You are managing a portfolio of $2.8 million. Your target duration is 13 years,

Question

You are managing a portfolio of $2.8 million. Your target duration is 13 years, and you can choose from two bonds: a zero-coupon bond with maturity 5 years, and a perpetuity, each currently yielding 8%.

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

You are managing a portfolio of $2.8 million. Your target duration is 13 years, and you can choose from two bonds: a zero-coupon bond with maturity 5 years, and a perpetuity, each currently yielding 8%.

Explanation / Answer

Let x=weight of zero coupon bonds and 1-x =weight of perpetuities.

The duration of perpetuity is given by:

1+y/y=1.08/ 0.08=13.5 years

13=5x+(1-x)13.5

13 = 5X + 13.5 - 13.5X

8.5X = 0.5

X = 0.0588

Thus $2.8M (0.0588)=$0.16464 M in Zeros,

and $2.8 M (0.9412)=$2.63536 M in perpetuities.

These fractions will change in next year if target duration is 10 years.

10=4x+(1-x)13.5

9.5X=3.5

X = 0.3684

Thus $2.8 M (0.3684)=$1.0315 M in Zeros,

and 2.8 M (0.6316)=$1.7685 M in perpetuities.

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.