Question

You are managing a portfolio of $1.3 million. Your target duration is 10 years, and you can choose from two bonds: a zero-coupon bond with maturity 5 years, and perpetuity, each currently yielding 8%.

a. How much of each bond 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 the target duration is now twelve years? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Zero-coupon bond. %

Perpetuity bond %

Answer 1

Duration of zero coupon bond = 5 years

Duration of perpetual bond = (1+8%)/8% = 13.50 years

Let us Zero-coupon bond % be hold be x

a.) x * 5 + (1-x) *13.5 = 10

5x +13.5 -13.5x = 10

=> -8.5x + 13.5 = 10

=> x = 41.18%

Zero-coupon bond 41.18%

Perpetuity bond 58.82%

b) target duration =12

x * 4 + (1-x) *13.5 = 12 [zero coupon bond duration as 4 as only four years left]

4x +13.5 -13.5x = 12

=> -9.5x + 13.5 = 12

=> x =15.79%

Zero-coupon bond 15.79%

Perpetuity bond 84.21%