You are managing a portfolio of $1.9 million. Your target duration is 11 years, and you can choose from two bonds: a zero-coupon bond with maturity 5 years, and a perpetuity, each currently yielding 5%. |
Required: |
(a) |
How much of each bond will you hold in your portfolio? (Round your answers to 4 decimal places.) |
Zero-coupon bond | |
Perpetuity bond |
(b) |
How will these fractions change next year if target duration is now ten years? (Round your answers to 4 decimal places.) |
Zero-coupon bond | |
Perpetuity bond |
a.
Duration of Zero Coupon Bond = 5 years
Duration of Perpetuity = 1.05/0.05 = 21 years
Let weight of Zero Coupon BOnd is w
11(1,900,000) = 5(w) + (1,900,000 - w)(21)
20,900,000 = 5w + 39,900,000 - 21w
w = $1,187,500
Amount in Zero Coupon BOnd = $1,187,500.0000
Amount in Perpetuity = $712,500.0000
b.
Target Duration = 10 years
Duration of Zero Coupon Bond = 4 years
Duration of Perpetuity = 1.05/0.05 = 21 years
Let weight of Zero Coupon BOnd is w
10(1,900,000) = w(4) + (1,900,000 - w)21
19,000,000 = 4w + 39,900,000 - 21w
w = $1,229,411.7647
Amount in Zero Couon Bond = $1,229,411.7647
Amount in Perpetuity = $670,588.2353
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