Answered: Reformulate the model given by (8.10)…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

In the Markowitz portfolio optimization model defined in equations (8.10) through (8.19) in the text, the decision variables represent the percentage of the portfolio invested in each of the mutual funds. For example,

FS = 0.25

in the solution means that 25% of the money in the portfolio is invested in the foreign stock mutual fund. It is possible to define the decision variables to represent the actual dollar amount invested in each mutual fund or stock. Redefine the decision variables so that now each variable represents the dollar amount invested in the mutual fund. Assume an investor has $50,000 to invest and wants to minimize the variance of his or her portfolio subject to a constraint that the portfolio returns a minimum of 10%.

(a)

Reformulate the model given by (8.10) through (8.19) based on the new definition of the decision variables.

min

((R1 − R)² + (R2 − R)² + (R3 − R)² + (R4 − R)² + (R5 − R)²)

s.t.

R1 =

R2 =

R3 =

R4 =

R5 =

FS + IB + LG + LV + SG + SV =

R =

(R1 + R2 + R3 + R4 + R5)

R ≥

FS, IB, LG, LV, SG, SV ≥ 0

(b)

Solve the revised model with Excel Solver or LINGO. (Round your answers to three decimal places.)

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