You are managing a portfolio of $1 million. Your target duration is 10 years, and you...

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You are managing a portfolio of $1 million. Your target duration is 10 years, and you can invest in two bonds, a zero-coupon

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Answer 1

Answer #1

a.

Duration of Zero Coupon Bond = 5 years

Duration of Perpetuity = 1.086/0.086 = 12.63 years

Let w be weight invested in Zero Coupon Bond,

10 = 5w + ( - w)(12.63)

w = 0.3447

So,

Weight of Zero Coupon Bond = 34.47%

Weight of Perpetuity = 1 - 0.3447 = 65.53%

b.

Duration of Zero Coupon Bond = 4 years

Duration of Perpetuity = 1.086/0.086 = 12.63 years

Let w be weight invested in Zero Coupon Bond,

9 = 4w + ( - w)(12.63)

w = 0.4206

So,

Weight of Zero Coupon Bond = 42.06%

Weight of Perpetuity = 1 - 0.4206 = 57.94%

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Answer 2

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