are not permitted. ncuritnt ) A portfolio manager in charge of a bank portfolio

Question

are not permitted. ncuritnt ) A portfolio manager in charge of a bank portfolio hss $10 million to ields, vailable for purchase, as well as their respective quality rating yields, are shown below. Bond Bond nane type Quality scales Years to Yield to After-taxt loody Bank maturity maturity yield 2.7% MunicipalA2 1.3% 8 Agency Aa2 5.4 5.0% 12.5 15 Government Aaa 12.2% 4.4% 4.5% E Munici 4.5 The ban k places the following policy limitations on the portfolio manager s " Goverument and agency bonds must total at least $4 milion. . The average quality of the portfolio cannot exceed 1.4 on the bank's quality The average years to maturity of the portfolio must not exceed five years. A tax rate of 45% will be applied to the after-tax yield, and the manager's after-tax earnings? Formulate a linear programming model for this problem. remaining is the portfolio earnings. The portfolio manager's objective is to maximize his after-tax a) define the decison variables b) write dovwn the lnear pogrammim Por mueuthon

Explanation / Answer

Let a, b, c, d and e is the amount in million dollars invested in 5 different bonds A, B, C, D and E respectively

Total amount to be invested is $10mn
a + b + c + d + e = 10

Govt. and agency bonds must total at least $4mn
b + c + d >= 4

Quality constraint
2a + 2b + c + d + 5e <= 1.4*5*10
2a + 2b + c + d + 5e <= 70

Maturity constraint
9a + 15b + 4c + 3d + 2e <= 5*5*10
9a + 15b + 4c + 3d + 2e <= 250

Here we need to maximize the yield
Z = 0.043a + 0.027b + 0.025c + 0.022d + 0.045e

Hence formulated LPP is
maximize Z = 0.043a + 0.027b + 0.025c + 0.022d + 0.045e
subject to
a + b + c + d + e = 10
b + c + d >= 4
2a + 2b + c + d + 5e <= 70
9a + 15b + 4c + 3d + 2e <= 250

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