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Linear programming models are used bymany Wall Street firms to select a desirable bondportfolio. The following is a simplified version of such amodel. Solodrex is considering investing in four bonds;$1million is available for investment. The expected annualreturn, the worst-case annual return on each bond, and the“duration” of each bond are given in the tablebelow:
expectedreturn worst casereturn duration
bond 1 13% 6% 3
bond 2 8% 8% 4
bond3 12% 10% 7
bond4 14% 9% 9
(The duration of a bond is a measure of the bond’s sensitivity to interest rates.) Solodrex wants to maximize theexpected return from its bond investments, subject to threeconstraints: The worst-case return of the bond portfolio mustbe at least 8%. The average duration of the portfolio must be atmost 6. For example, a portfolio that invests $600,000 in bond1 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 totalamount invested can be invested in a single bond.
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