Example: You are managing a portfolio of $1.8 million. Your target duration is 1

Question

Example:

You are managing a portfolio of $1.8 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 10%. 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 target duration is now nine years? (Do not round intermediate calculations. Round your answers to 2 decimal places.) Perpetuity bond

Explanation / Answer

a. duration of perpetual bond = 1+r/r

= (1+.10) / .10 = 11 years

Target duration is 10 years

If w is the weight of zero coupon bond , (1-w) is the weight of perpetual bond

w*5 + (1-w)*11 = 10

5w + 11 -11w = 10

6w = 1

weight of zero coupon bond = w = 1/6

weight of perpetual bond = 5/6

b. if target duration is 9 years, zero coupon bond will have a duration of 4 years

w*4 + (1-w)*11 = 9

= 4w + 11 - 11w = 9

7w = 2

weight of zero coupon bind = w = 2/7

weight of perpetuity = 5/7

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