Question

You are managing a portfolio of $1.0 million. Your target duration is 16 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 (1) 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.) Zero-coupon bond Perpetuity bond b. How will these fractions change next year if target duration is now fifteen years? (Do not round intermediate calculations. Round your answers to 2 decimal places.) Zero-coupon bond Perpetuity bond

Answer 1

Target duration =16 years

Zero coupon bond duration = Maturity i.e.5 years

Perpetuity bond duration =(1+ yield)/yield

=1.05/.05 i.e.21 years

Let Weight of zero coupon bond is WZ and other is WP

PT a

WZ*Zero coupon bond duration +WP*Perpetuity bond duration = Target duration

WZ*5+(1-WZ)*21 =16

5WZ+21-21WZ=16

WZ =0.3125 i.e.31.25%

WP =1-0.3125 i.e.0.6875 i.e. 68.75%

PT b

Zero coupon bond duration = 5-1 i.e.4 years

Perpetuity bond duration =21-1 i.e.20 years

WZ*Zero coupon bond duration +WP*Perpetuity bond duration = Target duration

WZ*4+(1-WZ)*20 =15

4WZ+20-20WZ=15

WZ =0.3125 i.e.31.25%

WP =1-0.3125 i.e.0.6875 i.e. 68.75%