Lecture 2


Example 1

Estimates from three independent experts of the future prices are in the following table. The price
of the security in the time of purchase was 100,--.  Calculate the expected return and risk of this
security.


The estimates of experts:

                                             Expert 1

                                                                                                     Expert 2

                                                                                                               Expert 3

                                               Price

                                                     v %

                                                                                                       Price

                                                               v %

                                                                                                                 Price

                                                                        v %

                                                80

                                                                                                    10

                                                                                                        100

                                                                                                             20

                                                                                                                  120

                                                                                                                       50

                                                100

                                                                                                    80

                                                                                                        120

                                                                                                             30

                                                                                                                  160

                                                                                                                       50

                                                180

                                                                                                    10

                                                                                                        150

                                                                                                             50





Example 2

Consider several portfolios created from two assets.


                                                5%

                                                                                                   20%

                                                15%

                                                                                                   40%



Proportions (weights) of individual securities in the portfolio are:


1

                                                0,83

                                                                                                  0,67

                                                                                                      0,50

                                                                                                          0,33

                                                                                                              0,17

                                                                                                                    0

0

                                                0,17

                                                                                                  0,33

                                                                                                      0,50

                                                                                                          0,67

                                                                                                              0,83

                                                                                                                    1

Calculate the returns of each portfolio and their risk. Plot the results.


Example 3

Calculate and plot calculated portfolio, if you know the return and covariance matrix.




A

                                                     B

                                                                                                    C

                                                                                                        D

                                                                                                            E

0,20

                                                   0,25

                                                                                                  0,50

                                                                                                      0,30

                                                                                                          0,10

0,20

                                                   0,25

                                                                                                  0,10

                                                                                                      0,40

                                                                                                          0,20

0,60

                                                   0,50

                                                                                                  0,40

                                                                                                      0,30

                                                                                                          0,70







Example 4

The portfolio consists of two securities in following manner:

Security

        Expected return

                       Risk

                                                   Weight

        0,15

                                                                      0,28

                                                                                                  0,60

        0,21

                                                                      0,42

                                                                                                  0,40


Calculate the expected return of the portfolio. Then calculate the risk of the portfolio. Use the
whole interval for correlation  and the step will be 0,2. Determine the portfolio with the smallest
and largest risk.


Example 5

We have multi assets portfolio with following correlation matrix:

Security

        E(ri)

             Risk

                                                   Weight

        0,13

                                                            0,28

                                                                                                   0,2

        0,25

                                                            0,42

                                                                                                   0,4

        0,21

                                                            0,35

                                                                                                   0,1

        0,41

                                                            0,48

                                                                                                   0,2

        0,30

                                                            0,39

                                                                                                   0,1



Calculate the expected return of the portfolio and its risk.