You are managing a portfolio of $2.9 million. Your target duration is 14 years,

Question

You are managing a portfolio of $2.9 million. Your target duration is 14 years, and you can choose from two bonds: a zero-coupon bond with maturity 5 years, and a perpetuity, each currently yielding 5%.

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

zero- coupon bond=__________%

perpetuity bond=___________%

You are managing a portfolio of $2.9 million. Your target duration is 14 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) Let x = weight of zero coupon bonds and 1-x = weight of perpetuities and y = current yield.

Then duration of perpetuity is given by

(1+y)/y = 1.05/0.05 = 21 years.

Therefore, weight are as follows :-

=> 14 = 5x + (1-x)21

=> 14 = 5x + 21 - 21x

=> 16x = 7

=> x = 0.4375

Therefore, the amount of investment in Zero Coupon Bonds = 0.4375 * $2.9 M = $1.27 M

and in perpetuity bonds = (1 - 0.4375) * $2.9 M = 0.5625 * $2.9 M = $1.63 M.

(b) if the target duration is 13 years, the weight would be as follows :-

=> 13 = 5x + (1-x)21

=> 13 = 5x + 21 - 21x

=> 16x = 8

=> x = 0.5

Therefore, the amount of investment in Zero Coupon Bonds = 0.5 * $2.9 M = $1.45M

and in perpetuity bonds = (1 - 0.5) * $2.9 M = 0.5 * $2.9 M = $1.45 M.

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