You are managing a portfolio of $2.1 million. Your target duration is 20 years,
ID: 2756358 • Letter: Y
Question
You are managing a portfolio of $2.1 million. Your target duration is 20 years, and you can choose from two bonds: a zero-coupon bond with maturity 10 years, and a perpetuity, each currently yielding 4%.
How much of each bond will you hold in your portfolio? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
How will these fractions change next year if target duration is now nineteen years? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
How much of each bond will you hold in your portfolio? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
Explanation / Answer
a)
Duration of Zero coupon Bond = Maturity
Duration of Zero coupon Bond = 10 years
Duration of coupon Bond perpetuity= (1+YTM)/YTM
Duration of coupon Bond perpetuity = (1+4%)/4%
Duration of coupon Bond perpetuity = 26 Years
Target duration = Weight of Zero coupon Bond * Duration of Zero coupon Bond + Weight of coupon Bond perpetuity * Duration of coupon Bond perpetuity
20 = Weight of Zero coupon Bond*10 + (1-Weight of Zero coupon Bond)*26
20 = 10Weight of Zero coupon Bond + 26 - 26Weight of Zero coupon Bond
16Weight of Zero coupon Bond = 26-20
Weight of Zero coupon Bond = 6/16
Weight of Zero coupon Bond = 37.50%
Weight of coupon Bond perpetuity = (1-Weight of Zero coupon Bond )
Weight of coupon Bond perpetuity = (1-37.50%)
Weight of coupon Bond perpetuity = 62.50%
Answer
Zero coupon Bond = 37.50%
Perpetuity bond = 62.50%
b)
Duration of Zero coupon Bond = Maturity
Duration of Zero coupon Bond = 9 years
Duration of coupon Bond perpetuity= (1+YTM)/YTM
Duration of coupon Bond perpetuity = (1+4%)/4%
Duration of coupon Bond perpetuity = 26 Years
Target duration = Weight of Zero coupon Bond * Duration of Zero coupon Bond + Weight of coupon Bond perpetuity * Duration of coupon Bond perpetuity
19 = Weight of Zero coupon Bond*9 + (1-Weight of Zero coupon Bond)*26
19 = 9Weight of Zero coupon Bond + 26 - 26Weight of Zero coupon Bond
17Weight of Zero coupon Bond = 26-19
Weight of Zero coupon Bond = 7/17
Weight of Zero coupon Bond = 41.18%
Weight of coupon Bond perpetuity = (1-Weight of Zero coupon Bond )
Weight of coupon Bond perpetuity = (1-41.18%)
Weight of coupon Bond perpetuity = 58.82%
Answer
Zero coupon Bond = 41.18%
Perpetuity bond = 58.82%
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