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.

---

Definitions:

Revenue Recognition Principle

A rule in accounting that outlines the exact circumstances in which income is considered as earned and documented.

Adjusted Trial Balance

A statement that lists all accounts and their balances after adjusting entries are made, ensuring the total debits equal total credits.

Debit

An accounting entry that increases asset or expense accounts, and decreases liability, equity, or revenue accounts.

Credit

A financial arrangement where goods, services, or money is borrowed by one party from another, with the promise of repayment usually with interest.