Linear programming models are used by many WallStreet firms to select a desirable bond portfolio. Thefollowing is a simplified version of such a model. Solodrexis considering investing in four bonds; $1,000,000 isavailable for investment. The expected annual return, theworst-case annual return on each bond, and the “duration”of each bond are given in Table 15. The duration of a bondis a measure of the bond’s sensitivity to interest rates.Solodrex wants to maximize the expected return from itsbond investments, subject to three constraints.Constraint 1 The worst-case return of the bond portfoliomust be at least 8%.Constraint 2 The average duration of the portfolio must beat most 6. For example, a portfolio that invested $600,0003.8 Blending Problems 93in bond 1 and $400,000 in bond 4 would have an averageduration of5.4Constraint 3 Because of diversification requirements, atmost 40% of the total amount invested can be invested in asingle bond.Formulate an LP that will enable Solodrex to maximize theexpected return on its investment
Linear programming models are used by many Wall
Street firms to select a desirable bond portfolio. The
following is a simplified version of such a model. Solodrex
is considering investing in four bonds; $1,000,000 is
available for investment. The expected annual return, the
worst-case annual return on each bond, and the “duration”
of each bond are given in Table 15. The duration of a bond
is a measure of the bond’s sensitivity to interest rates.
Solodrex wants to maximize the expected return from its
bond investments, subject to three constraints.
Constraint 1 The worst-case return of the bond portfolio
must be at least 8%.
Constraint 2 The average duration of the portfolio must be
at most 6. For example, a portfolio that invested $600,000
3.8 Blending Problems 93
in bond 1 and $400,000 in bond 4 would have an average
duration of
5.4
Constraint 3 Because of diversification requirements, at
most 40% of the total amount invested can be invested in a
single bond.
Formulate an LP that will enable Solodrex to maximize the
expected
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