Linear Programming Models Are Used by Many Financial Firms to Select

question 59

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 her 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.

Recognize the role of working memory in processing and recalling information.

Identify practices that contribute to effective memory recall and retention.

Understand the concept of systematic and unsystematic risk and their significance in portfolio theory.

Recognize the role of diversification in reducing unsystematic risk.

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Definitions:

Utility Functions

Mathematical expressions used in economics to represent a consumer's preference ranking for various bundles of goods.

Consumption

The utilization of goods and services by households or individuals to satisfy their needs and wants.

Grain

The small, hard seeds of cereal plants like wheat, rice, and corn, used as a primary source of food for humans and animals.

Rats

Small mammals known for their sharp teeth, keen sense of smell, and often considered pests in many societies, but also used extensively in scientific research.