Bond Investment:

• A company is planning to invest exactly $1 million among four bonds. The expected annual return, the worst-case annual return, and the duration of each bond are given in the table below. (The duration of a bond is a measure of the bond's sensitivity to interest rates.)

• 	Bond 1	Bond 2	Bond 3	Bond 4
  Expected	13%	8%	12%	14%
  Worst case	6%	8%	10%	10%
  Duration	3	4	6	9

• The company wants to maximize the expected return from its bond investments, subject to 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.

• Develop a linear program to determine how the company can maximize the expected return on its investment. Answer the following questions in the highlighted cells in the worksheet:

  1. What is the maximum expected return (in $) that can be achieved under these circumstances?

  2. By how much would the optimal expected return increase if they had one additional dollar to invest?

  3. By how much could the expected return for Bond 1 decrease without changing the optimal allocation of funds?

• HINT: This can be set up as a blending problem, but it doesn't necessarily have to be.

A company is planning to invest exactly 51 milion among four bonds. The expected anneal return, the worst-case anmual return, and the duration of each bond are siven in the table below. (The duration of a bond is a meastere of the bonds sensitivity to interst rates.) The company wants to maximize the expected return from its bood investements, sibject to three constraints: * The worst-eave return of the bond portiolio must be at least 8% - The average duration of the portfolio mast be at most 6 . (For example, a portfolio that invests 5600,000 in bond 1 and 5400,000 in bond 4 ) has an average duration of (600,0003)+400,000(9)/1,000,000=5.4.) * Because of diversification requirenents, at most 40% of the tocal anount invested ean be invested in a sipule bend. Develop a linear prognam to deternine how the company can maximixe the expected return on its investment, Answer the following questions in the bightiphted cells below: a) What is the maximum expected return (in $ ) that can be achieved under these circunstances? b) By how much would the ogtimal expected return increase if they had one additional dollar to invest? c) By how much could the expected return for Bond I decrease without changing the optimal allocation of funds? FINT: This can be set up as a blending problem, but it doesn't necessarily have to be