7*e17      b10*b7*f17    b11*b7*g17    b12*b7*h17
32      UK             b6*b8*b18     b7*b8*c18      b8*b8*d18     b9*b8*e18      b10*b8*f18    b11*b8*g18    b12*b8*h18
33      Japan          b6*b9*b19     b7*b9*c19      b8*b9*d19     b9*b9*e19      b10*b9*f19    b11*b9*g19    b12*b9*h19
34      Australia      b6*b10*b20    b7*b10*c20     b8*b10*d20    b9*b10*e20     b10*b10*f20   b11*b10*g20   b12*b10*h20
35      Canada         b6*b11*b21    b7*b11*c21     b8*b11*d21    b9*b11*e21     b10*b11*f21   b11*b11*g21   b12*b11*h21
36      France         b6*b12*b22    b7*b12*c22     b8*b12*d22    b9*b12*e22     b10*b12*f22   b11*b12*g22   b12*b12*h22
37
38                     Covariance Matrix: Results
39
40                           US         Germany         UK            Japan        Australia      Canada       France
41      US                 445.21        195.18        262.80         145.93        250.41        360.43       246.95
            A               B            C             D             E             F             G            H          I
42      Germany           195.18       625.00        276.13        239.40        200.10        210.60       418.95
43      UK                262.80       276.13        552.25        268.79        324.30        296.95       318.80
44      Japan             145.93       239.40        268.79        707.56        190.88        180.51       297.18
45      Australia         250.41       200.10        324.30        190.88        761.76        361.67       249.61
46      Canada            360.43       210.60        296.95        180.51        361.67        547.56       242.75
47      France            246.95       418.95        318.80        297.18        249.61        242.75       707.56
48
49   Table 8.4 (C)      Border-Multiplied Covariance Matrix for the Equally Weighted Portfolio and Portfolio Variance:
50                      Cell Formulas
51                           US         Germany       UK            Japan       Australia      Canada        France
52        Weights       a69          a70          a71            a72          a73          a74           a75
53         0.1429       a69*b68*b41 a69*c68*c41 a69*d68*d41 a69*e68*e41 a69*f68*f41 a69*g68*g41 a69*h68*h41
54         0.1429       a70*b68*b42 a70*c68*c42 a70*d68*d42 a70*e68*e42 a70*f68*f42 a70*g68*g42 a70*h68*h42
55         0.1429       a71*b68*b43 a71*c68*c43 a71*d68*d43 a71*e68*e43 a71*f68*f43 a71*g68*g43 a71*h68*h43
56         0.1429       a72*b68*b44 a72*c68*c44 a72*d68*d44 a72*e68*e44 a72*f68*f44 a72*g68*g44 a72*h68*h44
57         0.1429       a73*b68*b45 a73*c68*c45 a73*d68*d45 a73*e68*e45 a73*f68*f45 a73*g68*g45 a73*h68*h45
58         0.1429       a74*b68*b46 a74*c68*c46 a74*d68*d46 a74*e68*e46 a74*f68*f46 a74*g68*g46 a74*h68*h46
59         0.1429       a75*b68*b47 a75*c68*c47 a75*d68*d47 a75*e68*e47 a75*f68*f47 a75*g68*g47 a75*h68*h47
60   Sum(a53:a59)       sum(b69:b75) sum(c69:c75) sum(d69:d75) sum(e69:e75) sum(f69:f75) sum(g69:g75) sum(h69:h75)
61   Portfolio variance sum(b76:h76)
62   Portfolio SD       b77^.5
63   Portfolio mean     a69*c6+a70*c7+a71*c8+a72*c9+a73*c10+a74*c11+a75*c12
64
65   Table 8.4 (C)      Border-Multiplied Covariance Matrix for the Equally Weighted Portfolio and Portfolio Variance:
66                      Results
67       Portfolio             US       Germany          UK         Japan        Australia       Canada        France
68        Weights           0.1429       0.1429        0.1429       0.1429         0.1429         0.1429       0.1429
69         0.1429             9.09         3.98          5.36         2.98           5.11           7.36         5.04
70         0.1429             3.98        12.76          5.64         4.89           4.08           4.30         8.55
71         0.1429             5.36         5.64         11.27         5.49           6.62           6.06         6.51
72         0.1429             2.98         4.89          5.49        14.44           3.90           3.68         6.06
73         0.1429             5.11         4.08          6.62         3.90          15.55           7.38         5.09
74         0.1429             7.36         4.30          6.06         3.68           7.38          11.17         4.95
75         0.1429             5.04         8.55          6.51         6.06           5.09           4.95        14.44
76         1.0000            38.92        44.19         46.94        41.43          47.73          44.91        50.65
77   Portfolio variance         314.77
78   Portfolio SD                  17.7
79   Portfolio mean                16.5
80   Table 8.4(D)       Border-Multiplied Covariance Matrix for the Efficient Frontier Portfolio with Mean of 16.5%
81                      (after change of weights by solver)
82
              A                B              C              D              E              F             G           H           I
 83       Portfolio            US        Germany             UK           Japan         Australia        Canada   France
