You are managing a portfolio of $1 million. Your target duration is 10 years, and you can invest in two bonds, a zero-coupon bond with maturity of five years and a perpetuity, each currently yielding 10.0%.
a. What weight of each bond will you hold to immunize your portfolio? (Round your answers to 2 decimal places.)
b. How will these weights change next year if target duration is now nine years? (Round your answers to 2 decimal places.)
a.
Duration of Zero Coupon Bond = 5 years
Duration of Perpetuity = 1.10/0.10 = 11 years
Let weight of zero coupon bond be w,
So,
10 = 5w + (1 - w)(11)
w = 0.1667
Weight of Zero Coupon Bond = 16.67%
Weight of Perpetuity = 1 - 0.1667 = 83.33%
b.
Duration of Zero Coupon Bond = 4 years
Duration of Perpetuity = 1.10/0.10 = 11 years
Let weight of zero coupon bond be w,
So,
9 = 4w + (1 - w)(11)
w = 0.2857
Weight of Zero Coupon Bond = 28.57%
Weight of Perpetuity = 1 - 0.2857 = 71.43%
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 bond
with maturity of five years and a perpetuity, each currently
yielding 7.5%.
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