You are managing a portfolio of $1 million. Your target duration is 10 years, and you can choose from two bonds: a zero-coupon bond with maturity five years, and a perpetuity, each currently yielding 5%. a. How much of (i) the zero-coupon bond and (ii) the perpetuity will you hold in your portfolio? (Do not round intermediate calculations. Round your answers to 2 decimal places.) b. How will these fractions change next year if target duration is now nine years? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
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Ответ:
Ai.Zero coupon bonds = 68.75%
Aii. Perpetuity= 0.3125
Bi. Zero coupon bonds = 70.58%
Bii. Perpetuity= 0.2942
Explanation:
ai. Calculation for How much of the zero-coupon bond
Duration of Zero Coupon Bond = 5 years
Duration of Perpetuity = 1.05/0.05 = 21 years
Using this formula
Dp=W×D1 +(1-W)×D2
Let plug in the formula
10 = 5w + (1 - w)21
10 = 5w + 21 - 21w
21w-10w=21-5
11w=16
w=11/16
w = 0.6875*100
w=68.75%
Zero coupon bonds = 68.75%
Therefore How much of the zero-coupon bond
you hold in your portfolio will be 68.75%
aii. Calculation for the perpetuity you will hold in your portfolio
Perpetuity= 1 - 0.6875
Perpetuity= 0.3125
Therefore the perpetuity you will hold in your portfolio will be 0.3125
bi. Calculation for how will these fractions change next year if target duration is now nine years
Duration of Zero Coupon Bond = (5 -1) =4years
Duration of Perpetuity = 1.05/0.05 = 21 years
Using this formula
Dp=W×D1 +(1-W)×D2
Let plug in the formula
9 = 4w + (1 - w)21
9 = 4w + 21 - 21w
21w-9w=21-4
12w=17
w=12/17
w = 0.7058×100
w=70.58%
Zero coupon bonds = 70.58%
Therefore How much of the zero-coupon bond
you hold in your portfolio will be 70.58%
bii. Calculation for the perpetuity you will hold in your portfolio
Perpetuity= 1 - 0.7058
Perpetuity= 0.2942
Therefore the perpetuity you will hold in your portfolio will be 0.2942
Ответ:
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