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Securities Expected Return Standard Deviation
X                        20                 15
Rf                        8                  0

      Riskfree Lending
Portfolios X                     Rf              Expected Return Standard Deviation
A                            0               1               8.00              0.00
B                         0.25            0.75              11.00              3.75
C                          0.5             0.5              14.00              7.50
D                         0.75            0.25              17.00             11.25
E                            1               0              20.00             15.00
F                         1.25           -0.25              23.00             18.75
G                         1.50           -0.50              26.00             22.50                  35
H                         1.75           -0.75              29.00             26.25
                                                                                                     30
I                         2.00           -1.00              32.00             30.00
                                                                                                     25

                                                                                                     20

                                                                                                     15

                                                                                                     10

                                                                                                      5

Security   ER                                                                                         0
X                        20.00                                                                            0        5
Y                        25.00
Rf                        8.00                                                      30


                                                                                    25


Variance-Covariance Matrix                                                          20


      146              187                                                          15


      187              854                                                          10


                                                                                     5


                                                                                     0

                                                                                         10     15            20   25
Proportion
X          Y                     Rf              ER(P)             Er of Risky           SD
       0.8                 0.2               0                21                    21        13.69
     0.25                 0.25             0.5             15.25                 11.25         9.27
     0.35                 0.35             0.3             18.15                 15.75        12.97
       0.1                 0.1             0.8              10.9                   4.5         3.71
35

          30

          25

          20

          15

          10

           5

           0
               0        5      10                    15     20     25      30   35




                                    Column K




10   15            20   25    30               35




                                1                      0      20   12.08
                             0.75                   0.25   21.25   14.34
                              0.5                    0.5    22.5   18.53
                             0.25                   0.75   23.75   23.66
                                0                      1      25   29.22
Rf              8
E(Rm)          18

        Beta         E(Ri)
               0.5           13
               0.9           17
               1.1           19
               1.4           22
               1.5           23
               1.9           27
                 2           28
                                                         E(Ri)
                                  30
                                  25
                                  20
                                  15                                         E(R
                                  10
                                   5
                                   0
                                       0.5   0.9   1.1     1.4   1.5   1.9
E(Ri)




1.5   1.9           2
ER                                 Var
Rf                                8%               0%
X                                12%               0%


     Probability of Occurrence          T-Bills
                                 0.05             0.08
                                  0.2             0.08
                                  0.5             0.08
                                  0.2             0.08
                                 0.05             0.08
sd          Cov       Correlation
        0         0      #DIV/0!
     0.05


Equity B Devg of Rf Devg of X Codeviation
     -0.02        0          0         0
      0.09        0          0         0
      0.12        0          0         0
      0.15        0          0         0
      0.26        0          0         0
Riskfree and Risky
14.00%




12.00%




10.00%




 8.00%


                                                             Column E

 6.00%




 4.00%




 2.00%




 0.00%
     0.00%   1.00%   2.00%      3.00%        4.00%   5.00%              6.00%
Portfolio       Wt of Rf Wt of X    ER (P)    SD (P)
            1        100%        0%     8.00%     0.00%   0   0.00%
            2         80%      20%      8.80%     0.96%   0   0.96%
            3         60%      40%      9.60%     1.93%   0   1.93%
            4         40%      60%    10.40%      2.89%   0   2.89%
            5         20%      80%    11.20%      3.85%   0   3.85%
            6          0%     100%    12.00%      4.82%   0   4.82%

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Riskfree lending and borrowing

  • 1. Securities Expected Return Standard Deviation X 20 15 Rf 8 0 Riskfree Lending Portfolios X Rf Expected Return Standard Deviation A 0 1 8.00 0.00 B 0.25 0.75 11.00 3.75 C 0.5 0.5 14.00 7.50 D 0.75 0.25 17.00 11.25 E 1 0 20.00 15.00 F 1.25 -0.25 23.00 18.75 G 1.50 -0.50 26.00 22.50 35 H 1.75 -0.75 29.00 26.25 30 I 2.00 -1.00 32.00 30.00 25 20 15 10 5 Security ER 0 X 20.00 0 5 Y 25.00 Rf 8.00 30 25 Variance-Covariance Matrix 20 146 187 15 187 854 10 5 0 10 15 20 25 Proportion X Y Rf ER(P) Er of Risky SD 0.8 0.2 0 21 21 13.69 0.25 0.25 0.5 15.25 11.25 9.27 0.35 0.35 0.3 18.15 15.75 12.97 0.1 0.1 0.8 10.9 4.5 3.71
  • 2. 35 30 25 20 15 10 5 0 0 5 10 15 20 25 30 35 Column K 10 15 20 25 30 35 1 0 20 12.08 0.75 0.25 21.25 14.34 0.5 0.5 22.5 18.53 0.25 0.75 23.75 23.66 0 1 25 29.22
  • 3. Rf 8 E(Rm) 18 Beta E(Ri) 0.5 13 0.9 17 1.1 19 1.4 22 1.5 23 1.9 27 2 28 E(Ri) 30 25 20 15 E(R 10 5 0 0.5 0.9 1.1 1.4 1.5 1.9
  • 4. E(Ri) 1.5 1.9 2
  • 5. ER Var Rf 8% 0% X 12% 0% Probability of Occurrence T-Bills 0.05 0.08 0.2 0.08 0.5 0.08 0.2 0.08 0.05 0.08
  • 6. sd Cov Correlation 0 0 #DIV/0! 0.05 Equity B Devg of Rf Devg of X Codeviation -0.02 0 0 0 0.09 0 0 0 0.12 0 0 0 0.15 0 0 0 0.26 0 0 0
  • 7. Riskfree and Risky 14.00% 12.00% 10.00% 8.00% Column E 6.00% 4.00% 2.00% 0.00% 0.00% 1.00% 2.00% 3.00% 4.00% 5.00% 6.00%
  • 8. Portfolio Wt of Rf Wt of X ER (P) SD (P) 1 100% 0% 8.00% 0.00% 0 0.00% 2 80% 20% 8.80% 0.96% 0 0.96% 3 60% 40% 9.60% 1.93% 0 1.93% 4 40% 60% 10.40% 2.89% 0 2.89% 5 20% 80% 11.20% 3.85% 0 3.85% 6 0% 100% 12.00% 4.82% 0 4.82%