You are managing a portfolio of $2.4 million. Your target duration is 10 years,

Question

You are managing a portfolio of $2.4 million. Your target duration is 10 years, and you can choose from two bonds: a zero-coupon bond with maturity 5 years, and a perpetuity, each currently yielding 5%.

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 nine years? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

You are managing a portfolio of $2.4 million. Your target duration is 10 years, and you can choose from two bonds: a zero-coupon bond with maturity 5 years, and a perpetuity, each currently yielding 5%.

Explanation / Answer

a)

Duration of Zero Coupon Bond = Maturity

Duration of Zero Coupon Bond = 5 Years

Duration of Perpetuity bond = (1+r)/r

Duration of Perpetuity bond = (1+5%)/5%

Duration of Perpetuity bond = 21 Years

Target Duration= 10 years

Target Duration= Weight of Zero Coupon Bond * Duration of Zero Coupon Bond + Weight of  Perpetuity bond * Duration of Perpetuity bond

10 = Weight of Zero Coupon Bond*5 + (1-Weight of Zero Coupon Bond)*21

10 = 5Weight of Zero Coupon Bond + 21 - 21 Weight of Zero Coupon Bond

Weight of Zero Coupon Bond = (21-10)/16

Weight of Zero Coupon Bond = 68.75%

Weight of  Perpetuity bond =  (1-Weight of Zero Coupon Bond)

Weight of  Perpetuity bond = 1-68.75%

Weight of  Perpetuity bond = 31.25%

Answer

b)

Next Year

Duration of Zero Coupon Bond = Maturity

Duration of Zero Coupon Bond = 4 Years

Duration of Perpetuity bond = (1+r)/r

Duration of Perpetuity bond = (1+5%)/5%

Duration of Perpetuity bond = 21 Years

Target Duration= 9 years

Target Duration= Weight of Zero Coupon Bond * Duration of Zero Coupon Bond + Weight of  Perpetuity bond  * Duration of Perpetuity bond

9 = Weight of Zero Coupon Bond*4 + (1-Weight of Zero Coupon Bond)*21

9 = 4Weight of Zero Coupon Bond + 21 - 21 Weight of Zero Coupon Bond

Weight of Zero Coupon Bond = (21-9)/17

Weight of Zero Coupon Bond = 70.59%

Weight of  Perpetuity bond =  (1-Weight of Zero Coupon Bond)

Weight of  Perpetuity bond = 1-70.59%

Weight of  Perpetuity bond = 29.41%

Answer

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