Linear Programming Models Are Used by Many Financial Firms to Select

question 109

Essay

Linear programming models are used by many financial firms to select a desirable bond portfolio.The following is a simplified version of such a model.Abby is considering investing in four bonds; $1.5 million is available for investment.The expected annual return,the worst-case annual return on each bond,and the "duration" of each bond are given below (The duration of a bond is a measure of the bond's sensitivity to interest rates.) Abby wants to maximize the expected return from its bond investments,subject to the following three constraints:
-The worst-case return of the bond portfolio must be at least 8%.
-The average duration of the portfolio must be at most 6.For example,a portfolio that invests $600,000 in bond 1 and $400,000 in bond 4 has an average duration of [600,000(3)+ 400,000 (9)]/1,000,000 = 5.4
-Because of diversification requirements,at most 40% of the total amount invested can be invested in a single bond.
Determine how Abby can maximize the expected return on her investment.

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Definitions:

Choanoflagellates

Aquatic microorganisms thought to be the closest living relatives of animals, characterized by their flagellum and collar structure.

Foraminiferans

Marine protozoans characterized by their porous shells, or tests, through which pseudopodia extend for feeding and locomotion.

Rhizarians

A group of mostly unicellular eukaryotes, characterized by their production of pseudopods, which are extensions used for movement and feeding.

Freshwater Algae

Simple, often microscopic, plant-like organisms that live in fresh water and are capable of photosynthesis.