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:

Other Comprehensive Income

Other Comprehensive Income includes revenues, expenses, gains, and losses that are not included in net income, affecting the equity section of the balance sheet.

IFRS

International Financial Reporting Standards, a set of accounting guidelines that provide a global framework for how public companies prepare and disclose their financial statements.

Statement of Comprehensive Income

A financial statement that includes all changes in equity from non-owner sources, in addition to net income.

Retained Earnings Restriction

Limitations or requirements placed on the portion of earnings not distributed as dividends but kept by the company for reinvestment.