 84        weights          0.3467         0.1606          0.0520        0.2083           0.1105         0.1068   0.0150
 85         0.3467           53.53          10.87            4.74         10.54             9.59          13.35    1.29
 86         0.1606           10.87          16.12            2.31          8.01             3.55           3.61    1.01
 87         0.0520            4.74           2.31            1.49          2.91             1.86           1.65    0.25
 88         0.2083           10.54           8.01            2.91         30.71             4.39           4.02    0.93
 89         0.1105            9.59           3.55            1.86          4.39             9.30           4.27    0.41
 90         0.1068           13.35           3.61            1.65          4.02             4.27           6.25    0.39
 91         0.0150            1.29           1.01            0.25          0.93             0.41           0.39    0.16
 92         1.0000          103.91          45.49           15.21         61.51            33.38          33.53    4.44
 93   Portfolio Variance    297.46
 94   Portfolio SD            17.2
 95   Portfolio mean          16.5
 96   Table 8.4(E)       The Unrestricted Efficient Frontier and the Restricted Frontier ( with no short sales)
 97
 98                         Standard Deviation                                      Country Weights in Efficient Portfolios
 99         Mean         Unrestricted Restricted             US         Germany          UK         Japan        Australia    Canada
100          9.0            24.239     not feasible       -0.0057        -0.2859      -0.1963      0.2205         0.0645       0.9811
101         10.5            22.129                         0.0648        -0.1966      -0.1466      0.2181         0.0737       0.8063
102         10.5                         23.388            0.0000         0.0000       0.0000      0.0007         0.0000       0.9993
103         11.0            21.483                         0.0883        -0.1668      -0.1301      0.2173         0.0768       0.7480
104         11.0                         22.325            0.0000         0.0000       0.0000      0.0735         0.0000       0.9265
105         12.0            20.292                         0.1353        -0.1073      -0.0970      0.2157         0.0829       0.6314
106         12.0                         20.641            0.0000         0.0000       0.0000      0.1572         0.0325       0.7668
107         14.0            18.408                         0.2293         0.0118      -0.0308      0.2124         0.0952       0.3982
108         14.0                         18.416            0.2183         0.0028       0.0000      0.2068         0.0884       0.4020
109         15.0            17.767       17.767            0.2763         0.0713       0.0023      0.2108         0.1013       0.2817
110         16.0            17.358       17.358            0.3233         0.1309       0.0355      0.2091         0.1074       0.1651
111         17.0            17.200       17.200            0.3702         0.1904       0.0686      0.2075         0.1135       0.0485
112         17.5            17.216                         0.3937         0.2202       0.0851      0.2067         0.1166      -0.0098
113         17.5                         17.221            0.3777         0.2248       0.0867      0.2021         0.1086       0.0000
114         18.0            17.297                         0.4172         0.2499       0.1017      0.2059         0.1197      -0.0681
115         18.0                         17.405            0.3285         0.2945       0.1157      0.1869         0.0744       0.0000
116         18.5            17.441                         0.4407         0.2797       0.1182      0.2051         0.1227      -0.1263
117         18.5                         17.790            0.2792         0.3642       0.1447      0.1716         0.0402       0.0000
118         21.0            19.036                         0.5582         0.4285       0.2010      0.2010         0.1380      -0.4178
119         21.0                         22.523            0.0000         0.8014       0.1739      0.0247         0.0000       0.0000
120         22.0            20.028     not feasible        0.6052         0.4880       0.2341      0.1994         0.1442      -0.5343
121         26.0            25.390     not feasible        0.7931         0.7262       0.3665      0.1929         0.1687      -1.0006
     J
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 99   France
100    0.2216
101    0.1803
102    0.0000
103    0.1665
104    0.0000
105    0.1390
106    0.0435
107    0.0839
108    0.0816
109    0.0563
110    0.0288
111    0.0012
112   -0.0125
113    0.0000
114   -0.0263
115    0.0000
116   -0.0401
117    0.0000
118   -0.1090
119    0.0000
120   -0.1365
121   -0.2467

								
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