Problem 8-18 (Algorithmic)

Refer to the Markowitz portfolio model, which maximizes expected return subject to a constraint that the variance of the portfolio must be less than or equal to some specified amount:

Let: FS = proportion of portfolio invested in the foreign stock mutual fund IB = proportion of portfolio invested in the intermediate-term bond fund LG = proportion of portfolio invested in the large-cap growth fund LV = proportion of portfolio invested in the large-cap value fund SG = proportion of portfolio invested in the small-cap growth fund SV = proportion of portfolio invested in the small-cap value fund = the expected return of the portfolio R_s = the return of the portfolio in year s Var = the variance of the portfolio

Max

s.t.

10.51 FS

+

18.09 IB

+

32.86 LG

+

32.81 LV

+

33.89 SG

+

25.01 SV

=

R1

13.57 FS

+

3.71 IB

+

19.16 LG

+

21.06 LV

+

19.85 SG

+

25.77 SV

=

R2

13.82 FS

+

7.96 IB

+

33.73 LG

+

13.38 LV

+

4.22 SG

-

7.15 SV

=

R3

45.87 FS

-

1.78 IB

+

41.91 LG

+

7.51 LV

+

59.13 SG

+

5.88 SV

=

R4

-22.38 FS

+

7.81 IB

-

23.71 LG

-

5.82 LV

-

9.47 SG

+

17.76 SV

=

R5

FS

+

IB

+

LG

+

LV

+

SG

+

SV

=

1

=

Var

FS, IB,

LG,

LV, SG, SV

0

Use the model to solve a series of models by varying the maximum allowable variance from 20 to 60 in increments of 5 and solving for the maximum return for each (solve a total of nine models). Round your answers to 3 decimal places. If there is no optimal solution, enter "NA" as your answer.

Max Variance	Exp Return
20
25
30
35
40
45
50
55
60